{"archive_ref": "pat-us2563503", "canonical_url": "https://patents.google.com/patent/US2563503A/en", "char_count": 27102, "collection": "archive-org-bell-labs", "doc_id": 22, "document_type": "patent", "id": "bella-qwen-pretrain-doc22", "record_count": 1, "release_policy_version": "hf_public_v1", "rights_status": "public_domain", "selected_extraction_backend": "pdftotext", "selected_extraction_score": 1.0, "source_family": "google_patents", "source_url": "https://patents.google.com/patent/US2563503A/en", "split": "validation", "text": "Yj a FIG. 2\nALLS 45 47 A? 47, Ad 43 [-48\n(90 A _FAIIV ;\nog Lea to\na 46 INVENTOR\n- ay R.L. WALLACE JR.\n\nNonny C Nant\n\nATTOANEY\n\nPatented Aug. 7, 1951\n\n2,563,503.\n\nUNITED STATES PATENT OFFICE\n\nTRANSISTOR >\n\n_ Robert L. Wallace, Jr., Plainfield, N. J., assignor\n_ to Bell Telephone Laboratories, Incorporated,\nNew York, N. Y\u00a5., a corporation of New York \u2014\n\nApplication April 29, 1949, Serial No. 90,533\n\n|\nThis invention relates to the translation of\nelectric signals and particularly to semiconduc-\nror translating devices of improved construc-\nion. |\nA primary object of the invention is to improve\nthe stability of a semiconductor translator. .\nAnother primary object is to increase the in-\nput impedance of a semiconductor translating de-\nvice. | \u2014 7\nA related object is to improve the operation of\na semiconductor translator at high frequencies.\nThe invention provides specific improvements\nin the construction and mode of operation of a\n\nthree electrode semiconductor amplifier of the\n\ntype which forms part of the subject-matter of\n\nan application of John Bardeen and W. H. Brat-\n\ntain, Serial No. 33,466, filed June 17, 1948: now\nPatent No. 2,524,035, which is a continuation in\npart of an earlier application of the same inven-\n\ntors Serial No. 11,165, filed February 26, 1948, and\n\nlater abandoned. This central element comprises\n\n19 Claims. (Cl. 175\u2014366)\n\n10\n\n15\n\nsions of the voltage, current, and power of: the\noriginal signal appear in the load. The device,\nWhich may take various forms has received the\nappellation \u201cTransistor\u201d and will be so designated\nin the present specification. oe |\n_In a modified transistor described in an applica- |\ntion of W. E. Kock and R. L. Wallace, Jr., filed\nAugust 19, 1948, Serial No. 45,023, now Patent No.\n2,960,579, the block takes the form of a disc into\nopposite faces of which hemispherical depressions\nhave been ground to depth such that the block\nthickness, at its thinnest part, is only a few thou-\n\nsandths of aninch. The emitter makes point con- -\n\ntact at the low point of one of the depressions\nand the collector makes point contact substan-\n\n_ tially colinearly with the emitter, at the low\n\nPAL\n\npoint of the opposite depression. The base elec-\ntrode makes low resistance contact with the pe-\nripheral surface of the disc. \u2018The base is thus\nseparated from the other electrodes by the full \u2014\n\nYadiusofthedise. |\n\na small block of semiconductor material such as. .\n\nBermanium having in its original form at least\nthree electrodes electrically coupled thereto,\nwhich are termed the emitter, the collector and\nthe base electrode.\ntor are point contact electrodes making rectifier\ncontact with one face of the block and spaced\napart by a few thousandths of an inch, while the\nbase electrode may be a plated metal film making\n_ @ low resistance contact with the opposite face\nof the block. The base electrode is thus sepa-\nrated from the emitter and the collector by the\nfull thickness of the block. The emitter may\nbe biased for conduction in the forward direc-\ntion and in this condition its impedance is a few\n\nhundred ohms. On the other hand the collector |\n\nIs biased for conduction in the reverse direc-\n\ntion in which case its impedance is several thou-\n\nsand ohms. The forward emitter bias results in\nthe injection of charges into the block through\nthe comparatively low emitter impedance and\nthese charges are transported under the influence\nof electric fields within the block to the collector\nwhere they are withdrawn through the compara-\ntively high collector impedance. The application\nof 2 Signal current or voltage to the emitter re-\nsults in variation of the injected charges and so\nof the charges transported to the collector. The\nhigh ratio of the collector impedance to the emit-\nter impedance results in voltage amplification. In\naddition the transported charges serve to modify\nthe currents flowing from the base to the collec-\ntor so that current amplification results as well.\n\nDue to either or both phenomena amplified ver-\u2014\n\nThe emitter and the collec-\n\n25\n\nFor some purposes it is desirable to introduce\na time delay between the introduction of signal\nat the emitter and its recovery from the collector.\nYo this end the transistor may be drawn out an\n\nelongated filament on which the emitter and the\n\nBt\n\n35\n\n40\n\n45\n\n50\n\n55\n\ncollector make point contact at widely spaced\npoints. In place of a single base electrode there\nare now two low resistance electrodes, one at each\nend, the emitter making contact with the fila-_\nment near the\u2019 one and the collector making con-~\ntact with the filament near the other. In par-\nticular, the low resistance end electrodes may\nbe metal annuli on the end faces of the filament,\nthe point electrodes protruding through the holes\nin these annuli. Certain features of this elon-\ngated transistor form the subject-matter of an\napplication of G. L. Pearson and W. Shockley,\nSerial No. 50,897, filed September 24, 1948 now\nPatent No. 2,502,479, while certain other features\nform the subject-matter of an application of J. R.\nHaynes and W. Shockley, Serial No. 50,894, filed\nSeptember 23, 1948. | :\n\n_ The performance of transistors is conveniently\ndescribed in terms of an equivalent four terminal\nnetwork comprising an emitter resistance re, a\nbase resistance rp, a collector resistance 7c, and\nan internal electromotive force which is propor-\n\ntional to the emitter current. In this network\n\nthe base resistance is common to the input cir-\ncuit and the output circuit and is therefore a\nsource of feedback which, if sufficiently great,\nmakes for instability and in any event reduces\nthe effective input impedance of the device. To\nthis extent the base resistance is objectionable.\n\nTransistors of the close-spaced electrode variety\nare characterized. in general. by base resistances\nof the order of 100-500 ohms, which, in compari-\nson with the usual values of emitter resistance,\nwhich are of the order of 300-800 chms, is suf-\nficiently high to be objectionable. \nor film of metal which encircled the cylindri-\neal surface of the disc. In accordance with the\npresent invention, however, a substantial area\n\nof one face of the disc is provided with a metal\n\nfilm 23 which constitutes the base electrode and\nthe remaining portion of the surface of this face\nis suitably treated as with the etching and wash- |\ning process described above. The emitter 2l\nmay be a point contact electrode which engages\nthe treated surface close to the edge of the metal\n\nfilm 23, e. g., spaced from this ed&e by not more\nthan twice the diameter of the emitter contact\narea, while the collector electrode 22 engages the\n\ndisc in the center of the oppositely located de-\npression and in collinear alignment with the\nemitter. | |\n\nFig. 7 shows another modification in which the\nentire surface of one face of the disc 29 is pro-\nvided with a metal film 24 serving as the base\nelectrode with the exception of a minute hole\n25 at the base of the depression through which\nthe surface of the semiconductor material is ex-\nposed. This exposed surface is then suitably\ntreated as by the etching and washing process\n\nand a metal point electrode 2! serving as the\n\nemitter makes point contact directly with the\nsensitized semiconductor surface exposed through |\nthis hole. The diameter of. the hole 1s prefer-\nably not more than twice the diameter of the >\nemitter contact area. As before, the collector\nelectrode 22 makes contact at the center of the\noppositely located depression, and preferably in\naxial alignment with the emitter electrode.\nAs an alternative to the fabrication technique\ndescrised in connection with Fig. 1, a modified\ntechnique may be employed to produce the struc-\nture of Fig. 7, as follows: The metal point con-\ntact electrode which is to serve as the emitter\nis first covered with a thin coat of insulating\nmaterial such as wax. The surface of the semi-\nconductor block is then treated with the etch-\ning, washing and\u2019 drying process to sensitize it. |\nNext, the wax-coated electrode is pressed into\ncontact with this sensitized surface. The sur-\nface is then sandblasted and plated with an\ninert metal such as rhodium to serve as the base\nelectrode. The wax coating of the emitter elec- _\ntrode, and. especially that portion of it which at\nfirst covered the metal point and which, in the\n\ncourse of pressing the point into engagement\n\nwith the semiconductor surface is forced radi-\nally outward, operates to protect a minute area\nsurrounding the emitter, both from the sand-\nblast and from the deposition of the metal in the\nplating process. As before, a barrier surround-", "title": "Transistor", "trim_reasons": ["leading_ocr_noise", "leading_ocr_noise", "leading_ocr_noise", "leading_ocr_noise", "leading_ocr_noise", "leading_ocr_noise", "leading_ocr_noise"], "year": 1951} {"archive_ref": "sim_record-at-t-bell-laboratories_1926-01_1_5", "canonical_url": "https://archive.org/details/sim_record-at-t-bell-laboratories_1926-01_1_5", "char_count": 84072, "collection": "archive-org-bell-labs", "doc_id": 119, "document_type": "journal_issue", "id": "bella-qwen-pretrain-doc119", "record_count": 20, "release_policy_version": "hf_public_v1", "rights_status": "public_domain", "selected_extraction_backend": null, "selected_extraction_score": null, "source_family": "archive_org", "source_url": "https://archive.org/details/sim_record-at-t-bell-laboratories_1926-01_1_5", "split": "validation", "text": "over open-wire circuits. This led to\nthe preparation by P. H. Pierce and\n\nThe messages were carried on cur-\n\nrents of twenty frequencies between\n3,000 and 11,000 cycles. Each oneway transmission had its own carrier\nfrequency and adjacent frequencies\nwere used for transmission in opposite\ndirections. The outgoing and incoming currents at each end were separated\nin part by the use of a balanced cir-\n\nO. A. Pawlick (now Long Lines), of\n\nan experimental carrier-telegraph system by which four duplex telegraph\n\nchannels were provided over a single\ncircuit, using carrier\n\nfrequencies\n\nfive, six, nine, and\n\nten\n\nof\n\nkilocycles.\n\nLike the original carrier telephone,\nthis depended, for two-way operation,\n\noe\n\ni.\n\nTUNED\nRCUITS\n\n\u201csll\n\n:\n\n?\n\nThe receiving apparatus for the experimental installation at Maumee\n\non the balancing of the impedance of\nthe open-wire line at the carrier frequencies by means of an artificial line\nor network. This experimental appa-ratus was set up at Maumee and\nChicago in September, 1917; and in\n\nits test the Laboratories engineers\ncooperated with the engineers of the\nAmerican Telephone and Telegraph\nCompany. The system included, at\nSouth Bend, a carrier-current repeater\nin which for each direction of transmission a single amplifying circuit\nrepeated all the messages. The experimental tests were followed by\n\ncuit, including a network to balance\nthe impedance of the line. The\napparatus was mounted on unit racks,\nsome of which are shown in the picture\nof part of the Pittsburgh installation.\nAmong the Laboratories engineers\nwho worked on this system were G. C.\nCummings, N. H. Slaughter, M. B.\n\nLong, A. J. Eaves, J. B. Harlow (both\nnow in the Western Electric), H. J.\nVennes (now in the Northern Electric),\nand L. W. Wickersheim (now with the\n\nPacific Telephone Company).\nFollowing the success of this system,\nthe so-called Type \u201c\u2018A\u201d\u2019, a number of\ncommercial operation with satisfac- similar carrier-telegraph systems were\ntory results.\ninstalled. These systems were arAbout the beginning of 1919, prep- ranged for directional grouping of\narations were made for the installation frequencies, using eight frequencies\nof a carrier-telegraph system between between 3,600 and 5,500 cycles for the\nHarrisburg and Chicago with inter- transmission of messages in one direcmediate terminals at Pittsburgh. Ten\ntion, and eight frequencies between\ntwo-way telegraph channels were 6,500 and 10,000 cycles for the\nprovided over a single circuit, in opposite direction.\n\naddition to the usual channels for tele-\n\n{ 189}\n\nAfter several of the Type \u201cA\u201d\n\nchannel\n\ncarrier.\n\nIn\n\naddition,\n\nthe\n\nlent to twenty-six channels or messages\n\nordinary telegraph circuits, obtained\nby compositing,\ncan be operated simultaneously with the voice-frequency\ncarrier, thereby providing two more\n\nper wire, whereas, as I pointed out at\nthe beginning of this article, LeSage\nproposed to: use twenty-six wires to\ntransmit one message. The total improvement in message capacity is thus\n\nsignal channels in each direction over\n\n|\n\nthe two cable pairs.\n\n(26)? or 676 times.\n\nThe rate of\n\n\\\n\n(\n\ni\n\n(\n\n\u2018\n\nOAKLAND\n\n26\n\n(\n\n--\n\n4\n\ni\n\n>\n\nnro\n\nwooesta\n\n\\\n\nFresno\n\n05 ancturs\n\nSs?\n\\\n\nba\n\n=\n\n\\\n4\n\nkey weer\n\nRoutes and locations of carrier telegraph systems, present and proposed\n\noperation over these channels however\n\n\u2014 Although we may, in the fullness of\n\nis not as high as over the carrier chan-\n\nour greater knowledge, smile at these\n\nnels and would enable only two\nprinters per channel to be operated as_\n\nearly efforts, still we are indebted to\nmany of these pioneers of an earlier\n\nagainst four printers per carrier channel. This, however, would add four\n\nage for a little something which we\nhave extracted from their achieve-\n\nmore printer channels, making fifty_ two printer channels in each direction,\nor a total of 104 printer channels over\none four-wire circuit. This is equiva-\n\nments and adapted to our structures\nof today. Perhaps it will not be many\nyears before posterity indulges in a\nkindly smile at our own efforts.\n\n\u201c*\n\n{ 192}\n\n|\n\n|\n\nAN\n\nENGINEERING\n\nCAREER\n\nBy E. H. Cotpirrs\nA note of appreciation\n\nof the scientific\n\nand engineering work of Harold W. Nichols\n\nS ONE intimately associated\nwith Dr. Harold W. Nichols\nduring the eleven years in which he\n\nonly to carry on investigational work\nhimself but also, as soon appeared\n\nwas active in the research and devel-\n\nevident, to undertake direction of the\n\nsonal characteristics fitting him not\n\nwork of others.\nIn no respect did\nhis performance\ndisappoint those\nbroadly responsible for the work\n\nopment work of\nthe Bell System as\na member of the\nEngineering\n\nDe-\n\npartment\n\nof the\n\nWestern\n\nElectric\n\nCompany,\n\nInc.\n\n(now the\n\nBell\n\nwith which he was\nconnected.\n\nHis personal\ncontributions to\nthe development\nof the communication art can to\n\nTelephone Laboratories, Inc.), I\nwelcome the op-\n\nportunity\n\n||\n|\n\nof\n\nrecording a few\n\na slight degree be\n\nwords appreciative of his work as\n\nmeasured by the\n\nan engineer.\n\nHe entered the\n\nHarold W. Nichols\n\nwork of the West-\n\nern Electric Company in 1914, at a\nperiod standing out as one when new\ntools and new methods applicable to\ncommunication were being found and\napplied. The first commercial applications of vacuum tubes in telephone\nrepeaters were being made; and in this\ndevice, and in the application of the\nmore complete theory of electrical\ncircuits then becoming available, radically new developments were foreseen\nin the fields of radio and carriercurrent systems, as well as in applications to voice-frequency telephony.\nHe entered upon his work with training, initiative, imagination, and per-\n\nfact that twentyone United States\npatents were issued to him and\n\nsome eight applications are still pend-\n\ning. These patents cover important\nelements of carrier currents and radio.\nThrough his papers on scientific and\ntechnical subjects, as well as through\nhis personal contacts, he was well and\nfavorably known in the scientific and\ntechnical world. When in February,\n1923, he delivered an address before a\nmeeting of the British Institution of\n\nElectrical Engineers at London on the\nMethods of Transatlantic Telephony,\n\n|\n\nhe was awarded by the Institution\u2019the\n\nFahie Premium. He served for some\nyears on the Board of the Institute of\n\nRadio Engineers; and just prior to his\n\n{ 193}\n\n|\n\ndeath he had been nominated as one\n\nunderlie much of the art today. To\nattempt a discussion of this, however, would too greatly expand this\n\nof the candidates for President of that\nInstitute.\nWhat promises to be a basic con-.\ntribution to the theory of propagation\n\nnote.\nHe was recognized as an authority\n\nof electric waves in radio is contained\n\nin electrical theory, and his advice and\nsuggestions were highly valued and\n\nin his most recent paper, a joint\npublication with J. C. Schelleng, in\nwhich the authors discussed the effect\nof the earth\u2019s magnetic field upon\n\nappreciated. Very generously hemade\nhimself always available to his colleagues as a consultant\n\nradio transmission.\n\non problems\n\nwhich arose in connection with their\n\n\u201cAs I view his career, however, im-\n\nwork in lines outside of his own par-\n\nportant as were his own personal contributions, his greatest contributions\n\nticular activity.\nI cannot conclude this brief and\n\ngeneral note without expressing the\n\nwere indirect, in the guidance and\nstimulus which he gave to the able\n\ndeep sense of loss which I know is felt\nby the whole group who in the Laboratories and in the American Telephone\nand Telegraph Company were associated with Dr. Nichols.\nIn the\nrelatively few years of his engineering\ncareer, he won a position attained by\nfew men, even of those to whom many\nmore years of activity have been\nallotted.\n\ngroup of engineers and scientists who\nin\n\nour\n\nfunctionalized\n\norganization\n\nlooked to him for broad general direction. The contribution of this group\nto the fields of communication employing high-frequency\n\ncurrents\n\nranging\n\nfrom voice frequencies up to the frequencies in \u201cshort wave\u2019\u2019 radio have\nbeen of the greatest importance and\n\nOur\n\nBuDGET\n\nBy A. O. JEHLE\n<+\n\nURING 1926 the Laboratories\nwill expend a very considerable\nsum, millions of dollars, in carrying\non the work with which it is charged.\n\nern business administration. In our\nLaboratories a budgetary procedure\nis required to coordinate the activities\nof the various functional departments\nAuthority to spend this money* will and to serve as a basis for centralized\narise from the action of its Board of executive control. The budget which\nDirectors in the approval of a budget our Directors will approve for 1926\nof expenditures; and with this ap- will be presented to them by the Presiproval our executives may proceed dent, and represent the summarized\nwith their working program for 1926 reports of anticipated expenditures\nand know definitely what expense prepared and estimated by the departmental heads. The individual\nmay be incurred.\nBudgeting is an essential of mod- _departmental estimates of expense,\nclassified by the kinds of work in*\u201cWho Pays our Salaries\u201d in the October Record, p.- 62,\ntells where this money comes from.\n\nvolved, will be consolidated\n\n{ 194}\n\ninto a\n\nCompany budget by the Statistical\n\nDepartment. This budget, after approval by the Executive Vice-Presi-\n\nthe various functional departments of\nthe Laboratories the probable expense\nfor their departments for the coming\n\ndent, is forwarded to the President\nfor his consideration and approval\nand subsequent\n\nyear in terms of (a) salaries, (b) supplies and outside shop work, (c)\ntraveling, and (d)\n\nmiscellaneous.\nThe first two of\nthese groups represent by far the\nmajor part of our\nas prepared by\nSALARIES\nexpense. In fact,\nthe Statistical De=\npartment, sumsalaries alone are\nen FURS =\n|\nalmost threemarizes the operquarters.\n\u201cSupating expense for\nthe entire year\nplies and outside\nand also the exshop work\u2019\u2019 cover the cost of\npenditures to be\nmaterials and\nmet in plant and\nequipment. A\nsupplies withknowledge of\ndrawn from the\nplant expenses\nstorerooms, or\neach dollar of operating expense is divided.\nfor the year is How\npurchased from\n\u201cMiscellaneous\u201d includes interest charges,\nnecessary for the\nthe Western Elecbenefit fund reserve, rentals for property\npreparation of the\ntric Company or\nother than West Street, etc.\nbudget of operatoutside suppliers.\ning expense, since the latter must It covers the material with which our\ninclude the additional depreciation scientists and engineers work. Under\ncorresponding to the recently added miscellaneous expense, as estimated\nplant and equipment.\nby the department heads, are such\nIt is the budget of operating ex- items as outside rentals\u2014for example,\npense, however, which from the standthe space occupied by the Tube Shop\npoint of the laboratory engineer is at Hudson Street\u2014and other expense\nmost interesting and important. This like express and freight charges.\ndetermines the total salaries which\nIn arriving, however, at the\nmay be expended and the value of total operating-expense budget\nsupplies and shop work which may the Statistical Department includes\nbe obtained for carrying on our in addition to these items, as estiresearch and development activities. mated by the department heads,\nThis operating-expense budget is several others. First among these is\nprepared on two bases: in one the depreciation and outside repairs.\nproposed expenditures are classified This expense arises from the fact\nas to type of expense, and in the other that plant items, such as buildings,\nas to type of work.\npermanent fixtures, machinery, and\nIn obtaining the data on which to furniture cannot be kept in service\nmake its budgetary conclusions the indefinitely but must from time to\nStatistical Department, in the late time be replaced or retired.\nIt is\nautumn, requested from the heads of recognized as sound business practice\n\nconsideration by\nthe Directors.\nThe budget for\nthe Laboratories,\n\n|\n\n|\n\nSUPPLIES\nISe.\n\n|\n\n{195}\n\n|\n\nb\n\nto set aside each year reserves against\nsuch plant depreciation. Therefore,\nthe cost of such plant should be distributed as evenly as may be throughout the service life of the property.\nAnother item which is included in\nthe operating-expense budget is the\npayments made to employees for\npensions, sickness, accident, and dis-\n\nability, in accordance with the provisions of the Benefit Plan of the\nCompany. It is interesting to note\nthat these are not included as salaries\nalthough\nbudget.\n\nthey enter\n\ninto the total\n\nFor any proposed expenditure of\nthe\n\nLaboratories,\n\nas\n\nexpressed\n\nin\n\nkinds of work, there corresponds an\nequal proposed expenditure in kinds\nof expense. Suppose, for example,\n\nthat all the engineers and scientists in\n\nthe Laboratories were to be engaged\n\non\n\na single\n\none\n\nof the executive\n\ncontrol classifications of work, for\nexample, \u2018Transmitters, Receivers\nand Induction Coils.\u201d The cost of\nthis piece of work would then include\nall building expense, heat, light,\nservice, and the like as well as all\n\nother expense of a clerical and com-\n\nThere is presented then to the\nBoard of Directors a budget for our\nLaboratories as a whole, classified as\ndescribed above and giving the total\n\nmercial nature.\n\nSince, however, there\n\nare several different types of work,\neach of them must bear its proportionate part of this general expenditure. The Statistical Department,\n\noperating expense for the year. Although this covers the total expense therefore, advises the heads of the\nit does not tell the kinds of work pro- functional departments as to the proposed and the expense involved in portion of such general expense with\neach kind. With the formation of which their departments will be\nour Laboratories the first of last year, charged as a result of their departthere was set up an entirely new mental requirements for floor space,\nclassification of expense, by kinds of telephone service, and the like. With\nwork.\nThe Laboratories\u2019 work is this information in hand the departestimated on an annual basis and is ment heads are able to estimate the\ngrouped for statistical summaries in expense which will be met by their\nso-called \u201cexecutive control classifica- departments in each of the types of\ntions,\u201d such for example as \u201cTrans- work with which they are concerned.\nThese estimated expenditures, by\nmitters, Receivers and Induction\nCoils,\u201d \u201cWire Transmission Systems,\u201d types of work, are then summarized\n\u201cResearch and Development of Gen- and their total is, of course, equal\nto the total budget by kinds of exeral Application,\u201d and a\nSystems and Apparatus.\u201d\npense.\n\nA Binder for the Record\nThose who wish to preserve a permanent file of the RECORD may\nsecure through the Personal Purchase Department a binder of the\nsame style as that used for the technical reprints.\n\n{ 196}\n\n|\n\nSouND\n\ni\n\nRECORDING\n\nBy Josep P. MaxrFie_p\nT the time of its formal introduction to the public, the new\nmethod of sound reproduction developed in our Laboratories was outlined\n\nby the RECORD.\u201d\n\nAs\n\nwas\n\nthere\n\nnoted, to take full advantage of the\n\nnew apparatus records of equally high\nquality must be used. Since the technique of making these records has\nbeen developed in our Laboratories,\nit is felt that an account of the general\nfeatures of the problem and its solution will prove of interest.\n\nExperiment has shown, however, that\nthe shape of the room and the position\nin which the curtains and other absorbing materials are hung play a\npart in the excellence of the music.\nBy a proper control of the acoustic\nproperties of the recording room, it\nhas been possible to record the socalled \u201catmosphere\u201d surrounding the\nmusic. When this result has been\naccomplished, the listener seems to\n\u201cfeel\u201d the presence of the artists to\nwhose record he is listening.\n\nBefore considering the methods in-\n\nvolved it may be well to make a rough\ndivision of the problem into its component parts. A first consideration is\nthe character of the sound which is to\nbe recorded, including the effects of\nreverberation and general studio de-\n\nwe\n\nsign. The storing or recording of\nsound requires first a mechanical system which will respond faithfully to\nsound waves. There is also required\nsome \u2018material in or on which this\nsound may be recorded, and an intervening electro-mechanical system\nwhich permits the sound waves to\nmake the record in this material.\nSrup1o\n\nAcoustics\n\nIMPORTANT\n\nIn recording work, therefore, one of\n\nthe important factors deals with the\nacoustics of the room in which the\nrecording is done. It is probable that\nthe most comprehensive single factor\nin this connection is the time of\nreverberation, i.e., the time taken for\n\na sound of given intensity to die away\nafter the source has been stopped.\n\nErrects\n\noF DAMPING\n\nIf a studio is too highly damped or\nas a musician would say, \u201ctoo dead\u2019,\nall of the instruments lack the vibrant,\n\nringing tone which lends life and\nspirit to the music and to which we\nareallaccustomed. The impression on\nthe listener is very similar to that\nproduced by music played in the open\nair where no floor or sounding boards\n\nare provided to reflect the sound. Ifa\nroom is insufficiently damped, cr in\nthe musician\u2019s terminology \u201c\u2018too live,\u201d\n\ntwo effects are produced,\nwhich are disagreeable.\n\nboth of\n\nThe first is a\n\ntendency of one set of notes to blur\nwith those produced immediately before and after; and in the case of large\norchestras, blurring is so bad as to\n\nmake it impossible to pick one instrument from another. The second effect\nis to leave the listener with the\nimpression that he is listening to\nmusic being played in a totally bare\nand empty room. It is interesting in\nthis connection that the studio must\n\n1197}\n\n|\n\nbe slightly more damped than the\nrooms in which we are accustomed to\nlisten to music, because the phonographic process is what we call single\nchannel\u2014that is, it \u201clistens\u201d with one\n\near only. The effect of slightly too\nlive a room can be produced by\nstopping up one ear and listening with\nthe other one alone. However, where\nacoustic conditions are correct, the\n\nillusion produced is so good that the\nreproduction is raised from the class of\nminor amusement to that of an artistic\nproduction.\nIn the case of large orchestras and\nsimilar types of music, the reverberations in the hall or theatre constitute\npart of the musical and artistic effect.\nThe solution of the problem of recording these effects in such a manner that\n\nwhen the music is reproduced in a\nliving room the effects appear to be\nthose desired, has constituted one of\nthe real advances in the recording art.\n\nThe second important factor is the\n\nrange of notes or frequencies which\nit is possible to record and reproduce.\nThis subject was covered sufficiently\nin the RECORD article* mentioned.\nIn attacking the problem of improved recording methods there are\n\ntwo obvious lines of procedure. The\nfirst is to make use of the energy of the\nsound waves for the purpose of operating the recording instrument. This\nis the method which has been in use\nfor many years. The second is to\nmake use of high-quality electrical\n\napparatus, associated with vacuum-\n\ntube amplifiers, in order to give more\nfreedom to the control of the process.\nThis second method has been adopted\nbecause the amount of the energy\navailable directly from the sound to\nbe recorded is so small as to make its\nuse extremely difficult, particularly if\nthe artists are to play or sing in a\nnatural manner. In the case of the\nweaker instruments such as the violins,\n\u201c*Bell Laboratories Record, November 1925, page 99.\n\n4\n\n|\n\n|\n\nTo record by the old acoustic method it was necessary to crowd the players close to the collecting horn,\nand equip some of the violins with special resonators, such as shown in the foreground\n\n{ 198}\n|\n\nit has been possible to use only two of\n\nhappened that after the instruments\n\nstandard construction.\n\nrest of\n\nhad been arranged in such a manner\n\nthe violins are of the type known as\n\nthat the relative loudness of the\nvarious parts had been balanced correctly, it was found that the whole\nselection was either too loud or too\nweak. This usually meant a complete\n\nThe\n\nthe \u201cStroh\u201d, which is a device strung\nin the manner of a violin but so\narranged that the bridge vibrates a\ndiaphragm attached to a horn. This\n\nThe modern recording studio looks very much like that of a broadcasting station with the orchestra\ngrouped in comfortable positions with normal instruments\n\nhorn is directed toward the recording\nhorn, as shown in one of the accom-\n\npanying illustrations. With such an\narrangement of musicians, it is very\ndifficult to arouse the spotaneous enthusiasm which is necessary for the\nproduction of really artistic music.\nIn the picture showing the new\nmethod, the musicians are sitting at\nease more nearly\nin their usual arrangement\n\nand all are using the instru-\n\nments which they would use were they\nplaying at a concert. Furthermore,\nthe microphone is now sufficiently far\naway from the orchestra to receive the\nsound in much the manner that the\nears of a listener in the audience would\nreceive it. In other words, it picks up\nthe sound after it has been properly\nblended with the reflections from the\n\nwalls of the room. It is in this way\nthat the so-called \u201catmosphere\u201d or\n\u201croom-tone\u201d\u2019 is obtained.\nIn the old process, it sometimes\n\n\u2014\n\nrearrangement of the players. With\nthe flexibility introduced by the use of\nelectrical apparatus including amplifiers, the control of loudness is ob- -\n\ntained by simple manipulation of the\namplifier system and is in no way\nrelated to the difficulties of the relative\nloudness of one instrument to another.\nThe only problem for the studio\ndirector in this case is to obtain the\nproper balance among the various\nmusical instruments and artists. The\nadvantages derived from this added\n\nease of control are also made manifest\nin that it is much easier and less tiresome for the artists and it is usually\npossible to make more records in a\ngiven time.\n\nIt may be interesting to follow the\ncourse of the sound vibrations from\nthe time they are produced until they\nappear as an irregular groove on the\nphonograph record. The sound is\nfirst picked from the air by means of\n\n{199}\n\na special telephone transmitter which\nis essentially an instrument which\n\norder factors which have been left\nout of this diagram, as they would\n\ntranslates into voltage fluctuations the\n\ngreatly increase its ety.\n\nair-pressure fluctuations which strike\n\nReferring to Fig.2, the inductance\n\nits diaphragm. These voltage fluctuations, which are exceedingly small, are\n\nlabeled m: represents the mass of the\narmature which when acted on by the\n\nmagnetic field forms the driving por:\n\n\\\n\n\\\n\n\\\n\n\\\n\ntion of the mechanical*system.\n\n\\\n\nThe\n\ncondenser c, represents the flexibility\nof the shaft connecting the armature\n\n1\n\nto the stylus holder; m: represents the\nmass of the stylus holder and stylus;\nc, the flexibility of the shaft connecting the stylus holder with the\nmetal piece which fits into the rubber\ndamping element; m; the mass of this\n\nmetal piece; and c; and r represent the\ncharacteristic of the damping element.\nThe two condensers, shown dotted and\n\n\u201c4\n\nN\n\nunlabeled, represent two of the second\norder factors mentioned above.\nThose who are at all familiar with\n\nNASR\n\nelectrical filter design will immediately -\n\nsee that, providing the two undesignated condensers are omitted, this\nFig. 1.\n\nA sketch of the rubber line recorder\n\namplified by distortionless vacuumtube amplifiers until they are of sufficient power to operate the device\nwhich cuts the permanent record in\nthe disc of soft wax. This instrument,\nknown as the recorder, is one of the\n\nexamples of the application of the wavetransmission theory of\nelectric circuits to\nmechanical systems.\nA picture of one of\n\nis a filter of the low-pass type.* In this\nparticular case the filter has three sections and a terminating resistance. In\ndesigning mechanical analogues of\n\nsuch a system, the problem presented\nis three-fold\u2014first, that of arranging\nthe parts so that they form repeated\n*Bell Laboratories Record, October 1925, page 59.\n\n:\n\nthese recording instruments is shown in Fig.\n1, while a simplified di-\n\nAl\n\nagram ofits equivalent\nelectric circuit is shown\nin Fig. 2.\n\nIn actual\n\npractice\n\nit has\n\nnecessary\n\nto take ac-\n\nbeen\n\ncount of some second||\n\n~J\n\nAn up-side-down view of the \u201crubber line\u201d recorder\n\n{ 200}\n\nseparate sections all have the same\ncharacteristics; third, that of providing the proper resistance termination.\nThe use of the third section and the\n\na loss of response at the low-pitch end.\nThis loss is unfortunately necessary in\norder to avoid the large amplitudes\nwhich accompany the low pitched\nnotes and which would cause the trace\non the record to cut from one groove\n\nterminating\n\nover into its neighbor.\n\nWhile we have\n\n=\n\nTie\n\nfilter sections; second, determining the\n\nmagnitudes of these parts so that the\n\nresistance\n\nwas\n\ndecided\n\n4\n\n5\n\nupon after a considerable amount of\n\nexperimental work.\n\nIt was hoped that\n\nthe resistance of the wax to the backand-forth motion of the cutting stylus\n\ni\n\nmight be used as the terminating\n|\n\nresistance.\n\nIt was\n\nfound, however,\n\nthat under the conditions existing in a\n\ni\n\ncommercial recording-room, the value\n\nof this resistance, even though of a\nright character, varied so greatly from\naa\u2019\n\none wax blank to another as to be un-\n\nsuitable for the purpose.\nable\n\nalso\n\nthat\n\nthe\n\nIt is prob-\n\nvalue\n\nof\n\nthis\n\nresistance is not the same for all notes\nor pitches lying within the range\nwhich it is desirable to record.\n\nrecorder\n\nIn the\n\nas finally developed,\n\nthis\n\nterminating resistance has been made\n\nso large that effect of the wax\nnegligible in comparison.\n{\n\nis\n\nPractically,\n\ntherefore, it acts as the complete\ncontrol element of the mechanical\nfilter.\n\nSuch a filter when properly designed\nwill have: a response versus pitch\ncharacteristic\n\nwhich\n\nis flat, within\n\npractical limits. The actual recorder\nowing to the presence of the two\nundesignated condensers of Fig. 2, has\nmM\n\ni\n\n\u2014=\n\ni\"\n\nThe amplifier operator in a.recording studio has\n\nready control of the overall loudness of the record\n\nno accurate calibration of the older processes of recording, thereis considerable\nevidence to indicate that the fundamentals of notes below middle C were\nnot recorded and that fundamentals or\n\nharmonics lying above the middle of\nMa\n\n(0000 4\n\n|\n\nM3\n\nELECTRO-\n\n'\n\n|\n\nMAGNETIC\nMOTOR\n\nC 3\n\nELEMENT\nAMPLIFIER\nFROM\n\n=>\n\n\u00a5\n\n=\nFig. 2.\n\nSchematic of Electrical System Analogous to Recorder\n\n{ 201}\n\ntones\n\ni\n\naccompanied\n\nphono-\n\nthe music while the higher harmonics\n\n=\n\n&\n\ni\n\nwhich\n\ngraphic reproduction, while the loss\nof the higher harmonics was responsible for the general muffled quality\nand the inability to hear the sybilants\nof speech. In other words, the low\nrange is responsible for the naturalness or what is termed the \u201c\u2018body\u201d\u2019 of\ni\n\nA rubber-line recorder being adjusted by\nHarry Summers\n\nthe upper octave on the piano also\nfailed to record.\nThe loss of the\nfundamentals of the low notes was\n\nlargely responsible for the metallic\n\nDLE\nMeEcHANICAL\n\nare largely responsible for the details\nand clarity of the tone.\nWhen this complete range of notes\nis properly reproduced in conjunction\nwith the proper amount of reverberation effect, it is easy for the listener\nto imagine himself actually present at\nthe original performance.\nThe exactness of the sound records\nproduced by this new method has\nalready made something of a revolution in the phonograph art and will\npermit the application of that art to\nnew fields.\n\nLES YE DLE YE YE PE PEPER,\nDEVELOPMENTS\n\nANUFACTURE by the Western Electric Company is the\nstage in the production of communication apparatus which follows its development in our Laboratories and its\nfinal specification as a design acceptable to the engineers of the American\n\nfactured\n\nAT\n\nHAwTHORNE\n\narticle\n\nwhether\n\ntelephone\n\ncord, coil, transmitter, complete\nswitchboard, or radio broadcasting set,\n\nthere intervene a number of processes\nof manufacture, each a step in the\nevolution of the final form. It is the\ntask of the Development Branch to\n\nTelephone and Telegraph Company. maintain at the highest state of\nIn the functionalized division of the development these processes and macreative work of the Bell System it - chines so that manufacture will always\nfalls to the Laboratories to specify the be carried on at lowest possible costs\ndesign\u2014i.e.,what\nshall bemade\u2014and to consistent with a high standard of\nthe Manufacturing Department of the quality and the best working conWestern to determine the manufactur- ditions for the employees. Several\ning processes\u2014i.e., how the specified hundred engineers and scientists are\napparatus shall be made. Between\nengaged in fulfilling this task under\nthe raw materials, such as metals,\nglass, wood, insulating textiles and\n\nthe leadership of David Levinger,\nSuperintendent of Development. As-\n\ncompounds, and each finished manu-\n\nsisting him and in charge of various\n\n{ 202}\n\n|\n|\n\ndivisions of the work are: R. A. Price,\n\nF. W. Willard, J. R. Shea, C. D. Hart,\n\nA. H. Adams, H. L. Ward, and F. C.\n\nSpencer.\nTheir work\n\ninterest\n|\n\n|\n|\n\nis always\n\na source\n\nto their colleagues\n\nof\n\nin the\n\nLaboratories. In the first place, for\nthe proper design of commercial equipment the Laboratory engineer needs\nto be informed of the possible methods\nand limitations of different manufacturing processes and methods. In the\nsecond place, there is the pleasure\nwhich he takes in observing development work well done, a finished performance and the accompanying\neconomies.\nOne of the responsibilities of this\ngroup at Hawthorne 1s reduction in\ncost of manufacture by improvements\nin methods. Some recent developments in cost reduction were described to members of the Laboratories\nina talk by Mr. Levinger upon the\noccasion\n\nof a visit to New\n\nof more rapid and economical produetion. Where, for example, the existing\nplants rolled from billets to onequarter inch rod with eighteen passes,\nthe new Hawthorne plant started out\nwith sixteen and was soon operating\nwith fourteen passes. Similarly, in\nthe drawing of wire the studies of the\nprinciples of wire drawing and the\ndetermination of the optimum shape\nand size for dies resulted in an increase in the speed of drawing fine\ncopper wire from about 700 feet per\nminute to cover 2000 feet per minute.\nIn addition the plant occupies only\nfrom one-quarter to one-third the\nspace that was ordinarily required for\nthe same output. Such improvements\n\nYork,\n\nDecember fourth and fifth.\nHis visit to the Laboratories was\nunexpected, but when he consented to\nspeak our largest classroom (R. 411)\nwas quickly filled with interested engineers who applauded enthusiastically\nhis accounts of recent advances in\ntechnique and their resulting economies in cost and human effort. At the\nrequest of George B. Thomas, who\nmade the arrangements, Mr. Levinger\nrepeated his talk the next day for\nanother roomful.\nAmong many matters discussed perhaps the most spectacular was the\nrod and wire mill which was built at\nHawthorne comparatively recently\nupon plans made by the Development\nBranch. The rolling of rods and the\ndrawing of wire had become rather\ndefinitely standardized processes before this groupstarted its development\nstudies which showed the possibility\n\npe\n\nMr. Levinger explains old and new ways of\nmaking transmitter face-plates\n\nin producing one of the necessities of\ncommunication equipment mean continuing savings to the Bell System\nand a source of pride to the colleagues\nof the Hawthorne engineers.\n\n{ 203}\n\n|\n\ni\n\n|\n\n|\ni\ni\n\nTo the Employees of the Bell System:\n_\n\nThis is the season when friendships are\nrenewed and when we like to say the things\n\nwhich are in our hearts but which are us-\n\nually left unsaid in the rush of busy days.\nThe spirit of service and the satisfaction\n\nwhich comes from doing useful work is some-\n\n|\ninf\n|\n\nthing which can be shared, and I believe, is\n\nshared by every individual, young or old, in\nthe Bell System.\n\nI know of no other business\n\n\u2018where the opportunity for service is greater,\nor where the individual effort of each man\nand woman\n\nWe can\n\ncounts for more.\n\nall be proud of the splendid\n\nenterprise in which we are\n\nengaged.\n\nIt 4s\n\nworthy of the best that is in us, and I want\n\nto express the hope that, in the year just\n\nclosing, each ofyou has found real happiness\n2\n\n\u2014that happiness which comes from serving\nothers.\n|\nZz\u2018congratulate you upon the success\n\n|\n\ni\nWi\n\nHi\n\nand\n\nhappiness that have been, and wish you all\ngreater success and greater happiness in the\n\nJ\n\nyear to come.\nWalter 8. Gifford\n|\n\n|\n1\n\n{ 205 }\n\n}\n\n|\n\nHis\n\nFirst\n\nHEN R. L. Jones came to the\nLaboratories from Massachusetts\n\nInstitute of Technology\n\nin\n\nIg11, our era of scientific research was\n\nvarious frequencies, natural frequencies and damping constants.\nThis\n\ninvestigation was a part of the Research Department\u2019s outstanding\n\njust getting under\n\nproblem of the day\n\nway. Mr. Jones had\nbeen thinking of\nhydro-electric power\n\n\u2014 the development\nof atelephone\nrepeater.\nBefore long, his\n\nengineering as a lifework.\nBut Dr.\n\nassociates began to\n\nsee evidences of the\nabilities which were\nto carry Mr. Jones\nto his present position as head of Inspection Engineering. His interests\nwere those looking\nto the future; study-\n\nJewett had been one\nof his instructors;\nH. S. Osborn, a close\nfriend at Tech, had\n\ni\n\nenteredtheA.T.&T.\na year before; Mr.\nShreevecametoTech\nand talked to him\nabout telephone research. So on July\n31, 1911, after ob-\n\ning the\n\n4\n\nbroad\n\nas-\n\npects of his problems,\nplanning methods\n\ntaining his Doctor\nof Science degree, he\nif\n\nJos\n\nof attack, develop-\n\nR. L. Fones\ning men to carry out\nreported to E. H.\nthese plans, and inColpitts and was\nfusing\nthem\nwith\nhis own enthusiasm.\nassigned to Mr. Shreeve\u2019s group to\nwork on mechanical telephone re- Gradually a group was assembled\nunder his supervision, and in 1914 he\npeaters. Our present series of numbered laboratory notebooks had just was put at the head of the Transmisbeen started and Book No. 8 was sion Branch reporting to Dr. Jewett,\nassigned to Mr. Jones. Its first entry then Assistant Chief Engineer. As\nis a study of the motion of carbon the Engineering Department grew, it\nfinally became apparent that transgranules in a glass-walled transmitter\nbutton. Another project was a mag- mission investigations were a logical\nnetostriction element to drive the part of its research work, and Mr.\nmechanical repeater.\nBut his most Jones and his group were made a part\nimportant early contribution was the of the Research Department. Some\nidea of making accurate quantitative years later Mr. Jones carried his remeasurements of the mechanical char- search point of view into the developacteristics of vibrating apparatus\u2014 ment of a new department, that of\nsuch quantities as amplitudes at Inspection Engineering.\n\n{ 206}\n\n|\n\nYEO YE YE YE YL\nEarty\n\nDEVELOPMENTS\n\nIN [TELEPHONE\n\nALS,\n\nSIGNALLING\n\nATURALLY, the apparatus for\nN transmitting speech-currents\nand for reproducing the speech are the\nmost vital parts of the complete telephone. Yet there are many indis-\n\nguidance of the operator and enable\nthe modern telephone plant to function smoothly and efficiently.\nIt is a universal practice to attract\nthe attention of a subscriber by means\nof an electric bell. Although the elecpensable accessories to the telephone,\nof which one of the most important is tric bell antedates by many years the\nthe intricate but highly efficient sys- telephone, various methods of signalling were employed before the bell was\ntem of signalling.\nThe simplest telephone system is associated with the telephone circuit.\nformed by joining two telephones perEarty SIGNALLING METHODS\nmanently through a single line consisting of a pair of wires. The next\nThe first outdoor telephone line\nstep is a line connecting more than was between the office of Charles\ntwo telephones. In neither of these Williams at 109 Court Street, Boston,\nforms is the question of signalling a and his home at Somerville. When\nvery great problem. But the modern\nMr. Williams wished to call his home\nconception of the telephone plant, the he thumped with the butt of a lead\nultimate aim of which is universal pencil the diaphragm of the instruservice, is that every line shall connect ment which served both as transwith some intermediate agency where mitter and receiver. If there was\nit can be connected at will with any someone close to the telephone at the\nother line. Were there no means other end, and if the room was quiet,\nwhereby the individual initiating a the tapping noise could be heard.\ncall could attract the attention of the However, it was unreliable at best and\nperson at the other end of the line the the repeated tapping injured the diatelephone would be of but little use in phragm and rendered it useless in a\nany form, nor would a modern ex- short time.\nchange be possible could not the caller\nThe first commercial telephone user\nattract the attention of the inter- was Russel C. Downer of Somerville,\nmediate agents who make the neces- Massachusetts. In May, 1877, sersary connections and so complete the vice was established between his\ncalls. Therefore the matter of signal- Somerville home and the banking\nling is one of prime importance.\noffice of Stone and Downer, Boston.\nElectrical signalling used in con- Mr. Downer leased two telephones\nnection with telephony may be broad- and connected them with an existing\nly divided into two classes. The first private wire telegraph line.\nincludes all the methods whereby the\nFor signalling purposes the telecentral office operator attracts the at- phones on this line were equipped with\ntention of the subscriber; the other the then late development known as\nembraces all those signals which are Watson\u2019s \u201cThumper.\u201d In this device\nused for the information and the a small hammer was mounted within\n\n{ 207 }\n\n4\n\nt\n\n||\n\n|\na\n\n|\n\nH\n\n}\n\n|\n\n|\n\n|\n\n|\n\nef\n\nj\n\nWatson\u2019s \u201cThumper\u201d\nNumber 22 of first series manufactured.\nThe small hammer strikes rear edge of\ndiaphragm when button is pressed\n\n|\n\n|\n\nthe telephone in such a manner that\npushing a button in the front of the\nbox would cause the hammer to thump\nthe edge of the diaphragm. The only\nadvantage that this system had over\nthe pencil method was avoiding injury\nto the diaphragm.\nThere followed a period of experimentation, with many attempts to\ndevise a telephone instrument capable\nof transmitting speech with sufficient\nloudness that a loud \u201c\u2018ahoy\u201d or \u201c\u2018hello\u201d\u2019\nat the transmitter would attract the\nattention of the person at the other\nend of the line. All of these attempts\nwere failures, fortunately, -as_ the\nprivacy with which telephone con-\n\nversations may be conducted is one\n\nof the most desirable and useful\nfeatures of the modern plant.\nAll of these methods were obviously\ntransitory. Although they made pos-\n\nsible a limited use of the early private\nlines, they were impracticable for use\nwith a switchboard. So, with the advent of switchboards, it became cus-\n\ntomary to call by electric bells operated by batteries. A switch was provided in the circuit so that the bell\ncould be cut out of the line when\ntalking. This was a great improvement, but it was not satisfactory because of the limited length of line over\nwhich batteries of a reasonable voltage could operate the bells. Furthermore, the batteries and bells needed\n\nconstant attention and the cost of\nupkeep was prohibitive.\nIn 1878 Thomas A. Watson devised\na calling system which became known\nas Watson\u2019s \u201cBuzzer.\u201d It was a development from one of Dr. Bell\u2019s early\nharmonic telegraph experiments and\nutilized a vibrating reed and an induc-\n\n{ 208}\n\n|\ntion coil. When\n\nthe reed, or spring,\n\nwas twanged it caused\n\na make\n\nand\n\nbreak contact in the primary circuit\nof the coil.\n\nThen, as the secondary\n\nwas connected to the line, a rasping\n\nnoise was produced in the receiver of\nthe called station.\n\nThis system pro-\n\nvided enough current to operate over\nmoderately long lines.\nAlthough it was more satisfactory\nthan any previous method the buzzer\nwas short-lived. It was succeeded the\nsame year by the \u201cmagneto bell,\u201d so\ncalled from the machine which generated its electric power. A popular toy\nof that day was the \u201cshocking machine,\u201d a hand-driven generator with\npermanent magnets, hence called a\nmagneto. The ringer consisted of two\ncoils and a polarizing magnet with an\narmature pivoted at its middle. Practically, the ringer is a small synchronous motor which makes one\ncomplete vibration for each cycle of\nalternating current from the magneto.\nThis form of ringer permits the use of\nalternating current and avoids the\ntroubles which occur in an ordinary\n\nelectric bell where moving contact\npoints must make and break the\ncurrent for every blow of the clapper.\nWith the expansion of the telephone\nbusiness it became desirable to have\nmore than one subscriber on a line.\n\n|\nWatson's Hand Generator\nUsed with polarized ringer\n\nSo party lines were adopted and the\nringer for each subscriber was connected in series with the line. This\narrangement materially decreased the\ntransmission efficiency of the telephone circuit because all the ringer\ncoils offered paths through which the\nspeech current passed to reach a distant telephone receiver.\nIn 1890, J. J. Carty invented the\nbridging bell. There was provided \u00ab\nringer the coils of which offered a high\nimpedance to the talking current.\nWhen this ringer was bridged across\nthe two wires of the line the transmission currents were little affected\nand yet the signalling currents could\noperate the bells effectively.\nSUBSCRIBER\u2019S SIGNALS\n\nWatson\u2019s Polarized Ringer\n\nUsed\n\nin conjunction\n\nwith\n\nWatson\u2019s\n\ngenerator; the forerunner of modern\nringing apparatus\n\nhand\n\nThe development of the magneto\ngenerator with its associated ringer\nbrings telephone signalling down to\nthe present era, for this method of\nsignalling is still used in rural systems.\nSince telephones of the type with\n\n{ 209}\n\n|\n\n|\n\n|\n\n|\n|\n\n|\n\n|\n\nwhich the magneto generator is asso-\n\nTwo-Party SELECTIVE System\n\nciated employ local batteries for furnishing the transmitter with current,\n\nThis is one of the most widely used\nmethods of selective signalling. Its\n\nthey are generally designated\n\u201cmagneto telephones\u201d to\ndistinguish them from\n\u2018\u2018central battery telephones,\u201d which have no\nlocal battery and no magneto generator.\nThe magneto telephone\nis more generally found in\nrural districts, where party\nlines are universally used.\nSuch lines may have from\ntwo to twelve or more sta-\n\nfundamental idea is the fact that\nthree circuits may be ob-\n\ntions.\n\nas\n\ntained from the two wires\n\nof one metallic circuit by\nthe use of the ground as a\nthird conductor. The bell\nof one station, in series\nwith a condenser, is con-\n\nnected between ground\nand one wire of the pair\nleading to the subscriber\u2019s\nset. The bell of the other\nstation is connected similarly with the other side of\n\nEach station is, in\n\nthe line. Thus, each wire\n\neffect, a complete plant\nwith its own battery for a\npower source and its own\nsignalling apparatus in the\n\nis used with ground to\nform a circuit for ringing,\nwhile the two wires together constitute a metallic circuit for talking. The\ncentral-office operator has\ntwo keys each of which\ngrounds one side of the\nline and applies alternating current to the other\nside to ring the bell connected thereto.\nThis method may be\nexpanded into a_ semiselective system if it is\ndesired to apply it to a\nfour-party line. In that\n\nform of a magneto generator. When a subscriber\n\nor an operator rings onsuch\na line all of the bells respond. Such a system is\n\n\\\n\n\u201cnon-selective\u201d and signal-\n\nling must be by code.\nEach station has its individual signal formed by a\ncombination of long and\nshort rings. This method\nhas several disadvantages.\nIt may annoy subscribers\nand \u2018lessen privacy by\ngiving\n\ngeneral\n\nnotice\n\nLaw Subset\u2014\nLong Type\n\nof conversa-\n\ncase,\n\nthere\n\nare\n\ntwo\n\nbells on\n\neach\n\ntions. There are also limits to the\nnumber of stations on a line because\nof the small current generated by a\nmagneto.\nIn order to overcome these disad-\n\nside of the line. Both bells on a side\nrespond to the ringing current on that\ncircuit and the subscribers are distinguished by code, one ring for one\nand two rings for the other.\n\nvantages and limitations, there have\n\nbeen evolved several systems, each\n\nTHE PoLarity SYSTEM\n\naptly named by a word picture of the\nfundamental idea of the method involved.\nThey are the two-party\n\nThe polarity method depends for\nits operation on the use of bells which\nwill respond to a current in one direction only. The idea of selective signalling by changing the polarity\u2014thatis,\n\nselective, the polarity, the harmonic,\n\nand the step-by-step system.\n\n{ 210}\n\n|\n\n|\n\nthe direction of a current\u2014was well\nknown in telegraphy before the birth\nof the art of telephony.\n\nThe desired\n\nresult is obtained by \u201cbiasing\u201d the\narmature of the bell, which means\n\nholding the armature at one end of\nits stroke by a spring in such a manner that it can only respond to current\n\nimpulses tending to move\ndirection.\n\nit in one\n\nA \u201cpolarized\u201d current is one obtained by superposing a battery in\nseries with an alternator.\n\na current\n\nflows\n\nthrough\n\nWhen such\n\na biased\n\nringer, its direct current component\nmay aid the biasing spring, in which\n\ncase the alternating component will\nnot be able to overcome the resulting\nforce on the armature and the bell will\nnot ring. Ifthe direct current flows\nin the opposite direction, it will\noppose and in effect cancel the biasing\naction of the spring, and the alternating component will be free to move\nthe armature and ring the bell. In\npractical use, one terminal of the\nalternator is grounded, and the other\n\nis connected to the negative pole of\none battery and the positive pole of\nanother battery. The other battery\nterminals are connected to the appropriate ringing keys to give positively\n\nand negatively polarized currents respectively.\nThis system in combination with\nthe two-party method just described\nforms a widely-used four-party selective system.\nIn this scheme two\nbiased bells are connected between\neach of the line wires and ground.\n\nwith a current properly polarized.\nIn common battery telephones a\ncondenser must be connected in series\nwith each bell so as to block the flow\nof direct current from thecentral-office\nbattery through the line relay; otherwise a steady signal would be given\nto the operator. When polarized current is applied to such a circuit the\ndirect-current component is blocked\nby the condenser, and the alternating\ncomponent is then free to operate both\nbells. One method used to overcome\nthis difficulty was to connect across\nthe condenser a resistance which would\npass enough current to aid or oppose\n\nsystem, the proper one of which serves\n\nto connect the desired side of the line\n\n|\n\nthe biasing spring, but not enough to\n\noperate the central-office relay and\nsignal the operator.\nIn present standard practice this\nresistance is eliminated in an ingenious\nway. A special alternating-current\nrelay is provided in each set bridged\nacross the line in series with the condenser.\nWith the application of\npolarized currents to the line for calling any of the parties, alternating current flows through all four relays and\nin operating they connect the respective bells directly between both\nsides of the line and ground.\n\n4\n\nThe\n\npolarized current then operates the\nbells selectively as described above.\nInasmuch\n\nas with this arrangement\n\nthe bells are only connected to the\nline during the ringing period they do\n\n|\n\nnot interfere with the signals to the\noperator.\nHarmonic SystTEMs\n\nOn\n\neach side of the line one bell is rung by\npositively polarized current and the\nother by negatively polarized current.\nThe two bells on the other wire are\noperated in similar fashion.\nFour\nringing keys are necessary with this\n\nA\n\nHarmonic systems utilize the fact\nthat a pendulum or an elastic reed so\nsuspended as to be able to vibrate\nfreely will have one particular rate of\nvibration. In this method of signalling\na different type of ringer is employed.\nThe armature and striker of the bell\nare mounted on a rather stiff spring so\n\n|\n\n|\n|\n\n{211}\n\n|\n\n|\n\n|\n\nthat the moving parts constitute, in\neffect, a reed tongue possessing a\nnatural period of vibration. Therefore, it may be easily vibrated by impulses of the same frequency as its\nnatural rate of vibration while those\nof different frequency will not disturb\nit sufficiently to strike the gongs.\nOrdinarily harmonic systems are\nlimited to four stations on a line and\nthe frequencies usually employed are\n\nator presses once the so-called \u201ccalling\nkey\u201d which sends out a large current.\nThis single impulse of large current\n\nthus operates both types of magnets,\nby one releasing all the lock arms on\nthe line and by the other moving the\nwheel forward one step at each station.\n\nAfter this another key is depressed.\n\nThis throws on the line a series of\nweak impulses the number of which is\npredetermined to correspond to the\n\n1624, 3334, 50, and 66% cycles per\n\nsetting at the station of the desired\n\nsecond. These frequencies correspond\nto 1000, 2000, 3000 and 4000 cycles\nper minute.\n\nsubscriber. At all the stations the\ncontact arms move gradually. When\nthe required number of impulses have\n\nStEp-By-STEP\n\nbeen sent, the ratchet\n\nSySTEMS\n\nIn the step-by-step method the\nbells are not connected to the line\nnormally but, preliminary to ringing,\nany bell may be made responsive by\nsending a certain number of impulses\nover the line. Although several methods of step-by-step signalling have\nbeen successfully reduced to practice\nthey are used very little in ordinary\ncentral-office telephony. The principles are applied, however, in train\ndispatching and radio telephony, and\nin the stock exchange ticker and other\napplications of telegraphy.\nA typical step-by-step system illustrates the underlying principles. At\neach subscriber\u2019s station there are in\nseries two electromagnets of high and\nof low resistance respectively, the\ntormer operating on a much smaller\ncurrent than the latter. The high resistance magnet operates a ratchet\nwheel which carries a contact arm and\na stop arm and the low resistance\nmagnet controls another contact arm\nand a separate arm which locks the\nratchet wheel when the desired contact is made. These contacts are adjustable and each station has a different setting.\n7\nWhen signalling a station the oper-\n\nwheels\n\nhave\n\nturned, but only at the called station\nare two contacts opposite each other.\nThe operator then depresses again\nthe calling key, sending out a strong\nimpulse which operates the other\nmagnet and closes the contacts of the\nbell circuit.\nLimitTiInc Facrors\n\nWhile selective signalling places\nlimits on the number of telephones\nthat may be served by one line, this\nlimit is usually greater than that imposed by traffic conditions. Rural\nlines are often built and maintained\nby their users, and in order to reduce\nthe expense they put a rather large\nnumber of telephones on each line.\nAlthough this means that they may\nhave to wait until others have finished\ntalking, they are not often seriously\ninconvenienced by the delay. Further,\nthe cheery tinkle of the bell breaks\nthe monotony of the long days and\nsuggests to subscribers an opportunity for neighborly gossip. Since\nfew calls for such lines originate outside the local central office, the cost of\nhandling calls which receive a \u201cbusy\u201d\n\nsignal is small.\nIn suburban and small city areas,\non the other hand, the parties per\n\n{ 212}\n\n4\\\n\ncircuit, each applying ringing current\nto its side of the line; or by using the\nso-called \u201cjack per station\u201d switchboard. In the multiple of this board\nthere are two jacks for each party line\nand the talking wires are interchanged\nwhen they are cross-connected at the\nmain distributing frame. Hence applying ringing current to the \u201ctip\u201d\nconductor of the cord circuit will apply\nit to one or the other line wires according to which of the two jacks is\nplugged into. This system simplifies\nthe ringing circuit and will effect an\noverall saving in areas where only a\nfew party lines are served. It also\ngives no indication of the class of\nservice.\nFor four-party selective ringing\nfour keys are usually provided for\neach cord circuit. A simple mechanism locks down the last key to be\npressed, as an indication to the\noperator.\n\nSection of a key shelf of 1880\n\nline are\n\nlimited\n\nto\n\nfour.\n\nWhere\n\nthe calling rate is still higher, as for\n\nexample business telephones, no more\nthan two parties are connected to a\nline, and most of these telephones are\nserved by individual lines.\nRincinc EQuIPMENT ON THE\nKry SHELF\n\nAssociated with every cord circuit\nthere must be some means for starting\nand stopping the ringing current. In\nthe simplest case this is merely a pushbutton key which disconnects the line\nfrom the rest of the circuits and connects it to the ringing generator. In\nmagneto and toll boards a ringing\nkey is associated with each cord of\nthe pair; in most other boards, only\nwith the calling cord. T'wo-party\nselective ringing may be given in two\nways: by two ringing keys in the cord\n\nWhere ringing is controlled\n\nonly by the operator the last key to be\npressed locks half-way down as an indication to the operator to relieve her\nmemory, in case a re-ring is necessary.\nAll the later \u201cB\u201d boards and some\n\u201c\u201cA\u201d boards have \u201c\u2018machine\u201d\u2019 ringing\nin which the operator merely sets upa\nrelay circuit. When most of the lines\nare individual, the B-operator glances\nat the keys to be sure that \u201cparty W\u201d\nis depressed, and plugs into the line\njack. In the latest type of machineringing boards, a common set of ring-\n\nne\n4\n>\n\nA listening and four-party selective ringing key\n\n{213}\n\n=\n\ning keys controls the ringing on all of\nthe cord circuits.\nIn contrast to the signals just dis-\n\nthrough the primary of a transformer\nwhich delivers a suitably higher voltage to a low-pass filter. In larger\n\ncussed is the so-called \u201caudible ring-\n\noffices,\n\nback.\u201d It was introduced because of\nthe psychological effect on the calling\nsubscriber of receiving an indication\nthat his call was being attended to.\nTraffic observations show a large de-\n\ncrease in recalls by the subscriber to\nask the operator to \u201cring them again.\u201d\nThe most common circuit involves a\nsmall condenser bridged across the\nringing key so as to allow the higher-\n\nfrequency harmonics of theringing current to flow to the calling subscriber.\nPoweErR For RINGING\n\nIn the smallest magneto offices,\nringing current comes from a hand\ngenerator mounted under the keyshelf. Where traffic keeps the operator\nbusy, she is relieved from turning the\ngenerator crank by the provision of a\npole-changer. This device is a relay\nwith a heavy armature whose period\nis twenty cycles a second. It is kept\nvibrating by a number of Edison\nprimary cells, and auxiliary contacts\non the armature reverse the polarity\nof a battery of dry cells. Two polechangers are used in the smallest common-battery offices; they are driven\nfrom the 24-volt battery, and they\nreverse current from this battery\n\none\n\npole-changer\n\nand\n\none\n\nmotor-generator outfit are used; in\nthe still larger offices, two or more\n\nmotor-generator outfits. These consist of a motor driving a double current\ngenerator. From a commutator at\none end of the armature comes direct\n\ncurrent to excite the field and when\ndesired to operate the coin mechanism\nin public telephones; from a pair of\nslip rings at the other end comes\ntwenty-cycle alternating current\u2014\nusually at eighty volts\u2014for ringing.\nAnother commutator interrupts current from the central-office battery to\ngive the \u201ctrouble\u201d and \u201cbusy\u201d tones.\nA slow-speed shaft driven by a worm\nand gear from the main shaft carries\na number of commutators to control\ncurrents for intermittent ringing,\n\u201cbusy flash,\u201d and other signals.\nTo guard against failure of the\npublic service power by which these\nmachines are driven, one ringing machine is always equipped with a motor\nwhich can be run from the centraloffice battery. In some of the largest\noffices, both motors are built into the\n\nmachine. Then if the outside power\nfails, a relay at once throws the other\nmotor onto the central-office battery\nand the machine never stops.\n\nAll who are interested in the trend of modern atomic theory will\nwelcome the announcement that the Nobel prize for physics for\n1924 has been awarded to Prof. Manne Siegbahn of Upsala. His\nmost notable researches, and those for which the award has been\nmade, have been in X-ray spectroscopy. Since Moseley\u2019s first\nmeasurements, the technique has been improved to such an extent\nthat it is now possible to measure wave-lengths in this region of the\nspectrum to six significant figures. This advance is due, almost\nentirely, to the work of Prof. Siegbahn. In addition to these high\nprecision measurements, he has made an exhaustive study of the\nsoft radiations which lie between the ultra-violet and the ordinary\nX-ray region. From \u201cNature,\u201d November 21, 1925\n\n{214}\n\nOur\nHE\n\nTransmission\n\nCaANnaDIAN\nEngineer\n\nCorRESPONDENCE\n\nof\n\nthe Northern Electric has many\nfriends in the Laboratories and they\nwill be interested in the following\nletter written by him to Burton W.\nKendall. In this letter Mr. Vennes\nrefers to the statement on page 152\nof the November RECORD that \u201cThe\nAustralians compliment themselves\nupon the fact that, with the exception\nof the United States, Australia is the\n\nonly country in the world operating\nlong-distance telephone traffic on the\ncarrier-wave principle.\u201d The Sidney\n\u201cDaily Guardian,\u201d for example, said\nin its issue for September roth:\n\u201cWith the exception of the United\nStates, Australia will be the only\ncountry in the world operating long-\n\ndistance telephone traffic on this\nsystem.\u201d\nActually, the carrier-current systems developed for the Bell System\nhave been made available to other\ncountries through the International\nWestern Electric Company.\nThe\nAustralian installation is not the only\ninstallation of this Western Electric\nequipment for there are installations\nin Canada and Brazil. The Aus-\n\n\u201cDear Kendall:\n\nI have read with great interest the articles\nin the December issue of the Record, dealing\nwith carrier-current systems.\nI was particularly interested in noting how successfully\nthe Australian project \u201cwent across\u201d and\nmore so on account of my early connection\nwith that job. Mr. Jammer is certainly to be\ncongratulated on the successful way in which\nhe has made the carrier \u201ctalk for itself.\u201d\nThere is one point, however, on which I must\ncomment, and if only the Editor of the Sydney\n\u201cDaily Guardian\u201d were not so far away I\nmight be able to vent my feelings in the\nproper direction. Does Australia forget that\nshe has a sister country by the name of Canada\nand that carrier-current telephones have been\nin successful operation in that country for over\nfour years? or is Canada considered to be a\npart of the United States as far as Australia is\nconcerned? I feel sure our Alberta friends\nwould beat it across the Pacific with sixshooters if they were shown the \u201cGuardian\u201d\narticle.\n\nMr.\n\nVennes refers, being intended to\nshow the attitude of the Australians\ntoward their new equipment, was\nmade up of direct and _ indirect\nquotations from their newspapers;\nand hence no criticism of their comments entered the article.\nMr. Vennes writes:\n\nYour article on \u201cCarrier-Current Telephone\nSystems\u201d is very interesting, and I note with\nmuch pleasure the honorable mention you have\ngiven me. Memories of Maumee come to me\nquite often, and even Baltimore leaves no uncertain recollection of pleasant work. Even\nthe memorable Sunday morning on which the\nSystem was to be cut into service can be looked\nback on with fond recollections.\n\nnewspapers\n\nwere\n\nlaboring\n\nunder a misapprehension\ncomments.\nThe article\n\nin their\nin the\n\nRECORD,\n\nhowever,\n\nto which\n\n|\n\nHow about our friend Mills who burnt\nmidnight oil in writing up operating instructions for the Edmonton-Calgary System? He\nshould have challenged the statement of the\n\u201cGuardian.\u201d How about your good self who\nknows very well that the Edmonton-Calgary\nSystem has band filters?\nIn writing this I am trusting that you will\nhave checked your razor with the doorman\nwhen I see you next time\u2014but I simply had to\nget this off my chest. I feel better already. I\nhave heard several cutting remarks from some\nof our people here and hence the reaction.\nOnly dead balls refuse to bounce.\n\ntralian\n\n|\n\n{ 215}\n\n|\n\n|\n\nIn\n\nr\n\nMontu\u2019s\n\nNews\n\nDurinc the recent conference of\nbuilding and equipment engineers\nheld by the American Telephone and\nTelegraph Company, about forty-five\nof the visiting engineers, at the invita-\n\nSpeech\u201d and \u201cThrough the Switch-\n\ntion of Amos F. Dixon, made an in-\n\nScientific Fraternity on \u201cPutting a\n\nspection trip through the Laboratories. The visitors, who represented\nthe American T elephone, Western\nElectric, and associated telephone\ncompanies, were divided into small\ngroups and guided through the various\n\nlaboratories by supervisors of our Systems Development Department.\nHarvey FLercHer spoke to the\nstudents and faculty of the Cornell\nUniversity School of Electrical Engineering on \u201c\u201cThe Physical Nature of\n\nSpeech,\u201d and to the Ithaca Section of\nthe A.I.E.E.\n\u201cELECTRICAL TRANSMISSION OF\nSPEECH,\u201d a motion picture film, was\n\npresented by the Laboratories at the\nDecember 9 meeting of the New York\n\nboard.\u201d\nJoun\n\nJ.\n\ndelivered\n\nan\n\naddress before the New York Alumni\nChapter of Gamma Alpha Graduate\n\nKick into Submarine Cables.\u201d\nFrancis\n\nF.\n\nLucas\n\ndescribed\n\nto\n\nstudents of the Harvard Engineering\nSchool the technique of high power\nphoto-micrography of metals, and discussed\n\nthe structure\n\nof steel under\n\nvery high magnification.\n\nNationaL ACADEMY ofSciences\nand the National Research Council of\nthe United States have announced the\n\nforthcoming publication of International Critical Tables of Numerical\n\nData of Physics,\nTechnology.\nThe\n\nmaterial\n\nChemistry\n\nand\n\nfor the Tables has\n\nbeen collected and critically evaluated\nby some 300 cooperating experts, including chemists, physicists, and en-\n\nElectrical Society. The meeting was\ngiven over to a discussion and demon-\n\ngineers of the United States and many\n\nstration of the use of motion pictures\nas a pictorial record of the progress of\nscience and industry.\nKart K. Darrow recently spoke\nbefore the physics\u2019 colloquium of\nHarvard University on researches in\nthermionics, photoelectricity, and the\nscattering of electrons by atoms.\nLecrures BEFORE the student body\nof Lehigh and before upper-class\n\ntributors is Harvey Fletcher of Bell\nTelephone Laboratories.\nHis con-\n\nengineering\n\nstudents.\n\nat\n\nLafayette\n\nwere given on November 12 by John\nMills, speaking on the \u201cChoice of\nan Engineering Career.\u201d At Lafayette\nthere was also a showing of the films\n\u201cThe Electrical Transmission of\n\nforeign countries.\n\nAmong\n\nthe con-\n\ntribution was numerical constants of\n\nspeech and hearing. The material\nwhich he furnished is essentially that\ncontained in his article \u201cUseful Numerical Constants of Speech and\n\nHearing\u201d? which was published in\nBell System Technical \u2018Fournal, Vol.\nIV, No. 3, of July, 1925.\n\nMr. Jewett\n\nand Mr. Craft were trustees for the\npublication of these tables.\nSERGIUS P. Grace delivered an\naddress on \u201cResearch in the Bell\n\nTelephone Laboratories\u201d\n\nbefore the\n\nRochester Section of the A.I.E.E.\n\n{ 216}\n\nil\n\nIE YE\n\nEYE\n\nI Give\n\nYE PE PES\n\nBEQUEATH\n|\n\nYa to all my worldly goods, now\nor to be in store,\n\nI give them to my beloved wife, and\nhers evermore.\n\nI give all freely; I no limit fix;\nThis is my will, and she\u2019s executrix.\u201d\n\nSuch was the unique last will and\ntestament said to have been drawn\nby one Smithers, a London\n\nlawyer,\n\nin which he made provision for\nthe disposition of his property upon\nhis death. In the past many means\nhave been used for the disposition\nof property by will and many odd\nways\n\nhave\n\nbeen\n\ndevised;\n\nbut,\n\nas\n\nthe making of a will is now generally\ngoverned by statutory requirements,\nthe odd and novel method is not\nusually a safe one to employ.\nMany years ago the matter of making a will was considered an omen of\napproaching death, but this superstition no longer prevails. The prudent man or woman looks upon the\nmaking of a will as similar to any\nother business transaction except that\nin the case of a will it does not become\neffective until the death of thetestator.\nEveryone admits the necessity of\nmaking provision for his or her dependents, but many, while they have good\n\nintentions in regard to the making of a\nwill, for one reason or another put the\ntask off too long. Failure to make a\nwill results in the distribution of\nproperty in accordance with the laws\nof the state; and the law will, in such\ncases, make a will for the person who\nfails to make one for himself or herself.\n\nThe results in cases of this character\nare that the distribution of the property at death is not made in the\nmanner or proportion which always\nworks for the best interests or needs of\nthose dependent.\nFor example, suppose a man in New\nYork died without a will and left\nan estate of $10,000.00.\nIf he left\nsurviving him a wife and one minor\nchild, the estate would be divided,\none-third to the wife and two-thirds\n\nto the minor child. It would be necessary to apply for letters of administration of the estate, for the administrator\nto file a bond covering the faithful\n\nperformance\n\nof his duties as such\n\nadministrator, and to arrange for the\n\nappointment of a guardian who would\nbe in charge, during the infancy of the\n\nminor, of the person and of the estate\nof the minor. All these proceedings\nwould involve expense much of which\nwould have been avoided if a will had\nbeen made and provision inserted for\nthe payment of the legacies in the\nproportion desired, for the waiving of\nthe bond of the executor, and for the\n\nnominating of a relative or friend who\nwould act without expense as guardian\nof the minor.\nThe administration of an estate disposed of by will is through an executor,\nor an executrix if a woman handles the\nestate. The estate and the person so\ncharged with this responsibility are\nunder the jurisdiction of the Surrogate or Probate\n\nCourt, to whom\n\naccountings covering the management\nof the estate must be made from time\nto time. In many states at least one\n\n{217}\n\n|\n\n|\nThe preparation of a will, like an\n\nyear must elapse before an estate can\nbe finally settled.\nThe general legal requirements to\nbe considered in the preparation of a\nwill are:\n\nother business document,\n\nshould be\n\naccomplished only after careful consideration and after competent advice\nis obtained.\nare\n\ndesirable\n\nThe services of a lawyer\nnot\n\nonly so\n\nthat the\n\nbody of the will may properly reflect\n\n1. The person must be competent to make\na wiil.\n\nthe testator\u2019s intentions as to the.dis-\n\n2. It must be in writing, signed, sealed, and position of his property but also for\nthe purpose of ascertaining that the\nattested before at least two witnesses\nwho must not be legatees.\nstatutory requirements are adhered to\nwith respect to the execution of the\n3. An executor or executrix must be\nwill.\nappointed.\n\n|\nOn\n\nTHE\n\nRoap\n\nDurRING\n\nN the September issue of the\nRECORD there was described in\n\u201cOur Far-Flung Outposts\u2019? some of\nthe work carried on outside of New\nYork by members of the Laboratories\nwho have more or less permanent\nassignments in the field. In-addition to\n\nthese \u201coutposts\u201d? many occasions arise\nwhen our engineers make trips of\nshort duration on special assignments\nor in connection with their usual\nduties.\nThese short absences from West\nStreet are usually one or another of\nfour kinds. In the first place they\noccur in the co-operation of our\nengineers with those of the American\n\nTelephone and Telegraph Company\nin the field trials of recently designed\nequipment. In the second place and\nwith more frequency they arise from\nthe need of co-operation and conference with the engineers at Haw-\n\nthorne in connection with equipment\nwhich the Western Electric is to manufacture. A considerable number occur\nas part of the engineering services\nwhich were mentioned in \u2018Who Pays\n\nNoOvEMBER\n\nOur Salaries\u201d (RECORD, Vol. I, No.\n\n2) as performed by the Laboratories\nfor the Western Electric Company.\nThese include all absences for the\nengineering and installation of public\naddress systems, radio broadcasting\nstations and power line carrier. Jn addition another group of absences from\nNew York are occasioned by attendance at meetings of professional and\nscientific societies and by the acceptance of invitations to speak on technical subjects before technical societies\nand university audiences.\nAs an example of the range and\n\nvariety of these outside contacts of\nmembers of the Laboratories the\nRECORD presents a brief statement\nas to the travels and business of some\nof the men who were on the road during the single month of November.\n\nFrom the Apparatus Development\nDepartment L. W. Conrow was in\nChicago, Milwaukee, Champaign, and\n\nDes Moines, making surveys for prospective public address system installations. He was also in St. Louis completing work on a public address\n\n{ 218}\n\n|\n\nsystem for the Hotel Coronado, where\nT. L. Dowey assisted in the final tests.\nR. E. Kuebler in Philadelphia demonstrated to Mr. Shibe, at the Shibe\n\nBall Park, the application of the No. 1\n\nPublic Address System for announc-\n\ning athletic events. KF. M. Ryan is\nin Hawaii in connection with a radio\nsurvey\n\n|\n\nto check\n\nthe feasibility\n\nof\n\nconnecting the telephone systems on\nthe various islands by means of radio\ntoll circuits,\n\nand\n\nto determine\n\nthe\n\n\u2018 general requirements to be met by the\nradio transmitting and receiving apparatus which would be required.\nP. H. Evans made a three weeks\u2019\ntour of inspection of some of the broad|\ncasting stations using Western Electric\nequipment. The stations visited were\nWWJ (c KW), WCX-WJR (5 KW),\nDetroit; WENR (1 KW), WQJ (500\nwatts), WLS (5KW), Chicago;WCBD\n\n(5; KW) Zion; WCCO\nneapolis; WOC\n\n(5 KW) Min-\n\n(5 KW)\n\nDavenport\n\nand WSAI (5 KW) Cincinnati. On the\nPacific Coast\nD.H. Newman was super-\n\n|\n\nvising\n\ninstallation\n\nof\n\nbroadcasting\n\nequipment (500 watts) for Nichols and\nWarinner, Long Beach; Pasadena\nStar News (1KW), Pasadena; and the\n\nFirst Avenue Baptist Church (500\nwatts), San Jose.\nW.L. Tierney and J. C. Herber in\nChicago supervised the installation of\n1 KW broadcasting equipment for the\nChicago Daily News. This equipment\nreplaces the 500 watt equipment\ninstalled in September, 1922. Mr.\nHerber later made surveys for proposed installations at the Universities\nof Illinois and Notre Dame.\nP. A. Anderson returned from Jacksonville, Florida, where he supervised the installation of a 1K W broadcasting equipment for that city. J.\nC. Crowley supervised the completion\n\nof 1 KW broadcasting equipments for\nLarus Brothers, Richmond, Virginia,\n\nand M. M. Johnson and Company,\nClay Center, Nebraska. C. Flannagan\nin Baltimore supervised a 5 KW installation for the Consolidated Gas,\n\nElectric Light and Power Company.\nJ. S. Ward expects to complete the\ninstallation of the 5 KW equipments\nfor Sears, Roebuck and Company,\nChicago, and the Bankers Life Com-\n\n|\n\npany, Des Moines, and to get back to\n\nNew York before Christmas.\nL. B. Cooke installed a power-line\ncarrier system on the lines of the\nNorthern States Power Company between Minneapolis and Eau Claire.\nW. V. Wolfe was investigating carrier\ntransmission characteristics on powerlines between Toccon and Stevens\nCreek, Georgia.\n\nR. D. Gibson\n\nand\n\nJ. B. Irwin were installing power-line\ncarrier telephone equipment for the\nAugusta-Aiken Railway and Electric\nCompany, Georgia. D. C. McGalliard\nwas similarly engaged for the Alabama\nPower Company between Magella\nand Sheffield, Alabama.\nW. T. Booth, H. H. Glenn, E. B.\nWheeler, F. F. Lucas, H. N. Van\nDeusen, J. T. Butterfield, J. R. Townsend, W. Fondiller, R. E. Schumacher,\nJ. E. Harris, R. L. Burns, C. D.\nHocker, W. C. Redding, and C. H.\n\nMatthewson were at Hawthorne discussing questions of apparatus design.\nR. H. Hart, R. M. Moody and W. C.\nMiller attended service conferences on\nvarious types of apparatus.\nC. R. Steiner has been in Hawthorne studying the manufacture of\nstep-by-step central office apparatus.\nH. A. Anderson attended a meeting .\n\nin Cleveland of the American Society\nfor Testing Materials.\n\nTogether with\n\nH. T. Martin and H. N. Van Deusen\nhe visited Camden, New Jersey, to\ndiscuss improved designs for parts\nof the Victor talking machine.\nH. C. Harrison spent several days\n\n{ 219}\n|\n\n|\n\nat Camden in the laboratories of the\n\nare in England\n\nVictor Talking\n\nCompany.\n\nnational Standard Electric Company\n\nA. B. Sperry, also of the Systems\nDevelopment Department, has been\nat Hawthorne in connection with the\nmanufacture of step-by-step machine\nswitching equipment. J. A. Mahoney\nand T. C. Campbell of the Equipment\nDevelopment group are spending\nthree months at Hawthorne on a\nspecial training program planned to\nacquaint them with manufacturing\nmethods and the work of the Switch-\n\nby supervising the installation and\nfinal test of the Rugby Transatlantic\n\nboard Planning Division.\n\nwith patent matters.\n\nW. C. Jones of the Research Department has been in Boston. R. R.\nWilliams went to Huntington, West\nVirginia, for a meeting of the Club\n\nScranton with Mr. Lysons of the\nNorthern Electric Company and Mr.\n\nMachine\n\nRadio Station\nOffice.\n\nassisting the Inter-\n\nof the British Post\n\nSeveral other research men, includ-\n\ning W. A. Knoop, W. S. Gorton, W.\nOrvis, J. F. Wentz have been working\n\nin England on permalloy-loaded cables with G. A. Anderegg.\n\nFrom the Patent Department, E.\nW. Adams is in London in connection\nW. H. Matthies\n\nmade a trip to\n\nBrockwell of the staff of the Com-\n\nmissioner of Telephones of Manitoba.\nThe trip was made in order that Mr.\nBrockwell might see the working of\nEngineers at Cincinnati.\nthe 200 point line finder in the ScranJ. A. Becker presented a paper to ton trial. The Manitoba Administrathe American Physical Society at its\u2019 tion is considering equipment using\n\nof Industrial Research Directors and\n\nalso attended the annual meeting of\nthe American Institute of Chemical\n\nChicago\n\nmeeting,\n\nwhich\n\nwas\n\nalso\n\nattended by K. K. Darrow.\nRadio tests took G. Thurston, F. A.\nHubbard, F. B. Llewellyn, S. Wright,\nE. G. Ports, G. Thurston, E. Bruce,\n\nsimilar apparatus\n\nand Mr. Brockwell\n\ndesired to familiarize himself with its\ncharacteristics.\nMany members of the Inspection\nEngineering Department\n\nare located\n\nR. A. Heising, J. G. Chaffee, J. F.\nFarrington, J. C. Schelling, F. R.\nLack, and E. Kraut to various parts\nof the country.\n\noutside of the city in the regular\n\nP.B. Flanders has been assisting the\n\nDecember first W. K. St. Clair, for-\n\nVictor Company of England in applying the latest improvements in the\nphonograph art to their product; and\nT. C. Kinsley is assisting him.\nA. A. Oswald and H. R. Knettles\n\ncourse of their business. Two changes\nin location which were in the nature\n\nof promotions\nmerly Local\n\noccurred\n\nwhen\n\non\n\nEngineer of the New\n\nYork district, became Local Engineer\n\nof the Philadelphia district, and J. A.\nSt. Clair was appointed Local Engineer of the New York district.\n\n{ 220}.\n\n|\n\nWestTERN\n\nEvectric\n\nINcorPoRATES\n\nHE morning papers of December\n23, carried the interesting announcement that the electrical supply\nbusiness\n\nof\n\nthe\n\nWestern\n\nElectric\n\nCompany had been segregated from\nthe telephone manufacturing business\nand incorporated under the name\n\u201cGraybar Electric Company.\u201d\n\nton, the partnership formed between\nProfessor Elisha Gray and Enos M.\nBarton in 1869 to manufacture electrical equipment. The small shop of\nGray & Barton, which produced telegraph apparatus, call boxes, fire and\nburglar alarms, developed into the\nWestern Electric Company.\nIt is\n\nof\n\nbelieved that this is the first instance\nwhere a corporation after such a lapse\n\nPresident\n\nWestern Electric, becomes President;\nFrank A. Ketcham, General Manager\n\nof the Supply Department, becomes\nExecutive Vice-President; George E.\nCullinan, General Sales Manager,\nbecomes Vice-President in charge of\nsales; Leo M. Dunn, General Mer-\n\nchandise Manager, becomes VicePresident in charge of merchandising\nand accounting; Elmer W. Shepard,\nGeneral Credit Manager of Western\nElectric has been made Treasurer; and\n\nN. B. Frame of the legal staff of the\nWestern Electric Company has been\nmade secretary of the new company.\nThe board of the new company includes George E. Cullinan, Albert L.\nSalt, Charles G. DuBois, Frank A.\nKetcham, Leo M. Dunn, R. H.\n\n|\n\nDEPARTMENT\n\nWestern Electric is Chairman of the\nBoard of the new company; Albert\nL. Salt, formerly Vice-President in\ncharge of purchases and traffic of\n\nCharles G. DuBois,\n\n|\n\nSupPLY\n\nGregory, Controller of Western Electric, Howard A. Halligan, Vice-President of Western Electric; George C.\nPratt, General Attorney of Western\nElectric, and William P. Sidley, VicePresident and General Counsel of\nWestern Electric.\nThe name of the new company is\nderived from that of Gray and Bar-\n\n|\n\nof time and a period of such tremend-\n\nous growth has reverted to its original\ndesignation for a corporate name.\nChanges have been made in the\norganization of Western Electric necessitated by creation of the new company. Jay B. Odell, Assistant to the\nPresident of Western Electric Company, becomes Vice-President, succeeding Mr. Salt. Mr. Odell will be\nin charge of purchases and traffic.\nF. L. Gilman, manager of the Kearny\nworks, becomes Treasurer of Western\n\nElectric, succeeding J. W. Johnston,\nwho is retiring after thirty years of\nservice. C. G. Stoll, manager of the\nHawthorne works in Chicago, will be\ngeneral manager of manufacturing,\nin charge of all manufacturing in addition to his present duties.\nR. C. Dodd, assistant manager othe Kearny works, has been appointed works manager at Kearny\nunder Mr. Stoll.\nAs a result of these changes, Mr.\nSalt, Mr. Johnston and Mr. Ketcham\n\nare replaced as directors of Western\nElectric by Mr. Odell, Mr. Stoll and\nGeorge C. Pratt, the company\u2019s\ngeneral attorney. The changes are\neffective January first.\n\n{221}\n\n|\n\nNores\n\nCLuB\n\nDavid D. Haggerty, Secretary\n\nCLus\n\nELECTIONS\n\nMEMBERSHIP\n\nMembership cards are obtainable\n\nAs a result of the recent elections\n\nthe following candidates\n\nhave been\n\nelected to office:\nFor President\n\nWilliam Wilson\n\nFor First Vice-Pres.\nFor Second Vice-Pres.\n\nDaniel R. McCormack\nMarion G. Mason\n\nApparatus Design\nPatent Inspection\nShops\n\nNo election for mayor of New York\nCity was ever harder contested or\nbetter managed than the fights carried\non by the campaign managers for the\n\ni\n\n108 or\nBesides\n\nbeing certificates of membership these\ncards are very valuable as a means of\nidentification\ntaking\n\nadvantage of\nany of the\nClub\u2019s_priv-\n\nL. B. Eames\nG. Heydt\nJ. Motley\n\nvarious candidates.\n\nby either calling at room\ntelephoning extension 542.\n\nwhen\n\nDepartmental Representatives\n\nCArRDs\n\nThe popularity\n\nof all the candidates made the election\nextremely close, and during the count\nof ballots some of the elections were\nnot decided until all votes were in. A\n. total of 3100 ballots was cast.\n\nileges.\nPins\n\nDuring the\n\npast few months\nthe club has enrolled\n\nover\n\n:\nDaniel R. McCormack\n\n1,000new members. In David D. Haggerty\u2019s office\nthere is available a supply of very\nattractive club pins. They are of ten\ncarat gold with blue enamel face, gold\n\nlettering and safety catch; and the\nprice is $1.65. All members, new and\nold, are invited to inspect these pins.\nCuHeEss ACTIVITIES\n\nVe\u2019\n\u201cJ\n\n;\n\n7\n\n|\n\nWilliam Wilson\n\nIf the results of the chess matches\nwhich have been played so far this\nseason may be taken as any indication, the Potter trophy will have the\nWest Street Trophy Case as its permanent home.\nAgain our chess\nplayers are carrying off the honors in\nthe championship matches of the\nCommercial Chess League of New\nYork City. On November 21, captained by F. A. Voos, the West Street\nteam met and defeated the repre{222}\n\n|\n\n|\n\nDecember 14, they won three out of\n\nApparatus Design.\nToll Circuit\u2019s\nspeedy and wide-awake quintet staged\na sensational rally during the last\nfew minutes of play and pulled out a\nvictory over Apparatus Design after\napparently being beaten. The final\n\nfour games from the Western Union\n\nscore was 23-18.\n\nsentatives of the Henry L. Doherty\nCompany\n\nfour straight games.\n\nOn\n\nDecember 5, they repeated the performance by defeating the McGraw-\n\nHill Publishing Company 4\u2014o.\n\nOn\n\nrepresentatives.\n\nThe team will play the Chase\nNational Bank, New York World,\nGuarantee Trust Company, New\nYork Edison Company, Tidewater\nOil Company, and Brooklyn Edison\nCompany, in the order mentioned.\nThe Club\u2019s own tournament for\n\u201cA\u201d and \u201cB\u201d class players is now in\nprogress. [our groups of five men\neach are entered in the first Round\nRobin contest. From the result of\nthese matches will be determined the\ngrouping for the second contest which\nwill start early in January.\nThe ladder tournament for class\n\u201cC\u201d players is now under way with\nthirteen contestants.\n\nThose\n\nwho finish at\nthe top are entitled to compete in the final\nRound\n\nRobin\n\nTwo games are played every Tues-\n\nThe Colvoy Quartette: F.M. Costello, F. von\nSchlichten, F. F. Lee, R. P. Yeaton\n\nday and Friday evening, starting at\n\n5:30, at Labor Temple, Fourteenth\nStreet and Second Avenue.\nClub\nmembers are. invited to attend.\n\ntournament\nwhich will be\nheld to determine who shall\n\nrepresent West\nStreet in the\nmatch with Haw-\n\nMiss Marion G. Mason\n\ntelegraph\nthorne.\n\nchess\n\nBasket\n\nror MEN\n\nCLUB QUARTETTE\nThe quartette representing and\nmade up of members of The Bell\nTelephone Laboratories Glee Club is\nworking on a program of favorite\nsongs of long ago; songs which,\nthough old, will always be enjoyed.\nThe personnel of this quartette, known\nas The Colvoy Quartette, is as fol-\n\n8, when\n\nlows: F. F. Lee, First Tenor; R. P.\nYeaton, Second Tenor; F. M. Costello, Baritone; and F. von Schlichten,\n\nPresident Kendall threw up the ball\nwhich started play in the first league\n\nBass. This organization has broadcast on numerous occasions through\n\ngame.\n\nWOR,\n\nThe\n\nbasket\n\nball league\n\nfor men\n\nstarted the 1925-26 season on Tuesday\n\nEvening,\n\nDecember\n\nThe game\n\nwas between\n\nthe\n\nteams representing Toll Circuit and\n\nWGY\n\nand WEAF,\n\nand the\n\nprogram of old songs is being pre-\n\n{ 223 }\n\n|\n\npared to fill a request for this class\nof song. At the dance held recently\nby The Bell Laboratories\u2019 Club at\nthe Pennsylvania Hotel the quartette\nsang a number of selections and was\nreceived with great enthusiasm.\nBasket\n\nBALL\n\nror\n\nWomMEN\n\nThe women of the Club are organized into four basket ball teams which\nrepresent Equipment, Transcription,\nPatent, and Research Departments,\nrespectively. These teams are play-\n\nfile entry blanks at once with Mr.\nHaggerty or Miss Hence.\nWomen\u2019s\n\nEach\n\nSwiMMInNG\n\nMEET\n\nOn January 20, the club will present\nsomething new\u2014a swimming meet\nfor women, to be held: at the Carroll\nClub, 121 Madison Avenue. It will\ninclude swimming and diving contests\n\nevening\n\nat 6\n\nparty in the rest room.\nMiss\nMurtagh, who is in charge, invites all\nthe women of the building to take\npart. She is glad to plan for a new\nplayer. Players are assessed a small\nsum for the prizes.\nSEWING\n\nCLASSES\n\n\u201cWomen\u2019s Wear\u2019 hints that this\nyear\u2019s display of feminine apparel\nwill exceed\n\nin\n\ncharm, grace,\nand simplicity\nof line the\ngowns of any\nother\n\nWoMEN\n\nWednesday\n\nPartigs\n\no\u2019clock our Club women hold a card\n\ning three series of games: the first on\n\nThursdays in December, the second\nduring January, and the third in\nFebruary. Games start at 5:30 p.m.\nat Friends School, Stuyvesant Square.\nIt is hoped that Correspondence\nFiles, winners of last year\u2019s championship, will be ars in the January series.\n\nBripcE\n\nseason.\n\n|\n\nThe very latest\nare being designed and\ncreated by the\ngirls of the Laboratories under\n\nErvin\n\nE. Hence\n\nfor Club members and a swimming\nand diving exhibition by the Volunteer Life Saving Corps of America.\n\nthe skillful\nguidance of Mlle. Bowman.\nWe\nare told the designs include simple\n\nAlthough the contests are for the girls\n\nfrocks for office wear,\n\nparty frocks,\n\nand\n\nfor the more\n\nonly, members and their guests are\nwelcome. No entry fee nor admission\ncharge.\n\nAll members, and especially those\nwho asked tor the meet, are urged to\n\nevening gowns\n\nformal occasion.\nstudio classes are\n\nMlle. Bowman's\nin session every\n\nThursday evening and\n$4.00 for eight lessons.\n\n|\n\n|\n\n{ 224}\n\nthe fee 1s", "title": "Bell Laboratories Record 1926-01: Vol 1 Iss 5", "trim_reasons": ["leading_ocr_noise"], "year": 1926} {"archive_ref": "sim_record-at-t-bell-laboratories_1927-02_3_6", "canonical_url": "https://archive.org/details/sim_record-at-t-bell-laboratories_1927-02_3_6", "char_count": 73873, "collection": "archive-org-bell-labs", "doc_id": 127, "document_type": "journal_issue", "id": "bella-qwen-pretrain-doc127", "record_count": 95, "release_policy_version": "hf_public_v1", "rights_status": "public_domain", "selected_extraction_backend": null, "selected_extraction_score": null, "source_family": "archive_org", "source_url": "https://archive.org/details/sim_record-at-t-bell-laboratories_1927-02_3_6", "split": "validation", "text": "E are accustomed to the \nidea that in an electrical \nconductor there are elec-\n\ntrons or ions in a state of random \nmotion which has partly to do with \nthe temperature of the conductor. \nWe have had less occasion to consider \nthat this motion may result in a spon- \ntaneous fluctuation of potential be- \ntween points in the conductor. This \nthermal agitation, this motion of elec- \ntric charges, this potential fluctuation, \ndoes exist and can be measured under \nsuitable conditions.\n\nThe effect is most readily detected \nin a conductor having high electrical \nresistance. It is characterized by a \ncontinually changing or fluctuating \nvoltage generated by the resistance \nitself, unconnected to any other \nsources of potential. An alternating \ncurrent instrument is therefore re- \nquired to measure the effect, an in- \nstrument which reads the root-mean- \nsquare or effective voltage.\n\nIf an ordinary voltmeter is con- \nnected to a resistance as shown in Fig. \n1, of course, nothing happens. The \neffect is far too feeble to be thus de- \ntected. A vacuum-tube amplifier ca-\n\npable of multiplying the voltage by \nabout one million must be inserted, \nbetween the resistance and the meter, \nas shown in Fig. 2. The amplifier and \nthe meter, which may be formed by \nthe combination of a thermo-couple \nand galvanometer, then constitute a \nsensitive voltmeter which can be used \nfor accurate measurements.\n\nWith such a system measurements \nhave been made on resistances com- \nposed of a wide range of materials, \nincluding advance wire, carbon fila- \nment, metallic films, and various elec- \ntrolytes. In all cases a mean-square- \nvoltage, proportional to the resist- \nance, was observed. In all the mate- \nrials the ratio of this mean-square \nvoltage to the value of the resistance \nwas the same and was independent \nof the shape or dimensions of the re- \nsistance.\n\nThis voltage effect might be caused \nby the thermal agitation of the elec- \ntrical constituents of the material or \nit might arise from some property of \nthe amplifier whereby its own noise \nis increased when resistance is con- \nnected to its input. In order to settle \nthis point a measurement was made\n\non the resistance at liquid-air temper- \nature, and the ratio of mean-square \nvoltage to resistance was found to be \nless than that at room temperature \nin the proportion of the absolute tem- \nperatures. This relation held accu- \nrately in the case of advance-wire re- \nsistances over, the temperature range \nfrom liquid oxygen to boiling water.\n\nThe same satisfactory agreement was \nobtained with other resistances, in- \ncluding electrolytes. There can there- \nfore be no question about the fluctua- \ntion originating in the resistance and \nnot in the amplifier.\n\nWhen a different amplifier is used \na different value is obtained for the \nratio of mean-square voltage to re- \nsistance. For the purpose of deter- \nmining the value of this ratio the fre- \nquency characteristic only of the am- \nplifier must be known. This means its \namplification squared must have been \nmeasured at a sufficient number of fre- \nquencies to plot a complete character- \nistic curve. The mean-square output- \ncurrent, induced in the thermocouple \nof Figure 2 by the voltage fluctuations \nin the input resistance, is then propor- \ntional to the area under the frequen- \ncy characteristic. Since there is pro- \nportionality also to the resistance and \nthe absolute temperature, the empir- \nically derived expression for the \nmean-square output-current is propor-\n\ntional to the product of these factors. \nThe introduction of a fourth factor \n\u2014a numerical multiplier which turns \nout to be closely connected with Boltz- \nmann\u2019s gas constant and with the en- \nergy of a gas molecule at a given tem- \nperature\u2014completes the expression. \nA knowledge, therefore, of the resist- \nance in the input and of the frequency \ncharacteristic of the amplifier is all \nthat is necessary for predicting, in any \nparticular case, how much current will \nbe induced in the output branch by \nthe resistance in the input of an am- \nplifier.\n\nThis thermal agitation of elec- \ntricity in a conductor has certain very \npractical aspects. When a telephone \nis connected to the output of a sensi- \ntive amplifier a characteristic sound \nmay be heard\u2014the \u201c\u2018sh-sh-sh\u2019\u2019, com- \nmonly called \u2018\u2018tube noise\u2019. At least \na part of this is the spontaneous noise \narising from the input resistance \nitself. In fact, if the input resistance \nis high and the tubes are of the best, \nthe noise due to thermal agitation in \nthe resistance is so large as entirely\n\nto mask the noise contributed by the \ntubes. To the smallness of the volt- \nage which can be successfully ampli- \nfied, there is then set a limit by the \nvery nature of the substance of which \nelectrical circuits are built.\n\nIn order to give the exact magni- \ntude of the effect both the resistance \nand the amplifier would have to be\n\nspecified in the terms described above. \nApproximate figures may be given, \nhowever, for a usual type of circuit, \nwith which comparisons can then be \nmade. Such a circuit is an amplifier \nwhich covers the voice-frequency \nrange, to the input of which a resist- \nance of one-half megohm is connect- \ned. There then appears to exist across \nthe resistance a root-mean-square \nvoltage of the order of a few micro- \nvolts. This is equivalent to a \u201cpower \nlevel\u201d of about \u2014140 T. U., and \nthis power level is independent of \nthe resistance. The smallest power \nwhich can be usefully amplified by \nthis system depends upon the amount \nof distortion and superimposed noise \nwhich can be tolerated, but it cannot \nbe much less than the power of the \nnoise itself. It is possible, of course,\n\nto handle smaller powers in propor- \ntion as the frequency range of the \namplifier can be made narrower; that \nis, to have a smaller area under its \nfrequency characteristic.\n\nReturning to the physical facts in- \nvolved, these can now be summarized: \nEvery resistance is a source of ran- \ndom voltage fluctuations, the effects \nof which can be heard or measured \nwith suitable amplifying apparatus. \nExperiments at different temperatures \nprove conclusively that in an ampli- \nfier a component of \u2018\u2018noise\u201d comes \nfrom the resistance in addition to that \nfrom the vacuum tube or other ele- \nments. The discovery of this phe- \nnomenon, in our laboratories, there- \nfore, is not only of scientific interest \nbut finds an application in the prac- \ntical problems with which we deal.\n\nAU CLAIRE STEVE! JOINT \nORTSMOUTH \n? PBUFFALO \\ ALBAN? WORGE BOSTON \n70 L WEST UNITY EVEL HD \nOT TA: BOGART eRISTOWN 3 \n| CHESTERTON | \u00bb IEW CASTLE \n| CUYRHOGA FALLS A \nSPEORIA YWATSEKA | i ALTO iN \nTERRE HAUTE /\n\nG\u00a2 ISTEN to the band, marching \nup the street,\u2019 as a song of \nthe Gay Nineties advised: a \ncurious effect is noticeable. As the \nband approaches and its music grows \nlouder the bass notes come out most \nstrongly. The same band, the same \nmusic, but there is a different empha- \nsis to the notes when the band is near \nand the music loud than there is when \nit sounds faintly from far away. The \nexplanation of this and other anoma- \nlies of hearing is to be found in some \nrecent measurements of loudness \nwhich have been conducted in our \nLaboratories.\n\nLoudness is a psychological phe- \nnomenon depending upon the struc- \nture and action of the human ear. \nPhysically, behind the impression \nwhich a listener receives is the alter- \nnating pressure of the train of sound \nwaves upon the ear drum. Loudness \ndoes not inhere in the sound waves; \nthey transmit energy and exert on the \near drum an effective or so-called \n\u201croot-mean-square\u201d pressure which \nthe physicist measures in units of \nforce (dynes) per square centimeter \nof area affected.\n\nHow does loudness, which is a sen- \nsation, correspond to effective pres- \nsure, which is the physical character- \nistic of a compressional wave in air? \nAt first thought it might appear that \nthe two should be directly propor- \ntional, that is, have a linear relation \nbetween them. Not so readily would \none expect that there would be a\n\nlinear relationship between loudness \nand pitch, since the receptive fibres of \nthe basilar membrane are not equally \ndistributed with reference to pitch, as \nthe \u201c\u2018piano model\u201d of the ear so plain- \nly illustrates. Having two notes of \ndifferent pitches, that is different fre- \nquencies, and of equal effective pres- \nsures will they produce similar sen- \nsations of loudness? Or, in other \nwords, having two notes of different \nfrequencies both equally loud, will \ntheir effective pressures be the same?\n\nThe experiments answer that, in \ngeneral, they will not be; and more \nthan that, the difference of effective \npressure between notes of two pitches, \nwhich seem equally loud, is not a con- \nstant difference but depends upon the \npressure. These somewhat compli- \ncated and unexpected relationships \nare illustrated in the accompanying \ngraphs which give the results of com- \nparisons of the sensation of loudness \nfor various pure tones, differing in \npressure and frequency.\n\nThe observers listened to pure mu- \nsical notes from a telephone receiver \ndriven by current from a vacuum-tube \noscillator. The listeners compared \ndifferent notes, two at a time, as to \nthe sensation of loudness and by ad- \njustment of the current brought them \nto perceptibly equal loudness. The \nvalue of current corresponding to any \nnote, and hence the pressure exerted \nby its sound wave, was known from \nthe setting of the current control.\n\nment of apparatus for the tests. The \nobservers listened alternately to notes \non circuits A and B. That on circuit \nA was kept constant at a pitch about \n\u2018an octave and a half above Middle C. \nIts intensity was set to some value \nunknown to the listener who was par- \nticipating in the test. This was con- \nveniently done by turning the dial of \nthe attenuator marked \u2018\u201c\u2018A\u2019\u2019. The note \nof circuit B was then set to some \nother pitch; and the listener varied its \nintensity by turning attenuator B un- \ntil it seemed just as loud as that of \nthe comparison note of circuit A. To \nmake sure that his settings, which \nwere repeated several times, were un- \ninfluenced except by the sensation of \nloudness, the attenuator dial B was \nhidden by a loosely fitting screen\n\nThe comparison note of \u201cA\u201d was \nsuccessively set at nine different inten- \nsities; and a family of notes of other \npitches, but of equal loudness, deter- \nmined for each listener. There were \nas listeners eleven men and an equal \nnumber of women. The average de- \nterminations of each listener were \nthen averaged to obtain the curves of \nFigure 2.\n\nAll the points on one of these \ncurves represent in terms of the root- \nmean-square pressure the physical \nstimuli, corresponding to the indicated \npitches, which acting on the human \near will give sensations of equal loud- \nness. This follows from the assump- \ntion that the old axiom of \u201cthings \nequal to the same thing are equal to\n\nFig. 1\\\u2014The attenuators which vary the intensity of tone in the receiver. With the \nswitch in left-hand position, \u201cA\u201d tone is heard; in right-hand, \u201cB\u2019 tone is heard\n\neach other\u201d applies to the sensation \nof hearing. Each of the various notes \nrepresented by a curve sounded just \nas loud as the comparison note, and \nhence was assumed to be equally loud. \nAs a check of the application of the \naxiom in this particular case, one of\n\nnot at all equally sensitive to all notes. \nAt the highest level of loudness which \nwas studied, however, there is ap- \nproximately equal sensitivity over the \nentire frequency range.\n\nFig. 2\u2014Points on one of these curves represent, for the indicated frequencies, the \nphysical stimuli which, acting on the ear drum, give sensations of equal loudness\n\nthe lower tones was directly compared \nwith one of the higher tones. The re- \nsult was found to agree with the de- \ntermination previously made by com- \nparing these same tones through the \nmedium of the \u201cA\u201d test-tone.\n\nThe curves now show why the band \nsounds as it does. The loudness of \nthe low-pitch tones increases more \nrapidly than does that of the high- \npitch tones, for equal increments in \npressure ratios. That is, suppose au- \nral observation to start with wave \npressures only just sufficient to give \naudibility. As hearing begins the ear is\n\nloud speakers when the volume is in- \ncreased. Even though the intensities \nof all the pitch components of the \nmusic are amplified nearly equally, a \nrelatively increased effect on the ear \nthen comes from the bass portion of \nthe music. The remedy for the con- \ndition is the reduction of the volume \nuntil the music, as a whole, is of about \nthe volume to which the listener is \naccustomed for music of its type. \nThen the various components do not \ngive rise to unusual relative sensations \nof loudness and hence to an apparent \ndistortion.\n\nHE single-tube radio re- \nceiver, popular five years ago, \ndemanded but a modest bat- \ntery equipment to supply its filament \nand plate circuits. As the art devel- \noped, receiving sets became more \ncomplex; reliable operation on weaker \nradio field-strengths and ample vol- \nume on loud speakers became essen- \ntial. The number of tubes increased, \nand with it the need not only for more \npower, but for higher plate-circuit \nvoltages. While the need can be met, \nas originally, by batteries, they re- \nquire a certain amount of attention in \nthe way of inspection, replacement \nand recharging. Of this responsibil- \nity most radio listeners would gladly \nbe relieved, even at some additional \nfirst cost and operating expense. In \neffect, they ask for a power supply \nwhich needs no attention other than \nto turn the set on and off. As a re- \nsult, there have appeared many dif- \nferent forms of \u201cbattery eliminators\u201d\u2019 \nintended to supply suitable power by \nconversion from the commercial sup- \nply of 110-volt 60-cycle alternating \ncurrent.\n\nIn some cases this \u201cconversion\u201d is \nthe simple one of voltage-reduction \nthrough a transformer. More often \nit requires conversion of alternating \ncurrent into direct, by means of a rec- \ntifying element which will pass cur- \nrent in one direction only. The \nvacuum-tube is itself a rectifying ele- \nment; through it current can flow only \nwhen the plate is positive to the fila-\n\nment. When three-element tubes are \nused, as for example the 205-D in \nthe 25-B amplifier, the grid plays no \npart in controlling electron-flow and \nit is strapped to the plate. No grid is \nprovided in rectifier tubes, such as the \n217-A. The rectified output of a tube \nis limited as to current by permissible \nheating and by filament-life. It is \nlimited as to voltage by the potential- \ndifference which the tube will block \nwhen its plate is negative to its fila- \nment.\n\nAnother type of rectifying element \ninvolves an electrolytic cell, in which \none electrode is of an inert material, \nfrequently lead, and the other is alu- \nminum or tantalum. Both of the lat- \nter metals have the property of form- \ning a film of oxide on their surfaces \nwhich blocks current-flow from elec- \ntrode to electrolyte, but allows cur- \nrent to flow in the opposite direction. \nWith the aluminum electrode, a so- \nlution of borax is commonly used; \nwith the tantalum electrode, a dilute \nsolution of sulphuric acid. The cur- \nrent through either type of cell is \nlimited by heating, which decreases \nthe life of the active electrode, and \nby excessive loss of water due to elec- \ntrolysis.\n\nAnother limitation to the useful- \nness of the electrolytic rectifier is the \nlow value of reverse-voltage which it \ncan be depended on to block. This is \nof the order of forty volts for the \naluminum type and sixty-five for the \ntantalum type. For higher voltages,\n\nit is necessary to use an appropriate \nnumber of cells in series. When out- \nput voltages up to 135 are desired \nthis is not a serious factor. Much \nhigher voltages are required for the \npower tubes now coming into use; and \nfor this service the number of elec- \ntrolytic cells becomes excessive. On \nthe other hand, a single vacuum tube \nmay be selected from available types \nfor use in rectifier circuits delivering \nas high as 10,000 volts. As a prac- \ntical example in the field of radio re- \nception were an aluminum rectifier to \nbe used in place of the single 205-D \nrectifier tube in the 25-B amplifier, as \nmany as twenty cells in series might\n\nbe required to supply sufficient voltage. \nHow a rectifier operates is illus- \ntrated by Fig. 1, which shows a cir- \ncuit commonly as \u201c\u2018half- \nwave\u201d since only one half of each \ncycle produces current-flow. In cir- \ncuits of this type the heating effect of \nthe current through the rectifier is \nequivalent to that of a steady current \ntwice as great as that which is deliy- \nered to the load. The peak voltage \nacross the tube during the non-con- \nducting half-cycle is equal to the peak \nvalue of the alternating e.m.f. plus \nthe voltage of the first filter-con- \ndenser; the total will approach at \nlight loads twice the peak voltage. \nAn alternating com- \nponent in the rectified \ncurrent is quite objec-\n\nmay be greatly reduced \nby inserting one sec- \ntion of a simple low- \npass filter as shown in \nFig. 1. The propor-\n\n7 tion of alternating cur- \nAPPLIED rent which remains in \nVATACE the output of the filter\n\nCONDENSER C, \nAPPLIED the filter constants, but \n\\ 4.0. VOLTAGE \n: its effect on the opera- \nj tion of the amplifier \nVS can be determined ex-\n\nactly only by expe- \nrience or trial. Any \ndegree of filtering can \nbe obtained by using\n\nmore capacity, more \ninductance, or both; \nand by using more than \none section of fil-\n\nFig. 1\u2014A \u201chalf wave\u201d rectifier; (a) its circuit; (b, c, d, e) \nwave-forms of current and voltage\n\nminimum when that capacity is equal- \nly divided between C, and C,. On the \nother hand, the larger is C,, the lower \nis the output impedance of the recti- \nfier circuit, and the less likely is \u201c\u2018sing- \ning\u201d when several stages of an ampli- \nfier are fed in parallel from a single \nrectifier.\n\nCondenser C, may be omitted from \nthe filter; this has the effect of mak- \ning the wave-form of the rectifier \ncurrent much less peaked. In turn \nthis reduces the heating of the recti- \nfier element for the same quantity of \nelectricity through it,* but the impe- \ndance of the filter is increased, so \nthat a higher alternating voltage \nmust be impressed. In the case of a \nvacuum tube the decrease in heating \nmay more than compensate for the \nincrease in reverse voltage to be \nblocked, but no advantage is secured\n\nwhen electrolytic cells are used be- \ncause the increase in voltage will re- \nquire a proportionate increase in the \nnumber of cells.\n\nIn the so-called \u2018\u201c\u2018full-wave\u201d\u2019 recti- \nfier both halves of the alternating \ncurrent cycle are used, with advan- \ntages in both efficiency and lower \nnoise-level. The most common type \nof circuit is shown in Fig. 3; it em-\n\n_ * Total current per cycle is the integral of the \ninstantaneous current; heating is proportional\n\nploys a transformer with a mid-tap \non the secondary winding, and two \nrectifying elements. To deliver the \nsame voltage to the load this circuit \nrequires twice as many turns on the \ntransformer secondary as in the cir- \ncuit of Fig. 1 (a) but the current is \ndivided between the two rectifying \nelements and their associated trans-\n\nformer-windings. Hence this circuit \nis adapted to use with vacuum tubes \nwhere current-flow is a limiting fac- \ntor. While the load can be equally \nbalanced with tube and tantalum rec- \ntifiers, it is difficult to do this if alu- \nminum cells are used. This difficulty \nis avoided if the circuit of Fig. 4 is \nused. No transformer mid-tap, and \nonly half as many secondary turns, \nare needed. At least four rectifying \nelements are used, instead of two, but \nsince two elements are always in se- \nries to oppose the reverse voltage, the \ncircuit has an advantage when the \nbreakdown voltage of the rectifying \nelements is a consideration. Where \nfour elements would be required in \nthe circuit of Fig. 3, they could be \nrearranged according to Fig. 4 with a \ntransformer of half the secondary \nvoltage to give the same output volt- \nage.\n\nFull-wave rectification with two \nelements may be effected by the cir- \ncuit of Fig. 5. With a transformer \nsecondary equal to that of Fig. 1 (a),\n\napproximately twice the output volt- \nage is secured at no-load; each con- \ndenser in Fig. 5 is charged in turn to \nthe voltage of C, in Fig. 1 (a) and \nboth in series discharge through the \nload; each carries full load-current.\n\ncy of the alternating component in \nthe output is doubled, and to atten- \nuate it an equal degree requires a \nfilter of higher cut-off and therefore \nsmaller and less expensive. On the \nother hand the ear is much more sen- \nsitive to the 120-cycle tone resulting \nfrom full-wave rectification than to \nthe 6o0-cycle tone of half-wave recti- \ncation, so that the noise level is about \nthe same in the two cases. Where a \nradio receiving system is quite in- \nsensitive to these low-frequencies, no \naudible hum may be heard at all in \nthe loud speaker, yet there may be a \nlarge ripple present in the supply \nwhich under some conditions will be \nsufficient to modulate the received \nspeech or music. This condition may \nmake itself known by bad quality \nor a peculiar fuzziness in the pro- \ngram which is being received.\n\ntion, the rectifier is at a considerable \ndisadvantage as compared to the dry- \ncell battery, since its internal resist- \nance is so high that changes in load \nproduce large changes in output volt- \nage. For example, one commercial \nrectifier shows a 15 percent drop in \nvoltage when the output current is \nincreased from five to twenty-five \nmilliamperes and another under simi- \nlar circumstances gives a drop of 55 \npercent. Dry cells, on the contrary, \nhave sufficiently low internal resist- \nance, especially when new, that their \noutput voltage will change but little \nover the range of loads ordinarily \nimposed on them.\n\nElectric power for heating the fila- \nments of vacuum tubes is supplied un- \nder conditions quite different from \nthose attending its use in plate cir- \ncuits. Impedance of filament circuits \nis relatively low: currents are rela- \ntively large and voltages small. Un- \nder these circumstances disadvantages \nof storage batteries are much less \nmarked. Since most radio outfits have \nbeen designed for this source of fila- \nment power there is a decided appeal\n\nin a device which combines with a \nsmall battery a rectifier whose cur- \nrent can be allowed to flow through \nthe battery continuously when the\n\nradio set is not in use. A battery op- \nerated in this manner requires little \nattention other than the addition of \nwater at intervals; it has long life and \ngives good service.\n\nSeveral \u2018trickle\u2019 chargers employ \nrectifiers of the contact type. One of \nthese consists of a disc of oxidized \ncopper held in contact under pressure \nwith lead or other soft metal. The \ncuprous oxide film has a low resist- \nance to voltage in one direction and a \nhigh resistance in the other direction, \nthus fulfilling the requirements for a \nrectifier. The ordinary crystal detec- \ntor is a rectifier of this general type.\n\nA rectifier widely employed in bat- \ntery chargers and capable of passing \nseveral amperes is of the hot cathode \ntype, but the tube, instead of a \nvacuum, contains an inert gas which is\n\nSTEP-DOWN \nTRANSFORM \u201cRECTIFIER \nSTORAGE-= \nBA \nO-A \nON o AUXILIARY \nSOCKET FOR \n\u2018B\u2019 BATTERY \nELIMINATOR \nOF F \nDPDI \nSW/TCH \nVOLT \n60~\n\nionized by the electrons emitted from \nthe hot filament. When the anode, \nwhich is usually a piece of graphite, \nis positive, electrons are drawn from \nthe filament; these ionize the gas \nmolecules by collision, so making them \nconductive in the direction of anode \nto cathode. During the half-cycle \nwhen the anode is negative any elec-\n\ntrons emitted from the filament are \nrepelled and the gas in the tube is not \nconductive during that period. The \ninternal resistance of a tube of this \ntype is much lower than that of a \nvacuum tube and larger currents can \nbe rectified, but on the other hand the \nreverse voltage which can be blocked \nis lower.\n\nFig. 7\u2014Low-pass filter for filament circuits \ncurrent is of the order of two am- \nperes, as against a few milliamperes \nin plate-current supply. This necessi- \ntates a costly and unwieldy choke coil \nin the filter. Since the impedance of \nthe load is low, quite large values of \ncapacity become necessary. Condens- \ners may be replaced by resistances as \nshown in Fig. 7, but at a sacrifice of \nefficiency. The filter problem is con- \nsiderably simplified by using so-called \n\u2018\u201c60-mil\u201d tubes with filaments in se- \nries with the plate circuit of the last \naudio-frequency stage. This raises \nthe load impedance to a value which \ngives satisfactory filtering, and re- \nquires no more current than can be \nhandled by a choke-coil of moderate \nsize. In the typical circuit shown in \nFig. 8, the plate and grid voltages of \nthe 205-D tubes are such as to allow \na current of thirty milliamperes \nthrough each of these tubes, giving\n\nsixty milliamperes through the fila- \nments of the three tubes in preceding \nstages.\n\nFor the filaments of tubes in cer- \ntain stages, sixty-cycle alternating cur- \nrent may be employed. This is par- \nticularly true of the last audio stage\n\nin which the filaments usually require \nmore power than do the other tubes \nof the receiver, and where any alter- \nnating current hum will not be ampli- \nfied by succeeding stages. In the 25-B \namplifier, suitable voltage for this \npurpose is given by one of the sec- \nondary windings of the 60-cycle power \ntransformer. To the midpoint of this \nwinding are connected the grid and \nplate circuits. This balances out to a \nconsiderable degree the effect on the \ngrid and plate circuits of the alternat- \ning voltage across the filament. The \nsame end may be achieved by con- \nnecting a potentiometer of equal re- \nsistance across the filament leads. \nWhen necessary, a better balance \ncan be secured with a variable poten- \ntiometer adjusted for minimum noise.\n\nAudio-amplifier tubes of other than \nthe last stages may also be lighted by \nalternating current, but naturally \nnoise introduced in these tubes will be \namplified by succeeding stages and \nmay become objectionable. These \nnoises may be minimized by using \ntubes with low-voltage filaments, such \nas the 215-A, and carefully adjusted \npotentiometers. Radio-frequency am- \nplifier tubes may be lighted by alter- \nnating current. If the detector tube \nis lighted by alternating current a com- \nplicated and carefully adjusted circuit \nis required, else noise will be excessive.\n\nBoth plate and filament circuits re- \nquire a supply of power; the grid cir- \ncuit, however, requires only a voltage \nof proper value. Since no current \nflows, and no work is done, it is cus- \ntomary to use small dry-cells. Elimi- \nnation of these batteries, desirable for \nmaintenance reasons, may be effected \nby using in their place the fall-of- \npotential across a resistance in which \ndirect current is flowing. This cur- \nrent may be that required to light \nsingle filaments, as in Fig. 9; or to \nlight filaments in series as in Fig. 8. \nIn the latter circuit a potential of 9\n\nFig. 9\u2014How a grid bias can be supplied \nby potential drop in a filament circuit\n\nvolts, negative with respect to the \npower amplifier filament, is available \nat \u2018-B\u2019\u201d. Where series filaments are \nnot used, their place may be taken \nby resistance, as is done in the 25-B \namplifier. It should be remembered,\n\nhowever, that potential thus obtained \nfor grid bias is deducted from that \navailable for the plate circuit of the \nlast tube; and that a certain amount \nof power is lost in the resistance. \nThis method is coming into use be- \ncause it eliminates an element whose \nreplacement is annoying and often \nforgotten, and because for large val- \nues of grid-potential as required by \nthe 25-B amplifier, a resistance takes \nup much less space than would the \nequivalent number of dry-cells.\n\nAny consideration of the relative \ncosts of supplying power to a radio \nset by various methods involves the \ncorrelation of data as to the load, the \nnumber of hours\u2019 use per day, cost \nand life of different kinds of batteries, \ncost of electric power, and efficiency \nof each piece of apparatus through \nwhich that power must pass. All of \nthese quantities vary over so wide a\n\nrange that data of practical value \nwould be too bulky for this article. \nThe \u201cpractical value\u2019, even, of data \nis doubtful since the annual charge is \nprobably one of the least important \nfactors in the selection of power- \nsources for radio reception. Far \ngreater weight is given to such points \nas low first-cost, ease of maintenance \nby unskilled hands, warning of im- \npending failure, and adaptability to \nsets of different types. The annual \ncharge for power is practically the \nonly operating expense in connection \nwith a radio set; compared with the \npleasure of radio reception this ex- \npense is so moderate that it is gener- \nally ignored. After all, what the \nuser buys is satisfactory reception of \nradio programs. Given this, at a \nprice within his means, and a differ- \nence of a few dollars is counted of \nlittle importance.\n\nHard-grained scientists seldom make predictions as to develop- \nments likely to occur in their particular field of experiment \nand research. At least such has been the rule among responsible \nsavants. . . . During the past three weeks, however, three venerable \nscientists and inventors have voiced predictions which occasioned \nno end of excitement. . . . Predictions are romantic and \u2018 \nfurnish . . . interesting copy for newspapers . . . Unfortunately \neven scientists do not qualify to visualize scientific achievement as \nyet unaccomplished. \nThe policy of the Western Electric Laboratories furnishes an \nexcellent case in point. Here are employed a great number of \nthe shrewdest engineers in the world. It is the method of these \nlaboratories to successfully perfect new inventions, try them out \nsecretly over a long period of time, and when they are classed as \npositive and fool-proof, announce them to the public. In other \nwords they accomplish first and predict afterward. Such practice \nmay lack the romance attached to the perfection of a publicly \npredicted device, but in the long run it is the best method for the \ngood of the general public.\n\nN December 15, 1926, the \n() long distance cable between \nChicago and St. Louis was \nformally opened with ceremonies ap- \npropriate to the most western strand \nof a cable network which, paralleling \nthe Atlantic from Portland to Wash- \nington, stretches inland to join most \nof the principal cities in the industrial \narea of the United States.\n\nThe new cable* is 344 miles long, \nprovides more than 250 telephone \nand telegraph circuits and represents, \nwith its associated apparatus, an out- \nlay of about $7,000,000. While this \nproject will supply circuit facilities \nequivalent to ten open-wire pole-lines,\n\nit was undertaken at this time to give \nincreased protection against storm \ndamage. Wires grouped into cable, \nwhich is in turn suspended from steel \nstrand, offer less surface to wind and \nsleet and more resistance to loads im- \nposed by both. Safe inside a leaden \nsheath, their paper covering main- \ntains its insulation through good \nweather and bad. But the sheath \nmust be continuous, else rain and \nmelting ice will find their way inside, \nwet the paper and quickly put the \ncable out of service. Evaluation of \nthe ability of cable-sheathing to main- \ntain its integrity is a subject of contin- \nuous study in these Laboratories. \nAs a material for cable sheath, lead \nand certain of its al- \nloys are almost ideal. \nThey are easily ap- \nplied to the cable core; \nthey have sufficient \nflexibility to allow the \ncompleted cable to be \nreeled, unreeled and \nbent into place; they \nare strong enough to \nprotect the cores, im- \npervious to moisture, \nand highly resistant to \ncorrosion. Consider \nnow the other side of \nthe picture; thousands \nof miles of cable, aloft\n\nMachine for vibrating short lengths of cable. Cracking of ste ae ee ae \nany sheath admits air to a partial vacuum in the samples; t at- \nmercury manometer then closes its contact and indicates that \u2018 to the jar of pass-\n\nand shrinking as the sun warms them \nor the frost chills. Here are forces \ntending to open cracks in the lead \nsheath through which moisture may \nenter. For example, the rate of ex- \npansion with change of temperature \nis 60 per cent greater for cable than \nfor its supporting strand. In a hun-\n\nyield or plastic flow of the metal but \na definite separation of the crystal \ngrains.\n\nEarly sheaths of commercially pure \nlead were not sufficiently resistant to \nfatigue or to corrosion to give com- \nplete satisfaction. A lead alloy con- \ntaining 3 per cent tin was substituted,\n\nFatigue-tester with a capacity of fifty-six specimens of sheath material\n\ndred-foot span an unstressed cable, \njust the length of the strand at sixty \ndegrees Fahrenheit, at 120 degrees \nwould be a half-inch longer than the \nstrand. This extra length is taken \ncare of, in part, by actual compres- \nsion of the cable. But the cable also \nlengthens and shortens in relation to \nthe strand, and so moves into and out \nof a \u201cbow\u201d at each pole because there \nthe cable is already bent. These slight \nbut repeated bendings and straighten- \nings with vibration due to wind and \nroad traffic, combine in tending to \u201c\u2018fa- \ntigue\u201d the lead sheath. Under severe \nconditions it may eventually crack \nopen, with disastrous results, certain- \nly when the next rain falls. Lead al- \nloys differ from ferrous metals in fa- \ntigue failure in that the fracture \nalways passes between the crystal \ngrains. Under stresses producing this \ntype of failure, lead alloys show no\n\nsince it had greater resistance to se- \nvere service stresses than had lead \nalone. Later due to economic condi- \ntions an alloy containing 1 per cent \nantimony was used in place of the \nlead-tin alloy. This material could \nbe used because of its still greater re- \nsistance to fatigue and because it was \nsatisfactory in all other respects. Each \nof these changes in composition of \nsheath was made only after exhaus- \ntive laboratory tests in which samples \nwere exposed to vibrations and to \nbending under measurable conditions.\n\nFor these tests two different ma- \nchines were developed to take sam- \nples of actual cable. In one machine \nshort specimens are clamped at one \nend while their other ends are set \ninto rapid vibration by motor-driven \ncams, In the other a bending test is \ngiven to U-shaped pieces of cable sev- \neral feet long, by vibrating the free\n\nends toward the clamped ends. These \ntwo types of machines are used in \nevaluating the ability of proposed \nsheath materials to withstand service \nconditions. They were seen to be\n\nbulky and require considerable test \nmaterial, so it was thought advisable \nto develop a test based on a simpler \nform of specimen. Careful studies of \nreported field conditions and com- \nparative analysis of a large amount \nof data have shown that the extreme \nservice conditions causing failures \nmay be simulated by stressing at a \nreasonably rapid rate a small speci- \nmen of lead sheath.\n\nThis specimen was designed so that \nthe maximum stress will not occur at \nthe clamped portion, thus eliminating \nthe unknown effect of stress due to \nclamping. One end of the specimen \nis clamped, the other end is inserted \nin a phosphor-bronze boot which is \nheld against a cam by a helical spring.\n\nThe machine has a capacity of fifty- \nsix specimens. It can produce a break \nin a specimen of standard sheath ma- \nterial in three days whereas it may \ntake the bending-machine six weeks \nto cause a break in a specimen cable. \nThe high speed and large capacity of \nthis machine permits the testing of \n150 to 200 times as many specimens \nas the bending machine.\n\nAll of the characteristics of fatigue \nfailure are exhibited in specimens \ntested on this machine. All proposed \nalloys and modified sheaths are inves- \ntigated also by testing sample lengths \nof cable in the vibrating and bending \nmachines. Decisions are based on con- \ncurrent results only. As a further pre- \ncaution it is customary to make trial\n\ninstallations of cable under actual \nservice conditions. Such searching in- \nvestigation is necessary in view of the \nimportance of cables in our communi- \ncation system and the investment in \ntheir manufacture and installation. \nIn addition to meeting the require- \nments for aerial use, all cable must be \nable to withstand the mechanical \nstrain of pulling into conduits, since \nit is most economical to employ \nthe. same type of cable for both \nunderground and aerial service.\n\nESEARCH problems some- \ntimes require the measure- \nment of small displacements.\n\nFor those approaching the order of \none part in 100,000, simple and di- \nrect methods of measurement can no \nlonger be applied and recourse must \nbe had to various artifices. In a prob- \nlem bearing on the physical nature of \npermalloy it was desired, in detecting \nchanges of length, to extend the lower \nlimit of measurement to a few parts \nin 1,000,000,000. The actual accom- \nplishment, measuring to four parts in \na billion, resulted from the develop- \nment of a new method of measuring \nincrements of length which is more \nsensitive and more accurate than any \nused heretofore.\n\nSince 1847 it has been known that \nmagnetic substances change their di- \nmensions with magnetization. This \nphenomenon, called magnestostric- \ntion, was also early recognized as \nhighly significant in explaining certain \nferromagnetic phenomena. On the \nother hand within our Laboratories \nexperiments on the effect of tension\n\nrods had confirmed the existence of a \ncritical composition of nickel-iron al- \nloy which has no magnetostriction. \nThis led L. W. McKeehan to formu- \nlate his atomic theory of magneto- \nstriction which relates the properties \nof permalloy to its magnetostrictive \nbehavior.*\n\nTo test the theory there were re- \nquired measurements of magnetostric- \ntion, at low magnetizations, in iron, \nnickel and permalloy. Relatively \nlarge magnetostrictive effects repre- \nsent only exceedingly small changes \nin length. To be able, therefore, to \ndetect such effects in the case of \npermalloys where it is very much\n\nsmaller there is required a method of \ndetermining, in a centimeter of length, \na change of the order of one-tenth of \nthe diameter of an atom.\n\nmeasurements there was the photo- \nelectric cell. \u2018This cell connected to a \nsensitive galvanometer forms an ex- \nceedingly accurate and sensitive in- \nstrument for measuring\u2019 changes in \nlight intensity. The method first pro- \nposed, therefore, was to direct light \nby a concave mirror from an illumi- \nnated slit onto an unilluminated slit \nin such a way that the quantity of \nlight transmitted through the latter\n\nslit would be proportional to the \nangle of tilt of the mirror. If the \nmirror was tilted by a change in length \nof the specimen under examination \nthen the change could be sensitively \nmeasured.\n\nThat the sensitivity could be much \nincreased if the single slits were re- \nplaced by screens with parallel stripes \nof equal width, alternately transpar- \nent and opaque, was pointed out by \nE. C. Wente.\n\nThis idea was embodied in the sys- \ntem finally employed. Light from a \nlamp was directed by a lens onto a \nconcave mirror. Between the light \nsource and the mirror was interposed \na glass screen, with opaque and trans- \nparent stripes half a millimeter wide. \nThe mirror acted to form an image \nof the series of slits in the screen. It \nwas set so as to form this image on \na continuation of the screen, which \nprojected beyond the original beam \nof light and received illumination \nonly from the reflected beam. When \nthe bright images of the slits coin- \ncided with the opaque stripes of the \nscreen no light was transmitted. As \nthe mirror was tilted, transmission \nbecame possible and the amount of \nlight increased to a maximum and \nthen decreased to zero when coinci- \ndence with the opaque stripes again \noccurred. It required but a small tilt \nof the mirror to pass from full trans- \nmission to complete extinction. The \ntransmitted light was collected by an- \nother lens onto a photo-electric cell. \nThe changes in photo-electric emis- \nsion, as affected by the changes in the \nlight intensity, were then read on a \ngalvanometer.\n\nThe magnetostriction which was \nmeasured was that occurring in the \nmiddle portion of the specimen under \nexamination. The specimen was in\n\nthe form of a wire and the portion \nmeasured was that between a rigidly \nsupported upper sleeve and a lower \nsleeve which rested upon the short \narm of a lever. The long arm of this \nlever actuated another lever which \ntilted the mirror.\n\nWhen magnetostriction changes \nthe length of the specimen and the \nmirror tilts, the galvanometer read- \ning changes. If, for example, at the \nstart there is no current because the \nimzge of the slits coincides with the \nopaque stripes of the screen, then the \ncurrent and galvanometer reading in- \ncrease to maximum, and then decrease \nto zero when such coincidence again \noccurs. As the length continues to \nchange this cycle repeats; and the ob- \nserver knows the whole number of \nspaces on the screen over which the \nmirror image has been shifted from \nhis count of the number of times the \ngalvanometer has swung back to its \nzero. The fraction of a space is de- \ntermined by the galvanometer read- \ning; this could be read to one-tenth \nof a centimeter on a scale one meter\n\naway from its mirror. And that de- \nflection corresponded to a magneto- \nstrictive displacement of about four \nbillionths of a centimeter for each of \nthe ten centimeters of length of speci- \nmen between the clamping sleeves.\n\nSo sensitive a system necessitated \ncomplete protection from building vi-\n\nbrations. The apparatus was accord- \ningly mounted on a heavy plank and \nthe whole was supported upright on a \nJulius suspension of damped springs. \nThermal changes were also to be \navoided. These arose from the mag- \nnetizing winding surrounding the wire.\n\nby jacketing the solenoid with a \nvacuum as shown in the accompany- \ning diagram. This, however, did not \nresult in constant temperature within \nthe solenoid and an additional non- \nmagnetizing winding was imbedded \nin the upper sleeve. Current was also \nsupplied to this winding so that the \nheating of the specimen was due to \nboth magnetizing and non-magnetiz- \ning windings. This made the wire \nslightly hotter than it would other- \nwise have been but its temperature \ncould be maintained by small adjust- \nments of the current through the aux-\n\niliary, or heater, winding. The natu- \nral drift in equilibrium temperature \nwithin the solenoid was thus very \nclosely compensated.\n\nThe results of the experiments \ndemonstrated that permalloy, consist- \ning of approximately 80 percent \nnickel and 20 percent iron, has no \nmagnetostriction for moderate mag- \nnetizations and expands only slightly \nfor intense magnetization. Permal- \nloys having less than 80 percent \nnickel expand with magnetization and \nthose having greater than 80 percent \nnickel contract with magnetization.\n\ntelephone engineer this question is an- \nswered by curves expressing the nu- \nmerical\u2019 results of articulation-tests. \nBut to the public, hearing is believ- \ning: a demonstration to the ear leaves \nan impression lasting beyond the \nmemory of curves and tables. And \nsO, in conjunction with technical pa- \npers by R. L. Jones and Harvey \nFletcher, use was made of speech and \nmusic transmitted through a public \naddress system into which distortion \ncould be introduced at will. So effec- \ntive were those initial demonstrations \nthat many requests were made that \nthey be given before other audiences. \nOn account of the expense and effort \ninvolved in setting up bulky appara- \ntus which was required, only a few of \nthese invitations could be accepted.\n\nTo simplify the apparatus problem \nthrough the use of phonograph rec- \nords was a logical step. Cooperation \nof the Research group engaged in de- \nvelopment of electrical recording and \nreproducing was enlisted, and a se- \nries of records was made in May, \n1925. With these records a demon- \nstration required only a phonograph \nturntable and reproducer, a suitable \namplifier and a loud speaker; the \nwhole being readily transported, and \nset up in a few minutes. Such an out- \nfit was used on a number of occasions, \namong them a series of talks to non- \ntechnical audiences in Pittsburgh, \nCincinnati, St. Louis, Chicago and \nCleveland by Paul B. Findley of the \nBureau of Publication.\n\nDuring these talks it was realized \nthat certain improvements could be \nmade in the sound-quality of the rec- \nords and in the selection of material.\n\nAccordingly a new set of records was \ncut in the autumn of 1926 which has \nbeen favorably received by technical \nand general audiences alike. Its pres- \nentation is accompanied by an expla- \nnation, couched in terms to suit the \nprevious experience of the audience. \nA brief recapitulation of this mate- \nrial will serve here to introduce a de- \nscription of the records themselves.\n\nResearch efforts in our laboratories \nhave been devoted for a number of \nyears to investigations into the char- \nacter of speech\u2014a fundamental study \ncarried on for the American Tele- \nphone and Telegraph Company as \nbasic to its program of improving the \ntelephone art. To proceed with this \nimprovement on a systematic basis it \nwas necessary to know the importance \nin speech of its various pitches, and \nthis is most easily found by determin- \ning the relative degrading effects on \nthe intelligibility of speech resulting \nfrom the suppression of certain pitch- \nranges. Since electrical filters may be \ndesigned to pass, unhindered, electric \ncurrents corresponding to the sound \nvibrations of certain pitches while en- \ntirely suppressing those of other \npitches, suitable filters were construct- \ned to suppress any desired range of \npitches. Statistical studies were then \nmade of the transmission of each of \nthe characteristic speech sounds \nthrough a telephone system contain- \ning these filters. Since speech is com- \nposed of vibrations varying in fre- \nquency from 100 to about 8000 cycles \nper second, the filters were construct- \ned so that the upper and lower limits \nof transmission could be imposed at \nwill on the various pitches of the \nvoice range. The transmitted band, \nfor example, could be set to include \nfrom 60 to 3000 or 60 to 2000 cycles \nper second; or some of the lower\n\ntones might be suppressed by adjust- \ning the filter to pass only the region \nabove, say, 375 cycles per second. \nThe results of the studies have been \nextremely valuable in engineering im- \nprovements in the telephonic appa- \nratus both for wire and for radio \ncommunication.\n\nListening to a demonstration of \none of these records, concerned with \nspeech, we hear part of an essay by \nPoe, the speaker\u2019s voice sounding \nvery natural with the fundamental \ntones well rounded out and the higher \npitched endings of the consonants be- \ning in proper proportion. As the rec- \nord progresses the lower tones sud- \ndenly disappear from the speaker\u2019s \nvoice and it loses its character al- \nthough the intelligibility is perfect. \nSince no vibrations below 375 cycles \nper second were passed through the \nfilter inserted at this point in the \nprocess of recording, they do not ap- \npear in the sounds of the loud speaker. \nContinuing, the record reaches a point \nat which the filter was adjusted so \nthat no sound below 750 cycles per \nsecond was recorded. The voice is \nthen without character and most un- \nnatural. The higher tones are, how- \never, unhindered and without difficul- \nty we interpret the speech by the con- \nsonants although the vowels are badly \ndistorted. The importance of the \nconsonants for interpretation is thus \nemphasized.\n\nThe record continues and the lower \ntones are restored, but all the vibra- \ntions above 2500 cycles per second \nare suppressed. The voice sounds \nnatural but the interpretation is not \nso good as before. The consonant \nendings are missing and one gets the \nimpression that the speaker\u2019s mouth \nis full of mush. When the record \nprogresses to the point where nothing\n\nabove 1000 cycles per second is trans- \nmitted the speaker\u2019s voice has a gut- \ntural character, and in the absence of \nthe consonants it is extremely difh- \ncult to interpret the speech. At times \nwhole phrases are missed. This rec- \nord illustrates well the contribution \nof the various regions to the intelli- \ngibility of speech.\n\nA second record shows the effects \nof the same type of transmission on \npiano music. The prelude to the \nWaltz from the Ballet \u201cNaila\u2019\u2019 is \nheard, first with extremely natural re- \nproduction. We note that the selec- \ntion is one which encompasses almost \nthe entire range of the piano. As the \nrecord reaches the first point at which \nthe filter was introduced in the process \nof recording, the bass notes are sud- \ndenly stilled. The filter passes only \nthe vibrations above 375 cycles per \nsecond. This corresponds to F-sharp \nabove middle C and all the lower \ntones are therefore suppressed. The \nmelody is present but the tonal char- \nacter is missing. When the record \nprogresses to the point at which the \n750-cycle filter was introduced, cor- \nresponding to a pitch an octave still \nhigher, the music begins to assume a \ntinkling character.\n\nThe lower tones are then restored \nand those above 2500 cycles per sec- \nond are eliminated. The selection as- \nsumes a rather dull character; the \nbrilliance of tone is gone and the mu- \nsic becomes almost a thumping noise\n\nas the 1250-cycle point is reached, the \npreponderance of the bass and the \nabsence of the treble causing the re- \nproduction to lack musical character.\n\nA third record shows the effects of \nforcing a vacuum tube to carry more \nthan its rated load. We have often \nheard the effects of such over-loading \nin radio receiving sets perhaps with- \nout knowing its cause. By contrast \nwith a condition of normal load, we \nnotice in the over-loaded condition \nmany harsh extraneous sounds in the \nmusic or the speech, sometimes de- \nscribed as \u201cbuzzing\u201d or \u201crattling.\u201d \nWhen the reproduction is further lim- \nited by the transmission of only the \nband of frequencies from 375 to 2000 \ncycles per second we are reminded of \nradio sets in the days before much \nattention was paid to the quality of \nthe reproduction, when the receiving \nset reproduced only a limited part of \nthe speech band and the vacuum tubes \nwere over-loaded in the process.\n\nDue to the simplicity and reliability \nof such records for demonstrating the \nfundamental ideas as to the transmis- \nsion of speech and music, it is prob- \nable that the new records will find \nmany uses. They can serve for \ndemonstrations to almost any group \nwhich is interested in speech and mu- \nsic and their transmission. This month \nthey are being used for this purpose \nin a series of talks which L. S. \nO\u2019Roark is giving before A. I. E. E.\n\nDuRING THE MONTH OF FEBRU- \nARY there will be delivered to mem- \nbers of the Laboratories on com- \npleted subscriptions, 4,448 shares of \nAmerican Telephone and Telegraph \nCompany stock. This is the largest \nnumber delivered to our staff in any \none month and represents total sav- \nings through salary deductions and \ninterest of $511,520.\n\nW. A. SHEWHART has been ap- \npointed to represent the American \nPhysical Society on the Sectional \nCommittee of the American Society \nof Mechanical Engineers, organized\n\nfor the standardization of graphic \npresentation. The scope of the com- \nmittee\u2019s work includes standard meth- \nods for the graphic presentation of \nbusiness and other data.\n\nR. D. Gipson AND K. O. THorpP \nare in Birmingham, Alabama, making \nan investigation of the power-line car- \nrier-telephone system of the Alabama \nLight and Power Company.\n\nL. B. Cooke is installing for the \nPenn Public Service Corporation a \npower-line carrier-telephone system \nwhich employs a repeater of recent \ndesign. This system will provide\n\nAt the inauguration by the American Telephone and Telegraph Company of commer- \ncial telephone service between New York and London. In the foreground, left to \nright: President Gifford, B. Gherardi, E. B. Craft, N. T. Guernsey\n\ncommunication between the follow- \ning cities: Erie, Piney Dam, Seward, \nGlory, Johnston and Deep Creek.\n\nR. M. PEASE has joined Henry B. \nArnold in Atlanta, where they are in- \nvestigating the power-line carrier- \ntelephone system of the Georgia Rail- \nway and Power Company.\n\nSHEET BRASS for Bell System use \nwill now conform to specifications \nagreed upon at a conference held in \nMontreal on December 2 and 3 be- \ntween representatives of the Haw- \nthorne Works of Western Electric, \nAmerican Brass Company, and \nMessrs. Fondiller, Van Deusen, Town- \nsend, and Hayford of the Laborato- \nries. Several months\u2019 work were in- \nvolved in developing the specifica- \ntions; similar work on other non- \nferrous metals is now in progress.\n\nL. J. StviAn of the Laboratories \nand H. S. Osborne of A. T. & T. re- \ncently returned from five weeks in \nLondon and Paris. While in Paris \nthey represented the Bell System at \nthe plenary meeting of the Comit\u00e9 \nConsultatif International des Com- \nmunications Te\u00e9l\u00e9phoniques, which \nadopted for its Transmission Refer- \nence Standard a replica of the one de- \nveloped in the Laboratories. This \nwill be built here and installed at the \nConservatoire des Arts et M\u00e9tiers in \nParis. At this meeting it was also de- \ncided to recognize as the admissible \nunits both the \u2018\u201c\u2018napier\u201d\u2019 and the \u201c\u2018deci- \nmal unit\u201d, which equals ten TU.\n\nON THE EVENING of December 9, \n1926, Mr. Craft spoke on the gen- \neral subject of \u2018\u201c\u2018Research\u201d\u2019 at the an- \nnual dinner of the Alumni of Worces- \nter Polytechnic Institute, of which he \nis an honorary alumnus. In empha- \nsizing the need for research, Mr. \nCraft said, \u201c\u201cWe cannot make the en- \ngineering applications unless we en-\n\ncourage research, and research devel- \nopments cannot reach their fullest \nutilization for public welfare unless \nthe engineer is interested, sympa- \nthetic, and appreciative of their im- \nportance.\u201d\n\nEdward Buttner of the Engineering Shop \nDepartment has been forty years with the \nBell System\n\nkilowatt broadcasting equipment for \nthe Fisher Blend Station of the B. F. \nFisher Flouring Mill in Seattle. Be- \nfore leaving the coast he made a sur- \nvey for a similar installation at Santa \nBarbara, California.\n\nOn January 8, D. H. Newman \nleft New York for Montevideo, Uru- \nguay, where he is supervising the in- \nstallation of a one-kilowatt broad- \ncasting equipment for the Republic \nof Uruguay.\n\nUNDER THE SUPERVSION OF H. S. \nPrice the National Life and Accident \nInsurance Company of Nashville has \nreplaced its one-kilowatt broadcast-\n\nP. A. ANDERSON has completed the \ninstallation of a one-kilowatt broad- \ncasting equipment which replaces the \n500-watt set at WBBR, the Staten \nIsland Station of the People\u2019s Pulpit \nAssociation. In addition this cus- \ntomer operates a one-kilowatt equip- \nment at Cleveland, and a five kilo- \nwatt one at Batavia, Illinois.\n\nPhilip C. Rossi of the Patent Drafting \nGroup has had thirty-five years\u2019 service\n\nat Gibson, Indiana, on January 6 and \n7, to observe the operation of the \nsystem recently installed there for \ntransmitting orders to the engineers \nof switching locomotives by radio \ntelephone.\n\nTHE LABORATORIES signified their \nadvent at Whippany by taking active \npart in the Community Christmas \nCelebration on December 26. A brief \naddress was given by L. S. O\u2019Roark \nand music for the occasion was sup-\n\nplied by engineers, attached to the \nstation, who used a Public-Address \nSystem in combination with an elec- \ntric phonograph.\n\nington and Baltimore when the Bal- \ntimore toll board was changed over \nto the C. L. R. method of operation.\n\nTHE COMMERCIAL DESIGN of gen- \nerators for charging central-office bat- \nteries was successfully tested recently \nat Reading. Use of this generator is \nmade possible by the electrolytic con- \ndenser. The tests were observed by \nmembers of the engineering staffs of \nthe Telephone Company and the \nAmerican Telephone and Telegraph \nCompany, and by A. E. Petrie, R. L. \nLunsford, and M. A. Froberg of the \nLaboratories.\n\nF. F. SreBpert has been at East \nPittsburgh, in connection with tests \non small unit gasoline engines.\n\nTION of the new single-channel car- \nrier system are in active progress. \nDuring December K. M. Fetzer, A. \nChaiclin, H. S. Black and A. C. Dick- \nieson visited Watertown and Syracuse \nin connection with these tests.\n\nE. W. Hancock Anp W. J. La- \nCERTE visited Hartford in connection \nwith a trial installation of new multi- \nlevel hunting connectors.\n\nW. BENNETT has been at Spring- \nfield, making tests on the step-by-step \nswitches which were made in Haw- \nthorne.\n\nR. B. BUCHANAN visited Lehigh \nOffice, Pittsburgh, in connection with \nthe introduction of straightforward \ntrunking equipment.\n\nDurinGc DEcEMBER, W. A. Boyd \nand H. G. Eddy were in Hawthorne \non regular Survey Conference work.\n\nAT THE ANNUAL MEETING of Ed- \nward J. Hall Chapter, Telephone \nPioneers of America, held on Decem- \nber 16, 1926, the following members \nof the Laboratories were elected to \noffice and as delegates to the next an- \nnual convention: J. E. Moravec, \nmember of Executive Committee; W. \nB. Sanford and W. C. F. Farnell, \ndelegates; G. F. Atwood and G. F. \nMorrison, alternates.\n\n\u2018\u201cRECENT DEVELOPMENTS IN \nCOMMUNICATION\u201d was the subject of \na talk given by M. B. Long, Educa- \ntional Director, on the evenings of \nJanuary 10, 11 and 13, before the \nIndianapolis, Purdue University and \nArmour Institute Sections, A. I. E. E. \nAlso, Mr. Long informally addressed \nthe Telephone Luncheon Club at In- \ndianapolis on January tenth.\n\nJ. F. Newcomb, Assistant Treasurer; H. G. Eddy, Inspection; C. Westerburg, En- \ngineering Shop\n\nECONSTRUCTING the \npast from such traces as may \nremain is one of the tasks of\n\nthe historian. From finds like the \ntomb of Tut-ankh-Amen there are \npictured for us the lives and customs \nof ancient civilizations. Of times more \nremote, the geologist and palaeontolo- \ngist draw inferences from the occa- \nsional finds of fossils. \u2018Their tasks are \nfrequently most difficult. Is some \nparticular fossil, for example, the\n\nskull of a primeval man, or the knee- \ncap of an elephantine animal? Some- \ntimes sufficient material is found to \npermit a rather complete reconstruc- \ntion, and in museums of natural his-\n\nThe processes of evolution with \nwhich these historians deal were not \nonly slow but lie obscured in times of \nunwritten history. Another type of \nevolution occurring in these present \ndays, when records are easily made \nand preserved, is that of science and \nits associated arts. The marvelous \nevolution of the telephone has all oc- \ncurred within the brief span of fifty \nyears.\n\nA historian of the art of telephony \ndoes not lack written material from \nwhich accurately to reconstruct the \npast. In our Bell Telephone Histori- \ncal Museum there are also many and \ninteresting exhibits of early appara- \ntus or of models of such apparatus \nreconstructed on the basis of pictures\n\nand written descriptions. We can \nbuild, for example, actual reproduc- \ntions of the instruments with which \nAlexander Graham Bell carried on \nthe first telephone conversation; one \nsuch model was used by him at the \nopening ceremonial of the transconti- \nnental line in 1915 when he spoke \nfrom New York to Thomas A. Wat- \nson in San Francisco.\n\nAnother model, also of the first \napparatus of its kind, has recently \nbeen built in our engineering shops \nunder the advice of W. L. Richards, \nConsulting Historian. There was re- \nconstructed the equipment of the first \ncommercial telephone-exchange sys-\n\nhibit it at the New Haven Progress \nExposition from January twenty- \nsixth to February fifth.\n\ntures. These were taken while Mr. \nRichards, with the assistance of the \nwriter, was demonstrating this first \ncentral-office system to A. F. Dixon, \nSystems Development Engineer. \nThe eight lines terminated in eight \nbinding posts at the top of the board. \nThere were also available, what were \nin effect, two cord circuits, each con- \nsisting of two rotary levers electri- \ncally connected. On a circle, about \nthe pivot of each lever as a center, \nare eight discs or studs. Discs corre- \nsponding in position with reference to \nthe two levers are connected in mul-\n\ntiple to the eight lines. Below the \nlevers of each cord circuit are the line \nswitches for the annunciator circuits, \none for each line. And below these, \nis a strip to which is connected one\n\nas \u201cCoy\u2019s Chicken\u2019\u2019. It consists of a \nlarge induction coil and a flat steel- \nspring which is caused to vibrate by \nthe hand operation of a lever making \nand breaking a local circuit. The cur-\n\nT the annual convention of \nA the Institute of Radio Engi- \nneers, Dr. Ralph Bown, new- \nly elected president of the Institute, \nwas presented with the Liebmann \nMemorial Prize awarded him by the \nBoard of Directors of that body \u201c\u2018for \nhis researches in \u2018Wave Transmission \nPhenomena.\u2019 \u201d\n\nDr. Bown received his Ph.D. from \nCornell in 1917. He entered the \narmy in 1917, where he was commis- \nsioned as Captain in the Signal Corps. \nHe was in charge of development of \nradio apparatus for the Army at the \nSignal Corps Radio Laboratory, \nCamp Alfred Vail, until June, 1919. \nIn August, 1919, Dr. Bown took up \nhis present work in the American Tel- \nephone and Telegraph Company.\n\nThe Morris Liebmann Memorial \nPrize, consisting of the sum of five \nhundred dollars in cash, is awarded \nannually by the Board of Directors \nof the Institute in recognition of note- \nworthy inventions or other develop- \nments in radio technique.\n\nDr. Bown well merits this recog- \nnition, as he has been an outstanding \nexponent of the development of meth- \nods and equipment to place radio \ntransmission studies on a quantitative \nbasis. His outstanding researches re- \nlate particularly to transatlantic radio \ntelephony and radio broadcast trans- \nmission. Dr. Bown has presented \nmany of the important results of the \nwork of this organization in technical \npapers before the Institute.\n\nwas presented by DeLoss K. Martin, \nGlenn D. Gillett and Isabel S. Bemis \non the subject, \u201cSome Possibilities \nand Limitations in Common-F requen- \ncy Broadcasting,\u201d reviewing experi- \nmental work done by these engineers \nand their associates.\n\nEarly in 1926, the Bell Telephone \nLaboratories devised and built for the \nInformation Department of the \nAmerican Telephone and Telegraph \nCompany three portable talking mov- \ning picture outfits for use in connec-\n\ntion with celebrations throughout the \nUnited States commemorating the fif- \ntieth anniversary of the birth of the \ntelephone. The portable equipments \nwere placed at the disposal of the As- \nsociated Companies with engineers\n\nfrom this company and the Laborato- \nries, to supervise the installation and \noperation of the pictures in the field.\n\nTwo talking pictures were exhib- \nited\u2014one of Thomas A. Watson, as- \nsistant to Professor Alexander Gra- \nham Bell at the time of the invention \nof the telephone, and the other a pic- \nture illustrating the development of \nthe telephone switchboard from the \ndays of its infancy up to the present \ntime.\n\nDuring the year which has just \npassed, the two pictures were shown \nin twenty-six different cities and towns \nover nine hundred times to audiences \ntotaling over 206,000. This includes \nthe installation which was made at \nthe Bell System exhibit at the Sesqui- \ncentennial, where the pictures were \nshown over a period of twenty-three \nweeks.\n\nNaturally, the \u201cone-night stand\u201d\u2019 \ninstallations throughout the country \nintroduced many difficult and varying \nconditions. In view of this, credit is \ndue W. W. Sturdy of A. T. & T.., \nand to R. E. Kuebler and J. B. Irwin \nof the Laboratories for meeting all \nthe dates:assigned to them, and show- \ning the pictures on schedule time.\n\n1926 one hundred and thirty-four pat- \nents were issued to the following \nmembers of the Department of De. \nvelopment and Research:\n\nE. H. Colpitts, L. F. Morehouse, \nO. B. Blackwell, H. A. Affel, R. S. \nBailey, F. H. Best, W. G. Blauvelt, \nR. K. Bonell, L. L. Bouton, R. Brown, \nA. Carpe, A. B. Clark, S. I. Cory, \nG. Crisson, C.S. Demarest, E. Dietze, \nW. H. Edwards, L. Espenschied, H. \nA. Etheridge, J. M. Fell, C. H. Fet- \nter, D. K. Gannett, L. L. Glezen, C. \nS. Gordon, E. I. Green, I. W. Green, \nR. A. Haislip, H. S. Hamilton, J. \nHerman, W. H. T. Holden, R. K. \nHonoman, R. S. Hoyt, A. E. Hunt, \nL. M. Ilgenfritz, A. H. Inglis, E. \nJacobsen, O. H. Loynes, D. K. Mar- \ntin, W. H. Martin, A. L. Matte, R. \nG. McCurdy, N. D. Newby, H. Ny- \nquist, R. S. Ohl, J. T. O\u2019Leary, G. \nH. Peterson, K. W. Pfleger, H. E. \nPhelps, R. K. Potter, F. W. Rey- \nnolds, W. A. Rhodes, F. W. Schramm, \nJ. T. Schott, S. P. Shackleton, R. B. \nShanck, H. F. Shoffstall, E. St. John, \nM. E. Strieby, C. V. Taplin, H. M. \nTrueblood, G. S. Vernam, E. Von \nNostitz, J. N. Walters, E. F. Wat- \nson, A. Weaver, S. B. Wright, M. K. \nZinn, O. J. Zobel.\n\nThe 1927 social season will open \non Thursday evening, February 17, \n1927, with the midwinter dance to be \nheld on the Roof of the Hotel McAl-\n\nThis will be the ninth dance given \nby the Club since February, 1924, \nand we are sure that all of the Club \nmembers and their friends who have \nattended these parties have spent \nvery enjoyable evenings. It has been \nthe policy of the Club to hold all \ndances in New York hotels, and to \nhave the best music obtainable. The \nCommittee wishes to announce that \nthis policy will be followed through- \nout 1927.\n\nThe sale of tickets for the Febru- \nary dance has been limited to five \nhundred by the management of the \nHotel McAlpin and, as only this \nnumber has been printed, we advise \nyou to purchase your tickets at once \nto insure having them. Admission \nwill be $1.10 each, including tax. No \ntickets will be sold at the door. D. R. \nMcCormack will manage all of our \ndances and entertainments for 1927.\n\n1927, the winter session of the Men\u2019s \nBridge Club started in room 269. \nThese meetings will be held every \nMonday at 6:30 p.M.\u2014all men \nbridge players are welcome. Prizes \nwill be given each evening for the \nbest scores, and also at the end of the \nseason for the best three all-season \nscores. Players must attend seven \nnights to be eligible for season prizes. \nA weekly fee of fifty cents is charged.\n\n27, 1926 \n1. H.M.Hagland 6. H.B. Barber \n2. A. L. Thuras 7. T.C. Rice \n3. D. Wetherell 8. M. N. Smalley \n4. E. Rahn g. J. E. Cassidy \n5. D.S. Myers 10. A. Zitzman\n\nThe church at Stoke Poges\u2014where Thomas Gray wrote his \u201cElegy in a Country \nChurchyard.\u201d First prize, Landscape Class; W. Orvis\n\npicture contest. The Club surely is \nproud of its first picture exhibition \nand is already looking forward to \nmaking it a yearly event. _\n\nThe judges, H. E. Ives and I. B. \nCrandall, found before them a rather \ndificult task when it came to choos- \ning the best picture, but we feel that \nthey have succeeded very well in \nawarding the prizes to these contest- \nants :\n\nLandscape Class: \nFirst prize, W. Orvis \nSecond prize, W. Orvis \nThird prize, J. Popina \nHonorable mention. J. Popina and\n\nPortrait Class: \nFirst prize, J. Popina \nSecond prize, H. Maude \nThird prize, P. D. Hance \nHonorable mention, J. Popina, H. \nMaude and K. B. Lambert.\n\nChristmas Card Class: \nFirst prize, H. Maude \nSecond prize, E. Alenius \nThird prize, E. Alenius \nHonorable mention, E. Alenius,\n\nThe prize for the picture showing \nthe greatest amount of thought when \nphotographing was most difficult to \njudge. These were awarded in this \norder:\n\nThe prize for the best group of \npictures was awarded to H. Maude, \nwith J. Popina a very close second.\n\nThe Department prizes were \nawarded to M. G. Allison in the In- \nspection, A. S. Curtis in the Research, \nR. H. Mills for the Apparatus De- \nvelopment, J. Popina for the Com-\n\nThe color plates submitted were \nespecially fine. The prize in this group \nwas given to A. S. Curtis, while R. \nH. Mills received honorable men- \ntion. Among the color plates were \nsome very interesting technical studies \nmade under the microscope.\n\nThe Club is very well pleased with \nthe response it received and wants to \nextend to all the contestants a word \nof praise for the good work that was \nrepresented by the pictures sub- \nmitted.\n\nIn one of the hottest basketball \ngames ever seen by our friends across \nthe River, the Bell Laboratories Club \ndefeated by a score of 34-23 an all- \nstar team from the Kearny Works of \nthe Western Electric Company. This \ngame took place on Wednesday eve- \nning, January 12, in the 4th Regi- \nment Armory in Jersey City.\n\nThe Wekearnians fought our men \nduring every second of play but when \nit was all over West Street had \nscored its third straight victory over \nKearny in as many years.\n\nAt no time during the game was \nthere a difference of more than two \npoints, and with two minutes to play \nKearny was leading 23 to 21. A \ndaring shot by Maurer for a clean \nbasket brought the score to 23-23, \nand with only seconds to play Git- \ntenberger dropped a foul almost as \nthe whistle blew, ending what the \nJersey daily papers referred to as the \nbest game ever staged on the floor of \nthe Old 4th Regiment.\n\nWhile Maurer starred for West \nStreet our victory was due to very \nfine all-around team work. The en- \ntire team worked as one man with\n\nThis portrait of a young seaman took first prize in the Portrait Class; J. Popina\n\nno thought of individual honors. \nThe details and line-up of this game \nare given below.\n\nNot to be outdone by our star \nteam, our Juniors met and defeated \nthe Junior team from the Western \nElectric Company, 195 Broadway, \non Friday evening, January 14, in \nthe gymnasium of the Labor Temple,\n\nThis organization of Juniors is \nplaying in the Club Tournament and \nat present is tied for second place.\n\n\u201cWhat does it cost me in days of labor to satisfy my desires for \nthe unnecessary things of life?\u201d You will probably be surprised \nwhen you figure out just how hard you are making yourself work \nfor some of the casual bits of expenses you incur regularly without\n\nLet us say that your income is $2000 per year, and that your \nfood, shelter, clothing and other actual necessities cost $1600. \nYour net income which you can spend for other than necessities \nis $400; you have no choice as to how you will spend the $1600, \nbecause this must go to the butcher, grocer, landlord, public service \ncompany and others who are on your payroll.\n\nTherefore, if you feel like spending $10 for something you \ncould do just as well without\u2014some luxury which must be paid \nfor out of your net income\u2014you can calculate that this $1o net \nincome is equivalent to eight days\u2019 work.\n\nTHE LABORATORIES were well rep- \nresented at the Christmas meeting of \nthe American Association for the Ad- \nvancement of Science held in Phila- \ndelphia on December 28 and 29. The \nfollowing papers were presented:\n\n\u201cPhotoelectric Emission as a Func- \ntion of Composition in Sodium Po- \ntassium Alloys,\u201d by H. E. Ives and \nC. R. Stillwell, presented by H. E. \nIves; \u2018\u201c\u201cThermal Agitation of Elec- \ntricity in Conductors,\u201d by J. B. John- \nson; \u201cThe Life History of an Ad- \nsorbed Atom,\u201d by J. A. Becker; \u2018\u201cThe \nDirect Comparison of Loudness of \nPure Tones,\u201d by B. A. Kingsbury.\n\nARTHUR W. PAGE assumed on \nJanuary first his duties as Vice-Presi- \ndent of the American Telephone and \nTelegraph Company. Upon gradua- \ntion from Harvard in 1905 Mr. Page \nentered Doubleday, Page and Com- \npany, of. which he later became Vice-\n\nT. C. Fry is planning to give a se- \nries of lectures at the Massachusetts \nInstitute of Technology on the engi- \nneering application of the theory of \nprobability, beginning the early part \nof February and continuing until the \nend of the school term in June.\n\nJoun C. Latuam, until January \nfirst in charge of technical informa- \ntion in the Bureau of Publication, was \non that date transferred to A. T. \n& T. He recently sailed for Lon- \ndon to become assistant to H. E. \nShreeve, the technical representative \nof the Bell System in Europe.\n\nField Engineering work of the In- \nspection Engineering Department in \nthe Up-State Territory of the New \nYork Telephone Company, was held \nin Albany on December 8. On De- \ncember 16 a conference on similar \nwork in the territory of the New \nEngland Telephone and Telegraph \nCompany was held in Boston. In ad- \ndition to Telephone Company engi- \nneers and representatives of Western \nElectric Distributing Houses, R. L. \nJones, G. D. Edwards and R. J. \nNossaman were present at the Al- \nbany conference, and G. D. Edwards \nand R. J. Nossaman were present at \nthe Boston conference.\n\nR. B. MILLER spent the gth and \n10th, of December in Toledo observ- \ning a trial which the Installation De- \npartment of Western Electric Com- \npany was making of a sampling in- \nspection plan.\n\nD. A. QuarRtLes and E. G. D. Pat- \nERSON were in West Lynn, Mas- \nsachusetts, in connection with a Sur- \nvey Conference on telephone power \nequipment manufactured by the Gen- \neral Electric Company.\n\nAN ELECTRIC STETHOSCOPE oper- \nated by H. F. Hopkins figured in the \ndetection of a \u201ccrime\u201d as part of a \ndemonstration before the New York \nElectrical Society on December 15. \nAs each of three volunteer \u201c\u2018suspects\u201d\u2019 \nwas examined about the affair, the \nstethoscope and a loud speaker made \nthe thumping of his heart plainly au- \ndible to a large audience. The quick- \nened beat of the guilty person\u2019s heart \nwas instantly evident.", "title": "Bell Laboratories Record 1927-02: Vol 3 Iss 6", "trim_reasons": [], "year": 1927} {"archive_ref": "sim_record-at-t-bell-laboratories_1933-05_11_9", "canonical_url": "https://archive.org/details/sim_record-at-t-bell-laboratories_1933-05_11_9", "char_count": 80175, "collection": "archive-org-bell-labs", "doc_id": 204, "document_type": "journal_issue", "id": "bella-qwen-pretrain-doc204", "record_count": 76, "release_policy_version": "hf_public_v1", "rights_status": "public_domain", "selected_extraction_backend": null, "selected_extraction_score": null, "source_family": "archive_org", "source_url": "https://archive.org/details/sim_record-at-t-bell-laboratories_1933-05_11_9", "split": "validation", "text": "even from a large symphony or- \nchestra, should be picked up by micro- \nphones, transmitted over telephone \nwires, and reproduced at a distant \npoint. Most of us probably hear it \naccomplished every day by means of \nthe radio, and radio transmission and \nreproduction would, in general, be \ncalled good. Between good reproduc- \ntion and perfect, however, there is a\n\ncrossing it are probably not realized \nby those not technically familiar \nwith the subject. Perfect reproduc- \ntion, of a symphony concert for ex- \nample, would make it impossible for \none listening with his eyes blindfolded \nto know that the actual orchestra was \nnot on a stage before him. Not only \nwould every tone and over-tone be \npresent in its correct relative volume, \nbut there would be a depth and color \nwhich is not ordinarily obtained when \nelectrical apparatus intervenes\n\nbetween theorchestraand theaudience. \nThree classes of requirements must \nbe met if the reproduced sound is to \nbe indistinguishable from the original. \nTwo of them, that both the complete \nfrequency and complete volume ranges \nbe transmitted, have been generally \nrecognized for some time. The third, \nthat the sounds must be reproduced \nwith the correct auditory perspective, \nhas been fully appreciated only by \nthose most closely associated with the \nscience of sound reproduction. \nSounds in general are composed of a \ngroup of tones and over-tones ranging \nfrom the deep bass of the lowest organ \nnotes, or those of a bass drum, to the \nshrillest tones the ear can hear. Each \nnote of a musical instrument has a \nfundamental tone and a group of \nharmonics. The fundamental tone \nsets the pitch, and the harmonics give \nthe note its quality. It is the har- \nmonics that make it possible to dis- \ntinguish a note on a violin from one on \na trumpet or from any other of the \nsame pitch. It is in the harmonics that \nreside the richness of music and the \nwealth of sensuous appeal. These \ntones and over-tones are known and \nrecognized by their frequency, or \nvibratory rate; and the range of fre- \nquencies to which the ear responds \nruns from about 16 cycles per second \nto 16,000, or even 20,000 cycles for \nsome ears. The sensitivity of the ear \nfalls off rapidly at the higher fre- \nquencies, however, so that the effect \nof frequencies above 15,000 cycles is \nnegligible for the most part. The \nhighest note on the piano has a funda- \nmental frequency of only about 4,000 \ncycles, and few of the musical instru- \nments exceed this pitch, but the ac- \ncompanying harmonics or over-tones, \nwhich are of still higher frequencies, \nare very necessary to the proper \nquality and richness of the notes.\n\nOf no less importance, if the full \naesthetic effect of music is to be ob- \ntained, is the range in volume. The \near has a recognizable range of volume \nas it has of frequency. This extends \nfrom sounds so low that the ear cannot \nhear them, to sounds so great that the \nsensation is one of pain rather than of \nhearing. For convenience in scientific \nstudy, the power of sounds is graded \nin units known as decibels (abbrevi- \nated db). The threshold of hearing is \ntaken as a reference base, and the \nordinary audible range runs from the \nvolume of sound one would hear in a \nquiet garden, or that of an average \nwhisper at a distance of four feet, \nwhich are at a level of 20 db, to that \nof a pneumatic riveter, at a level of \n100 db\u2014a total range of about 80 db. \nThe range of a large symphony or- \nchestra is about 70 db, so if the music \nof such an orchestra is to be faithfully \ntransmitted electrically, a volume \nrange of the order of 70 db must be \ntransmitted: a range of power of ten \nmillion to one.\n\nThe third requirement becomes of \nparticular importance when the sound \nto be transmitted and reproduced is \nthat from a large and relatively widely \nspaced group of instruments, such as \na complete symphony orchestra. \nWhen one sits in an auditorium and \nlistens to a symphony concert he ex- \nperiences something that is over and \nabove the effect produced by the \nactual frequency and volume range \ngiven out by the orchestra. This ad- \nditional appeal is difficult to describe, \nand almost impossible to measure. It \nis partly due to a spreading of the \nsound in all directions so that it fills \nthe entire volume of the auditorium \nand thus reaches one\u2019s ears by various \npaths. It is partly due to other factors; \nbut whatever its cause it results in a \nrichness and texture of tone that no\n\nordinary electrical reproduction can \nprovide. For lack of a better term, the \neffect may be called auditory per- \nspective. Without it the music would \nbe one dimensional and not expanded \ninto its true spatial relationship. The \ndifference may be compared to that \nbetween the appearance of a photo- \ngraph of a scene and the same scene \nwhen viewed through a stereoscope.\n\nHow to obtain this auditory per- \nspective in music transmitted and re- \nproduced electrically was discovered \nby the scientists of Bell Telephone \nLaboratories as a result of their funda- \nmental investigations in acoustics and \ntelephonic transmission. During the \ncourse of those investigations they \nhad developed telephonic systems of \nhigh quality, but for their further re- \nsearches they needed opportunity to \nutilize music in its most perfect forms. \nNow it happened that Dr. Leopold \nStokowski, Director of the Philadel- \nphia Orchestra, was interested in the \npossibilities of electrical systems for \nthe production of exceptional or- \nchestral effects. Through his volun- \ntary cooperation, therefore, the Lab- \noratories\u2019 scientists were able to make \nquantitative physical studies of music \nas rendered by his orchestra, and so to \nperfect their designs; and with the \ncompletion of the new equipment \nsome of the possibilities which Dr. \nStokowski had hoped for became \npracticable. An extended series of \ntests was then carried on in Phila- \ndelphia in which the Laboratories\u2019 \nscientists were generously assisted by \nDr. Stokowski. As a result of these \nstudies, it was found that by employ- \ning two microphones, one properly \nlocated on each side of the stage, and \nby transmitting over two separate \ncircuits to two of the newly developed \nloud speakers, similarly placed, the \neffect of the actual presence of the\n\nEven with the discovery of a com- \nparatively simple means of obtaining \ntrue auditory perspective, the prob- \nlem was not completely solved. Never \nbefore had either the complete fre- \nquency, or the complete volume range, \nof a symphony orchestra been com- \nmercially transmitted and_ repro- \nduced. No complete chain of appa- \nratus, from microphone to loud \nspeaker, was available that would \nfaithfully transmit the entire range of \nfrequency and volume. Microphones \nperhaps offered the fewest difficulties. \nBell Laboratories had already de- \nsigned sensitive microphones that \nwould transmit practically the entire \nrange required, and only minor modi- \nfications were needed to make them \nentirely suitable.\n\nThis was not true of the amplifiers. \nThere had to be developed amplifiers \nwhich would faithfully transmit all \nfrequencies from 35 to 16,000 cycles \nat levels from the barely audible \npianissimo effects to the resounding \norchestral crashes of ten million times \ngreater power; and all the pieces of \napparatus had to be so designed that \neven during intervals of complete \nsilence not the slightest noise would \nbe introduced to suggest the presence \nof electrical apparatus. No underlying \nhum or noise, such as is commonly \npresent in radio or other systems of \nreproduction, could be tolerated with \nthe new apparatus. In the intervals of \nsilence there must be real silence: a \ndead auditory void in which the fall \nof the lightest pin could be heard. \nThis has actually been accomplished \nto a degree heretofore unknown. \nProbably the most quiet electrical re- \nproduction up to the present is that \nobtained with high-grade sound pic- \nture apparatus; but such apparatus at \nits most quiet moments gives off 300\n\nControl room in the basement of the Academy of Music in Philadelphia. W. A. \nMunson of the Laboratories is standing at the voltage amplifiers\n\nOf even greater difficulty possibly \nwas the design of suitable loud \nspeakers. It is not practicable to ob- \ntain the entire frequency range with a \nsingle unit, and so two types of loud \nspeakers are used. One, somewhat \nresembling the horns used for sound \npictures, is employed for the frequen- \ncies from 35 to 300 cycles; and another \ntype, for the range from 300 to 16,000 \ncycles. These loud speakers are dif- \nferent from anything previously pro- \nduced commercially. Never before \nhave these elements fulfilled such \ndificult requirements of frequency \nrange and volume. The best sound \npicture systems record and reproduce \napproximately half the range of fre- \nquencies handled by the new loud \nspeakers, and the best radio systems \neven less. In volume range the com- \nparison is equally remarkable. Al- \nthough sound picture systems under \nthe most favorable conditions may \nprovide a volume range of 40 or 45\n\ndb, radio systems rarely exceed 30, \nwhile the range provided by the new \napparatus is well above 80. Whereas \nthe power range of radio is of the \norder of 1000 to 1, the new equipment \nis capable of yielding a range of \n100,000,000 to I.\n\nThe new loud speakers and their \nassociated equipment of amplifiers \nand microphones are, therefore, fully \ncapable of handling the entire volume \nrange of a symphony orchestra. When \none speaks of range of loudness which \ncan be handled by an electrical \nsystem for reproduction, one is con- \ncerned with the differences between \nthe loudest and faintest passages of \nthe music which it can reproduce. \nThere is in addition the problem of \nhandling the peaks of maximum loud- \nness. These peaks in the case of music \nfrom a symphony orchestra are be- \nyond the possibilities of the ordinary \nloud speaker to reproduce without \ndistortions which seriously affect the \nmusical sonority. The low frequency \nsounds make the largest contribution\n\nto the peaks of sound power which \nmust be handled to meet these con- \nditions. The diaphragm of the low \nfrequency element in the new loud \nspeaker has been made nearly seven \ntimes larger than that of the elements \nused ordinarily for sound picture re- \nproduction. By these diaphragms a \nlarge column of air is set into motion.\n\nThe ordinary loud speaker also be- \ncomes directional in its characteristics \nat the higher frequencies. Low fre- \nquency sounds spread in all directions \nfrom the mouth of the horn, but the \nhigher frequencies tend to concen- \ntrate into a beam projected directly \nahead of the horn; and the width of \nthe beam becomes narrower and \nnarrower as the frequency increases.\n\nBecause of this fact, the audience, in a \nlarge hall equipped with the ordinary \nloud speakers, never hear quite the \nproper blending of frequencies. Those \ndirectly in front of the horn receive \ntoo great a proportion of the higher \nfrequencies, while those on the sides \nreceive too much of the low frequen- \ncies. To avoid this effect, the horn of \neach high-frequency element is di- \nvided into 16 diverging rectangular \nsections which spread the sound over \nan arc of 60 degrees vertically and \none of 60 degrees horizontally. Two of \nthese units placed side by side thus \nspread the sound over a horizontal \nangle of 120 degrees--a far wider \ncoverage than has been obtained be- \nfore and one which distributes the \nsound throughout the \nauditorium with a \nfaithful blending of the \nfrequencies.\n\nR. . Tillman of A. T. & T. (left), and A. R. Soffel of the 200 watts. This addi- \nLaboratories at the voltage amplifiers in Constitution Hall, tional gain allows ef-\n\nwhich have been impossible before. \nBesides the effects of range and \nquality of tone, the total aesthetic \nappeal of an orchestra is due in no \nsmall degree to the range in volume. \nThe number of musicians one can \nplace on a stage is limited. To put \nten times as many as contained in a \nmodern symphony orchestra is im- \npossible in any existing hall. The con- \ntrol of volume given by the new ap- \nparatus enables the director to secure \nat will the equivalent of an orchestra \nof nearly a thousand musicians.\n\nThe advantage of this control of \nvolume does not end here, however. \nIts presence makes it possible to re- \nproduce operatic music, where a \nsoloist is accompanied by an orchestra, \nwithout allowing the voice of the \nsinger to be drowned out by the \nlouder passages. For this purpose a \nthird channel, including its separate \nmicrophone, transmission line, and \nloud speaker, has been provided in \nthe new system primarily for the \nsinger. The volume of output of this \nchannel is controllable independently \nof the other two. In this way the \nloudness of the voice may always be \nkept just above that of the orchestra \nand the desired musical effect be ob- \ntained. There thus reside in the newap- \nparatus possibilities heretofore unat- \ntainable; and telephonic research has \nlaid a foundation for what may be one \nof the greatest advances in musical \naesthetics of the present scientific era.\n\nThe first public demonstration of \nthe new apparatus was given in \nWashington on the evening of April \n27 under the auspices of the National \nAcademy of Sciences. At that time \nDr. Stokowski, Director of the Phila- \ndelphia Orchestra, manipulated the \ncontrols from a box in the rear of \nConstitution Hall, while the Phila- \ndelphia Orchestra, led by Associate\n\nConductor Alexander Smallens, played \nin the Academy of Music at Phila- \ndelphia. Between Philadelphia and \nWashington, the music was trans- \nmitted over telephone cable circuits. \nThe program consisted of the Toccata \nand Fugue in D Minor, of Bach; \nBeethoven\u2019s Symphony No. 5 in C \nMinor; L\u2019apr\u00e9s-midi d\u2019un Faune, of \nDebussy; and the Finale of G\u00e9tter- \ndammerung. A visual accompaniment \nwas provided for the music by \nElectrical Research Products, Incor- \nporated. Its stage direction\u2014through \nthe courtesy of the Yale School of \nDrama\u2014was by S. R. McCandless, \nand the designs were by Eugene \nSavage and George Davidson. \nDuring the intermission Dr. W. W. \nCampbell, President of the National \nAcademy of Sciences, introduced Dr. \nHarvey Fletcher, Director of Acous- \ntical Research at Bell Telephone \nLaboratories. With the assistance of \nthe orchestra in Philadelphia, Dr. \nFletcher then performed several ex- \nperiments to demonstrate the im- \nportant characteristics of the new \napparatus. On the stage of the Acad- \nemy of Music in Philadelphia, where \nthe pickup microphones were in- \nstalled, a workman busily construct- \ning a box with hammer and saw was \nreceiving suggestions and comments \nfrom a fellow workman in the right \nwing. All the speech and accompany- \ning sounds were transmitted over \ncable circuits to the loud speakers on \nthe stage of Constitution Hall in \nWashington. So realistic was the \neffect that to the audience the act \nseemed to be taking place on the \nstage before them. Not only were the \nsounds of sawing, hammering and \ntalking faithfully reproduced, but the \ncorrect auditory perspective enabled \nthe listeners to place each sound in its \nproper position, and to follow the\n\naudience heard a soprano sing \u201c\u201cCom- \ning Through the Rye\u201d as she walked \nback and forth through an imaginary \nrye field on the stage in Philadelphia. \nHere again her voice was reproduced \nin Washington with such exact audi- \ntory perspective that the singer ap- \npeared to be strolling on the stage of \nConstitution Hall.\n\nAn experiment which demonstrated \nboth the complete fidelity of repro- \nduction and the effect of auditory \nperspective was performed by two \ntrumpet players. One, in Philadelphia \nat the left of the stage of the Academy \nof Music, and the other in Washing- \nton at the right of the stage of Con- \nstitution Hall but invisible to the \naudience, alternately played a few \nphrases of the same selection. To \nthose in the audience there seemed to \nbe a trumpet player at each side of \nthe stage before them. It was not \nuntil after the stage was lighted that \nthey realized that only one of the \ntrumpet players was there in person. \nThe music of the other was trans- \nmitted from Philadelphia with such \nperfect fidelity and reproduced in \nsuch true perspective that it was im- \npossible to tell that one of the players \nwas absent.\n\nThe auditory perspective effect is \nnot restricted to placing sounds in \ntheir correct positions across the \nstage, but is three dimensional. This \nwas shown by having several sources \nof sound moved around the stage in \nPhiladelphia, not only back and forth \nbut high up in the center of the \nstage as well. The movement of each \nsound was faithfully reproduced by \nthe loud speakers in Washington even \nwhen the sounds were carried high \nabove the level of the stage floor.\n\nTo show the volume range possible \nwith the new equipment, the orches. \ntra played a selection at a constant \nlevel of loudness while the output of \nthe loud speakers was varied from a \nlevel so low that the instruments could \nscarcely be heard, up to a loudness \nalmost great enough to be painful, \nThroughout the whole range, the re- \nproduction was faithful in all re \nspects except the level of loudness; \nthere was no distortion or noise to \nmar the perfection of the reproduc- \ntion, and the wide range in volume \u00a9 \nwas vividly impressed on the audience.\n\nThe effect of limiting the range in \npitch, or frequency, was illustrated \nby employing electric filters to cut \nout one octave at a time\u2014first from \nthe upper end of the range and then \nfrom the lower. The new apparatus \nreproduces faithfully about 9 octaves \nor from 35 to 16,000 cycles, com- \npared to about six for ordinary radio \nreproduction. By this demonstration \nthe audience had the opportunity of \njudging the importance of the com- \nplete range to the full aesthetic appeal \nof music, and of comparing it with the \nmore limited ranges ordinarily heard.\n\nThe technical features of these new \ndevelopments, which were carried on \nas part of the research program of the \nAmerican Telephone and Telegraph \nCompany, were disclosed for the first \ntime by Dr. F. B. Jewett, Vice Presi- \ndent of the American Telephone and \nTelegraph Company in charge of \ndevelopment and research, at a meet- \ning of the National Academy of \nSciences on Tuesday afternoon of \nApril 25. In discussing the future of \nthe new system, Dr. Jewett said:\n\n\u201cAs to the future of the accom- \nplishment shown here today, it is \ndifficult to make any definite predic- \ntion. What we have done is to pro- \nduce pickup microphones, amplifiers,\n\nelectrical filters, transmission lines \nand loud-speaking reproducers so \nperfect that the entire frequency and \nvolume range of the most exacting \norchestral and vocal music can be re- \nproduced at a distance without im- \npairment of quality. We have also \nworked out the arrangements by \nwhich substantially perfect auditory \nperspective is possible. This latter is \nan essential part of the problem if \nrealistic illusion as to the physical \narrangement of the component parts \nof an orchestra is desired.\n\n\u201cWe can place at the disposal of the \nmusical director instrumentalities \nwhich will enable him to produce at a \ndistant point, or at many distant \npoints simultaneously, a completely \nfaithful replica of the tonal effects \nproduced locally in the auditorium \non the stage of which the orchestra is \nperforming. Likewise, portions of \nthis same equipment place at his dis- \nposal the means of very greatly ex- \ntending the range of orchestral repro- \nduction and of making possible ar- \ntistic effects hitherto unattainable.\n\n\u201cWith these instrumentalities avail- \nable, the questions of the manner and \nextent of their use are primarily ques- \ntions for the musician and those in- \nterested in music rather than for the \nphysicist and the engineer. Our job \nhas been to produce a set of tools. \nThe musicians and musical directors, \nand back of them the musical com- \nposers, must determine just how these \ntools can best be used and what they \ncan best produce. By its very nature \nthe ensemble of what we have created \nis primarily of value for musical pro- \nduction or reproduction in_ halls, \ntheatres or auditoriums. In a word, its \nfield of applicability is where a large \nnumber of people might congregate \nfor the common enjoyment of music \nof distinction. In its present form it is\n\n\u2018These new tools offer not only an \nenlarged field of possibility to the \nmusician and the composer for the \nproduction of auditory effects, but \nlikewise a great broadening of the\n\nD. T. Bell of the Laboratories at the power \namplifier panels in Washington\n\naudience which derives pleasure from \nsuch effects. Many people, especially \nin our smaller cities, are now deprived \nof the ability to hear good orchestral \nmusic by the factors of cost and \ndistance, and the element of time in \ngoing to the cities where orchestral \nmusic is normally produced. What we \nas physicists and engineers have done \nis to provide a mechanism for obviat- \ning these factors. Whether the results \njustify our hopes is for others to say.\u201d\n\nonstration before the National Academy of Sciences \non _ Twenty-seventh, 1933, at Washington,\n\nyears of generally reduced com- \nmercial activity, has steadily increased \nits volume of business. Graphs show- \ning miles flown and passengers car- \nried both present a striking contrast \nto a plot of the general index of \nindustrial production. Along with \nthis rapid growth in volume of trans- \nport business has gone an increase in \ncruising speed, and even greater \nspeeds are an immediate prospect. \nRadio aids, by making flying safer \nand times of departure and arrival \nmore certain, have contributed in no \nsmall degree to the general success of \nthe industry. Such aids are, in general, \nof two types: the beacon signals and \nweather reports of the Department of\n\nCommerce, and the radio telephone \nsystems operated by the transport \ncompanies themselves. The growth of \nboth of these types of service has \nparalleled that of the air transport \nindustry itself.\n\nhowever, the transport communica- \ntion picture has changed considerably \nwith the large increase in the number \nof planes equipped for radio telephony. \nThe frequency band available for air- \nplane telephony is strictly limited, \nand the increased demand for chan- \nnels has made it necessary to squeeze \nthe assignments closer together. With \nthe old equipment this has resulted in \ninterference between channels oper- \nated by different transport organiza- \ntions. An imperative need has thus \narisen for receivers of greater selec- \ntivity.\n\nAnother feature which it seemed \nhighly desirable to incorporate in the \nnew apparatus is the ability to change \nthe frequency easily. Radio trans- \nmission conditions at night are dif- \nferent from those during the day so \nthat two frequencies are universally \nemployed: one in the vicinity of five \nmegacycles best adapted to day con-\n\nditions and the other, about three \nmegacycles, best adapted to night. \nThe equipment which has been avail- \nable to the air transport industry \npreviously has not been arranged so \nthat the frequency could be changed \nduring flight. It sometimes happened, \ntherefore, that during transition per- \niods between day and night fre- \nquencies, some of the planes with \nwhich a certain ground station had to\n\ncommunicate would be set for one \nfrequency and others for the other. \nUnder such conditions regular com- \nmunication with airplanes became \ndisrupted and position reports were \nmissed.\n\nFrequent conferences have been \nheld between representatives of the \nlarger transport companies, and the \nWestern Electric Company and engi- \nneers of the Laboratories, and a close \nagreement has been reached regarding \nthe requirements for radio telephone \nequipment for airplanes. As a result a \nnew line of radio telephone equipment \nhas been made available which, al- \nthough embodying many features of \nthe earlier apparatus, has a number of\n\nnovel features and is greatly improved \nin many respects. Notable among \nthese are provisions for changing the \nfrequency while in flight and for \ngreater selectivity in the receiver, the \ntwo problems of most immediate \nconcern. |\n\nThe change from day-time to night- \ntime frequency or vice versa is accom- \nplished by the operation of switches in \nthe receiver and transmitter. These \nare connected mechanically and oper- \nated by the pilot through a single \ncontrol. In planes where the trans- \nmitter and receiver are close to the \npilot\u2019s position, the switches are con- \ntrolled by a pull wire, but for greater \ndistances, a flexible shaft drive is em- \nployed which shifts the switch in both \nreceiver and transmitter at the same \ntime. The connection of this shaft to \nthe base structure of the apparatus is \nshown in Figure 3. This arrangement \npermits the shift between day and \nnight conditions to be made at pre- \nestablished times regardless of where \nthe plane happens to be.\n\nExcept for this frequency shifting \narrangement and certain simplifica- \ntions, the control is similar to that for \nthe earlier equipment. The equipment \nis made ready for operation by two\n\ncontrol switches. When one of these jg \nthrown the two receivers are placed \nin operating condition, and when the \nother is thrown, the transmitter js \nmade ready for operation. In either \ncase, an interphone circuit is available \nbetween pilot and co-pilot. For this \nservice the audio-frequency amplifier \nof the receiver is used to amplify the \nsignals from the microphone. The \ncomplete equipment, including two \nreceivers, a transmitter, and all ac- \ncessories, is shown in Figure 4, where \nis shown also the flexible conduit used \nfor the wiring between the various \npieces of apparatus.\n\ndynamotors have now been assembled \nwith their accessory equipment on a \ndetachable base, which makes instal-\n\nFig. 3\u2014A single flexible shaft drives, through a worm and segment, the frequency \nchanging switch in both transmitter and receiver\n\nFig. 4\u2014The 208A radio telephone equipment. The main pieces of apparatus, from \nleft to right, are: dynamotor power unit, controls, weather-and-beacon receiver, trans- \nmitter, receiver for two-way system\n\nIn the other and newer type, power \nis obtained from a double voltage \nengine-driven unit, shown in Figure 5, \nwhich may be employed as either a \ngenerator or dynamotor at the pilot\u2019s \nvolition. Under normal operation the \nunit is operated through a centrifugal \nclutch as an engine-driven generator \nsupplying both low voltage, for the \nfilament and control circuits, and \nhigh voltage for the plate circuits of \nthe transmitter. There is also sufficient \ncapacity in the low voltage windings \nto keep the airplane storage battery \nin a charged condition. When the \nengine is running below some definite \nlow speed, the clutch disengages and \nthe pilot may pull a control handle \nwhich changes the electrical connec- \ntions to enable it to be operated by \nthe battery as a dynamotor. Under \nthese conditions, and with a fully \ncharged 65 ampere-hour battery, the \nradio equipment may be operated for \ntwo hours with the receiver con- \ntinuously in service and the trans- \nmitter operating on a cycle of one\n\nminute on and five minutes off. With \na smaller\u201435 ampere-hour\u2014bat- \ntery, which is adequate for the new \nequipment, a similar cycle may be \nmaintained for one hour.\n\nThe present airplane equipment in- \ncludes two fixed antennas. One of \nthese is used for the low frequency \nreceiver over which weather reports \nand beacon signals are received, and \nthe other for the high frequency \nchannel\u2014both for transmitting and \nreceiving. A push button on the new \nanti-noise microphone, developed by \nthe Research Department and em- \nployed as part of the new telephone \nequipment, is employed to operate \nrelays in the receiver and transmitter \nwhich connect the antenna to either \nreceiver or transmitter as required \nand make the other circuit changes \nnecessary for the transfer between \ntalk and receive conditions.\n\nConsiderable attention has been \ngiven to making all the various pieces \nof apparatus readily removable for \ninspection, repairs, or replacement. \nAll the major units\u2014the transmitter\n\nand both of the receivers\u2014are pro- \nvided with separable bases which are \npermanently secured to the plane and \nto which the wiring is run. In these \nbases the wiring terminates in re- \nceptacles, and the radio units them- \nselves have plugs which fit in the re- \nceptacles when the units are pushed \ninto place. The base of the power unit \nhas plugs at the ends of short flexible \nconduit connections which allow it \nalso to be readily removed if desired.\n\nAlthough the new equipment pro- \nvides for multiple-frequency opera- \ntion, and offers many other new \nfeatures, it is possible for a transport \noperator to install it with the new \npower supply to weigh, complete, \nabout fifteen per cent less than the \nequipment formerly available. Con-\n\nsiderable savings will also follow from \nthe convenient mountings and wirin \narrangements, and from the smaller \nnumber of units to be installed. \nMaintenance savings can also be ex. \npected, due to the accessibility of ad- \njustment points when the apparatus \nunits have been removed, as they \nreadily can be, to the service shop. \nThe cordial cooperation of the air \ntransport companies, not only in the \ndesign of the new apparatus but in \nthe more than seventy million miles of \nflight of the earlier models, has con- \ntributed notably to the excellence of \nthis radio equipment. It may reason- \nably be expected that it will be an im- \nportant factor in the reliability and \nsafety on which the transport industry \nbasesitsexpectation for futureprogress,\n\nment during the last few years \nhas served to emphasize the need for \nfacilities permitting rapid change of \nthe operating frequency. The large \nincrease in night flying has made \ngeneral the use by each transport \ncompany of at least two frequencies: \none best suited to day conditions and \none, to night. It is apparent that the \ntransition from day to night frequency \nwill result in confusion unless all \nstations on the system, including \nplanes in flight, can change frequency \nsimultaneously. In a new airplane\n\ntransmitter which has been developed, \ntherefore, provision is made for chang- \ning the frequency by operating a \nsimple manual control. This allows \nthe pilot to change from day to night \nfrequency or vice versa at a preestab- \nlished time. No technical skill is \nrequired for this procedure as it in- \nvolves no tuning operations whatever.\n\nBesides this feature, the new trans- \nmitter\u2014known as the 13-A\u2014in- \ncorporates a third frequency channel \nwhich may be selected by the same \ncontrol that changes from day to night \nfrequencies. This arrangement con- \ntributes greatly to safety because all\n\nDepartment of Commerce stations \nkeep constant watch on 3105 ke, \nwhich frequency is not assigned to \nany transport company. By being \nable to transmit on 3105 kc, therefore, \nan airplane pilot can communicate at \nany time with a Department of Com- \nmerce station to ask for weather re- \nports or other information or to \nrequest assistance in emergencies. \nThese government stations reply on \nthe weather broadcast frequency so \nthe pilot can have two way communi- \ncation with them at any time without \nrequiring an additional channel in his \nhigh-frequency receiver. These out- \nstanding improvements, as well as \nothers in the control and maintenance \nfeatures, arise from certain novel \nrefinements both in the electrical \ncircuits and in the mechanical \ndesign.\n\nThe principal circuit features of the \nnew transmitter are shown in the \nsimplified schematic of Figure 1. For \nclearness only one frequency channel \nis shown and the dc circuits are \nomitted. The radio frequency cir- \ncuits consist of a crystal controlled \noscillator, and two stages of amplifica-\n\nFig. 2\u2014A combination of coil and mica \ncondenser forming the antenna coupling \ncircuit is built as a single plug-in unit\n\ntion employing screen grid tubes. The \nuse of these four-element tubes\u2014 \nespecially designed for this service by \nH. E. Mendenhall\u2014eliminates the \ndelicate and troublesome neutralizing \nadjustment, which is very advanta- \ngeous in portable apparatus.\n\nFig. 1\u2014Simplified schematic of transmitter showing only one frequency channel and\n\nIn developing methods and providing \napparatus for the reproduction of sym- \nphonic music with its original quality and \nin true auditory perspective, the com- \nbined efforts of many engineers of Bell \nLaboratories have been required. The \nnecessary telephone repeaters and termi- \nnal equipment were developments of \nH. S. Black and R. W. Chesnut. Loud \nspeakers and microphones were developed \nunder the direction of Dr. E. C. Wente \nand A. L. Thuras. The provision of suit- \nable amplifiers with the necessary equa- \nlizers and volume controls was undertaken \nby E. O. Scriven, R. A. Miller, and A. F. \nPrice. The acoustic and electrical re-\n\nsearches have in part been carried on by \ntests in Philadelphia with the codperation \nof Dr. Stokowski. The conduct of the \ntests has largely been the work of Dr. \nJ. C. Steinberg and W. B. Snow of Bell \nLaboratories. The engineers of the Ameri- \ncan Telephone and Telegraph Company \nsolved the several problems of trans- \nmitting over cable circuits ranges of \nvolume and pitch never before attempted. \nFor their solution H. A. Affel and R. G. \nMcCurdy were largely responsible. \n* * *\n\nDr. Fewett holds the diaphragm of the low-frequency loud speaker, while Dr. Fletcher \nshows where the driving coil fits on the diaphragm\n\nApril twelfth. Seated in the auditorium \nand facing the stage hidden by its curtain, \nmusic critics and press representatives \nheard selections played by the Philadel- \nphia Symphony Orchestra under the di- \nrection of Dr. Leopold Stokowski, and \nreproduced by loud speakers from the \nempty stage. Although the orchestra \nmembers were playing in the foyer, the \nmusic sounded as if they were in their \nregular places on the stage. The capa- \nbilities of the new apparatus which made \npossible this remarkable illusion were \ndemonstrated by Dr. Harvey Fletcher \nby a set of experiments similar to those \ngiven in Washington and described in the \naccompanying article.\n\nThe usual artist\u2019s palette consists of a \ndozen or more pigments, with the result \nthat the number of ways of making de- \nsired colors by mixture is very large and \nquite unamenable tosystemization. Learn- \ning how to use these numerous pigments \nis a matter of long experience. The simpli- \nfication indicated by the three-color prin- \nciple has been retarded in realization\n\nlargely owing to the mistaken, but widely \nheld, belief that the primary pigment \ncolors are red, yellow and blue. Actually \nthe pigment primaries, which act by sub- \ntraction or absorption of light from white, \nshould be complementary in hue to the \nred, green and blue which are the pri- \nmaries for mixing light by addition. Those \ncolors are: a minus red, (spectrum minus \nred) or turquoise; a minus green, or \ncrimson; and a minus blue, or yellow, \neach having wide overlapping spectral re- \nflection bands. Pigments of these colors, \nof proper spectral characteristics, are \ncapable of mixing in pairs to make red, \ngreen and blue, and all three together to \nmake black. When mixed with white all \nvariations of saturation and hue are ob- \ntained. |\n\nThe practical problem consists in pro- \ncuring pigments possessing the indicated \nspectral reflectivities, and having satis- \nfactory chemical properties, such as free- \ndom from reaction with the oil or other \nmedium, and satisfactory permanence. \nDue to the very great advances which \nhave been made in the dye industry to \nmeet recent demands for permanent \ncolors for automobiles and outdoor signs, \nit is now possible to select pigments nearly \nenough meeting the scientific require- \nments to test the practicability of the \nprinciple. This has been done with success, \nand Dr. Ives exhibited pictures so painted, \nin connection with the presentation of his \npaper.\n\nThe great advantage of a three-color \npalette is its simplicity and freedom from \nambiguity. Only three colors (and white) \nare needed in place of the large number \nordinarily used by artists. All colors can \nbe obtained from these, in just one way, \nwhich is indicated by a simple and easily \ngrasped theory. The perfection and adop- \ntion of a three-color palette will open the \nway to the teaching of color to artists on \na scientific instead of an empirical basis.\n\nOn MarcH 20 Dr. G. A. Campbell of the \nAmerican Telephone and Telegraph Com- \npany spoke before the Colloquium on\n\nSystems of Units and Their Unification. Dr. \nCampbell has recently concerned himself \nwith the familiar annoyance of the multiple \nsystems of electrical units, and pointed \nout in his address the road to a solution.\n\nOn apriv 3 Dr. I. I. Rabi of Columbia \nUniversity gave an address on Dvirect \nMeasurement of Nuclear Angular Mo- \nmentum. During a stay at Hamburg some \nyears ago, Dr. Rabi collaborated with Pro- \nfessor Stern (who addressed the Collo- \nquium two years ago) in developing the \nmethods of producing and detecting nar- \nrow straight beams of neutral atoms and \nmolecules and of sending them across \nnon-uniform magnetic fields in order to \ndetermine the magnetic moments of the \nparticles. In previous experiments the \nparticles of these beams have the Max- \nwellian distribution, in velocity corre- \nsponding to the temperature of the furnace \nwhence they come. As a result, the several \npencils into which such a beam is split by \na non-uniform magnetic field are broader \nand hazier than is desirable. Dr. Rabi per- \nfected a technique for sending a beam \nthrough two fields in succession. After \ngoing through the first field, one of the \nbroadened pencils is intercepted by a \nscreen with a narrow slit which allows \nonly particles of a narrow range of \nspeeds to pass so that it functions as a \nvelocity-filter. The beam thus filtered out \nis sent through a second and much \nweaker non-uniform field, and is sub- \ndivided into several pencils much finer \nand sharper than had earlier been ob- \ntained. The manner of subdivision gives \ninformation about the nuclear spin of the \nkind of atom or molecule in question. As \nestimates of the spin can also be made \nfrom features of band-spectra and from \nhyperfine structure of line spectra, inter- \nesting comparisons are possible. Dr. Rabi \ndescribed details of the method and \nfurther inferences from the data.\n\nMeet1nG aT the Deal Laboratories on \nApril 6, the Radio Colloquium heard Mr. \nR. C. Mathes speak on Volume Control \nCircuits.\n\nSEVERAL members of the Laboratories \ntook an active part in the scientific con. \nference and dinner held at the Masgsa- \nchusetts Institute of Technology on \nMarch 29 to celebrate the eightieth birth- \nday of Elihu Thomson, distinguished engi- \nneer and inventor. The committee in \ncharge of arrangements included Dr, \nJewett and Mr. Charlesworth. Among the \nspeakers at the conference in the after. \nnoon was Dr. K. K. Darrow, who dis- \ncussed the trends of research, and at the \ndinner in the evening Mr. Charlesworth, \nas President of the A.I.E.E., spoke for the \nengineering societies.\n\nTo the Review of Scientific Instruments \nK. K. Darrow has contributed an account \nof Neutrons in February and one of New \nAchievements in Transmutation in March. \nA. W. Kishpaugh and R. E. Coram have \nwritten on Low Power Radio Transmitters\n\nfor Broadcasting in the February issue of \nthe Proceedings of the Institute of Radio \nEngineers. A paper by F. A. Polkinghorn \non Short-Wave Transoceanic Telephone \nReceiving Equipment, which first appeared \nin the Proceedings of the Radio Club of \nAmerica, has been reprinted in Radio \nEngineering for February. The same \nmonth, in the Journal of the Society of \nMotion Picture Engineers, E. F. Kings- \nbury reviews a book on Photocells and \nTheir Applications by V. K. Zworykin \nand E. D. Wilson. In the March issue of \nthe Proceedings of the Institute of Radio \nEngineers appear Some Results of a Study \nof Ultra-Short-Wave Transmission Phe- \nnomena by C. R. Englund, A. B. Craw- \nford, and W. W. Mumford, and an article \non Ultra-Short-W ave Propagation by J. C. \nSchelleng, C. R. Burrows and E. B. \nFerrell. The Journal of the Optical Society \nfor March contains H. E. Ives and T. C. \nFry\u2019s article on Standing Light Waves; \nRepetition of an Experiment by Wiener \nUsing a Photoelectric Probe Surface. \nMarch also saw the publication of Pu/p\u2014 \nThe New Cable Insulation by L. S. Ford in\n\nWire, an abstract of H. A. Frederick and \nH. C. Harrison\u2019s paper on Vertically Cut \nSound Records in Electrical Engineering, \nand W. H. Brattain and J. A. Becker\u2019s \naccount of Thermionic and Adsorption \nCharacteristics of Thorium on Tungsten \nin the Physical Review.\n\nIn addition to the articles mentioned \nin last month\u2019s issue of the Recorp, \nseveral others appeared in January publi- \ncations. The Journal of the Acoustical \nSociety of America contained an article \nby R. R. Riesz on The Relationship Be- \ntween Loudness and the Minimum Per- \nceptible Increment of Intensity, and a re- \nview by R. L. Wegel of A. L. Kimball\u2019s \nbook, Vibration Prevention in Engineering. \nJohn Mills\u2019 paper on Technical Exposition \nfor the General Reader has been printed in \nthe Journal of Engineering Education, \nand his description of The Bell System \nExhibit at the \u201cCentury of Progress\u201d Ex- \nposition appears in the Bell Telephone \nQuarterly. The recently issued Annals of \nOtology, Rhinology, and Laryngology for \nSeptember, 1932, contains Harvey\n\nFletcher\u2019s answer to the question, Can We \nScientifically Advise Patients as to the\n\nEffectiveness of Hearing Aids? and R. L. \nWegel\u2019s account of Physical Data and \nPhysiology of Excitation of the Auditory \nNerve.\n\nIn The Engineer's Manual of English, \nby W. O. Sypherd and Sharon Brown, \nrecently published by Scott, Foresman \nand Company, The Magic of Communica- \ntion by John Mills is quoted to furnish \n\u201can admirable example of effective non- \ntechnical English\u2019; and his address, Some \nUniversal Principles of Communication \nis reprinted as a model for technical \npresentation. In the same text book \nthe Western Electric instruction bulle- \ntin on the No. 13-A Oscillator is cited \nas an example of good instruction \nbulletins.\n\nTHE ANNUAL spring exhibition of the \nTelephone Camera Club of Manhattan \nwill be on display in the club rooms at 178 \nFulton Street from May 15 to 26, in- \nclusive. The photographs in this exhibi- \ntion are all the work of members of the \nclub, and several of the exhibitors are \nmembers of the Laboratories.\n\nG. K. Situ discussed problems arising \nin connection with wiper cords on step-by- \nstep switches with New York Telephone \nCompany engineers at Albany.\n\nR. H. Miter and F. B. Biake visited \nPhiladelphia to discuss a new panel \ntandem project with engineers of the \nBell Telephone Company of Pennsylvania \nand the Western Electric Company.\n\nG. A. Benson visited Wilkes-Barre to \naid in the introduction of a new type of \ntoll ticket.\n\nC. H. BrpweE tu inspected one of the \ninitial installations of No. 16 toll test \nboard at Bristol, Connecticut.\n\nON THE ELEVENTH of last month \nAdolph Bregartner completed thirty-five \nyears of continuous service with the \nWestern Electric Company and the Lab-\n\noratories. Mr. Bregartner joined the \nWestern Electric Company in New York \nin 1898, and after a few months in the \nmachine shop, entered the group handling \nthe assembly and adjustment of relays.\n\nLater he worked on special apparatus, \nsuch as the early equipment for train dis. \npatching, and then became associated \nwith the semi-mechanical central office \ndevelopment. For nearly four years he \ntook part in the early installations of this \nequipment, in the Mulberry, Market, \nand Branch Brook offices of Newark, and \nsince their completion he has been a \nmember of the staff of the dial circuit \nlaboratory.\n\nW. L. Berrs visited Washington during \nMarch to discuss several new develop- \nments with members of the Bureau of \nEngineering of the Navy Department.\n\nF.R. McMurry, incompany withE. F. \nWatson of the A. T. & T. Company, \nvisited the Teletype Corporation in con- \nnection with the manufacture of tele- \ntypewriter apparatus.\n\nJ. R. Barpstey and C. C. Hipxins \nvisited Huntington, L. I. to inspect a new \nfinish on underground loading coil cases.\n\nW. E. Kau visited Washington in con- \nnection with filters for high quality \nprogram circuits.\n\nR. W. DE Monte and D. E. Trucksgss \nvisited Kearny for a discussion of battery \ncharging rectifier equipment.\n\nJ. M. Witson, W. A. Evans, R. Burns \nand K. G. CouTLee attended meetings of \nCommittee D-g, on Electrical Insulating \nMaterials, of the American Society for \nTesting Materials held at the Hotel \nGramatan, Bronxville.\n\nRoy E. Coram completed twenty \nyears of service in the Bell System on \nthe seventeenth of last month.\n\nT. E. SHea and H. C. Curt visited \nNewport News and Washington in con- \nnection with Naval equipment problems.\n\nR. M. Pease set up and operated a \npublic address system used during the \ndinner given to Dr. Elihu Thomson at \nMassachusetts Institute of Technology. \nThe speakers used lapel microphones con- \nnected to this system.\n\nR. A. Mitier and A. F. Price visited \nWashington in connection with the trans- \nmission and reproduction of the program \nof the Philadelphia Symphony Orchestra. \nD. T. Bell has spent the last month in \nWashington and Philadelphia on the same \nproject.\n\nTuomas W. Criarke, head of the Mer- \nchandise Department of the Laboratories, \ndied on April 8. Mr. Clarke joined the \nWestern Electric Company in 1906, and \nafter broad experience in the commercial \nactivities of the Engineering Department \nand the Laboratories, took charge of the \nbranches of our General Service Depart- \nment devoted to storing, shipping, receiv-\n\nOsvatp E. Rasmussen completed \ntwenty years of service in the Bell \nSystem on the twenty-first of last month.\n\nDr. J. S. Waterman, A. F. WEBER \nand J. S. Epwarps attended the Fourth \nAnnual Greater New York Safety Con- \nference held at the Hotel Pennsylvania on \nMarch 1 and 2. W. W. Schormann acted \nas a member of the Committee on Ar- \nrangements for this conference.\n\nF. D. Leamer talked on February 10 \nbefore the Graduate Physics Seminar of \nNew York University at Washington \nSquare College on Diffraction of X-Rays \nin Liquids.\n\nD. G. Btatrner visited Newport \nNews, Va. in connection with loud \nspeaker equipment for U. S. S. Ranger.\n\nR. R. Witirams, R. M. Burns, A. R. \nKemp, J. H. Incmanson, A. E. Scuuu \nand B. L. CiarKkeE attended the meetings \nof the American Chemical Society in \nWashington, D. C., the week of March 27. \nWhile there Mr. Burns and C. L. Hippen- \nsteel presented a paper at the Bureau of \nStandards Soil Corrosion Conference.\n\nA. L. Samuet talked before a meeting \nof the Radio Club of Brooklyn on the de- \nsign of transmitting tubes for use at \nultra-high frequencies, and on the prob- \nlems encountered at these frequencies. \nHe stressed the fact that this large and \nunexplored field was open to amateurs \nand urged them to work in it as they did \nearlier in developing short wave radio on \nlower frequencies. Several tubes were \nexhibited for use in the wave-length \nrange from 12 centimeters to 3 meters.\n\nBancroft Gherardi and Herbert E. Ives \nAre Elected Members of the \nNational Academy of Sciences\n\nBancroft Gherardi, Vice President and Chief Engineer \nof the American Telephone and Telegraph Company, and \nDr. Herbert E. Ives, Electro-Optical Research Director of \nthese Laboratories, were elected to membership in the \nNational Academy of Sciences at its annual meeting in \nWashington on the evening of April 25. At the same meet- \ning Dr. fewett presented a paper on the new method of \nmusic reproduction in auditory perspective, demonstrated \nto the Academy two days later and described elsewhere in \nthis issue of the REcorv.\n\nThe National Academy of Sciences was incorporated in \n1863, by act of Congress approved by President Abraham \nLincoln. At that time its membership was limited to fifty. \nSeven years later this restriction was removed, but the \nmembership has been kept small, and election to it remains \na signal honor. No more than fifteen members are ad- \nmitted annually, and the Academy numbers less than \nthree hundred. Dr. Fewett and Dr. C. F. Davisson are \nother members of the Bell System who have been so honored.\n\nFig. 3\u2014The 13A radio telephone trans- \nmitter with cover removed showing one of \nthe plug-in transformer units being inserted\n\nthe oscillator and amplifier, and be- \ntween the two amplifier stages. These \nare radio frequency transformers \nwhich in conjunction with the tube \nand wiring capacities (shown on the \ndiagram as dotted condensers) form \nband pass filters. The two trans- \nformers for each of the three frequency \nchannels are built as a single plug-in\n\nation night frequencies and another, \nthe day frequencies. Transformers \nsuited to other bands than those \nused for aircraft communication are \nalso available. R. C. Newhouse was \nlargely responsible for their develop- \nment.\n\nThe crystals are also arranged in \nplug-in units, and may be seen behind \nthe transformers in the photograph. \nThe crystal is connected in the grid \ncircuit of the oscillator tube, and \noperates at one-half of the desired \noutput frequency. The primary of \nthe transformer coupling the oscil- \nlator to the first amplifier presents a \nhigh inductive reactance to the plate \nof the oscillator at the crystal fre- \nquency, which is necessary to produce \noscillations. The second harmonic of \nthe crystal frequency is passed by this \ntransformer and drives the first am- \nplifier at output frequency. Similarly \nthe other transformer passes the out- \nput frequency and drives the second \namplifier.\n\nCoupling between the second ampli- \nfier and the antenna is secured by a \nsimple tuned circuit which must be \nadjusted in the field to tune various \nantennas of widely different char- \nacteristics. There are also three of \nthese circuits which, consisting of a \ncoil and a fixed mica condenser, are \nbuilt in the form of a plug-in unit as\n\nshown in Figure 2 and in the front of \nthe transmitter in Figure 3. A con- \ntinuous winding of bare tinned copper \nis wound on an isolantite form, and \nclips on slide rods can be set on any \nturn. When clamped in place they \nmake good contact directly with the \nwinding itself. Fine tuning is done by \na small inductance wound on the in- \nside of the coil form at the low po- \ntential end of the coil. This contact \nis adjusted with a screw-driver which \nmay be inserted through a small door \nin the front of the transmitter.\n\nThree-point switches are employed \nto select the desired crystal, pair of \ninterstage transformers, and antenna \ncoupling units, and all the switches \nare mechanically connected together \nand operated by a single control. An \ninterlocking switch is also connected \nto the same control which prevents \napplication of high voltage to the \ntransmitter except when the switches \nare centered on one or another of the \nthree channels. This switch also \nlights a lamp in the control unit near \nthe pilot when the switches are off \nposition.\n\nA novel system of modulation is \nused in the new transmitter which \npermits deep modulation of the fifty \nwatt carrier with only about one watt \nof audio-frequency power. This fea- \nture is directly responsible for the very \nsatisfactory overall efficiency. The \naudio amplifier\u2014like the oscillator a \n205D tube\u2014is employed to modulate \nthe screen bias of both of the radio \nfrequency amplifier stages. The over- \nall characteristic of these two modu- \nlating amplifiers in cascade is nearly \nlinear up to substantially complete \nmodulation. With maximum modu- \nlation, the largest harmonic in the \nrectified output is less than 10% of the \nfundamental. The overall audio-fre- \nquency characteristic of the trans-\n\nFig. 6\u2014 The new ballast lamp, employing a \ntwo-contact Ediswan base, is of unusually \nsmall size\n\nmitter is shown in Figure 4. The low \nfrequencies are purposely attenuated \nby a series condenser in the input \ncircuit to reduce the amplitude of \nairplane noise picked up by the micro- \nphone.\n\nA schematic circuit of the complete \ntransmitter is shown in Figure 5. A \nthermocouple in the radio-frequency \nground circuit is employed to operate \nan antenna ammeter near the pilot, \nwho can therefore note whether the \ncurrent is normal and whether it \nmodulates when he speaks into the \nmicrophone\u2014a_ positive assurance \nthat his transmitting equipment is \nworking properly. All grid and plate \ncircuits are equipped with jacks (not \nshown on the diagram) accessible \nthrough a door on the front of the \ntransmitter, which facilitate the loca- \ntion of trouble and routine checking \nby the maintenance men. An antenna \nrelay, employed to switch the antenna\n\nbetween the transmitter and_ re- \nceiver, is made part of the transmitter \nto reduce the number of component \nparts of the system. The development \nof miniature ballast lamps by the \ngroup under J. R. Wilson has made \nit possible to use a lamp in each fila- \nment branch. The small size of these\n\nFig. 7\u2014Separable transmitter mounting \nwhich allows the transmitter to be readily \nremoved or replaced as desired\n\nOperation of the equipment re- \nquires the transmitter to stop im- \nmediately when the microphone but- \nton is released and to produce no \nnoise in an adjacent receiver of very \nhigh gain. This was greatly facili- \ntated by the development, in coopera- \ntion with V. L. Ronci, of a high \nvacuum relay which opens the 1050 \nvolt plate supply. This relay is very \nsmall and light and is entirely safe to \nuse where gasoline fumes may be \npresent.\n\nIn the mechanical design of the \ntransmitter, for which P. S. March \nwas responsible, several novel features \nare incorporated. A separate mount- \ning is designed for permanent in- \nstallation in the airplane. An upright \nsection at the rear of the mounting,\n\nshown in Figure 7, carries a multiple \ncontact jack terminating all connec. \ntions to the transmitter except the \nantenna, and a coupling to connect to \nthe switches that select the frequency \nchannel. All wiring is run to this \nmounting in either flexible or rigid \nconduit. A lever projecting from the \nfront operates a cam which, when the \ntransmitter is placed on the mounting, \nslides it back into contact with the \nreceptacle and the frequency changing \nswitch.\n\nThe entire structure of the trans- \nmitter itself is fabricated from sheet \nduralumin, and not only supports \nthe apparatus but provides the \nnecessary shielding. It is divided in- \nto two irregularly shaped compart- \nments by interior partitions. Part \nof the outer casing is perforated and \nthe space between the inner par- \ntition and the perforated section of \nthe outer case forms a ventilated com- \npartment into which is placed only \nthe heat dissipating apparatus, such \nas the vacuum tubes, ballast lamps, \nresistances, and crystals. All other \napparatus and wiring is completely \nenclosed for protection against dust \nand moisture. A new type of vitreous \nenamel resistor with rear connections \nwas developed to keep the wiring out \nof the ventilated compartment.\n\nThe 13A radio transmitter is an \nexcellent example of the great im- \nprovement that can be made in \napparatus by a careful study of the \nmost desirable form of the various \ncomponent parts and their relative \nlocations based on an intimate knowl- \nedge of service conditions. Even \nwithout a radical change in funda- \nmental performance, the new trans- \nmitter is so superior to the old in \nmany respects that it is expected to \nreceive an enthusiastic reception from \nair transport operators.\n\nratus indicated, among other \nthings, that there was need for greater \nselectivity in the receiver, and that \nthe changes between night and day \nfrequencies should be easy to make \nduring a flight. Because of the \nlimited width of the frequency band \navailable for aviation telephone com- \nmunication and of the large number \nof operating companies desiring fre- \nquency allocations, it has been neces- \nsary to assign channels with a fre- \nquency separation of only about one- \ntenth per cent. Since this is only one \nor two tenths of the separation of \nbroadcast channels, the difficulty in \nselecting the channel desired without \ninterference from the adjacent ones is \nevident. The requirement of being \nable to change frequencies while in \nflight arises because the ground sta-\n\ntion must be able to be in continual \ncommunication with a group of planes, \nsome of which may be just beginning \na flight and others about to terminate \none. At transition periods between \nday and night conditions, a plane \nabout to end a flight may be set for \none frequency and a plane beginning \na flight, at another. Without the \nability to change frequency at a \ndefinite time while in the air, ready \ncommunication with the ground neces- \nsarily becomes handicapped.\n\nIn the development of the Western \nElectric 12A receiver, which is a part \nof the new aviation radio equipment, \nthese two requirements have been \nfully and satisfactorily met. Certain \nother improvements which a study of \npast experience indicated to be de- \nsirable have also been made. In spite \nof these many improvements, the new \nreceiver will weigh no more than the\n\nA schematic of the receiver is shown \nin Figure I. To obtain the required \ndegree of selectivity and sensitivity, \na superheterodyne circuit 1s employed. \nFrom left to right in the diagram, \nthere is one stage of tuned radio- \nfrequency amplification, a first de- \ntector or modulator, three stages of \nintermediate frequency amplification \nat 385 kc, a detector and automatic \nvolume control tube, and one stage \nof audio frequency amplification. A \nseparate tuned circuit for each fre- \nquency is employed for the radio \nfrequency stage and for the oscillator. \nOperation of a shifting mechanism \nselects the proper circuits for the \nfrequency desired, the circuits having \nbeen properly tuned while the plane \nwas on the ground.\n\nIn any radio receiver the usable \nsensitivity is limited by the tube and \ncircuit noises. When this limit has \nbeen reached, sensitivity to still \nweaker signals is obtainable only by \nincreasing the voltage input. For a \ngiven field strength, \nthe voltage induced in \na given antenna is \nfixed, but the voltage \nacross a tuned circuit \nin series with the an- \ntenna can be much \ngreater. Antennas or- \ndinarily used for air- \nplanes have a com- \nparatively low resist- \nance, and so lend \nthemselves to the series \ntuning which is em- \nployed in this receiver \nwith excellent effect.\n\nthe frequency of the beating oscillator, \nthus insuring the correct frequency for \nsatisfactory operation under all condi- \ntions and without attention on the part \nof the operator. Two oscillators are \nprovided, and the one required is select- \ned by the operation of the same control \nthat selects the proper tuned circuits.\n\nUnder some operating conditions \nthe high degree of frequency stability \nand freedom from attention on the \npart of the operator provided by the \nquartz plates may not be required. \nThe 12A receiver has therefore been \ndesigned so that in such cases a tuning \nunit, either the 8A or 8B, may be used \nin place of the quartz plates. These \nare plug-in tuned circuits whose con- \nstants are much more stable than are \nthose of ordinary tuned circuits. The \ncoil is wound on an isolantite form, \nand the adjustable condenser has a \nthermostatic metal plate to reduce \nvariations due to temperature changes. \nThe units are mounted in moisture \nproof aluminum cans to avoid changes \nin the oscillator frequency caused by \nchanges in humidity.\n\nFig. 2\u2014 Tuned transformers in cylindrical cans are placed \nadjacent to the tubes with which they are associated\n\nThese precautions, together with \nthe careful design of the oscillator \ncircuit, minimize frequency variations \ncaused by changes in the supply \nvoltage, and provide a high degree of \nfrequency stability. Small variations \ndo occur, however, and a vernier con- \ndenser is required to compensate for \nthe frequency drift. To avoid the use \nof a mechanical drive for the vernier \nwhen the receiver is controlled from a \nremote point, the vernier condenser is \nlocated at the operating point and \nconnected to the set through a shielded \nradio-frequency transmission line of \nlow impedance.\n\nTo obtain the high degree of selec- \ntivity required, three intermediate- \nfrequency amplifier tubes with four \ndouble tuned transformers are em- \nployed. Each such double tuned trans- \nformer comprises a filter section and, \nmounted in an aluminum shield, is \nplaced next to the amplifier tube, as \nmay be seen in Figure 2. The fourth \ntuned transformer is connected to the \ndetector which operates as a two- \nelement rectifier and not only supplies \nsignal output, but furnishes voltage\n\nFig. 3\u2014The 12A receiver showing door on front and the \nshock-proof base on which it mounts\n\nAll but the audio frequency tube \nare the recently developed Western \nElectric 283A tubes, which have \nvariable mu and high gain. The de. \ntector and oscillator are operated as \ntwo and three element tubes re. \nspectively by connecting certain elec- \ntrodes together. By this arrangement \nthe number of different types of tubes \nis reduced. For the audio frequency \nstage a 285A tube is employed. This is \na pentode capable of delivering a \nsufficiently high output for the satis- \nfactory operation of several pairs of \nheadphones. When the receiver is \nused as part of an airplane system, \nthis tube also acts as the amplifier for \nthe side tone circuit when the trans- \nmitter is operated. A relay in the \nreceiver makes the necessary change \nin connections when the button on \nthe microphone is pushed.\n\nAutomatic gain control, widely \nused with present-day broadcast re- \nceivers, is even more important with \nairplane receivers, since in addition to \nthe usual fading due to variation in \nthe transmission path, \nthere is a large change \nin signal strength due \nto the travel of the \nplane. With the sys- \ntem employed in the \n12A receiver there is a \nbarely noticeable \nchange in audio output \nwith a variation in \nsignal input of 10,000 \nto 1. Even with this \nwide range in auto- \nmatic control, how- \never, a certain amount \nof manual control is \ndesirable. An input in \nexcess of half a volt is \ntoo great to be properly\n\nhandled by the automatic control, and \nsince voltages of this magnitude may \nbe applied when the plane is flying \nclose to the transmitter, a manual \ncontrol is provided near the operator\u2019s \nposition, where it may be adjusted as \nrequired. Under normal conditions no \nadjustment is necessary during flight. \nA variable level control, also, is pro- \nvided to allow the operator to adjust \nthe headset volume to a comfortable \nvalue.\n\nThe power required for the heaters \nof the vacuum tubes is 3.2 amperes at \n12 volts. A ballast lamp in the heater \nsupply circuit provides adequate regu- \nlation for applied voltages from 11.5 \nto 14.5 volts. When the quartz plates \nare employed for frequency control, \nan additional intermittent drain of \n2.4 amperes is required at the same \nvoltage. For the plates and screens \nsome 40 milliamperes is required at \n200 volts, which is furnished by a \nsmall dynamotor operated from the \nbattery.\n\nTo secure rigidity and still allow \neasy access to the various parts of the \ncircuit, the apparatus is mounted on a \ndished aluminum chassis, as may be \nseen in Figure 2. The radio-frequency \ntuning coils, the intermediate fre- \nquency filters, the quartz crystal \nfrequency controls, the filter system \nfor the power supply, the various \nrelays, and all vacuum tubes are \nmounted on the upper or flush surface \nof this chassis, while the radio-fre- \nquency tuning condensers, the high \nfrequency choke coils, and the asso- \nciated by-pass condensers are mounted \nunderneath on the dished side of the \nchassis. An aluminum box surrounds \nthe chassis and apparatus to provide \nmechanical protection and overall \nshielding. A removable top gives ac- \ncess to the tubes and frequency con- \ntrols, and a small hinged door on the\n\nfront gives access to the antenna \ntuning condensers and the indicator \nlamps of the crystal heater, as shown \nin Figure 3.\n\nThe complete receiver is placed on \na base which has rubber shock proof- \ning to protect the receiver from vibra- \ntion normally found in an airplane. \nThis mounting is permanently in- \nstalled in the plane and to it is run \nthe power supply cable, the leads of \nwhich terminate in a multicontact re- \nceptacle to which a plug on the re- \nceiver makes contact when the re- \nceiver is placed in the mounting. The \nfrequency changing mechanism is also \npart of the mounting and connects \nto the receiver through a coupling. \nThis arrangement permits the receiver \nto be readily removed for repair or \nreplacement without requiring any\n\nOne of the outstanding charac- \nteristics of this receiver is its high \nvalue of selectivity. The response \nfrom an interfering signal only ten \nkilocycles from the desired one is \nabout 1/1000 of that due to the de- \nsired signal. A selectivity curve is \nshown in Figure 4. Although the re- \nceivers used for this service at the \nground stations have similar selec- \ntivity, it far surpasses anything pre- \nviously attained in airplane sets.\n\nThe sensitivity obtained in the \nthree stages of intermediate-frequency\n\namplification and one of radio-fre. \nquency, is very high. An i input of one \nmicrovolt at the antenna gives an \noutput of over twelve milliwatts, \nwhich is more than _ sufficient io \nheadphone reception. Such high sen- \nsitivity is not required for normal \noperation, but it insures a sufficient \nreserve of amplification to give satis. \nfactory reception under abnormal con- \nditions. The outstanding performance \nof this receiver, together with its sim- \nplicity of operation, should be of con- \nsiderable value in increasing the re. \nliability of aviation communication.\n\nOn March 20 the telephones of Costa Rica were tied to the \nBell System by a radio link between the American Tele- \nphone and Telegraph Company\u2019s new station at Miami \nand the station at Cartago, near San \u2018fose, of the Interna- \ntional Radio Company of Costa Rica.\n\nOn March 29 the Bell System\u2019s radio stations in Cali- \nfornia, which have been operating on the link to the \nHawaiian Islands, undertook communication with the \nPhilippine Islands as well. Radio facilities in the Philip- \npines are provided by the Radio Corporation of America, \nwhose stations tie in with the wire lines of the Philippine \nLong Distance Telephone Company.\n\nOn April 7 the cities of Ferusalem, Haifa and Faffa \nwere placed within reach of American telephones by ar- \nrangements for connecting the regular transatlantic radio- \ntelephone circuits with a short-wave channel between \nLondon and Cairo, Egypt, and thus with land wire\n\nA three-minute conversation between New York and \nPalestine costs $37.50, and between New York and San \nFose, Costa Rica, $27. A similar conversation between \nSan Francisco and Manila costs $30.\n\nthe synthesis on a commercial \nscale of several materials which were \nformerly obtainable only from natural \nsources. As the limit of possible \npressures has been raised, many in- \nvestigators have attempted to imitate \ngeological processes, including those \nby which coal is formed. Constituting \nas it does the best material yet found \nfor the preparation of transmitter \ncarbon, the possibility of discovering \nand reproducing Nature\u2019s method of \nmanufacturing anthracite is alluring \nto the telephone chemist.\n\nCurrent theories of coal formation \nhave already been summarized in the \nRecorp*. Past attempts to reproduce \nthis procedure have been at the hands \nof men primarily interested in check- \ning these theories, in improving their \nunderstanding of the formation of \nbituminous coals, or in the manu- \nfacture of oils from coal and hydrogen. \nTheir reports of the formation of \nanthracite-like substances by the ap- \nplication of heat and pressure to vari- \nous starting materials gave encourage- \nment to these Laboratories to extend \nthe range of investigation, with the \nproduction of anthracite-like coals \nmore definitely in mind.\n\nThe most generally accepted start- \ning material is vegetation high in \ncellulose content but also containing \nlignin, such as the ordinary woods. \nThe lignin which constitutes the\n\nbinder in such vegetation may be im- \nportant in forming a binder in the \nultimate coal, but vegetation in which \nthe lignin content is high probably \nproduces the brown coals rather than \nanthracite. In the formation of an- \nthracite and other high rank coals \nsome materials other than lignin have \nbeen important. These are supposed \nto be the products resulting from the \ndecomposition of the cellulosic con- \nstituents of the original vegetation \neither by the action of bacteria or\n\nFig. 1\u2014Closing the autoclave in which the \nraw materials for artificial anthracite were \npretreated at low temperatures\n\nyeasts or by the prolonged influence \nof temperature and pressure. Known \nto be effective in the decomposition of \nvegetation, certain types of bacteria \nhave probably been important in the \ninitial chemical changes occurring in \nthe formation of coals. However it is \npossible in the laboratory to bring \nabout similar changes by the effect of \ntemperature and pressure alone, and \nat a great saving of time.\n\nWood begins to decompose at tem- \nperatures a few degrees above 100\u00b0 \nCentigrade. As the temperature rises, \nthe decomposition increases, and at \nabout 300\u00b0 C. a reaction takes place \naccompanied by the evolution of heat \nand of large quantities of gases and \nliquids, chiefly water vapor, oxides of \ncarbon, methane and tar when no added \npressure is applied. At 400\u00b0 C. under \natmospheric pressure the decomposi- \ntion is complete, and the solid residue \nof charcoal is nearly pure carbon. \nApplying pressure to this charcoal \nfails to produce anything resembling \nanthracite, at least at the tempera- \ntures used in this investigation, prob- \nably because the binding materials \nhave been destroyed.\n\nWhen the same progressive heating \nis carried out in a sealed tube, the re- \naction products build up a consider- \nable pressure, the carbonization is less \nnearly complete, and the proportion \nof solid and liquid to gaseous products \nis higher. The residual peat-like solid, \nof rather low carbon content, is \nprobably very similar to that formed \nat an early stage in the natural con- \nversion of vegetation to coal. It was \ntherefore decided to attempt the syn- \nthesis of anthracite by pretreating the \nraw material so as to convert it into \nsomething resembling peat, and then \nsubject this peat to higher tem- \nperatures and pressures.\n\nbirch wood, cotton cloth, sugar, and \njute fiber of high lignin content. For \npretreatment the material was placed \nin a special electrically heated steel \nautoclave (Figure 1), along with vary- \ning quantities of water. The water \nadds somewhat to the pressure de- \nveloped, prevents local heating, and \nat elevated temperature and pressure \nprovides a_ slightly acid medium \nwhich has been suggested as having \na catalytic effect on the carboniza- \ntion. Pretreatments of different \nsamples have covered the range of \ntemperatures from 180\u00b0 C. to 300\u00b0C, \nand of pressures from 800 to 10,000 \npounds per square inch.\n\nAt temperatures up to 230\u00b0 C. the \nproducts of this pretreatment were not \nat all like coal but quite like peat: \nbrown in color, still showing much of \nthe original structure, readily pow- \ndered, and with a hydrogen content \nof about six per cent. Neither these \nnor the products of pretreatment at \nhigher temperature could be converted \nto anthracite-like coal at the lower \ntemperatures of final treatment. The \ngases produced during pretreatment \nconsisted chiefly of carbon dioxide, \nmixed with amounts of carbon mon- \noxide and methane which increased \nwith the treating temperature. Only \nsmall amounts of tar were produced, \nfar less than by heating at atmospheric \npressure.\n\nFor final treatment, charges of 100 \nto 200 grams of the pretreated ma- \nterials were placed between two plun- \ngers in a heavy steel cylinder, heated \nelectrically, and subjected to pressure \nin a hydraulic press (Figure 2). To \nextend to the utmost the range of \ntemperatures and pressures which \ncould be used, the cylinder was lined \nwith a special chrome-nickel steel, de- \nveloped by the Society of Automotive \nEngineers, which will retain good\n\nFig. 2\u2014In the final step in producing experimental samples of artificial anthracite, the \nmaterials were subjected to high temperatures and high pressures in a steel cylinder\n\nhardness and elasticity under 100,000 \npounds per square inch up to 500\u00b0 C. \nThe clearance between the plungers \nand the cylinder walls was made \nample to permit the escape of gases, \nsince it is believed that rock fissures \nand lines of fracture permit such \nescape in the natural formation of \nanthracite. Final treatments in this \nbomb covered a range of pressures up \nto 56,700 pounds per square inch.\n\nAt the outset of the experiments \nhigh pressure was applied to the \ncharges while they were being heated. \nIt was soon found that a strong re- \naction evolving heat set in at about \n320\u00b0 C., accompanied by the volumi- \nnous escape of gases which would \noften blow most of the charge out past \nthe piston. In some cases a shell of coal \nwould be formed against the walls of \nthe bomb which prevented the escape \nof gas, with the result that the center \nof the charge was dull, porous and \ncrumbly. Unsatisfactory also was the \ntechnique of applying high pressure\n\nIt was finally found best to hold \nthe charge under low pressure at the \nfinal operating temperature of 400\u00b0 C. \nto 450\u00b0 C. for about an hour, and then \nto apply high pressure gradually and \nto maintain this pressure during the \nheating and while the charge was later \nallowed to cool to room temperature. \nIn this manner uniform and firmly \nbound products were obtained.\n\nThe majority of the products, and \nthe most successful, were obtained \nfrom wood. Many of the samples \nshowed the lustre of natural anthra- \ncite, had comparable hardness and \napparent density, and fractured to \nleave conchoidal surfaces. They \nburned quite slowly in a slow stream \nof pure oxygen, with little or no visible \nflame, and negligible evolution of tar \nand coal gas. The residual ash, weigh- \ning usually less than one per cent of the \noriginal sample, consisted mostly of \niron oxide, probably because of the\n\nuse of iron vessels in pretreatment and \nfinal treatment. The content of car- \nbon in the best samples obtained \nvaried from 71 to 89 per cent, and of \nhydrogen from 3.9 to 3.2 per cent, \nwell within the reported range of \nlower grade natural anthracites but \nnot sufficiently high in carbon nor \nlow in hydrogen to correspond with \nanthracites of the best grade.\n\nThe hydrogen content was lower, \nthe higher the temperature of final \ntreatment; and when this content was \nplotted against temperature, the \ndownward slope of the curve became \ngreater above 400 degrees Centigrade. \nGreater lengths of treatment at any \nfixed temperature also decreased the \nhydrogen content, but the rate of de- \ncrease diminished as the period of \ntreatment was prolonged. The varia- \ntion in hydrogen content was such as \nto offer little encouragement to in- \ncreasing the pressure, and indicated \nthat the low hydrogen content of \ncertain natural anthracites must be \ndue to factors other than pressure \nalone.\n\nSamples of the more promising \nproducts were ground, screened, \nroasted by the methods used in pre- \nparing transmitter carbon.* The \nground and screened material did not \ndisplay the mechanical uniformity of \nthe natural product. Although it did \nnot show excessive porosity, it con- \ntained many granules either flat or \nbearing pronounced promontories. \nRoasting brought about considerable \nshrinkage but no coking. Almost \nwithout exception, the resulting ma-\n\nterials had resistances lower than that \nof transmitter carbon, in extreme \ncases approaching that of graphite \nThe efficiencies of the materials pe \nmodulators were also lower than the \nstandard, approaching non-modula. \ntion in materials with resistance as \nlow as graphite.\n\nUltimate success in the project \nwaits upon a satisfactory adjustment \nof both the chemical and the physical \nproperties of the final material. The \nresults already obtained indicate that \nthe chemical adjustment depends \nlargely upon the final treatment, \nwhere temperature is the most im- \nportant factor provided the period of \nits application is sufficiently long. In \ndetermining the physical character- \nistics, both the preliminary and final \ntreatments are important, the former \nconsiderably influencing fracture and \nbinding.\n\nIt seems probable that further ex- \nperimentation, varying the many de- \ntermining factors, would ultimately \nreveal a procedure for producing \nanthracite at least as good as the \nnatural. Necessarily empirical and \nlengthy, such experimentation ap- \npears at present unjustified since the \ncondition of natural beds of anthra- \ncite today suggests no pressing need \nfor substitutes. The experiments so \nfar performed have broken the way \nto filling the need when it arises, and \nhave meanwhile contributed toward \na better understanding of the funda- \nmental principles of coal formation \nand of how to select the best anthra- \ncite for manufacture into transmitter \ncarbon.\n\nD. K. Martin had been actively in- \nterested and engaged in radio work before \ngetting his B.S. degree, in 1916, from \nthe Polytechnic College of Engineering \nat Oakland, California. Shortly after \ngraduation he went to Alaska for the \nAlaska Packers Association where he was \noccupied with the installation and opera- \ntion of their radio facilities. During the \nWorld War he was an En- \nsign in the United States \nNavy, spending much of \nhis time as radio instructor. \nIn 1919 he joined the Ameri- \ncan Telephone and Tele- \ngraph Company where he \ncontinued his radio work in \nthe Department of Devel- \nopment and Research. \nTransferring to the Lab- \noratories in 1928 he engaged \nin the development of air- \ncraft radio apparatus, and \nat present he is supervisor \nof the group which is hand- \nling radio transmission\n\nW. C. Tinus began his radio career \nwith an amateur radio station immedi- \nately after the war. He was later with \nseveral of the early broadcasting stations \nin the southwest and also served at sea \nas a radio operator. He received the B.S. \ndegree in Electrical Engineering from \nTexas Agricultural and Me- \nchanical College in 1928 \nand then joined the Tech- \nnical Staff of these Lab- \noratories. Since that time \nhe has been concerned with \nthe development of airplane \nradio equipment and with \nits application to the rapid- \nly growing commercial air- \nlines throughout the United \nStates.\n\nH. B. FiscuHer received a \nB.S. degree in Electrical \nEngineering from the Uni- \nversity of Wisconsin in 1924\n\nand immediately joined the Technical \nStaff of the Laboratories. With the radio \ndepartment he first worked on broadcast \nreceivers, but after the development of \naircraft communication apparatus was \nstarted, he engaged in the design of avia- \ntion receivers. At the present time, he is \nin charge of the group developing radio \nreceivers for mobile systems.\n\nThe first call from an airplane in flight through the \nBoston Marine Radiotelephone system was made on \nFriday, March 10, when Capt. A. R. Brooks, piloting the \nLaboratories\u2019 trimotor plane, talked with the skipper of\n\nGeorges Bank, about 200 miles offshore. The call passed \nthrough the Mendham laboratory and land lines via \nBoston to the marine station of the New England Tele- \nphone and Telegraph Company at Green Harbor, Mass.", "title": "Bell Laboratories Record 1933-05: Vol 11 Iss 9", "trim_reasons": [], "year": 1933} {"archive_ref": "sim_record-at-t-bell-laboratories_1938-05_16_9", "canonical_url": "https://archive.org/details/sim_record-at-t-bell-laboratories_1938-05_16_9", "char_count": 90192, "collection": "archive-org-bell-labs", "doc_id": 256, "document_type": "journal_issue", "id": "bella-qwen-pretrain-doc256", "record_count": 106, "release_policy_version": "hf_public_v1", "rights_status": "public_domain", "selected_extraction_backend": null, "selected_extraction_score": null, "source_family": "archive_org", "source_url": "https://archive.org/details/sim_record-at-t-bell-laboratories_1938-05_16_9", "split": "validation", "text": "flat type.* These have proved \neconomical to manufacture; and ex- \nperience extending over a quarter of a \ncentury has testified to their satis- \nfactoriness in operation. During this \ntime, however, the telephone system \nhas changed, and upon relays there \nhave been imposed operations more \ncomplicated and critical than were in \nmind at the time of their development. \nMaterials and manufacturing meth- \nods also have changed, so that all in \nall it seemed desirable a few years ago \nto undertake the design of a new all- \npurpose relay. The vu-type relay\u2014 \nshown in the photograph at the head \nof this article\u2014is the result.\n\nReliability in relay operation has \nbecome of increasing importance in \nrecent years. The intricacies of the \ndial systems require the operation of a \nlarge number of relays on each call, \nand for the satisfactory functioning of \nthe system many of these relays must \noperate and release at just the right \ntime and without fail. The existing \ntypes of relays do this, of course, with \nwhat is really remarkable precision, \nbut occasionally a speck of dirt will \nget between the contacts to prevent \ntheir closing. Also the contacts may \n\u201cchatter\u201d \u2014rapidly opening and clos- \ning as a result either of the rebounding \nof the armature when the relay is de- \nenergized, or of the independent vi- \nbration of the springs. One of the \nobjectives of the new design, there-\n\nfore, was to improve reliability by \nmaking dirt particles less effective, \nand by reducing the tendency to \nchatter. Another objective was to \nsecure a greater number of contact \nsprings per relay. A study indicated \nthat an increase from the twelve \nsprings of the present relay to twenty- \nfour would be satisfactory. To obtain \nthe full advantage of such an increase, \nhowever, the gain in number of con- \ntacts must not be offset by a cor- \nresponding increase in size or in \nenergy required. In other words, more \neffective and efficient use of materials \nwas sought.\n\nAn increased number of contacts \nrequires a larger magnetic flux; and if \nthe energy consumed by the winding \nis not to be increased, this flux can \nmost effectively be secured by pro- \nviding a magnetic path of lower re- \nluctance. Such an improved magnetic \npath was secured, first, by using a \nlarger core of circular cross-section, \nwhich provides the greatest flux for a \ngiven length of wire; and second, by \nreducing the air-gap reluctance and \nmaking more advantageous use of it. \nIn both the E- and r-type relays, \nwhich are of the flat type, a u-shaped \narmature is hinged to the yoke at the \nrear of the core by a piece of thin \nmagnetic iron, as shown in Figure 1. \nThe spring hinge is so thin that only \na small part of the flux can be carried \nby it; the rest of the flux passes \nthrough air, which introduces into the \ncircuit an additional reluctance that \nserves no useful purpose. The gap \nat the hinge is kept as small as possi- \nble, of course, but it must be large \nenough to permit free movement of \nthe armature after allowing for un- \navoidable unevenness at the hinge.\n\nThe armature of the new relay is of \nthe same u shape as that of the \nR-type relay, but overlaps the end\n\nyoke, instead of being hinged to it, and \nis held loosely in place by a pin in each \narm of the vu. The construction is \nshown in Figure 2. In its unoperated \nposition, the armature pivots on the \nfront edge of the rear bracket\u2014 \nleaving a long wedge-shaped air gap \nbetween this edge and the rear end of \nthe armature. As the armature closes, \nthis wedge-shaped air gap narrows \ndown until, in the operated condition \nof the armature, it almost disappears. \nThis form of mounting tends to intro- \nduce only a small reluctance, which is \nmade still smaller by the compara- \ntively large cross-sectional area of the \nhinge gap as compared with former \nrelays. Moreover, the flux in this gap \nperforms a useful function, since the \nresulting force of attraction on the \nrear end of the armature tends to \nrotate the armature around the pivot- \ning point in the same direction as does \nthe relatively greater pull at the gap \nat the front end. The core is milled \nflat at its rear where it fastens to the \ncross yoke, and also at its front to \nform a broad flat surface for the arma- \nture. This front gap is limited in \nwidth by the diameter of the core, but \nit is made long enough to give a large \narea and thus a low reluctance.\n\nHow effective this construction is \nin increasing the pull is shown by \nFigure 3, which gives a typical rela- \ntionship between the force which the \narmature can develop, and the power \nrequired to maintain this force, for \nboth the r- and u-type relays. The pull \nprovided for six make contacts is \nsomewhat greater for the u-type relay \nthan for the R\u2014more contact pressure \nbeing provided\u2014but the power re- \nquired is only about a fifth. The \nR type would be incapable of closing \n12 make contacts, while the vu type \ncloses them with less than half the \npower required by the r type.\n\nBesides contributing to the pull of \nthe relay, this construction tends to \nreduce the likelihood of chatter caused \nby the armature rebounding after it \nhas opened. With the reed-hinged\n\narmature of former relays, the full \nforce of the rebound occurs at the \nfront end of the relay where the \ntendency to close the contacts is \ngreat. With the u-type relay, how- \never, the rebound divides between the \nfront gap and the loosely mounted \npivoting point farther back; and the \nnet consequence at the contacts is far \nless than if the armature were free to \nrecoil only at the front.\n\nOf at least equal importance is the \nchatter caused by vibration of the \nsprings. Considerable study, both \ntheoretical and experimental, was \nnecessary to determine the nature and \ncauses of this vibration and the best \nmethod of its elimination. It was \nfinally found that by properly propor- \ntioning the dimensions of both the \nstationary and the movable springs \nthis form of chatter could be elimi- \nnated as a source of serious trouble.\n\nThe other major improvement in- \ncorporated in this new relay is the use \nof twin contacts. Each contact spring \nCarries two separate contacts in \nparallel, so that even though one of \nthem should be held open by a speck \nof dust, the other would close. Ags \nalready noted, the failure of a relay to \nmake contact is of comparatively rare \noccurrence, but the provision of \ndouble contacts very greatly decreases \nthis likelihood. The probability of a \nrandom failure when two parallel \ncontacts are employed is the square \nof the probability for a single contact. \nIf, for example, a single contact fails \nto make once in ten thousand times, \nthen a pair of contacts in parallel \nunder similar conditions will fail only \nonce in a hundred million times.\n\nWith these various improvements \na relay has been made available that, \nbesides being able with less power to \nclose twice as many contacts as the \nR type, is practically free from chatter \nand from contact failure. In designing \nthe vu-type relay every advantage \nhas been taken of past experience and\n\nof recent developments, not only to \nmake it more effective but also to \nkeep its manufacturing cost low. \nWith this in view a striking change \nwas incorporated in the method of \nwinding. In previous relays the front \nand rear of the core are larger than the \nsection on which the winding is \nplaced, and the wire for the coil is \nwound in place on the core. With the \nnew relay the core has been made of \nthe same diameter throughout its \nlength, so that it 1s possible to wind \nthe coils separately and then slip \nthem over the cores. This change in \nthe core was adopted largely to take \nadvantage of a method of winding \ncoils in multiple which was developed \nby the Western Electric Company. \nOn a single arbor, as shown in Figure \n4, seven coils are wound at the same \ntime from seven spools of wire. Be- \ntween adjacent windings are slight \nseparations so that they may be cut \napart when completed. Between suc- \ncessive layers of wire are very thin \nlayers of cellulose acetate sheet, which \nrun the full length of the arbor and \nhold the wire in place.\n\nThe collection of spring contacts \nconsists of stationary and movable \nsprings, separated in their mounting \nby strips of insulation. The stationary \nones are considerably thicker than the \nmovable, and do not bend appreciably \nas the relay operates. The movable \nsprings are controlled by the armature \nthrough insulating rods, which are \nfastened to alternate springs and pass \nthrough openings in the stationary \nsprings. The general appearance of a \nspring assembly for twelve make con- \ntacts, which is the full complement of \na relay, is shown on page 300. Each \nstationary spring is a single piece \nwith the two contacts near the ends. \nThe movable springs are forked a \nlittle beyond the point of attachment\n\nto the operating rod, with each branch \ncarrying one contact. This gives com- \nparative independence between the \ntwo contacts of a pair, so that if one \nis held open the other will still be free \nto make contact. The soldering termi- \nnals of these springs fan out at the \nrear in the usual manner. For the \nwindings, soldering terminals are simi- \nlarly arranged, but they are also \nextended toward the front of the\n\nrelay. This arrangement gives access \nto the windings when testing from \nthe front.\n\nThe headpiece illustrates a relay \nprovided only with make contacts \nbut, as with most relays, other combi- \nnations may be built up, such as \nbreak-contacts, make-before-break, \nbreak-before-make, or make-before- \nmake; several hundred combinations \nmay be obtained. For the windings \nalso there is a large number of pos- \nsible ratings depending on the voltage \nof the circuit in which the relay is to \noperate and on other circuit charac-\n\nteristics or on the type of \noperation required. Other \noptional features are copper \nand aluminum sleeves which \nare slipped over the core \nwhen slower operation is \ndesired, and a split perm- \nalloy sleeve to give the \nwinding a high impedance \nto voice frequencies. The \ncores are usually of mag- \nnetic iron, but permalloy \nmay be used when condi- \ntions warrant it.\n\nBecause relays are used \nin large numbers, their \nspace requirement becomes \nof considerable importance. \nThe vu type requires verti- \ncally the same space as the \nflat relay; and horizontally, \nspace determined by its \nnumber of springs. When \nequipped to capacity, it has \na spring-pair density in the \nplane of the mounting rack \nof 4.2 pairs per square inch, \nwhile the greatest density \nbefore, which was with the \nR type, was 3.4 pairs.\n\nIn the development of \nthe relay, many of the \nmechanical and magnetic \nproblems have had to be \nstudied from both their the- \noretical and experimental \nsides, and contributions \nto the completed apparatus \nhave come from Labora- \ntories specialists in many \ndifferent fields. Such mod- \nern research tools as the \nhigh-speed motion-picture \ncamera and the string oscil- \nlograph,* arranged to give \nsimultaneous electrical and \nmechanical records, have\n\nbeen indispensable in the \nextensive tests that followed \nthe original design work. It \nseems fair to say that only \nthrough the insight afforded \nby these instruments was \nit possible to recognize the \ntrue nature of many of the \ndesign problems; and onl \nthrough their use did the \nfinal design come to so suc- \ncessful a conclusion.\n\nDevelopment of this re- \nlay had its inception in the \nneed for more contacts and \nfor lower battery drain; but \nin the course of its design it \nwas found possible to add \nmany other desirable fea- \ntures, such as twin contacts \nand freedom from chatter. \nAs a result, it has become of \nmuch wider utility than \nwas originally anticipated. \nIt seems not unlikely that \njust as the need for new \nswitching mechanisms led \nto its development, so its \nnew and better features \nwill open an avenue to \nfurther progress in_ the \nswitching art. The 755A \nPBX, which will be de- \nscribed in a forthcoming \nissue, introduced the new \ndesign and was the first of \nmany systems to utilize it. \nThe most extensive use of \nthis relay is in the cross- \nbar system, the first instal- \nlation of which has been \nmade at the Troy Avenue \nOffice in Brooklyn.\n\nFig. 4\u2014For the U-type relays \nseven separate windings are \nwound on a single arbor and \nthen cut off and assembled over \nthe core\n\npositive electrode in a \nvacuum tube, other electrons are \ngiven off. These are called secondary \nelectrons. In ordinary vacuum tube \napplications an effort is made to \nreduce the number of secondary \nelectrons or to return them to the \nelectrode from which they came. If \nnot thus controlled, these secondaries \nmay introduce undesirable modifica- \ntions in the tube characteristics. In \nrecent years a number of workers in \nthe vacuum tube field have endeav- \nored to apply this phenomenon to use- \nful purposes and as a result of their \nefforts various devices known as elec- \ntron multipliers have appeared. These \ndevices seemed to have potential \nvalue in the field of applied electronics \nand work has accordingly been under- \ntaken by the Laboratories with the \nobject of evaluating their worth and \nof developing electron multipliers \nthat may be adapted to our purposes.\n\nThe number of secondary electrons \nleaving a surface struck by a stream \nof electrons is proportional to the \nnumber of primary electrons striking \nit. The proportionality factor varies \nboth with the potential drop through \nwhich the primary electrons fall \nbefore striking, and with the nature \nof the emitting surface. If there is to \nbe amplification this proportionality \nfactor must be greater than one, so \nthat both the potential drop and the \nnature of the electrode surface are \nimportant factors in the design of the \nmultipliers. With silver-oxygen-cesi- \num surfaces, similar to those used in \nmodern photoelectric cells, and a \npotential drop of 100 volts, it is \npossible to get a proportionality factor \nof four. Under these conditions the \nelectron stream is multiplied fourfold \nevery time it strikes an emitting sur- \nface, and by arranging a number of \nsuch stages in series, a considerable \namplification can be obtained.\n\nthus consists of a photoelectric surface \non which light falls to produce the \ninitial stream of electrons, and a \nseries of plates, each at a higher \npotential than the preceding one, to \nprovide successive stages of ampli- \nfication. The operation of such a \nmultiplier is illustrated schematically \nin Figure 1. Light falls on the photo- \ncathode, 0, and produces an electron \ncurrent 1. This current falls through\n\nFig. 1\u2014Many of the previous electron \nmultipliers have used a series of metal \nplates at successively higher potentials, and \nhave employed a magnetic field to guide the \nelectrons from one plate to the next\n\nthe potential drop v, which is the \npotential difference between plate 1 \nand the photo-cathode, and on strik- \ning plate 1 produces mi secondary \nelectrons, where m is the proportion- \nality factor. These electrons falling \nthrough a similar potential drop to \nplate 2 produce a group of secondary \nelectrons m times as great, so that the \ncurrent leaving plate 2 will be m?1. \nThis process is continuous over the \nentire series of plates, and results in \nan output current of m1, where k \nis a number of plates or stages. The \nlast plate acts as a collector and is \nconnected to the output circuit.\n\nIf such a multi-stage multiplier is \nto function satisfactorily, the electron \nleaving one plate must be guided by \nelectric or magnetic fields so that they \nwill all strike the next plate within a \nsmall area, which should preferably \nbecome smaller from plate to plate. \nIf the area within which the electrons\n\nstruck increased from plate to plate, \nsome of the electrons would sooner or \nlater fail to reach the next plate, and \nthere would be a loss in amplification \ndue to diffusion. If the electrons can \nbe made to fall within smaller and \nsmaller areas in going from plate to \nplate, there will be no diffusion loss, \nMoreover, there should be a strong \nfield away from each plate, or space \ncharge will form, and the secondaries \nwill not all leave.\n\nIf the electrons are to follow a con- \nverging path in a multiplier with \nmagnetic focussing, there must be an \naccurate balance between the electric \nand magnetic fields. If the voltage \ndrops a little while the magnetic field \nremains constant, the electrons will \ngo to the wrong place, and multipli- \ncation will be markedly lowered.\n\nFig. 2\u2014Diagrammatic arrangements of \nplates of one of the recently developed elec- \ntron multipliers\n\nBecause of this critical balance that \nmust be maintained between the two \nfields, and because the presence of \nmagnetic fields may in itself be ob- \njectionable, it was desirable to develop \na multiplier that did not require a \nmagnetic field. Although some of the \nearly multipliers used only an electric\n\nfield, they all had low efficiency \nbecause of weak fields away from the \nplate, and poor convergence due to \ninadequate control of the paths of \nthe electrons.\n\nTo design a satisfactory multi- \nplier, the paths of the electrons must \nbe accurately known, but in struc- \ntures as complicated as multipliers, \ncomputation of the paths is so difficult \nas to be almost out of the question. \nFortunately, however, where the field \nis only two dimensional it is possible \nto establish an analogy between the \npath of an electron in an electric field \nand the path of a ball on a tightly \nstretched horizontal membrane that \nis deflected slightly in certain places. \nSuch a two-dimensional field will \nexist wherever a group of electrodes \nform equipotential surfaces extending \nparallel for a long distance in one \ndirection. In Figure 3, for example, a \nset of such equipotential surfaces is \nshown, which extend parallel for a \nlong distance in the direction of the \nz axis. With voltages on these plates \nas indicated the electric field would be \ntwo dimensional; the field at any \npoint between the two rows of plates \nwould have an x and a y component \nbut no z component. An electron \nmultiplier employing only an electric \nfield to guide the electrons is essen- \ntially this sort of a thing, the electrons \npassing successively from plate to \nplate in order of increasing voltage.\n\nA mechanical analogy of such a \ntwo-dimensional field can be formed \nby stretching a rubber sheet tightly \nin a horizontal plane with sections of \nit depressed to form levels of different \ngravitationed potential. Small balls \nrolling along such a surface under the \ninfluence of the difference in gravi- \ntationed potential, or height, would \nfollow paths exactly like those of \nelectrons in a similar distribution of\n\nelectric potentials. In this analogy the \ncharge of the electrons is proportional \nto the weight of the ball, the mass of \nthe electron to the mass of the ball, \nthe electric potential difference be- \ntween plates to the difference in\n\nFig. 3\u2014A two-dimensional field exists be- \ntween a series of equipotential plates that \nare very long compared to their width\n\nheight between successive level areas \nof the rubber diaphragm, and the \nelectric field strength to the slope of \nthe rubber surface, while the equi- \npotential electrodes correspond to the \nlevel areas of the rubber surface.\n\nTo determine the proper arrange- \nment of electrodes to cause the elec- \ntrons to pass through the multiplier \nin the desired manner, such mechani- \ncal analogs have been constructed. \nThe equipment in the accompanying \nphotographs was constructed under \nthe direction of W. Shockley. A sheet \nof rubber is stretched tightly to a \nrectangular frame of angle iron, which \nis held horizontal but arranged so \nthat it can be raised or lowered with\n\nFig. 4\u2014Side view of the mechanical analog showing the \nstretched rubber sheet and the metal vanes that press it down \nfrom above so that it lies across the blocks beneath\n\nrespect to a rigid horizontal surface \nbeneath it. Wood blocks, with accu- \nrately leveled top edges, are set up on \nthe lower horizontal surface to form \nsurfaces of constant height when the \nrubber sheet is lowered to rest on top \nof them. To force the rubber to lie \nalong surfaces, metal \nvanes with horizontal \nlower edges are ar- \nranged to press down \nthe rubber sheet so \nthat it lies across the \ntops of the wooden \nblocks beneath. To \nmake them show up \nmore clearly in the \nphotograph, the equi- \npotential surfaces are \nmarked by straight \nchalk lines, and two \npossible paths of balls \nrolling from one sur- \nface to the next lower \none are also marked \nclearly with chalk. The\n\ninvestigation is to try \nvarious sizes, shapes, \nand positions of blocks \nuntil balls rolled from \none level surface to the \nnext lower one tend to \nconverge smaller \nareas in each succes- \nsive stage. A ball \nstarted any place over \na wide area of plate 1, \nfor example, should \nroll so as to strike the \nnext lower plate in the \ncorresponding _ region \nbut over a narrower \narea. The arrangement \nshown in the photo- \ngraphs is that actually \nemployed for one of \nthe recently developed \nmultipliers, and the convergence of \nthe balls under actual rolling condi- \ntions is shown in Figure 6.\n\nThe arrangement of the blocks, and \nof the plates of the multiplier based \non it, is shown in Figure 2. The con- \nvergence of this multiplier is very\n\ngood, and in addition there is a strong \nfield away from all portions of the\n\nlates where the electrons strike. The \neffect of initial velocities in the paths \nof the electrons was investigated by \nstarting the balls on the rubber model \nwith a slight initial velocity, and was \nfound not to be particularly serious.\n\nA number of multi- \npliers of this type have \nbeen built, and one of \nthem is shown in the \nphotograph at the \nhead of this article. \nThe photo-cathode \nhas an effective sur- \nface considerably \nlarger than that of the \nmultiplying plates, of \nwhich there are six \nbetween the photo- \nelectric surface and the \nanode, or collector. All \nof the plates are long \ncompared to their \nwidth, in a direction at \nright angles to the \nplane of travel of the \nelectrons, and the ends \nof the plates are bent \nin toward the center to keep the \nelectrons from drifting out. The \nproblem of activating the multiplier \nso as to get a good photoelectric \nresponse and at the same time good \nsecondary emission was solved by \nM. S. Glass, and at 750 volts, overall, \nthis multiplier has an output of thirty \nmilliamperes per lumen, which is over \na thousand times greater than that of \na vacuum photocell. The safe output \ncurrent is of the order of a few milli- \namperes, and the collector voltage \nmay swing as much as 70 volts each \nside of the mean value without ser- \nlously affecting the operation of the \nmultiplier. The output resistance, \nwhich varies inversely with the out-\n\nThe electron multiplier has a num- \nber of advantages as compared with a \nphotoelectric cell and an equivalent \nvacuum-tube amplifier. In the first \nplace it is much smaller, not being \nmuch larger than the photoelectric\n\nFig. 6\u2014Top view of analog showing two balls rolling from \nwidely separated points at one potential level and converging \nas they approach the next lower level\n\ncell alone. Further, experience has \nshown that for high-frequency work, \nthe electron multiplier is less noisy.\n\nThe multiplier is also practically \nnon-microphonic; the noise in the \noutput is little higher than the un- \navoidable \u201c\u2018shot\u201d noise of the photo- \nelectric cell multiplied by the gain. \nStill another advantage is that its \namplification is practically constant \nat all frequencies up to several mega- \ncycles. The emission of the secondary \nelectrons is so nearly simultaneous \nwith the impact of the primaries that \nthe multiplying action faithfully re- \nproduces the very rapid changes in \ncurrent necessary to transmit these \nvery high frequencies.\n\nN many of their applications in the \nBell System, relays are required to \nact as rapidly as possible. They\n\nshould operate promptly when volt- \nage is applied to them, and release \npromptly when the circuit to their \nwinding is opened. There are numer- \nous applications, however, where it is \nnecessary for the relay to remain \noperated for an interval after the \ncircuit to its winding is opened, and \nthis release interval is often specified \nwithin very close limits. Precise be- \nhavior of this kind is not easy to \nsecure; only careful design and accu- \nrate control of manufacture make it \npossible. Relays that are most eco- \nnomical for general uses will not meet \nthe very exacting requirements laid \ndown to secure a precise slow-release \nperiod. When the general utility v- \ntype relay was developed, it seemed \ndesirable, therefore, to develop at the \nsame time a slow-release relay that so \nfar as possible would use the same \nparts, manufacturing tools, and proc- \nesses. The result was the y-type\n\nThe need for dependable slow- \nrelease relays can be well illustrated \nby one of their applications in the \npanel system. A group of relays in the \nsender records each digit dialed, and it \nis necessary to switch the dialing cir- \ncuit from one group to the next after \neach digit of the called number. As \nthe dial returns after having been \npulled around to one of the digits, it \nopens and closes the circuit in rapid \nsuccession to indicate the digit dialed. \nThus in dialing 2 the circuit will be \nopened and closed twice, and in dial- \ning 4 the circuit will be opened and \nclosed four times. Immediately after \nits return, the dial is pulled around \nfor the next digit, and during this \nshort interval between digits the cir- \ncuit must be switched to the next \ngroup of recording relays. This 1s \naccomplished through a slow-release \nrelay that does not release during the \nshort open periods of each digit, but \ndoes in the slightly longer period be-\n\ntween digits. It must do this regard- \nless of the commercial range in dial \nspeeds, of voltages and line variations, \nand in the speed with which the dial \njs pulled around. In the latest type \nsender the actual requirements for \nthe y-type relay are that it shall re- \nlease in not less than 0.080 second nor \nin more than 0.120 second. The ordi- \nnary relay, however, releases in from \n0.005 to 0.015 second. In designing a \nslow-release relay, therefore, there are \ntwo objectives sought: first to provide \nthe slow-release action, and second to \nprovide for an accurately controlled \nrelease time.\n\nIn the case of an ordinary relay \nwhen the winding circuit is opened \nto release the relay the current de- \ncreases almost instantly to zero value \nexcept for the duration of any arcing \nat the opening contacts. The relay \ncontinues to hold in the operated \nposition, however, because a consider- \nable portion of the flux in the mag- \nnetic circuit is maintained by eddy \ncurrents which are induced in the iron \nupon breaking of the winding circuit. \nThe effect of the eddy currents is more \nprolonged if the air gaps in the mag- \nnetic circuit are small. \nTohastentheactionof\n\nmade of brass or other non-magnetic \nmaterial. In the y-type relay, however, \nthey are omitted so that when the \nrelay is operated, the armature is di- \nrectly in contact with the core.\n\nThe omission of the stop discs re- \nduces the current necessary to hold \nthe relay operated, and since the \nrelease time is a function of the \ndifference between the maximum flux \nand the flux at which the relay just \nholds, there will be a longer time \nbetween the opening of the circuit and \nthe release of the relay. To make a \nfurther decrease in the reluctance of \nthe magnetic circuit, the cross-yoke \nat the rear of the core of the y-type \nrelay and the hinge bracket on which \nthe rear ends of the armature rest are \nmade of magnetic iron instead of cold- \nrolled steel, as are those that are used \nin the u-type relay.\n\nThe major means of securing slow \nrelease, however, is by retarding the \nrate of decrease of flux in the core by \nproviding during the release period a \nmagnetizing force that tends to main- \ntain the flux at its original value. This \nis done by placing directly over the \ncore a sleeve of copper or other con-\n\ncomparable action on o 4 \nstill other relays is \nobtained also by means \nof an adjustable screw\n\nducting material. As the flux tends to \ndecrease, when the winding circuit \nis opened, a current is induced in this \nsleeve which is in a direction tending \nto maintain the flux. The lower the \nresistance of the sleeve, the larger will \nbe the current that will flow, and the \nless the rate of dissipation of energy \ndue to resistance. To provide control \nby this means, three copper sleeves of \ndifferent thickness and one of, alumi- \nnum are employed. Aluminum is used \nfor the shortest release period because \nof its high resistance. To obtain a high \nenough resistance with copper, the \nsleeve would be too thin for satis- \nfactory manufacturing conditions. \nThese sleeves provide four degrees \nof delay that may be obtained with \nthe y-type relay. The actual release\n\nFig. 2\u2014Simplified cross-section of the \nmagnetic circuit of the U-type relay\n\ntime, however, depends not only on \nthe resistance of the sleeve and on the \nreluctance of the magnetic circuit, \nbut on the restoring force of the \nsprings tending to open the relay. \nThis, in turn, is a function of the \nnumber of springs with which the \nrelay is equipped, so that the same \nsleeve will give different release times \ndepending on the springs used. The \nnumber of ampere turns required to \nhold the relay operated also depends \non the spring load, so for each sleeve \na curve can be plotted showing the \nrelationship between release time and \nthe ampere turns required to hold the \nrelay operated. A set of such curves\n\nfor the four sleeves is given in Figure \n1; the No. 1 curve is for the aluminum \nsleeve and the other three are for \nthose of copper.\n\nThese copper sleeves provide the \nmost effective means of retarding the \ndecrease of flux in the core after the \nwinding circuit is opened. Any short- \ncircuited winding on the core, how- \never, would provide the same action \nonly less effectively. Advantage is \ntaken of this fact in a few applica- \ntions where the release time desired \nfalls between two of the curves of \nFigure 1. Short-circuited windings are \ndesigned to give the desired inter- \nmediate release times.\n\nAfter having decided on_ these \nvarious features to secure a longer \nrelease time, it is necessary to make \nother changes to hold the desired time \nwithin very close limits. The design \nmust provide not only that any one \nrelay will always release after the \ndesired interval within narrow limits, \nbut that all relays built for the same \nrelease interval will meet their re- \nquirements within similar limits.\n\nThe chief factor causing variations \nin release time may be illustrated by \nFigure 2, which is a simplified cross- \nsection of the magnetic structure of \nthe u-type relay. The contact surface \nof the relay core and of the hinge \nbracket are both flat, and so are the \ntwo corresponding surfaces of the \narmature. If the armature, core, and \nhinge bracket could be _ perfectly\n\nFig. 3\u2014Simplified cross-section of the \nmagnetic circuit of the Y-type relay\n\naligned, the area of contact, and thus \nthe contact reluctance, would be the \nsame under all conditions. Actually, \nhowever, slight variations in the thick- \nness or position of the hinge bracket \nor of the armature itself, cause the \narmature to meet the pole face at a \nsmall angle, which will vary with \ndifferent relays and with the same \nrelay at different times.\n\nWith the u-type relays variations \ndue to these causes at the front end of \nthe relay are reduced by the stop \ndiscs, and the variations at the rear \nend are not great enough to cause de- \nviations that exceed the requirements. \nWith the y-type relay, however, \nwhich does not employ the stop discs, \nthese variations would seriously im- \npair the accuracy of the release inter- \nval. The variations are avoided, \nhowever, by the construction shown \nin Figure 3. A small spherical surface \nis embossed on the front end of the \narmature so that the armature always \nmeets the core in what is essentially a \npoint contact. The front end of the \nhinge bracket is embossed to form a \ncylindrical surface at right angles to \nthe axis of the armature; and so the \narmature and hinge bracket always \nmeet in what is essentially a line con- \ntact. Regardless of the alignment of \nthe armature, therefore, there is \nalways a point contact at the front \nend and essentially a line contact at \nthe rear end.\n\nThe effects of these structural \ndifferences on the reluctance are \nshown in Figure 4 for relays with flat \nsurfaces and for those with the \nspherical and cylindrical surfaces of \nthe y-type relay. With perfect align- \nment the reluctance of the flat sur- \nfaces is very low, but it increases \nrapidly with an increase in the angle \nbetween core and armature. The \nreluctance of the rounded surfaces is\n\nmuch higher for perfect alignment, \nbut it increases only very slightly as \nthe deviation in the alignment in- \ncreases, and thus gives the constancy \nof reluctance particularly desirable \nfor a slow-release relay.\n\nFig. 4\u2014Variations in reluctance of relay \nwith angle at which armature meets the core \nfor both flat and embossed pole pieces\n\nment\u2014zero angular deviation\u2014the \ncontact is spread over the entire \nsurface, and the reluctance as a result \nis very low. When the armature meets \nthe pole face at an angle, however, \nthere is a wedge-shaped air gap \nformed, and the greater the angle of \ncontact, the greater will be the width \n\u2014and thus the reluctance\u2014of this \ngap. With the spherical or cylindrical \nsurfaces, the contact is always in a \npoint or line with a narrow air gap at \nthe sides regardless of the angle with \nwhich the armature meets the con- \ntacting surfaces. The reluctance of \nsuch a contact is higher than that of \ntwo flat surfaces where the angle is \nsmall, but remains essentially con- \nstant, while that of the flat surfaces\n\nFig. s\u2014Variations in release times for flat and rounded pole \nsurfaces. Shaded area shows variations for Y-type relays\n\nA protective coating is plated on \nthe magnetic structure to prevent \ncorrosion of the iron, but since this \ncoating is non-magnetic, it introduces \nwhat is effectively an air gap in the \nmagnetic circuit. Variations in the \nthickness of this plated coat would \naffect the release time by varying the \nreluctance of the magnetic circuit. \nThe closeness with which the release \ntime must be held with the y-type \nrelay, therefore, requires that the \nthickness of the plating be held within \nvery close limits; the actual range is \nfrom 0.0003 to 0.0006 inch. Chromium \nis used for the outer plating to pro- \nvide a very hard surface to resist wear \nat points of contact between the arma- \nture and core.\n\nAs a result of the consistency in \nreluctance obtained by these various \nmeans, the variations in release time \nare considerably reduced. For the \ny-type relay the variations in release \ntimes are shown by the shaded area \nof Figure 5. For a corresponding relay \nwith flat surfaces, the release time \nmight fall anywhere between the \ncurves A and B. With rounded sur-\n\nHeretofore it has been \nnecessary to check the \noperation of slow-re- \nlease relays by actually \nmeasuring the release \ntimes, which is a rather slow and \nexpensive procedure. With the y-type \nrelay such measurements are un- \nnecessary; it is sufficient to measure \nthe holding current, because of the \nclose correspondence between holding \ncurrent and release time.\n\nExcept for these differences, the \ny-type relay is the same as the u type, \nand to the casual glance one could not \nbe told from the other. Moreover, the \ncopper sleeves designed for the y-type \nrelay may be employed with the \nU type to secure somewhat slower \nrelease, although the long release \nobtained with the y-type relay cannot \nbe secured with the vu type, nor can \nthe accuracy of release time for the \nrelay be maintained.\n\nAs the u-type relay is intended to \nbe the general utility relay of the \nfuture, replacing ultimately the & and \nR types, so the y type will be the \nslow-release relay of the future\u2014 \nreplacing the 149, 162, 178, and T \ntypes. One of its first applications 1s \nin the new 755A PBX, where it will \nbe used, in conjunction with other \nrelays, to simulate the action of a \nringing interrupter.\n\nA movEL showing the general exterior \ndesign of the Bell Telephone System \nBuilding at the New York World\u2019s Fair in \n1939 has been approved, and construc- \ntion is now under way. The building \nwill occupy a triangular plot of slightly \nmore than three acres immediately north \nof the Theme Center; formal entrance is \nthrough a pavilion at the point of the \nplot adjacent to the Theme Plaza. In the \nsemi-circular court of this pavilion is a \nsculptured group by Carl Milles. From \nthis point to the building proper a walk \nleads through a grove of 150 mountain \npine trees, chosen because they allow \nample room for people to move about \nunder their spreading lower branches. \nSeveral pools and fountains add to the\n\nThe other entrances to the building, \nfronting on the two main avenues which \nbound the plot, will be flanked by tall \nvermilion panels which will be decorated, \nrespectively, by Hildreth Meiere and \nEdward Trumbull. The mass of the \nbuilding rises to different heights to \nhouse the varied exhibits that are now \nbeing developed in Bell Telephone Lab- \noratories. Along the south side of the site \nruns a decorative colonnade. Where the \naxis of the Transportation of the Fair \nmeets this side of the plot, the building \nwall presents a surface fifty feet high \nwhich it is proposed to cover by a large \nmap showing cities in relief and animated \nby changing lights to indicate the main \nlines of telephonic communication around \nthe world. Above the large circular wing\n\nmunication surmounts the _ building, \nwhich is lighted in such a manner to form \na distinctive night display.\n\nThis exhibit of the American Telephone \nand Telegraph Company, like its other \nrecent exhibits, is being carried out \nunder the direction of Vice Presidents \nArthur W. Page and Frank B. Jewett. \nTo the Laboratories there was dele- \ngated the conception and execution of the \nexhibits; responsible for these develop- \nments are John Mills and M. B. Long.\n\nThe building, the architect\u2019s model of \nwhich is shown on page 299 and also on \nthe preceding page, is a design of Voor- \nhees, Gmelin and Walker. The interior, \nincluding the display of exhibits and the\n\nW. H. Harrison, a member of the Board of Directors \nof these Laboratories, has been elected to succeed \nBancroft Gherardi, who retired on the thirtieth of \nApril, as Vice President and Chief Engineer of \nthe American Telephone and Telegraph Company\n\ndecorations, is being designed by Henry \nDreyfuss. The building itself will be con- \nstructed by Marc Eidlitz and Son.\n\nWhen the building has been com- \npleted and its exhibits installed the opera- \ntion and management will be turned over \nto the New York Telephone Company, \nunder the general supervision of its Vice \nPresident Carl Whitmore and the direct \ncharge of Thomas W. Williams.\n\nBancroft Gherardi, a Director of these \nLaboratories from 1925 to 1937, retired on \nApril 30 from the office of Vice President \nand Chief Engineer of the American \nTelephone and Telegraph Company. So \nended a distinguished career in the Bell \nSystem, whose forty-three years \nhave seen almost the entire de- \nvelopment of the telephonic art. \nUnder the continuous leadership \nof Mr. Gherardi, the Department \nof Operation and Engineering of \nthe American company has be- \ncome a vital force in the progress \nof the Bell System. Throughout \nthe period of rapid evolution in \nthe communication art, nothing \nhas stood out more than the suc- \ncessful organization of the tech- \nnical forces in all the branches of \nbusiness activity involved. In the \ndirection of this organization \nwork the record of Mr. Gherardi \nhas been outstanding.\n\nIn 1895, with the degrees of \nB.S. from the Brooklyn Poly- \ntechnic Institute and M.E. and \nM.M.E. from Cornell University, \nBancroft Gherardi started his \ntelephone career testing some of \nthe relatively few telephone \ncables in the area now operated \nby the New York Telephone \nCompany. Within eleven years, \nduring which time he gained con- \nsiderable traffic as well as plant \nengineering experience, be- \ncame assistant chief engineer of \nboth the New York and New \nJersey companies. In 1907, he\n\njoined the American \nTelephone and Tele- \ngraph Company as eng}- \nneer of building and \ncentral office equipment. \nThree years later he be- \ncame engineer of plant in \ncharge of plant develop- \nment and standardiza- \ntion for the Bell System. \nWhen the Engineering \nDepartment was reor- \nganized in I919, Mr. \nGherardi became Vice \nPresident and Chief En- \ngineer in charge of the \nDepartment of Opera- \ntion and Engineering.\n\nIn technical associa- \ntion work and in co- \noperating with related \nindustries, Mr. Gherardi \nhas always been very \nactive. He led in the for- \nmation of the Joint Gen- \neral Committee of the \nEdison Electric Institute \nand the Bell System and \nhas served as Bell Sys- \ntem Chairman. He has \nalso been Bell System \nChairman of the Joint \nGeneral Committee of the Association of \nAmerican Railroads and the Bell System \nconcerned with somewhat similar prob- \nlems. In the American Institute of Elec- \ntrical Engineers he has been a manager, \nVice President, and was President during \nthe 1927-1928 year. He has served on such \ncommittees as the Executive, Edison \nMedal, Finance, Headquarters, Public \nPolicy, Research and Constitution Re- \nvision. He has represented the Institute \nupon the Board of Trustees of the \nUnited Engineering Trustees, the Library \nBoard, the National Research Council, \nthe United States National Committee of \nthe International Electrotechnical Com- \nmission, the John Fritz Medal Board of \nAward, and other bodies. He has also \nbeen associated with other activities, \nsuch as Trustee of Cornell University,\n\nPresident of the American Standards As- \nsociation, representative of the Bell \nSystem in charge of relations with the \nInternational Advisory Committee on \nTelephony and chairman of the Engi- \nneering Section of the National Academy \nof Sciences.\n\nSome of the honors conferred on Mr. \nGherardi are honorary degrees of Doctor \nof Engineering from the Brooklyn Poly- \ntechnic Institute and from the Worcester \nPolytechnic Institute, the emblem of the \nFourth Order of the Rising Sun from \nJapan and the A.I.E.E. Edison Medal.\n\nImproved methods of manufacture at \nHawthorne, illustrative of the system \nof product shop organization, was the\n\nsubject of an interesting talk given on \nApril 7 by David Levinger, Engineer of \nmanufacture of the Western Electric \nCompany, before over 500 members of the \ntechnical staff of the Apparatus Develop- \nment Department. Mr. Levinger de- \nscribed the principles and advantages of \nthe new system and illustrated his talk \nwith lantern slides of the plant set-up \nand motion pictures of processes of manu- \nfacture of station apparatus. The talk \nwas arranged by a committee consisting \nof O. A. Shann, chairman, P. S. Darnell, \nJ. B. Dixon, E. C. Edwards, R. C. Koer- \nnig, G. Puller, W. H. Sellew, H. D. \nWilson, and J. M. Wilson.\n\nTHE TRIAL of the Type-K carrier tele- \nphone systems which were installed be- \ntween Toledo, Ohio, and South Bend, \nIndiana, during May and June, 1937, has \nbeen completed. Additional equipment is \nnow being installed between Toledo and \nDetroit and it is expected that the com- \nplete project which will provide three \nsystems between South Bend and Detroit \nand six system between Toledo and \nDetroit will be placed in service within \na few months. Each system provides \ntwelve telephone circuits. An article \ndescribing the Type-K carrier system was \npublished in the April issue of the Recorp.\n\nDuring the trial period, the operation \nof the systems was carefully studied. A \nconsiderable number of Laboratories\u2019 \nengineers were involved in these tests, \nand in addition active codperation was \nobtained from the Long Lines Depart- \nment and the Department of Operation \nand Engineering of the American Tele- \nphone and Telegraph Company. The per- \nformance of all parts of the circuit was \nchecked in detail, and the cable pairs \nbalanced to reduce crosstalk. Measure- \nments were made of the overall perform- \nance, including such items as transmission \nregulation, equalization, noise, crosstalk, \noverall stability, and reliability of opera- \ntion. Tests were made of the echo, singing, \nand transient characteristics of these cir-\n\ncuits, especially as affected by switched or \npermanent connections to other types of \nfacilities. All troubles experienced were \ninvestigated, improvements in design \nmade where necessary, and testing and \nadjusting methods worked out which \nwill facilitate maintenance of the system. \nMuch of the information obtained in this \ntrial is of value in applying the Type-K \nsystem over longer distances than the 150 \nmiles between Toledo and South Bend.\n\nDuring the month of December, 1937, \nten circuits on each of the two trial sys- \ntems were placed in regular commercial \nservice for a period of several weeks. They \nwere used to provide additional circuits \nrequired for the Christmas and New Year \nholidays, and many were extended by \nother facilities to form circuits between \nwidely separated points. During the \nservice period, observations were made by \nspecial service observers. No troubles \nwere experienced attributable to the \nType-K systems, and the performance \nwas entirely satisfactory. This repre- \nsented the first commercial operation of \nsystems comprising as many as twelve \ncarrier channels each on existing toll \ncable pairs.\n\nK. K. Darrow discussed neutrons at \nthe March 7 meeting of the Colloquium. \nHe described the career of the free neu- \ntron from its beginning in a process of \ntransmutation to its end in another such \nprocess. Of the neutron-releasing proc- \nesses, several were singled out for presen- \ntation because of one feature or another, \nending with the one from which the most \naccurate currently accepted value of neu- \ntron-mass is derived. Of the neutron- \ncapturing processes, several were singled \nout because of particular features, such \nas the formation of free alpha-particles, \nthe formation of radioactive substances or \nthe generation of helium in quantities \nlarge enough to be detected by micro- \nchemical methods. The deflections and \nscatterings, with and without energy loss, \nto which a neutron is subject as it passes \nclose by nuclei between its release and its\n\nPrecise measure- \nment is basic to all \nscience; hence the \nendless variety of \nmeasurements made \nin Bell Telephone \nLaboratories. For \nmany projects no \nstandardized meas- \nuring apparatus ts \navailable; hence it \nmust be built to \norder.\n\nII \nMeasuring the sepa- \nration between pole \npieces and dia- \nphragm of an audi-\n\nMeasurement of the \nthickness under com- \npression of a paper \ndamping-ring book \nfor a transmitter\n\nultimate capture, were discussed to- \ngether with the observations on the \nnuclei which recoil from these impacts.\n\nAt the March 21 meeting, Dr. D. W. \nBronk, Director of the Eldridge Reeves \nohnson Foundation for Medical Physics, \nthe School of Medicine of the University \nof Pennsylvania, spoke on The Physical \nBasis of Sensory Mechanisms. According \nto Dr. Bronk the contacts which a living \norganism maintains with its environment \nthrough the sense organs depends upon \nthe reactions of the organized matter in \nnerve tissue. The existence of living mat- \nter in such a state of organization de- \npends upon a continual expenditure of \nenergy. Alterations in the energy supply \nmay under appropriate conditions initiate \na series of propagated waves of activity \npassing from the sense organ to the brain. \nIn terms of these series of events it is \npossible to analyze many of the compli- \ncated processes set up in the brain and to \nobtain a clearer understanding of the \nfundamental physico-chemical properties \nof the sensory receptors.\n\nF. S. Goucuer presented a paper en- \ntitled The Physics of Microphonic Con- \ntacts, before the Metropolitan section of \nthe American Physical Society at a meet- \ning held at Columbia University on \nMarch 25. Dr. Goucher traced the evo- \nlution of the carbon microphone, showing \nslides of early models and demonstrating \nthe action of some of these with the aid of \na magnetic tape recorder. He discussed \nthe first quantitative theories as pre- \nsented by Pedersen in 1916 and by Gray \nin 1920 and then described the research \nwork carried on more recently by the \nLaboratories with special emphasis on the \nelastic behavior of microphone contacts.\n\nDr. Bucktey attended part of the \nGeneral Plant Managers\u2019 Conference \nheld at Virginia Beach during the week of \nMarch 21. This conference was arranged \nby the Department of Operation and \nEngineering of the A. T. and T. Company.\n\nW. Witson has been appointed chair- \nman of the Papers Committee of the \nInstitute of Radio Engineers and a mem- \nber of the Board. of Editors and of the \nStandards Committee.\n\nL. Monramar attended a meeting of \nthe National Executive Committee of the \nTelephone Pioneers of America.\n\nTHE MATHEMATICS DEPARTMENT of \nPrinceton University is sponsoring, dur- \ning the current academic year, a series of . \nlectures by men in industry to give the \nundergraduate students some idea of the \nmathematics plays in industrial \nwork. On March 14, W. A. Shewhart \nspoke on Some New Fields of Application \nof Mathematics in Industry, setting forth \nthe way in which statistical method plus \nmass production equals a new tool of re- \nsearch, applicable in every stage of the \nproduction process from raw materials to \nfinished product.\n\nR. H. Couey lectured on wood preser- \nvation before an advanced short course \nfor tree wardens and town foresters. This \ncourse was sponsored by the Massachu- \nsetts State College at Northampton.\n\nDurinc Marcu various problems were \ndiscussed by members of the Labora- \ntories with members of the manufac- \nturing organization at Hawthorne. Prob- \nlems of switchboard cord developments \nwere discussed by C. H. Greenall and R.T. \nStaples; lineman\u2019s handsets, station hand- \nsets and repeater headbands by A. F. \nBennett; handsets by J. Dalton and \nW. G. Turnbull, Jr.; central office alarms \nfor dial offices by N. H. Thorn; crossbar \nequipment by D. H. Wetherell; general \ncircuit and central-office developments \nby W. L. Filer and J. Irish; and step-by- \nstep equipment by C. G. McCormick. Mr. \nMcCormick also visited central offices in \nMinneapolis and St. Paul to observe the \nperformance of this type of equipment.\n\nG. R. Lum visited the Ingraham Clock \nCompany at Bristol, Connecticut, to \ndiscuss loudspeaker cabinet design.\n\nC. F. Wigsuscu was at Virginia Beach \nfrom March 18 to 22 to assist in arrang- \ning equipment shown at the General \nPlant Managers\u2019 Conference.\n\nM. W. Lane of Hawthorne visited the \nLaboratories the week ending March 11 \nand discussed problems associated with \nthe manufacture of the combined set. \nJ. T. Kane of Hawthorne also visited the \nLaboratories the week ending April 1 to \nconfer on similar problems.\n\nW. A. Evans and R. Burns attended \ncommittee meetings of the American \nSociety for Testing Materials held at \nPhiladelphia. Later meetings held at \nRochester were attended by J. R. \nTownsend, Mr. Evans, Mr. Burns, C. H. \nGreenall, H. E. Haring, H. G. Arlt, and \nW. J. Clarke. Mr. Greenall was elected \nchairman of the committee on Copper and \nCopper Alloys, Cast and Wrought.\n\nJ. R. Townsenp, on April 8, spoke be- \nfore the Hawthorne Science Club on New \nMaterials and Procedures in Telephony.\n\nW. W. Werrinc visited Schenectady \nto discuss, with Professor Sayre of Union \nCollege, plans for the forthcoming sym- \nposium on impact testing to be held \nunder the auspices of the American \nSociety for Testing Materials.\n\nAT THE REGULAR meeting of the Radio \nColloquium held at the Holmdel labora- \ntory, A. P. King discussed the latest de- \nvelopments in wave-guide transmission.\n\nW. L. Brack inspected speech-input \nequipment installations at WJR, Detroit \nand WBNS, Columbus.\n\nE. G. Fracker and H. C. Rusty con. \nferred with members of the Ingraham \nClock Company at Bristol, Connecticut, \non March 7.\n\nA. F. Price and A. H. super. \nvised the installation of flight deck an- \nnouncing equipment on the U.S.S. Enter \nprise at Newport News during the past \nmonth. Mr. Price also inspected the \nelectric clock system of the U.S.S. Phila. \ndelphia at the Philadelphia Navy Yard \non March 14.\n\nJ. D. Kvetnxaur and H. C. Curt \nvisited the Navy proving grounds at \nDahlgren, Virginia, during March in con- \nnection with the installation and testing \nof loudspeaker systems.\n\nAN INVESTIGATION of vacuum-tube per- \nformances in telephone repeater circuits \nmade it necessary for J. R. Wilson and \nH. A. Pidgeon to visit Atlanta, Washing- \nton and Princeton.\n\nV. L. Roncei and Mr. Wilson discussed \nglass problems with engineers of the \nGeneral Electric Company, Schenectady.\n\nF. S. Goucher, assisted by F. R. Haynes, demonstrating the behavior of the earliest forms \nof telephone transmitter as compared with some of the later types\n\nA. E. Rueuwve and E. K. Jaycox at- \ntended a meeting of the Intersociety \nColor Council at the Electrical Testing \nLaboratories held in New York.\n\nR. M. Burns attended a conference \nheld at Rochester, which was called to \nconsider the feasibility of organizing the \nAmerican Joint Committee on Corrosion. \nHe also addressed the Southern Tier \nChapter of the American Society for \nMetals at Waverly, New York, on \nProtection of Metals from Corrosion.\n\nHarvey FLETCHER is the author of an \narticle entitled Loudness, Masking and \nTheir Relation to the Hearing Process and \nthe Problem of Noise Measurement, pub- \nlished in the April issue of The Fournal of \nthe Acoustical Soctety.\n\nW. SHocKLEy spoke before a group at \nthe Massachusetts Institute of Tech- \nnology on April 6 on Order and Disorder in \nAlloys. On the next day he also spoke \nbefore another group of the Institute on \nthe subject Elementary Notions About \nElectrons in Atoms and Crystals.\n\nAN arTIcLeE entitled 4 Theory of Noise \nfor Electron Multipliers, by W. Shockley \nand J. R. Pierce, was published in the \nMarch issue of the Proceedings of the \nInstitute of Radio Engineers.\n\nA. E. Bowen, on March 3, discussed \nWave Guide Transmission before the \nPhiladelphia Section of the Institute of \nRadio Engineers.\n\nG. C. SourHwortH discussed and \ndemonstrated the propagation of ultra- \nhigh frequency radio waves through wave \nguides before the Pittsburgh section of \nthe IL.R.E. on March 14.\n\nK. K. Darrow spoke on modern de- \nvelopments in the field of radioactivity on \nMarch 10 before the Rensselaer Poly- \ntechnic Institute\u2019s chapter of Sigma Xi. \nOn March 29, Dr. Darrow addressed the \nElectrophysics Group of the A.I.E.E. on \nElectrical Phenomena in Gases.\n\nA. R. Kemp, Chairman of the Rubber \nDivision of the American Chemical \nSociety, has been appointed by President \nWhitmore as representative of the Society \nat the Rubber Technology Conference to \nbe held under the auspices of the Insti-\n\ntution of the Rubber Industry in London, \nEngland, May 23 to 25. As a member of \nthe Papers Committee of the Conference, \nMr. Kemp has been handling all of the \npapers prepared by engineers in this \ncountry. He will also present two papers\n\nof the Central Office Switching Develop- \nment Department completed thirty years of \nservice in the Bell System on April 11\n\nhimself, entitled, Composition and Col- \nloidal Properties of Balata Latex and \nDielectric Measurements in the Study of \nCarbon Black and Zinc Oxide Dispersion in \nRubber with D. B. Herrmann as co-author \nof the latter.\n\nOn March 28 and 29, Mr. Kemp at- \ntended a meeting of the Rubber Division \nof the American Chemical Society held \nin Detroit.\n\nR. L. Lunsrorp and J. T. Morrer, to- \ngether with representatives of the General \nInstallation Engineer\u2019s organization, in- \nspected the 350-type unattended dial \noffice at Brewster, New York.\n\nF. F. Stepert observed the perform- \nance of Diesel engines at Baldwin, \nPennsylvania.\n\nJ. L. Larew observed the operation of \nthe 410-A power plant in the Pennsy]l- \nvania Railroad Offices at Harrisburg.\n\nJ. W. Scumiep and W. F. Simpson ap- \npeared before the Court of Customs and \nPatent Appeals in Washington in inter- \nference proceedings.\n\nO. E. Rasmussen was at the Patent \nOffice in Washington appearing before \nthe Board of Appeals relative to an appli- \ncation for patent.\n\nMr. Rasmussen completed twenty- \nfive years of service with the Bell System \non the twenty-first of April.\n\nA coMPLETE installation of toll cable \nequipped with telephone repeaters, sig- \nnaling and telegraph equipment of \nWestern Electric manufacture is now in \nservice on the Pennsylvania Railroad be- \ntween New York, Philadelphia and \nHarrisburg in connection with their elec- \ntrification project. The equipment on the \nPhiladelphia-Harrisburg route in- \nspected recently by A. Kenner.\n\nTHE TRIAL of the initial installation of \nthe new Type-K carrier telephone system \non the Toledo-South Bend cable has been \ncompleted. The following engineers, who \nhave been observing at the terminals and \nintermediate points, have returned to \nNew York: C. A. Grierson, J. P. Kinzer, \nW. D. Mischler, L. H. Schwartz and R. L. \nTambling. F. A. Brooks with S. Lewis, \nC. Randa and T. J. Williams, of the \nWestern Electric Company, visited sev- \neral points along the Toledo-South Bend \ncable, to inspect the equipment that is \nused on this installation.\n\nJoun Ma terr inspected the Fourth \nTranscontinental Line between Albu- \nquerque and Whitewater, California, to \nselect test sites for Type-J carrier cross- \ntalk tests. Mr. Mallett and Joseph L. \nLindner are now making performance \ntests of these Type-J transposed open- \nwire circuits between Albuquerque, New \nMexico, and Holbrook, Arizona.\n\nIn CONNECTION with vacuum tube \ntrials, A. A. Heberlein visited the Long \nLines offices at Cincinnati, Atlanta, \nCharlotte, and Washington during March,\n\nH. E. Curtis and A. W. Lesert re. \nturned recently from Albuquerque, New \nMexico, where they conducted trans- \nmission tests on a new disc-insulated \nspiral-four toll entrance cable.\n\nW. H. Tipp is conducting tests between \nJacksonville and West Palm Beach in \nconnection with the trial installation of \nthe Type-J system.\n\nDurING THE first quarter of 1938, the \nfollowing Laboratories employees have \nbeen enrolled as members of the Tele- \nphone Pioneers of America:\n\nC. J. Beck E. L. Nelson \nH. B. Brown Michael O\u2019Connell \nMiss G. R. Callender L. D. Plotner \nL. P. Collins Erich von Nostitz \nA. W. Horne Miss M. G. Reilly \nJ. B. Kelly E. C. Wente\n\nH. W. Evans recently made transmis- \nsion tests on a sample length of a new \ntype of tree wire at Chester.\n\nL. R. Monrrorr inspected Type-G \ncarrier telephone systems in the vicinity \nof Bluefield, West Virginia, and Cum- \nberland, Maryland.\n\nRecentiy, A. G. Chapman, W. E. \nMougey, J. F. Wentz and E. I. Green \nvisited Point Breeze to inspect and dis- \ncuss the manufacture of disc-insulated \nspiral-four cable and other types of cable.\n\nH. A. ETHERIDGE made a trip to Dur- \nham to investigate return loss conditions \non the \u201cB\u201d cable between Petersburg \nand Greensboro.\n\nO. D. Grismore and P. A. JEANNE \nvisited Knoxville recently in connection \nwith an oscillograph installation on a \ndistribution circuit of the Tennessee \nPublic Service Company. This installa- \ntion was made as part of the study of joint \nuse of power and telephone facilities at \nthe higher distribution voltages by the \nJoint Subcommittee on Development and \nResearch of the Edison Electric Institute \nand the Bell Telephone System.\n\nit became apparent that im- \nportant advantages would result if the \nsame channel terminal equipment \ncould be used for all systems. Such a \ngenerally applicable terminal not only \nwould reduce the total amount of \ndevelopment required, and the manu- \nfacturing preparation that would later \nbe needed, but would permit a larger \nquantity production of the individual \napparatus units with its consequent \neconomies, and would give greater \nfacility of interconnection of different \ntypes of systems. To obtain such a \ncommon channel terminal arrange-\n\nment, numerous frequency alloca- \ntions and groupings of channels were \nstudied, and a scheme was finally \nworked out which meets the require- \nments of each system. Both the type \nJ, Or open-wire system, and the type \nK, or cable system, provide twelve \ncarrier channels; and the coaxial \ncable system, which will provide \nseveral hundred channels, uses a \nbasic twelve-channel group, which is \nraised by other modulations into suc- \ncessive positions in the frequency \nspectrum. The twelve-channel group \nis thus common to all these systems, \neach having different types of group \nmodulators, demodulators, and filters\n\nwith the appropriate carrier \nsupply to adapt the set of \ntwelve channels to any of the \nthree systems.\n\nThe channel terminal equip- \nment is practically identical \nfor all systems, and naturally \ndivides itself into two sections: \nmodulating and selecting cir- \ncuits, and the carrier supply \ncircuits. The carrier supply \nequipment provides twelve \ncarrier frequencies spaced 4000 \ncycles apart and extending \nfrom 64 to 108 kilocycles, \ninclusive, with certain other \nfrequencies for special pur- \nposes. Sufficient capacity is \nprovided to supply a number \nof groups from the same \ncarrier source. Ten groups, or \na total of 120 channels, may \nbe supplied from a single \ncarrier unit, and more could \nbe supplied if, at any time, it \nshould prove desirable.\n\nFig. 2\u2014Installation of channel equipment located at \n32 Sixth Avenue, New York\n\nchannel terminal. Each unit occupies \n1214 inches on a standard relay rack \nbay, and eighteen of them mounted \non two bays are shown in Figure 2 as\n\nMODULATOR \n2 MODU-| TO TRANS- \n= LATOR| MITTING \n3 BAND | GROUP \nred FILTER| CIRCUITS \nTO CARRIER\n\n2 MODULATING \nUNITS SUPPLY \nx \n\\ \n= oc \npemoou-| DEMODU-| TO \n\u00b0 LATOR LATOR | RECEIVING \nF AMPLI- BAND | _GROUP\n\nFig. 1\u2014Schematic diagram of the channel terminal \nequipment for a single two-way channel\n\nset up for the experimental \ncoaxial demonstration at 32 \nSixth Avenue. The bay at the \nleft of the channel terminal \nunits includes the carrier sup- \nply equipment.\n\nThe modulating and select- \ning equipment for a single two- \nway telephone circuit is shown \nin schematic form in Figure I. \nInthetransmitting side, above, \nthere are, from left to right, \na repeating coil, a copper- \noxide modulator, a resistance \nnetwork, and a_ band-pass \nfilter. On the receiving side\n\nthere are, from right to left, a band- \npass filter, a resistance network, a \ncopper-oxide demodulator, and the \ndemodulator amplifier. Equipment \nfor two of such circuits comprises the \nunit panel shown in Figure 2. A small \njack strip, which projects through the \nfront cover as shown in the photo- \ngraph at the head of this article, \nprovides a simple means of reading \nvalues of the currents and voltages of \nthe amplifier tubes.\n\nOne of the outstanding features of \nthis equipment is its simplicity and \nsmall size. The modulator and de- \nmodulator each consist of four copper- \noxide discs only three-sixteenths inch \nin diameter and connected in a \n\u201cbridge\u201d network. This network may \nbe considered as a variable resistance \nshunt across the signal circuit, which \nchanges from a low to a high re- \nsistance under control of the carrier \nfrequency. Because of the balanced \nform of this circuit, practically none \nof the carrier appears in the output \nside, which in the transmitting channel \nincludes the two sidebands only. For \nthe same reason none of the voice or \nsideband frequencies can get into the \ncarrier supply to interfere with other \nchannels. The resistance network be- \ntween modulator and filter serves to \ngive a constant impedance termina- \ntion for the filter instead of the \nvarying impedance termination that \nwould be offered by the copper-oxide \nnetwork.\n\nThis balanced condition of the \nmodulator and demodulator is very \nimportant, and is secured by careful \nselection of the discs during manu- \nfacture. There are in reality two \ntypes of balance to be considered. In \nthe first place, the four discs compris- \ning a single modulator are selected to \nhave the same resistance within very \nclose limits. This insures the balance\n\nthat prevents carrier getting into the \noutput circuits, or voice or sideband \ninto the carrier circuits. Besides this \nform of balance, it is desirable that \nthe output of all channels be approxi- \nmately at the same level. Since the \ntransmission loss through the modu- \nlator is an important factor in de- \ntermining this level, the discs for the \nmodulator are further selected to \nhave substantially the same trans- \nmission loss.\n\nThe filters are of the recently de- \nveloped quartz-crystal type, and pro- \nvide a pass-band about 3000 cycles \nwide and with very steep sides, as \nshown in Figure 3. This type of filter \nis very economical of space; each \nfilter requiring only one side of a 3%4-\n\nFig. 3\u2014Frequency characteristics of the \ncrystal filters for the channels\n\ninch panel. Two of the four filters \nrequired for the two channels are \nmounted at the top and bottom of the \npanel in the photograph at the head \nof this article; the other two occupy \ncorresponding positions on the rear of \nthe panel. The twelve transmitting \nfilters of a group are multipled to- \ngether at their output terminals, \ntogether with a compensating net- \nwork to improve the impedance \ntermination. A similar network is \nconnected to the multipled terminals\n\nof the twelve receiving filters. These \ncompensating networks are housed on \nthe narrow panels between the third \nand fourth panels from the bottom \nas seen in Figure 2.\n\nTo take care of losses that may be \ninterposed between the two-wire cir- \ncuit at the toll board and the four- \nwire circuit at the channel terminal, \nit is necessary to have the level at the \nreceiving circuit higher than that at \nthe sending circuit. Since the same \ncarrier supply is employed for both \nmodulator and demodulator, however, \nthe output of the demodulator is at \na lower level than that of the input \ncircuits because of the losses in the \ndemodulator. An amplifier is there- \nfore provided to raise the level of the \ndemodulated signal to the desired \nlevel. Gain adjustment of the ampli- \nfier is provided by a small potenti- \nometer. For all the channels, both \ntransmitting and receiving, the voice \ncircuits are terminated in jacks all \ngrouped at one location; and the gain \npotentiometers of the demodulator \namplifiers are mounted above their \ncorresponding jacks. This makes a \nvery convenient arrangement for \nmaintenance, since the level of all \nchannels at the output of the carrier \nequipment may be measured and ad- \njusted in rapid succession at the \nsame place on the panel equipment.\n\nCarrier current for the twelve \nchannels is provided by a harmonic. \nproducing circuit supplied from 4 \n40o0o-cycle source. The circuit ar. \nrangement is shown in Figure 4. The \nprecision required of the basic supply \nfrequency depends on the highest \ncarrier frequency to be supplied. For \nthe type J and kK systems, with an \nupper frequency of about 60 and 140 \nkilocycles respectively, the precision \ndoes not need to be so great as for the \ncoaxial system where the upper \ncarrier is a million or more cycles. A \n400o0-cycle tuning fork is adequate for \nthe low-frequency systems, while for \nthe coaxial system, the high-precision \nstandard frequency of 4000 cycles now \nsupplied from New York may be \nemployed. The alternative connec- \ntions are indicated on the diagram. \nThe fork is actually employed in both \ncases, but for the low-frequency \nsystems it is used to control the \noscillator frequency, while for the \nhigh-frequency system it is used only \nas a 4-kc band-pass filter.\n\nThe output of the oscillator passes \nto a single-tube amplifying stage, and \nthence to a push-pull stage and an \noutput transformer. This transformer \nis tuned to 4000 cycles on its output \nside, and it feeds the harmonic-pro- \nducing circuit through another tuning \nstage to insure a pure 4000-cycle wave.\n\nFig. 4\u2014Simplified schematic of the carrier-supply circuit for the channel terminals of \nbroad-band carrier systems\n\nThe harmonic-producing circuit con- \nsists of a shunt coil, two series \ncondensers, and a copper-oxide bridge \ncircuit. At the beginning of the \ncurrent wave the coil is of high in- \nductance, and the condensers charge, \nbut as the current increases, the core \nof the coil becomes saturated, and as \na result the inductance decreases so \nthat the coil approxi- |\n\nodd harmonics of 8000 cycles are even \nharmonics of 4000 cycles, this circuit \nproduces the even harmonics of the \n4000-cycle fundamental, which are \nselected by a second group of filters. \nThe requirements placed on these \nfilters are made easier because of the \nbalanced arrangement of the copper- \noxide discs, which tends to prevent\n\nPATCHING \nThis transition from \nhigh inductance to MoDU- TO TRANS- \nlowoccurs rapidly with circuits | | BAND \nthe result that the HT \ncondenser discharges | \nthrough the coil in a | conapen- \nrush of current. The NETWORK \nresult is \u201d sharply TO OTHER MODULATORS \npeaked current wave, AND, DEMODUL ATORS \ndecomposable into a \u2018eee \n4ooo-cycle fundamen- \ntal and its odd har- \u201cFILTERS. \nmonics. The odd har- t\n\nmonics desired are se- \nlected by a group of \nfilters as indicated on \nthe diagram.\n\nEven harmonics are \nproduced by the \ncopper-oxide _ bridge, \nwhich, acting as a full- \nwave rectifier, causes a \nseries of current peaks \nin its output branch. \nThere is a peak for\n\nsame sign because of \nthe rectifying action \nof the bridge. A cur- \nrent of this kind is\n\nCOMPEN- \nSATING \nNETWORK \nDEMODU- TO \nDEMODU- LATOR RECEIVING \nLATOR BAND GROUP. \nFIER FILTER EQUIPMENT\n\ndecomposable into a \nfundamental of 8000 \ncycles and all har- \nmonics, both even and \nodd. Since even and\n\nFig. s\u2014Simplified schematic of channel terminal unit for \nbroad-band systems\n\nThe filters used to select the carrier \nfrequencies are also of the crystal \ntype, but contain only one section. \nBeyond them, a set of resistances is \nprovided through which connection \nis made to the various circuits as indi- \ncated in Figure 5. These resistances \nprotect the common carrier supplies \nagainst possible short circuit in any \nlead. As mentioned above certain \nother harmonics may be employed \nalso, such as the 24-ke current that\n\nwas used as the fundamental fre. \nquency for the production of carrier \nfrequencies in the million-cycle coaxial \nsystem trial, and the 60-ke current used \nas a pilot frequency.\n\nA photograph of a carrier-supply \nbay, with the protective resistances \nabove, is shown in Figure 6 as set up \nin the Laboratories for the coaxial \ntests. Two harmonic-producing cir- \ncuits, one a_ regular and one an \nemergency, are normally provided to \nsafeguard the carrier supply. Means \nare provided for automatically trans- \nferring from the regular to the emer- \ngency in case of failure, and of manu- \nally transferring in either direction \nwith very slight interruption to any \nof the circuits involved.\n\nOf the many interesting charac- \nteristics of this channel-terminal \nequipment, one of the most impressive \nis that of its compactness. Due to the \nuse of crystal filters, of small size coils \nwith improved core material, and of \nthe copper-oxide modulator and de- \nmodulator units, the complete channel \nmodulating and selecting equipment \nfor three groups, each of twelve \ntwo-way telephone circuit capacity, \ncan be mounted on two relay rack \nbays, as shown in Figure 2. All the \nwiring between units is arranged to \nrun up both sides of the relay racks \nin metal compartments which provide \nshielding. This permits the use of \nmore unshielded wire than would be \npossible otherwise.\n\nThe first use of this equipment was \nwith the experimental coaxial cable \nsystem between New York and Phila- \ndelphia, which was demonstrated to \nthe press in November, 1936.\n\nilluminated, the current \nthrough it increases very rapidly at \nfirst but attains its maximum value \nafter only about a thousandth of a \nsecond. Likewise when the light is \nabruptly extinguished some current \nflows through the darkened cell for \nabout the same brief interval. This \ndelay has been ascribed to the time \nrequired for the gas ions which are \ngenerated in the tube to move to the \ncathode. The failure of the output \nto follow the light variation exactly \ncan be explained readily on this \nassumption at frequencies of about \n10,000 cycles; but considerable doubt \nhas been expressed that the lag at \nlower frequencies could be due to the \nsame cause.\n\nThe current in a gaseous cell in- \nvolves not only the electrons which \nthe light liberates at the cathode but \nalso all the other electrons and ions\n\nwhich these photoelectrons produce \nin collision with gas molecules. Thus \nfor each primary photoelectron liber- \nated at the cathode, a number of \nelectrons arrive at the anode. The \npositive ion formed at each ionizing \ncollision travels in the opposite direc- \ntion toward the cathode, but moves \nmuch more slowly through the gas \nbecause of its larger size and mass. \nIn studies in gas-filled cells com- \nmercial designs are not particularly \nsuitable, mainly because in them the \nelectric field is not uniform and hence \nsome ions take longer to reach the \ncathode than others. The design \nshown in Figure 3 overcomes this de- \nfect, for its anode is small and all parts \nof the cathode are approximately \nequidistant from it. As a consequence \nof this geometrical form, the electric \nfield is distributed uniformly through- \nout the entire tube as shown in \nFigure 2, and the transit time of all \nthe ions is approximately the same.\n\nFig. 1\\\u2014The magnitude of the alternating current output of the other pulse of current \ncell varies with the frequency of the incident light because the to flow. The second \ncomponents of the current carried by the electrons and the pulse flows after a time\n\nIf the photosensitive cathode 1s \nilluminated by light whose intensity \nvaries sinusoidally, the emission of the \nprimary photoelectrons and the con- \nsequent production of positive ions \nwill also vary sinusoidally. \nWaves of ions will travel from \nthe region of the anode to the \ncathode, slowing up as they \napproach the cathode like \nocean waves rolling in on a \nsandy beach. Now it so hap- \npens that the current in the \nexternal connecting circuit due \nto the transit of a charged \nparticle across the cell flows \nduring the whole time the \nparticle is in motion, ceasing \nwhen it delivers up its charge \non reaching an electrode. Fur- \nthermore, most of this current \nflows while the particle (ion or \nelectron) is in the vicinity of \nthe anode and is moving \nswiftly. The electrons get\n\nproximately equal to \nthe transit time of the ions and suc- \nceeding pulses of decreasing ampli- \ntude follow at intervals equal to this. \nThus if the release of photoelectrons \nvaries sinusoidally, a series of sinu-\n\nacross the cell very quickly Fig. 2\u2014The symmetrical construction of the photo- \nand the ions get out of the electric cell gives a uniform distribution of the\n\nsoidally varying currents will flow in \nthe external circuit. These will all be \nin phase when the transit time of the \nions is equal to the period of the cur- \nrent variations, for then the crests of \nthe waves fall together and the total \nalternating current output is a maxi- \nmum. Conversely, when the transit \ntime of the photoelectrons is equal to \nhalf a period, the total current falls \nto a minimum value.\n\nBy measuring the magnitude of the \noutput of the cell for different fre- \nquencies of light variation and plot- \nting the data, Figure 1, the first \nminimum and subsequent maximum \nare found to occur where expected on \nthe assumption that the effect is due \nto the relatively slow velocity of the \ngas ions. Other maxima and minima \nmight be anticipated at higher fre- \nquencies, for which the times of flight \nwould be multiples of the periods and \nhalf periods. They are not observable, \nhowever, because the ions move about \nin a very irregular manner with the \nresult that at the higher frequencies \nindividual ions wander from their \npositions in the wave, the crests and \ntroughs merge, and the waves lose \ntheir identity.\n\nIt is possible to calculate, from the \nspeed at which argon ions drift, what \nthe average velocity of the ions at \ndifferent distances along the radius \nshould be; and to deduce therefrom \nthe total time taken by an ion in going \nfrom the vicinity of the anode to the \ncathode. As stated in the preceding \nparagraph the value thus determined \nis the same as the period of the light \nfrequency at the first maximum, or \nhalf the period at the first minimum. \nThis confirms the theory given above \nand thus establishes the nature of the \ntime lag in this cell.\n\n_ In commercial cells large variations \nin the time delay are to be expected be-\n\ncause of their non-uniform fields, men- \ntioned earlier in the article. Thus the \nfact that maxima and minima have \nnot been observed in curves taken\n\nsmall and all parts of the cathode are ap- \nproximately equidistant from it\n\nwith commercial cells of usual design \nis reconcilable with the theory that \nhas been developed. But the lag in \nresponse is there just the same.\n\nFor the voice-frequency band used \nin sound pictures the distortion caused \nby the lag in the photoelectric cell is \nnot serious. There is some phase dis- \ntortion but fortunately the ear can- \nnot detect it. The most obvious \npractical consequence of the lag is a \nsmall loss in efficiency which, now ex- \nplained, could be reduced if necessary \nby modifying the cells. Where fre- \nquencies much above 10,000 cycles \nare involved the lag becomes large \nand has to be taken into consideration \nin the design of cells.\n\nVERY year approximately a \nhalf million new poles of south- \nern yellow pine are used in the \nBell System either for replacements or \nfor new lines. If these poles were left \nunprotected from the action of lower \nforms of plant and animal life\u2014fungi \nand termites\u2014the economic loss would \nbe serious. Their life can be greatly \nextended, however, by treating the \npoles with a suitable preservative. \nThere are many preservatives on the \nmarket, and new ones are being \noffered from time to time to pole \nmanufacturers, so that techniques for \nevaluating them must be available. \nOutdoor exposure tests of wood \npreservatives are usually slow and \nexpensive and it is necessary to sup- \nplement such studies with quick and \ninexpensive laboratory methods. \nRecent experimentation has evolved \nan improved laboratory test which is \nsimple and adaptable and yet gives\n\nreproducible results which are con- \nsistent with field trials of the same \nmaterial. Briefly, it involves the im- \npregnation of small pieces of blocks of \nwood with the preservative to be \ntested, and their exposure in separate \nglass jars to the action of different \nfungi. After several weeks, the pre- \nservative\u2019s effectiveness is rated by \nthe amount and density of the fun- \ngus growth, the decrease of weight \nof the samples, and their loss of \nmechanical strength.\n\nThe blocks used in testing preserva- \ntives are from the sap-wood of south- \nern yellow pine, of uniform density \nand rate of growth, cut usually into \ncubes, two centimeters on a side. \nSince the moisture content of the wood \nvaries over a wide range, depending \non the relative atmospheric humidity \nto which it has been exposed, the \nblocks have to be brought to a definite \nhumidity content before each weigh-\n\ning at the various stages of the test. \nFor this purpose there is used an \nordinary bacteriological incubator, \nFigure 3, fitted with slow-moving fans \nand pans of saturated solution of \nsodium chloride. It maintains a rela- \ntive humidity of 76 per cent at 30 de- \ngrees Centigrade which gives the \nblocks a moisture content of about \n14.1 per cent when compared with the \noven-dry state.\n\nThe procedure usually followed in \nstudying a new preservative is to in- \nject blocks, conditioned as above, \nwith a solution of the preservative. \nThe pieces are weighed immediately \nafter impregnation to determine the \namount of preservative injected, and \nafter evaporation of the solvent they \nare reweighed under the standard con- \nditions, referred to above, to serve as a \nfurther check on their actual content \nof preservative. This is of extreme \nimportance in working with volatile \npreservatives.\n\nEach impregnated block is sup- \nported by a thin slab of untreated \nwood on the top of a small wide- \nmouthed bottle which contains water. \nThe slab also acts as a secondary food\n\nsource for the growth of the fungus. \nWooden surgical applicators, cut in \nhalf, are used to anchor the wood and \nto serve as wicks for conducting water \nthrough the test pieces, Figure 2. For \nprotection the small bottles are \nwrapped in cotton and placed in \nlarger bottles with screw caps. The \ncomplete set-up is sterilized for fifteen \nminutes at fifteen pounds pressure and \nthen cooled to room temperature. \nThen a small section, cut from a pure \nculture of a wood-destroying fungus, \nFigure 1, is placed on the untreated \nslab of wood opposite the test speci- \nmen. The bottles are kept in an incu- \nbation room, and observed every four \nweeks for the extent of the fungus \ngrowth. After an exposure to the \nfungus of about twenty-four weeks \nthe blocks are again brought to equi- \nlibrium in the humidity chamber and \nweighed. The loss in weight so deter- \nmined serves as one of the indications \nof the efficacy of the preservative that \nhas been employed.\n\nAt the present time some six hun- \ndred species of fungi are known to at- \ntack wood, and since all cannot be \nused in each test for preservatives\n\nFig. 1\u2014Component parts of the apparatus used for the wood-block assay of preservative \nmaterials. These tests are carried on at the Summit Laboratory\n\ncare must be exercised to select repre- \nsentative fungi. Previous experience \nhas shown that in addition to extreme \nvariability in virulence to different \nspecies of wood the fungi display \nmarked idiosyncrasies towards var- \nious preservatives. On the basis of\n\nFig. 2\u2014Test apparatus assembled and the \nwood inoculated with a small piece of \nfungus culture\n\nthese two factors, many of the fungi \nchosen have been found in southern \npine telephone poles which had failed \nin service.\n\nOne of these, the fungus Lentinus \nlepideus, has been repeatedly found on \ntest specimens in the Laboratories\u2019 \ntest \u201cgarden\u201d at Gulfport, Mississippi, \nand on poles in widely separated areas \nin the United States. It possesses a \nmarked resistance to certain organic\n\npreservatives, and is mentioned by \nseveral investigators as being of wide- \nspread economic importance in the \ndecay of building and structural tim- \nbers. Another fungus, Lenzites trabea, \nalso exerts a strong resistance to or- \nganic preservatives but since the type \nof decay produced is unique in that it \ntakes place primarily at the surface, \nthis fungus is also included in most \ntests. The resistance of Fomes roseys \nvaries greatly, but this flat-growing \nand innocent-looking fungus masks an \noccasional virulence which makes it \nan essential member of every test. \nAnother organism included in all \ntests has not been identified as yet, \ndespite attempts by several mycolog- \nical authorities. It masquerades un- \nder the designation U-1o. Isolated a \nfew years ago from a decayed pine \ntelephone pole, it is especially valu- \nable when a quick indication of the\n\nvalue of a new pre- \nservative is needed, as \nit is capable of pro- \nducing a very appreci- \nable weight loss in \nabout three months. \nWhen preservatives of \nthe inorganic type are \nunder consideration \ncommon dry-rot fungi \nare used because of \ntheir specific resist- \nance to this particular \nclass of compounds. \nFrom time to time \nother wood-destroying \norganisms have sup- \nplemented those in \nregular use.\n\nTo aid in interpret- \ning the results of tests \non the efficacy of a \npreservative, un- \ntreated controls are \nalso exposed to the \ndifferent test fungi; \nand treated controls \nare put through the \nentire test cycle with- \nout inoculation. These \ncontrols are valuable \nindicators of the na- \nture of the preservative from the \nstandpoint of solubility, volatility and \nchemical stability; and particularly of \nthe strength that is lost by the ex- \nposed test blocks.\n\nThree criteria are available as \nmeasures of the value of a preserva- \ntive. First there is the growth rating \nwhich is made every four weeks with \nreference to the untreated norm. This \nrating is designated by a pair of num- \nbers, the first of which indicates the \nextent of the test block covered with \nthe fungus, and the second the in- \ntensity and vigor of the growth. \nBased on 4 as the maximum, 2-4\n\nFig. 4\u2014Incubation room where the bottles are stored during \nthe twenty-four-week test period at a constant temperature of \ntwenty-six degrees Centigrade\n\nwould mean that the block was partly \ncovered with normal growth and 4-2 \nwholly covered with sparse growth. \nA second measure is the weight loss \ncomputed from the equilibrium \nweights before and after exposure to \nthe fungus, with corrections for leach- \ning, volatility or other causes as mani- \nfested in the uninoculated but treated \ntest-blocks. The third basis for judg- \ning the merits of the preservative is \nthe dissection or strength rating de- \ntermined by breaking the blocks in \nsmall pieces and comparing them with \nthe uninoculated controls that had \nbeen treated in a similar manner.\n\nFig. s\u2014Test of a preservative with the wood-block method showing the effect of increasing \nconcentration on the growth of the test fungus Lenzites trabea. Growth ratings of these \ntypical test blocks from left to right are 4-4, 4-3, 3-2, 0-0\n\nThis modification of previous wood- \nblock test methods is no doubt cap- \nable of still further development, but \nseveral years\u2019 experience with it has \nprovided case histories for many pre- \nservatives which show a gratifying \ncorrelation between results of this ac-\n\ncelerated and inexpensive laboratory \ntest and of the slower and more ex- \npensive field trials. The severity of the \nmethod may in some cases be criti- \ncized but this very severity is essential \nin the elimination of mediocre ma- \nterials unworthy of further study.\n\nF. A. Zupa came to the Laboratories in \n1918, and engaged first in testing and \ndevelopment work on materials and tele- \nphone apparatus in the Physical Labora- \ntory until 1924. This included two years \non photomicrographic and microscopic \nanalysis of materials. Since 1924, he has \nbeen engaged in the design and develop- \nment of telephone relays; recently he has \ndevoted most of his time to the U and Y \ntypes. He obtained his technical educa- \ntion at the College of the City of New \nYork and Cooper Union, receiving the \ndegree of B.S. in Electrical Engineering \nfrom the latter school in 1922.\n\nH. N. Wacar received the S.B. de- \ngree in physics from Harvard University \nin 1926, and shortly afterward joined \nthese Laboratories. As a member of the \nApparatus Development Department \nsince that time he has participated in de- \nvelopment work on practically all classes \nof telephone relays. During this period he \nalso continued his studies at Columbia \nUniversity, and received the M.A. de- \ngree in 1931. In the course of his studies \nof dynamic problems relating to relays, he \ndeveloped the first oscillographic system\n\nfor obtaining simultaneous records of \nmechanical and electrical vibrations in \nelectromechanical devices, and has made \nseveral contributions to this rapidly \ngrowing technique. He is at present asso- \nciated with development work on relays \nand magnet coils intended for manufac- \nture on a large scale.\n\nJ. R. Pierce received his B.S. degree \nin 1933 from the California Institute of \nTechnology, and from the same insti- \ntution received an M.S. in 1934 and a \nPh.D. in Electrical Engineering in 1936. \nHe then joined the Technical Staff of Bell \nTelephone Laboratories where he has \nbeen engaged in the development of \nvarious types of vacuum tubes.\n\nJoun Leurrirz received the degree of \nB.S. in Chemistry from Bowdoin College \nin 1929 and an A.M. in Botany from \nColumbia University in 1934. From 1921 \nto 1925 he was with the U. S. Navy \nMedical Corps. He joined the Bell Tele- \nphone Laboratories in 1929 and has been \nengaged in research along biological lines \nprimarily relating to wood preservation.\n\nimmediately joined the Engineering De- \npartment of the Western Electric Com- \npany. He has been engaged since that \ntime in development work on carrier tele- \nphone systems. For the last several years \nhe has been in charge of a group which \nhas been concerned with the terminals of \nbroad-band carrier systems, principally \nthose for application to voice-frequency \nand coaxial cables.\n\nA. M. Skettetr joined the Labora- \ntories in 1929 after spending several \nyears teaching, finally as instructor and \nassistant professor of physics at the Uni-\n\nversity of Florida. He also worked one \nsummer as physicist with the Westing- \nhouse Company and served as chief \nengineer of Station WRUF. Long-wave \nantenna design and general problems of \nradio transmission occupied Dr. Skellett\u2019s \ntime when he first came to the Labora- \ntories. Since 1934 he has been with the \nphysical research group studying the ap- \nplication of atomic and electronic devices \nto telephony. Dr. Skellett received the \nA.B. and M.S. degrees from Washington \nUniversity in 1924 and 1927, respectively, \nand the Ph.D. from Princeton in 1933.", "title": "Bell Laboratories Record 1938-05: Vol 16 Iss 9", "trim_reasons": [], "year": 1938} {"archive_ref": "R00047", "canonical_url": "https://archive.org/details/R00047", "char_count": 34600, "collection": "archive-org-bell-labs", "doc_id": 291, "document_type": "technical_report", "id": "bella-qwen-pretrain-doc291", "record_count": 32, "release_policy_version": "hf_public_v1", "rights_status": "public_domain", "selected_extraction_backend": null, "selected_extraction_score": null, "source_family": "archive_org", "source_url": "https://archive.org/details/R00047", "split": "validation", "text": "A Description of the Unit of Telephone Transmission \nRecently Adopted by the Bell System and \nA Discussion of the Reasons for its Selection\n\nResearch Laboratories of the American Telephone \nand Telegraph Company , and the Western \nElectric Company , Incorporated.\n\nnection is a question of both technical and \ncommercial importance. The advances that \nhave been made in long distance telephony, both \nby wire and by radio, are emphasizing the need \nof cooperation in Europe in the engineering and \noperation of interconnecting systems. The \nsimplifications in engineering specifications that \nwould result if the present diversity of units in \nEurope could be replaced by a single one are obvi- \nous. At the same time the interchange of in- \nformation through the technical press would be \ngreatly facilitated.\n\nThe experience of the engineers of the Bell \nSystem led them, a short time ago, to the con- \nclusion that the type of unit discussed in this \npaper is the most suitable for present conditions \nin the telephone art. This unit is called, for the \npresent at least, the 11 transmission unit\u201d and \nabbreviated T.U. 1 This unit was submitted for \nconsideration to many of the leading telephone \nestablishments of the world. The response to \nthis proposal was favorable, in general, although \nthere were several exceptions. The American \nTelephone and Telegraph Company are adopting \nthis new unit as standard in the Bell System. 2\n\nThe transmission unit is of the same general \nnature as the \u201cMile of Standard Cable at 800\n\n1 For convenience it is intended to dispense with periods \nand with s as indicating a number of TV .\n\n2 \u201cThe Transmission Unit and Telephone Transmission \nReference System\u201d; VV. II. Martin; Journal of the \nA. I. E. E., June, 1924, p. 504.\n\nCycles\u201d and the (31 unit, both of which it is \nintended to replace. It is used to measure the \nsame quantities as are now measured in those \nunits. At the same time it is defined in such a \nway as to facilitate the extension of its applica- \ntion to meet the needs of the newer develop- \nments in the communication art. Its magni- \ntude is very nearly the same as that of the 800 \ncycle mile. It is, however, so chosen as to \nmake the use of common or Briggs\u2019 logarithms \nconvenient in transmission computations. The \nnumber of 800 cycle miles corresponding to a \ncondition wherein the currents under com- \nparison are i\\ and /*> is given by\n\nfrom which it follows that the TU is a loga- \nrithmic measure of power ratio and is numer- \nically equal to log 10 01 .\n\nThe use of powers rather than currents is \nconnected with the breadth of application \nalready referred to, and will be discussed in \nmore detail later. In case the currents associ- \nated with the powers under comparison are\n\nThe reasons for selecting this particular unit \nrather than some other will probably not be \nobvious at first sight. They should, however, \nbecome apparent as we run over what the re- \nquirements for such a unit are, and in what \nrespects the various possible units may differ \nfrom one another.\n\nThe \u201cmile of standard cable\u201d as originally \nused gave a means of comparing the loudness of \nthe sound emitted by a receiver under any two \nconditions in terms of the number of miles of \nactual physical cable that had to be inserted \nunder one of the conditions to make the two of \nequal loudness. In practice, of course, ad- \njustable artificial cables were used. The defini- \ntion of the unit then was in terms of the con- \nstants per mile of the cable chosen as standard. \nUnfortunately two slightly different cables have \nbecome standard. That used in America has a \nloop resistance of 88 ohms and a capacity of \n.054 microfarads per mile. Some of the other \ncountries use a cable of the same resistance \nand capacity which has in addition an induc- \ntance of 1 milhenry and a conductance of 1 \nmicromho per mile.\n\nThe effect on the output of the receiver of \ninserting such a cable is much greater at high \nfrequencies than at low; that is, it distorts the \nspeech at the same time that it attenuates it. \nMoreover, the distortion increases with the \nlength of the cable used. This distortion was \nrather a desirable property so long as the use of \nthe unit was confined to talking comparisons of \nlines having roughly the same distortion as the \nstandard cable. This condition no longer exists, \nhowever. Many of the circuits now in use have \nmuch less distortion than has a length of stand- \nard cable having the same attenuation. Also \nthe unit is used to express the effect of inserting \npieces of apparatus whose frequency character- \nistic bears no resemblance to that of the cable. \nIn America at least the use of voice testing in \nthe plant has been practically replaced by \nmethods employing sine wave currents and \nelectric measuring instruments. As these tests \nmay be made with currents of various fre- \nquencies, it is important that the results be \nexpressed in units which are independent of the \nfrequency.\n\nAs this need arose it was natural to adapt the \nexisting unit to meet it. Thus the effect of the \ncircuit under test for a current of any particular \nfrequency came to be compared with that of the \nstandard cable for a current of one standard \nfrequency; namely, 796 cycles per second, for \nwhich 27r/=5000. In this way a new unit was \nintroduced which came to be called the \u201c800 \nCycle Mile.\u201d It has, of course, two slightly \ndifferent values corresponding to the two speci- \nfications for the standard cable. So far as our \nfurther discussion goes we may eliminate the \noriginal mile of standard cable as a possible \nunit on the ground that it fails to meet the \nfundamental requirement of being independent \nof frequency.\n\nBefore proceeding, however, let us look more \ncarefully at what was involved in the transition\n\nto the 800 cycle mile. The artificial cable box \nhas been replaced in substitution measurements \nby an artificial line calibrated in 800 cycle miles, \nwhich is made up of resistances only and so has \nthe same effect on all frequencies. This fact \ntends to suggest that the 800 cycle mile, like the \nmile of standard cable, has, or may have, an \nactual physical existence. This, however, is not \nthe case. The 800 cycle mile is a purely theo- \nretical unit based on certain mathematical \nrelationships. This is evident from the fact that \nthe specifications to be met in designing a \u201cre- \nsistance line\u201d are that the overall effect shall \nvary with the length in the prescribed fashion, \nwhereas the magnitude of the resistances used \nand their particular arrangement in the circuit is \nimmaterial. The theoretical nature of the unit \nis still more evident when it is used for expressing \nthe transmission of a system as determined by \nthe ratio of two electric quantities such as \ncurrents, which may have been either measured \nor computed without making use of any artificial \nline.\n\nThe relation which defines the unit is that \nwhich connects the number of miles of standard \ncable with the effect which it produces at 800 \ncycles. The particular effect which came to be \nmost commonly taken as a criterion was the ratio \nof the received current before and after the \ninsertion of a length of standard cable. To \navoid ambiguity due to terminal conditions, the \nline was assumed long enough so that the effect \nof the inserted cable is independent of the im- \npedances at the ends of the cable in which it \nis inserted. The ratio of the currents under \nthese conditions is identical with that of the \ncurrents at two points in an infinite line separ- \nated by a length equal to the number of miles\n\ninserted. This ratio j is an exponential func- \ntion of the distance x y which, because of the\n\noccurrence of the naperian base e in line theory, \nis ordinarily expressed in the form\n\nwhere a is a constant depending on the cable \nand the frequency. It should be noted, however, \nthat the use of e is purely arbitrary, as the rela- \ntion can be completely expressed with a single \nconstant as,\n\nThe arbitrary introduction of this unneces- \nsary constant e is only justifiable if it simplifies \nthe treatment of the whole problem. Since, as \nwill be brought out more fully later, it is uniquely \nrelated to only a small part of transmission \nengineering, its inclusion at this point tends \nrather to confuse than clarify the situation.\n\nExpressing the number of units x as an ex- \nplicit function of the current ratio gives\n\nFrom this expression we may deduce the \nnature and magnitude of the 800 cycle mile as a \nunit. If we wish to find the number of seconds \nin any interval of time we divide the length of \nthe interval by the length of the second. If we \nwant the number of hours we divide by the \nlength of the hour. Here the quantity which the\n\nunit expresses is the logarithm of a current \nratio. The number of units x is the logarithm \nof the ratio being measured divided by the unit, \nwhich is log b. Thus the nature of the unit is \nthe logarithm of a current ratio. Its magnitude \nis the logarithm of that particular current ratio \nb which is chosen for defining it; in this case \n1.115. It should be noted that (11) is true \nregardless of the base of the system of loga- \nrithms used. The numerical value of the unit \nwill , of course , vary with the base chosen , but the \nnumber of units corresponding to the particular \ncurrent ratio will not.\n\nThe fit unit is of the same nature as the 800 \ncycle mile, and differs from it only in its magni- \ntude, which has been selected to facilitate the \ncomputation of the transmission of a long line \nfrom its primary constants. Its theoretical \nbasis is more obvious than in the case of the \nmile, although its evolution from the theory of \nline transmission has tended to associate it more \nclosely with long lines than is perhaps justified \nin view of the other uses to which it is now put. \nThus while the idea of its being the product of a \nlength by an attenuation per unit length is \nretained in the symbol 0l } for practical purposes \na single letter would be equally useful.\n\nThe 01 unit, like the 800 cycle mile, is the \nlogarithm of a current ratio. The number of \nunits is given directly by the natural logarithm \nof the current ratio in question. Thus in (7) a \nis unity. This means that in (11) b is equal \nto \u20ac, and so the unit itself is log e. When \nexpressed in natural logarithms the absolute \nvalue of the unit is therefore unity, as would be \nexpected.\n\nThe TU is like the other two units in that it is \ndefined theoretically and measures the loga- \nrithm of a ratio. The fact that the ratio meas- \nured is that of powers rather than currents is a \nseparate question from that of its meeting the \nfundamental requirement of being the logarithm\n\nof a ratio. 3 The magnitude of the transmission \nunit is readily deducible from the relation given \nin (3). Dropping subscripts, this may be written\n\nFollowing the same reasoning as was applied \nto (11) with reference to the 800 cycle mile, we \nsee that the TU is a unit for expressing the \nlogarithm of the ratio of two amounts of power, \nand that it is numerically equal to the logarithm \nof a power ratio of 10 0 \u2019 1 . When common \nlogarithms are used its value is 0.1 and the \nnumber of units corresponding to any power \nratio is ten times the common logarithm of the \nratio.\n\nBefore discussing the reasons for proposing \na unit based on power rather than current ratio \nsome misunderstanding may be prevented by \npointing out that the power ratio as here used \nis not to be confused with the ratio commonly \nused for expressing the efficiency of electrical or \nother machinery, it is not necessarily the \nratio of the power delivered by a device to \nthat entering it, but may be the ratio of any \ntwo amounts of power whatsoever. Just what \npowers are to be taken in any case will be de-\n\n3 Units of this general type are not confined to trans- \nmission, hut have come into use for expressing various \nratios. Thus the octave and the musical tone are units \nof different magnitudes for expressing the logarithm of \na frequency ratio. The stellar magnitude is one for ex- \npressing the logarithm of the ratios of the light received \nfrom the stars. They all are aimed at substituting addi- \ntion for multiplication in combining ratios.\n\ntermined by what quantity is being measured \nin transmission units and how that quantity \nis defined. It may, for example, be the efficiency \nof a system as compared with some reference \nsystem, the crosstalk between two lines, or \nthe relative power at two points in a system.\n\nNo attempt will be made here to define \nthese quantities beyond pointing out that it \ncan be done more generally in terms of powers \nthan currents. As the general includes the \nspecial, such a definition need not interfere \nwith the practical use of currents under those \nconditions where this gives satisfactory results. \nThat there are, however, conditions under \nwhich this is not the case is evidenced by the \nfact that in certain branches of transmission \nengineering the \u201c800 cycle mile\u201d has already \ncome to be used as a unit defined on a power \nbasis. In laying out a circuit containing a \nnumber of repeaters it is customary to construct \nwhat is called a transmission level chart. 4 \nCorresponding to each point along the circuit \nis plotted the \u201clevel\u201d at that point relative to \nsome point, usually the entrance to the long \ndistance line, which is taken as a reference level. \nThe level at any point is determined by the ratio \nof the power passing that point to that passing \nthe point of reference. The purpose of such a \nchart is to indicate on the one hand what power \nthe various repeater tubes will be called upon to \nhandle, since they are limited in this respect, \nand, on the other hand, what is the ratio of the \npower of the voice currents to that of the inter- \nfering currents. This ratio is important because \nit determines the detrimental effect of the inter- \nference when it reaches the listener. These \nrelative levels are most conveniently plotted \nin logarithmic units, so it was natural to use \n800 cycle miles. Since, however, the impedances\n\n4 Telephone Transmission over Long Cable Circuits: \nA. B. Clark; 'Frans. A. I. E. E. Vol. XXXVIII, Part 2, p. \n1 287, Electrical- Communication , Vol. I, No. 3. Feb., 1923.\n\nof the various line sections and of the apparatus \nincluding vacuum tubes vary over a wide range, \na very misleading picture would be obtained if \nthe ratios of the currents at the various points \nto that at the reference point were used directly \nin calculating the levels. To avoid this diffi- \nculty and still permit the use of formulae based \non the mile as defined in terms of current ratio, \nthe square root of the power at the various \npoints has come to be used as a soft of fictitious \nequivalent current. Had the impedance been \nthe same at all points, the use of the currents \ndirectly would have given a correct picture.\n\nThis example serves to illustrate the arguments \nin favor of the power ratio unit. It brings out \nthe fact that the really important quantity in \ntransmission is the power. So long as the \npowers under comparison are associated with \nequal impedances, the corresponding currents \ngive a correct measure of relative powers. In the \nearlier stages of the art very few of the com- \nparisons were between powers in unequal im- \npedances, and so a current unit was satisfactory. \nThe more recent developments, particularly \nthose associated with the use of vacuum tubes, \nhave introduced an increasing proportion of \ncases in which the impedances are unequal, and \nhence an increasing demand for a unit which \nexpresses power ratio regardless of the associated \nimpedances. Such an extension of the unit in no \nway interferes with the use of current ratios in \ncases involving equal impedances, such as the \ncomputation of specific equivalents of lines, or \nthe determination of transmission loss by ob- \nserving the change in current in a fixed receiving \ninstrument. All that is necessary here is to use \ntwice as large a constant in the formula when \ncomputing units from the current ratio as is \nused for power ratios. Thus the number of TU \nis twenty times the common logarithm of the \ncurrent ratio.\n\nSome other illustrations of cases where a \ncurrent ratio unit is inadequate may be men- \ntioned.\n\nReceivers are often compared by determining \nthe ratio of the currents which must be passed \nthrough them to secure the same loudness of \nsound from both. Such a comparison means \nvery little unless the impedances of the two \nhappen to be the same. A high impedance \nreceiver appears at a distinct advantage in such \na test, owing to the fact that it receives more \npower for the same current flowing through it. \nFor such a test to give a true picture, correc- \ntion must be made for the difference in im- \npedance in a manner which is equivalent to \nreducing the comparison to a power basis.\n\nIn computing the transmission efficiency of a \nline involving inserted apparatus a type of \nquantity which has been found cpiite useful is \nthe so-called loss at a junction. This includes \nreflexion, transition and other similar losses. \nThese can be expressed independently of the \nrest of the circuit in the form of the ratio of the \npower actually transferred across the junction \nto what would be transferred if the circuit re- \nceiving the energy were replaced by one having \nan impedance, as measured from the junction, \nbearing some prescribed relation to that of the \ncircuit supplying the energy. Such a loss is \nexpressible directly in terms of the power ratio \nused, whereas the application of a current ratio \nunit to such a case is forced, to say the least.\n\nAgain, in the application of line transmission \nmethods to radio telephony 5 level diagrams \nsimilar to those on long lines are useful. Here \nwe may wish to compare power in the form of \nether waves with that in the form of currents in \nwires. Just what currents would here be used \nis not obvious.\n\n5 Application to Radio of Wire Transmission Engineer- \ning: L. Espenschied; Inst, of Radio Eng., Oct., 1922, p. \n344.\n\nIn the treatment of the mechanically vibrating \nparts of a telephone system, such as a receiver, \nthere is a tendency in the direction of consider- \ning the electrical and mechanical parts as a \ncontinuous transmission system. In such an \narrangement the comparison of electric and \nmechanical power at two points would be \nnatural in terms of a power ratio unit, whereas \nthe analog of a current ratio would be the ratio \nof current to mechanical velocity.\n\nIt might be argued that the use of a power \nratio would be undesirable because there is no \ninstrument available which measures power \ndirectly. This difficulty is, however, more ap- \nparent than real. Power is commonly measured \nin telephony by measuring a current (or voltage) \nin an impedance which is known either by \nmeasurement or by computation. The use of \ncurrent ratios as a measure of transmission is all \nbased on an implied knowledge of the impedances \ninvolved, or at least of their relative values. \nWhere this knowledge is available no more \nmeasurements are required to give the neces- \nsary information about the powers than about \nthe currents. Where it is not available the \nsame steps as are involved in measuring powers \nmust be taken before a knowledge of the cur- \nrents can have any significance as a measure of \ntransmission. The desire to measure power \narises from its own importance in engineering, \nand not from any arbitrary selection of a unit. \nThat it cannot be measured directly may per- \nhaps be considered unfortunate, but it would \nbe more unfortunate still if, having measured \nit by indirect methods, no units were available \nfor expressing the result.\n\nNor does a definition in terms of power ratio \ndo any violence to the concept of the unit as \nbeing derived from the standard cable or the \nso-called \u201cunit line,\u201d which is sometimes asso- \nciated with the 0/ unit. It will be remembered \nthat in tracing the evolution of the S00 cycle\n\nmile there was found a point at which it was \nnecessary in fixing the unit to choose some \ncriterion of the effect of the cable on the wave \ntransmitted over it. While its effect on the \ncurrent has been most commonly chosen, there \ncan be no logical reason other than usefulness \nfor choosing this rather than any one of the \nother quantities which are affected, such as \nvoltage or power. Since, however, experience \nis showing power to be the most useful quantity \nit is obvious that if the 800 cycle mile continued \nin use its natural evolution would be to a power \nbasis. The same is true of the 0/ unit. It would \nseem foolish, therefore, to set up a new unit on \nanything but a power basis.\n\nThe question of power ratio is really one of \nmaking the definition of any unit of the type \nunder consideration broad enough to meet the \nneeds of the art. All of the proposed units \nmay be so defined without restricting their \nusefulness in other directions. Assuming that \nthis is 'done, the choice between them is then \nto be based on other considerations.\n\nUnits which are independent of frequency and \nmeasure the logarithm of a power ratio may \ndiffer only in the magnitude of the unit; that is, \nin the ratio corresponding to one unit. Here \ntwo factors are important: the order of magni- \ntude of the unit and its relation to the systems \nof logarithms in common use. Obviously the \nsimplest units from the latter standpoint would \nbe the logarithms of power ratios of 10 and e. \nTheir values would then be unity in the com- \nmon and natural systems, respectively. How- \never, if some other order of magnitude is more \ndesirable it may be approximated with either \nsystem by taking a multiple or sub-multiple, \njust as the kilometer and centimeter are derived \nfrom the meter. The TU is such a sub-multiple \nof the simplest unit employing the base 10.\n\nLet us consider then the approximate size \nof the unit regardless of the logarithmic base. \nThis question is complicated by the fact that \ntwo quite different sizes are already in use. \nThose familiar with each have acquired a sense \nof the practical significance of any particular \nnumber of the units to which they are accus- \ntomed. Also measuring apparatus and data \nadapted to each unit have been accumulated. \nThe adoption of any universal unit must there- \nfore involve a considerable readjustment of ideas, \nand some expense in conversion of equipment \nand data. The aim then should be to make this \nreadjustment as small as is consistent with \nmaking the most of the rare opportunity of \nselecting the intrinsically best size of unit.\n\nOther things being equal, there is some ad- \nvantage in a unit which bears a unique relation \nto the physical quantity which it measures. \nThe TU, like the \u201c800 cycle mile,\u201d represents \nabout the least difference in loudness which \ncan be detected by the ear without special \ntraining. From this standpoint, therefore, it is \npreferable to the 0/ unit. From the standpoint \nof practical convenience the use of unnecessarily \nlarge or small numbers in expressing commonly \noccurring quantities is to be avoided. With a \nunit of the size of the TU it is seldom necessary \nto use more than two places on either side of the \ndecimal point. Losses approaching 100 TU \nmay be encountered in crosstalk considerations, \nfor example, while the loss of an individual \ncircuit element such as a transformer may be \nexpressible in hundredths of a 1 U. Even such \nsmall losses may become important where the \ncumulative effect of a large number is involved.\n\nThe situation, then, is that the adoption of a \nunit of the size of the TU involves a consider- \nable readjustment on the part of the users of \nthe 0/ unit and a comparatively small readjust- \nment by the much greater number of users of \nthe 800 cycle mile. At the same time, it gives\n\nsome advantages which are inherent in a unit \nof that general size. The adoption of a unit \nof the size oi the pi, on the other hand, would \ninvolve practically no readjustments by those \nnow using pi, but extensive readjustments by \nthose using the mile. It would seem then that \nthe greatest advantage with the least sacrifice \nwould be given by the smaller unit.\n\nComing back to the choice between a unit \nadapted to the use of common vs. natural loga- \nrithms, we may be guided by the general prin- \nciple that in the scientific and engineering world \ncommon logarithms have been shown by their \nextended use to be the more convenient except \nin cases where some special consideration makes \nnatural logarithms preferable. Unless, there- \nfore, it can be shown that such a special con- \nsideration holds in the case of transmission \nengineering, it would be going against well \nestablished experience to select anything but \ncommon logarithms.\n\nThe occurrence of the base e in formulae for \nline attenuation might be advanced as such a \nspecial consideration. While it is true that the \ncomputation of the attenuation of a uniform \nline from its primary constants is simplified by \nusing natural logarithms, the cases where such \nan advantage exists form a small and pro- \ngressively decreasing part of all the uses of \nsuch a unit.\n\nThe practice in certain countries of solving \napparatus problems by reducing them to \nequivalent smooth lines tends to give the im- \npression that the natural base is uniquely \nrelated to a larger field of computation than is \nactually the case. Most of these problems can \nbe solved at least as easily by other methods \nwhich do not introduce the natural base. There \nare, in fact, two distinct methods of attacking\n\ncircuit problems in current use. The one which \nis used largely in those countries where the 0 / \nunit is employed reduces everything to its \nequivalent smooth line. The other, which is \nmore generally used elsewhere, reduces the part \nof the circuit under consideration to a rela- \ntively simple network, which may then be \nsolved by the application of Kirchhoffs Law. \nNatural logarithms are doubtless more con- \nvenient for the first method, and common \nlogarithms for the second. So far as the theo- \nretical man is concerned the choice of unit then \nwould be based on which of these methods is \npreferable. A consideration of this question \nseems to indicate that of the problems en- \ncountered in practical work none are solved \nmore easily by the first method than the second, \nwhereas a considerable number are solved more \neasily by the second. If this is true, the second \nmethod should ultimately replace the first, \nand the demand for the base e, except for \nlong line computations would then largely \ndisappear.\n\nThe increasing use of interconnected lines of \ndifferent types and of terminal equipment, \nsuch as repeaters and carrier current apparatus, \nis reducing the relative importance of long line \ncomputations. Also as a reference to the illus- \ntrations cited under the discussion of power \nratio will show, there is coming to be an increas- \ning need for expressing power ratios which are \nmeasured or else calculated by formulae which \ndo not involve e. Much of this work is done by \nmen engaged in the more practical phases of \nengineering, to whom the convenience of com- \nmon logarithms is very considerable. The fact \nthat the ordinary slide rule gives the result \ndirectly in such cases is a point of considerable \nimportance. On the other hand, the cases in \nwhich natural logarithms are of advantage are \nhandled largely by men of considerable training, \n10 whom the conversion to common logarithms\n\nmay offer a slight inconvenience in manipula- \ntion, hut no theoretical difficulty.\n\nIn view of these considerations it does not \nappear that transmission engineering is so \ndifferent from other branches as to justify a \nspecial type of logarithm.\n\nIt was emphasized in the foregoing discussion \nthat the TU is suitable for expressing a wide \nvariety of different quantities. Space will not \npermit a discussion of all these, but there is one \nwhich deserves attention because of its own \nimportance and because of the fact that its \nmeasurement involves the use of physical stand- \nards. This is the measurement of the overall \nreproduction efficiency of a system for speech as \ncompared with some reference system, the com- \nparison being made by adjusting the \u201cline\u201d in the \nreference system so that speech is reproduced \nby it with the same loudness as by the system \nunder test. The number of units in the line is \nthen taken as the \u201c equivalent\u201d of the system \nrelative to the reference system.\n\nTwo such reference systems based on the two \ntypes of standard cable are in common use, and \nthe specifications for their construction are \nquite well standardized. No such general agree- \nment exists, however, on a reference system \ncalibrated in pi units.\n\nIt should be noted that the use of these refer- \nence systems based on miles gives the results \nin miles of standard cable, and not in \u201c800 cycle \nmiles.\u201d They are, therefore, subject to the \nsame objections as were raised to the mile of \nstandard cable as a unit. The transmission of \nthe system under test is expressed in terms which \ndepend upon the particular distortion intro- \nduced by the standard cable. Furthermore,\n\nowing to the difference in impedance between \nthe cable and the terminal instruments reflec- \ntion effects enter in such a way that when only a \nsmall amount of cable is in the circuit the loud- \nness actually increases with increase of \u201cline\u201d \nup to a certain point beyond which it decreases. \nAs a result certain values of reproduction can be \nobtained with two distinct line settings.\n\nThat the reference systems now standard are \nnot suitable for expressing transmission equiva- \nlents in TU is obvious. The Bell System has \ntherefore, undertaken the development of a \ntransmission reference system designed pri- \nmarily for use with the new unit. While this is \nnot fully developed and calibrated, a general \nidea may be given of the factors entering into its \ndesign and the form which it is taking.\n\nIn line with the fact that the TU is inde- \npendent of frequency, a distortionless reference \nsystem was chosen as the ideal. It might be \nargued that such a system would be unsuitable \nfor comparison with practical systems because \nof their distortion. However, the systems in \nactual use vary in distortion over a wide range, \nfrom heavy loaded cable circuits on the one \nhand to the very high quality systems used for \ntransmitting and reproducing music and other \nentertainment material on the other. 6 It would, \ntherefore, be impossible to select a reference \nsystem having a distortion typical of operating \nconditions in general. Hence it seems prefer- \nable to refer all systems finally to a distortion- \nless standard, thereby eliminating one variable \nfactor.\n\nThe system which is being constructed to ap- \nproximate this ideal has as its adjustable portion \nan artificial line of 600 ohms characteristic \nimpedance made up of resistances and cali-\n\n6 High Quality Transmission and Reproduction of \nSpeech and Music; W. H. Martin and 11. Fletcher; \nJournal of the A. I. E. E. f March, 1924, p. 230; Electri- \ncal Communication, Vol. II, No. 4, April, 1924.\n\nbrated in TU. At one end is a transmitting \ncircuit and at the other a receiving circuit. \nThese are made as nearly distortionless as possi- \nble. Their impedances are GOO ohms pure re- \nsistance, so that no reflection effects enter at the \njunctions with the line. The transmitter is of \nthe condenser type, and is connected with a \nmulti-stage amplifier. The receiving circuit \ncontains an amplifier and a specially damped \nreceiver.\n\nThese circuits are to be defined by assigning \nto them certain conversion ratios between the \nacoustic and electric portions of the system. In \norder to minimize the readjustment of working \nconcepts based on the present reference system \nit is proposed to make the receiving circuit in \nthe new system of approximately the same \nefficiency as that in the old. The transmitting \nefficiency is then to be so chosen that some par- \nticular reproduction efficiency which is repre- \nsentative of operating conditions will correspond \nto the same equivalent in TU with reference to \nthe new system as it does in miles with reference \nto the old. Efficiencies in the neighborhood of \nthis will then differ very little on the two \nsystems.\n\nThe practical determination of the trans- \nmitting efficiency necessary to satisfy this con- \ndition will require a very extended series of \nobservations, since the error in a single obser- \nvation is likely to be large where the distortion \nis so different in the two systems. Owing to this \ndifficulty of comparison it is probable that the \ndistortionless reference system will be used in \npractice only for circuits of relatively high \nquality. Such routine talking comparisons as \nare made on ordinary commercial circuits will \nprobably be made against sub-standards each \nhaving distortion typical of a limited class of \ncommercial circuits. These substandards, will \nbe calibrated against the transmission reference \nsystem by extended laboratory tests.\n\nIn the actual use of the TU , time saving \ndevices such as tables, curves and approximate \nrelations are important. Of these the ordinary \nslide rule has probably the widest application, \nas it permits the conversion between a power \nor current ratio and TU to be made by a single \nsetting. For more accurate results a table of \ncommon logarithms is sufficient. I he curves of\n\nFigure 1 \u2014 Transmission Unit Diagram. For power or \ncurrent ratios greater than 10, move the decimal point \nto the left until the ratio lies between 1 and 10; and for \neach place the decimal point is moved, add 10 or 20 to \nthe figures on the lower or upper scales, respectively. \nFor power or current ratios less than 0.1, move the decimal \npoint to the right until the ratio lies between 0.1 and 1; \nand for each place the decimal point is moved, add 10 \nor 20 to the figures on the lower or upper scales, respectively\n\nFigure 1 furnish a simple means of graphical \nconversion. For very rough mental estimates \nthe approximate relations of Table 1 are con- \nvenient. The error involved in the use of such \napproximations is indicated by the more exact \nfigures given in parenthesis.\n\nTables 2 and 3 furnish the necessary con- \nstants for converting from the TU to other units.\n\nInternational Western Electric \nCompany, Inc., Rio de Janeiro \n(Rua dos Ourives 91-1)\n\nUnited Incandescent Lamps and \nElectrical Company, Ltd., Ujpest \n4 near Budapest", "title": "R 00047", "trim_reasons": [], "year": 1924} {"archive_ref": "sim_att-technical-journal_1931-01_10_1", "canonical_url": "https://archive.org/details/sim_att-technical-journal_1931-01_10_1", "char_count": 273048, "collection": "archive-org-bell-labs", "doc_id": 321, "document_type": "journal_issue", "id": "bella-qwen-pretrain-doc321", "record_count": 338, "release_policy_version": "hf_public_v1", "rights_status": "public_domain", "selected_extraction_backend": null, "selected_extraction_score": null, "source_family": "archive_org", "source_url": "https://archive.org/details/sim_att-technical-journal_1931-01_10_1", "split": "validation", "text": "The Detection of Two Modulated Waves Which Differ \nSlightly in Carrier Frequency\u2014Charies B. Aiken\n\nPublished quarterly by the | \nAmerican Telephone and Telegraph Company \n195 Broadway, New York, N. Fe\n\nBancroft Gherardi Jewett \nH. P, Charlesworth W. H. Harrison B. Colpitts \nL. Morehouse H, D. Arnold 0. B, Blackwell \nPhilesader Norton, Editor J. \u00a9. Perrine, Associate Editor\n\nSUBSCRIPTIONS | \nSubscriptions are acc sted at $1.S0 per year. Singls copies are fifty cents each. \nThe forsign postage ie 38 cents per year or 9 conte per copy,\n\nThe Detection of Two Modulated Waves Which Differ \nSlightly in Carrier Frequency *\n\nThe present paper contains an analysis of the detection of two waves \nmodulated with the same, or with different, audio frequencies and differing \nin carrier frequency by several cycles or more. Both parabolic and straight \nline detectors are treated and there are derived the expressions for all of the \nimportant audio frequencies present in the output of these detectors when \nsuch waves are impressed. There are discussed the types of interference \nwhich result when one station is considerably weaker than the other and \nsimple attenuation formule are employed in estimating the character and \nextent of the interference areas around the two transmitters. Beyond the \nuse of such formule no attention is given to phenomena which may occur in \nthe space medium such as fading, diurnal variations in field intensity, ete.\n\nlength assignment wanders from its proper frequency, waves \nare likely to be received which differ in carrier frequency by several \ncycles or more. Under such conditions the two signals may be thought \nof as made up of entirely distinct frequencies and phase relations \nbetween analogous components of the two waves need not be con- \nsidered. In the important case in which the carriers are of identical \nfrequency this is no longer true and phase and its dependence on \nposition and transmission phenomena must be taken into account. \nThis case will be reserved for future study, the present work being \nlimited to a consideration of the phenomena connected with the \ndetection of distinct frequencies. -\n\nThe most important undesired frequency which is present in \nthe output of the detector is the beat note between the two carriers. \nIt is sometimes carelessly assumed that if the frequency of this beat \nnote is reduced below the audible range the only remaining interference \nwill be due to the speech from the undesired station. Such is not the \ncase and it will be shown later on that when the beat frequency is \nreduced below the audible range, but not to zero, there remains a group \nof spurious frequencies which will introduce an interfering background. \nWhen the undesired carrier is of relatively small intensity this back- \nground is a great deal stronger than the interfering speech. It is \ntherefore desirable to obtain quantitative data on the interfering spec-\n\ntrum which occurs in the receiver output, in terms of the intensities \nand degrees of modulation of the input signals.\n\nIt is to be expected that the results obtained will depend, to some \nextent at least, on the type of detector which is used. The square law \ncharacteristic is a fair approximation to that of any detecting device \nwhich is worked over only a small range and hence an analysis of this \ncharacteristic may be expected to serve as an excellent guide to general \ndetector performance. When large signals are impressed on the \ndetector the functioning of the device may approximate more closely \nto that of the ideal straight line detector. It has been felt that a study \nof these two types would furnish data from which the performance of \nany intermediate type of detector could be inferred without great error. \nAs the problem of the square law detector is very much the simpler it \nwill be considered first.\n\nThere will be assumed two broadcasting stations transmitting on \nfrequencies which differ by a relatively small amount, the beat fre- \nquency being restricted to the audible range or less. Each of the \ncarriers will be assumed to be modulated by a single audio frequency, \nthe modulating frequencies at the two stations being, in general, \ndifferent. The total signal impressed on the receiving detector will \nthen be of the form\n\nv is the total alternating voltage impressed on the detector. \nE is the amplitude of the desired carrier.\n\nm is the degree of modulation of the undesired signal. \nw,/2m is the frequency of the desired carrier.\n\nw2/2m is the frequency of the undesired carrier. \np/2x is the frequency of the desired modulation. \nq/27m is the frequency of the undesired modulation.\n\nWe shall first suppose this signal to be impressed on a detector which \nwill be assumed to have a characteristic in the neighborhood of the \noperating point, of the form\n\nAn expression of this type will accurately represent a small portion of \nany continuous characteristic. The present analysis requires that the \nimpressed e.m.f. shall be of small amplitude in order that the limits of \nthe portion of the characteristic thus represented may not be exceeded. \nThis restriction is necessary in treating square law detectors.\n\nThe audio frequency output of the detector will be due entirely to \nthe second order term in (2). Hence it will be sufficient, for our \npurposes, to square the expression for v. We are interested primarily \nin the ratios of the amplitudes of the various undesired audio fre- \nquencies produced to the amplitude of the desired signal of frequency \np/2x. Such a ratio will be designated as a relative amplitude. Neg- \nlecting circuit constants, etc., which will apply equally in all the \nexpressions for the various frequencies, the amplitude of the desired \ncomponent of the audio frequency output is readily shown to be /2.1/. \nThe expression for v* is reduced to first power sinusoids and the ampli- \ntude of each frequency converted to a relative amplitude by dividing \nby #\u00b0M/. The case in hand yields twelve undesired audio frequencies, \nthe relative amplitudes of which are listed in table I. Before com- \nmenting on these results we shall consider the straight line detector.\n\nTABLE I \nAngular Ratio to | Angular | Ratio to \nVelocity | | Velocity \nM e \nem \nq EM | salmaaa 2EM \np + | em \ne \nEM\n\nIn making analyses of rectification by a straight line detector it is \ncustomary to reduce the sum of the various impressed radio frequencies \nto a single radio frequency, the amplitude and phase angle of which are \nslow functions of time. The most common example of this type of \ntreatment is a combination of the carrier and two side bands of single \nfrequency modulation into the familiar expression for a modulated\n\nwave in which the amplitude of the radio frequency is an audio \nfrequency function. In this case the radio frequency phase angle is \nconstant. In the case of a single frequency modulation with one side- \nband eliminated there are impressed on the detector input only two \nfrequencies. These may be combined in a well known manner.! \nThus, if the impressed voltages are of the form acosx and bcosy, then \nthe amplitude is given by\n\nThe expression for the phase angle will not be given here as it can be \nshown that if a and b are unequal and the difference between the \nfrequencies x/27 and y/27m is small compared with either frequency, \nthen the variation of the phase angle with time may be neglected in \ncomputing the audio frequency components. In the present case we \nhave two radio frequency waves the amplitudes of which are not \nconstants but are slow functions of time and these may be substituted \nfor a and b in (3). Thus the effective amplitude of the total input \nsignal may be taken to be\n\nu = @1\u2014 Wo. \nThe problem then resolves itself into an analysis of the detection, by a \nstraight line detector, of a single radio frequency component. The \nresults of such an analysis are well known and it can be readily shown \nthat the audio frequency output may be obtained, except for a factor \nof proportionality, by resolving the amplitude into its audio frequency \ncomponents. In the present case the amplitude to be resolved is \ngiven by (4) which may be written\n\nThe interfering signal B will be taken to be always less than the de- \nsired signal A, and hence A? + B? > 2AB, from which it follows that \n(A + B)? > 2AB(1 \u2014 cos ut.) Hence the radical may be expanded \nby the binominal theorem, giving\n\nIt is to be observed that each of the terms of this series, except the \nfirst, contains time in the denominator and hence further expansions \nare necessary. The denominators of the various terms can be ex- \npanded by the binominal theorem in such a way as to put all the \nexpressions containing time in the numerators, the expansions being in \npowers of \n(ME cos pt + me cos gt)/(E + e).\n\nBy the proper trigonometric transformations it is possible to reduce the \nfinal expression for S to frequencies in p, g, \u00ab and the sums and differ- \nences of the various multiples of these quantities. An additional \ndiscussion of this analysis is given in an appendix. In order that the \nvarious series involved may converge with a manageable degree of \nrapidity it is necessary to limit the relative amplitudes of the interfering \ncarriers and the degrees of modulation as well. Consequently the \nsolutions are restricted to intensities of the interfering carrier of 0.1, or \nless, of the desired carrier and to degrees of modulation of either signal \nranging from 0.1 to .5. These limits are suitable also because we are \ninterested chiefly in interference by a relatively weak signal, the inter- \nference caused by a signal, the carrier amplitude of which is greater \nthan 0.1 of that of the desired carrier amplitude being near the tolerable \nlimit in the majority of cases. The upper value for the modulation of \n0.5 is approximately equal to the average degree of modulation of a \nstation employing as deep modulation as is practical, only the peaks \nrunning up to nearly unity. The value of 0.1 for the lower limit is of \ncourse transgressed by soft passages in speech or music. However, the \nrange here specified is sufficiently large to give an excellent idea of \nwhat may be expected from various degrees of modulation of desired \nand interfering signals and the results of more extreme cases may be \ninferred from the data here developed. Under these limits it is found \nthat the only audio frequencies of any importance which appear in \nthe output are:\n\nIt is now possible to make a comparison between the performance \nof the straight line and the square law detectors. In Figs. 1 to 4 are \nshown the relative amplitudes of the interfering frequencies in the two \ncases for various degrees of modulation. The data for the square law \ncase are indicated by dashed lines and for the straight line case by \nsolid lines, and where the two coincide this is noted on the figures. It \nis to be noted that the expression for the amplitude of the desired \nfrequency p/27 is a complicated function. However, computation \nshows that over the range in which we are interested, the value of this \nexpression does not differ from .\\JE by more than 1 per cent and, \ntherefore, this value has been assumed in computing the relative \namplitudes of the other frequencies.\n\nProbably the most striking feature to be noted-in comparing the two \ncases is the similarity of the results. This is particularly evidenced by \nthe carrier beat note of frequency u/27 the amplitude of which differs \nin the two cases by an inappreciable amount. The spurious fre- \nquencies (\u00a2 + \u00ab)/2m also are practically identical for both detectors. \nThere are, however, several important differences as follows:\n\nThe group of spurious frequencies of angular velocity p + q + u, \nwhich is of appreciable importance in the square law case, is entirely \nabsent from the range of magnitude considered when a straight line \ndetector is employed. The frequencies (p + u)/27 are greater in the \nsquare law case over the range which we have considered, but the \ncurve which represents them has a smaller slope than in the straight \nline case and for larger values of the interfering signal the intensities of \nthese frequencies would be relatively less with the square law detector. \nThe intensity of the undesired speech q is definitely less in the straight \nline case than in the square law case but the slope of the g curves is\n\nabout the same for both except for 1J = m = 0.5. It is of interest to \nobserve that the interfering speech received on the straight line detector \nis very much less in intensity than would be the case if the strong \ndesired signal were absent, and that the variation of the amplitude of \nthis frequency with intensity of the undesired carrier is greater when \nthe desired frequency is present. We have here an analytical descrip- \ntion of the familiar masking effect which occurs when a strong unmodu- \nlated carrier is received simultaneously with a weak modulated signal. \nFor example, when e/E = 0.1 it can be seen from Fig. 1 that the \nrelative amplitude of the component of frequency g/27 is 0.0063 for \nthe case of the straight line detector. If this component were un- \naffected by the presence of the strong signal it would have an amplitude \nproportional to em and a relative amplitude of em/E.\\W which for the \nvalues here considered is 0.1. Hence the \u2018 masking\" effect is here \nresponsible for a reduction of 24 db.\n\nLastly, it may be mentioned that there are in the case of the straight \nline detector certain frequencies of small amplitude which are entirely \nabsent from the square law case. However, no frequency is shown \nthe relative amplitude of which is less than 0.01 for all four pairs of \nvalues of .\\/ and m, as such frequencies are unimportant. An exception \nis made with regard to p + u. This is always less than 0.01 over the \nrange considered but is included for the sake of comparison with the \nsquare law results.\n\nThe second harmonic of the desired signal is of importance only in \nthe square law case. It is of the nature of a distortion which is inde- \npendent of the interference and may be omitted from the consideration \nof the undesired audio frequencies which are a result of the interference. \nFrom Figs. 1 to 4 it is evident that the most important interfering \nfrequencies are those of angular velocity, +u, p+uand p+tg \n+ u, the last being of importance only in the case of the square law \ndetector. It is with these frequencies, together with that of the \ninterfering speech g/27, that we shall be chiefly concerned.\n\nWhen the relative magnitudes of the interfering frequencies, which \nare tabulated on page 3, are multiplied by *.V/, the resulting quantities \nare proportional to the absolute magnitudes of these frequencies. It \nis to be noted that the frequencies of greatest interest have absolute \nmagnitudes which are linear functions of \\/ or m except (p + q + u)/27 \nwhich is proportional to mM, and u/2x which is independent of both 1/ \nand m and will, therefore, be unaffected by the type of modulation \nemployed at either station. In case there are several frequencies\n\npresent in the modulation of each station the radio frequency waves \nwill be of the form E(1 + VM, cos pit + Me cos pot + +++) cos wit and \ne(1 + m, cos git + me Cos got + +++) cos wet. For every frequency of \nthe former case which contained ./ as a factor of its amplitude we shall \nnow have several frequencies respectively proportional to 1,, M2 etc. \nwhile an analogous new group will correspond to the former frequencies\n\nDESIRED SIGNAL=E (i+MCOSPT) COS w,T \n>, UNDESIRED SIGNAL = e(i+MCOSQT) COSwaT \n3 |_ DATA FOR SQUARE LAW DETECTOR \u2014\u2014\u2014\u2014 \nWw DATA FOR STRAIGHT LINE DETECTOR \n& \nfa) \nied \n2, \n2 \nWw \n/ \n/ \na \nno! \n3 o \nQ \n< es \nVA) \n\u00a5 \n/ | \n.001 CY, | \n0001 001 01\n\nFig. 1\u2014Relative amplitudes of undesired frequencies as a function of the ratio of \nthe amplitudes of the desired and the interfering carriers. Modulation of both \nstations small and equal.\n\ncontaining m. Hence we shall have two frequency spectra derived \nfrom the desired speech spectrum containing the p\u2019s, but one of the \nspectra will be shifted upward in frequency by an amount u/27 and \nthe other downward by the same amount. Two additional spectra \nwill be derived in a similar manner from the undesired speech spectrum \ncontaining theg\u2019s. The frequencies of the type (p + q + u)/27 will be\n\nnumerous as there will be a product of the .\\/\u2019s with each of the m\u2019s. \nHowever, these are of even moderate importance only when the \nmodulations of both stations are high, and a square law detector is \nemployed at the receiver.\n\nHence we may picture the interference as made up chiefly of dis- \nplaced frequency spectra of the type mentioned above, of a carrier\n\nFig. 2\u2014Relative amplitudes of undesired frequencies as a function of the ratio \nof the amplitudes of the desired and the interfering carriers. Modulation of desired \nstation small and of interfering station large.\n\nbeat and of the interfering speech, which is weak but important because \nof its intelligibility. The results in the case of a straight line detector \nwould not be very greatly different. The frequencies of the type \n(p +q +u)/2r would be negligible, the two spectra derived from \np + u would be much less important and certain new, but rather small \ncross product frequencies would appear.\n\nIn estimating the interference the carrier beat can be considered by \nitself and from the data at hand there can be derived the areas around \neach of two stations having approximately the same carrier frequency, \ninside of which the amplitude of the beat note will be down a given \nnumber of db from that of the desired speech. The same is true of the \ninterfering speech when it is different from the desired speech. The\n\nFig. 3\u2014Relative amplitudes of undesired frequencies as a function of the ratio \nof the amplitudes of the desired and the interfering carriers. Modulation of desired \nstation large and of interfering station small.\n\nfrequencies (p + u)/27,(q + u)/27,(p & q + u)/27z, etc., will combine \nto form a disturbing background which we shall designate as \u201cdisplaced \nside band interference.\" This may be taken to include all of the \ninterfering frequencies except those of the undesired speech and its \nentirely unimportant harmonics. (The frequency 2/27 is not here \nclassed as an interfering frequency.)\n\nFrom Figs. 1 and 4 it is to be noted that when m = M the frequencies \n(g + u)/2e are the largest components of the displaced side band \ninterference if a straight line detector is used and have the same \namplitude as the (p + u)/27 components if a square law detector is \nused. When m > VM the g + u group is much more important than \nthe p + u group as is evident from Fig. 2. When \\J > m the g + u\n\nf \n4 \u201c| \n44 \nOl \n4 \n207 fy \nA | \n7 \n/ \nfe? \n001 af \n000! e OO! Ol \n/e= RATIO OF CARRIER AMPLITUDES \nFig. 4\u2014Relative amplitudes of undesired frequencies as a function of the ratio of\n\nthe amplitudes of the desired and the interfering carriers. Modulation of both \nstations large and equal.\n\ngroup is less important but this case is of no great interest for if the \nstations are transmitting identical programs, with similar degrees of \nmodulation, it cannot occur and if the programs are different then the \ninterference is determined primarily by what happens when m > JM. \nConsequently we may consider that the g + u group constitutes the \nmost important part of the displaced side band interference except\n\nwhen a square law detector is used and the programs are identical. In \nsuch a case we shall assume that both stations employ the same degree \nof modulation and that therefore the g + u and p + wu groups are of \nthe same importance.\n\nWe have distinguished between three types of interference, namely, \ncarrier beat, unwanted speech and displaced side band. We shall now \ncompute, for several values of attenuation, percentage modulation \netc., the areas around a transmitting station inside of which each of \nthese types of interference, due to a second station, will have a relative \nimportance which is not greater than a certain specified amount.\n\nIn estimating these areas we must deal with two possible cases which \nmay arise in practice: (1) The two stations transmit different programs. \n(2) The programs are the same. The carriers are assumed to differ in \nfrequency in both cases.\n\nThe importance of the various types of interference which are \npresent, will be determined by their ratios to the intensity of the \ndesired speech. In the present case in which the two stations transmit \ndifferent programs, the amount of interference which may be tolerable \nwill be determimed by what occurs when the modulation of the desired \nstation is low, while that of the interfering station is high. Hence, in \nstudying this case we shall make use of Fig. 2, which gives data com- \nputed on the basis of a modulation of 0.1 for the desired station and \n0.5 for the interfering station.\n\nTaking up first the consideration of the carrier beat note, we shall \ndetermine the curve along which the intensity of the beat is down a \ngiven number of db from the desired speech. The position of this \ncurve will depend on the degree of modulation of the desired signal, \nsince the lower the modulation the more noticeable will be a beat note \nof a given intensity. When we have specified the db difference which \nmust exist between these two components of the receiver output the \ncarrier ratio can be picked off from the u line of Fig. 2.\n\nIn order to determine the curve along which this carrier ratio exists \nwe shall proceed as follows:\n\nThe desired station will be considered to be at the origin of a system \nof rectangular coordinates and the undesired station will be at the \npoint (D, O). We shall assume that the powers of the desired and \nundesired stations are P; and P2, respectively, and that their distances \nfrom a point in the coordinate plane are d; and d2; then if we denote the\n\nThis equation is based upon a convenient form of the Austin-Cohen ? \nformula for the intensity of the field radiated from a radio transmitter.\n\nin which J is the wave-length in meters, d is the distance from the \ntransmitter in miles and @ is an attenuation constant which may range \nfrom zero up to 0.01 or even more. In writing down equation (8) we\n\nFrom (8) there have been computed curves for the case in which \nP, = P, and for various values of K and @. X has been taken as 300 \nmeters and D, the distance between the stations, as 1,000 miles.\n\nIn Fig. 5 are shown several curves for a = 0.001. For small values \nof K, the curves are practically circular and are of small area. As K \nincreases, the curves become oval shaped and it can be readily shown \nthat for values of K greater than a certain critical amount, the curves \nwill not close but will be of a shape which is roughly hyperbolic.\n\nIn Fig. 6 are shown curves corresponding to a value for @ of 0.002. \nIt is to be noted that an increase in a enormously increases the area \ninside of which the ratio of the carriers is less than a certain value. \nThe effect of a will of course be dependent upon the magnitude of the \ndistance between the stations and will be more pronounced the larger \nthis distance. For the present case in which D = 1,000 miles, there \nis not much point in considering values of a larger than 0.002, since the \nattenuation would be so great as to make the effect of one station on the \nservice area of the other of very little consequence.\n\nIf we specify that the carrier beat must be at least 40 db down from \nthe speech output due to a 10 per cent modulated signal, then curve 1 of \nFigs. 5 and 6 will represent the areas inside of which this requirement \nwill be met, while if we call for an interval of 20 db between these two \ncomponents, curve 5 of Figs. 5 and 6 will represent the areas in which the \ncondition is satisfied. It is evident that if a rigid restriction is placed \non the permissible beat note interference which may be allowed, and if \nthe attenuation is of a small value then the area in which the beat\n\nnote may be neglected is extremely small. On the other hand this \narea increases very rapidly as the attenuation increases.\n\nWe may use the same sets of curves in considering the displaced \nside band interference. From Fig. 2 it is evident that by far the most \nimportant components of this interference are those represented by the \n(g + u) group. In order to estimate this interference we must follow \nsome rule for combining the g + u component with the g \u2014 u com- \nponent. In order to do this in a strictly correct manner we should \nhave to take into account the frequencies and sensation levels of the \ncomponents. However, it has been shown * that over a considerable \nportion of the audio frequency range, and for sensation levels of \napproximately the magnitude in which we are interested, the inter- \nfering effect of these frequencies may be taken to be approximately \nequal to that due to a single frequency of twice the amplitude of \neither component. We shall therefore take our data from the dash-dot \ncurve of Fig. 2. From this curve it appears that if the displaced side \nband interference is to be 40 db down from the desired speech, we must \nhave a carrier ratio of 0.002, while if it is to be 20 db down from the \ndesired speech the corresponding carrier ratio is 0.02. The curves \ncorresponding to these values are shown by 2 and 6, respectively, on \nFigs. 5 and 6.\n\nFrom this it appears that the area in which the side band noise is not \nobjectionable may be a great deal larger than that in which the carrier \nbeat is of a tolerable intensity. If the frequency of the carrier beat is \nreduced below the useful audible range then the former area may be \nconsidered to be entirely free from interference of any kind. Conse- \nquently, it is highly desirable to limit the maximum possible differences \nin the carrier frequencies to a value which is definitely below the audio \nfrequency pass band of commercial radio receivers and loud speakers.\n\nTurning now to the undesired speech, we note that it is of very little \nimportance compared with the displaced side band interference. Thus, \nif this speech is to be 40 db down from the desired speech, the value of \nthe carrier ratio is 0.044 for the case of a square law detector, while for a \ndifference in level of 20 db, the carrier ratio is 0.14. A curve for the \ncase of a 40 db difference is indicated by 7 of Fig. 5.\n\nThe comparison between curves 7 and 6 emphasizes the fact that we \nmay have considerable areas of intolerable displaced side band inter- \nference in which the intelligible speech from the undesired station is \nnot noticeable. Of course, this interference is often classed as distorted \nspeech but the distinction is convenient in the present discussion.\n\n3 J.C. Steinberg, \u2018\u2018The Relation Between the Loudness of a Sound and its Physical \nStimulus,\u201d\u2019 Phys. Rev., Sec. Ser., Vol. 26, pp. 507-523.\n\nIn this case the programs are identical and consequently the speech \nfrom the two stations will undergo simultaneous fluctuations of \nintensity. We shall here assume that the two stations have the same \ndegree of modulation at any instant. We may then take our data \nfrom the curves for which 1f = m. However, this does not apply to \nthe carrier beat note, since its intensity is independent of the degree of\n\nFig. 5\u2014Curves along which the ratio of the carrier amplitudes received from two \nstations has a constant value K, as indicated. Attenuation small.\n\nmodulation of either station and its interfering effect will be determined \nby conditions which exist when the desired station has a low degree of \nmodulation. Hence the discussion of this component of the inter- \nference will be exactly the same as in the preceding case.\n\nReferring to Figs. 1 and 4, it is evident that by far the greatest \nportion of the displaced side band interference is due to the gq + u \ncomponents, in the case of the straight line detector, and the g + u \nand p + \u00ab components in the case of the square law detector. The\n\nidentity of the curves for these components in the two figures shows \nthat the degree of modulation has practically no effect on the relative \nimportance of the interference which occurs when the same programs \nare transmitted.\n\nIf we again assume that the total interference may be represented by \na fictitious component of twice the amplitude of the g + u component,\n\nFig. 6\u2014Relative amplitudes of undesired frequencies as a function of the ratio of \nthe amplitudes of the desired and the interfering carriers. Attenuation constant \na twice that of Fig. 5.\n\nwe may take our data from the dash-dot line of Fig. 4. This should \nrepresent the case fairly well for the straight line detector but when a \nsquare law detector is used, greater interference should result due to the \nimportance of the p + u terms. However, we shall consider only the \nq + u group and the phenomena associated with the square law case \nmay be readily inferred. In order that the displaced side band \ninterference may be 40 db down from the desired speech the carrier \nratio must have a value of 0.01, while if it is to be 20 db down, this \nvalue must be 0.1. The first value corresponds to curves 5 of Figs.\n\nDETECTION OF TWO MODULATED WAVES 17 \n5 and 6, while the second value corresponds to curves 8. We observe \nthat there is a tremendous difference between the areas which may be \nconsidered to be free from displaced side band interference and those \nwhich will be free from carrier beat interference, in case the beat \nfrequency is allowed to wander into the audible range. The comparison \nbetween the two areas is given by curves 1 and 5 for the 40 db interval \nand by curves 5 and 8 for the 20 db interval.\n\nThe speech from the interfering station will now be the same as the \ndesired speech and can have effect only in so far as it adds to or subtracts \nfrom the desired speech. It will be noted from Figs. 1 and 5 that for \ncarrier ratios of less than 0.1 this component is always down more than \n40 db and may be safely neglected.\n\nThe foregoing discussion serves to illustrate the types of interference \nwhich may be expected when two stations are operated on approxi- \nmately the same frequency. The data discussed have involved low \nvalues of attenuation. This is of particular interest when the distance \nbetween stations is large since with high values of attenuation either \nstation will have very little effect on the service area of the other. Of \ncourse at night time we may have signal strengths which will be of the \norder of magnitude of that given by the simple inverse distance law \ninvolving zero attenuation. This possibility probably presents a \nserious limitation on night time common frequency broadcasting but \nshould be of little consequence during the daylight hours. Conditions \nwill be somewhat different for stations that are placed nearer together \nand specific results can be readily computed for any given spacing. \nThe equations which have been discussed can be applied to any such \ncase and the areas corresponding to those in Figs. 5 and 6 determined.\n\nOne point which is emphasized by the results which have been \nobtained is, that with a carrier frequency difference of several cycles \nsatisfactory reception cannot be expected in the regions which lie \nmidway between two transmitters. The field strength of one station \nmust be at ali times predominately higher than that of the other and \nconsequently the use of pseudocommon frequency broadcasting should \nbe restricted to stations of wide geographic separation. It should then \nbe possible to furnish high grade service to relatively small densely \npopulated areas in the immediate vicinity of either transmitter, \nreception at a considerable distance from both stations being ad- \nmittedly unsatisfactory. However, if the carriers are strictly isoch- \nronous much larger service areas should be feasible.\n\nAPPENDIX \nEquation (5) is \nI II \nAB(1 \u2014 cos ut) \nIll IV \n_ A*B(1 \u2014 cos ut)? A*B(1 \u2014 cos ut)? (5) \n2(A + 2(A + B)\u00ae \nTo expand these terms we write \n1 1 \n(A+B)\"\u201d (E+e+ME cos pt+me cos qt)\" \no 1 (1 _ n(ME cos pt+me cos qt) \n~ (E+e)\" E+e \n4 n(n+1)(.ME cos pt+me cos qt)? \n+e)? \nrE +e)\"\n\nIt is evident there are present in S an infinite number of frequencies \nand it is necessary to select those which are of appreciable magnitude \nrelative to that of the desired frequency of amplitude E./. Fortu- \nnately these are not very numerous.\n\nIn deciding whether or not a given term should be retained there \nare two points to be considered: (1) whether all the terms of a given \nfrequency total to a value sufficiently large to call-for the presence of \nthis term in the final result; (2) what per cent accuracy should be \nrequired in the frequencies which are retained. Thus if it is desired to \nretain all frequencies the relative amplitude of which is greater than \n_ 0.01 we cannot arbitrarily retain all individual terms which make a \ncontribution of 0.01 or greater and neglect those of relative importance \nof less than 0.01. Thus if a term of a given frequency has a relative \namplitude of 0.01 and another term of the same frequency a relative \namplitude of 0.009 the second term should be retained. Otherwise we \nshould have a large percentage error in the value of the amplitude of \nthis frequency. On the other hand it is not desirable to maintain \nthe same degree of accuracy for the case of retained frequencies of \nslight relative importance as for those of large importance. As a \ncompromise all individual terms have been retained which, after \ndivision by E.M, are of a magnitude greater than 0.005 for any values \nof \\/, m and e/E which are here dealt with. An exception is made in\n\nthe case of a term in cos pt derived from term III of (5). This term is \nslightly larger than the above limit when J = 0.5 and e/E = 0.1 but \nas it decreases rapidly with a decrease in e/ it has been omitted for the \nsake of simplicity.\n\nHaving chosen this limit of 0.005 for the relative magnitude of \nindividual terms it can be shown to be permissible to neglect term IV \nand all subsequent terms of (5). Furthermore, only a few of the large \nnumber of terms yielded by III need be retained.\n\nAfter applying these rules there appear several frequencies that are \nnever as large as 0.01 in relative magnitude and these have been \nomitted from consideration. As has been stated in the body of the \npaper, an exception is made in the case of the frequencies (p +g +1)/27. \nIf a given frequency exceeds 0.01 for any one of the four pairs of \nvalues of ./ and m, it has been shown on the figures for all of the \npairs.\n\nAfter the formula (5a) has been applied to S and the expressions for \nA and B inserted there remains the necessity of reducing products and \npowers of various sinusoidal terms to sums of simple first order \nsinusoids. This is a tedious procedure but is a matter of simple \ntrigonometry and will not be set forth in detail.\n\nFrom (5a) it can be seen that if .W or m is near unity the series will \nconverge very slowly. Furthermore, since to obtain relative magni- \ntudes we divide by .V/, it is impossible to obtain satisfactory convergence \ndue to small values of ./ in the denominator. Hence it is necessary to \nlimit ./@ and m to 0.5 or less and in addition .\\/ must be no smaller than \n0.1. It would be permissible to allow m to become less than 0.1 but as \nlittle would be gained by this m has been restricted to the same range \nas M.\n\nPor accurate determinations of hysteresis loops and initial magneti- \nzation curves of magnetic specimens, a laborious routine involving \nthe use of a ballistic galvanometer is usually necessary. This article \ndescribes an apparatus by means of which these curves may be obtained \nphotographically with quantitative accuracy. Attempts to devise \nsuch a scheme have previously been made. Ewing! describes one \nwhich was used with short, thick specimens in a magnetic yolk. \nFleming? invented a device, the Campograph, which made use of a \nmagnetometer and had the advantage of making possible the use of \nlong, thin, specimens, thus reducing eddy current and demagnetization \neffects. J. B. Johnson * describes the most recently published design, \nembodying a vacuum tube amplifier and a Braun tube oscillograph. \nThis hysteresigraph is used with frequencies of the order of five cycles \nper second, or higher, and consequently introduces an eddy current \nloss, a disadvantage in a great many measurements.\n\nThe greatest difficulty has always been to devise an instrument \nwhich would accurately record the total change in magnetic flux in \nthe specimen. The ideal instrument would be a fluxmeter with no \n- restoring force and no friction. Fluxmeters are on the market in \nwhich the restoring force is negligible only over short periods of time \nor in which there is no restoring force but where the friction is appreci- \nable; but if it is required that the magnetic cycle have a period of more \nthan a few seconds, such fluxmeters are out of the question. In \naddition they require that the search coil be of such low resistance \nthat it must have too few turns for use with long thin specimens, in \nwhich the flux is small. These difficulties have been overcome in the \napparatus described below, in which the principal feature is the use of a\n\nfluxmeter in which the suspended coil has its restoring torque counter- \nbalanced for all deflections within a range sufficient for accurate \ndelineation of magnetic curves. \nDESCRIPTION OF THE APPARATUS\n\nThe operation of the apparatus is as follows: a long, sensitive, photo- \nelectric cell is fitted with a V-shaped slit, as shown in Fig. 1; a beam of\n\nlig. 1\u2014The photoelectric cell circuit. \nlight is reflected from the mirror of the fluxmeter and focused on the \nslit of the photo-electric cell, which is connected, in series with a \nsource of e.m.f., across the terminals of the fluxmeter; the e.m.f. is \nadjusted once for all to such a value that, if the beam is at rest when \nat the narrow end of the slit, at any other position the current con- \ntrolled by the cell will develop a torque in the Muxmeter coil which just \nbalances the restoring torque of the suspension. The fluxmeter \ndeflection will then be proportional to the change of flux which has \noccurred within the search coil S. It may be found necessary to shape \nthe slit empirically to correspond to the unequal sensitivities of the \nphoto-electric cell at different spots. The fluxmeter used is a Leeds \nand Northrup type 2290 HS galvanometer. It has a critical damping \nresistance of about 100,000 ohms, and when used with about one \nhundred ohms in the external circuit it is much over damped.\n\nfor changing the magnetic field in the specimen, is shown in Fig. 2. A \ndrum D, carrying photographic paper, is placed in a light-tight box \nprovided with a long, narrow slit parallel to the axis of rotation of the \ndrum. A beam of light froma second lamp is reflected by the fluxmeter \nmirror and focused on the slit. This beam is reflected by the same \nmirror which reflects the beam onto the photo-electric cell, the two\n\nbeams being incident at different angles. Attached to the shaft of \nthe drum is an arm A, which slides along the rheostat R. A battery B \nis connected across R, and a center tap soldered to it. Between the \narm A and the center tap a varying e.m.f. is produeed which is applied \nto the field coil #. This e.m.f. reverses its sign every time the arm A \nslides past the center of the rheostat, and the latter is curved in a \nmanner calculated so that the field current will be proportional to the \nangle of rotation of the drum from the position for zero current. The \nsearch coil S of Fig. 1 is placed within F, and consequently when D is \nrotated it moves the photographic paper past the slit so that the \ndistance moved is propwrtional to the change in field current, while at \nthe same time the fluxmeter deflects the beam of light along the slit so \nthat the deflection is proportional to the time integral of the changes \nof flux within S. As the drum is turned from one position to another, \na curve with rectangular axes is thus registered, the scales of which \nmay be calibrated in terms of Band H. Figs. 4 to 7 are some examples \nof curves taken with the apparatus.\n\nIn Fig. 3 the electrical circuits are shown in detail. R; is the rheostat \ncontrolling the field current, and A is the arm which rotates with the\n\nout thermo-electric potentials and current from the photo-electric cell \nPHOTO\n\ndue to stray light. R,and R; are adjusted according to the amount of \nflux in the specimen, in order to keep the maximum deflection within \nthe desired limits. The mutual inductance J/ is used to balance out \nthe potentials produced in S when no specimen is within it, so that the\n\nfluxmeter deflection is proportional to the change in B -- 77. The \ndrum is conveniently rotated by an electric motor, connected by gears \nso that the drum makes about one revolution in two minutes, and it is \ndesirable to have this rate variable. The motor may be reversed, so \nthat complete hysteresis loops may be recorded.\n\nIn setting up the apparatus the photo-electric cell may be con- \nveniently placed above or below the drum, and one lamp above the \nother. The lamp used to illuminate the photo-electric cell should \nfurnish a brilliant beam, and it was found that a 250 watt Mazda \nprojection lamp was quite satisfactory.\n\nThe circuit is calibrated by passing a known current through the \nprimary of a known mutual inductance, the secondary of which is \nconnected in series with the search coil S. By measurement of the\n\ndeflection _produced the relation between the quantity of electricity \npassing through the fluxmeter and its deflection can be determined. \nFrom this relation and other known constants the change in induction \nof a magnetic specimen producing a given deflection may be calculated.\n\nmagnetic specimen be removed, Ry and R, be set on infinite resistance, \nthe magnetizing coil F be shorted, and a change in the field current\n\nFig. 8\u2014Line taken for calibrating the apparatus. \n= instantaneous primary current, \ninstantaneous secondary current, \nresistance of secondary circuit, \nmutual inductance of , \nself inductance of secondary circuit.\n\nwhere Qs; is the quantity of electricity that has passed through the \nfluxmeter in time fo. Now let Qa = \u2014 K\u00e9y, where 6 is the deflection \nproduced when Qy flows. Then:\n\nand the quantity of electricity which has passed through the luxmeter \nfor any other deflection is \n1 \n(1)\n\nNow suppose a magnetic curve recorded with R, adjusted until the \ndeflection is due solely to the magnetization of the specimen. Let the \nresistance of the fluxmeter plus that of the secondary of M be denoted \nby R,, and that of S plus R; be denoted by R,. Then if the field\n\ncurrent ig is varied slowly enough, the time lag in the secondary \ncircuit will be negligible and we shall have for the instantaneous \ncurrent in the fluxmeter:\n\nwhere A is the cross sectional area of the specimen and _N is the number \nof turns in the search coil. Then\n\nr. being the total secondary resistance when K was determined. This \nequation, then, gives B \u2014 H for any given deflection 4, in terms of \nknown constants. For any fluxmeter, K is determined once for all by \npassing the current 7 through a mutual inductance and measuring the \ndeflection 54 on a photographic record. The other constants are \nchanged in a calculable way when the number of turns in the search \ncoil, the resistance settings, and the cross-sectional area of the sample \nare changed.\n\nSince it is the voltage applied to the magnetizing coil F which is \nproportional to the angle through which the drum has rotated, there\n\nis a lag in the field current behind the field registered on the drum, due \nto the self inductance of the coils. Added to this there is a lag in the \nsecondary due to its self inductance, and another lag due to the time \nrequired for the fluxmeter to act. The effect of these is to widen the \nloop. In Fig. 9 is shown a curve traced with no magnetic sample in \nthe field coil, and with d#//dt so great that the lag is appreciable.\n\nFig. 10 shows two loops, the outer one representing a loop as taken on \nthe apparatus, and the inner one the true loop corresponding thereto. \nLet B be some induction near zero, on the traced loop. B will be \nincorrect for the indicated value of JJ by an amount Bo -\u2014 B, such \nthat if the field were held constant at that point while the drum con- \ntinued to rotate the curve would approach By as an asymptote, as \nindicated by the dotted curve. If d///dt is not zero, B may be regarded \nas momentarily approaching By as an asymptote. The equation for \nB at any instant is:\n\nwhere \\, is the time constant of the circuit and Boy is not a constant\u201d \nbut a function of HJ and \u00a2. If we assume that dB/d/H/ is constant for a \nsmall region in the neighborhood of B = 0, we have, putting AJ/, \nequal to the error in coercive force IJ,\n\nData taken with no magnetic specimen inserted show that this linear \nrelation actually exists. Added to this there is an increase in /7, due to\n\neddy current lag. Johnson * has derived an equation for this, and with \na slight modification to make it applicable to cylindrical specimens, it \nis:\n\nwhere p is the resistivity of the specimen, and r its radius. This gives \nus for the total error,\n\nwith varying dH/di. The specimen used was a cylinder of 81 per cent \nNi permalloy, 60 cm. long and 0.1 cm. in diameter, and was placed in a \nmagnetic yolk. Its hysteresis loop, as shown in Fig. 11, has an\n\nunusual slope, 225,000 at B = 0. This gives \\2: = .055 sec. From \nthis series of curves the straight line showh in Fig. 12 was obtained, for \nwhich A; + Az = 0.314 sec. By another set of loops in which the\n\ndeflection is produced by an air core mutual inductance, A, is found to \nbe 0.134 sec. This determines dz as 0.180 sec., in disagreement with \nthe value 0.055 sec. calculated from Eq. 5. Johnson assumes in his \nderivation that dB/d// is constant and hence that the shape of the \ncurve before H, is reached has no effect on A/7,. It is probable that \nif the equation were changed to allow for dB/dH being a function H,\n\nthat the difference could be accounted for. At any rate, this error is \nnegligible for all but specimens with exceptionally high dB/dH or \ngreat thickness, and the true coercive force can always be found by \ntaking two loops with different values of d/Z/dt and extrapolating to \ndiI/dt = 0.\n\nAnother possible source of error is the passage of a large fraction of \nthe photo-electric cell current through the search coil, the field being \nthereby altered. The maximum photo-electric cell current used is on \nthe order of 5(10)-7 amperes. Since the search coil is unlikely to have \nmore than about 400 turns per centimeter, this would make the \nmaximum error in /7 about 2.5(10)~ gauss, which is negligible for most \nmeasurements.\n\nAs a test of the accuracy of the instrument, a comparison was made \nwith curves made by ballistic galvanometer measurements. Fig. 13 \nshows a loop taken of the specimen which Bozorth used in some \nprevious measurements.\u2018 Both the coercive force and the maximum \ninduction taken by the two methods agreed to within less than one\n\nper cent. Fig. 14 shows an initial magnetization curve which gives a \nvalue of the initial permeability agreeing accurately with the value \ndetermined ballistically.\n\nA fluxmeter with no restoring torque is also useful in certain types of \ncurrent measurements. If the average value of a current which \nfluctuates too much to be read on a slowly moving meter is desired, it\n\nFig. 14\u2014An initial magnetization curve of the specimen of 78.1 per cent \nnickel permalloy.\n\ncan be integrated on the fluxmeter, and the average value obtained by \ndividing the total quantity of electricity which has passed through by \nthe time during which the measurement was made. Also if a current is \ntoo small to be read directly on a galvanometer it may be possible to \nmaintain it for a sufficient length of time to give a readable deflection \non the fluxmeter, and again the current will be obtained by dividing \nby the time.\n\nIn conclusion I wish to thank Dr. R. M. Bozorth for suggestions \ngiven during the development of the apparatus, and Mr. A. W. Metz \nfor his assistance in taking the curves.\n\nA bar to the attainment of television images having a large amount of \ndetail is set by the practical difficulty of generating and transmitting wide \nfrequency bands. An alternative to a single wide frequency band is to \ndivide it among several narrow bands, separately transmitted. A three- \nchannel apparatus has been constructed in which prisms placed over the \nholes in a scanning disc direct the incident light into three photoelectric cells. \nThe three sets of signals are transmitted over three channels to a triple elec- \ntrode neon lamp placed behind a viewing disc also provided with prisms \nover its apertures so that each electrode is visible only through every third \naperture. An image of 13,000 elements is thus produced. For the suc- \ncessful operation of the multi-channel system, it is imperative to have very \naccurate matching of the characteristics in the several channels.\n\nas they should be, of such a size as to be just indistinguishable, or \nunresolved, at a given observing distance, the number of image ele- \nments increases directly with the area of the image. The number of \nsuch indistinguishable elements in everyday scenes, in the news \nphotograph, or in the frame of an ordinary motion picture is aston- \nishingly large. An electrically transmitted photograph 5 inches by 7 \ninches in size, having 100 scanning strips per inch, has a field of view \nand a degree of definition of detail, which, experience shows, are \nadequate (although with little margin) for the majority of news event \npictures. It is undoubtedly a picture of this sort that the television \nenthusiast has in the back of his mind when he predicts carrying the \nstage and the motion picture screen into the home over electrical \ncommunication channels. In this picture, the number of image \nelements is 350,000. At a repetition speed of 20 per second (24 per \nsecond has now become standard with sound films) this means the \ntransmission of television signals at the rate of 7,000,000 per second,\u2014 \na frequency band of 31% million cycles on a single sideband basis. \nThis may be compared to the 5,000 cycles in each sideband of the \nsound radio program, or it may be evaluated economically as the \nequivalent of a thousand telephone channels.\n\nWhen we examine what has been achieved thus far in television, we \nfind that the type of image successfully transmitted falls very far \nshort of the finely detailed picture just considered. Probably the \nmost satisfactory example of television thus far demonstrated is the\n\n72-line picture used in the two-way television-telephone installation of \nthe American Telephone and Telegraph Company in New York.! \nHere the object to be transmitted is definitely restricted to the human \nface, which fills the whole field of view, and is adequately rendered by \nthe 4,500 image elements used.\n\nThe gap between the 4,000 elements of this image and the 350,000 \nconsidered above is enormous, not only in figures, but in terms of \ntechnical possibility of bridging. Even if we are forced to content \nourselves with relatively simple types of scenes for television trans- \nmission, still the fact must be squarely faced that a very much larger \nnumber of image elements must be transmitted than has thus far been \nfound possible; and a far wider frequency band utilized than has ever \nbeen used in any communication problem. Now the situation is, \nsimply stated, that all parts of the television system are already having \nserious difficulty in handling the 4,500-element image. Consequently, \na major problem in television progress is to develop means to extend the \npractical frequency range.\n\nIt will be worth while to survey briefly the points in a television \nsystem where difficulty is now encountered when the attempt is made \nto increase the amount of image detail and the accompanying band of \ntransmitted frequencies. Consider in turn the scanning discs at \nsending and receiving ends, the photoelectric cells, the amplifying \nsystems, the transmission channels, the receiving lamps.\n\nIn the scanning disc at the sending end, which we shall assume \narranged for direct scanning, increased detail means either loss of \nlight or increase in the size of the disc. In either case, the factor of \nchange involved is large. For instance, if the number of scanning \nholes is doubled in a disc of given size, providing four times the number \nof image elements, the holes must be spaced at half the angular distance \napart, and twice the number of holes, imagined placed end to end, \nmust be included in this half diameter scanning field. The holes will \ntherefore be of one-quarter the diameter or 1/16 the area. The light \nfalling on the photoelectric cell at any instant is the light transmitted \nby one hole; in this case, 1/16 the amount with the disc of half the \nnumber of holes. In general, the light transmitted by the disc to the \ncell decreases as the square of the number of image elements. If the \ndisc is enlarged so as to hold the transmitted light unchanged, its \ndiameter increases directly as the number of image elements. It is \nobvious that any considerable increase in the number of image ele- \nments\u2014such as ten times\u2014demands either enormously increased \nsensitiveness in our photo-responsive devices, or quite fabulous sizes of\n\ndiscs. Perhaps the most pertinent conclusion from this survey is that \nthe disc, while quite the simplest means for scanning images of few \nelements, is entirely impractical when really large numbers of image \nelements are in question. As yet, however, no practical substitute \nfor the disc of essentially different character has appeared.\n\nTurning now to the photoelectric cell. The question of adequate \nsensitiveness to handle a large number of image elements is intimately \nconnected with the method of scanning, as has just been brought out, \nso that no simple answer is possible. It is, however, probable that a \nvery considerable increase in sensitiveness over anything now available \nmust be anticipated, whatever scanning device is adopted. In the \nmatter of frequency range there is definite information.? In cells \ndepending on gas amplification (such as argon or neon) a characteristic \nbehavior is a falling off of output with frequency, greater the higher \nthe voltage used, which, becoming noticeable at about 20,000 cycles, \nmay at 100,000 cycles be so considerable as to constitute a practical \nblock to transmission. Vacuum cells are free from this failing, but \nare much less sensitive. Systematic experiment and development of \nphotoelectric cells with particular reference to extending their range of \nfrequency response is indicated as a necessary step in the attainment \nof a many-element image.\n\nTaking up next the circuits associated with the photoelectric cell, we \nfind, in general, that the higher frequencies progressively suffer from \nthe electrical capacity of cells and associated wiring and amplifier \ntubes. This in turn calls for auxiliary equalizing circuits, with \nattendant problems of phase adjustment, and for increased amplifica- \ntion. Amplifiers capable of handling frequency bands extending from \nlow frequencies up to 100,000 cycles or over offer serious problems.\n\nCommunication channels, either wire or radio, are characterized by \nincreasing difficulty of transmission as the frequency band is widened. \nIn radio, fading, different at different frequencies, and various forms of \ninterference stand in the way of securing a wide frequency channel of \nuniform efficiency. In wire, progressive attenuation at higher fre- \nquencies, shift of phase, and cross-induction between circuits offer \nserious obstacles. Transformers and intermediate amplifiers or re- \npeaters capable of handling the wide frequency bands here in question \nalso present serious problems.\n\nAt the receiving end of the television system, conditions are similar \nto the sending end. The neon glow lamp, commonly used for re- \nception, is already failing to follow the television signals well below \n40,000 cycles, and, in the case of the 4,500-element image above \n* Loc. cit., p. 456.\n\nreferred to, the neon must be assisted by a frequently renewed ad- \nmixture of hydrogen, which again cannot be expected to increase the \nfrequency range indefinitely. In the scanning disc, as at the sending \nend, increasing the number of image elements rapidly reduces the \namount of light in the image. With a plate glow lamp of given \nbrightness, the apparent brightness of the image is inversely as the \nnumber of image elements.\n\nFrom this rapid survey, it is clear that at practically every stage in \nthe television system, we encounter serious difficulties when a large \nincrease in image elements is contemplated. It is not claimed that \nthese difficulties are insuperable. One of the chief uses of a tabulation \nof difficulties is to aid in marshalling the attack upon them. But the \nexisting situation is that if a many-element television image is called \nfor today, it is not available, and one of the chief obstacles is the difficulty \nof generating, transmitting, and recovering signals extending over wide \nfrequency bands.\n\nOne alternative, which prompted the experimental work to be \ndescribed below, is the use of multiple scanning, and multiple-channel \ntransmission. The general idea, which is obvious from the name given \nto the method, is to divide the image into groups of elements, the \nvarious groups to be simultaneously scanned, and to transmit the \nsignals from the several groups through separate transmission channels. \nIn place of apparatus to generate and transmit a frequency band of n \ncycles, we arrange m scanning processes each to provide frequency \nbands of n/m cycles width; n/m being chosen as within the limits set by \nthe available practical elements of a television system. It will appear \nthat the method which has been developed does provide an image of \nmanyfold more image elements than heretofore, and may make easier \nthe problem of transmission over practical transmission lines.\n\nThe multi-scanning apparatus which has been constructed and \ngiven experimental test uses scanning discs over whose holes are \nplaced prisms of several different angles. At the sending end, the \nbeams of light from successive holes are thereby diverted to different \nphotoelectric cells. At the receiving end, the prisms similarly take \nbeams of light from several lamps and divert them to a common \ndirection. The mode of action of the prisms is illustrated in Fig. 1a, \nwhere a three-channel arrangement is shown, which is that actually \nused in the experimental apparatus. In the figure, the disc holes are \nshown disposed in a spiral, at such angular distances apart that \nthree holes are always included in the frame f. Over the first hole of a\n\nset of three is placed a prism P, which diverts the normally incident \nlight upward; the second hole is left clear; the third is covered by a \nprism P, turned to divert the light downward. If we imagine the \nprisms removed and a single channel used instead of the three that are \nproposed, it is clear that the holes would have to be spaced three times \nas far apart so that no more than one would be included in the frame f \nat one time. The diameters of the holes, and the radial separation of \nthe first and last in the spiral would be unchanged. Quite apart, \ntherefore, from the smaller frequency bands which are sufficient to \ncarry each of the three sets of signals, which is the principal objective \nsought, there is realized in this arrangement a reduced size of apparatus \nfor the same size of disc holes.\n\nStudying more closely the division of the light into three sets of \nbeams, it is important to note that the signals transmitted by any one \nof the three sets of holes are continuous\u2014as one hole of a given prism \nseries passes out of the frame the next of the same series comes in. \nThe signals generated in each photoelectric cell are accordingly exactly \nlike those of a single-channel system.\n\nBefore describing the details of the apparatus, the general relation- \nship between the number of image elements, band width, number of \nchannels, and shape of picture may be developed. For this purpose, \nlet the following symbols be used.\n\nB = frequency band available in one channel, in cycles per second. \nF = repetition frequency of images, per second.\n\na/b = ratio of tangential to radial dimensions of frame. \na = angular opening of frame.\n\nWe shall assume that the picture elements into which the frame is \nimagined divided are symmetrical in shape, i.e. either circles or squares. \nWe then have that\n\nthe number of picture elements in the radial direction = number of \nholes = n; \nthe number of picture elements in the tangential direction = (a/b)-n.\n\nNow the number of signal cycles corresponding to this number of \nelements is (1/2): (a/b)n.\n\nand the number of cycles per second for each channel = (1/c) \n-(1/2)(a/b) Fn? = B. \nThe angular opening of the frame a = 360 C. \nThe number of picture elements = m?*- (a/b). \nThese formule may be utilized upon assuming values for any of the \nvariables, to fix the values of the other. In the present case, it was \ndecided for reasons of simplicity to restrict the number of channels to 3.\n\nFig. 1\u2014Schematic of three-channel television apparatus. (a) Receiving end \ndisc with spiral of holes provided with prisms. (6) Sending end disc with circle of \nholes provided with prisms. (c) General arrangement of apparatus.\n\nThe band width was chosen as that found feasible in the two-way \ntelevision system, namely 40,000 cycles. The picture shape chosen \nwas that of the sound motion picture, for which a/b = 7/6. The \nrepetition frequency assumed was 18 per second, again following \nclosely that of existing experimental synchronizing apparatus. Sub- \nstituting these values in the formula rearranged to give , we get for \nthe number of holes,\n\nscanning, in which the object is imaged on the disc, was chosen, since \nbeam scanning would introduce the problem of separating the light \nreflected from the object from the several spots simultaneously pro- \njected from the disc. Since the light going through the disc must be \nseparated into several beams to be directed into separate photoelectric \ncells, the full aperture of the image forming lens must be divided by C, \nthe number of channels, with a consequent proportional loss of light to \neach cell. (This loss counterbalances the decreased size of disc above \nnoted.) It therefore becomes necessary to insure a very high illumi- \nnation of the object. In the present case, it was decided to use motion \npicture film to provide the sending end image, since this can have a \nlarge amount of light concentrated through it by an appropriate lens \nsystem.\n\nThe use of motion picture film permitted a simplification of the \ntransmitting disc, which is illustrated in Fig. 1b. This consists in \narranging the scanning holes in a circle instead of a spiral, and pro- \nducing the longitudinal scanning of the film by giving it a continuous \nuniform motion at right angles to the motion of the scanning holes. \nThe continuous motion of the film also avoids the loss of transmission \ntime that an intermittent motion demands for the shutter interval.\n\nAt the receiving end, a spiral of holes is used as shown in Fig. la. \nThere again, because of the division of the light into three beams, the \nangle which can be subtended by the light source (neon lamp) is much \nrestricted. In consequence, the neon lamp cathodes are of small area, \nand a lens system has been used to focus their images on the pupil of \nthe observer\u2019s eye. Other methods of receiving, which promise to be \nless restricted as to position of observation, are possible, however, as \ndiscussed below.\n\nWith this survey of certain of the more important features of the \nsystem, we may proceed to a more detailed account of the apparatus as \nconstructed. The general arrangement of parts is shown in Fig. 1c \nand in the photographs, Figs. 2, 3, 4 and 5 in all of which the symbols \nare uniform. Both sending and receiving discs were, for simplicity of \noperation, mounted on the same axis, driven by the motor \\/. This \nmeans that no question of synchronization entered. Synchronization \nis in fact a separate problem, having nothing to do with multi-channel \noperation and has been very completely solved in connection with other \ntelevision projects.' If it should be decided to transmit the multi- \nchannel image to a distant point, the apparatus could be cut in two \nand each end, after separation to the desired distance, operated by \nsynchronous motors controlled in approved fashion. Similarly, no \nlong transmission lines were included.\n\nStarting at the extreme right end of the schematic drawing Fig. 1c, \nwe have an arc lamp 4, a cylindrical lens L;, a condensing lens Ls, the \ntwo lenses together concentrating a line of light on the film F. Be- \ntween the film and the disc is a lens L; which images the film on the \ndisc. Directly behind the disc D,, with its circle of prism covered \nholes, is a second cylindrical lens L4 which concentrates the transmitted\n\nFig. 2\u2014Sending end of three-channel television apparatus, showing film driving \narrangements.\n\nlight laterally, upon the three photoelectric cells S;, Sz, S;. By virtue \nof this lens arrangement, the light falls upon the cells in three small \npractically stationary spots. Additional apparatus not shown in the \ndiagram but visible in the photographs are gears by means of which the \nfilm is driven from the disc axle through a differential, which permits \nthe film to be framed up and down. The light beam is directed through \nthe film at right angles to the axis of the discs by means of two prisms, \nwhereby certain conveniences in driving and handling the film are \nattained.\n\nAt the receiving end, the three sets of signals were supplied to the \nthree electrodes of a special neon lamp .V, shown in Fig. 5, which is \nprovided with a hydrogen valve to enable it to respond to the higher \nfrequencies. Condensing lenses L; and Ls image the three electrodes\n\nFig. 3\u2014Sending end of three-channel television apparatus, showing sending prism \ndisc and photoelectric cells.\n\nat the eye, where another lens L; is placed at the eye to focus the face \nof the disc D.. By this system, nine electrode images are formed, of \nwhich three are superposed at the eye, an successive scanning holes are \nseen illuminated by each electrode in turn. This viewing arrangement, \nby which the image is visible to only a single eye, is adequate for an \nexperimental investigation of the multi-channel method, but some other \nscheme would of course be needed if the method were developed into a \npractical form. Of several schemes, mention will be made here only\n\nof the possible use of a triple grid of neon tubes, using a triple distrib- \nutor of the type used in displaying images to a large audience in our \ninitial work in 1927.4\n\nThe three-channel apparatus, when all parts are properly function- \ning, yields results strictly in agreement with the theory underlying \nits construction. The 13,500-element image, in resolving power and\n\namount of detail handled, is a marked advance over the single-channel \n4,500-element image. Even so, the experience of running through a \ncollection of motion picture films of all types is disappointing, in that \nthe number of subjects rendered adequately by even this number of \nimage elements is small. \u2018\u2018Close-ups\u2019\u2019 and scenes showing a great \ndeal of action, are reproduced with considerable satisfaction, but \nscenes containing a number of full length figures, where the nature of \nthe story is such that facial expressions should be watched, are very\n\nFig. 5\u2014Three-electrode neon lamp used for three-channel television reception.\n\nfar from satisfactory. On the whole, the general opinion expressed in \nan earlier paragraph is borne out, that an enormously greater number \nof elements is required for a television image for general news or \nentertainment purposes. This, however, was anticipated, and the \nreal question is whether the results of this experiment indicate that \nthe finer grain image is best attained by resort to multi-channel means.\n\nThis leads to a discussion of what has proved to be a serious practical \ndifficulty with the multi-channel apparatus. This is the problem of \nkeeping the several channels properly related to each other in signal \nstrength. In the experimental apparatus, the direct current com- \nponents (introduced at the receiving end) and the alternating current \nsignals, are separately controlled, manually, by potentiometers. \nThese have fine enough steps so that with care, with a non-changing \nimage, a uniform picture may be obtained. If, however, for any \nreason the signals on one of the channels becomes too strong or too \nweak, the picture exhibits at once a strongly lined appearance. The \neye is quite sensitive to irregularity of this sort, and the transition \nfrom a smooth grainless image to one showing a periodicity of 1/3 the \nnumber of constituent lines largely offsets the higher resolving power \nafforded by the actual number of scanning lines used. A characteristic \npractical defect of the system as set up is that any marked change in the \ngeneral character of the signal, such as is produced by a shift from \nclose-up to a wide angle view may throw out the existing signal \nbalance sufficiently to show objectionable grain in the picture.\n\nDifferences of this sort in the three signals are of course caused in \ngeneral by differences in the characteristics of the three circuits. Such \ndifferences can arise from overloading of amplifier tubes, whereby one \nor more may be working on a non-linear portion; by rectifying action \nof different amounts in the tubes immediately associated with the neon \nlamps, or in the neon lamp electrodes themselves. A remedy is the \ncareful design and test of all parts of the system to insure the greatest \npossible uniformity of performance. When this is carefully done, the \nbehavior of the three signals is reasonably satisfactory.\n\nWe are, as a consequence of this work, in a position to make a \ngeneral comparison of the two chief theoretical means for achieving a \ntelevision image of extreme fineness of grain, which are (1) extension \nof the frequency band, and (2) the use of several relatively narrow \nfrequency bands. Both, because of the diminished amount of light \nwhich finer image structure entails, demand enhanced sensitiveness of \nthe photo-sensitive elements at the sending end, and increased efficiency\n\nfo the light sources at the receiving end. The multi-channel scheme \ndescribed has some advantage in compactness over the equivalent \nsingle-channel apparatus, but since it is restricted to narrow angles of \nillumination of the discs the overall efficiency of light utilization is not \nessentially different. Comparing now the demands made upon the \nelectrical systems the differences between the two methods are clear \ncut. Method (1) demands an extension of the frequency range of all \nparts of the apparatus, the attainment of which depends upon physical \nproperties and technical devices whose mastery lies in the indefinite \nfuture. Method (2) demands a multiplication of apparatus parts, and \ncareful design and construction of these parts so as to insure accurately \nsimilar operation of a considerable number of electrical circuits and \nterminal elements. The attainment of the necessary uniformity of \nperformance of the several electrical circuits and terminal elements, \nwhile involving no fundamental problems, must present increasing \ndifficulty with the number of channels used.\n\nOf the numerous microphones which have been developed since Bell's \noriginal work on the telephone, only two are used extensively in sound \nrecording for motion pictures, namely, the condenser microphone and the \ncarbon microphone.\n\nThe condenser microphone was first proposed in 1881 but owing to its \nlow sensitivity was limited in its field of usefulness until the development \nof suitable amplifiers. In 1917, E. C. Wente published an account of the \nwork which he had done on a condenser microphone having a stretched \ndiaphragm and a back plate so designed as to introduce an appreciable \namount of air damping. \u2018The major portion of the condenser microphones \nused today in sound recording embody the essential features of the Wente \nmicrophone. Marked progress has, however, been made in the design and \nconstruction of these instruments with the result that they are not only more \nsensitive but also more stable. \u2018The factors which contribute to this im- \nprovement are described in detail in this paper. Recently a number of \narticles have appeared in the technical press calling attention to certain \ndiscrepancies between the conditions under which the thermophone calibra- \ntion of the condenser microphone is made and those which exist in the studio. \n\u2018The nature of these discrepancies and their bearing on the use of the micro- \nphone are discussed.\n\nMicrophones in which the sound pressure on the diaphragm produces \nchanges in the electrical resistance of a mass of carbon granules interposed \nbetween two electrode surfaces have been used commercially since the \nearly days of the telephone. In recent years the faithfulness of the repro- \nduction obtained with the carbon microphone has been materially improved \nby the introduction of an air damped, stretched diaphragm and a push-pull \narrangement of two carbon elements. This instrument is finding extensive \nuse in sound recording and reproduction fields where carbon noise is not an \nimportant factor. The outstanding design features of the push-pull carbon \nmicrophone are described in this paper and suggestions made as to the \nprecautions to be taken in its use if the best quality, maximum life, etc. \nare to be obtained.\n\nBell\u2019s original work on the telephone, only two are used exten- \nsively in sound recording for motion pictures, namely, the condenser \nmicrophone and the carbon microphone. It has therefore been \nsuggested that it would be fitting to review at this time the con- \nstruction of these instruments and consider some of their trans- \nmission characteristics and the precautions which should be exercised \nin their use.\n\nIn 1881, A. E. Dolbear! proposed a telephone instrument which \ncould be used either as an electrostatic microphone or receiver. This\n\n* Presented at Soc. of Motion Picture Engineers\u2019 Convention, Oct. 20, 1930; \nJournal, Soc. of Motion Picture Engineers, Jan., 1931.\n\ninstrument consisted of two plates insulated from one another and \nclamped together at the periphery. The back plate was held in a \nfixed position whereas the front was free to vibrate and served as a \ndiaphragm. It is obvious that, if the diaphragm were set in vibration \nby sound pressure, the electrical capacitance between the two plates \nwould be changed in response to the sound waves, and if a source of \nelectrical potential were connected in series with the instrument a \ncharging current would flow which would be a fairly faithful copy of \nthe pressure due to the sound wave. Apparently Dolbear realized \nthat the current developed in this way would be minute, for in the \ntelephone system which he proposed as a substitute for the one using \nBell\u2019s magnetic instruments he employed the electrostatic instrument \nonly as a receiver and adopted the loose contact type of microphone. \nAt approximately the same time an article appeared in the French \npress ? calling attention to the use of a condenser as a microphone and \ncommenting on the fact that this type of microphone had been found \nto be less sensitive than the loose contact type.\n\nOwing to the low sensitivity of the condenser microphone, the field \nof usefulness of this instrument was extremely limited for a number \nof years and it did not assume a position of importance among the \ninstruments used in acoustic measurements and sound reproduction \nuntil suitable amplifiers had been developed. The development of \nthe vacuum tube amplifier, however, filled this need. In 1917 E. C. \nWente ? published an account of the work which he had done on an \nimproved condenser microphone having a stretched diaphragm and a \nback plate so located relative to the diaphragm that in addition to \nserving as one plate of the condenser it added sufficient air damping \nto reduce the effect of diaphragm resonance to a minimum.\u2019 The \nresponse of this instrument was sufficiently uniform over a wide range \nof frequencies to make it not only useful in high quality sound repro- \nduction but a valuable tool in acoustic measurements in general.\n\nThe major portion of the condenser microphones used today in \nsound recording embody the essential features of the Wente micro- \nphone. Marked progress has, however, been made in the design and \nconstruction of these instruments since the initial disclosure and it \nwill no doubt be of interest to many to consider briefly the nature of \nthis advance.\n\n3 **A Condenser Transmitter as a Uniformly Sensitive Instrument for the Absolute \nMeasurement of Sound Intensity,\u201d E. C. Wente, Physical Review, July 1917, pp. \nee \u201cElectrostatic Transmitter,\u201d E. C. Wente, Physical Review, May 1922, pp.\n\n_ *A discussion of the theory of air damping is given in \u201cTheory of Vibrating \nSystems and Sound,\u201d I. B. Crandall, pp. 28-39.\n\nIn the early microphones employing air damping the diaphragm was \ncomposed of a thin sheet of steel which was stretched to give it a \nrelatively high stiffness. When assembled in the microphone the \nstiffness was further increased by that of the air film between diaphragm \nand the damping plate with the result that the resonant frequency \nwas well above the frequencies which it was desired to transmit and \nthe diaphragm vibrated in its normal mode over a wide frequency \nrange. In such a structure the mechanical impedance for frequencies \nbelow resonance is due almost entirely to stiffness reactance. Hencea \nconstant sound pressure produces substantially the same displacement \nof the diaphragm at all frequencies within this range and uniform \nresponse results except at the very low frequencies where an appreciable \nreduction in the stiffness of the air film occurs. The effective mass of \na steel diaphragm is, however, relatively large and necessitates a \ncomparatively high stiffness to secure the desired resonant frequency. \nFrom the standpoint of securing maximum sensitivity of the micro- \nphone, i.e. displacement of the diaphragm per unit force, it is of course \nimportant to make the stiffness as low as possible and employ as small \na value of mechanical resistance as is consistent with the degree of \ndamping required. An improvement in both respects can be effected \nby decreasing the mass of the diaphragm for with a reduced mass a \ngiven resonant frequency can be obtained with lower values of stiffness \nand the desired damping constant secured with less mechanical \nresistance.\n\nThe aluminum alloys have therefore replaced steel in the diaphragms \nof most of the condenser microphones in use today. 3.0 + \nWwW \n| \n4 a \n| | \nz 20 amt \nr < | | \n| | \nI \nLe | \nDEPROTEINIZED \n05 + RuBBER = \n= | | \n| | it \n) 2 3 4 5 \nt TIME IN WEEKS \n{ Fig. 1\u2014Effect of washing and removal of protein on the water absorption of crude \nrubber when immersed in 3.5 per cent NaCl solution at room temperature. \n| \n$ 2 35 4 4 + \n| \n< / | / | \n: > 25 / / t \n| \n\u2018 | \n20 t 4 \nSMOKED | / \ni SHEET | WASHED | \n= | \n| | \nwl | | | \na DEPROTEINIZED | \nRUBBER \n2 3 4 5 \nTIME IN WEEKS \nFig. 2\u2014Effect of washing and removal of protein on the dielectric constant of crude \nrubber when immersed in 3.5 per cent NaCl solution at room temperature.\n\nthan is the case with crude rubber, thereby yielding a product with \nbetter thermoplastic properties.\n\nAs previously stated, the principal con ituents of paragutta are \ndeproteinized rubber and purified gutta hydrocarbon. Specially \ntreated hydrocarbon or montan waxes may also be added as a third \nconstituent to modify mechanical properties and reduce cost. The \nproportions of these constituents may be varied over a wide range to \nachieve the desired characteristics, but in general rubber and gutta\n\nFig. 3\u2014Effect of washing and removal of proteins on resistivity of crude rubber, \nwhen immersed in 3.5 per cent NaCl solution at room temperature. \nare used in about equal proportions and purified montan wax may be \nadded up to about 40 per cent. Superior electrical properties, how- \never, result from the use of hydrocarbon waxes, which may be added \nin amounts up to about 20 per cent. By the proper blending of these \nmaterials, a thermoplastic insulation is obtained which closely ap- \nproximates gutta percha in mechanical properties and is fully its equal \nas to electrical stability in water. Its specific electrical characteristics\n\nrepresent a substantial ir rovement over those of the classical insula- \ntion compounds and its st is lower.\n\nThe final steps in pro ssing paragutta are very similar to those \nused for gutta percha and involve blending and washing the depro- \nteinized rubber and deresinated balata or gutta together, masticating \nto remove excessive water and at the same time incorporating such \nwaxes as are found necessary. The material is then strained through \nfine sieves under hydraulic pressure to remove adventitious impurities, \nkneaded to remove air and finally placed on the covering machine rolls \nto be forced around the conductor. The machinery in use for pro-\n\nFig. 4\u2014Effect of washing and removal of proteins on conductivity of crude rubber \nwhen immersed in 3.5 per cent NaCl solution at room temperature.\n\ncessing gutta percha is suitable for handling paragutta in these \noperations.\n\nTensile Properties: Although submarine insulation is not subjected \nto tensile deformation in practice, tensile properties indicate to some \ndegree the relative mechanical suitability of a given material for the \npurpose. Figure 5 shows the stress-strain characteristics of paragutta \nand gutta percha submarine cable insulation. These results show\n\nthat paragutta has tensile properties equal to cable gutta percha \nalthough its gutta content is substantially lower.\n\nCompression Properties: The insulated submarine cable conductor \ncommonly known as the core is frequently subjected to uneven com- \npression stresses during manufacture, laying and repairing. The \ninsulation must therefore be capable of withstanding these stresses \nwithout appreciable deformation. \u2018To determine the relative merits \nof paragutta and gutta percha in this respect their comparative stress- \nstrain characteristics under compression have been measured, using a \nspecial compression machine,\u2019 and are shown in Fig. 6. In this test\n\na steel rod 1.6 cm. in diameter was forced endwise into a sheet of the \nmaterial .375 cm. in thickness at a rate of about 4 cm. per minute \nwhile simultaneously recording the deformation and load. These \nresults show that very little difference exists between these materials \nin this test, and factory handling of cores confirms the general con- \nclusion.\n\nFlexibility: The flexibility of submarine cable insulation is important \nbecause the core is subjected to considerable flexing during manu-\n\nfacture, laying and repairing and possibly at times during use, espe- \ncially where tidal currents may cause movement in the cable. Para- \ngutta and gutta percha cores have been subjected to slow and con- \ntinuous flexing at 0\u00b0 and 25\u00b0 C. for long periods and it was found that \nboth materials will withstand millions of repeated flexures at small \namplitudes without failure. When the amplitude of flexure was \nincreased to strain the conductor slightly beyond its elastic limit, \nthe conductor always failed in advance of the insulation.\n\nPlasticity Tests: Laboratory tests were made to determine the rela- \ntive plasticity of paragutta and gutta percha, using both the Williams *\n\nFig. 6\u2014Comparative compression properties of paragutta and gutta percha at 25\n\nand the Marzetti\u00ae type of plastometers. These tests are valuable \nguides but the final judgment of a material as regards thermoplasticity \nwas made by determining its workability on commercial gutta percha \ninsulating machines. Paragutta is somewhat more resistant to flow \nthan gutta percha at temperatures ranging from about 40\u00b0 to 70\u00b0 C. \nWhen applied to the conductor, however, its greater resistance to flow \nat elevated temperatures can be taken as an advantage as it lessens \nthe danger of faults occurring if the core should be accidentally exposed \nto elevated temperatures or to conditions which might exist in con- \nnection with cable used in the tropics.\n\nFigure 7 shows the relative plasticities of cable gutta percha and \nparagutta at several temperatures as determined by the Williams 4 \nmethod, which can be taken to indicate the relative plasticities of \nthese materials at working temperatures.\n\nBrittle Temperature: It is extremely important that the temperature \nat which submarine cable insulation becomes brittle should be far \nbelow the range of sea bottom temperatures to be encountered in use. \nThis is one of the properties in which rubber and gutta percha greatly \nexcel any other available insulating material. Kohman and Peek \u00b0\n\nTEMPERATURE -DEG. C. \nFig. 7\u2014Effect of temperature on the plasticity of cable gutta percha and paragutta.\n\nThe amount of water absorbed by rubber and gutta percha when \nimmersed in water is the result of a complicated mechanism. \u2018The \nquantity and nature of water soluble or water absorbing impurities\n\nTABLE II \nBRITTLE TEMPERATURE OF PARAGUTTA AND OTHER INSULATING MATERIALS\n\nMaterial ( \nGutta Percha (Cable Insulation 23 to \u201436 \nParagutta 45 to \nBalata (Washed) 44 to \u201452 \nBalata (Washed and Deresinated 62 to \u201467 \nCrude Rubber 57 to \u201458 \nVulcanized Rubber (Soft) \u2014\u00a73 tp \u2014 58\n\nin the rubber or gutta percha and the salt concentration of the water \nin which the samples are immersed are controlling factors. The \nenormous increase in the quantity of water absorbed by ordinary \nrubber when immersed in distilled water as compared with its absorp- \ntion in salt solutions has been explained on the basis of osmotic \ntheory.!. In accordance with this theory rubber acts as a semi- \npermeable membrane. Water soluble crystalloids or hydrophillic \ncolloids (proteins) attract the water which enters the rubber by \ndiffusion. When immersed in distilled water these impurities tend \nto reach infinite dilution with water, being opposed in this by the \nresistance of the rubber itself to swelling. In salt solutions the \namount of water absorbed is finite and depends on the equalization \nof osmotic pressures of the internal and external solutions. The \nchange in water absorption of pure rubber hydrocarbon with the salt \nconcentration of the external solution is small over the whole range, \nwhich indicates that the water enters by a process of solution. This \nhas also been found to be the case for gutta hydrocarbon and is more \nor less true for paragutta and gutta percha. The water absorption \nin distilled water can therefore be taken as a measure of the freedom \nfrom water soluble or water absorbing impurities. Figure 8 shows \nthe effect of NaCl concentration in the immersion solution on the \nquantity of water absorbed by samples of rubber, paragutta and gutta \npercha at room temperature. Samples of rubber containing water \nsoluble matter or proteins do not readily reach an equilibrium water \ncontent in distilled water. Crude rubber has been found to absorb \nmore than 100 per cent water in distilled water at ordinary temperature \nwithout reaching equilibrium.! Gutta percha, paragutta and pure \nrubber hydrocarbon on the other hand reach a definite and lower \nequilibrium water content in distilled water, which shows their greater \nfreedom from water soluble or water absorbing matter.\n\nAs the electrical stability of paragutta in sea water is of paramount \nimportance an exhaustive study has been made on a large number of \nspecimens as regards their changes in electrical values over long periods \nof immersion in 3.5 per cent salt solution. Gutta percha insulation\n\nCONCENTRATION NaCl IN IMMERSION SOLUTION-PER CENT \nFig. 8\u2014Relation of water absorption to salt concentration in immersion solution,\n\nThe overall quantity of water absorbed, however, cannot be used \nas a final criterion by which to judge insulation for it has been pre- \nviously shown (Figs. 1 to 4) that washed crude rubber completely \nfails as an insulator after absorbing less than one per cent water. The \nmode of distribution of water absorbing impurities in an insulating \nmaterial has been found to be of utmost importance as regards the \nmagnitude of the effect of moisture in various insulating materials. \nExamples where large effects on insulating properties are caused as a \nresult of moisture absorption by localized impurities are found in the \nabove case of proteins in crude rubber, water soluble salts associated\n\nwith fillers in vulcanized rubber ! and hygroscopic salts on the surfaces \nof textile fibers.\u2019\n\nOn the other hand, the electrical properties of paragutta or gutta \npercha are not impaired when several times their equilibrium water \ncontent is incorporated with them. Gutta percha, however, does \nshow an increase in capacitance of about 10 per cent as a result of \nwater absorbed by a completely dried specimen, but as it is always \nthe practice to apply it to the conductor in a wet condition this\n\nFig. 9\u2014Changes in water content of 50 mil wet and dry paragutta and gutta percha\n\nchange is not of practical significance. The electrical properties of \nparagutta on the other hand show practically no changes as a result \nof moisture absorption by a dry sample. \u2018These facts are taken to be \nthe best evidence of the electrical stability of paragutta in contact \nwith water.\n\nHundreds of specimens of paragutta and gutta percha have been \nstudied as regards changes taking place in electrical characteristics \nafter long periods of continuous immersion in 3.5 per cent salt solution. \nThese tests, some of which have been for periods of three to five years, \nshow that paragutta is fully equal to gutta percha as regards its\n\nstability. When properly prepared both of these materials show \npractically negligible changes in electrical properties as a result of \nprolonged submergence in water. Sea bottom conditions are even \nless likely to affect these materials than those existing in the laboratory. \nThis is because of the absence of light, limited oxygen supply and \nlow temperature, all of which reduce the tendency of materials such as \nparagutta or gutta percha to oxidize or otherwise deteriorate. It \nhas also been shown? that the low temperature and high pressure \nexisting at sea bottom reduce the rate of water absorption but do not \nmaterially affect the amount absorbed.\n\nElectrical Characteristics: The electrical properties of paragutta \ndepend upon the particular composition chosen, the quality of the \nraw materials and the care exercised in processing them. For long \ntelephone cable insulation, it is necessary to exercise the utmost care \nto obtain a material having dielectric constant and specific conductance \nvalues suthciently low to reduce to the minimum its effect on the \nattenuation. On the other hand, for ordinary telegraph cables these \nvalues are less critical and it may be advantageous to modify the \npractice for purposes of economy. Representative values for the \nelectrical properties of a superior grade of paragutta and typical cable \ngutta percha under sea bottom conditions are given in Table III. It \nwill be seen in this table that paragutta has a 20 per cent lower dielec- \ntric constant and a specific conductance one-thirtieth that of ordinary \ncable gutta percha under sea bottom conditions. The insulation \nresistance and dielectric strength of the two materials are practically \nthe same.\n\nCOMPARATIVE ELECTRICAL PROPERTIES OF PARAGUTTA AND CABLE GUTTA PERCHA \nAT SEA BottOoM CONDITIONS\n\nSpecific Inductive Effective A-C \nCapacity 2\u00b0 C., Conductivity 2\u00b0 C., \n400 Atm., 2000 Cycles 400 Atm., 2000 Cycles \nUnit = 10712 mho. cm. \nCable Gutta Percha. .. \n3\n\nThe author wishes to acknowledge his indebtedness to Mr. R. R. \nWilliams for counsel and assistance during the prosecution of the \nwork and writing of the paper.\n\nAn Efficient Loud Speaker at the Higher Audible Frequencies. L. G. \nBostwick. This paper describes a loud speaker designed for use as an \nadjunct to existing types for the purpose of extending the range of \nefficient performance to 11,000 or 12,000 cycles. A moving coil piston \ndiaphragm structure is used in conjunction with a 2000-cycle cutoff \nexponential horn having a mouth diameter of about 2 inches. Mo- \ntional impedance measurements on this loud speaker indicate an aver- \nage absolute efficiency of about 20 per cent within the frequency range \nfrom 3000 to 11,000 cycles. The variation in response within this \nband does not exceed 5db. By using a high-frequency loud speaker of \nthis type the efficiency and power capacity of the associated low-fre- \nquency loud speaker can be improved and a uniform response-fre- \nquency curve from 50 to 12,000 cycles can be obtained.\n\nResults of Notse Surveys. Part I. Noise Out-of-Doors2 ROGERS \nH. Gat. The purpose of a noise survey of a locality is to study the \nspace and time distribution of noise intensity, the frequency composi- \ntion of the noise, the contributions of various noise sources, the relation \nbetween the annoyance effect of the noise and its physical and auditory \ncharacteristics, and the effectiveness of methods of noise reduction. \nThe extent to which each of these phases of the noise problem has been \ninvestigated heretofore has depended upon the point of view of the \ninvestigator and upon the apparatus employed. From one standpoint \nor another, any audible sound may fall within the category of noise; \nhence the variety of possible noise surveys is almost unlimited. Not \nmany such surveys have been carried out, however, partly because the \nappropriate apparatus is of recent development; nor has any extensive \ncomparison been published between the results obtained in different \nplaces and with different instruments. It has therefore seemed worth \nwhile to assemble such previously published results as are available, \nand certain new observations, in the present series of papers, of which \nthis paper deals with noise out-of-doors.\n\ncontact behavior of granular carbon of the type used in commercial \nmicrophones.\n\nThrough a study of the temperature coefficients of resistance of such \ncontacts it is possible to conclude that the conducting portions of the \ncontact junctions are of the nature of carbon and that new contact \npoints are established or broken when the resistance is varied in a \nreversible resistance force cycle.\n\nThe experiments show that for such reversible cycles the relation \nbetween the resistance and force is of the approximate form \nR= K(F)-\". The exponent 7 varies considerably from cycle to cycle \nbut its average value depends on the force limits. The largest values \nof n are obtained with the aggregates of granules under such conditions \nof force limits that the elastic strains must be relatively large. A \nmaximum mean value substantially independent of the force limits \nover a wide range closely approximates the value 7/9.\n\nThis value 7/9 is the maximum given by a theory of contact resistance \nworked out by F. Gray, assuming that the contact is made between \ntwo spheres of conducting material having surface roughness equivalent \nto an assembly of minute spherical hills. On account of the elasticity \nof the material both the microscopic area of contact between the spheres \nand the microscopic areas of contact between the hills increase with \ncontact force. A strained aggregate of granules may therefore be made \nto behave like an ideal single contact between spheres having a rough \nsurface.\n\nFor single contacts and for aggregates at small strains the value of 7 \nfalls below the minimum value 1/3 which is accounted for by theory. \nThis is associated with internal contact forces, or cohesion, which render \nthe contacts relatively insensitive to changes in the applied force. \nThe existence of cohesion is readily demonstrated by the fact that \ncontacts always require a finite force to break them even when no \ncurrent has passed through the contact.\n\nMetallography, at first thought, appears wholly unrelated to his- \ntology or other branches of biology but the two branches of science do\n\nhave many points incommon. Both deal in the last analysis with the \nstructure of matter and, in each, the microscope is an indispensable \ntool. Improvements in microscopic vision which enlarge the world of \nvision in one branch of science inevitably have a reflection in the other.\n\nIt is not the purpose of this paper to enter into a discussion of struc- \ntures of living cells as revealed by the ultra-violet microscope. More \nparticularly, the object is to present a tool for biological research; a \ntool which enables us to photograph the structure at different planes or \nlevels within a single cell or group of cells; one which enables us to see \nthe living cell with a degree of precision and clarity not heretofore \npossible\u201d by any other known means and with a potential resolving \nability at least twice that of the best apochromatic system using visible \nlight.\n\nProduction of Plustic Molded Telephone Parts\u2019 A.M. Lynn. The \nWestern Electric Company now manufactures for Bell System ap- \nparatus a large number of different phenol-plastic, shellac, and hard- \nrubber molded parts, the output of which varies from a few thousand \nto several million per year. The majority of these molded parts are \nproduced in comparatively small quantities, but certain of them, such \nas the phenol-plastic molded parts used in the hand-set type of tele- \nphone, a new molded subscriber\u2019s set housing, and the receiver shell, \ncap, and mouthpiece used on the older type of desk-stand telephone, \nare heavy-running parts. The tools and press equipment used in the \nproduction of these parts are described in this paper.\n\nVariation of the Inductance of Coils Due to the Magnetic Shielding \nEffect of Eddy Currents in the Cores\u00ae Kk. L. Scott. An analysis is \nmade of the shielding effect of eddy currents on the flux in the interior \nof cores of cylindrical or flat sheet material. It is shown that the \ncounter voltage of self inductance of an iron-cored coil is due only to \nthe component of flux in the core which is in phase with the flux at \nthe surface of the core. Expressions are obtained and curves plotted \nshowing the variations of inductance of a coil with frequency, or with \nthe conductivity and permeability of the core material. Sample \ncalculations and some experimental results are given. The results \nshow that the inductances at high frequencies are actually less than \nthe predicted values, which leads to the suspicion that some factor \nother than eddy currents causes the flux in the interior of the cores to \ndecrease with increasing frequency.\n\nResults of Noise Surveys. Part IT, Noise in Buildings? R. S. \nTucKER. Noise experienced indoors is in one sense more important \nthan that experienced outdoors, for, with the growth of our industrial \ncivilization, increasing numbers of people are spending most of their \nwaking hours indoors. They are thus exposed to indoor noise for a \nlarge part of the time, including the hours of work when noise has its \nopportunity to impair their working efficiency.\n\nCertain typical values for noise in various locations in buildings \nhave been published, and are summarized in this paper. Our knowl- \nedge of indoor noise levels is far from complete, however. Further \ninformation has been obtained in a survey of room noise in New York \nCity and the surrounding area which was made in 1929 by the National \nElectric Light Association and the American Telephone and Tele- \ngraph Company in the course of the work of their Joint Subcommittee \non Development and Research. Some results of the New York City \nmeasurements are given. About 70 test locations are included. It \nwill be realized that this is only a small sample of the total number of \nplaces where indoor noise is experienced in New York City alone. The \nconclusions given must therefore be regarded only as suggestive rather \nthan as holding true in any general sense.\n\nCHARLES B. AIKEN, B.S., Tulane University, 1923; M.S. in Electrical \nCommunication Engineering, Harvard University, 1924; M.A. in \nPhysics, 1925. Bell Telephone Laboratories, 1928-. Mr. Aiken has \nbeen engaged on work in connection with aircraft communication and \nmore recently with the design of broadcast radio receiver equipment.\n\nF. E. Hawortn, A.B., University of Oregon, 1924; M.A., Columbia \nUniversity, 1929; Bell Telephone Laboratories, 1925-. Mr. Haworth\u2019s \nwork has been in crystal analysis by means of X-rays, magnetic mate- \nrials, and more recently in studies of dielectrics.\n\nHERBERT E. Ives, B.S., University of Pennsylvania, 1905; Ph.D., \nJohns Hopkins, 1908; assistant and assistant physicist, Bureau of \nStandards, 1908-09; physicist, Nela Research Laboratory, Cleveland, \n1909-12; physicist, United Gas Improvement Company, Philadelphia, \n1912-18; U.S. Army Air Service, 1918-19; research engineer, Western \nElectric Company and Bell Telephone Laboratories, 1919 to date. \nDr. Ives\u2019 work has had to do principally with the production, measure- \nment and utilization of light.\n\nW. C. Jones, B.S. in E.E., Colorado College, 1913; Western Elec- \ntric Company, 1913-25; Bell Telephone Laboratories, 1925-. As \nTransmission Instruments Development Engineer, Mr. Jones has \nspecialized in the development and application of instruments for the \ntransmission of speech and music.\n\nA. R. Kemp, B.S., California Institute of Technology, 1917, M.S., \n1918; Engineering Department, Western Electric Company, 1918-25; \nBell Telephone Laboratories, 1925-. Mr. Kemp has been engaged in \nchemical research on rubber and allied materials used for submarine \nand other types of insulation.\n\nW. H. Martin, A.B., Johns Hopkins University, 1909; B.S., Mas- \nsachusetts Institute of Technology, 1911; American Telephone and \nTelegraph Company, Engineering Department, 1911-19; Department \nof Development and Research, 1919-. As Local Transmission En- \ngineer, Mr. Martin has been engaged in development work on the \ntransmission of telephone sets and local exchange circuits, transmission \nquality and loading.\n\nL. J. Sivran, A.B., Cornell University, 1916; Engineering Depart- \nment, Western Electric Company, 1917-19 and 1920-25; Bell \nTelephone Laboratories, 1925-. Mr. Sivian\u2019s work is in acoustics, \nchiefly in connection with methods of electroacoustic measurements.\n\nGEORGE C. SoutHwortu, B.S., Grove City College, 1914, M.S., \n1916; Ph.D., Yale, 1923; assistant physicist, Bureau of Standards, \n1917-18; instructor, Yale University, 1918-23; Information De- \npartment, American Telephone and Telegraph Company, 1923-24; \nDepartment of Development and Research, 1924-. Mr. South- \nworth\u2019s work in the Bell System has been concerned chiefly with \nthe development of short-wave radiotelephony. He is the author of \nseveral papers on radio-frequency phenomena.", "title": "The Bell System Technical Journal 1931-01: Vol 10 Iss 1", "trim_reasons": [], "year": 1931} {"archive_ref": "sim_att-technical-journal_1937-10_16_4", "canonical_url": "https://archive.org/details/sim_att-technical-journal_1937-10_16_4", "char_count": 241088, "collection": "archive-org-bell-labs", "doc_id": 347, "document_type": "journal_issue", "id": "bella-qwen-pretrain-doc347", "record_count": 357, "release_policy_version": "hf_public_v1", "rights_status": "public_domain", "selected_extraction_backend": null, "selected_extraction_score": null, "source_family": "archive_org", "source_url": "https://archive.org/details/sim_att-technical-journal_1937-10_16_4", "split": "validation", "text": "In this paper are discussed several types of crystal band-pass \nfilters which can be used in unbalanced circuits. These types of \nfilters are all resistance compensated, i.e., the resistances associated \nwith the filter elements are in such a position in the filter that they \ncan be effectively brought to the ends of the filter and combined \nwith the terminal resistances with the result that the dissipation \nproduces an additive loss for the filter characteristic and does not \naffect the sharpness of cut-off attainable. It is shown that all these \ntypes of networks can be reduced to three lattice types of crystal \nfilters, and the formulae for these three networks are given. A \ncomparison is given between the characteristics obtainable with \nresistance compensated crystal and electrical filters and a conclu- \nsion regarding their comparison given by V. D. Landon \u2018 is shown \nto be incomplete.\n\nemploying quartz crystals as elements. Most of these filters were \nof the lattice type and hence were inherently balanced. For some \npurposes, however, such as connecting together unbalanced tubes, it is \ndesirable to obtain a filter in an unbalanced form and it is the purpose \nof this paper to show several forms for constructing resistance com- \npensated band-pass crystal filters which will give results similar to \nthose described previously. Another purpose is to give a numerical \ncomparison between the characteristics obtainable with resistance \ncompensated crystal and electrical filters.\n\nII. A COMPARISON OF THE PERFORMANCE CHARACTERISTICS OF \nCRYSTAL vs. CoIL AND CONDENSER FILTERS\n\nfilters it is instructive to give a comparison between the types of \ncharacteristics which can be obtained by using crystal and coil and\n\n1\u201cElectrical Wave Filters Employing Quartz,Crystals as Elements,\u201d W. P. Mason, \nB.S. T. J., July, 1934, p. 405. a\n\ncondenser filters. The quartz crystal filter considered here is shown \non Fig. 1. :\n\nBy using the balancing resistance R, of Fig. 1 the crystal filter can be \nmade entirely compensated for coil resistance ; i.e. the resistance associ- \nated with the coils of the network is in such a place in the network that\n\nit can be effectively brought to the ends of the filter and combined with \nthe terminal impedances with the result that the effect of the dissipa- \ntion in the coils is only to produce an additive loss for the filter charac-\n\nteristic and does not affect the sharpness of cut-off attainable. In fact\n\nif the filter works into a vacuum tube the dissipation in the coil can be \nused to terminate the filter completely, and introduces no loss.\n\nFor the electrical filter, however, the dissipation introduced by the \nelectrical elements which replace the crystal is not compensated and \ncauses a considerable distortion of the pass band which becomes more \nprominent as the band width is narrowed. To show this let us consider\n\nthe network of Fig. 2. In analyzing such networks it is usually more \nconvenient to reduce them to their equivalent lattice form and apply \nnetwork equivalences holding for lattice type networks. This can be \ndone by applying Bartlett\u2019s Theorem? which states that any network \nwhich can be divided into two mirror image halves can be reduced to an \nequivalent lattice network by placing in the series arms of the lattice a \ntwo-terminal impedance formed by connecting the two input terminals \nof one half of the network in this arm and short-circuiting all of the cut \nwires of the network, and in the lattice arm placing the same network \nwith all its cut wires open-circuited. Applying this process to Fig. 1, \na lattice network equivalent to the network of Fig. 1 is that shown on \nFig. 3. In this network the capacitances can be considered as sub-\n\nstantially dissipationless and if the network representing the crystal can \nalso be considered dissipationless, the resistance introduced by the \ncoils can be effectively brought outside the lattice and incorporated \nwith the terminal resistances. This follows from the fact that an \ninductance with an associated series resistance can just as well be \nrepresented over the narrow-frequency range of the filter by an in- \nductance paralleled by a much higher resistance. The impedance of an \ninductance and resistance in series and the impedance of an inductance \nand resistance in parallel are given by the expressions\n\nThis relation holds strictly only for a single frequency, but over a \nnarrow-band filter the relation holds quite accurately.\n\nEmploying this conception, the lattice network can be reduced to \nthat of Fig. 4 in which a resistance R parallels each arm of the lattice.\n\nThis is made possible by the adjustable resistance R, which is fixed at \nsuch a value that the parallel resistance associated with the inductance \nL; + 2Lz is equal to that associated with L;. Then by employing the \ntwo lattice equivalents shown on Fig. 5, first proved by the writer,? it is\n\npossible to take these resistances outside the lattice and combine them \nwith the terminating impedance, leaving all the elements inside the \nlattice dissipationless. The two remaining arms of the lattice have the \nimpedance characteristic shown on Fig. 6A. A lattice filter has a pass \nband when the two impedance arms have opposite signs and an at- \ntenuation band when they have the same sign. When the impedance \nof two arms cross, an infinite attenuation exists. Hence the character- \nistic obtainable with this network is that shown on Fig. 6B.\n\nNext let us consider an electrical filter in which coils and condensers \ntake the place of the essentially dissipationless crystal. In this case the \ndissipation due to L; and Lz can be balanced as before and the only \nquestion to consider is the effect of the dissipation associated with L; \nand C;. Ina similar manner to that employed for the coil we can show\n\nthat a series tuned circuit with a series resistance R, is equivalent to a \nsecond series tuned circuit having the same resonant frequency as the \nfirst shunted by a resistance R,\u2019 where \nAl \nC,\\\n\nAt two frequencies for which the absolute values of the reactances are \nthe same and therefore the value of Q equal, it is possible to replace the \nseries resistance by a shunt resistance and hence compensate it by \nvarying the resistance R,. Since, however, the reactance of the tuned \ncircuit varies from a negative value through zero to a positive value \nover the pass band of the filter, the value of this shunt resistance is not\n\neven approximately constant and hence the filter cannot be resistance \ncompensated throughout the band of the filter. It cari, however, be \ncompensated at the frequencies of infinite attenuation and high losses \ncan be obtained at these frequencies.\n\nThe effect of the lack of resistance compensation throughout the \nband can best be shown by a numerical computation of the loss of an \nelectrical filter as compared to that for a crystal filter. A practical \nexample has been taken of a filter whose band width is 12 kilocycles \nwide with the mean frequency at 465 kilocycles. In order to obtain the \nbest Q\u2019s with reasonably sized coils an arrangement suggested by R. A. \nSykes is used. The coils L; are obtained by using the two equal wind- \nings of a coupled coil series aiding so that ZL; equals the primary induct- \nance plus the mutual inductance. Since in an air core coil all of the \ndissipation is associated with the primary inductance and none with the \nmutual this gives a high Q for L;. The inductance L\u00bb neutralizes the \nnegative mutual inductance \u2014M and supplies in addition a small \npositive inductance. The Q of this combination is poor but it makes \nunnecessary the use of a high resistance R, for balancing purposes. By \nthis method a much higher effective Q is obtained than can be obtained \nby a single coupled coil or by three separate coils.\n\nThe calculated curve for the electrical filter assuming Q\u2019s of 150 for all \nthe coils is shown on Fig. 7 by the dotted lines. A similar curve for a \ncrystal filter is shown on Fig. 7 by the full lines. As is evident the \neffect of the coil dissipation is to round off the edges of the pass band \nand to limit the effective discrimination between the passed and \nattenuated bands.\n\nThis result does not agree with that given by Landon,\u2018 who in a \nrecent paper makes a comparison between the results obtained with \ncrystal and elec rical filters which appears to be somewhat misleading. \nIt is stated in this paper that the electrical filter circuits given are com- \npletely resistance compensated and \u201c\u2018in crystal filters in which the \ncrystal is confined to the rejector meshes of the network, the limitation \nis about the same as for electrical filters.\u201d By referring to the curves \nof Fig. 7 it is readily seen that high losses can be obtained outside the \npass band with resistance compensated electrical filters,\u00ae but that the\n\n4\u201c *VW Derived\u2019 Band-Pass Filters with Resistance Cancellation,\u201d Vernon D. \nLandon, R. C. A. Review, Oct. 1936, Vol. 1, No. 2, Page 93.\n\n5 The use of resistance for compensating and balancing the attenuation in electrical \nfilters has been worked out by H. W. Bode and S. Darlington (see U. S. patents \n2,002,216, 1,955,788, 2,029,014, 2,035,258). The first work was done for low- and high- \npass filters but it was later extended also to band-pass filters. Some of these results \nare analogous to those of Landon, while others give a better compensation within the\n\ntransmitted band. The use of the resistance in the crystal filter of Fig. 1 was sug- \ngested by Mr. Darlington.\n\nFig. 7\u2014Numerical comparison_between the loss characteristics of a crystal filter and\n\npass band of the filter is seriously distorted unless elements, such as \ncrystals, are used which have negligible dissipation.\n\nAll of the wide-band resistance compensated crystal filters proposed \nso far can be shown to be equivalent to the two general types of lattice \ncrystal filters shown on Fig. 8. For example the crystal filter of Fig. 1 \nwas shown to be equivalent to the lattice type filter of Fig. 8 (b) in which \nthe crystals in the lattice arms are left out.\n\nIn the lattice filters of Fig. 8 the number of crystals employed can be \ncut in half by employing in two similar arms a crystal with two pair of \nequal plates. It can be shown that such a crystal used in similar arms \nis equivalent to two identical crystals of twice the impedance of the \ncrystal used as a single plate and having the same resonance frequency. \nHence the lattice filters of Fig. 8 are as economical of elements\u2014except \nfor two condensers\u2014as an unbalanced type filter. For some purposes, \nhowever, such as connecting together unbalanced tubes, it is desirable \nto obtain a filter in an unbalanced form. Also, at high frequencies the \ncrystals become quite small and hence it becomes difficult to divide the\n\naS plating on such crystals. It is the purpose of this section to list a \nnumber of filters of the unbalanced type which are equivalent to the \nlattice filters of Fig. 8. They do not have as general filter character-\n\nspectively to the lattice crystal filters of Fig. 8. The equivalent lattice \nconfigurations are shown on Fig. 9. The first two filters have series \ncoils which inherently give low-impedance filters. The second of these \nis equivalent to the filter of Fig. 8 (a) with one pair of the crystals \neliminated. If the inductance L2 were eliminated from Fig. 9 (a) or (b) \nthe filters will be resistance compensated, for all of the resistance will \nbe on the ends of the filter. Furthermore if a small amount of coupling \nis allowed between the two end coils, the effect of this will be to intro- \nduce the small coil L2/2 in the desired place as can be seen from the 7 \nnetwork equivalent of a coupled coil as shown on Fig. 10. Further- \nmore if the coils are air core, no dissipation is associated with the mutual \ninductance and hence if coupled coils are used the networks still have a \nresistance balance. Similarly the filters shown on Figs. 9 (c) and (d) are \nequivalent to the high-impedance type filter shown on Fig. 8 (b) with all \ncrystals present or with crystals missing from the lattice arms. By\n\nemploying coils with a small amount of mutual inductance these types \ncan also be made with a resistance balance. They can also be made to \nbalance for physical coils by employing the resistances shown. It is \nobvious from the equivalent lattice structures that these networks have \nlimitations on band widths and allowable attenuation which are not \npresent for the original lattice structures of Fig. 8. However, for filters \nwhose pass bands are less than the maximum pass bands, useful results \ncan be obtained.\n\nAnother method for obtaining results similar to that obtainable in a \nlattice network is to use a hybrid coil with series aiding secondaries \nwhich are connected to a crystal and a condenser as shown on Fig. 11, \nThis circuit, which has been used extensively to provide a narrow band \ncrystal filter in telegraph work, was invented first by W. A. Marrison \u00b0 \nof the Bell Telephone Laboratories. Under certain circumstances this \nconfiguration can be shown to give results similar to the narrow-band\n\nlattice filter of Fig. 12. A hybrid coil with series aiding windings con- \nnected to two impedances 2Z; and 2Z2 as shown by Fig. 13A can be \nshown to be equivalent to the circuit of Fig. 13B in which a lattice\n\nnetwork with the branches Z; and Z; is placed in series with the trans- \nforming network and the series terminating inductances. Hence if the \nhybrid coil has nearly a unity coupling between its secondary coils and\n\nthe remainder of the transformer is designed to work into the impedance \nof the filter, the network of Fig. 11 is equivalent to the narrow-band \nlattice filter of Fig. 12 with crystals removed from the lattice arms, plus\n\na transformer. As usually used, however, the impedance of the trans- \nformer is much lower than that of the filter and as a consequence the \nband-pass characteristic of the filter is lost. As a result the network \npasses only a single frequency and gives results similar to those obtain- \nable with a very sharply tuned circuit. By placing a crystal in the \nother arm of the network as shown by Fig. 14,\u2019 this configuration can \nbe made equivalent to the filter shown in Fig. 12.\n\nIt is obvious from the equivalence of Fig. 13 that the configurations of \nFig. 11 and Fig. 14canalsobe used togivea wide-band filter. This follows \nsince the series inductances can be taken inside the lattice and the low- \nimpedance crystal filter of Fig. 8 (a) results. The Q of the coils included \nin the filter will ordinarily not be high since the inductance is obtained \nby a difference of primary and mutual inductances, and a better result \nwill be obtained by making the secondary coupling high and including \nphysical coils in series with the crystals.\n\nWe see then that all of the resistance compensated wide-band filters \nare equivalent to the lattice filters of Figs. 8 and 12, and all their design \nequations are known when the design equations of the equivalent \nlattices are calculated. This requires two steps, first the calculation of \nthe spacing of the resonant frequencies of the network to give the \nrequired attenuation and secondly the calculation of the element values \nfrom the known resonances by means of Foster\u2019s theorem. Such \ncalculations are familiar in filter theory and hence only the results are \ngiven here. The results are given in Tables I, II, and III for the \nnetwork of Figs. 8 (a), 8(b) and 12 respectively. These values are given \nin terms of the characteristic impedance Zp of the filter at the mean \nfrequency, the lower and upper cut-off frequencies f; and fz respectively \nand the b\u2019s of the network. These last, are parameters which specify\n\nTABLE III \nElement Formula Element Formula \nC + be) C biba(f2? \u2014 \n+ firbibe L Zo( + fi2bibe)* \n2aZof i + b2) + b2)(fs? \u2014 fi?) \nC (by + be) (fe? \u2014 fi?) L Zof + bs) \n2aZofi(1 + bibs) (fo? + 2afibiba( \u2014 fi*)\n\nthe location of the attenuation peaks of the network with relation to the \ncut-off frequencies and are given by the expression :\n\nThese tables give the design formulae for the networks of Figs. 8 and \n12. To obtain the equations for a network having crystals in the \nseries arms alone, it is only necessary to let b; = 0. If one of the \npeaks of the filter of Fig. 8 (a) is placed at infinity-\u2014\u2014-which results when\n\n= fe/f:\u2014the two coils will have equal values and by the theorem \nillustrated by Fig. 5 can be brought out to the ends of the filter, \nsimplifying the construction. In a similar manner if one of the peaks \nof the filter of Fig. 8 (b) is placed at zero frequency, i.e. b2 = 1, the two \nshunt inductances are equal and can be brought out to the ends of \nthe filter. The design equation of the narrow band filter of Fig. 12 \nwith the lattice crystals replaced by condensers can be obtained from \nTable III by letting b. =\n\nMagnetic Generation of a Group of Harmonics* \nBy E. PETERSON, J. M. MANLEY and L. R. WRATHALL\n\nA simple physical picture of the action of the circu t has been \nderived from an approximate mathematical analysis. The prin- \ncipal roles of the non-linear coil may be regarded as fixing the \namount of charge, and timing the charge and discharge of a con- \ndenser in series with the resistance load. By suitably propor- \ntioning the capacity, the load resistance, and the saturation in- \nductance of the non-linear coil, the amplitudes of the harmonics \nmay be made to approximate uniformity over a wide frequency \nrange. The sharply peaked current pulse developed by condenser \ndischarge passes through the non-linear coil in its saturated state \nand so contributes nothing to the eddy current loss in the core. \nIn this way the efficiency of frequency transformation is main- \ntained at a comparatively high value for the harmonics in a wide \nfrequency band, even with small core structures. The theory has \nalso been adequate in establishing a basis for design, and in evalu- \nating the effects of extraneous input components.\n\nHE use of non-linear ferromagnetic core coils to generate har- \nmonics started with a simple type of circuit due to Epstein ! \nwhich appeared in 1902. Application of the idea was not made to any \ngreat extent until it was elaborated by Joly ? and by Vallauri * in 1911. \nThe frequency multipliers thus developed were limited to doublers and \nto triplers, polarization being required for the doubler. In these, as \nwell as in subsequent developments, single and polyphase circuits were \nused, and various arrangements were adopted for the structure of the \nmagnetic core and for the circuit, by which unwanted components were \nbalanced out of the harmonic output path. Later developments had \nto do with improvements in detail, and with the generation of higher \nharmonics in a single stage and in a series of stages. The applications\n\n* Presented at the Pacific Coast Convention of A. I. E. E., Spokane, Washington, \nSeptember 2, 1937. Published in Elec. Engg. August 1937.\n\nof perhaps greatest importance were to high power, long-wave radio- \ntelegraph transmitters, where the fundamental input was obtained \nfrom an alternator. Other applications of the idea of harmonic pro- \nduction by magnetic means have been made in the power and com- \nmunication fields.\u2018\n\nIt appears that these circuits were all developed primarily to generate \na single harmonic. Comparatively good efficiencies were obtained, \nvalues from 60 to 90 per cent being reported for the lower harmonics. \nThe theory of frequency multiplication was investigated by a number \nof workers, among whom may be mentioned Zenneck \u00b0 and Guillemin.\u00b0 \nThe latter, after analysis which determined the optimum conditions for \nthe generation of any single harmonic, found experimentally that the \nefficiency of harmonic production decreased as the order of the har- \nmonic increased. He obtained efficiencies of 10 per cent for the 9th \nharmonic, and 3 per cent for the 13th harmonic of 60 cycles.\n\nWhere the circuits are properly tuned and the losses low, free oscilla- \ntions may be developed. The frequencies of these free oscillations may \nbe harmonic, or subharmonic as in the circuit described by Fallou; 7? \nthey may be rational fractional multiples of the fundamental, or in- \ncommensurable with the fundamental, as in Heegner\u2019s circuit. The \namplitudes of these free oscillations are usually critical functions of the \ncircuit parameters and input amplitudes, and where the developed \nfrequencies are not harmonic, they are characterized by the fact that \nthe generated potentials are zero on open circuit. The theory of the \neffect has been worked out by Hartley.\u00ae It is presumably this effect \nwhich is involved in the generation of even harmonics by means of an \ninitially unpolarized ferromagnetic core, an observation which has been \nattributed to Osnos.'\u00b0\n\nThe harmonic producer circuit which forms the subject of the \npresent paper differs from those mentioned in that it is designed to \ngenerate simultaneously a number of harmonics at approximately the \nsame amplitude.\n\nHarmonics developed in circuits of this type have been used for the \nsupply of carrier currents to various multi-channel carrier telephone \nsystems, for synchronizing carriers used in radio transmitters, and for \nfrequency comparison and standardization. Only odd harmonics are \ngenerated by the harmonic producer when the core of the non-linear \ncoil is unpolarized, as is the case here. To generate the required even \nharmonics, rectification is employed. This is accomplished by means \nof a well balanced copper oxide bridge, which provides the even har- \nmonics in a path conjugate to the path followed by the odd harmonics.\n\nA typical circuit used for the simultaneous generation of a number of \nodd and even harmonics at approximately equal amplitudes is shown \nschematically in Fig. 1. Starting with the fundamental frequency\n\ninput, a sharply selective circuit (F) is used to remove interfering com- \nponents, and an amplifier (A) provides the input to the harmonic \ngenerator. The shunt resonant circuit (ZoCo) tuned to the funda- \nmental serves primarily to remove the second harmonic generated in \nthe amplifier. The elements C,Z; are inserted to maintain a sinusoidal \ncurrent into the harmonic producer proper, as well as to tune out the \ncircuit reactance.\n\nFig. 2\u2014Cathode ray oscillogram of output current wave form with fundamental input \ncurrent as abscissa,\n\nL2 is a small permalloy core coil which is operated at high magnetiz- \ning forces well into the saturated region. The circuit including Le, C2, \nand the load impedance, which is practically resistive to the desired \nharmonics, is so proportioned that highly peaked current pulses rich in \nharmonics flow through it. Two such pulses, oppositely directed, are \nproduced during each cycle of the fundamental wave, the duration of \neach being a small fraction of the fundamental period. The typical \noutput wave shown in Fig. 2 was obtained by means of a cathode ray \noscillograph, the ordinate representing the current in the load re- \nsistance, and the abscissa representing the fundamental current into the \ncoil. The desired odd harmonics are selected by filters connected \nacross the input terminals of the copper oxide bridge. The even har- \nmonics are obtained by full-wave rectification in the copper-oxide \nbridge. They appear at the conjugate points of the bridge, and are \nconnected through an isolating transformer to the appropriate filters. \nThus the harmonics are produced in two groups, with the even harmon- \nics separated from the odds to a degree depending largely upon the \nbalance of the copper-oxide bridge, as well as upon the amount of \nsecond harmonic passed on from the amplifier. In this way the re- \nquired discrimination properties of any filter against adjacent harmonics \nare reduced to the extent of the balance.\n\nA particular application of the circuit described above to the genera- \ntion of carriers for multi-channel carrier telephone systems uses a \nfundamental frequency of 4 kc., from which a number of harmonics \nare developed. Of these the 16th to the 27th are used as carriers. \nA photograph of an experimental model of this carrier supply system * \nis shown in Fig. 3. The top panel includes an electromagnetically driven \ntuning fork serving as the highly selective circuit (F), the amplifier (A), \nthe output stage of which consists of a pair of pentodes in push-pull, and \nthe tuned circuit LoCo. The next panel includes the elements L,C), Ls, \nC2, B, and T, together with a thermocouple and meter terminating in a \ncord and plug for test and maintenance purposes. The last two panels \ninclude the twelve harmonic filters, with test jacks and potentiometers \nfor close adjustment of the output of each harmonic.\n\nA few of the more interesting performance features are given in \nFig. 4. The harmonic power outputs shown in Fig. 4a represent \nmeasurements at the input terminals of the filters. The variation \nobserved is produced by the non-uniform impedances of the filters. \nWhen these are corrected, the variations due to the harmonic generator \nproper are less than + 0.2 db from the 16th to the 27th harmonic. \nOutside this region the amplitudes gradually decrease to the extent\n\nFig. 3\u2014Carrier supply unit, furnishing twelve harmonics of 4 kc. \n(experimental model).\n\nof 4 db at the 3d and 35th harmonics, and 11 db at the fundamental \nand the 61st harmonic. The variation of harmonic output with \nchange of amplifier plate potential is given for the two harmonics \nindicated in Fig. 4b. Figure 4c shows the 104 kc. output as a function \nof the 4 kc. input. Arrows are used to indicate normal operating \npoints. The input amplifier is operated in an overloaded state so that \nbeyond a critical input, the fundamental output of the amplifier and\n\nFig. 4\u2014Performance curves of channel harmonic generator. (A) Harmonic \noutputs; (B) Variation of 16th and 26th harmonics with amplifier plate potential; \n(C) Variation of 26th harmonic with fundamental input.\n\nFig. 5\u2014Construction of experimental non-linear coils used for harmonic generation, \nshowing core forms, magnetic tape, wound coils, and assembled units.\n\nthe harmonic output corresponding are but little affected by change of \ninput amplitude. With a linear amplifier the harmonic output current \nwould vary roughly as the four-tenths power of the input current.\n\nAnother application involving higher frequencies has been made to \nthe generation of the so-called \u2018\u2018group\u201d\u2019 carriers used in conjunction \nwith a coaxial conductor.\" There odd harmonics of 24 kc. from the \n9th to the 45th are used. The circuit differs from Fig. 1 in that the \ncopper oxide bridge is omitted, and the non-linear coil is provided with \ntwo windings to facilitate impedance matching. The performance of \nan experimental model is similar to that of the generator described \nabove. A notion of the physical size and construction of the non- \nlinear coils used may be had from the photographs of Fig. 5.\n\nIn both applications the required harmonics are generated at ampli- \ntudes high enough to avoid the necessity for amplification.\n\nTo avoid these difficulties, an expedient is adopted by which the \nhysteresis loop is replaced by a single-valued characteristic made up of \nconnected linear segments \u00b0 as shown in Fig. 6b. It is then possible to \nformulate a set of linear differential equations with constant coefficients, \none for each linear segment. The solutions are readily arrived at and \nmay be pieced together by imposing appropriate conditions at the \njunctions, so that a solution for the whole characteristic is thereby \nobtained. From this solution the wave form of current or voltage \nassociated with any circuit element may be calculated. Resolution of \nthe wave form into components may then be accomplished by an \nindependent Fourier analysis.\n\nThe assumed B-H characteristic of Fig. 6b is made up of but three \nsegments. While it is manifestly a naive representation of a hysteresis \nloop, it will be shown by comparison with experiment that the main \nperformance features of harmonic generators may be reproduced by \nthis crude model.\n\nIt will be noted on Fig. 6b that the differential permeability of the \nassumed non-linear core, a quantity proportional to dB/dH, takes on \none of two values, determined by the absolute value of the magnetizing \nforce. These are designated by u in the permeable region and y, in the \nsaturated region. The corresponding inductances are Loo and Lo, Loo \nbeing many times greater than L2,. The values of current through the \ncoil at which the differential inductance changes are designated + [o,\n\nFig. 6\u2014Diagrams illustrating operation of the harmonic generator. (A) Harmonic \ngenerator circuit; (B) Differential inductance and flux density of assumed non-linear \ncoil as functions of magnetizing force; (C) Variation with time of currents in primary \nand secondary meshes, and in non-linear coil; (D) (EZ) (F) Equivalent circuits of the \nharmonic generator for the three time intervals indicated.\n\nThe current flowing in the input mesh is made practically sinusoidal \nby tuning Z;, C;. If now we start at the negative peak of the sinus- \noidal input current of amplitude 7, and frequency p/27, the non-linear\n\nBm \nLINEAR \n-Io| Io H \n(a) \nI \nlp} \nfe) \n(c) \nte tg \nt ta 3, the discharge is an exponentially decaying oscillation; if\n\nk = }, the discharge is an exponentially decaying pulse. This last \ncondition is the one assumed in the description of operation given \nabove.\n\nIf the discharge is oscillatory, and if further the second peak is large \nenough, the current through the coil may become less than J\u00bb during \nthe discharge interval. Thus Lz will return to its larger value, and \nrecharging of the condenser will result. This process may lead to large \nand undesired variations in the amplitudes of the harmonics. To \nmaintain the frequency distribution as uniform as possible over the \nfrequency range of interest, the circuit parameters are usually adjusted \nso that recharging does not occur.\n\nHarmonic analysis shows that the nth harmonic amplitude under the \nabove assumptions is given by\n\nwhere n is odd. This expression neglects the contributions due to the \ncharging stage, which are usually small for harmonics higher than \nthe ninth.\n\nwhere W, is a convenient parameter which does not vary with nm and \nhence serves as an indication of the power of the output spectrum. It \nis related to W, the total power delivered to the load resistance, by \nthe equation,\n\nand NV is the number of turns wound on the toroidal! core of diameter d \ncm. and cross-sectional area A cm.?\n\nIn Fig. 7 the power spectrum is shown by plotting W, in db above or \nbelow Ws as a function of npC2R, for several values of k. These \ncurves illustrate the degree of uniformity obtainable in harmonic am-\n\nFig. 7\u2014Harmonic power spectrum plotted from eq. (2) as function of npC2R2 with k \nas parameter.\n\nplitudes under different conditions. It may be shown from (3) that \nW,, has a maximum with respect to n when k is greater than }, if\n\nA number of relations may be derived from these equations which \nare useful for design purposes. Thus the form of harmonic distribution \nis fixed by k and pC:R2. The output power for a given magnetic ma- \nterial worked at a given fundamental magnetizing force then depends \nsolely upon the volume of core material. Finally, the impedance is fixed \nby the number of turns per unit length of core. If the impedances \ndesired for primary and secondary circuits differ, separate windings \nmay be used for each circuit.\n\nIn order to make practical use of the results given above, we need \nsome basis for deriving the assumed parameters of the non-linear coil \nfrom the physical properties of the magnetic materials used in harmonic \nproducers.\n\nThe fact that the actual magnetization curve is a loop instead of a \nsingle-valued curve as assumed requires increased power input to the \ncircuit to provide for the hysteresis and eddy losses in the core. Other \nthan this, the principal remaining effect of the existence of a loop is a \nlag in the time at which the pulses occur, an effect which is of no great \nmoment in determining the form or magnitude of the resulting pulses.\n\nThe next point requiring consideration is the effect introduced by the \nassumed abrupt change of slope contrasted to the smooth approach to \nsaturation actually observed. While no rigorous comparisons can be \ndrawn, the effect of the more gradual approach to saturation was ap- \nproximated analytically by introducing an additional linear segment \nbetween the permeable region and each saturated region of the B-H \ncharacteristic, at a slope intermediate between the two, so as to form a \nB-H characteristic of five segments in place of the original three. The \nsolutions for these two characteristics were found to yield negligibly \nsmall differences in the amplitudes of the higher harmonics. It was \ninferred from this result that no substantial change would be introduced \nby a smooth approach to saturation.\n\n- saturated region, while the analysis considered a small linear variation.\n\nA rough approximation for the effect of this curvature, which leads to \nfair agreement with experiment, consists in taking for Ls, the average \nof the actual slope, from its minimum value reached during the dis- \ncharge peak down to the point at which the slope is one-tenth maxi- \nmum. To this is added the linear inductance contributed by the \ndielectric included within the winding.\n\nTo summarize then, the harmonic outputs obtained from the \nanalysis with the assumed B-H characteristic may be brought into line \nwith experimental observations by the introduction of quantities ob- \ntained from actual B-H loops at appropriate frequencies and magnetiz- \ning forces. In these the maximum slope found on the loop is taken for \nLo, the average slope over the saturated region is taken for L2,, and the \nenergy corresponding to the area of the real B-H loop must be added to \nthat originally supplied the harmonic generator input.\n\nA comparison between measured and calculated harmonic distri- \nbutions obtained with a 4-kc. fundamental input is shown in Fig. 8. In \nthis case the harmonic distributions were measured for four different\n\nvalues of the secondary condenser C; as shown by the plotted points. \nThe power output of each harmonic is plotted in terms of the quantity \nnpC2R:z. Calculated values are indicated by dashed lines. It is \nobserved that while the agreement between calculation and experiment\n\n30 \nTHEORETICAL \nOBSERVED \nFUNDAMENTAL (4 KILOCYCLES) \nMAGNETIZING FORCE =8.1 OERSTEDS\n\nFig. 8\u2014Comparisons of calculated and measured harmonic distributions, plotted as \nfunctions of npC;R:, with C; as parameter.\n\nis perhaps as good as could be expected for the two highest curves, a \nsubstantial divergence is noticed in the two lowest sets; the forms of the \ntwo sets are significantly different, and it seems that the divergence \nmight become even greater at larger values of mpC2,R2 than those \nshown. Upon examination of the equations, however, it turns out that \nthe conditions existing for the lowest pair of curves are just those for \nwhich recharging occurs, so that the conditions for which the equations \nwere framed hold no longer. The calculated distributions might be \nexpected to be too low for the higher harmonics, since we have taken an \naverage value for the saturation inductance. This means that the peak \nof the discharge pulse will be sharper than that calculated, with a \ncorresponding effect upon the higher harmonics.\n\nAnother comparison between calculated and observed values is \nshown in Fig. 9 for a fundamental input of 120 kc. with two values of \nresistance load. Fair agreement is observed over the greater part of \nthe frequency range which extended to5 MC. The distribution curve \nfor the smaller resistance load undulates as the load resistance is re- \nduced, since multiple oscillations and recharging are then promoted, in \nconsequence of which the output power tends to become concentrated \nin definite bands of harmonics. In general, agreement within a few db \nis found over a wide range of circuit parameters when working into a \nresistance load, provided that recharging does not occur.\n\nFig. 9\u2014Comparisons of calculated and measured harmonic distributions plotted as \nfunctions of npC:R2, with R; as parameter.\n\nWhen the resistance termination is replaced by a bank of filters as it \nis in practice, the resistance termination is approximated over the \nfrequency band covered by the filters. Where the band is wide the \nresults obtained do not differ greatly from those with the pure resist- \nance load, but when only a few harmonics are taken off by filters and \nthe impedances to the other harmonics of large amplitude vary widely \nover the frequency range, then the wave form of the current pulse is \nsubstantially altered, with corresponding effect upon the frequency \ndistribution, and the calculations for a pure resistance termination do \nnot apply.\n\nfundamental input and harmonic output may vary widely with small \nchanges in supply potentials and circuit parameters. This troublesome \nsource of variation may be avoided in a number of different ways, of \nwhich the simplest is to increase the resistance of the resonant mesh. \nIn the present case this is effectively accomplished without sacrificing \nefficiency by using pentodes, which have high internal resistances, in \nthe amplifier stage connected to the resonant mesh.\n\nThe efficiency of power conversion from fundamental to harmonics \nmay be found from the fundamental power input to the circuit, as \nderived from measurements on a cathode ray oscillograph, and from the \ntotal harmonic output measured by means of a thermocouple. The \nmaximum efficiency obtainable with the low-power circuits described in \nthe second section is in the neighborhood of 75 per cent, and decreases \nwith increasing fundamental frequency because of the increased dissi- \npation due to eddy currents. It should be noted that this figure does \nnot include losses in the primary inductance Z;. When only a few \nharmonics are used, the efficiency of obtaining this useful power \nnaturally drops to a much lower value, which for the particular \ncases mentioned in the second section, is between 15 and 25 per cent.\n\nIn any practical case the fundamental input to the harmonic pro- \nducer is accompanied by extraneous components introduced by cross- \ntalk, by modulation, or by an impure source. Thus if the fundamental \nis derived as a harmonic of a base frequency, small amounts of adjacent \nharmonics will be present. Or if the amplifiers are a.-c. operated, side- \nfrequencies are produced differing from the fundamental by 60 cycles \nand its multiples. Extraneous components of this sort in the input \nmodulate the fundamental and produce side-frequencies about the \nharmonics in the output. When the harmonics are used as carriers, \nthe accompanying products must be reduced to a definite level below \nthe fundamental if the quality of the transmitted signal is to be un- \nimpaired. The requirements imposed by this condition can be calcu- \nlated by simple analysis, the results of which agree rather well with \nexperimental values.\n\nThe method of analysis used is to consider the extraneous component \nat any instant as introducing a bias\" to the non-linear coil. The \nprimary effect of a small bias (0) is to shift the phase of the discharge \npulse by + }/H, radians, H, being the amplitude of the fundamental \nmagnetizing force. The sign of the shift. alternates so that intervals \nbetween pulses are alternately narrowed and widened.\n\nThe effect of this shift on the harmonics produced may be found by \nstraightforward means in which the amplitude of any harmonic is \nexpressed in terms of the bias. Hence when the extraneous component \nor components vary with time, the sidebands produced may be evalu- \nated when the bias is expressed by the appropriate time function.\n\nIf the bias is held constant, the wave is found to include both odd and \neven harmonics, the amplitudes of which are given by\n\nI(n) being the harmonic distribution in the absence of bias as given \nby eq. (2). \nIf the extraneous input component is sinusoidal, we have\n\nSubstituting this expression for } in the equation for the harmonic com- \nponents yields odd harmonics of the fundamental, and modulation \nproducts with the angular frequencies mp + /g, which may be grouped \nas side-frequencies about the odd harmonics. The amplitude of the \nnth (odd) harmonic is\n\nConsidering the side-frequencies about the mth harmonic, the largest \nand nearest of these are (n + 1)p \u2014 q and (m \u2014 1)p +, m being \nodd. The ratio of the amplitudes of either side-frequency to the mth \nharmonic is\n\non the assumption that the harmonic distribution in the neighborhood \nof is uniform so that J(n +1) = J(m). If the arguments of the \nBessel functions are less than four-tenths, a good approximation to the \nright member of eq. (9) is (m + 1)Q/2H;. Hence with sufficiently \nsmall values of interference, the sidebands produced are proportional\n\nto the amplitude of the interference, and increase linearly with the \norder of the harmonic. These relations apply to harmonic generators \nwhich produce sharply peaked waves in general, and are not peculiar \nto the magnetic type.\n\nNeighboring modulation products involving the interfering com- \nponent g more than once have much smaller amplitudes in normal \ncircumstances than the product considered above. Because of the \ntuning in the input mesh, interfering components far removed in fre- \nquency from the fundamental are greatly reduced and the most \ntroublesome interference is likely to be close in frequency to the \nfundamental.\n\nIt may be noted that where the interference is produced by amplitude \nmodulation of the fundamental, so that two interfering components \nenter the input, the distortion produced may be approximated by \ndoubling the amplitudes of the side-frequencies produced by one of the \ninterfering components. If the disturbance is the second harmonic of \nthe fundamental, the effect is nearly the same as that for constant bias, \nand the relations (5) may be used if } is taken as the amplitude of the \nsecond harmonic magnetizing force. '\n\nFig. 10\u201473rd and 74th harmonic amplitudes as functions of direct current flowing \nthrough non-linear coil. Ordinate is ratio of harmonic amplitude with bias indicated, \nto that of 73rd harmonic with zero bias. Abscissa is harmonic number multiplied by \nthe \u2014 of bias to fundamental. Dashed lines calculated from eq. (5), full lines \nmeasured.\n\nTo illustrate the effects of d.-c. bias, Fig. 10 shows the amplitudes of \nthe 73d and 74th harmonics of 4 kc. as functions of the parameter \nnQ/H;. The agreement between measured and calculated values \nindicates that the most important effects of bias have been included in \nthe simple analysis.\n\nSince the first transatlantic radio telephone circuit was opened \nfor service over ten years ago, an increasing number of voice- \noperated switching devices has been added to the international \ntelephone network. All of these have the common purpose of \npreventing echo and singing effects due to arranging the facilities \nto give the best possible transmission, even under difficult radio \nconditions. Differences in the design and performance of the \nseveral types of devices suggest that the advantages and dis- \nadvantages of each be made available.\n\nHE interconnection of ordinary telephone systems by means of \nlong radio-telephone links presents some unique and interesting \ntechnical problems. Since radio noise is often severe as compared\n\nwith that in wire lines, radio transmitter power capacity is relatively \nlarge and expensive, and it is in general economical to control the \nspeech volumes so that the radio transmitter will be fully loaded and \nthus the effect of noise minimized for a given transmitter power rating. \nThis volume control, to be fully effective, calls for voice-operated \nswitching devices to suppress echoes and singing.\n\nThe general principles and applications of the vodas have been \ndiscussed from time to time in various papers listed at the end of this \ntext. The present paper goes somewhat more into detail regarding the \ntransmission performance of the vodas, including a description of an \nimproved form of circuit which discriminates between line noise and the \nsyllabic characteristics of speech.\n\n* Presented at the Pacific Coast Convention of A.I.E.E., Spokane, Washington, \nSeptember 2, 1937. Published in Elec. Engg., August, 1937.\n\nThe two-way problem in telephony began with the invention of the \ntelephone itself, and was the subject of considerable pioneering activity \nduring the latter part of the nineteenth century. The invention of the \namplifier brought about new problems when applied in a repeater for \ntwo-way op\u00aeration. Even before a practical repeater had been devised, \ninventors visualized controlling the direction of transmission through \namplifiers in a line by relays controlled from switches associated with \nthe subscribers\u2019 instruments, an idea which is in use today on airplanes \nand small boats and in special circuits where this type of two-way \noperation is practicable. It is also used by amateur radio telephone \noperators. But for public telephone service more rapid and automatic \ncontrol of two-way conversation is preferable.\n\nTo control the direction of transmission in a manner that would meet \npublic convenience, invention progressed through the early part of the \ntwentieth century toward devices for switching the speech paths \nautomatically by voice waves. During this period, long distance radio \ntelephony was first demonstrated to be practical on a one-way basis.\n\nFrom that time until the first transatlantic radio telephone circuit \nwas placed in service on January 7, 1927, anti-singing voice-operated \ndevices underwent a process of development aimed at meeting the \nrequirements of two-way radio telephone service. The vodas was one \nresult. Since 1927, improvements have been made in cheapening and \nsimplifying the equipment and in making a vodas that will operate \nbetter on speech and not so frequently on noise. It has also been \npossible to arrange a vodas so as to permit using the same privacy \napparatus for both directions of transmission, thereby saving the cost \nof duplicate apparatus.\n\nThe conditions encountered when joining two-wire two-way circuits \nby radio links are illustrated in Fig. 1 in which (a) shows a connection \nbetween two subscribers, W and E, while (b) shows the paths of direct \ntransmission and echo when E talks. In addition to the talker and \nlistener echoes which arise in such a connection, singing can occur \naround the closed circuit CAFGDBC if the amplification is great \nenough. Also, when the same frequency band is used to transmit in \nboth directions, two cross-transmission paths AB and DF are set up, \nand echoes and singing can take place around the end paths ABC and \nDFG. Any echoes or singing are of course primarily due to reflections \nof energy at points of impedance irregularities in the two-wire plant, \nincluding the subscribers\u2019 telephones themselves.\n\nIn wire circuits, simple hybrid coils and echo suppressors? are \nusually adequate to prevent such effects because the gains are not \nincreased to provide for loading the circuit with energy when speech is \nweak, and also because the cross-transmission paths are absent. In \nlong radio circuits, however, singing may result from the adjustments \nof amplification made to load the radio transmitter in case of weak \nspeech and thus override noise, even though separate frequency bands \nare used in the two directions. Moreover, it is desired that the users of \nthe service have as good transmission over the entire connection, \nincluding these radio links, as that to which they are accustomed in \ntheir own wire telephone systems, and even better transmission may \nbe desired owing to differences in the language habits of the sub- \nscribers. Consequently, the overall transmission efficiencies of inter- \ncontinental radio circuits are sometimes better than those of the best \nland lines in the areas to be interconnected.\n\nA voice-operated device to suppress singing effects can be designed \nto have three possible arrangements:\n\n1. The terminal can normally be blocked in one direction and con- \nnected through in the other.\n\n2. Both directions of transmission can normally be blocked and \nactivated in either direction but not both directions by the voice \nwaves.\n\n3. The circuit can remain activated in the last direction of speech \nand blocked in the other direction.\n\nWhere there is no noise on the transmission system under con- \nsideration any of these three arrangements will give satisfactory opera- \ntion as there is then nothing to prevent making the voice-operated \ndevices as sensitive as may be necessary to obtain full operation on \nweak as well as on strong voice waves. If there is any noise on the \nsystem which tends to operate the device it is necessary to make it less \nsensitive to avoid false operation. A point may be reached where the \nsensitivity is so low that the weakest parts of speech will not cause \noperation, and the weak consonants will be lost. The reduction in \narticulation has been found to be proportional to the time occupied by \nthese lost or \u2018\u2018clipped\u201d\u2019 sounds.*\u00ae\n\nIf the device is located at a point in the circuit where the signal-to- \nnoise ratio coming from one direction is poorer than that coming from \nthe opposite direction it is obvious that a considerable advantage will \nbe gained by using arrangement 1, since the device may be pointed in\n\n| 3SION | \ni \nT \n1 \n| \nd | 2 | \nALIALLISN3S \n| 40193130 \n| \nS BS | \nW3LSAS \n| ADWAINd | | \n| \n1102 109 \nNv \nWY | 40193134 _. TIGL OL \nONILLINSNVEL \nNANI | 3WMOA SANIOd \n| SONOOSITIN OZ | OL \n| q \nYBLLINSNVYL LINDUID | | \nONIHDLIMS ADWAIS | SVOOA 3dAL | TOYLNOD\n\nthe direction in which the normally blocked path is exposed to the \nbetter signal-to-noise ratio and the normally activated path is exposed \nto the poorer signal-to-noise ratio. The vodas is, of course, arranged so \nthat the normally blocked (transmitting) side is exposed to the land \nlines, which are usually quieter than the radio links. In the receiving \nside, the device can be less sensitive because there is no need for having \nit completely operated under control of the voice waves. All that is \nnecessary is to have this side sensitive enough to operate in response to \ncomparatively large voice or noise waves which might otherwise, after \nreflection and passage into the outbound path, result in false operation \nof the more sensitive side associated with this path.\n\nIn the vodas the principle of balance is used to keep the reflected \ncurrents small and thus allow the sensitivity of the normally activated \ndevice to be further reduced if necessary. Where a high degree of \nbalance is not obtained and when noise from the radio limits the \nsensitivity of the receiving device it is sometimes necessary, particularly \nfor weak outgoing volumes, to reduce the incoming volume so as to \nprevent echoes from operating the normally blocked transmitting side.\n\nThis echo limitation is primarily due to noise in the radio link, \nreflections from the two-wire plant and weak volumes from the \nsubscribers. It is difficult to produce any large improvement in talker \nvolumes and balance; so it would appear that the solution of the \ndifficulty would probably come from the direction of improving radio \ntransmission. Some benefit has also been obtained by reducing the \neffect of radio noise on the vodas with special devices of which the \n\u201cCompandor\u201d\u2019 18 and the \u2018\u201c\u2018Codan\u201d\u2019 2\u00b0 are examples. More re- \ncently, use has been made of a new voice-controlled device called a \n\u201cNoise Reducer\u201d\u2019 *!: 2 which reduces the received noise between speech \nsounds.\n\nThe diagram of the relay circuit in Fig. 3 shows how various time \nactions are obtained. Relays 1, 2, 4 and 5 are operated from battery \nB, when the ground contact of relay TM is opened. Thus the travel \ntime of any relay armature is not a factor in securing fast initial\n\n* The vodas apparatus, together with the volume control devices and technical \noperator\u2019s circuits, go to make up what is called a Type A Control Terminal.\n\noperation. When the armature of relay 7M reaches its left-hand \ncontact, relay H; operates and delays release of the relay train even if \nTM is at once restored to normal. J/; is delayed in releasing by the \ntime required to charge condenser C;. The final release of relays 1 \nand 4 is then controlled by the time constant of an auxiliary circuit \ninvolving relay H2 and condenser C2, while that of relays 2 and 5, \nwhich is made later so as to suppress delayed echoes, is controlled by \nthe circuit charging C;. On the receiving side, condenser C, is ad- \njustable so as to permit the technical operator to select the shortest \nrelease time for suppressing the delayed echoes in a given land line \nextension.\n\nThe vodas control terminal of the A type * used at New York con- \nsists of a line of technical operating positions with cross-connections to \nother lines of equipment containing the delay units, repeaters, vodas \namplifier-detectors and privacy apparatus. Figure 4 shows an \narrangement of a single terminal at San Francisco. The control bay \nis placed between two line testing bays on the left and two trans- \nmission testing bays on the right of the operating lineup. The dis- \ntributing frame is in the center of the picture; and repeaters, ringers \nand privacy apparatus are shown at its left. At the extreme left is \nthe vodas bay.\n\nThe desire for a cheaper control terminal than the Type A led to \nthe development of a second type, known as Type B, in which the \nvodas employs the same fundamental principles. In this vodas added \nprotection against false operation from line noise is secured by the use \nof a new principle in voice-operated devices, called \u2018\u2018syllabic\u2019\u2019 \noperation.\n\nIt is observed that in many types of noise a large component of the \nlong-time average power is steady. Speech, however, comes as a \nseries of wave combinations of relatively short duration. These \nfacts suggested a device which distinguishes between the rates of \nvariation of the envelopes of the impressed waves. This is accom- \nplished by a filter in the detector circuit which passes the intermodu- \nlated components of speech in the syllabic range, but suppresses those \nof line noise which are above or below this range.\n\nFigure 5 shows a schematic diagram of the application of this device \nto a Type B control terminal. The privacy switching circuits are \nomitted from this drawing, as are also the circuits for delaying the \nrelease of the relays. In comparing this drawing with Fig. 2, it will \nbe seen that relays 1, 2 and 3 perform the same functions, but the \ntransmitting branch of the vodas consists of two portions, one a \nsensitive detector with a syllabic frequency filter, which on operation \nincreases the sensitivity of the second portion.\n\nConsidering the action of Fig. 5 on transmitted speech, the output \nof the sensitive detector of the syllabic device is a complex function \nof the applied wave having intermodulated components in the range \npassed by the tuned input circuit, together with a d-c. component and \nvarious low frequency components set up by the syllabic nature of \nthe speech. There are also various components of any noise waves \nwhich may be present including a d-c. component. The first step in \ngetting rid of the noise is to pass the detector output through a re- \npeating coil which blocks the d-c. component of both the speech and \nnoise, but passes frequencies above about 14 cycle per second. The \nresulting waves enter the low-pass filter, the output of which contains \nfrequencies between 144 and 25 cycles per second, which \u201csyllabic \nrange\u201d is between the d-c. component of zero frequency and the \nfundamental frequency of the line noise. These syllabic frequency \ncurrents cause momentary operations of relays (J) and (F). Relay (J) \noperates when a speech wave is commencing and relay (F), which is \npoled oppositely, operates while the impulse is dying out, thus sending \ncurrent out of the filter in the opposite direction. Operation of either \n(J) or (F) effectively inserts gain ahead of the upper detector, thereby\n\nFig. 6\u2014Technical operator at Forked River, N. J., using a type B control terminal to \nestablish a circuit between a steamship and a shore telephone operator.\n\nincreasing the sensitivity of relay (K), when speech is present. Even \nif the noise is strong enough to operate relay (K) over the upper \nbranch when the gain is inserted, the release of relay (F) at the end \nof a speech sound will remove the gain and permit (K) to fall back. \nThus, it is possible to work relay (K) more sensitively on weak speech \nthan would be possible without the syllabic device.\n\nFigure 6 shows a photograph of a B-type terminal in ship-to-shore \nservice at Forked River, New Jersey. The vodas and volume control \napparatus are in the left-hand cabinet. The right-hand cabinet \ncontains privacy apparatus, a signaling oscillator and a vodas relay \ntest panel.\n\nIn any system employing voice-operated devices it is necessary for \nthe time actions to provide for to-and-fro conversation with a minimum \nof difficulty, when the subscribers desire to reverse the direction. \nThe electromagnetic relays used in the vodas have advantages over \nother types of switching arrangements which have been proposed in \nthat they (1) operate and release at definite current values, (2) have \nfast operating and constant releasing times, (3) have their windings \nand their contacts electrically separated, thus simplifying the circuits, \nand (4) operate in circuits having low impedances.\n\nThe operating times of the two types of vodas are shown in Fig. 7 \nas a function of the strength of suddenly-applied single-frequency sine \nwaves in the voice range. These measurements were made with a \ncapacitance bridge.\u2019 The sensitivities of the two types were adjusted \nso that observers noted an equivalent amount of clipping. The Type \nA vodas was provided with a 20-millisecond delay circuit; the Type B \nhad no delay. For the Type A vodas, the operating time is quite \nsmall and constant just above the threshold of operation.\n\nFor weak inputs the operating time of the syllabic device is de- \ntermined by relay (J) and the filter, as shown in Fig. 7. As the \nsuddenly-applied input is increased, a point is reached where the less \nsensitive detector operates relay (K), reducing the operating time \nfrom around 20 milliseconds to values comparable to those of the \nType A.\n\nThe operation was also tested on waves formed by applying simul- \ntaneously two sine waves of equal amplitude but slightly different \nfrequencies. These waves were recorded on an oscillograph, together \nwith a d-c. indication of the operation of each of the vodas relays, with \nthe sensitivities adjusted the same as for Fig. 7. The time from the \nbeginning of a beat wave (null point) to the time of operation was \nmeasured from these oscillograms and plotted against various values of\n\ntotal applied voltages. Figure 8 shows the results for a 5-cycle-per- \nsecond difference between the two frequencies. Negative values of \ntime indicate that the path was cleared before the beginning of the \nwave, and these occur only with the Type A vodas due to the delay \ncircuit. The curves for frequency differences of less than 5 cycles \nper second show more clipping and greater differences between the \ndevices, while those for greater frequency differences show less time \nclipped and less difference between the two types of vodas. In the \ncase of weak waves it is evident that the syllabic will give less clipping\n\nbecause the energy of the wave does not rise to the value required to \noperate the Type A device until after the syllabic device has operated ; \nand for very weak waves the Type A does not operate at all. In the \ncase of strong waves, the Type A vedas is better due to its delay \ncircuit. However, since the clipped time is greater on weak sounds \nthan on strong ones, the two types give performances on speech which \nare judged to be equivalent.\n\nA comparison of operation of the two types of vodas on a speech \nwave is shown in Fig. 9. Reading from left to right, the middle trace \nof this oscillogram shows the wave recorded by saying the word\n\n\u2018six\u2019? over a telephone circuit transmitting a band of frequencies \nfrom about 800 to 2000 cycles per second, which is the range normally \neffective in operating the vodas. The upper trace shows the point at\n\nwhich the syllabic Type B device operated and the lower trace shows \nthe point at which the Type A device operated. Since the speech \nwave shown was used to operate both devices, the reduction of clipping\n\nby the delay circuit in the Type A vodas was not recorded. However, \nthe effect of a transmission delay of 20 milliseconds is shown by sub- \ntracting 20 milliseconds from the point at which operation occurred. \nThis is indicated on the oscillogram for both devices. It is concluded \nthat on this wave the syllabic device without a delay circuit would \ngive about the same clipping as the Type A vodas with its delay circuit. \nFigure 8 indicates that the Type A would be better for stronger speech \nand the Type B would be better for weaker speech. The advantage of \na delay circuit in either case is evident.\n\nIt is evident from this analysis that the reason for using delay \ncircuits is not primarily because the relays are slow in operating. \nWhen the sensitivity is limited by noise, clipping of initial consonants \ncan occur with infinitesimal operating times. One way of reducing \nthe clipping is to use long releasing times so that the relays remain\n\nFig. 9\u2014Oscillogram of the word \u2018\u2018SIX,\u201d\u2019 illustrating clipping and its reduction by a \ndelay circuit in the transmission path.\n\noperated between syllables. This has the disadvantage of making it \nharder for the opposite talker to break in. To avoid this difficulty, \nthe relays in the vodas are given releasing times that permit the \ndistant speech to break in about one sixth of a second after a United \nStates talker ceases to speak.\n\nOne advantage of delay circuits is to reduce the clipping of initial \nconsonants and thus permit using short releasing times, thereby \nmaking it possible to reverse the circuit more readily. In addition, \ndelay circuits permit using a lower relay sensitivity which has two \nadvantages. First, more noise can be tolerated without causing false \noperation. Second, more received volume can be delivered without \nthe echoes causing false operation of the normally blocked trans- \nmitting side.\n\nThe advantage of artificial delay of various amounts has been \ndetermined by using different types of normally blocked arrangements\n\nto find the relation between the delay and the sensitivity required to \nproduce given amounts of clipping of initial sounds. The results are \nshown for a Type A vodas in Fig. 10. The curves for the syllabic \ndevice are similar. The set-up was arranged so that various delays \ncould be inserted in either the transmission circuit (Delay X) or the \nrelay circuit (Delay Y). The left ends of the curves indicate that \nwhen delay Y is used, that is, when the net operating time of the \nrelay is great, a point will be reached where no reasonable increase in\n\n45 \n\\ DELAY} \n40 x | \nCIRCUIT \nDELAY|_] FOR OPER- \nog Y ATING \nRELAY | \n730 \n(a) \n> |25 \nCLIPPING JUST \n= NOTICEABLE \na \n20 = \nw \n= \n| MODERATE \ngoa CLIPPING \na\n\nsensitivity is sufficient to prevent intolerable clipping. The value of \n20 milliseconds of delay X as compared to zero is equivalent to an \nincrease of about 5 db in sensitivity for a given amount of noticeable \nclipping.\n\nA reasonable release time is of value in preventing clipping, as it \ncauses the relays to remain operated not only for trailing weak endings \nof sounds, but also when the energy is temporarily reduced by inter- \nmediate consonants which may be comparable with noise. Delayed \nrelease is also important when it is required to maintain the blocked \ncondition while delayed echoes are being dissipated. For these\n\nechoes, the hangover or release times should be constant for various \napplied voltages. In the vodas, the change in release time over a \nwide range of inputs is less than 1 per cent. Adjustments are made by \nvarying the condensers and resistances of the auxiliary circuits shown \nin Fig. 3. Typical values obtained by this method are indicated in \n\u201cig. 11.\n\nThe vodas amplifier-detectors have broadly tuned input circuits to \nexclude by frequency discrimination many of the frequencies induced \nby power sources and those which are unnecessary for speech opera- \ntion. The sensitivity-frequency characteristic is shown on Fig. 12.\n\nThis figure also shows the relatively narrow frequency range passed \nby the repeating coil and syllabic frequency filter of the Type B vodas.\n\nTo insure proper operation of a vodas a technical operator \u00ae is in \nattendance. He is provided with circuits which enable him to talk \nand monitor on the circuit as indicated in Figs. 2 and 5. His duties \ninclude adjusting the sensitivity of the receiving relays for the par- \nticular value of radio noise existing and adjusting the transmitting and \nreceiving speech volumes by the aid of potentiometers and volume \nindicators. He selects the proper hangover time and coordinates the \noperation of the circuit as a whole with the distant end. At times, \nhe may be required to increase the sensitivity of the transmitting side \nof the vodas in the case of talkers with poor ability to operate relays \nor to decrease the sensitivity when weak volumes are supplied from \nland lines with more than the usual amount of noise.\n\nThe vodas is used in radio telephony to switch the voice paths \nrapidly to and fro, and thus prevent echoes and singing that would \notherwise occur at unpredictable times. It is also used to save privacy \napparatus by permitting the use of the same apparatus for both \ndirections of transmission. The performance characteristics of the \nelectromagnetic relays used in the vodas are very suitable in that \nthey have small operating and constant releasing times.\n\nImproved performance of the voice-operated relays in the presence \nof line noise can be secured by the use of a syllabic type of vodas \nwhich discriminates between the characteristic voltage-time envelopes \nof the noise and speech waves. Laboratory and field tests indicate \nthat this device, even without delay circuits, gives slightly better \nperformance on most conditions than the original vodas with delay. \nWhen provided with a transmitting delay circuit, the syllabic device is \ndecidedly better than the older vodas.\n\nThe International Bibliography on the Coordination of Radio \nTelephony and Wire Telephony is given in the C.C.I.F. Green Book \nVolume I of the Proceedings of the Xth Plenary Meeting, held at \nBudapest, September 1934. Below is a chronological list of Bell \nSystem papers relating to the vodas.\n\n1. \u2018\u2018The Limitation of the Gain of Two-Way Telephone Repeaters by Impedance \nIrregularities,\u2019 George Crisson, Bell Sys. Tech. Jour., Vol. 4, No. 1, January, \n1925, pp. 15-25.\n\n\u2018Echo Suppressors for Long Telephone Circuits,\u201d A. B. Clark and R.C. Mathes, \nA.1.E.E., Jour., Vol. 44, No. 6, June, 1925, pp. 618-626; Elec. Commun.. \nbone a 1, July, 1925, pp. 40-50; A.J.E.E., Trans., Vol. 44, 1925, pp. \n481-490.\n\n. \u2018Echo Elimination in Transatlantic Service,\u201d G. C. Crawford, Bell Lab. Record,\n\n. \u2018Effects of Phase Distortion on Telephone Quality,\u201d J. C. Steinberg, Bell Sys.\n\n. \u201cCertain Factors Limiting the Volume Efficiency of Repeatered Telephone\n\nBroadcast Engg., Vol. 2, No. 10, October, 1935, pp. 9-11, 15. Tech. Digest in \nBell Sys. Tech. Jour., Vol. 14, No. 4, October, 1935, pp. 702-707.\n\n\u2018\u201cA Noise Reducer for Radio Telephone Circuits,\u201d N. C. Norman, Bell Lab. \nRecord, Vol. 15, No. 9, May, 1937, pp. 281-285.\n\nIn listening to speech transmitted over radio circuits, the noise \narriving in the intervals between the signals may be annoying. \nThere is also evidence that the intelligibility is reduced due to this \nnoise shifting the sensitivity of the ear. Reducing the noise \noccurring in the intervals of no speech should therefore improve \nreception.\n\nnumber of conventional methods of increasing the signal with \nrespect to the noise. Examples of such methods are the use of higher \npower, directive antennas, diversity reception and filters to narrow the \nreceived frequency band. In addition, there are other methods of a \nspecial character which reduce the effect of the noise interference with \nthe speech transmission. One example of such a device limits the \nnoise interference by eliminating the high peaks of noise of very short \nduration and depending upon the persistence of sensation of speech in \nthe ear to bridge the gaps. Another method diminishes the noise in \nintervals of no speech. This is the method which will be discussed \nhere.\n\nSpeech signals may be represented \u00bby a group or band of frequencies \noccupying a certain interval of time. In using the conventional \nmethod of narrowing the received frequency band, filters eliminate all \nnoise outside the band actually required. In fact we sometimes go \nbeyond this and remove some of the outer frequency components of\n\n* Presented at the Pacific Coast Convention of A. I. E. E., Spokane, Washington, \nSeptember 2, 1937. Published in Elec. Engg., August, 1937.\n\nspeech which are weak and submerged in the noise and therefore \ncontribute little or nothing to the intelligibility. Experiments have \nshown the effect on voice transmission of removing portions of the \nfrequency range.'! Articulation tests were used to afford a quantitative \nmeasure of the recognizability of received speech sounds. These show \nthat the upper frequencies may be cut off down to about 3000 cycles \nwithout serious reduction in articulation. After such treatment, as the \nnoise level increases, the weaker and less articulate sounds become more \nand more submerged in the noise and additional reduction in the \ndetrimental effect of the noise is required.\n\nIn addition to the speech waves covering a frequency band they \noccupy intervals of time. The unoccupied intervals between the \nspeech sounds contain noise. Reduction of the noise reaching the ear \nin these intervals has been found to result, under certain conditions, in \nan improvement in speech reception. This may possibly be explained \nby considering the characteristics of the ear.!. It has been shown that \nnoise present at the ear has the effect of shifting the threshold for \nhearing other sounds or has a deafening effect. That is, there is a \nreduction of the capacity of the ear to sense sounds in the presence of \nnoise. For example, if a person has been listening to a noise for a \ncertain period, his ear is made insensitive so that speech signals \nfollowing are not so easily distinguished. The ear has a sensory build- \nup time, that is, a time needed for the noise to build up to a steady \nloudness. By reducing the noise in the intervals of no speech the \naverage threshold shift seems to be diminished. Aside from this the \npresence of the noise tends to distract the attention from the perception \nof the speech. Removal of noise during the intervals of no speech \ntends to reduce this effect.\n\nIn considering the elimination of the noise during these intervals it is \nnecessary to bear in mind certain characteristics of speech.? Speech \nwaves may be regarded as nonperiodic in that they start at some time, \ntake on some finite values and then approximate zero again. In \nconnected speech it is usually possible to approximately distinguish \nbetween sounds and to ascribe to each an initial period of growth, an \nintermediate period which in some cases approximates a steady state \nand then a final period of decay. The duration intervals of various \nsyllabic sounds vary from about .03 to as much as .3 or .35 second. \nWhen noise is high the weaker initial and final sounds become obscured \nso that they contribute little to the intelligibility.\n\nIn connected speech, silent intervals occupy about one-fifth to one- \nthird of the total time. Also there are frequent intervals when the\n\ncondition for sufficient periods to override weaker intervals so that\n\nTo reduce the noise in the intervals between speech it is necessary to \ndepend for control upon either the speech itself or upon some auxiliary \nsignal usually under the control of the speech at some point in the \ncircuit where the signal-to-noise ratio is better. This latter condition \nis illustrated on a circuit where the carrier is transmitted only during \nspeech intervals. The carrier then acts as an auxiliary signal which \noperates a device at the receiver to remove loss.*:*+ The device to be \ndiscussed below utilizes the speech itself at the receiver to perform this \nfunction.\n\nIn using the speech in this way it is obvious that control can be \naccomplished only when the speech energy sufficiently exceeds the \nnoise energy so that the presence of the speech is distinguishable. The \ndevice could operate abruptly as, for example, a relay which removes a \nfixed loss in the operated position and restores it when non-operated. \nExperience indicates that the use of such a device makes the suppression \ntoo obvious if it is to follow the speech sounds closely. It is desirable, \nthen, to perform this reduction by more or less gradually removing loss \nas the speech increases to accentuate the difference between levels of \nspeech sounds and levels of noise which occur in the gaps between \nspeech.\n\nThis kind of performance has been secured in a device known as a \nnoise reducer. A comparison of the action of the noise reducer and a \nrelay having similar maximum loss is shown in Fig. 1. This figure \nshows the input-output characteristics of these devices over the voice \namplitude range to which they are subjected on a radio circuit. The \nnoise reducer may be likened to a relay with a variable loss, the loss not \nvarying instantaneously but over a short period of time. The loss, for \nany short period, may be any value within the loss range and the device \nhas, therefore, been likened to an elastic or shock absorbing relay.\n\nThe noise reducer has no loss for strong inputs, considerable loss for \nweak inputs and changes this loss gradually over a short interval of\n\ntime. It introduces loss in the absence of speech but reduces this loss \nin proportion to the amplitude and duration of waves impressed upon \nit. The time required for the loss change is such that abruptness of \nnoise change is absent and very short impulses of static do not effec-\n\ntively control the loss. This contrasts with a very fast limiter acting on \nhigh-peak crashes only.\n\nThe noise may control the loss if its average amplitude is strong \nenough. Therefore, the control is made adjustable so that the noise\n\nwaves are not permitted to control for any noise condition within the \nrange of usefulness of this device. Thus the noise in the absence of \nspeech is always reduced and the portions of the initial and decay \nperiods of the speech sounds which are also reduced vary with this \nadjustment for noise intensity. Of course, if the speech-to-noise ratio \nbecomes too small or if other transmission conditions interfere, an \nimprovement becomes impossible.\n\nFigure 2 shows the circuit of the noise reducer in simplified schematic \nform.\u00ae Incoming waves pass from left to right through the fixed pad,\n\nVARIO- \nFIXED LOSSER -STAGE \nINPUT PAD AMPLI- | OUTPUT \nFIER \nREDUCTION CONTROL \nCIRCUIT \nMW \nRECTIFIER \n' \niL \nIL \nREDUCTION \" \nIN \nMAX. MIN. \nOUT\n\nthe vario-losser and the amplifier to the output. At the input, part of \nthese waves pass through the reduction control branch circuit which \nincludes a variable resistor, an amplifier and a rectifier. The direct \ncurrent produced by the rectifier is applied through the condenser and \nresistance filter to the copper-oxide losser circuit. For current below a \nthreshold value, no appreciable change occurs in the losser and the loss \nintroduced is about 20db. As input increases, rectified current reaches \na value where the loss begins to change rapidly. It becomes 0 db at an \ninput about 20 db above the point at which the loss starts to change. \nThe design is such that the loss remains substantially constant for \nhigher inputs.\n\nThe vario-losser makes use of the resistance variation with current of \ncopper-oxide rectifier disks. This variable resistance shunts a fixed \nresistance in series with the windings of a repeating coil as shown in \nFig. 2. The maximum loss is determined by the fixed resistance when \nsmall current is flowing through the disks while the varying loss is \ndetermined by the shunting copper-oxide resistance which decreases \nrapidly with increasing current above a threshold value until a low \nvalue is reached. The minimum loss is limited by the output of the \ncontrol tube approaching a maximum and the shunting resistance \nbecoming so small that additional decrease affects the loss inappreciably.\n\nThe variable resistor setting in the reduction control circuit de- \ntermines the input amplitude at which reduction begins and therefore \nthe point above which the loss remains substantially constant. If there \nis a difference in amplitude between speech and noise, the reduction\n\ncontrol may be so adjusted that the noise on the circuit, when no speech \nis present, is appreciably reduced. The action then is as follows: In the \nabsence of speech, noise is reduced usually the maximum value of \n20 db; during intervals of lower speech amplitudes the loss decreases in \nproportion to the increase in amplitude, and during speech of high \namplitude both noise and speech are transmitted without loss. As the \nnoise encroaches upon the range of speech amplitude, it becomes \nnecessary to reduce greater amplitudes, thereby also further reducing \nthe weaker parts of speech.\n\nThe noise reducer is contained on a 7} inch panel for relay rack \nmounting. Figure 3 gives a front view. The panel contains the \nreduction control resistor and an IN-Out key which, in the Out \nposition, gives the device a fixed loss. Both resistor and key may be \nduplicated external to the panel with the wiring arranged to give \nremote control.\n\nFigure 4 gives the 1000-cycle input-loss characteristic for three \nsettings of the reduction control. For any setting, there is an input \nvolume above which the loss remains constant, while for volumes below \nthis the loss increases with decreasing input until the maximum loss is \nreached. The volume regulated speech range encountered on radio \ncircuits at some point in the circuit which is 5 db above reference \nvolume as measured on a volume indicator is indicated as extending \nfrom + 13 db to \u2014 17 db referred to 1 milliwatt for the purpose of \nshowing approximate corresponding speech amplitudes.\n\nFigure 5 shows oscillograms giving the input and output charac- \nteristics of noise for maximum reduction and of speech for maximum, \nmedium and minimum reduction. The upper trace is the input and \nthe lower trace the output. The middle trace is not used. It will be \nnoted by inspecting the IN and Out traces at the beginning and ending \nof the word \u201cbark\u201d that there is some distortion in speech for the \nmaximum reduction condition, but very little distortion for minimum \nreduction. Maximum reduction would be used only in case of high \nnoise where this distortion is less objectionable than the noise.\n\npaom ay) jo Surpua pur Suruurseq ym astou ysry (Z) uinwixeur yWM asiou :40J jndjyno pue ynduj\u2014g \u201c314\n\nLaboratory tests have been made in an attempt to evaluate the \nadvantages to be gained by the use of the noise reducer. It was shown \nthat, for the rather limited and controlled conditions which were \ntested, definite advantage can be observed in judgment tests of the \neffectiveness of speech transmission through noise with and without \nthe noise reducer. This advantage is of the order of magnitude of \n3 to 5 db at the border line between commercial and uncommercial \nconditions on the noisy circuit.\n\nThis figure is in approximate agreement with results obtained from \nrecords of performance on commercial connections. A curve is \navailable which shows the approximate relation between percentage \nlost circuit time and transmission improvement for a long-range short- \nwave radio telephone circuit. From the records of lost circuit time as \naffected by the noise reducer use, an improvement of 4 db is obtained \nfrom this curve.\n\nObservations were made and records kept for twelve months of the \nuse of the device at the land terminal of the high seas ship-to-shore \ncircuit and for shorter periods on New York-London circuits. These \nobservations indicate that the noise reducer most satisfactorily reduces \nobjectionable effects where the interference consists of noise of a fairly \nsteady character. As might be expected it is somewhat less effective \non crashy static. If the noise is very low there is no improvement; as\n\nthe noise increases the benefit increases up to a certain point; when the \nnoise amplitudes begin to approach too closely the peak amplitudes of \nthe voice waves it becomes impossible to distinguish between them \nwithout producing objectionable speech distortion and there is again no \nadvantage. Where volume fading is present there is a tendency to \naccentuate the volume changes and it becomes necessary to adjust the \nreduction control to limit this. Otherwise this effect may offset the \npossible noise improvement. The operating practice is to adjust the \nreducer control circuit for each noise or transmission condition so that \noptimum reception as judged by the technical operator is obtained. \nThe general rule is to use the minimum reduction possible.\n\nOn radio telephone circuits for connection to the land telephone \nsystem, control terminal equipment is used at the junction of the land \nlines and the two one-way radio channels (one transmitting the other \nreceiving) necessary for two-way communication. In making this \nconnection a widely used method is one in which the two-wire land \ncircuit is normally connected to the receiving radio channel and is\n\nFigure 6 shows the application of the noise reducer to such a control \nterminal. Speech entering the terminal from the left goes through the \nupper branch of the circuit, with volume regulating means and privacy \napparatus, to the radio transmitter. Speech received from the distant \nterminal enters at the lower right from the radio receiver and proceeds \nthrough the privacy apparatus, the noise reducer, receiving regulating \nnetwork and amplifier to the two-wire line. Outgoing speech operates \nthe transmitting path and disables the receiving path. Incoming \nspeech operates the receiving amplifier detector, which disables the \ntransmitting amplifier detector, thus preventing singing and reradia- \ntion of received waves.\n\nWithout the noise reducer the receiving relay may be operated by \nnoise in the receiving path and such operation to an excessive extent \nwill interfere with outgoing speech. To avoid this effect, it is custom- \nary to reduce its sensitivity so that noise may not operate it. This \nresults in the weaker speech parts also failing to operate the receiving \nrelay. This weak speech and noise returned to the transmitting path \nthrough the land line connection may be strong enough to operate the \ntransmitting relays and thus cut off incoming speech. This is avoided \nby reducing the volume to the land line. Therefore, any device which \nreduces noise in the receiving path in the absence of speech effects an \nimprovement not only in the switching operation but also in the \nreceived volume. By placing the noise reducer in the receiving path \nfalse operation is diminished and volume increases of 5 to 15 db are \nrealized. The noise reducer is applied to the receiving side of the \nterminal beyond the privacy apparatus so that it does not introduce \nany distortion in the privacy portion of the circuit. It is placed \nahead of the receiving amplifier detector, thereby reducing noise \nbetween words which might affect the operation of this relay apparatus.\n\nThe noise redicer, which is a voice controlled variolosser with \nlimited and controllable action, has been provided for use on short- \nwave radio telephone circuits and has proved to be a valuable and \nrelatively inexpensive means of securing noise reduction. Improved \nreception is obtained for many of the transmission conditions experi- \nenced on such circuits. This results in better intelligibility to the\n\n. \u201cEffects of Phase Distortion on Telephone Quality,\u201d J. C. Steinberg, Bell Sys. \nTech. Jour., July, 1930.\n\n. \u2018A Telephone System for Harbor Craft,\u201d W. K. St. Clair, Bell Laboratories \nRecord, November, 1932.\n\n. \u2018A Noise Reducer for Radio Telephone Circuits,\u201d N.C. Norman, Bell Labora- \ntories Record, May, 1937.\n\n. \u2018The Reliability of Short-Wave Radio Telephone Circuits,\u201d R. K. Potter and A. \nC. Peterson, Jr., Bell Sys. Tech. Jour., July, 1934.\n\n. \u2018\u2018Two-Way Radio Telephone Circuit,\u201d S. B. Wright and D. Mitchell, Bell Sys. \nTech. Jour., July, 1932.\n\nN utilizing the broad frequency ranges which the newer carrier \nsystems can transmit the telephone engineer has a problem of \nchoice in band width per channel to be allotted to speech currents. \nA sufficient width is vital to faithful speech reproduction ; and desire \nfor better telephone service always recommends an increase in band \nwidth over past practice. A reasonable balance, however, must ob- \ntain between various economic factors; and there must always be \nconsidered the relation between a proposed system and the other parts \nof the telephone plant, and also the trend of the art.\n\nThe message band widths and the channel spacing which have been \nchosen by the Bell System for various new systems are summarized \nand discussed in this paper. These systems are expected to play a \nlarge part in the future growth of its long distance plant; and the \nreasons underlying this choice may therefore be of general interest.\n\nDifferent broad band systems are under development: A 12-channel \nsystem for use on open-wire lines employing frequencies up to 140,000 \ncycles, a 12-channel system for use on 19-gauge pairs in existing toll \ncables using frequencies up to 60,000 cycles, and a coaxial system \ncapable of transmitting frequencies up to a million cycles or more, \nfrom which it is proposed to obtain 240 or more channels.\n\nIn the different systems noted above, terminal apparatus is em- \nployed which has many common features: The different channels are \nuniformly spaced at 4000-cycle intervals; the same band filters are \nused in the ultimate channel selecting circuits; and the derived voice \ncircuit band widths are substantially identical for all channels of all \nsystems. The transmission frequency characteristic of a single link \nof such systems, in accordance with present designs, is shown on Fig. 1. \nA curve for five similar links connected in tandem is also indicated. \nBased on a 10 db cutoff as compared with 1000-cycle transmission, \na single-link band extends from approximately 150 to 3600 cycles, and \na five-link band extends from about 200 to 3300 cycles.\n\nThere is, of course, no fixed relationship between the channel spacing \nand the frequency range of the derived voice-frequency circuit. This \nis largely a matter of economics in the design of a particular system. \n487\n\nThe 4000-cycle channel spacing would permit obtaining a narrower \nband width with some simplification in the selecting circuits. With \nfurther development in selecting circuits, it is believed that it would \npermit obtaining a somewhat wider band or, if desired, a reduction \nin the cost of apparatus, maintaining the same band.\n\nThe band chosen initially for the new systems is believed to be a \ndesirable and forward-looking step in the direction of improving the \nquality of speech transmission, a continuing trend which is as old as\n\ntelephony itself. Figure 2 shows typical band characteristics which \nmark the progress of transcontinental telephony since 1915. For \nshorter distances, the band widths have, of course, generally been \nwider than indicated on this series of curves. In the case of carrier \nsystems the band depends on the number of links. The curve shown \nfor 1937 is for the broad-band systems, estimated on the basis of a \nthree-link connection.\n\nThe increase in band width is achieved without material increase in \ncost, since in situations which favor their use, broad-band systems \nprovide circuits which are substantially more economical than other \nalternatives, and the improvement can therefore be obtained by giving \nup only a small portion of the savings which the systems themselves \nmake possible. If, as in some older types of systems, it had been \nchosen to maintain a standard of 250 to 2750 cycles for a single-link \nconnection in the broad band systems, this could have been accom- \nplished by the use of a channel frequency spacing of about 3000 cycles. \nThe wider transmission band is therefore obtained by a sacrifice in\n\nthe ratio of approximately 3:4 in the number of channels obtained \nwithin a given frequency range. However, this does not mean a \n4:3 increase in the cost per circuit. The amount is considerably less \nthan this\u2014depending somewhat on the type of system. In the pro- \nposed coaxial system, which appears to be a favorable example, where \nthe attenuation increases roughly as the square root of the frequency, \na frequency band increased by one-third means that for repeaters of \na given type and amplification the number of repeaters is multiplied \nby approximately \u00a5#; that is to say, approximately 15 per cent more \nrepeaters are required. Furthermore, the line and terminal apparatus \ncosts are not changed in a case of this kind, and since they constitute \na major part of the total cost, the net increase in cost for the wider\n\nFig. 2\u2014Representative transmission frequency characteristics of 3000-mile toll \ncircuits.\n\nper cent in the case of the longer systems where the terminal apparatus \ncosts are a small factor, and only a per cent or two in the case of the \nvery short systems where the terminal apparatus costs predominate.\n\nIn the ideal case, using substantially perfect transmitters and re- \nceivers, articulation is improved as the upper limit in frequency \ntransmission is raised, as shown in Fig. 3. The increase in transmission \nperformance, which a step from 2750 to 3300 cycles, or 3600 cycles \nfor a single link, makes possible, is evidently still on the part of the \nband width-articulation relationship where a measurable increase in \narticulation may be expected. An improvement in band width accord- \ningly reduces the effort needed to interchange ideas, since fewer repe-\n\ntitions occur and attention can be somewhat relaxed. It also enhances \nthe naturalness of the received speech, and so makes the conversation \nmore pleasing as well as easier. It should be noted also that the pro- \nposed broad-band systems will transmit frequencies approximately 50 \nto 100 cycles lower than earlier systems, which, while not contributing \nappreciably to articulation, has the effect of increasing naturalness. \nWhen applied in the telephone plant, the resultant effect of a given \nincrease in band width will of course depend on the other parts of the \ncircuit, and the transmission characteristics of the transmitters and \nreceivers. Improved transmitters and receivers are now being applied\n\nrapidly in the Bell System. They have much better transmission \ncharacteristics than earlier types and an effective upper frequency of \ntransmission for the new station set which is well above 3000 cycles, \nas shown on Fig. 4.\n\nThe toll connecting trunks are important links in a typical overall \nconnection, and here also there has been a continued trend to provide \nwider band circuits. Figure 5 shows the transmission frequency char- \nacteristics of representative types of toll connecting trunks which are \nbeing commonly installed at present. Both non-loaded and loaded \ntrunks are shown on the figure. Of course, in the non-loaded case, \nthere is no definite cutoff frequency. The curve for the loaded trunk\n\nshows a reasonably long trunk having a 5 db loss at 1000 cycles (6.4 \nmiles). In practice, of course, the trunk length may vary from a\n\nFig. 4\u2014New station-set characteristics (inckiding two one-mile 24-gauge loops con- \nnected by distortionless trunk).\n\nFREQUENCY-CYCLES PER SECOND \nFig. 5\u2014Toll connecting trunk characteristics.\n\nfraction of a mile to 10 miles or more, with a corresponding effect on \nthe transmission characteristic. It will be noted that the effective\n\ncutoff of the loaded trunk shown is about 3500 cycles based on a \n10 db cutoff point. Other types of loading, which will also be em- \nployed, will have still higher cutoff points. Evidently the band widths \nof the broad-band circuits, toll connecting trunks, and new station sets \nare well matched.\n\nLaboratory and field tests have been made with circuits simulating \nthe cutoff of the new broad-band systems and using various types of \nstation sets, including the new standard. These indicate that raising \nthe cutoff from 2750 cycles to 3600 cycles is equivalent to making a \nreduction of 3 to 4 db in the net overall loss of the circuit. Raising \nthe cutoff from 2750 cycles to 3300 cycles is equivalent to a lesser \nreduction. With older types of instruments which reproduce speech \nless faithfully, this difference is also less, and of course, with instru- \nments providing transmission up to considerably higher frequencies, \nthe difference is greater.\n\nIt will be appreciated, of course, that the wider speech band which \nwill be made available in the new broad-band systems will not be fully \neffective in all telephone connections unless other toll circuits and toll \nconnecting trunks and station sets are provided with improved trans- \nmission frequency characteristics. From a practical standpoint it is \nobvious that in a large telephone plant improvements cannot be made \nin all parts at one time. They must be introduced gradually as new \nsystems and apparatus are applied, and with a far-sighted concern for \nfuture trends.\n\nThe Dielectric Properties of Insulating Materials \nBy E. J. MURPHY and S. 0. MORGAN\n\nThis paper gives a qualitative account of the way in which \ndielectric constant and absorption data have been interpreted in \nterms of the physical and chemical structure of materials. The \ndielectric behavior of materials is determined by the nature of the \npolarizations which an impressed field induces in them. The \nvarious types of polarization which have been demonstrated to exist \nare listed, together with an outline of their characteristics.\n\nI. OUTLINE OF THE PHyYsICO-CHEMICAL INTERPRETATION \nOF THE DIELECTRIC CONSTANT\n\nalong such specialized lines that there is need of some correlation \nbetween the newer and the older theories of dielectric behavior to \nkeep clear what is common to both, though sometimes expressed in \ndifferent terms. The purpose of the present paper is to outline in \nqualitative terms the way in which the dielectric constant varies with \nfrequency and temperature and to indicate the type of information \nregarding the structure of materials which can be obtained from the \nstudy of the dielectric constant.\n\nThe important dielectric properties include dielectric constant (or \nspecific inductive capacity), dielectric loss, loss factor, power factor, \na.c. conductivity, d.c. conductivity, electrical breakdown strength and \nother equivalent or similar properties. The term dielectric behavior \nusually refers to the variation of these properties with frequency, \ntemperature, voltage, and composition.\n\nIn discussing the dielectric properties and behavior of insulating \nmaterials it will be necessary to use some kind of model to represent \nthe dielectric. The success of wave-mechanics in explaining why \nsome materials are conductors and others dielectrics suggests that it \nmight be desirable to use a quantum-mechanical model even in a \ngeneral outline of the characteristics of dielectrics, but for the aspects \nof the theory of dielectric behavior with which we are immediately \nconcerned here the behavior predicted is essentially the same as that \nderived on the basis of classical mechanics. However, in the course \nof the description of the frequency-dependence of dielectric constant \nwe shall have occasion to make a comparison between the dispersion\n\nand absorption curves for light and those for electromagnetic dis- \nturbances in the electrical (i.e., radio and power) range of frequencies. \nThe difficulty is then met that the quantum-mechanical model is \nthe customary medium of description of the absorption of light. \nBut, since the references to optical properties will be only incidental \nand for comparative purposes, there is little to be lost, even in this \ndomain in which quantum-mechanical concepts are the familiar \nmedium of description, in using the pre-quantum theory concepts of \ndispersion and absorption processes. Thus a model operating on the \nbasis of classical mechanics and the older conceptions of atomic struc- \nture will be sufficient for our present purposes.\n\nOn the wave-mechanical theory of the structure of matter a di- \nelectric is a material which is so constructed that the lower bands of \nallowed energy levels are completely full at the absolute zero of temper- \nature (on the Exclusion Principle) and at the same time isolated from \nhigher unoccupied bands by a large zone of forbidden energy levels.' \nThus conduction in the lower, fully occupied bands is impossible \nbecause there are no unoccupied energy levels to take care of the \nadditional energy which would be acquired by the electrons from the \napplied field, while the zone of forbidden energy levels is so wide that \nthere is only a negligible probability that an electron in the lower band \nof allowed levels will acquire enough energy to make the transition to \nthe unoccupied upper band where it could take part in conduction. \nThe bound electrons in a completely filled and isolated band of allowed \nlevels can, however, interact with the applied electric field by means of \nthe slight modifications which the applied field makes in the potential \nstructure of the material and hence in the allowed levels.\n\nOn the other hand in the older theory of the structure of matter the \nessential condition which makes a material a dielectric is that the \nelectrons and other charged particles of which it is composed are held \nin equilibrium positions by constitutive forces characteristic of the \nstructure of the material. When an electric field is applied these \ncharges are displaced, but revert to their original equilibrium positions \nwhen the field is removed. In this account of the behavior of di- \nelectrics this model will be sufficient, but no essential change in the \nrelationships which will be discussed here would result if a translation \nwere made to a model based upon quantum-mechanics.\n\nWhen an electric field is impressed upon a dielectric the positive \nand negative charges in its atoms and molecules are displaced in \nopposite directions. The dielectric is then said to be in a polarized\n\n1Cf., for example, Gurney, \u2018\u2018Elementary Quantum Mechanics,\u2019 Cambridge \n(1934); Herzfeld, \u2018\u2018The Present Theory of Electrical Conduction,\u201d Electrical Engt- \nneering, April 1934.\n\ncondition, and since the motion of charges of opposite sign in opposite \ndirections constitutes an electric current there is what is called a \npolarization current or charging current flowing while the polarized \ncondition is being formed.\n\nFor the case of a static impressed field a charging current flows in \nthe dielectric only for a certain time after application of the field, the \ntime required for the dielectric to reach a fully polarized condition. \nIf the material is not an ideal dielectric, but contains some free ions, \nthe current due to a static impressed field does not fall to zero but to \na constant value determined by the conductivity due to free ions. \nMore important than the static is the alternating current case, where \nthe potential is continually varying and where, consequently, there \nmust be a continuously varying current.\n\nThe dielectric behavior of different materials under different con- \nditions is reflected in the characteristics of the charging or polariza- \ntion currents, but since polarization currents depend upon the applied \nvoltage and the dimensions of condensers it is inconvenient to use \nthem directly for the specification of the properties of materials. \nEliminating the dependence upon voltage by dividing the charge by \nthe voltage, we have the capacity (C = Q/V); and the dependence \nupon dimensions may be eliminated by using the dielectric constant, \ndefined as \u00ab = C/Co, where C is the capacity of the condenser when the \ndielectric material is between its plates and Cy is the capacity of the \nsame arrangement of plates in a vacuum. The dielectric constant \nis then a property of the dielectric material itself.\n\nThe term \u2018\u2018dielectric polarization\u201d is used to refer to the polarized \ncondition created in a dielectric by an applied field of either constant \nor varying intensity. The polarizability is one of the quantitative \nmeasures of the dielectric polarization; it is defined as the electric \nmoment per unit volume induced by an applied field of unit effective \nintensity. Another quantitative measure of the dielectric polarization \nis the molar polarization; this is a quantity which is a measure of the \npolarizability of the individual molecule, whatever the state of ag- \ngregation of the material.\n\nThe concept of polarizability is as fundamental to, and plays about \nthe same role in, the theory of dielectric behavior as does the concept \nof free ions in the theory of electrolytic conduction. Just as the con- \nductivity of a material is a measure of the product of the number of \nions per unit cube and their average velocity in the direction of a unit \napplied field, so the polarizability is a measure of the number of bound \ncharged particles per unit cube and their average displacement in the \ndirection of the applied field.\n\nIn the early investigations of dielectrics two distinct types of charg- \ning current were recognized, the one in which the charging or dis- \ncharging of a condenser occurred practically instantaneously and the \nother in which a definite and easily observable time was required. A \ncharge accumulating in a condenser in an unmeasurably short time \nwas variously referred to as the instantaneous charge or geometric \ncharge or the elastic displacement. The current by which this charge \nis formed was called the instantaneous or geometric charging current, \nand similarly the terms instantaneous dielectric constant or geometric \ndielectric constant were used to describe the property of the medium \ngiving rise to the effect between the condenser plates. An even wider \nvariety of names has been used for the part of the charge which formed \nor disappeared more slowly. Among these are residual charge, \nreversible absorption, inelastic displacement, viscous displacement \nand anomalous displacement. The modern theory still recognizes \nthese two distinct types of condenser charges and charging currents \nbut the simple descriptive designations rapidly-forming or instantaneous \npolarizations and slowly-forming or absorptive polarizations will be \nadopted here, as they seem sufficient and to be preferred to terms \nwhich have more specialized connotations as to the mechanism upon \nwhich the behavior depends. The properties of these two types of \ncharging currents and the dielectric polarizations corresponding to \nthem appear prominently in the theories of dielectric behavior.\n\nThe total polarizability of the dielectric is the sum of contributions \ndue to all of the different types of displacement of charge produced in \nthe material by the applied field. Constitutive forces characteristic \nof the material determine both the magnitude of the polarizability and \nthe time required for it to form or disappear. The quantitative \nmeasure of the time required for a polarization to form or disappear is \ncalled the relaxation-time. In the following a description will be given \nof the physical processes involved in the formation of dielectric polari- \nzations, indicating the effect of chemical and physical structure upon \nthe two quantities, magnitude and relaxation-time, which determine \nmany of the properties of dielectric polarizations of the slowly-forming \nor absorptive type.\n\nThe magnitude of the polarizability k of a dielectric can be expressed \nin terms of a directly measurable quantity, the dielectric constant e, \nby the relation\n\nIt is sometimes convenient to use the polarizability and the dielectric\n\nconstant interchangeably in the qualitative discussion of the magnitude \nof the dielectric polarization. In dealing with alternating currents \nthe fact that polarizations of the absorptive type require a time to \nform which is often of the same order of magnitude as, or greater than, \nthe period of the alternations, results in the polarization not \nbeing able to form completely before the direction of the field is \nreversed. This causes the magnitude of the dielectric polarization\n\nFig. 1\u2014Schematic diagram of variation of dielectric constant and dielectric \nabsorption with frequency for a material having electronic, atomic, dipole and \ninterfacial polarizations.\n\nand dielectric constant to decrease as the frequency of the applied \nfield increases. An example of this variation of the dielectric constant \nwith frequency is shown in the radio and power frequency section of \nthe curve plotted in Fig. 1. It is often convenient to refer to the mid- \npoint of the decreasing dielectric constant-frequency curve as the \nrelaxation-frequency; this frequency f, is very simply related to the \nrelaxation-time 7, for the theory of these effects shows that f, = 1/27r.\n\nVarious types of polarization can be induced in dielectrics: There \nshould be an electronic polarization due to the displacement of electrons \nwith respect to the positive nuclei within the atom; an atomic polari- \nzation due to the displacement of atoms with respect to each other in \nthe molecule and in certain ionic crystals, such as rock salt, to the \ndisplacement of the lattice ions of one sign with respect to those of the \nopposite sign; dipole polarizations due to the effect of the applied \nfield on the orientations of molecules with permanent dipole moments; \nand finally interfacial (or ionic) polarizations caused by the accumula- \ntion of free ions at the interfaces between materials having different \nconductivities and dielectric constants.\n\nA classification of dielectric polarizations into rapidly-forming or \ninstantaneous polarizations and slowly-forming or absorptive polariza- \ntions has been made. Instantaneous polarizations may be thought of \nas polarizations which can form completely in times less than say 10~\"\u00b0 \nseconds, that is, at frequencies greater than 10! cycles per second or \nwave-lengths of less than 1 centimeter, and so beyond the range of \nconventional dielectric constant measurements. The electronic polari- \nzations are due to the displacement of charges within the atoms, and \nare the most important of the instantaneous polarizations. The \npolarizability per unit volume due to electronic polarizations may be \nconsidered to be\u2019a quantity which is proportional to the number of \nbound electrons in a unit volume and inversely proportional to the \nforces binding them to the nuclei of the atoms.\n\nThe effect of number of electrons and binding force is illustrated by \na comparison of the values for the polarizability per unit volume of \ndifferent gases; for the number of molecules per unit volume is inde- \npendent of the composition of the gas. Thus, although a c.c. of \nhydrogen with two electrons per molecule has the same number of \nelectrons as a c.c. of helium, which is an atomic gas with two electrons \nper atom, the quantity \u00ab\u20ac\u2014- 1, that is the amount by which the di- \nelectric constant is greater than that of a vacuum, is nearly four times \nas large for hydrogen as for helium. This shows that in hydrogen the \nelectrons are in effect less tightly bound to the nucleus than in helium, \nresulting in a larger induced polarization. Nitrogen has a larger \ndielectric constant than either hydrogen or helium because it has 14 \nelectrons per molecule. Some of these are tightly bound as in helium \nand some are more loosely bound as in hydrogen.\n\nThe dielectric constant of liquid nitrogen is 1.43, which is much \nhigher than the value 1.000600 for the gas. This is due to the fact\n\nthat the number of molecules, and consequently of bound charges, \nper unit volume is much greater in the liquid than in the gas. How- \never, the molar polarization, a quantity which is corrected for varia- \ntions in density, is the same for liquid as for gaseous nitrogen.\n\nThe time required for the applied field to displace the electrons \nwithin an atom to new positions with respect to their nuclei is so short \nthat there is no observable effect of time or frequency upon the value \nof the dielectric constant until frequencies corresponding to absorption \nlines in the visible or ultra-violet spectrum are reached. For con- \nvenience in this discussion the frequency range which includes the \ninfra-red, visible and ultra-violet spectrum will be called the optical \nfrequency range while that which includes radio, audio and power \nfrequencies will be called the electrical frequency range. For all fre- \nquencies in the electrical range the electronic polarization is indepen- \ndent of frequency and for a given material contributes a fixed amount \nto the dielectric constant, but at the frequencies in the optical range \ncorresponding to the absorption lines in the spectrum of the material, \nthe dielectric constant, or better the refractive index, changes rapidly \nwith frequency, and absorption appears. (The justification for using \nrefractive index m and dielectric constant \u00a2\u00ab interchangeably for the \nqualitative discussion of the properties of dielectric polarizations fol- \nlows from the relation, \u00ab = n?, which is known as Maxwell's rule. \nThis is a general relationship based upon electromagnetic theory and \nis applicable whenever \u00ab and m are measured at the same frequency \nno matter how high or low it may be.)\n\nThe electronic polarization of a molecule may be regarded as an \nadditive property of the atoms or of the atomic bonds in the molecule, \nand may be calculated for any dielectric of known composition with \nsufficient accuracy for most purposes. Within any one chemical class of \ncompounds such as, for example, the saturated hydrocarbons or their \nsimple derivatives, in which all of the bonds are C\u2014H, C\u2014C or C\u2014X, \nthe calculated values agree with the measured to within a few per \ncent. For other classes of compounds\u2014for example, benzene, in \nwhich there are both single and double bonds such calculations must be \ncorrected for the fact that some of the valence electrons have their \nbinding forces and hence their polarizabilities altered in the double \nbond as compared to the single bond. Such values of electronic \npolarization, usually called atomic refractions, have been determined \nfor all of the different types of bonds from the vast amount of experi- \nmental study of refractive indices of organic and inorganic compounds.\n\nIn some materials the electronic polarization is the only one of \nimportance. For example, in benzene the dielectric constant is the\n\nsame at all frequencies in the electrical range and is equal to the square \nof the optical refractive index. This must mean that the only polari- \nzable elements of consequence in CsHe are electrons which are capable \nof polarizing as readily in the visible spectrum, where the refractive \nindex is measured, as at lower frequencies where dielectric constant is \nmeasured. The refractive index in the visible spectrum provides the \nmeans of determining the magnitude of electronic polarizations, for \nother types of polarization are usually of negligible magnitude when \nthe frequency of the impressed field lies in the visible spectrum. For \nmaterials having only electronic polarizations the dielectric properties \nare very simply dependent upon the chemical composition and the \ntemperature, and are independent of frequency in the electrical \nfrequency range. In many materials, however, there are also other \npolarizations which can form at low frequencies but not at high; these \nare characterized by more complex dielectric behavior.\n\nIncluded among the polarizations which may be described as in- \nstantaneous by comparison with the order of magnitude of the periods \nof alternation of the applied field in the electrical frequency range are \nthose arising from the displacement of the ions in an ionic crystal \nlattice (such as rock salt) or of atoms in a molecule or molecular lattice. \nIn some few materials, for example the alkali halides, sufficient study \nhas been made of the infra-red refractive index to provide data on the \natomic polarizations, but for most substances little is known about \nthem. What is known has in part been inferred from infra-red absorp- \ntion spectra and in part from the infra-red vibrations revealed by \nstudies of the Raman effect.\n\nAtomic polarizations are distinguished from electronic polarizations \nby being the part of the polarization of a molecule which can be at- \ntributed to the relative motion of the atoms of which it is composed. \nThe atomic polarizations may be attributed to the perturbation by the \napplied field of the vibrations of atoms and ions having their character- \nistic or resonance frequencies in the infra-red. Atomic polarizations \nmay be large for substances such as the alkali halides and other in- \norganic materials, but are usually negligible for organic materials. \nThe exact value of the time required for the formation of atomic \npolarizations is unimportant in the electric range of frequencies with \nwhich we are primarily concerned. The essential thing is that atomic \npolarizations begin to contribute to e(or m*) at frequencies below \napproximately 10' seconds\u2014that is, in the near infra-red and that \nbelow about 10\u201d cycles per second, where the optical and electrical\n\nfrequency ranges merge, atomic polarizations contribute a constant \namount to e(or m?) for a given material. The atomic polarization is \ndetermined as the difference between the polarization which is meas- \nured at some low infra-red or high electric frequency and the electronic \npolarization as determined from refractive index measurements in the \nvisible spectrum.\n\nThe electronic and atomic polarizations are considered to comprise \nall of the so-called instantaneous polarizations; that is, the polariza- \ntions which form completely in a time which is very short as compared \nwith the order of magnitude of the periods of applied fields in the \nelectrical range of frequencies.\n\nThe remaining types of polarization are of the \u201c\u2018absorptive\u201d\u2019 kind, \ncharacterized by relaxation-times corresponding to \u2018\u2018relaxation- \nfrequencies\u201d in the electrical range of frequencies. These polariza- \ntions include the important type which is due to the effect of the applied \nfield on the orientation of molecules with permanent electric moments, \nthe theory of which was developed by Debye. Among the other \npossible polarizations of the absorptive type are those due to inter- \nfacial effects or to ions which are bound in various ways.\n\nDebye,\u2019 in 1912, suggested that the high dielectric constant of water, \nalcohol and similar liquids was due to the existence of permanent \ndipoles in the molecules of these substances. The theory which Debye \nbased upon this postulate opened up a new field for experimental \ninvestigation by providing a molecular mechanism to explain dielectric \nbehavior which fitted into and served to confirm the widely held \nviews of chemical structure. Debye postulated that the molecules \nof all substances except those in which the charges are symmetrically \nlocated possess a permanent electric moment which is characteristic \nof the molecule. In a liquid or gas these molecular dipoles are oriented \nat random and therefore the magnitude of the polarization vector is \nzero. When an electric field is applied, however, there is a tendency \nfor the molecules to align themselves with their dipole axes in the \ndirection of the applied field, or, put in another way, to spend more \nof their time with their dipole axes in the direction of the field than \nin the opposite direction. This dipole polarization is superimposed \nupon the electronic and atomic polarizations which are also induced by \nthe field. The theory as developed by Debye accounts for the ob- \nserved difference between the temperature and frequency dependence \nof the dipole polarizations and the instantaneous polarizations. While \nthe latter are present in all dielectrics, the dipole polarizations can \n2 P. Debye, Phys. Zeit., 13,97, (1912); Verh. d. D. phys. Ges., 15, 777 (1913).\n\noccur only in those made up of molecules which are electrically, \nasymmetrical.\n\nPolar molecules (that is molecules with permanent electric moments \nare, by definition, those in which the centroid of the negative charges \ndoes not coincide with the centroid of the positive charges, but falls \nat some distance from it. All materials must be classed either as \npolar or non-polar, the latter class including those which are elec- \ntrically symmetrical. Some simple examples of non-polar molecules\n\nFig. 2\u2014-Methane and carbon tetrachloride are non-polar molecules each having \nfour equal vector moments whose sum is zero. Methyl chloride is polar because the \nsum of the vector moments is not zero.\n\nare He, Ne, Oz, CCl, and CeH\u00a2. In these molecules each C \u2014 H, \nC \u2014 Cl or other bond may be regarded as having a vector dipole mo- \nment of characteristic magnitude located in the bond. Where the \nsum of these vector moments is zero the molecule will be non-polar. \nBoth CH, and CCl, meet this requirement but CH;Cl is polar because \nthe C \u2014 Cl vector moment is considerably greater than the resultant of \nthe three C \u2014 H vectors. (See Fig. 2.) Polar molecules are the rule \nand non-polar the exception.\n\nIn the discussion of dipole polarizations it has frequently been \npointed out that non-polar materials usually obey the general relation-\n\nthe dielectric constant as measured in the electric range of frequencies.\n\ndielectric constant only in the electrical frequency range; this is the \nmost frequent source of the above mentioned discrepancy. The \ngeneral relationship \u00ab = n? should apply for any material at any fre- \nquency provided \u00a2 and \u00bb are measured at the same frequency. The \nrefractive index of water when measured with electric waves,\u2019 for \nexample, at a million cycles, is found to be slightly less than 9, the \nsquare of which agrees very well with the observed value \u00a2 = 78. \nHowever, it does not always follow that when e > mn? the molecules of \nwhich the material is composed have permanent dipole moments, for \nthis condition can also result from the presence of any slowly-forming \nor absorptive polarization or of a large atomic polarization. Experi- \nmental investigations based upon the Debye theory have shown, \nhowever, that in the case of water and many other familiar compounds \nthe orientation of dipole molecules actually accounts for the high \ndielectric constant.\n\nThe Debye theory shows that the magnitude of the dipole polariza- \ntion of a material is proportional to the square of the electric moment \nof the molecule, which, as has been pointed out, may be regarded as \nthe vector sum of a number of constituent moments characteristic of \nthe individual atoms or radicals of which the molecule is composed, \nor alternatively, of the bonds which bind these atoms into molecules \nor more complex aggregates. The very great amount of experimental \nstudy of the Debye theory has shown that the NO, and CN groups \nhave the largest group moments while CO, OH, NHz, Cl, Br, I and \nCH; have progressively smaller group moments. The value 34 for the \ndielectric constant of nitrobenzene (CsH;NO2), as against 5.5 for \nchlorobenzene (C,H;Cl), 2.8 for methyl benzene (CsH;CHs) and 2.28 \nfor benzene (CsH,), which is non-polar, are evidence of the large \ndifferences in the magnitudes of these group moments and the large \npart that dipole moments can play in determining the dielectric \nconstant.\n\nAnother point regarding molecular structure shown by stich studies \nis that it is not only the presence of polar groups in the molecule bu: \nalso their position which determines the electric moment of the mole- \ncule. This is nicely illustrated by the dichlorobenzenes, of which \nthere are three isomers. As is shown in Fig. 3, ortho-dichlorobenzene, \nhaving the two substituent groups in adjacent positions, is the most \nasymmetrical of the three compounds, and consequently has the high-\n\nFig. 3\u2014Ortho dichlorobenzene being the more asymmetrical has a higher electric \nmoment than the meta isomer; the para isomer which is symmetrical has zero electric \nmoment.\n\nest electric moment, \u00ab = 2.3. The meta compound has about the \nsame moment as monochlorobenzene, w = 1.55. The para compound, \nhowever, is symmetrical and has zero electric moment because the \nCl atoms are substituted on opposite sides of the benzene ring so that \ntheir vector moments cancel. These values of electric moment are \nreflected in the values of dielectric constant which are respectively \n10, 5.5 and 2.8 for the three isomeric dichlorobenzenes.\n\nDIELECTRIC PROPERTIES OF INSULATING MATERIALS \u2014 505 \nDielectric studies of this kind have also shown, for example, that \nH,0 is not a symmetrical linear molecule, H \u2014 O \u2014 H, but rather a\n\nis determined to be a linear molecule O = C = O. Thus, dielectric \nmeasurements interpreted by the Debye theory have become estab- \nlished as one of the standard means of studying molecular structure. \nSince dipole polarizations depend upon the relative orientations of \nmolecules, rather than upon the displacement of charges within the \natom or molecule, the time required for a polarization of this type to \nform depends upon the internal friction of the material. Debye \nexpressed the time of relaxation of dipole polarizations in terms of the \ninternal frictional force by the equation:\n\n2kT = \nwhere \u00a2 is the internal friction coefficient, n is the coefficient of viscosity, \na the radius of the molecule and T the absolute temperature.t| This \nlatter expression, because it depends on Stokes\u2019 law for a freely falling \nbody, is rigidly applicable only to gases or possibly to dilute solutions \nof polar molecules in non-polar solvents in which the polar molecules \nare far enough apart that they exert no appreciable influence on each \nother.\n\nApplying this equation to the calculation of the relaxation-time of \nthe orientational polarizations in water at room temperature we obtain \nt = 10\u00b0-!\u00b0 seconds, assuming a molecular radius of 2 & 10~-* cm. and \ntaking the viscosity as 0.01 poises.2 The relaxation-frequency corre- \nsponding to this relaxation-time is about 1.6 & 10\u00b0 cycles/sec., agreeing \nwith the results of experimental studies on water which show that \nin the range of frequencies extending from 10\u00b0 to 10\" cycles the \ndielectric constant decreases from its high value to a value approxi- \nmately equal to the square of the refractive index. Thus the drop in \ndielectric constant occurs in the frequency range which corresponds to \nthe calculated value of the re!axation-time.\n\nSimilar experiments on dilute solutions of aicohols*\u00ae in non-polar \nsolvents yield values of r of about 10~* seconds. The shortest relax- \nation-times which dipole polarizations can have are probably not\n\n5 The viscosity of a liquid in poises is given by the force in dynes required to \nmaintain a relative tangential velocity of 1 cm./sec. between two parallel planes in the \nliquid each 1 cm.? in area and 1 cm. apart, the distance being measured normal to their\n\nmuch less than the order of 10~-!! seconds, since in general either the \ninternal friction or the molecular radius of materials having polar \nmolecules will be greater than those of water, resulting in longer \nrelaxation-times. No long-time limit can be placed on the relaxation- \ntimes which dipole polarizations may have, for they are limited only \nby the values which the internal friction can assume. For materials, \nsuch as glycerine, which tend to become very viscous at low tempera- \ntures the time of relaxation of the dipoles may be a matter of minutes. \nStudies of the dielectric constant of crystalline solids, to be discussed \nin a later paper, show also that in some cases polar molecules are able \nto rotate even in the crystalline state, where the ordinary coefficient \nof viscosity has no meaning because the materials do not flow. In \nconnection with the dielectric properties we are concerned only with \nthe ability of the polar molecules to undergo rotational motion and \nit is likely that in these solids, which constitute a special class, the \ninternal frictional force opposing rotation of the molecules is small \neven though the forces opposing translational motion may be very \nlarge. The particular equation for the calculation of the time of \nrelaxation given above obviously does not apply to solids.\n\nIn discussing the three types of polarizations which have been \nconsidered thus far, it has been pointed out that the magnitude of \nthe dielectric constant depends upon the polarizability of the material. \nEach type of polarization makes a contribution to the dielectric \nconstant if the measuring frequency is considerably below its relax- \nation-frequency. However, if the frequency of the applied field used \nfor measuring the dielectric constant is too high the presence of \npolarizations with low relaxation-frequencies will not be detected. \nThus the refractive index of water in the visible spectrum is 1.3 and \ntherefore gives no evidence whatever of the presence of permanent \ndipoles. This is due to the fact that the H,O molecules do not change \ntheir orientations rapidly enough to allow fields which alternate in \ndirection as rapidly as those of light to cause an appreciable deviation \nfrom the original random orientation which prevails in the absence of \nan applied field.\n\nThe band of frequencies in which the dielectric constant decreases \nwith increasing frequency because of inability of the polarization to \nform completely in the time available during a cycle, is called a region \nof absorption or of anomalous dispersion. The discussion of this \ncharacteristic of dielectric matetials forms an important part of \ndielectric theory. The term anomalous dispersion is no doubt usually \nthought of in connection with the anomalous dispersion of light: when \nthe refractive index of light decreases with increasing frequency the\n\nDIELECTRIC PROPERTIES OF INSULATING MATERIALS 507 \nmaterial is said to display anomalous dispersion in the range of fre- \nquencies concerned. However, in a paper published in 1898 Drude ? \napplied this term to the decrease of dielectric constant with increasing \nfrequency in the electrical range of frequencies. The justification \nfor this extension of the original application of the term is very direct \nfor electromagnetic theory shows that the dielectric constant and the \nrefractive index of a material are connected by the general relationship \n\u00ab = n* whatever the frequency of the electromagnetic disturbance. \nAs the dispersion of light by a prism is due to the variation of its re- \nfractive index with frequency, the use of the expression anomalous \ndispersion to refer to the decrease of dielectric constant with increasing \nfrequency is consistent and has become generally accepted.\n\nThe polarizations thus far considered are the main types to be \nexpected in a homogeneous material. They depend upon the effect \nof the applied field in slightly displacing electrons in atoms, in slightly \ndistorting the atomic arrangement in molecules and in causing a slight \ndeviation from randomness in the orientation of polar molecules. \nThe remaining types of polarization are those resulting from the \nheterogeneous nature of the material and are called interfacial polariza- \ntions. Interfacial polarizations must exist in any dielectric made up \nof two or more components having different dielectric constants and \nconductivities except for the particular case where eyy2 = eyi, y being \nthe conductivity * and the subscripts referring to the two components. \nHeterogeneity in a dielectric may be due to a number of causes, and \nin the case of practical insulating materials is probably the rule rather \nthan the exception. Impregnated paper condensers and laminated \nplastics are obvious examples of heterogeneous dielectrics. Paper \nis itself a heterogeneous dielectric, consisting of water and cellulose. \nIn all probability the plastic resins are also heterogeneous, and cer- \ntainly so if they contain fillers. Ceramics, being mixtures of crystalline \nand glassy phases, are also heterogeneous.\n\nThe simplest case of interfacial polarization is that of the two-layer \ndielectric, that is, a cornposite dielectric made up of two layers, the \ndielectric constants and conductivities of which are different. Max- \nwell showed that in such a system the capacity was dependent upon \nthe charging time. This is due to the accumulation of charge at the \ninterface between the two layers, for this charge must flow through a\n\n7 P. Drude, Ann. d. Phystk, 64, 131 (1898), \u2018Zur Theorie der anomalien elektrischen \nDispersion.\u201d\n\nIn this expression y represents the total a.c. conductivity, a quantity which \ndepends on the frequency.\n\nlayer of dielectric whose resistance may be high enough that the inter- \nface does not become completely charged during the time allowed for \ncharging. For the alternating current case this implies a decrease of \ncapacity with increasing frequency, which is equivalent to the anoma- \nlous dispersion which has been described for the case of dipole polariza- \ntions. It should be particularly emphasized that the term anomalous \ndispersion describes a type of variation of dielectric constant with \nfrequency which can be produced by a number of different physical \nmechanisms.\n\nThe two-layer dielectric is of less interest than a generalization of \nthis type of polarization which includes heterogeneous systems com-\n\nof heterogeneous dielectric is of considerable importance since such \nsystems represent the actual structure of many practical dielectrics. \nSuch a generalization of the two-layer dielectric has been made by \nK. W. Wagner * who developed the theory for the case of spheres of \nrelatively high conductivity dispersed in a continuous medium of low \nconductivity. The conditions for the existence of an interfacial \npolarization are, as in the two-layer case, that ey2 + ei, where the \nsymbols have the significance just given. This type of polarization, \nwhich is variously referred to as an interfacial polarization, an ionic \npolarization and a Maxwell-Wagner polarization, shows anomalous \ndispersion like other absorptive polarizations. When the particle \nsize is small as compared with the electrode separation it may be \ntreated as a uniformly distributed polarization.\n\nThe magnitude and time of relaxation of interfacial polarizations \nare determined by the differences in \u00ab and y of the two components. \nThere is a widely prevalent opinion that this type of polarization \nalways has such long relaxation-times as to be observed only at very \nlow frequencies. While this is true for mixtures of very low-con- \nductivity components, the general equations show that for the case \nwhere one component has a high conductivity\u2014for example equal to \nthat of a salt solution\u2014the dispersion may occur in the radio frequency \nrange.\n\nSeveral special types of interfacial polarization have been proposed \nto explain the dielectric properties of various non-homogeneous di- \nelectrics where something regarding the nature of the inhomogeneity \nis known. The dielectric constant of cellulose, for example, receives \na contribution from an interfacial polarization due to the water and \ndissolved salt which it contains. Experimental evidence indicates \nthat an aqueous solution of various salts is distributed through the\n\ncellulose in such a way as to form a reticulated pattern which may \ncorrespond to the pattern formed by the micelles or to some feature \nof it. An interesting feature of this structure is that the conductance \nof the aqueous constituent can be changed by varying the moisture \ncontent or the salt content of the material and the effect on the di- \nelectric constant observed.\"\n\nAs has been pointed out, each of the different types of polarization \nmay contribute to the dielectric constant an amount depending upon \nthe polarizability and its time of relaxation. The upper curve in Fig. \n1 shows schematically the variation of the dielectric constant (or of the \nsquare of the refractive index) for a hypothetical material possessing \nan interfacial polarization with relaxation-frequency in the power \nrange, a dipole polarization with relaxation frequency in the high \nradio frequency range and atomic and electronic polarizations with \ndispersion regions in the infra-red and visible respectively. If polariza- \nbility were plotted, instead of \u20ac (or n?), the curves would be of the same \ngeneral form but of different magnitudes, because of a relationship \nbetween the two given earlier.\n\nAt the low-frequency side of Fig. 1, the dielectric constant curve \nhas its highest value, usually called the static or zero-frequency \ndielectric constant. Here all of the polarizations have time to form \nand to contribute their full amount to the dielectric constant. With \nincreasing frequency \u00a2 begins to decrease as the relaxation-frequency \nof the interfacial polarization is approached and reaches a constant \nlower value (called the\u2019 infinite-frequency dielectric constant) when \nthe applied frequency is sufficiently above the relaxation-frequency of \nthe polarization that it has not time to form appreciably. It is this \ndecrease of \u00a2 with frequency which is called anomalous dispersion. The \nhorizontal arrows across the top of Fig. 1 indicate the frequency region \nin which the various types of polarizations indicated are able to form \nand contribute to the dielectric constant.\n\nAt still higher frequencies we see that e\u20ac again decreases as the \nrelaxation-frequency of the dipole polarization is approached, and \nagain reaches a constant lower value as the frequency becomes too \nhigh for the field to affect appreciably the orientation of dipoles. \nThis second region of anomalous dispersion is similar to the first, \nwhich was due to interfacial polarizations. It has been shown as \noccurring at a higher frequency, but it should be emphasized that the \nfrequency ranges chosen to illustrate anomalous dispersion in Fig. 1\n\nare purely arbitrary. Anomalous dispersion due to dipole polariza- \ntions has been observed at power frequencies while that due to inter- \nfacial polarizations has been observed at radio frequencies. The two \ntypes of polarizations may in fact give rise to anomalous dispersion \nin the same frequency range in a given dielectric.\n\nProceeding to still higher frequencies in Fig. 1 other regions of \ndispersion appear in the infra-red and visible spectrum. These \nregions show a combination of normal optical dispersion, in which the \ndielectric constant, or better now the refractive index, increases with \nfrequency, and anomalous dispersion in which it decreases. The \ndispersion in the visible range of frequencies is predominantly normal \n(anomalous dispersion being confined to relatively narrow frequency \nbands) whereas in the electrical range the reverse is true, normal \ndispersion not being observed; the infra-red represents an intermediate \nregion. Dipole and interfacial polarizations are not represented in \nthe dispersion in the optieal range, the dielectric constant (or refractive \nindex) in the visible being due to electronic polarizations and in the \ninfra-red to electronic and atomic polarizations.\n\nThe curves plotted in Fig. 1 are merely schematic and the relative \nmagnitudes of the different contributions to the dielectric constant \nare therefore arbitrary. However, experimental results indicate that \nthe contribution eg of the electronic polarization to the dielectric \nconstant is limited to values between 2 and 4 except for certain in- \norganic materials, since very few organic solids or liquids are known \nwhich have refractive indices in the visible spectrum which are greater \nthan 2 or less than 1.4. The contribution e4 of atomic polarizations \nto the dielectric constant is in general small and is usually negligible, \nas has been indicated on the curve, although the possibility exists of \nspecial cases occurring in which the infra-red refractive indices are \nvery high. The contributions ep and \u00a2\u00ab of dipole and interfacial \npolarizations to the dielectric constant may vary greatly from one \nmaterial to another, depending upon the symmetry of the molecule \nand the physical structure of the dielectric. From the above men- \ntioned limitations on the contribution to the dielectric constant which \ncan be expected from electronic and atomic polarizations, it is apparent \nthat the explanation of values of \u00ab higher than 3 to 4, at least in organic \nmaterials, requires the existence of some absorptive polarization such \nas arises from dipoles or interfacial effects. Thus all of the liquids \nwhich have high dielectric constants such as H,O (78), alcohol (24), \nnitrobenzene (34) have been shown to contain polar molecules.\n\nThe lower part of Fig. 1 shows a maximum in the absorption for \neach type of dielectric polarization. The absorption, at least in the\n\nelectrical frequency range, is due to the dissipation of the energy of the \nfield as heat because of the friction experienced by the bound charges \nor dipoles in their motion in the applied field in forming the polariza- \ntions. The theory of dispersion shows that the dielectric constant and \nabsorption are not independent quantities but that the absorption \ncurve can be calculated from the dielectric constant vs. frequency \ncurve and vice versa. The absorption maximum is greatest for those \nmaterials showing the greatest change in dielectric constant in passing \nthrough the dispersion region. Thus a material having a high di- \nelectric constant must have a large dielectric loss at the frequency at \nwhich \u00a2 has a value half way between its low and high-frequency values.\n\nThough the quantum theory is necessary for the explanation of many \noptical and electrical phenomena a simple explanation, sufficient for \nour purposes, of the general form of the curves of dielectric constant vs. \nfrequency in the infra-red and visible spectrum may be given in terms \nof the Lorentz theory of optical dispersion. In this theory the form \nof the dispersion curves depends upon the variation with frequency of \nthe relative importance of the inertia of the typical electron and of the \nfrictional forces and restoring forces acting upon it. For electronic \npolarizations the frictional or dissipative force is negligible, except \nin the narrow frequency interval included in the absorption band, and \nthe inertia and restoring force terms predominate. For the atomic \npolarizations the frictional force is larger and the absorption region \nextends over a wider interval of frequencies. For dipole and inter- \nfacial polarizations the influence of inertia is entirely negligible as \ncompared with the frictional or dissipative forces so that in effect these \npolarizations may be thought of as aperiodically damped.\n\nThe dielectric constant of a material is a constant only in the ex- \nceptional case. Besides the variation with frequency which has been \nconsidered the dielectric constant varies with temperature. Elec- \ntronic polarizations may be considered to be unaffected by the tempera- \nture. The refractive index does indeed change with temperature \nbut this is completely accounted for by the change of density, and the \nmolar refraction is independent of temperature. The atomic and \nionic vibrations are, however, affected by temperature, the binding \nforce between ions or atoms being weakened by increased temperature. \nThis factor of itself would yield a positive temperature coefficient for \nthe atomic polarizations but the decrease in density with the increase \nin temperature acts in the opposite direction. The result is that \ncalculation of the temperature coefficient of atomic polarizations\n\nusually yields zero or slightly positive values. What experimental \ndata there are indicate small positive temperature coefficients for \natomic polarizations.\n\nOne of the principal achievements of the Debye theory of dipole \npolarizations has been the manner in which it explains the large \nnegative temperature coefficients of polarization of many liquids. \nDebye showed that the variation of polarization with temperature \ncould be expressed by the relation P = A + (B/T), in which the \nconstant A is a measure of the instantaneous polarizations which are \nindependent of temperature and B is a measure of the dipole polariza- \ntions. In a liquid or gas the molecules are continuously undergoing \nboth translational and rotational motion, and the result of this thermal \nmotion is to maintain a random orientation of molecules. The action \nof the electric field in aligning the dipoles is opposed by the thermal \nmotion which acts as an influence tending to keep them oriented at \nrandom. As the temperature decreases, the thermal energy becomes \nsmaller and the dipole polarization becomes larger, resulting in a \nnegative temperature coefficient of dielectric constant.\n\nThe effect of temperature upon interfacial polarizations has not \nbeen experimentally investigated to an extent at all comparable with \nthat of dipole polarizations. However, interest in the interfacial or \nionic type of polarization has increased considerably in the past few \nyears, and it has applications of some importance. Among these is \ndiathermy which is becoming of considerable importance as a thera- \npeutic agency.\n\nThe foregoing qualitative description of the behavior of the di- \nelectric constant and the type of information regarding molecular \nstructure which has been derived from it will be followed in the next \nsection by the derivation of some of the quantitative relationships \nwhich are common to all polarizations of the absorptive type.\n\nVariable Frequency Electric Circuit Theory with Application \nto the Theory of Frequency-Modulation\n\nIn this paper the fundamental formulas of variable frequency \nelectric circuit theory are first developed. These are then applied \nto a study of the transmission, reception and detection of frequency \nmodulated waves. A comparison with amplitude modulation is \nmade and quantitative formulas are developed for comparing the \nnoise-to-signal power ratio in the two modes of modulation.\n\nREQUENCY modulation was a much talked of subject twenty \nor more years ago. Most of the interest in it then centered \naround the idea that it might afford a means of compressing a signal \ninto a narrower frequency band than is required for amplitude modu- \nlation. When it was shown that not only could this hope not be \nrealized,* but that much wider bands might be required for frequency \nmodulation, interest in the subject naturally waned. It was revived \nagain when engineers began to explore the possibilities of radio trans- \nmission at very short wave lengths where there is little restriction on \nthe width of the frequency band that may be utilized.\n\nDuring the past eight years a number of papers have been published \non frequency modulation, as reference to the attached bibliography \nwill show. That by Professor E. H. Armstrong \u00a2 deals with this \nsubject in comprehensive fashion. In his paper the problem of \ndiscrimination against extraneous noise is discussed, and it is pointed \nout that important advantages result from a combination of wide \nfrequency bands together with severe amplitude limitation of the \nreceived signal waves. His treatment is, however, essentially non- \nmathematical in character, and it is therefore believed that a mathe- \nmatical study of this phase of the problem will not be unwelcome. \nThis the present paper aims to supply by developing the basic mathe- \nmatics of frequency modulation and applying it to the question of \nnoise discrimination with or without amplitude limitation.\n\nThe outstanding conclusions reached in the present paper, as \nregards discrimination against noise by frequency modulation, may \nbe briefly summarized as follows:\n\n(1) To secure any advantage by frequency modulation as distin- \nguished from amplitude modulation, the frequency band width must \nbe much greater in the former than in the latter system.\n\n(2) Frequency modulation in combination with severe amplitude \nlimitation for the received wave results in substantial reduction of the \nnoise-to-signal power ratio. Formulas are developed which make \npossible a quantitative estimate of the noise-to-signal power ratio in \nfrequency modulation, with and without amplitude limitation, as \ncompared with amplitude modulation.\n\nIt is a pleasure to express our thanks to several colleagues who have \nbeen helpful in various ways: to Dr. Ralph Bown who in a brief but \nvery incisive memorandum, which was not intended to be a mathe- \nmatical study, disclosed all the essential ideas of the quasi-stationary \nmethod of attack; to Mr. J. G. Chaffee,* who has been conducting \nexperimental work on frequency modulation in these Laboratories for \nsome years past, by means of which quantitative checks on the \naccuracy of some of the principal results have been possible; and to \nvarious associates, especially Mr. W. R. Bennett and Mrs. S. P. \nMead, for detailed criticism of certain portions of the work.\n\nIn the well-known steady-state theory of alternating currents, the \ne.m.f. and the currents in all the branches of a network in which \nthe e.m.f. is impressed involve the time \u00a2 only through the common \nfactor e' where i = \u00a5\u2014 1 and w is the constant frequency. To this \nfact is attributable the remarkable simplicity of alternating current \ntheory and calculation, and also the fact that the network is completely \nspecified by its complex admittance Y(iw). Thus, if the e.m.f. is \nEe\u2018, the steady-state current is\n\nIn the present paper we shall deal with the case where the frequency \nis variable, and write the impressed e.m.f. as\n\nQ(t) will be termed the instantaneous frequency. This agrees with \nthe usual definition of frequency when & is a constant; it is the rate of \nchange of the phase angle at time \u00a2; and in addition the interval T \nbetween adjacent zeros of sin fQ(t)dt or cos fQ(t)dt is approximately \n7/Q(t) in cases of practical importance.\n\nInstead of dealing with an arbitrary instantaneous frequency {(f) \nwe shall suppose that\n\nQ(t) = w + u(t), (3) \nwhere w is a constant and u(t) is the variable part of the instantaneous os \nfrequency. In practical applications u(t) will be written as As(\u00a2) where os \n\\ is a real parameter and the mean square value s* of s(t) is taken as oo\n\nequal to 1/2. Other restrictions on y(t) will be imposed in the course \nof the theory to be developed in this paper. Fortunately these \nrestrictions do not interfere with the application of the theory to \nimportant problems.\n\nThe steady-state current as given by (1) varies with time in precisely \nthe same way as the impressed e.m.f. When the frequency is variable \nthis is no longer true. On the other hand, formula (1) suggests a \n\u2018\u2018quasi-stationary\u201d\u2019 or \u2018\u2018quasi-steady-state current\u2019? component, J ,,., \ndefined by the formula\n\nwhich corresponds exactly to (1) with the distinction that the ad- \nmittance is now an explicit function of time. We are thus led to \nexamine the significance of /,,, as defined above and the conditions \nunder which it is a valid approximate representation of the actual \nresponse of the network to a variable frequency electromotive force, \nas given by (2).\n\nWe start with the fundamental formula of electric circuit theory.' \nLet an e.m.f. F(t) be impressed at time \u00a2 = 0, on a network of indicial \nadmittance A(t); then the current /(t) in the network is given by\n\nHere A\u2019(t) = d/dt-A(t) and it is supposed that A(0) = 0. (This \nrestriction does not limit our subsequent conclusions and is introduced \nmerely to simplify the formulas. Furthermore A(0) is actually zero \nin all physically realizable networks. )\n\nSubstituting this expression in (5) for F(t \u2014 r) and writing \nJo \nwe have for the current in the network \nI = eS oat. M(t, (9) \nJo \nWe now split the integral into two parts, thus: \nt \nThe second integral on the right represents an initial transient which \ndies away for sufficiently large values of time, \u00a2, while the infinite\n\nintegral represents the total current, J, for sufficiently large values of \u00a2. \nWe have therefore\n\nThe foregoing formulas correspond precisely with the formulas for \na constant frequency impressed e.m.f.; these are\n\n2 Hereafter the transient term 7 of (10) will be consistently neglected and the \nsymbol J will refer only to the quasi-stationary current.\n\nWe have now to evaluate Y(iw,t) as given by (11). We shall \nassume tentatively, at the outset, that u = As(t) has the following \nproperties:\n\nWith these restrictions the instantaneous frequency lies within the \nlimits w + X. \nLet us now replace M(t, r) by the formal series expansion\n\nwhich converges in the vicinity of all values of \u00a2 for which s has a \ncomplete set of derivatives. Then, if we write\n\nNow consider the quasi-stationary admittance Y(iQ2). Writing \n2 = w+ u(t) and expanding as a power series, we have (assuming \nthat the series is convergent)\n\n., dp \nD; = \u2014 \u2014 20 \n3 Pit de\u201d ( ) \nae Consequently, the total current, after initial transients have died\n\nWe have thus succeeded in expressing the response of the network in \nterms of the quasi-stationary current\n\nand a correction series A, which depends on the derivatives of the \nsteady-state admittance Y(iw) with respect to frequency and the \nderivatives of the variable frequency u(t) with respect to time.\n\nIf the parameter ) is sufficiently large and the derivatives of s are \nsmall enough so that C, may be replaced by the two leading terms, \nwe get\n\nThe preceding formulas are so fundamental to variable frequency \ntheory and the theory of frequency modulation that an alternative \nderivation seems worth while. We take the applied e.m.f. as\n\nthe phase angle @ being included for the sake of generality. \nNow in any finite epoch 0 = \u00a2 = 7, it is always possible to write\n\nthus expressing the function on the left as a Fourier integral. For \npresent purposes it is quite unnecessary to evaluate the Fourier \nfunction F(iw).\n\nWe suppose as before that, in the interval 0 = \u00a2 = 7, u(t) and its de- \nrivatives are continuous. We can then expand the admittance func-\n\nI = E-exp (iat + 66) \u00a5 (ies) (27) \nBut by the identity (24) and repeated differentiations with respect \nto t, we have\n\nFormula (25), as it stands, includes the initial transients at time \nt = 0 as well as any which occur at discontinuities in u(t). Differ- \nentiation with respect to \u00a2 under the integral sign, however, in effect \neliminates these transients and (29) leaves only the quasi-stationary \ncurrent (plus the correction series given in (19)).\n\nThe series appearing in formula (29) may not be convergent; in any \ncase its computation is laborious. Furthermore, in its application to \nthe theory of frequency modulation, terms beyond the first two \nrepresent distortion. For these reasons it is often preferable to \nproceed as follows:\n\nmust be kept small if the finite series in (31) is to be an accurate repre- \nsentation of the current 7. While it is not in general computable, we \nsee that, in order to keep it small, R,(w., w) must be small over the \nessential range of frequencies of F(iw). In cases of practical im- \nportance we shall find (see Appendix 1) this range is from w = \u2014 Xd \ntow =\n\nIf the transducer introduces a large phase shift, the linear part of \nwhich is predominant in the neighborhood of w = w,, it is preferable \nto express the received current J in terms of a \u201c\u2018retarded\u201d\u2019 time. To \ndo this, return to (25) and write\n\nwhich corresponds precisely with (29) except that it is expressed in \nterms of the retarded time \u00a2\u2019.. If the transducer introduces a large \nphase delay, (35) may be much more rapidly convergent than (29) \nand should be employed in preference thereto.\n\nThe foregoing will now be applied to the Theory of Frequency \nModulation. A pure frequency modulated wave may be defined as a \nhigh frequency wave of constant amplitude, the \u2018\u2018instantaneous\u201d\u2019\n\nfrequency of which is varied in accordance with a low frequency signal \nwave. Thus\n\nis a pure frequency modulated wave. Here w, is the constant carrier \nfrequency and s(t) is the low frequency signal which it is desired to \ntransmit. 2 is a real parameter which will be termed the modulation \nindex. The \u2018\u2018instantaneous\u201d\u2019 frequency is then defined as\n\nIn all cases it will be postulated that \\ < \u00ab.. \nWith the method of producing the frequency modulated wave (38) \nwe are not here concerned beyond stating that it may be gotten by \nvarying the capacity or inductance of a high frequency oscillating \ncircuit by and in accordance with the signal s(t). \nCorresponding to (38), the pure amplitude modulated wave (carrier \nsuppressed) is of the form\n\nIf the maximum essential frequency in the signal s(t) is w., the wave \n(39) occupies the frequency band lying between w. \u2014 wa and w, + wa, \nso that the band width is 2w,. In the pure frequency modulated wave \nthe \u2018\u2018instantaneous\u201d\u2019 frequency band width is 2d. In_ practical \napplications \\ >> wa. We shall now examine in more detail the concept \nof \u2018\u2018instantaneous\u201d\u2019 frequency and the conditions under which it has \nphysical significance.\n\nThe instantaneous frequency is, as stated, w. + As(t); a steady-state \nanalysis is of interest and importance. To this end we suppose \ns(t) = cos wt so that w is the frequency of the signal. Then the wave \n(38) may be written\n\nwhere J, is the Bessel function of the first kind. Thus the frequency \nmodulated wave is made up of sinusoidal components of frequencies\n\nIf \\/w >> 1 (the case in which we shall be interested in practice) the \nterms in the series (40) beyond m = X\\/w are negligible; this follows \nfrom known properties of the Bessel functions. In this case the \nfrequencies lie in the range\n\nwhich agrees with the result arrived at from the idea of instantaneous \nfrequency. On the other hand, suppose we make X so small that \nA/w K1. Then (40) becomes to a first order\n\nso that the frequencies w,, w, +, we \u2014 w are present in the pure \nfrequency modulated wave.\n\nIt is possible to generalize the foregoing and build up a formal \nsteady-state theory by supposing that\n\nOn this assumption, it can be shown that the frequency modulated \nwave (38) is expressible as\n\nFormulas (42) and (43) are purely formal and far too complicated \nfor profitable interpretation. Consequently this line of analysis will \nnot be carried farther.\u2018\n\nIf we compare the pure frequency modulated wave, as given by (38), \nwith the pure amplitude modulated wave, as given by (39), it will be \nobserved that, in the latter, the low frequency signal s(\u00a2), which is \nultimately wanted in the receiver, is explicit and methods for its \ndetection and recovery are direct and simple. In the pure frequency \nmodulated wave, on the other hand, the low frequency signal is \nimplicit; indeed it may be thought of as concealed in minute phase or \nfrequency variations in the high frequency carrier wave.\n\nt \nexp ( ive f sit) (45) \n0 \nis still a pure frequency modulated wave. The second term, \nt \nAs(0)-exp ( sdt ), (46) \n0\n\nis a \u201c\u2018hybrid\u201d\u2019 modulated wave, since it is modulated with respect to \nboth amplitude and frequency. The important point to observe is \nthat, by differentiation, we have \u2018\u2018rendered explicit\u2019\u2019 the wanted low \nfrequency signal. We infer from this that the detection of a pure \nfrequency modulated wave involves in effect its differentiation. The \nprocess of rendering explicit the low frequency signal has been termed \n\u201cfrequency detection.\u201d\u201d Actually it converts the pure frequency \nmodulated wave into a hybrid modulated wave.\n\nEvery frequency distorting transducer inherently introduces fre- \nquency detection or \u2018\u2018hybridization\u201d\u2019 of the pure frequency-modulated \nwave, as may be seen from formula (16). The transmitted current is \nconveniently written in the form\n\nIn passing it is interesting to compare the distortion, as given by \n(47), undergone by the pure frequency-modulated wave, with that suf- \nfered by the pure amplitude-modulated wave (39), in passing through \nthe same transducer. The transmitted current corresponding to the\n\nIn this section we consider the recovery of the wanted low frequency \nsignal s(t) from the frequency-modulated wave. This involves two \ndistinct processes: (1) rendering explicit the low frequency signal \n\u2018\u201cimplicit\u2019\u2019 in the high frequency wave; that is, \u2018\u2018 frequency detection\u201d\u2019 \nor \u2018\u201c\u2018hybridization\u201d\u2019 of the high frequency wave; and (2) detection \nproper.\n\nsuppose that the transducer proper is equalized in the neighborhood of \nthe carrier frequency ,; that is,\n\nFrequency detection is then effected by a terminal network. We \ntherefore take as the over-all transfer admittance\n\ny(iw) represents the terminal receiving network; it is under control and \ncan be designed for the most efficient performance of its function. As \nwe shall see, it should approximate as closely as possible a pure reactance. \nTaking the over-all transfer admittance as (51), we have from (47),\n\nInspection of (52) shows that the terms beyond the second simply \nrepresent distortion. The terminal network or frequency detector \nshould be so designed as to make the series\n\nrapidly convergent from the start. In fact the ideal frequency de- \ntector is a network whose admittance y(iw) can be represented with\n\nSupposing that this condition is satisfied, the wave, after passing \nover the transducer and through the terminal frequency detector, is \n(omitting the constant y- Y)\n\nIf y is a pure reactance, w; is a pure real; due to unavoidable dissi- \npation it will actually be complex. To take this into account we \nreplace w; in (54) by w,e~** where now a; is real; (54) then becomes\n\nNow let A/w; be less than unity and let the wave (55) be impressed on \na straight-line rectifier. Then the rectified or detected output is\n\nThe second term is the recovered signal and the third term is the first \norder non-linear distortion.\n\nInspection of the foregoing formulas shows at once that, for detection \nby straight rectification, the following conditions should be satisfied:\n\n(1) /w: must be less than unity. \n(2) The terminal network should be as nearly as possible a pure \nreactance to make the phase angle a as nearly zero as possible.\n\n(3) To minimize both linear and non-linear distortion it is necessary \nthat the sequence \n\\3\n\nThe first term of (58) is simply direct current and has no significance \nas regards the recovered signal. When we come to consider the \nproblem of noise in the next section, we shall find that its elimination is \nimportant. This can be effected by a scheme which may be termed \nbalanced rectification. Briefly described the scheme consists in termi- \nnating the transducer in two frequency detectors y; and ye in parallel; \nthese are so adjusted that yi(iw.) = \u2014 ye(iwe) and dy;/dw, = dy2/dw.. \nw, is therefore of opposite sign in the two frequency detectors. The \nrectified outputs of the two parallel circuits are then differentially \ncombined in a common low frequency circuit. Corresponding to (58), \nthe resultant detected output is\n\nThis arrangement therefore eliminates first order non-linear distortion, \nas well as the constant term.\n\nRectification is the simplest and most direct mode of detection of \nfrequency-modulated waves. However, in connection with the problem \nof noise reduction other methods of detection will be considered.\n\nAs a specific example of the foregoing let the terminal frequency \ndetector, specified by the admittance y(iw), be an oscillation circuit \nconsisting simply of an inductance L in series with a capacitance C.\n\nthen the combined rectified output of the two parallel circuits is \nproportional to\n\nThus the constant term and the first order distortion are eliminated \nin the low frequency circuit.\n\nThe most important advantage known at present of frequency- \nmodulation, as compared with amplitude-modulation, lies in the possi- \nbility of substantial reduction in the low frequency noise-to-signal \npower ratio in the receiver. Such reduction requires a correspondingly \nlarge increase in the width of the high frequency transmission band. \nFor this reason frequency-modulation appears to be inherently \nrestricted to short wave transmission.\n\nIn the discussion of the theory of noise which follows, it is expressly \nassumed that the high frequency noise is small compared with the high \nfrequency signal wave. Also ideal terminal networks, filters and \ndetectors are postulated.\n\nIn view of the assumption of a low noise power level, the calculation \nof the low frequency noise power in the receiver proper can be made to \ndepend on the calculation of the noise due to the typical high fre-\n\nCorresponding to the noise element (60), the output of the ideal \nfrequency detector is\n\noccurs so frequently in the analysis which is to follow, it is convenient \nto adopt the notation \nQn, = wn \u2014 As(t),\n\nWith this notation and on the assumption that A, <1 and \u00ab, real, \nthe amplitude of the wave (61) is\n\nIn this formula the argument of the cosine function should be \nstrictly \nt \nf + On. \n0\n\nThe phase angle @, is random however and does not affect the final \nformulas; it may therefore be omitted at the outset. Consequently, \nif the wave (61) is passed through a straight line rectifier, the rectified \nor low frequency current is proportional to\n\nThe first term is the recovered signal and the second term the low \nfrequency noise or interference corresponding to the high frequency \nelement (60).\n\nNow the wave (63), before reaching the receiver proper, is transmitted \nthrough a low-pass filter, which cuts off all frequencies above wa; wa is \nthe highest essential frequency in the signal s(t). Consequently, in \norder to find the noise actually reaching the receiver proper, it is\n\nnecessary in one way or another to make a frequency analysis of the \nwave (63). This is done in Appendix 2, attached hereto, where \nhowever, instead of dealing with the special formula (63), a more \ngeneral expression\n\nis used for the low frequency current. This will be found to include, \nas special cases, several other important types of rectification, as well \nas amplitude limitation, which we shall wish to discuss later.6 Then, \nsubject to the limitation that the noise energy is uniformly distributed \nover the spectrum, it is shown in Appendix 2 that\n\nThese formulas are quite important because they make the calcula- \ntion of low frequency noise-to-signal power ratio very simple for all the \nmodes of frequency detection and demodulation which we shall discuss. \nApplying them to formula (63) we find for straight line rectification\n\nIt is known that in practice >> \\\u2019s? and >> w.2. Consequently \nin the factor + w? + the largest term is Therefore \nit is important, if possible, to eliminate this term. This can be \neffected by the scheme briefly discussed at the close of section III; \nparallel rectification and differential recombination. For this scheme \nthe low frequency current is found to be proportional to\n\nConsequently, for parallel rectification and differential recombination,\n\n6 The formula is also general enough to include detection by a product modulator, \nwhich however is not discussed in the text as no advantage over linear rectification \nwas found.\n\nHere, in the factor (4w,? + d*s), the term 42s? is predominant. The \nelimination of the term w,? has resulted in a substantial reduction in \nthe noise power.\n\nReturning to the general formula (66) for Py, it is clear, that, if in \naddition to eliminating the term w,*, the parameter v = yw/A can be \nmade equal to \u2014 1, the noise power will be reduced to its lowest \nlimits:\n\nThis highly desirable result can be effected by amplitude limitation, \nthe theory of which will now be discussed.\n\nWhen amplitude limitation is employed in frequency-modulation, \nthe incoming high frequency signal is drastically reduced in amplitude. \nIf no interference is present this merely results in an equal reduction \nin the low frequency recovered signal which is per se undesirable. \nWhen, however, noise or interference is present, amplitude limitation \nprevents the interference from affecting the amplitude of the resultant \nhigh frequency wave; its effect then can appear only as variations in \nthe phase or instantaneous frequency of the high frequency wave. To \nthis fact is to be ascribed the potential superiority of frequency- \nmodulation as regards the reduction of noise power. This superiority \nis only possible with wide band high frequency transmission; that is, \nthe index of frequency-modulation \\ must be large compared with the \nlow frequency band width wa. Insofar as the present paper is con- \ncerned, the potential superiority of frequency-modulation with ampli- \ntude limitation is demonstrated only for the case where the high fre- \nquency noise is small compared with the high frequency signal wave.\n\nadded the typical noise element A, exp (tw. + twat + 6,), the re- \nsultant wave may be written as\n\nPostulating that A, <1 and therefore neglecting terms in A,\u2019, \nthe real part of (71) is\n\nIf this wave is subjected to amplitude limitation, the amplitude \nvariation is suppressed, leaving a pure frequency-modulated wave, \nproportional to the real part of\n\n(but drastically reduced in amplitude). \nAfter frequency detection the wave (73) is, within a constant,\n\nThis is the amplitude of the low frequency wave after rectification; it is \nobviously proportional to\n\nwhich is a special case of (64) and may be used in calculating the \nrelative signal and noise power\u2019with amplitude limitation. Hence we\n\n(These are, of course, relative values and take no account of the \nabsolute reduction in power due to amplitude limitation.)\n\nComparing (78) with (68) it is seen that, for detection by straight line \nrectification, the ratio of the noise power with to that without amplitude \nlimitation is\n\nSince in practice w; >> w, and \\ > w,, amplitude limitation results in a \nvery substantial reduction in low frequency noise power in the receiver \nproper. Reference to formula (70) shows that, as compared with \nparallel rectification and recombination, amplitude limitation reduces \nthe noise power by the factor \n1\n\nIt should be observed that without amplitude limitation little reduc- \ntion in the noise-to-signal power ratio results from increasing the \nmodulation index A (and consequently the high frequency transmission \nband width). On the other hand, with amplitude limitation, the ratio \np of noise-to-signal power is\n\nThe ratio p is then (within limits) inversely proportional to the \nsquare of the modulation index X, so that a large value of } is indicated. \nIt should be noted that, within limits (A < w,), the power transmitted \nfrom the sending station is independent of the modulation index \\.\n\nIt might be inferred from formula (82) that the noise power ratio p \ncan be reduced indefinitely by indefinitely increasing the modulation \nindex \\. Actually there are practical limits to the sizeof \\. First, if \nis made sufiliciently large, the variable frequency oscillator generating \nthe frequency-modulated wave may become unstable or function \nimperfectly. Secondly, the frequency spread of the frequency modu- \nlated wave is 2\\ (from w, \u2014 \\ to w, + A) and, if this is made too large, \ninterference with other stations will result. Finally, the stationary \ndistortion of the recovered low frequen\u00e9\u00a2y signal s(t) increases rapidly \nwith the size of X.\n\nTo summarize the results of the foregoing analysis the potential \nadvantages of frequency-modulation depend on two facts. (1) By \nincreasing the modulation index it is possible to increase the recovered \nlow frequency signal power at the receiving station without increasing \nthe high frequency power transmitted from the sending station. \n(2) It is possible to employ amplitude limitation (inherently impossible \nwith amplitude-modulation) whereby the effect of interference or noise \nis reduced to a phase or \u2018\u2018instantaneous frequency\u201d variation of the \nhigh frequency wave.\n\nFormula (40) et sequa establish the fact that the actual frequency of \nthe wave (29) varies between the limits\n\nprovided s(t) is a pure sinusoid \\ sin wt and A>>w. This agrees with the \nconcept of instantaneous frequency.\n\nWhen s(t) is a complex function\u2014say a Fourier series\u2014the frequency \nrange of W can be determined qualitatively under certain restrictions, as \nfollows:\n\nThe Fourier formulation is supposed to be valid in the epoch 0 = \u00a2 = T \nand T can be made as great as desired. Then\n\nT \nsdt \n| Jo \nbecomes very large compared with 27. On this assumption, it follows \nfrom the Principle of Stationary Phase, that, for a fixed value of w, the\n\nimportant contributions to the integral (3a) occur for those values of \nthe integration variable \u00a2 for which\n\nConsequently the important part of the spectrum F(iw) corresponds \nto those values of w in the range\n\nTherefore the frequency spread of W lies in the range from w, + ASmin \nto We + MSmax or We + if Smax Smin =\n\n- where w, is the carrier frequency and s = s(t) is the low frequency co \nsignal. dis areal parameter, which fixes the amplitude of the frequency \nspread. \n7 Correspondingly, we take the typical noise element as \nAnos ((we + + On). (2b) \nes For reasons stated in the text, we take the more general formula for es \nhe the low frequency current as proportional to \nbe \nin\n\nwhere wo, A, wu are real parameters. The term As is the recovered signal \nand the second term is the low frequency noise corresponding to the \nhigh frequency noise element (25).\n\nWe suppose that the noise is uniformly distributed over the frequency \nspectrum, at least in the neighborhood of w = w,, so that, corresponding \nto the noise element \nA, COS (Wat + On),\n\nand the corresponding noise power for the frequency interval w; < w, < we \nis, by the Fourier integral energy theorem,\n\nThe Fourier integral energy theorem states that, if in the epoch \n0 = t= T, the function f(t) is representable as the Fourier integral\n\nReplacing (46) by (5d) to take care of the distributed noise, the \nnoise term of (3b) becomes\n\nNow this noise in the low frequency circuit is passed through a low \npass filter, which cuts off all frequencies above ws. wa is the maximum \nessential frequency in the signal s(\u00a2).\n\nIt is therefore necessary to express (9b) as a frequency function \nbefore calculating the noise power. To this end we write the Fourier \nintegrals\n\nSubstituting (10d), (115), (12d) and (13d) in (96) and carrying \nthrough straightforward operations, we find that the noise is given by\n\n7See \u2018\u2018Transient Oscillations in Electric Wave Filters,\u2019 Carson and Zobel, \nB.S. T. J:, July, 1923.\n\nThe limits of integration of w, are determined by the fact that, \nw \u2014 w, in the first integral of (146) and w + w, in the second, must \nlie between + w,; all other frequencies are eliminated by the low \npass filter.\n\nFrom formula (145) and the Fourier integral energy theorem, the \nnoise power Py is given by\n\n+ [(wo \u2014 (1 + v)w)? + (180) \nwhere vp = \nReplacing F,? and F,,? in (18b) by their values as given by (15d) \nand (16b), we get\n\nHere, for convenience, we have replaced N?/x? of (196) by N?, so that \nN? of (23) may be defined and regarded as the high frequency noise \npower level.\n\nIt remains to establish formulas (200), (21) and (226). From the \ndefining formulas (105) and (11b) and the Fourier integral energy \ntheorem, we have\n\nAdding we get (20d). \nNow differentiate (10) and (11) with respect to \u00a2 and apply the \nFourier integral energy theorem; we get\n\n57-64, Feb, 1922 \nFrequenzmodulation,\u201d Telefunken-Zeitung, 10, pp. 48-54, \nlec., 192 \nHeilmann, A., \u2018Einige zum der Frequenzmodulation,\u201d\u2019 \nElek. Nach. Tech., 7, pp. 217-225, June, 1930. \nB., \u201cFrequency Modulation,\u201d Proc. I. R. E., 18, pp. 1194-1205, \nuly, 1 4 \n. Eckersley, T. L., \u2018\u201c\u2018Frequency Modulation and Distortion,\u201d Exp. Wireless and \nWireless Engg., 7, pp. 482-484, Sept., 1930. \n\" Runge, W., \u201cUntersuchungen an amplituden- und frequenz-modulierten Send- \nern, ' Elek. Nach. Tech., 7, pp. 488-494, Dec., 1930. \nRoder, H., \u201c\u2018Amplitude, Phase and Frequency- Modulation,\u201d Proc. I. R. E., 19, \npp. 2145- 2173, Dec., 1931. \n. Andrew, V. J., \u201cThe Reception of Sey Modulated Radio Signals,\u201d Proc. \nI. R. E., 20, pp. 835-840, May, 1932. \n. Barrow, W. L., \u2018Frequency Modulation and the Effects of a Periodic Capacity\n\n. Barrow, W. te \u201cOn the Oscillations of a Circuit Having a Periodically Varying \nCapacitance; Contribution to the Theory of Nonlinear Circuits with -\u2014- \nApplied besa Proc. I. R. E., 22, pp. 201-212, Feb., 1934, also M. I. T. \nSerial 97, Oct., 1934.\n\nArmstrong, Kicthod of Reducing Disturbances in Signaling by \ni930 of Frequency- Modulation,\u201d Proc. I. R. E., 24, p 689-740, ay, \n1\n\nIrregularities in Broad-Band Wire Transmission Circuits \nBy PIERRE MERTZ and K. W. PFLEGER\n\nThe effects of inhomogeneities along the length of a wire trans- \nmission circuit are considered, affecting its use as a broad-band \ntransmission medium. These inhomogeneities give rise to reflec- \ntions of the transmitted energy which in turn cause irregularities \nin the measured sending or receiving end impedance of the circuit \nin its overall attenuation, and in its envelope delay. The irregu- \nlarities comprise departures of the characteristic from the average, \nin an ensemble of lines, or departures from a smooth curve of the \ncharacteristic of a single line when this is plotted as a function \nof frequency. These irregularities are investigated quantitatively.\n\nIRE transmission circuits in their elementary conception are \nconsidered as perfectly uniform or homogeneous from end to \nend. Actually, of course, they are manufactured in comparatively \nshort pieces and joined end to end, and there is a finite tolerance in the \ndeviation of the characteristics of one piece from those of the next and \nalso from one part of the same piece to another. A real transmission \ncircuit therefore has a large number of irregularities scattered along its \nlength which reflect wavelets back and forth when it is used for the \npropagation of a signal wave. When a cable pair, coaxial conductor, \nor similar medium is used for broad-band transmission it is important \nto know how these irregularities influence the transmission character- \nistics of the medium.\n\nThe transmission characteristics which will be studied are the im- \npedance, the attenuation, the sinuosity of the attenuation (to be \ndefined), and the delay distortion. The derivations for the first two \ncharacteristics parallel substantially those published by Didlaukis and \nKaden (ENT, vol. 14, p. 13, Jan., 1937). They are set forth here for \ncompleteness of presentation because the steps in them illustrate the \nmore complicated steps in the derivation of the last two characteristics.\n\nWhen the characteristic impedance changes from point to point, its \nvariation from the average characteristic impedance for the whole \nlength of conductor forms the irregularities which produce reflections. \nAssume that successive discrete elementary pieces of the circuit are \nhomogeneous throughout their length, that the lengths of these ele- \nmentary pieces are equal throughout the length of the whole circuit, \nand that there is no correlation between the deviations from average\n\ncharacteristic impedance of any two elementary pieces. This repre- \nsents a first approximation to the problem. It is fairly accurate for \npairs in ordinary cable in which the outstanding irregularities are devia- \ntions, from the average, between whole reel lengths; and in which the \nlengths of the successive: spliced pieces (reel lengths) are at least \nroughly the same.\n\nThere are irregularities in some coaxial conductors in which the \nimpedance change is gradual rather than abrupt from one element to \nthe next, and in which the elements can vary in length along the line. \nFor these cases the approximation is a little over-simplified. However, \nalthough this somewhat affects the echo wavelets as computed from \nthe impedance deviations along the line, Didlaukis and Kaden, as \nreferred to above, have shown that it does not affect the ratio between \nthe echo wavelets, suitably averaged, reaching the receiving end and \nthose, similarly averaged, returning to the sending end.\n\nWith the above assumptions there will be some correlation between \nthe reflections at the two ends of an elementary length. If, for \nexample, this length happens to be high in characteristic impedance the \nreflection at one end will tend greatly to be the negative of that at the \nother end. For this reason we are going to break up the reflection into \ntwo parts, at a point between any two successive elementary lengths of \ncircuit\u2014one part from one length of the circuit to an infinitesimal \nlength of cable of average characteristics inserted between the two \nelementary lengths\u2014and the other from this infinitesimal piece to the \nnext elementary length of circuit. There is then 100 per cent correla- \ntion between the reflections at the two ends of a given elementary \nlength (one being exactly the negative of the other); but there is no \ncorrelation between the reflections from any one elementary length to \nits adjacent infinitesimal piece of average cable, and the reflections \nfrom any other elementary length to its adjacent piece. This same \ntreatment is used in the calculation of certain types of \u201creflection\u201d \ncrosstalk.\n\nThe departure in characteristic impedance in the usual transmitting \ncircuit in the higher frequency range, where the irregularities are most \nimportant, results essentially from deviations in the two primary con- \nstants of capacitance and inductance, each per unit length. There isa \ncertain correlation between these, inasmuch as the capacitance devia- \ntion is contributed to both by differences in the dielectric constant of \nthe insulation and by differences in the geometrical size, shape, and \nrelative arrangement of the conductors; and the inductance deviation \nis contributed to by the latter alone. If there were no deviation in \ndielectric constant there would be no deviation in velocity of propaga-\n\ntion (phase or envelope), which (at the higher frequencies) is inversely \nproportional to the square root of the product of the capacitance by the \ninductance. Consequently the portion of the fractional deviation in \ncapacitance which is due to geometrical deviations correlates with an \nequal and opposite fractional deviation in inductance. Since in prac- \ntice the contribution from the geometrical deviation is apt to be \ndominating, that due to the variation in dielectric constant will be \nneglected and the above correlation assumed as 100 per cent.\n\nThe standard deviation of the capacitance of the successive ele- \nmentary lengths, as a fraction of the average capacitance, will be \ndesignated as 6.\n\nThe secondary constant of the line most affected by these irregulari- \nties is the sending end (or similarly receiving end) impedance. If we \nconsider a large ensemble of lines of infinite length of similar manufac- \nture (and equal average characteristics and 6) but in which the indi- \nvidual irregularities are uncorrelated, then the sending end impedances \nof these lines, measured at a given frequency, also form an ensemble. \nThe standard deviation of the real parts in this latter is VAK2, and \nthat of the imaginary parts VAK?.\n\nIn general, the departure in the impedance of one individual line \nfrom the average will vary with frequency; and perhaps over a moder- \nate frequency range a sizeable sample can be collected which is fairly \ntypical of the ensemble of the departures at a fixed frequency in the \ninterval. If this is the case, and if at the same time the average im- \npedance varies smoothly and slowly with frequency, and the standard \ndeviation of the ensemble of departures also varies smoothly and \nslowly with frequency, then the standard deviation of the sample of \ndepartures over the moderate frequency interval is substantially equal \nto that of the ensemble of departures at a fixed frequency in this inter- \nval. (It is clear that this disregards exceptional lines in the ensemble, \ncharacterized by regularity in the array of their capacitance deviations, \nfor which these conditions do not hold.) Under the circumstances \nwhere this observation is valid it makes it possible to correlate measure- \nments on a single line, provided it is not too exceptional, with theory \ndeduced for an ensemble.\n\nThe irregularities in the transmission line will also affect its attenua- \ntion. If again we consider an ensemble of lines and measure the at- \ntenuation of each at a given frequency these attenuations will also \nform an ensemble.\n\nIt will be found in this case, as will be demonstrated further below, \nthat the average attenuation is a little higher than that of a single \ncompletely smooth line having throughout its length a characteristic\n\nimpedance equal to the average of that for the irregular line. This \nrise varies slowly with frequency. The standard deviation of the at- \ntenuation will also include not only the effect of the reflections which \nwe have been considering but in addition one caused by the fact that \nthe attenuations of the successive elementary pieces are not alike, and \nhence their sum, aside from any reflections, will also show a distribu- \ntion. This additional contribution will vary only very slowly with \nfrequency. The standard deviation will be VAA? + AAg? where A \nrepresents the losses in the total line, the subscript 1 indicates the con- \ntribution due to the reflections, and the subscript 2 that due to the \ndistribution of the individual attenuations.\n\nThe same observation may be made about the attenuation that was \nmade about the terminal impedance, as regards measurements made \nat one frequency on an ensemble of lines and measurements over a \nrange of frequencies on one line; except that the contribution to the \ndeviation caused by the distribution of individual attenuations varies \nso slowly with frequency that on each individual line it will look like a \ndisplacement from the average attenuation, over the whole frequency \nrange. For the purposes of the present paper only the contributions \nfrom the reflections will be computed.\n\nWhen this information on irregularities is being used by a designer of \nequalizers he is interested in two characteristics: first, how far each \nattenuation curve for a number of lines will be displaced as a whole \nfrom the average; and second, how \u201cwiggly\u201d\u2019 each individual curve is \nlikely to be. While the observations above give the general amplitude \nof the latter they do not tell how closely together in frequency the \nindividual \u201c\u2018wiggles\u2019\u2019 are likely to come. To express this, the term \n\u201csinuosity\u2019\u201d\u2019 has been defined as the standard deviation of the difference \nin attenuation (for the ensemble of lines) at two frequencies separated \nby a given interval Af. By the previous observations this can be \nextended to the attenuation differences for successive frequencies \nseparated by the interval Af, for a range of frequencies in a single line.\n\nWhen the transmission line is used for certain types of communica- \ntion, notably for telephotography or television, it is important to \nequalize it accurately for envelope delay as well as attenuation. The \nenvelope delay is defined as\n\nwhere @ is the phase shift through the line and w is 27 times the fre- \nquency. For an ensemble of lines, the envelope delay at a given \nfrequency will also form an ensemble, the standard deviation of which\n\nthe same standard deviation also holds for the envelope delay depar- \ntures over a range of frequencies on one line.\n\nLet Fig. 1 represent a line of the type we have been discussing. \nThe successive n\u2019s represent the reflection coefficients between succes- \nsive elementary pieces of line. As mentioned before, to avoid correla- \ntion, each 7 is broken up as shown into two h\u2019s, representing reflections \nbetween the elementary pieces and infinitesimal lengths of average \nline.\n\nThe main signal transmission will flow as shown by the arrow a in \nFig. 1. In addition there will be single reflections as shown by the \narrow b. Following the assumptions we have set up, this really con- \nsists of two reflections from infinitesimally separated points. Further \nthere will be double reflections, that is reflections of reflections, as \nshown byc. Here again each reflection point, according to our assump- \ntions, consists of two infinitesimally separated ones. There will be a \nvariety of double reflections according to the number of elementary \nlengths between reflection points. Finally there will be triple, quad- \nruple and higher order reflections which are not shown. The wave \namplitude after reflection is cut down by the reflection coefficient. \nConsequently, even though there are more of them, the total of any \ngiven higher order reflections can always be made smaller than that of \nlower order reflections by a small enough reflection coefficient. We \nwill here study only small reflection coefficients and therefore neglect \nall reflections of higher order than needed to give a finite result. For \neffects on the impedance this means neglect of all but first-order reflec- \ntions. For the other effects studied it means neglect of all but first- and \nsecond-order reflections.\n\nThe reflection coefficient between two successive impedances (one \nbeing K), is, approximately\n\nFollowing our earlier assumptions, namely that the principal cause of \nimpedance departures lies in geometrical irregularities, and that these \nmay be expressed in terms of capacitance departures,\n\nK Cc 2C \nConsequently the reflection coefficients are real, namely, they intro- \nduce no phase shifts other than 0 or z in the reflections.\n\nThe irregularities in sending-end impedance have been computed in \nAppendix I from the single reflections of the type } in Fig. 1. The\n\nwhere \u00a2 is the phase shift in radians in two elementary lengths, \u00ab is \nthe attenuation in nepers of two elementary lengths, and 4 is, as men- \ntioned before, the standard deviation in C measured as a fraction of C. \nIt will be noted that as a consequence of the single reflections, the ir- \nregularities in impedance vary as the first power of 6.\n\nThe irregularities in attenuation have been computed in Appendix II \nfrom the double reflections of the type c in Fig. 1. It is found, as \nmentioned before, that there is a net rise in average attenuation caused \nby the reflections, equal, in nepers, to\n\nwhere n is the number of elementary lengths in the total line. Con- \nsidering the factor in parentheses in the expression above, although the \nterm \u00a2\u20ac is not usually wholly negligible compared with the term \u00a2?/2, \nnevertheless the latter is dominating and sets the order of magnitude \nof the factor. If the \u00a2 is disregarded, the expression can easily be put \nin terms of the impedance irregularities, giving\n\nwhere A as before represents the loss in the total line. \nThe standard deviation in the loss in nepers, when finally simplified, \nis, for the reflections, \n252 \nVAA 2 = e\n\nIt will be noted that these irregularities in the attenuation vary with \nthe square of 5, or the square of the impedance irregularities. This is a \nconsequence of the double reflections, and will continue to hold for the \nsinuosity and irregularities in envelope delay. It will also be noted\n\nthat in this form the equation is independent of \u00a2, \u00a2, and n. It is in \nthis case that Didlaukis and Kaden found that the result is independent \nof whether the reflection points are sharp and equally spaced or not.\n\nThe sinuosity has been computed in Appendix III. When finally \nsimplified and measured in nepers, it amounts to\n\n\u2014 = \u2014 Af. 9 \n1 1) 2683/2 df ( ) \nExpressed in terms of the impedance irregularities this amounts to \n[SEY \n(AA; \u2014 AA)? = \u2014\u2014 | \u2014\u2014Af, 10\n\nwhere T is, as mentioned before, the envelope delay of the whole line, \nin seconds.\n\nIn computing the above it is only the components of the echoes which \nare in phase (or 7 radians out of phase) with the main transmission \nwhich affect the results. If the echo components at right angles to \nthe main transmission are considered, they will give phase shifts in \nthe resultant signal wave. Further, an echo component whose ratio \nto the main transmission is x will, when z radians out of phase with it, \ngive a loss of x nepers; and when at right angles to it, a phase shift of x \nradians. Now the distribution of echo components in phase (or 7 \nradians out of phase) with the main transmission is substantially the \nsame as that of components at right angles to it. Consequently the \nsinuosity is also numerically equal to the standard deviation of the \ndifference in phase shifts at two frequencies separated by the given \ninterval Af. Therefore if the interval is called Aw/2m and the resulting \nnumerical value of the sinuosity is divided by Aw it will give the \nstandard deviation of the envelope delay. This is\n\nThe quantity which has been used in considering the suitability of a \nline from a delay standpoint for transmitting pictorial signals is its \nenvelope delay distortion, or maximum departure in delay each way \nfrom a fixed average in the frequency band studied. If we make the \nusual assumption that the maximum departure ordinarily met (strictly \nspeaking, except in about 3 cases out of 1000) is three times the \nstandard deviation, then the delay distortion contributed by the ir- \nregularities is + 3 times the expression given in equation (11).\n\nExpressed in more usual units, the results given in equations (6), \n(8), (10), and (11) are repeated here. \nAK,? | \naL,\n\nVAR? 2 \nSinuosity (db per kilocycle) = 0.0256 | \u00bb (10\u2019) \nK Va \nVAK2 12 IF \nDelay distortion (microseconds) = + 4.42 | (11\u2019) \nK Va \nwhere L = length of the line in miles, \na = attenuation of the line in db per mile, \n7 = envelope delay of the line in microseconds per mile.\n\nIn order to convey a notion as to possible orders of magnitude of \nthese effects of irregularities, and how they vary with changes in the \nparameters, a few calculations have been tabulated below for some \nhypothetical lines.\n\nIn Fig. 1 the circuit is divided into \u00bb homogeneous elementary \nlengths. For a current of unit value traveling down the circuit at the \njunction of the kth and (k + 1)th elementary lengths, the reflected\n\nwhere hi, denotes the reflection coefficient (assumed to be a real number) \nbetween the impedance of the kth elementary length and the average \nimpedance.\n\nHowever, if the current starts with unit value at the sending end, \nthen the wave has to be multiplied by the factor e~*?\u2019? in reaching the \npoint of reflection, where P is the propagation constant per two ele- \nmentary lengths. In returning to the sending end the reflected wave \nis again multiplied by a like amount so that its value on arrival there \nbecomes\n\nWhen 1 is large, it is permissible to use the assumption that k has \u00ab \nfor its upper limit in the above summation. The real part of EF, is \naccordingly\n\nThen, replacing \u00ab and neglecting higher-order terms in \u00a2 and \u00ab, \nwhich are small, and putting h? = 6\u00b0/4, equations (7) and (8) become\n\nThe echo Ey affects the measured impedance. If unit voltage is \nimpressed in series with the line, and a network having impedance K, \nthe current flowing, not counting the echoes, is 1/2K. The echo cur- \nrent is then (E,/1)(1/2K), and the total current\n\nFor K, the real part only is to be used as it is assumed that the \nimaginary part is negligible in comparison with it. Where departures \nfrom K are considered, however, this imaginary part may not be negli- \ngible in comparison with the departures.\n\nThe following is a derivation of the standard deviation of the real \npart of the echo currents (which are received in phase with the direct \ntransmission) over a circuit such as has been assumed in Appendix I, \nAccordingly, the reflected wave at the junction of the kth and (& + 1)th \nhomogeneous elementary lengths, for a current of unit value traveling \ndown the circuit at this point, is:\n\nThis wave returns toward the sending end and in turn suffers partial \nreflections. Consider this secondary reflection at the point between \nthe jth and (j + 1)th lengths where j = k. The wave arriving at the \npoint in question is\n\nso that the wave which starts back from this point in the same direction \nas the original wave is:\n\nIn traveling to the junction of the kth and (k + 1)th lengths it is \nagain multiplied by e~?\u201c-\u00bb/? so that the echo which is joined to the \nunit wave is therefore given by\n\nWhen m = 0, a slightly different treatment is necessary. Let the \ncircuit be represented as in Fig. 1.\n\nA unit current traveling down the circuit will suffer a reflection loss \nat each junction so that the current passing through the junction is \n(1 \u2014 n;) times the current entering. The ratio of the current received\n\nwhere the double reflected echoes of the previous type (m > 0) are \nomitted. The echo which is joined to the unit wave when m = 0 is\n\nBa = {5 (hi \u2014 cos ms, (15) \nj=0 \nassuming h\u2019s may be taken as real and as having a symmetrical distri- \nbution curve about zero, the square of whose standard deviation may be \ndenoted by h?. \nWe will consider the distribution curve of H,, which also is real. \nThe average value of a function H(h) in a given distribution is equal to\n\nthe integral of the product of the function by the frequency of occur- \nrence for each value of it, divided by the integrated frequency of oc- \ncurrence alone. The frequency of occurrence of individual values of \nthe function is the same as that of the corresponding values of its \nargument, and hence can be written as F(h)dh where F(h) is the distri- \nbution function of the variable h. The average value of H, is therefore\n\nConsidering the four products j4m, jht and \nit will be seen that they all integrate to zero by virtue of symmetry\n\nThe average value of E., is equal to the sum of the average values of \nits terms. Applying the results for Ho, Hi, and H,, we obtain\n\nMultiplying the factors containing the h's as indicated in (30) gives \nterms containing hehsh-ha where the subscripts denote some integer \nsuch as the value for p, p+ 1, p+ 7, etc. When\n\nthere is equality among subscripts so that the terms become h,2h,? or \nhw* the integration gives (h)? or h\u2018, respectively. However, if such \nequality does not exist, or if one of the subscripts is zero or m + 1, the \nintegration gives zero. By integrating term by term in the manner \nabove indicated, adding the results, and finally thereafter putting \nr = mands = m, the following result is obtained:\n\nIf the distribution of the h\u2019s is assumed to be a normal distribution, \nthen: \nh* = 3(h?)?. (32)\n\nWhen 1 is large, it is permissible to use the assumption that m has \u00ab \nfor its upper limit in the above summations. It is likewise permissible \nto neglect terms in the result which do not contain the factor n. \nAccordingly,\n\nThe echo current which is joined to the unit received wave affects \nthe final resultant and therefore the effective loss of the line. From \nequation (28), neglecting higher-order terms, the attenuation of the \nwhole line is increased (in nepers) by\n\nThe standard deviation of the attenuation (A, in nepers), from equa- \ntion (34) and neglecting higher order terms, is\n\nSinuosity \nThe following is a derivation of the sinuosity of the attenuation, \ndefined as the standard deviation of the difference A(f + Af) \u2014 A(f). \nHere A(f) is the loss in the circuit at the frequency, f. \nFor practical purposes, the difference of the expression E., \u2014 E. \nat two discrete frequencies is\n\nwhose standard deviation will be derived below. From values of E., \nand \u00a3,, given in Appendix II we obtain\n\nBy expanding S in powers of \u00a2 and \u00a2, and neglecting those higher \nthan needed to give a finite result, it is found that\n\nev? + D? \nS = \u2014>\u2014.\u2014 (Af). 14 \n(4f) (14) \nIn general, D is negligible compared to Q and the sinuosity is \n(aa AA)? = OG (15)\n\nEN years have elapsed since the opening to public use on January \n7, 1927, of the first long distance radio telephone circuit. This \nform of intercontinental communication has now come into practical \nbusiness and social use. A network of radio circuits interconnects \nnearly all the land wire telephone systems of the world. The art has \npassed through the pioneering stage and is well into a period of growth. \nThe technical side of this development, which the present paper \nreviews, divides naturally into four categories. The first covers those \nfactors which made possible the beginning of commercial radio tele- \nphony.' In the second are the things without which its rapid growth \nand wide expansion could not have occurred. In the third, are a few \nincidental but interesting or valuable technical features. The fourth \nconsiders future improvements now in view.\n\nRadio telephony presents difficulties in addition to those existing in \nradio telegraphy because: (1) The communication is two-way, and the \nradio system must be linked in with the wire telephone systems and \navailable to any telephone instrument; (2) The subscriber cannot \ndeliver himself of his message until the connection is actually estab- \nlished, and on this account delay due to unfavorable transmission con- \nditions is less tolerable; (3) The grade of transmission required to \nsatisfy the average telephone user is higher than that tolerable in aural \ntone telegraph reception by an experienced operator.\n\nThese requirements emphasized the need for accurate and quantita- \ntive knowledge of radio transmission performance as a basis for en- \ngineering radio telephone systems. There was at the same time a \nsimilar need for transmission data in the engineering of early radio \nbroadcast installations. The effort brought to bear on these twin prob- \nlems resulted in the development of practical field methods of measuring\n\n* Digest of a paper presented at the Spring Convention of the Institute of Radio \na New York, May 10, 1937, and published in full in Proc. I. R. E., September, \n; 1A description of the early years of radio telephone a preceding exten- \nsive commercial application, together with a discussion of the origins of the whole\n\nart, will be found in companion paper \u201cThe Origin and Development of Radio \nTelephony,\u201d by Lloyd Espenschied, published in Proc. I. R. E., September, 1937.\n\nradio signal strength and radio noise. The employment of long dis- \ntance radio telephony in commercial use was preceded by experimental \noperation and tests which gave a considerable fund of statistical in- \nformation covering the cyclical changes characteristic of overseas radio \ntransmission.\n\nThe realization that a relatively high degree of reliability was essen- \ntial to success discouraged any attempt at commercial service until \nhigh-power transmission on a practical basis was assured by the inven- \ntion of a method of making water-cooled tubes.\n\nIn searching for the most efficient way of applying the power made \navailable by water-cooled tubes telephone engineers were led to the \nemployment of a method which had already been successfully used in \n- high-frequency wire telephony. This method, now well known to \nradio engineers, is called single-sideband suppressed-carrier transmis- \nsion. As compared with the ordinary modulated carrier transmission, \nit increases the effectiveness of a radio telephone system by about 10 \nto 1in power. This accrues partly because none of the power capacity \nof the transmitter is used up in sending the non-communication bearing \ncarrier frequency and partly because the narrower band width permits \ngreater selectivity and noise exclusion at the receiver.\n\nA very important final element was also necessary to prevent voice- \nfrequency singing through residual unbalances and around the entire \nradio link when wire circuits and radio channels are connected together.\n\nRecourse was again had to a device newly worked out for wire \ntelephone transmission. By associating together and electrically inter- \nlocking several of the voice current operated switching devices which \nhad been developed for suppressing echoes on long wire lines, an ar- \nrangement now commonly known as a \u201cvodas\u2019\u2019? was developed. \nWhen the subscriber talks, his own speech currents, acting on the \nvodas, cause it to connect the radio transmitter to the wire line and at \nthe same time to disconnect the radio receiver. When the same sub- \nscriber listens the connection automatically switches back to the re- \nceiver. No singing path ever exists. The amplification in the two \noppositely directed paths can be adjusted substantially independently \nof each other, and constant full load output from the radio transmitters \nis secured. With this device it became possible to connect almost any \ntelephone line to a radio system and to adjust amplification so that a \nweak talker over a long wire line could operate the radio transmitter as \neffectively as a strong local talker.\n\n2 This word, \u2018\u2018vodas,\u201d is synthesized from the initial letters of the words \u201c voice- \noperated device, anti-singing.\u201d\n\nThe first long distance radio telephone circuit operated (and it still \noperates) between the United States and England with long-wave \ntransmission at about 5000 meters. We did not then, and we do not \ntoday, know how any considerable amount of intercontinental radio \ntelephony could have been accomplished with circuits of this kind. \nThe frequency space available in the long-wave range would accom- \nmodate comparatively few channels. The high attenuation to over- \nland transmission and the high noise level at these wave-lengths pre- \nclude their satisfactory use for very great distances or in or through \ntropical regions. The discovery that short waves could be transmitted \nto the greatest terrestrial distances and could be satisfactorily received \nin the tropics came at a most opportune time.\n\nShort-wave transmission not only released the limitations on distance \nand location inherent to long waves but also opened up such a wide \nrange of frequency space as to give opportunity for an extensive growth \nin numbers of both radio telegraph and radio telephone circuits. Short \nwaves further encouraged the growth of radio telephony by making it \ncheaper. Thus, it became possible to make directive antenna struc- \ntures of moderate size which increased the effectiveness of transmission \nmany times, thereby reducing the transmitter power required for a \ngiven reliability of communication. Short waves were the indis- \npensable element without which material growth could not have oc- \ncurred, but there were other significant things.\n\nAn important desideratum in telephony is privacy. Commercial \nradio telephony would have been severely hampered if privacy systems \nhad not been developed to convert speech into apparently meaningless \nsounds during its radio transit.\n\nAnother item of great aid in promoting growth was the development \nof methods of accurate stabilization of transmitted frequencies. The \nfirst effect of this was to eliminate the extreme distortion which charac- \nterized early short-wave telephone transmission and which was found \nto be due to parasitic phase or frequency modulation effects in the \ntransmitters. As the number of radio communication facilities, both \ntelegraph and telephone, grew, accurate stabilization of frequency be- \ncame a necessity in order to permit effective utilization of the available \nfrequency space without mutual interference between stations.\n\nThe \u2018rhombic\u2019 antenna is mechanically simple and electrically \nnearly aperiodic, covering a wide wave-length range efficiently. It\n\nhas radically changed the character of the physical plant and invest- \nment necessary to the employment of directivity in short-wave \ntransmitting and receiving.\n\nIn Hawaii and the Philippines on circuits to the United States the \n\u201c\u2018diversity\u2019\u2019 method of reception is used wherein three individual \nseparated antennas and receivers with interlocked automatic gain \ncontrols are combined to produce a common output having less distor- \ntion and noise than a single receiver.\n\nThe effects of distortion in short-wave circuits are avoided to some \nextent by an arrangement called a \u201cspread sideband system,\u201d which \nhas been used on circuits between Europe and South America. By \nraising the speech in frequency before modulation the speech sidebands \nare displaced two or three kilocycles from the carrier and many of the \nproduct frequencies resulting from intermodulation fall into the gap \nrather than into the sidebands.\n\nOn the Holland-Java route a system is being used whereby more than \none sideband is associated with a single carrier or pilot frequency, each \nsuch sideband representing a different communication.\n\nAn improved signal-to-noise ratio is given by a device called a \n\u201c\u2018compandor\u201d\u2019 * employed on the New York-London long wave circuit. \nIt raises the amplitude of the weaker parts of the speech previous to \ntransmission. In depressing these raised parts to their proper relative \namplitude, after reception, the compandor also depresses the accumu- \nlated radio noise.\n\nThe foregoing makes it evident that many fundamental engineering \nproblems have been solved and that the pioneering stage of the service, \nwhen its possibility of continued existence might reasonably have been \nin doubt, has definitely been passed. In looking toward the future we \nfind that the greatest needs are for improvement in reliability and in \ngrade of service, accompanied by reduced costs.\n\nImproving the reliability struggles against the fact that short wave \ntransmission varies through such a wide range of effectiveness, and \nseems to be so much influenced by the sun. We have not only a daily \ncycle in the transmission of a given frequency but also an annual cycle \nand beyond this an eleven-year cycle associated with the change in \nsunspot activity. Superimposed upon these are erratic and occa- \nsionally large variations associated with magnetic storms.\n\nA statistical study of the data secured from operation of transoceanic \nradio telephone circuits over the past several years has given valuable \nhelp in engineering circuits to meet a given standard of reliability. \nThis study has shown that the percentage of lost time suffered on a \ncircuit appears to follow a probability law and that its relation to the \ntransmission effectiveness of the circuit in decibels is given by a straight \nline when plotted to an arithmetic probability scale. Such a relation \ntells us, for example, that if a circuit as it stands suffers 15 per cent lost \ntime, the lost time can be reduced to a selected lower value, say 5 per \ncent, by improving the circuit a definite amount, in the assumed case \n10 decibels. It then becomes possible, by making engineering cost \nstudies of the various available ways of securing the necessary number \nof decibels improvement in performance, to choose the most economical \none. This approach is being applied to study of the radio telephone \ncircuits extending outward from the United States. Some of the tech- \nnical possibilities which are being considered for improving these cir- \ncuits are discussed below.\n\nThe performance of a radio telephone circuit may be changed by \ndynamically modifying the amplification or other characteristics of \nthe circuit in accordance with the speech transmitted. The compandor \nalready mentioned is an example of this kind of improvement on long \nwaves. Further developments particularly suited to the vagaries of \nshort-wave transmission are possible.\n\nThe operation of the vodas, or voice-operated switching device \nlinking the wire and radio circuits, is adversely affected by noise. \nMethods are being investigated for using single frequencies, called \n\u2018control tones,\u201d transmitted alongside the speech band and under the \ncontrol of speech currents, to give more positive operation of the \nswitching devices and reduce the adjustment required.\n\nThe transmission improvement of about 9 decibels (about 10 : 1 in \npower) offered by single-sideband suppressed-carrier transmission has \nbeen delayed in its application to short-wave transmission partly be- \ncause of the high degree of precision in frequency control and selectivity \nnecessary to its accomplishment. In recent years successful apparatus \nhas been developed and proved satisfactory in trials. The introduction \nof single sideband into commercial usage is already in progress.\n\nTurning now from the transmitting to the receiving end, one funda- \nmental way to reduce noise in radio telephony is to employ sharper \ndirectivity. It has been found by observation that there is a limit to \nwhich directivity, as ordinarily practiced, can be carried to advantage. \nIt is easy to design antennas so sharp that at times very large improve- \nments in signal-to-noise ratio are secured. But it is found that at other\n\ntimes these antennas are actually poorer than are much less sharply \ndirective systems. Such observations also indicate a wide variation in \nthe performance of antennas as regards selective fading, and the signal \ndistortion accompanying it.\n\nThe result of all this work has been the development of a system \nbased on an entirely new approach to the problem of sharp directivity \nand of telephone receiving. This system is called a MUSA System, \nthe word MUSA being synthesized from the initial letters of the \ndescriptive words Multiple Unit Steerable Antenna. An outline of \nthe principles and methods is given below.\n\nBy sending short spurts or pulses of short-wave radiation from one \nside of the Atlantic, and receiving on the other side, it has been observed \nthat each spurt may be received several times in quick succession. \nBut these echoes do not arrive like successive bullets from the same \ngun, all following the same path. They come slanting down to the \nreceiver from different angles of elevation, these vertical angular \ndirections remaining comparatively stable. While the signal received \nat each of the individual directions may be subject to fading, the fading \nis somewhat slower and is not very selective as to frequency. The \nsignal component coming in at a low angle takes less time in its trip from \nthe transmitter than a high angle component. Evidently the low- \nangle paths are shorter. All these facts fit in well; on the average, with \nthe ideal geometrical picture of waves bouncing back and forth between \nthe ionosphere and the ground and reaching the receiver as several \ndistinct components which started out at different angles, have been \nreflected at different angles, and have suffered different numbers of \nbounces.\n\nThe ordinary directive antenna is blunt enough in its vertical receiv- \ning characteristic to receive all or nearly all of these signal components \nat once. Because of their different times of transit the various com- \nponents do not mix well but clash and interfere with one another at the \nreceiver. This shows up as the selective fading and distortion which \ncharacterize short-wave reception much of the time. The MUSA \nmethod remedies this trouble.\n\nThe MUSA provides extremely sharp directivity in the vertical plane. \nBy its use a vertical angular component can be selected individually. \nIt consists of a number of rhombic antennas stretched out in a line \ntoward the transmitter and connected by individual coaxial lines to the \nreceiving apparatus. The apparatus is adjustable so that the vertical \nangle of reception can be aimed or \u2018\u2018steered\u201d\u2019 to select any desired com- \nponent as a telescope is elevated to pick out a star. The antennas re- \nmain mechanically fixed. The steering is done electrically with phase\n\nshifters in the receiving set. By taking several branch circuits in \nparallel from the antennas to different sets of adjusting and receiving \napparatus the vertical signal components may be separated from each \nother.\n\nNature breaks the wave into several components and jumbles them \ntogether. The first function of the MUSA system, as just described, \nis to sort the components out again. Its second function is to correct \ntheir differences so that they may be combined smoothly into a replica \nof the original signal. To do this the received wave components are \nseparately detected and passed through individual delay circuits to \nequalize their differences in transit time. They are then combined to \ngive a single output. As compared with a simple receiver the MUSA \nreceiving system gives (1) improvement in signal-to-noise ratio, as a \nresult of the sharp directive selectivity of the antenna; (2) improvement \nagainst selective fading distortion, by virtue of the equalization of the \ntime differences between the components before they are allowed to \nmix; and (3) improvement against noise and distortion, because of the \ndiversity effect of combining the several components.\n\nFortunately, it is found that the directive selection and the delay \ncompensation adjustments correct for one frequency are satisfactory \nfor a considerable band of frequencies adjacent thereto. Thus there is \noffered the possibility of receiving a number of grouped channels \nthrough one system and the prospect appears not only of improved \ntransmission but also of reduced cost per channel.\n\nThe possibility of grouping channels at the transmitting station may \nbe conceived on the basis of either \u2018\u2018multiple\u201d\u2019 or \u2018\u2018multiplex\u201d\u2019 trans- \nmission. In the multiple arrangement each channel has its own an- \ntenna and its individual transmitter whose frequency is closely spaced \nfrom and coordinated with the adjacent channels of the group. In \n\u2018multiplex\u2019 transmission, the channels are aggregated into a group at \nlow power and handled en bloc through a common high-power amplifier \nand radiating system. Particularly in the multiplex case, there are \npossibilities of important economies if the technical problems are \nsatisfactorily solved. Passing a multiplicity of channels simultane- \nously through a common-power amplifier involves interchannel inter- \nference due to modulation products which is not met with when only \none channel is present. Severe requirements are thereby placed on the \ndistortion characteristics of the power amplifier.\n\nIt seems a fair conclusion that the tendency in the engineering solu- \ntion of the problems of economy and growth in radio telephone de- \nvelopment (and perhaps also radio telegraph development) will be \ntoward channel grouping methods, especially for backbone routes\n\nbetween important centers where large traffic may develop. This will \nbe a considerable departure from past practice which has resulted in \nthe existing system of scattered frequency assignments. It is to be \nhoped that the obvious difficulties in rearranging frequency assign-\n\nments will not prove so unyielding as to preclude putting new engineer- \ning developments into service.\n\nA Negative-Grid Triode Oscillator and Amplifier for Ultra- \nHigh Frequencies *\n\nHE author describes three negative-grid triodes of unusual design \nwhich operate both as oscillators and as amplifiers at ultra-high \nfrequencies. The power output of the smallest tube as an oscillator at \n1500 megacycles is 2 watts, and is still capable of an output of 1 watt at \n1700 megacycles with an oscillation limit of 1870 megacycles cor- \nresponding to a wave-length of 16 centimeters. This tube also offers \npossibilities as an amplifier at frequencies as high as 1000 megacycles. \nSuch capabilities of the negative-grid triode are notable since this de- \nvice has appeared to lag behind the magnetron as an oscillator at fre-\n\n* Digest of a paper presented before International Scientific Radio Union April \n30, 1937 at Washington, D.C. Published in Proc. J. R. E., October, 1937.\n\nprimarily in the lead arrangement. From the section view of one of \nthese tubes, shown in Fig. 2, it will be observed that the grid and plate \nelements are supported by wires which in effect go straight through the\n\ntube envelope providing two independent leads to each of these ele- \nments. The filament leads are at one end only and one of these leads \nis extremely short. This unusual lead arrangement possesses a number \nof unique advantages.\n\nA typical oscillator circuit is shown in Fig. 3. Here the tube is \nmounted at the center of a half-wave Lecher system. This arrange- \nment provides a higher natural frequency circuit than that of the\n\nquarter-wave Lecher system formed by removing one set of leads. \nSince only half of the total charging current to the inter-electrode \ncapacitances flows through each set of leads, the losses due to the lead \nresistances are also reduced. In the tubes under discussion the electron \ntransit time limitation has been met by the use of extremely small \ninter-electrode spacings so that full advantage may be taken of the \nincreased frequency range.\n\nFor the purpose of confirming the above conclusion, efficiency curves \nhave been obtained on the large size tube, as shown in Fig. 1, when \noperated both single- and double-ended. The results are shown in \nFig. 4. It will be observed that the efficiencies for double-ended \noperation are always higher than for the single-ended case over the \nrange covered by the experimental data. In fact, usable outputs are \nobtained at frequencies well beyond the point where the single-ended \ntube fails to operate. The ratio of the cut-off frequencies for the two \ntubes happens to be 1.23 for the particular conditions under which \nthese data were obtained.\n\nOutput and efficiency curves for the large size tube are shown in \nFig. 5. The values of 60 watts at 300 megacycles and 40 watts at 400 \nmegacycles compare quite favorably with outputs reported from \nradiation-cooled magnetrons. When the problems of modulation and \nthe complications of the magnetron\u2019s magnetic field are considered, the \nadvantages of the negative-grid triode become more apparent. The \nimprovement in power output made possible by this departure in design \nis illustrated by the comparison plot shown in Fig. 6.\n\nThe double-lead arrangement is also responsible for an increase in the \nupper frequency limit at which stable operation as an amplifier may \nbe secured.\n\nThe primary cause for instability of the triode amplifier is the inter- \naction between the input and output circuits which results from the \nadmittance coupling. between these circuits provided by the grid-plate \ncapacitance. A second source of coupling is that caused by common \nimpedances in the two circuits in the nature of the self and mutual \ninductance of the tube leads. At moderately high frequencies this \nlatter coupling is usually of negligible importance. Stable operation is \nthus possible when suitable means are provided to compensate or \n\u2018neutralize\u2019 the admittance coupling. At ultra-high frequencies \nlead-impedance coupling can no longer be neglected. It may, of course, \nbe minimized by the use of short leads. The ultimate solution is to \nprovide independent leads for the input, output and admittance neu- \ntralizing circuits. The double-lead tube is an attempt to fulfill these \nconditions. It will be observed that the only common impedance\n\nremaining is that caused by one filament lead and that this lead is \nextremely short.\n\nIn the present investigation the method of neutralizing admittance \ncoupling has been that disclosed by H. W. Nichols in U. S. Patent\n\nFig. 4\u2014Comparison plot of output efficiency for the large tube when operated single- \nended and double-ended.\n\n1,325,879 and involves the resonating of the offending admittances at \nthe desired operating frequency so that the resulting parallel admit- \ntance is reduced to a very low value. This takes the form of an in- \nductance connected between the grid and plate of the tube and adjusted\n\nto resonate with the grid-plate capacitance. For ease of adjustment a \nsomewhat lower fixed inductance may be used and tuned by the ad- \njustment of a small variable condenser in parallel. This form of \nneutralization is commonly referred to as \u201ccoil\u201d neutralization. At \nultra-high frequencies where unavoidable inductances are already \npresent in the form of lead inductances, this \u2018\u201c\u2018coil\u2019\u2019 scheme possesses\n\nFig. 6\u2014Comparison plot of the outputs of the double-lead tubes and of commercially \navailable tubes.\n\noutstanding advantages over the more usual \u2018\u2018capacitance\u201d schemes. \nThese advantages become even more pronounced with the availability \nof the double-lead tube.\n\nVerifying this analysis, a \u2018\u2018coil-neutralized\u201d two-stage amplifier \nusing two of the largest size tubes was found to yield an output of 60 \nwatts at 144 megacycles for Class B operation. Stability, distortion, \nand band width were quite comparable to the results obtained on a\n\npentode of similar rating. A four-stage amplifier employing the inter- \nmediate tube gave comparable results and although experimental data \nare not yet available, it seems reasonable to assume that the small size \ntube will permit of stable operation as an amplifier at frequencies as \nhigh as 1000 megacycles.\n\nThe double-lead tube is therefore seen to possess a number of distinct \nadvantages, both as oscillator and as amplifier, in the frequency range \nfrom 100 megacycles to 1000 megacycles. While the ultimate limit to \nwhich such developments may be pushed is still a matter of conjure it \nseems safe to predict that the triode will be able to meet the demands of \nthe circuit designer at least for some time to come.\n\nN the paper of the above title in the January 1937 issue of the Bell \nSystem Technical Journal, an approximation which was not ex- \nplicitly pointed out was made in deriving equation (17). A note from \nMr. K. A. Norton* of the Federal Communications Commission points \nout that equation (17) does not give a reasonable result when r = 1. \nThe explanation is that two terms which are unimportant except near \nthe transmitter when the ground is a perfect dielectric were deleted. \nThe complete equation is\n\nWhen 7 = 1 by virtue of equation (13) W must equal 1/2 and accord- \ningly the first term on the right of equation (17) is 1/4. The second \n1/4 1/2 \nterm gives 1/4 + and the last term gives + (rid \nHence when 7 = 1 equation (17) gives the following relation for the\n\nThe terms added to equation (17) produce oscillations in the curves \nof Fig. 3 as shown on the following page. For any physical dielectric \nthe conductivity is not zero and the oscillations disappear at the greater \ndistances giving curves like those of the original Fig. 3.\n\nThis increases the deviation of the second factor on the right from unity \nbut if the ground is not a perfect dielectric the exponential reduces the \nsecond factor to unity at the greater distances irrespective of the\n\n* See the note at the end of \u2018\u2018 The Propagation of Radio Waves over the Surface \nof the Earth and in the Upper Atmosphere,\u201d Proc. J.R.E., 25, 1203-1236, September,\n\nThe situation in the immediate vicinity of the antenna is more \nclearly represented in Fig. 3A in which the attenuation factor is plotted \nagainst distance in wave-lengths. This allows inclusion of curves for \n\u00a2 = 1 (i.e. for the earth replaced by air) and e = \u00a9 (which is equiva- \nlent to perfectly conducting earth). Comparison of these curves with \nthe broken lines which are replotted from Fig. 2 shows that for dis-\n\nFig. 3A\u2014Variation of attenuation factor with distance in wave-lengths for trans- \nmission over a dielectric plane. For d/\\ small,\n\ntances greater than a wave-length the main effect of using the curves \nof Fig. 2 is to ignore the presence of the oscillations in the curves. For \na perfect dielectric the amplitudes of these oscillations do not decrease \nbelow + 1/e*/? even at great distances as can be seen from equation \n(19). The presence of some conductivity causes these oscillations to \nbe damped out. For example, a Q of 5 reduces the amplitudes of these \noscillations within the first four wave-lengths to a value too small to \nshow on the figure.\n\nThe second paragraph of the footnote referring to equation (17) \nshould read:\n\nwhen the value of y = (1 + 7)ATTo is substituted i in his equation (7) and the result \ndivided by 1 + 7\u00b0. The \u00a2 of this paper is equal to \u2014 \u00a2 in Wise\u2019s paper. By inter- \nchanging k; and kz in Wise\u2019s equation (7) and proceeding along parallel lines the \ncorresponding equation of DIT) = y/(1 + 7\u00b0) is found to be\n\nD 1 T 7? \nAdding these two relations gives an expression for (3 aa + q im) II, where \nII = 2(A +\n\nwhich when ge in the above equation for E and the result divided by 2B, \nwhere Eo = \u2014 240in\u00b0IEo/A, gives equation (17). Since. Eo is the inverse distance \ncomponent of the free space field, this relation for Eo follows from equation (11).\n\nRelation between Loudness and Masking.22) HARVEY FLETCHER and \nW. A. Munson. A functional relationship between the loudness of a \nsound and the degree to which it masks single frequency tones, that is, \nthe masking audiogram of the sound, is developed. A loudness- \nmasking function is determined experimentally. From this loudness- \nmasking relationship the loudness of a sound can be computed by \nsimply integrating the area under the masking audiogram plotted on a \nspecial chart. Comparisons of computed and observed loudness \nlevels are shown for a number of sounds and serve to illustrate the \nprecision to be expected from the method. Finally, the results of a \nlarge number of masking tests are given in the form of masking con- \ntours, which enable one to predict the masking audiogram of a sound \nfrom measurements of its intensity spectrum.\n\nCoupling between Parallel Earth-Return Circuits under D.-C. Tran- \nsient Conditions*\u00ae E. Goutp. In tests conducted in connection \nwith several d.-c. railway electrifications, the induced voltages re- \ncorded in paralleling communication circuits at times of short circuit \non the railway have shown marked divergences from values computed \non the basis of uniform earth resistivity and a rate of change of earth \ncurrent determined from measurements in trolley and rail circuits. \nDue to the numerous factors which might contribute to these divergen- \nces, such as non-uniform division of transient current along the tracks \nand associated return conductors, the presence of shielding conductors \nalong or near the right-of-way, etc., it was felt that a better under- \nstanding of the problem of induction under d.-c. transient conditions \ncould be obtained by experimental studies of the transient coupling \nbetween parallel earth-return circuits, free from the effects of shielding \nconductors, and with concentrated, rather than distributed, grounds. \nThe study described in this paper was undertaken for this purpose.\n\nThe locations for the tests were selected to provide a reasonably \nlarge range of earth resistivity; also, at one location it was known that \nthe earth structure departed substantially from uniformity. At each \nof these locations d.-c. transient coupling tests were performed in \nwhich transient currents, approximately of the form encountered \nduring faults on d.-c. railway electrifications, were produced in an earth- \nreturn circuit, herein referred to as the primary, and measurements \nwere made of the resultant voltages in earth-return circuits, herein \ncalled secondary circuits, parallel to and at separations from the \nprimary circuit of from 50 or 60 to 2,000 feet. In addition to the d.-c. \ntransient tests, measurements were made at each location of the steady \nstate a.-c. coupling, in magnitude and phase angle, over a range of \nfrequencies from 20 or 30 cycles to 3,200 cycles. From these a.-c. \nmeasurements the transient voltages were computed for a number of \ncases by evaluating the Fourier integral. The results of the a.-c. \ncoupling tests were useful also in helping to explain, in a general way, \nthe departures of the measured transient voltages from the voltages \ncomputed for uniform earth resistivity.\n\nThe measured transient voltages and voltages computed (1) from \nthe a.-c. coupling measurements and (2) on the basis of a uniform \nearth resistivity, are shown for several representative cases in figures \naccompanying the paper.\n\nThe Shunt-Excited Antenna. J. F. Morrison and P. H. Situ. \nThe paper describes an arrangement for exciting a vertical broadcast \nantenna with the base grounded. Construction economy results \nthrough the elimination of the base insulator, the tower lighting \nchokes, and the usual lightning protective devices. The coupling ap- \nparatus at the antenna end of the transmission line is reduced to an \nextent which may make unnecessary a separate building for its pro- \ntection. Greater freedom from interruptions resulting from static \ndischarges is expected. The performance of the design is substan- \ntially the same as that obtained from the antennas now in general use.\n\nfour feet long were used as the experimental guides. At one end of \nthese guides were launched waves having frequencies of roughly 150 \nmegacycles. The lengths of the standing waves so produced gave the \nvelocity of propagation. Other experiments utilizing a probe made up \nof short pickup wires attached to a crystal detector and meter enabled \nthe configuration of the lines of force in the wave front to be determined. \nThis was done for each of four types of waves. For certain types the \nproperties had already been predicted mathematically. For others \nthe properties were determined experimentally in advance of analysis. \nIn both cases analysis and experiment proved to be in good agreement.\n\nThe Dependence of Hearing Impairment on Sound Intensity... JOHN \nC. STEINBERG and MARK B. GARDNER. This paper discusses the \nmeasurement of hearing loss for levels of sound that were well above \nthe deafened threshold and hence were audible to the deafened person. \nIn the tests, observers having unilateral deafness, i.e., one impaired \nand one normal ear, balanced a tone heard with the deafened ear \nagainst the tone heard with the normal ear. For some persons, the \nimpaired ear heard less well than the normal ear for all sound levels. \nFor others, tones which were well above the deafened threshold were \nheard about equally well with either ear. In other words, such deaf- \nened ears tended to hear loud sounds with normal loudness. It was \nfound that this type of deafness could be represented quantitatively \non the assumption that it was due to nerve atrophy. Loudness\n\njudgments for a normal ear in the presence of noise were found to be \nsimilar to judgments by a nerve deafened ear. Relations, based on \nthe loudness properties of normal ears, have been extended to represent \nthe loudness heard by deafened ears.\n\nH. A. AFFEL, S. B. in Electrical Engineering, Massachusetts Insti- \ntute of Technology, 1914; Research Assistant in Electrical Engineering, \n1914-16. American Telephone and Telegraph Company, Engineering \nDepartment and the Department of Development and Research, \n1916-34; Bell Telephone Laboratories, 1934-. As Assistant Director \nof Transmission Development, Mr. Affel is engaged in development \nwork connected with carrier telephone and telegraph systems.\n\nRALPH Bown, M.E., 1913; M.M.E., 1915; Ph.D., 1917, Cornell \nUniversity. Captain, Signal Corps, U.S. Army, 1917-19. American \nTelephone and Telegraph Company, Department of Development and \nResearch, 1919-34; Bell Telephone Laboratories, 1934-. As Radio \nResearch Director, Dr. Bown is concerned with radio development \nproblems. He is a Past President of the Institute of Radio Engineers.\n\nCHARLES R. Burrows, B.S. in Electrical Engineering, University \nof Michigan, 1924; A.M., Columbia University, 1927; E.E., Univer- \nsity of Michigan, 1935. Research Assistant, University of Michigan, \n1922-23. Western Electric Company, Engineering Department, 1924\u2014 \n25; Bell Telephone Laboratories, Research Department, 1925-. Mr. \nBurrows has been associated continuously with radio research and is\n\nnow in charge of a group investigating the propagation of ultra-short \nwaves.\n\nJoun R. Carson, B.S., Princeton, 1907; E.E., 1909; M.S., 1912. \nAmerican Telephone and Telegraph Company, 1914-34; Bell Tele- \nphone Laboratories, 1934-. As Transmission Theory Engineer for the \nAmerican Telephone and Telegraph Company and later for the Labora- \ntories, Mr. Carson has made substantial contributions to electric \ncircuit and transmission theory and has published extensively on these \nsubjects. He is now a research mathematician.\n\nTHORNTON C. Fry, A.B., Findlay College, 1912; A.M., University of \nWisconsin, 1913; Ph.D., 1920; Instructor in mathematics, University \nof Wisconsin, 1912-16. Mathematician, Western Electric Company, \n1916-24; Bell Telephone Laboratories, since 1924. Lecturer electrical \nengineering, M.I.T., 1927; Lecturer mathematics, Princeton, 1929-30. \nDr. Fry\u2019s work in the Laboratories has been of a mathematical \ncharacter,\n\nJ.M. MANLEY, B:S. in Electrical Engineering, University of Missouri, \n1930; Bell Telephone Laboratories, 1930-. Mr. Manley has been en- \ngaged principally in theoretical studies of non-linear electrical circuits.\n\nW. P. Mason, B.S. in Electrical Engineering, University of Kansas, \n1921; M.A., Columbia University, 1924; Ph.D., 1928. Bell Telephone \nLaboratories, 1921-. Dr. Mason has been engaged in investigations \non carrier transmission systems and more recently in work on wave \ntransmission networks, both electrical and mechanical.\n\nPreRRE Mertz, A.B., Cornell University, 1918; Ph.D., 1926. \nAmerican Telephone and Telegraph Company, Department of De- \nvelopment and Research, 1919-23, 1926-34; Bell Telephone Labora- \ntories, 1934-. Dr. Mertz has been engaged in special problems in toll \ntransmission, chiefly in telephotography and television.\n\nS. O. MorGan, B.S. in Chemistry, Union College, 1922; M.A., \nPrinceton University, 1925; Ph.D., 1928. Western Electric Company, \nEngineering Department, 1922-24; Bell Telephone Laboratories, \n1927\u2014. Dr. Morgan\u2019s work has been on the relation between dielectric \nproperties and chemical composition.\n\nE. J. Murpny, B.S., University of Saskatchewan, Canada, 1918; \nMcGill University, Montreal, 1919-20; Harvard University, 1922-23. \nWestern Electric Company, Engineering Department, 1923-25; Bell \nTelephone Laboratories, 1925-. Mr. Murphy\u2019s work is largely con- \nfined to the study of the electrical properties of dielectrics.\n\nE. PETERSON, Cornell University, 1911-14; Brooklyn Polytechnic, \nE.E., 1917; Columbia, A.M., 1923; Ph.D., 1926; Electrical Testing \nLaboratories, 1915-17; Signal Corps, U. S. Army, 1917-19. Bell \nTelephone Laboratories, 1919-. Dr. Peterson\u2019s work has been largely \nin theoretical studies of carrier current apparatus.\n\nK. W. PFLEGER, A.B., Cornell University, 1921; E.E., 1923. Ameri- \ncan Telephone and Telegraph Company, Department of Development \nand Research, 1923-34; Bell Telephone Laboratories, 1934-. Mr. \nPfleger has been engaged in transmission development work, chiefly \non problems pertaining to delay equalization, delay measuring, tem- \nperature effects in loaded-cable circuits, and telegraph theory.\n\nA. L. SAMUEL, A.B., College of Emporia (Kansas), 1923; S.B. and \nS.M. in Electrical Engineering, Massachusetts Institute of Tech- \nnology, 1926. Instructor in Electrical Engineering, Massachusetts\n\nInstitute of Technology, 1926-28. Bell Telephone Laboratories, \n1928-. Mr. Samuel has been engaged in research and development \nwork on vacuum tubes.\n\nC. C. Taytor, B.S. in Electrical Engineering, Colorado College, \n1917. American Telephone and Telegraph Company, Long Lines \nDepartment, 1920-28; Department of Development and Research, \n1929-34. Bell Telephone Laboratories, 1934-. Mr. Taylor\u2019s work \nhas been concerned with radio-wire systems.\n\nL. R. WRATHALL, B.S., University of Utah, 1927; Graduate School, \n1927-28. Bell Telephone Laboratories, 1929-. Mr. Wrathall has \nbeen engaged in the study of non-linear reactances.\n\nS. B. Wricut, M.E. in Electrical Engineering, Cornell University, \n1919. Engineering Department and Department of Development and \nResearch, American Telephone and Telegraph Company, 1919-34; \nBell Telephone Laboratories, 1934-. Mr. Wright is engaged in trans- \nmission development of radio systems.", "title": "The Bell System Technical Journal 1937-10: Vol 16 Iss 4", "trim_reasons": [], "year": 1937} {"archive_ref": "sim_att-technical-journal_1959-07_38_4", "canonical_url": "https://archive.org/details/sim_att-technical-journal_1959-07_38_4", "char_count": 254097, "collection": "archive-org-bell-labs", "doc_id": 432, "document_type": "journal_issue", "id": "bella-qwen-pretrain-doc432", "record_count": 358, "release_policy_version": "hf_public_v1", "rights_status": "public_domain", "selected_extraction_backend": null, "selected_extraction_score": null, "source_family": "archive_org", "source_url": "https://archive.org/details/sim_att-technical-journal_1959-07_38_4", "split": "validation", "text": "Research Model for Time-Separation Integrated Communication \nH. B, VAUGHAN\n\nRecurrent Codes: Easily Mechanized, Burst-Correcting, Binary \nCodes D. W. HAGELBARGER\n\nRepresentation of Switching Circuits by Binary-Decision \nPrograms Cc. \u00a5.LEE 985\n\nEquilibrium Delay Distribution for One Channel with Constant \nHolding Time, Poisson Input and Random Service \nP, J. BURKE\n\nEvaluation of Solderless Wrapped Connections for Central Office \nUse 8. J, ELLIOTT\n\nH. I. ROMNETS, President, Western Electric Company \n3, B. FIsK, President, Bell Telephone Laboratories\n\nEB. J. McNEELY, Executive Vice President, American \nTelephone and Telegraph Company\n\n. M. FOSTER, 3R., Assistant Editor \n. PoLOGE, Production Editor \n. \u00ae. M\u00a5SAK, Technical Illustrations \n. N. PoPE, Circulation Manager\n\nTHE BELL SYSTEM TECHNICAL JOURNAL is published six times a year \nby the American Telephone and Telegraph Company, 195 Broadway, New York \n7, N. Y. F. BR. Kappel, President; S. Whitney Landon, Secretary; L. Chester \nMay, Treasurer. Subscriptions are accepted at $5.00 per year, Single copies $1.25 \neach. Foreign postage is $1.08 per year or 18 cents per copy. Printed in U.S.A.\n\nA new communication system concept which is an important step toward \nan all-digital telecommunication plant is discussed. A research model, \ncalled ESSEX (Experimental Solid State Exchange), which combines remote \nline concentration, time-separation switching and PCM transmission is \nintroduced to demonstrate the concept. The model, which uses solid state \ndevices, works at the speed of a full-size system.\n\nA communication system requires channels for transmission of infor- \nmation and switching arrangements to interconnect the channels. At \npresent, the transmission problem and switching problems are handled \nseparately. Transmission channels may be divided into three classes: \nspace separation, frequency separation and time separation. All have \nbeen in use for some time. Switching arrangements may be divided into \nthe same three classes.' The space-separation class includes all tele- \nphone switching systems in use today. Frequency separation systems \nhave been studied and are not economically feasible at this time. Ex- \nploratory switching systems in the time-separation class are being con- \nsidered in this country and abroad.\n\nThis paper reviews the use of time-separation techniques for trans- \nmission systems and for switching systems, points out that the avail- \nability of solid state devices has revived interest in the subject and\n\nindicates that techniques using these devices are now feasible for both \nsystems. It shows that an integrated communication system using \nthese techniques is much more attractive than a combination of sub- \nsystems using time separation and presents a research model which \ndemonstrates the technical feasibility of such an integrated system\n\nin a small group are connected over voice-frequency cable pairs to a \nsmall switching unit remote from the central switching point. This unit \nconnects them to a time-separation or multiplex channel group and con- \nverts the signals to digital form. The digital signals are transmitted and \nswitched at various locations and are reconverted to original analog form \nat another small remote switching unit, which serves another group of \nterminals, or at the originating switching unit.\n\nA laboratory model of this system has been built. It is known as \nESSEX (Experimental Solid State Exchange) and, as its name implies, \nis built of solid state devices.\n\nThe common control type of switching system has two basic sections: \n(a) the switching network for interconnecting channels and (b) the com- \nmon control section. Many proposals and experiments have been made\n\nadvantages over the slower electromechanical control systems. Electronic \ncomponents are at least one thousand times as fast as the mechanical \nones now in use. Common control systems made of such devices? time- \nshare the circuits, and thus can carry out their work with fewer devices. \nOne control unit plus one spare can handle a very large switching system, \nand it can be made so that it is sufficiently flexible to handle new services.\n\nThe development of an electronic common control system is sub- \nstantially complete. This system could be modified for use with a time- \nseparation system of the type discussed herein; therefore, it will not be \ntreated in this paper. The switching network is another story.\n\nExisting and most proposed networks are in the space-separation class. \nLarge numbers of switches are required to implement them. Substitution \nof electronic switches for electromechanical switches may afford indirect \nsaving in the control and reduce the cost of the switches, but it does not \nreduce the number of switches. Space-separation networks require many\n\nswitches or crosspoints per line. Time-separation switching networks, in \nwhich one physical path carries many conversations by time sharing, \nrequire something in the order of two switches per line. In addition, they \nrequire a few bits of memory per line to remember which switch is op- \nerated at what time interval. The switches, although fewer in number, \nmust operate much faster than those used in a space-separation network. \nPresent solid state switches are sufficiently fast that speed is no problem. \nSuch a network can now be built. And a time-separation switching net- \nwork is an important part of the research model.\n\nThe switching system mentioned above is only part of a communica- \ntion system. It may represent about one-half of the cost. The other por- \ntion of the cost is for the transmission channels. In a telephone system, \nthis is primarily copper cost, the cost of the cable pairs between sub- \nscribers and central office, and between offices. One way to reduce the \namount of cable is to locate part of the central office in small pieces near \nto groups of subscribers.\u2018 These remote pieces of the switching network \nare called line concentrators. They provide switching so that a group of \nsubscribers may share the use of cable conductors between the remote \nunit and the central switching point. The number of cable pairs required \nbetween the remote unit and the central point may be reduced by about \n80 per cent. Thus, a reorganization and dispersion of part of the switch- \ning network can reduce the amount of cable required. Line concentration \nis another important part of the research model.\n\nAdditional saving of cable conductors can be achieved by the use of \neither frequency-separation or time-separation techniques for interoffice \ntrunks. Cost savings depend on the lengths of the cable runs and the \ncost of the terminal equipment for multiplexing. The advent of solid \nstate devices is affording new opportunities for reducing the channel \nlength needed to prove in multiplexed channels in place of individual \nspace separated channels. One such method is time sharing of the cable \nconductors through the use of PCM (Pulse Code Modulation) transmis- \nsion. This is another important part of the research model.\n\nThe parts mentioned above could be all considered and used in a com- \nmunication system such as is shown in Fig. 1. In such a system voice- \nfrequency signals would be time-switched at the concentrator and then \nchanged back to voice frequency. For PCM transmission they would be \nconverted to digital signals and then back again to voice at the central \nswitching point; then again time-switched and changed back to voice, \netc. This process is quite involved and, in fact, unnecessary. It can be \nsimplified by removing all the transitions between time separation and \nspace separation except those at the ends of the system, thus producing\n\n: YOM 13N HLIMS \nYOLVYLN3DNO ONIHDLIMS 4O.LWYLN3DNOD \nNOILW \u00a5Wd3S Wu 1N3> NOILWdwd3S \nIW si } IW 4\n\na more economical system than that achieved by just building up sub- \nsystems. Such simplification leads to the system shown in Fig. 2\u2014the \nESSEX System. Voice-frequency signals from a group of subscriber lines \nare switched at a remote concentrator unit and converted to digital sig- \nnals. The digital signals are transmitted, switched at one or more central \nswitching points and handled as digital signals until they leave the sys- \ntem at another concentrator or trunkor, which is a converter for connect- \ning to voice-frequency trunks.\n\nESSEX employs all the parts mentioned above and combines them in \na manner which minimizes the amount of equipment and cable con- \nductors required and provides a uniform-quality fixed-loss path between\n\nany two voice-frequency terminals, independent of the distance and the \nnumber of switching points between them.\n\nThe quality is fixed by the characteristics of the line filters, the am- \nplitude range of the system and the noise. The voice is coded in digital \nform, and the pulses are retimed and reshaped at regular intervals. Thus, \nin the ideal case, the code at the distant end will be the same as that at \nthe transmitting end independent of distance. It follows that length of \nthe transmission path has no effect on the loss and quality, except as \nincreased length increases the probability of errors in transmission due \nto interference from external sources and to timing irregularities. ESSEX \nprovides analog-to-digital conversion as near to the subscriber as feasible \nand then operates as a digital system. In addition, the switches at the \ncentral switching point are simplified, since they handle digital signals \nonly.\n\nTime-separation techniques for transmission systems and for switching \nsystems have been under investigation for many years. The potential \nadvantages of an integrated digital communication system and increased \ndemands for various speeds of digital transmission have spurred the ef- \nforts on the present research model. The use of solid state devices makes \nthe system attractive. Such devices require less space and less power, \nand are fast enough to do the job. As the speed of the devices improves, \nmore operations may be performed with the same number of devices or \nthe same operations may be handled by fewer devices, and the picture \nwill become even more attractive.\n\nThe basic plan has a number of remote line concentrators, using time- \nseparation switching and transmission, connected at a central point in \na time- and space-separation switching network. Trunkors, which act as \nconnecting and converting units for trunks, registers, ete., are similarly\n\nYOLIVYLNSDNOD MHOMLIN YOIVYHLNSDNO \nNOlLVuvd3s SNIHDLIMS NOlivuvwd3s \n3WiL IWYLN3ZD IW\n\nconnected. Each concentrator has some switching and control circuits \nlocated at the central switching point. The switches connect the four- \nwire transmission circuits from the concentrators to other concentrators, \nto trunkors or to routes to other offices. The control circuits have a \nmemory which holds the information used to control both remote and \ncentral switches for the duration of a call. These circuits also control line \nscanning for supervision and handle programming for setting up and re- \nleasing calls. Each concentrator control unit is connected to the common \ncontrol for the office.\n\nBefore going further into the system, it will be well to mention the \nsampling and transmission action. It is a well-known fact that, if a short \ntime sample of a signal limited in frequency to x/2 eps is taken x times \nper second, transmitted and filtered, then any signal components in the \nband up to \u00ab/2 eps will be reproduced at the output of the filter.* In \nESSEX, the sampling rate has been set at 8000 per second. Thus, the \nperiod between one sample of a message and the next sample is 125 \nmicroseconds, which is called a frame. The number of channels that can \nbe inserted in a frame depends on the length of the sample and the guard \nspace between samples. In ESSEX, each channel uses a time slot of 5.2 \nmicroseconds, so 24 channels are handled in a frame. Twenty-three chan- \nnels are used for speech, and the 24th is used for supervisory functions. \nEach time slot has eight pulse positions, seven for the coded PCM \nsignal and one for other functions. Thus, the pulse repetition rate on \nthe four-wire digital transmission line is 1.536 me. The four-wire system \nwill use ordinary exchange cable pairs. Pulse regenerative repeaters are \nrequired every 6000 feet for transmitting pulses at the 1.536-me rate in \nthe case of 22-gauge paired cable. Closer repeater spacing may be re- \nquired if the noise is greater than that now anticipated.\n\nA concentrator module consists of a remote unit and a central unit, as \nshown in Fig. 3. Let us consider the remote part of the line concentrator, \nshown on the left side of the figure, which is the starting point in the \nsystem. A maximum of 255 voice-frequency lines appear as inputs, and \nthree cable pairs carry digital signals to and from the central unit. One \npair, designated S, the send pair, takes PCM signals to the central unit. \nThe second, the receive pair, R, brings PCM signals from the central \nunit. And the third, the control pair C, brings control words from the \nmemory in the central unit. Each line requires a line circuit, which con- \ntains a gate and a filter. The line circuit, a plug-in package, is the lowest-\n\nare connected to the concentrator. The ensemble of line-circuit packages \nmakes up a two-wire bilateral switching stage controlled by a selector. \nThe output of this stage is a two-wire time-separation PAM bus with \n23 time slots or channels for use as links to the central office. A time \ndiagram which may be helpful in visualizing some of the operation is \nshown on Fig. 4. The memory which controls the selection of the gates \nis located at the central point. The information from it is sent over the \ncontrol pair C as eight-bit words in each time slot. These words pass \nthrough the selector to control the line gates. Each word designates a \nline gate number (LGN) and can select one of 255 gates.\n\nThe PAM two-wire bus must be converted to a four-wire bus so that \nthe signals can be handled on a PCM basis. This conversion is accom- \nplished by a circuit called a time-division hybrid. In brief, it permits a \nsignal to pass from a line to the send bus or from a receive bus to a line, \nbut never permits a direct connection from send to receive. PAM signals \non the send bus are coded into seven-bit PCM signals and sent to the \ncentral point. Incoming PCM signals are decoded and presented as \nPAM signals to the two-wire bus and then to the voice-frequency line. \nNote that the line circuit is a passive circuit and that all the signal power \nneeded is supplied by the common receiving amplifier in the receive bus. \nTiming signals necessary for the operation of this remote unit are gen- \nerated by a local clock which is slaved to a master clock at the central \nswitching point. Since both switching control and timing control signals\n\nslave. The problems of timing and synchronizing both remote and \ncentral units will be discussed in Section 3.4\n\nThe central unit of the concentrator module shown on the right side \nof Fig. 3 is made up of digital circuitry that includes the memory to \ncontrol both remote and central switches, the central switches with their \nselector and a concentrator control unit. In addition, there is a delay \npad and servo, which is discussed in Section 3.4. As mentioned above, \nthe memory stores information which controls the operation of line gates. \nIt also stores words to control the operation of the central switches\n\nassociated with a particular concentrator unit and call progress informa- \ntion concerning the states of the calls being handled. For example, \u2018\u2018on- \nhook\u201d and \u2018off-hook\u201d conditions are recorded in this memory. The \nmemory stores 24 bits of information for each time slot or channel, \neight bits for the line gate, five bits for the central switch, eight bits for \n\u2018all progress marks, and three bits for checking. Each 24-bit word is \nread out every 125 microseconds; thus, the complete memory can be \nsearched in this period to determine which channels are busy or idle or \nfor any other pertinent information.\n\nThe central stage switches or junctor gates are simple digital AND \ngates which switch digital signals unilaterally. The switches handle low \npower, and thus the selector, which uses a five-bit input to mark one \npair of 32 pairs of switches, is rather simple. The central switches for \neach concentrator are connected to the central switches of all other \nconcentrators by junctors on a space-separation basis as in Fig. 5. Thus, \neach concentrator has access to all other concentrators, trunkors and \njunctors to other office modules over 32 separate paths in any of 23 \ntime slots. A call from one concentrator to another must use the same \ntime slot in each concentrator. The switching plan is really a four-stage \nnetwork, one stage at each remote unit and one for each central con-\n\ncentrator unit. Some blocking occurs due to the concentration to 23 \nchannels and some due to time slot mismatch. Although a remote unit \nxan handle up to 255 lines, about 115 lines, each submitting one tenth \nof an erlang, would load the 23 channels to 50 per cent of capacity. In \nthe future, new services may use lines with much lower traffic, and then \nthe large number of lines may be useful. If the call is to another module, \nthe same number of stages are used, since only one switch is made in \neach central unit. The only difference is in the length of the junctor. \nConsider a call from a concentrator to a trunkor \u2014 a dial tone connec- \ntion \u2014 and assume for the moment that there is no delay in the system. \nInformation in the memory for concentrator A opens a gate in time slot \n6 and opens the send and receive junctor gate pair 3 in the same time \nslot. Information in memory for the trunkor Z opens a gate in time slot \n6 in the trunkor and send and receive junctor gate pair 3. Information \nthen passes directly from A, to Z, and from Z, to A\u00a2 , and the operation \nis repeated 8000 times per second.\n\nAn important section of the central concentrator unit is the con- \ncentrator control, which works in cooperation with the common control. \nThe division of responsibility between concentrator control units and \ncommon control is a field for further investigation, since the present \ndivision is based on judgment with limited knowledge of the problem. \nA detailed treatment of the organization and operation of the con- \ncentrator control will be given in a future paper. A simplified diagram \nof the control section is shown on Fig. 6. The most complex part is the \nlogic which controls the generation, interpretation and modification of \n\u2018all progress marks. Some of these marks are operating orders to and \nfrom the common control. Supervisory information from the remote \nunit is held in the memory, and logical operations are performed on this\n\nanswer indications are also handled in this section. Line scanning also is \ncontrolled here.\n\nMany auxiliary functions must be performed in order to use this \ntransmission and switching system as a telephone system. Detection of \n\u201con-hook\u201d and \u201c\u2018off-hook\u201d line conditions to determine the subscriber\u2019s \nwishes is done by scanning. The central control sends out a line designa- \ntion in the 24th time slot, which is reserved for this purpose. This eight- \nbit word controls a transistor in the line package through the selector \nused to control the line gate. A combination of the pulse from the \nselector and current flowing in the subscriber\u2019s loop (\u2018\u2018off-hook\u201d\u2019 condi-\n\ntion) produces a pulse on a lead common to all such transistors. Thus, \nscanning requires little additional equipment in a time separation \nsystem. If the line is \u201coff-hook\u201d, a \u201c1\u201d is returned to central in the \neighth-bit position of the 23rd time slot on the S lead. Every fourth \nframe, a new number is sent to the remote unit, so that 255 lines are \nscanned in about one-eighth second. The result of the scan is stored in \nthe call progress mark section of the memory if action is called for. \nSwitching networks using electronic crosspoints have a limited power- \nhandling capacity; thus, it is necessary to use low-level tones. Ringing \nis done by sending tones in the voice band to actuate a tone ringer in \nthe subset.\u2019 Ringing tone in the form of PCM signals is applied through \na separate gate for each concentrator R lead, and audible ring in the \nsame PCM form is applied through a separate gate for return to the \noriginating end of the circuit (see Fig. 7). This arrangement permits \nfull access on a time-separation basis to all 23 channels. It can be shown \nthat this helps to reduce blocking. Busy tones or other tones in PCM \nform may be switched in the same way, and trunk splitting also can be\n\ntaken care of in this fashion. This simple means for applying special \ntones is one more advantage of digital time-division switching.\n\nDialing signals are \u201cin-band.\u2019\u2019 Frequency-shift dialing with one \nfrequency for \u201cmake\u201d and another for \u201cbreak\u201d is used, and a form of \nmultifrequency or pulse-coded signals may be employed. Registers con- \nnected to trunkors will be used to interpret the digits which will be \nassembled in the memory of the main common control. This is so similar \nto dialing methods in other electronic switching systems that no further \ndetail will be given here.\n\nThe synchronization of a point-to-point four-wire PCM transmission \nsystem is straightforward. A clock times the sending end, and the re- \nceiving end is slaved to it. The same operation is used in the opposite \ndirection. Synchronization between the two directions is not required. \nIn the ESSEX system, which uses two-wire switching at the remote \nterminals operating under a central common control, over-all syn- \nchronization is necessary. It is a problem; unless all switches operate \nat the proper time, chaos will reign. The transmission delay, about 7 \nmicroseconds per mile for cable pairs, further complicates the problem. \nThis problem was analyzed by Karnaugh, who has offered several solu-\n\ntions.\u2019 One of these, the use of a delay pad, was adopted for use in the \nlaboratory model.\n\nConsider the complete concentrator shown in Fig. 3, which illustrates \nthe delay-pad solution to the problem. Assume that control words are \nstored in the memory and that PCM words appear on the junctor pair, \ngoing in both directions at time 7. Just before 7, an eight-bit word is \nsent out to the remote unit and the central switch. The central switch \ncloses at + and permits the seven-bit word to go out over the R pair \nto the remote unit, so that it arrives there at + + a, where a is the \ntransmission delay. The eight-bit word on the C pair controls the line \ngate, so that it opens at r + @ and the decoded sample that arrived on \nthe R pair passes to the line. Now, in the opposite direction, a sample \nfrom the line passes to the coder and then to the S bus with some delay, \nd. The PCM representation of the sample arrives at the central switch, \nwith an additional delay, a, at the time\n\nEvery 125 microseconds after 7, the five-bit word again closes the \ncentral switch, and, if r + 2a + d = 125 microseconds, the PCM signal \nwould arrive just in time to pass through the junctor gate. However, a@ is \ndependent on the distance between the remote and central units, so the \ncondition above is not satisfied. But it can be satisfied if a variable \ndelay pad, x, is included in the send line, so that\n\nA variable-length delay line provides the necessary delay x. Each con- \ncentrator, trunkor and intermodule junctor must be padded with such \na delay to provide proper operation. Since the transmission time, a, \nvaries slightly with temperature, a servo unit on the delay line auto- \nmatically compensates for these small changes in a.\n\nThe clock at the remote unit is a erystal-controlled unit which is \nslaved to the master clock at the office module by monitoring the pulses \non the C pair. Counting circuits are used to produce timing pulses at \nsubmultiples of the clock frequency. Once every 125 microseconds, a \nframing signal is sent in the 24th time slot on the R pair to the remote \nunit. When this signal is recognized, all counting circuits are checked, \nand, if out of frame, they are reframed.\n\nThe term \u2018\u2018module\u201d has been used in some of the preceding sections. \nIt denotes a building block whose cost or complexity is significantly\n\ngreater than the cost or complexity of connecting it to the system. \n{SSEX has a hierarchy of modules. The smallest one is the line package \nused to switch voice-frequency lines selectively to a group of PAM \ntime-separated channels. It is a plug-in piece of hardware added at the \ntime a line is put into service.\n\nThe next larger module is the concentrator, including both remote and \ncentral units. It is the basic multifunction unit in the model. The central \noffice is built up of concentrators and trunkor modules and a common \ncontrol unit. The whole switching and transmission array is made by \nrunning wires between such units. The proposal is to install sockets with \njunctor wires between them and to have the office grow by plugging \nswitching units into these sockets.\n\nThe system as outlined so far permits the operation of only one switch \nin a time slot at the concentrator. For heavy intraconcentrator traffic, \nit is desirable to operate two switches simultaneously so that only one \ntime slot is required. In this case, speech is switched directly in PAM \nform and does not pass to the central point. One way to operate two \nswitches in one time slot is to provide extra line memory in the con- \ncentrator control, an extra control pair and an additional selector at the \nremote unit to control the second switch in a time slot. Such an arrange- \nment could handle a maximum of 23 simultaneous calls between 46 \ncustomers in one remote concentrator. A concentrator module with these \nadditions could then serve as a community dial office (CDO) or as a \nPBX with centralized control.\n\nThe largest module would be called the modular center. It would be \nmade up of several concentrators and trunkors and use about 30 junctor \npairs to serve between 2500 and 4000 lines, depending on the amount \nand characteristics of the traffic. Such a modular center could be located \nto minimize cable plant. Growth in an area could be handled by adding \nthese central modules. For instance, a 10,000-line office would be made \nup of four modules, as shown in Fig. 8. These units might be intercon- \nnected by four-wire PCM junctors equipped with delay pads. With the \npresent plan, each office module would have its own common control \nunit. Communication between the common control units in different \nmodules would use the eighth-bit position of each time slot. A 192 \nkilopulse per second channel is proposed for this purpose. Office modules, \ndistributed over an area, might use a single common office code, the \nsame office code for each one until 10,000 numbers are used. This would \nhelp to conserve office codes.\n\nThe use of small central modules is only one way to handle central \nswitching. Many valid arguments can be advanced to show that it is\n\nwasteful of common control equipment. There are many plans to have \none common control serve several office modules, but these are beyond \nthe scope of this paper.\n\nDigital data signals in the voice-frequency band may be handled \nthrough line circuits just as they are now handled. High-speed baseband \nsignals could be applied to the PCM channels through switches at the \noutput of the encoder, and incoming data pulses may be taken out \nthrough switches ahead of the decoder. Since each channel handles eight \nbits in a time slot, one channel will handle 64,000 bits per second. If \nhigher data rates are needed, more channels can be allocated for this \npurpose. The complete group could handle 23 X 64,000 bits per second.\n\nBroader-band analog channels may be made available by changing \nthe line package filter and by changing the sampling rate. If the address \nof a particular line terminal were stored in position n in the memory \nand again in position (n + 12) on a modulo 24 basis, the sampling rate \nfor the line would then be 2 X 8000, or 16,000 times per second. If it \nwere stored in positions n, (n + 6), (n + 12) and (n + 18) on a modulo \n24 basis, the sampling rate would then be 32,000 times per second. Thus,\n\nsampling rate may be increased, and a wider band may be provided. \nThis is another type of flexibility.\n\nTO \\ TO \nREMOTE REMOTE \nLINE MODULE | MODULE LINE \nCONCEN- | 3 CONCEN- \nTRATORS ; TRATORS\n\nThe prime objective of the experiment is to demonstrate the technical \nfeasibility of the system. Such research system experiments increase\n\nsaused by interaction of complex circuits which have been demonstrated \nindividually, and provide the stimulation to invent new circuits and \ntechniques to solve these problems.\n\nMost research systems are highly skeletonized. This one is skeletonized \nonly in the number of concentrators and trunkors. Two complete con- \ncentrators and one complete trunkor, along with a central clock, make \nup the model. Although each of these modules is capable of handling the \nmaximum number of lines or trunks, the number of operating-line \npackages is limited to 12 per unit. However, a plugboard arrangement \nis provided, so that each package may be associated with any terminal \non the selector.\n\nInitially, two partially equipped remote concentrators with a central \nmemory were connected together, with no delay between them. Each \nunit contained a two-wire PAM selective switching stage, a time- \ndivision hybrid or two-wire to four-wire converter, and synchronizing \nand timing circuits. Tests were made on this phase of the system until \nthe PCM equipment became available. In the next phase, the trans- \nmission path was opened, and PCM coding and decoding equipment \ncomplete with compressors and expandors were installed. These units \nintroduced some delay, so the delay pads were added. The latest phase \nbuilds the system up to include two complete concentrators, a complete \ntrunkor and an operator console to simulate many of the functions of \nthe common control. This gradual evolution of the model has made it \npossible for one phase of the evolution to provide most of the environ- \nment for testing the circuits added in the next phase. It is a case where \nserial construction has saved a lot of work by reducing the amount of \nequipment needed to synthesize input-output gear that would have been \nneeded to proceed in parallel on several parts at once.\n\nA layout of the laboratory model is shown in Fig. 9. The two racks \nat the left are a remote concentrator unit. The first rack contains the \nline selector, which takes the incoming serial eight bits of a word from \nthe C lead, assembles them in parallel, selects a line gate and applies a \nsampling pulse to it. A group of 12-line gates is in the upper section of \nthe rack, which also houses the plugboard that permits the interconnec-\n\ntion of any package to any one of 255 selector terminals. The outputs of \nthe gates are 23 time-separated channels on a two-wire PAM bus. This \ntwo-wire bus is connected to the second cabinet, which contains the \ntime-division hybrid, encoders, decoders, synchronizing and timing \ncircuits and other circuits common to the remote unit. The outputs from \nthe second rack are three exchange-area type 22-gauge cable pairs, which \nhandle digital signals at a 1.536-me pulse rate. These cable pairs require \na pulse regenerative repeater for each 6000 feet.\n\nA second remote unit is located in the two racks at the right side of \nthe figure.\n\nThe remote units are the only places where analog signals are handled. \nSince each of these units represents a small part of an office, the crosstalk \nproblem is simplified, because the exposure to other circuits is minimized. \nThis is an important feature in the organization of \u201csingle-wire-to- \nground\u201d switching systems.\n\nThe six racks in the center are all part of the office module. The third \nand fifth racks from the left are the control units for the two concen- \ntrators. Each one contains the delay pads, the three memory units, \ncontrol circuits and logic circuits for a remote unit.\n\nThe sixth rack is the trunkor control unit, which is much the same as \na concentrator control unit. The trunkor unit which converts from \nPCM to PAM and selectively switches voice frequency terminals for \ntrunks, registers, etc., is located in the seventh rack.\n\nThe fourth rack has room for the printed circuit cards for a central \nstage switch serving 30 concentrators or trunkors. Each card holds the \ncentral switches and selector for one concentrator. It is presently \nequipped with only three switch cards, one for each of the two con- \ncentrators and one for the trunkor.\n\nThe arrangement for the junctor wiring is shown in Fig. 10. The upper \nhalf of this rack represents the complete central switching network for a \n4000-line office module. The concentrator controls are connected by \nplugs, with only 420 wires being required to connect all 30 units, ex- \nclusive of power and clock pulses. The small size of this network demon- \nstrates a major advantage afforded by PCM switching. Since the \ncircuitry at the central module is all digital, the crosstalk in the wiring \npresents no formidable problem. The lower half of the fourth rack holds \nthe master clock and timing circuits for the office module. Care must \nbe taken in distributing timing pulses to the various control units to \nassure that timing pulses arrive at each one at the same time, plus or\n\nerate the supervisory control tones. These tones are switched, when \nneeded, to the concentrator R lead under control of call progress marks \nin its memory.\n\nA control console takes the place of the office common control. It \nprovides a visual display of calling number, called number, time slot \nnumber, ete. An operator manually performs operations on the console \nto interpret instructions from the concentrator controls and to issue \norders to them for setting up and taking down calls. The console is \nlocated in front of the group of racks and is used for testing and demon- \nstrating the system.\n\nMost of the circuitry is isochronous. Timing is furnished by a two- \nphase 1.536-me clock. Rise and fall times in the order of 50 millimicro- \nseconds are common.\n\ndiodes in conventional arrays . High-speed operation is achieved by use \nof clipping and clamping techniques, with a collector supply voltage \nmuch higher than the normal signal voltages. Since the emphasis is on \nthe system, the circuits are not necessarily minimal. They are assembled \non 5 X 8-inch wiring boards, which plug into sockets for convenience \nin testing and replacement. The boards or packages contain groups of \nbasic building blocks, such as diode logic units, flip-flops, shift register \nstages, pulse amplifiers and blocking oscillators. The laboratory model \nuses about 4000 transistors and 12,000. diodes.\n\nMany unifunction circuits that probably arouse curiosity have been \nmentioned previously. The description of these would surely drag this \npaper too far into detail. It is planned to treat these details in two \nadditional papers. However, it is unfair to leave the reader completely \nup in the air, so a few words are in order about some of these circuits.\n\nhas been published.\u00ae The time-division hybrid, a result of this experi- \nment, is a circuit which permits a sample from a line gate to be passed \nto the \u201csend\u201d bus, held, stretched for coding, and then removed by a \nclamp so that there is no inter-time-slot crosstalk. Just after that sample \npasses through the common \u201csend\u201d gate and that gate is blocked, a \ncommon \u201creceive\u201d gate opens and passes an incoming PAM signal to \nthe subscriber\u2019s line filter through his line gate, which is still open. This \nPAM signal is then dissipated by the subset which terminates the line \nfilter. Approximately 123 microseconds later, the \u201csend\u201d gating opera- \ntion is repeated. It is this time difference which provides the hybrid \naction, by preventing the receive signal from passing directly to the \n\u201csend\u201d bus.\n\nThe delay pads and the memories use magnetostrictive delay lines \nwith transistor drivers and amplifiers. A typical line is shown in Fig. 12. \nThe line, a 3-mil supermendur wire, is mounted so that the delay may \nbe set manually any place in the range from a few microseconds to 125 \nmicroseconds. The servo unit for temperature correction is used only \nwith the delay pads. It provides an automatic adjustment of +1.5 \nmicroseconds.\n\nThese lines have a wider bandwidth than those in common use. The \npulses applied are baseband, and the pulse rate is 1.536 me. The total \nloss in the two transducers and the line is about 50 db. The drive circuit \nuses two transistors, and the receiving amplifier uses four transistors, \nand the line with this associated circuitry is a delay unit with zero loss.\n\nacteristics are independent of the length of line between conversion \npoints and of the number of switching points.\n\nTwo research models of remote concentrators without controllers have \nbeen operating satisfactorily for more than six months. This part of the \nmodel uses about 1800 transistors and more than 5000 diodes. The \nperformance of the components has exceeded all expectations for a \nresearch model. The model, as outlined, complete with controllers, \ntrunkor and control console, has been operating for two months with \nequally satisfactory results.\n\n\u2018acilities are available for making listening tests to compare straight- \nthrough wire connections with the PCM connection, and only a few\n\npeople have been able to detect a difference between these conditions. \nThe quantizing noise on signals seems to be unnoticeable. The low-level \nnoise resulting from the indecision of the coders during silent periods \nseems to be more bothersome than the quantizing noise on the higher \nsignals.\n\nbility for new services. It might be arranged in a modular manner to \nhandle growth, and to facilitate manufacture and installation. A full- \nsize Office of this type would require less floor space than existing electro-\n\nmechanical systems. A laboratory model using solid state devices \nthroughout has been built and tested. It demonstrates the technical \nfeasibility of the concept and gives an indication of the number of \ncomponents that might be needed for such a system.\n\nThe success of this experiment is due to the ingenuity and continuing \nefforts of D. B. James, J. D. Johannesen, M. Karnaugh, W. A. Mal- \nthaner, J. F. Miller, J. P. Runyon and many of their associates in the \nSystems Research Department of Bell Telephone Laboratories.\n\nBasic designs of the coding, decoding and companding equipment \nwere supplied by H. M. Straube, C. P. Villars and their associates in \nthe Transmission Systems Development Department.\n\n1. Joel, A. E., Electronics in Telephone Switching Systems, B.S.T.J., 35, Septem \nber 1956, p. 91. \nMalthaner, W. A. and Vaughan, H. E., An Automatic Telephone System Em \nploying Magnetic Drum Memory, Proc. I.R.E., 41, October 1953, p. 1341. \nKetchledge, R. W., An Introduction to the Bell System\u2019s First Electronic \nSwitching Office, Proc. Eastern Joint Computer Conf., December 1957. \nJoel, A. E., An Experimental Remote Controlled Line Concentrator, B.S.T.J., \n35, March 1956, p. 249. \n5. Sumner, E. E., private communication. \n). Oliver, B. M., Pierce, J. R., and Shannon, C. E., Philosophy of PCM, Proc. \nI.R.E., 36, November 1948, p. 1324. \n. Meacham, L. A., Power, J. R. and West, F., Tone Ringing and Pushbutton \nCalling, B.S.T.J., 37, March 1958, p. 339 \nKarnaugh, M., private communication. \n. James, D. B., Johannesen, J. D. and Myers, P. B., A Two-Transistor Gate for \nTime-Division Switching, I.R.E.-A.1.E.E. Transistor and Solid State Cir \ncuits Conf., February 1958.\n\nThis paper gives a theoretical treatment of several properties which de- \nscribe certain variable-length binary encodings of the sort which could be \nused for the storage or transmission of information. Some of these, such as \nthe prefix and finite delay properties, deal with the time delay with which \ncircuits can be built to decipher the encodings. The self-synchronizing prop- \nerty deals with the ability of the deciphering circuits to get in phase \nautomatically with the enciphering circuits. Exhaustive encodings have the \nproperty that all possible sequences of binary digits can occur as messages. \nAlphabetical-order encodings are those for which the alphabetical order of \nthe letters is preserved as the numerical order of the binary codes, and would \nbe of possible value for sorting of data or consultation of files or dictionaries. \nVarious theorems are proved about the relationships between these properties, \nand also about their relationship to the average number of binary digits used \nto encode each letter of the original message.\n\nTable I gives three different encodings for representing the letters of \nthe alphabet and the space symbol in binary form. These encodings \nhave several special properties which are of some interest. First, each \nis a variable-length encoding; that is, the code for each letter is a sequence \nof binary digits, but the codes assigned to different letters are not all \nrequired to consist of the same number of binary digits. The first two \nof these encodings have the prefix property; that is, no one of the codes \nis a prefix of any other code of the same encoding. This property makes \nit easy to decipher a message, since it is only necessary to look at enough \nbinary digits of the message until it agrees with one of the codes if it is \ndesired to find the first letter of the deciphered message.\n\nThe first of these encodings, called the Huffman encoding, is con- \nstructed by the method given by Huffman,' and has the property of \nbeing a minimum-redundancy encoding; that is, among all variable- \nlength binary encodings having the prefix property, this is an encoding\n\nhaving the lowest possible cost (where the cost is defined as the average \nnumber of binary digits used per letter of the original message, assuming \nthat the message is made up of letters independently chosen, each with \nthe probability given).\n\nThe second of these encodings, called the alphabetical encoding, has \nthe property that the alphabetical order of the letters corresponds to \nthe numerical binary order of the codes. Among all such alphabetical- \norder-preserving binary encodings that are of variable length and have \nthe prefix property, the one given has been constructed to have the \nlowest possible cost. It can be seen that the cost 4.1978 of the alpha- \nbetical encoding is quite close to the cost 4.1195 of the Huffman encoding, \nas compared to the cost 5 of the more conventional fixed-length encoding \nfor the same alphabet, so that the alphabetical restriction adds surpris- \ningly little expense to a variable-length encoding.\n\nPart of this paper deals with the methods of constructing such best \nalphabetical encodings, and gives some theorems concerning their cost \nand their structure. However, this paper also includes theoretical results\n\nabout various properties of variable-length binary encodings in general. \nThe cost, the prefix property and unique decipherability have already \nbeen mentioned. The exhaustive property (roughly speaking, this \npermits all infinite binary sequences to occur as encoded messages) is \nalso shown to be relevant, as is the finite delay property, which has to do \nwith the amount of delay which must take place between receiving and \ndeciphering the enciphered message. Various theorems are proved con- \ncerning the relationships of these properties to each other and to other \nproperties. Some of these properties have also been considered by other \nauthors,! ?:3-4.5.6\n\nOne property of special interest is the ability of certain variable-length \nencodings (but not of fixed-length encodings) to automatically syn- \nchronize the deciphering circuit with the enciphering circuit. This self- \nsynchronizing property, while it has been previously mentioned, is a \nlittle-known property which might have practical significance in that it \nwould permit binary deciphering machines using variable-length encod- \nings to be built without requiring any special synchronizing circuits or \nsynchronizing pulses, such as are needed for fixed-length encodings. \nThus, there may be cases where (despite some present opinions to the \ncontrary) variable-length encodings lend themselves to simpler instru- \nmentation than fixed-length encodings.\n\nSince the probabilities given in Table I are derived from one of the \ntables of frequencies of letters in English text,\u2019 the encoding given \nshould be reasonably efficient for encoding English words or phrases. \nThe alphabetical property, together with the prefix property, implies \nthat two such words or phrases could be compared for alphabetical\n\norder merely by putting the two entire phrases into a simple comparison\n\ncircuit of the kind which would be used to compare binary numbers. If \nthe two phrases begin with the same sequence of letters, the correspond- \ning parts of their enciphered form would agree, and the outcome of the \nbinary comparison would be determined by the comparison between \nthe two binary codes corresponding to the first pair of letters which \ndisagree.\n\nPlacing the space symbol before the letter A of the alphabet corre- \nsponds to the usual convention governing the filing of multiple-word \nentries in alphabetical order, although if it were desired also to include \npunctuation marks or numerals in the alphabet, the conventions are not \nso universal, and might not be of the sort which can easily be expressed \nin a binary encoding.\n\nAn alphabetical encoding might be used as a means of saving memory \nspace needed for names or other alphabetical data that are to be sorted\n\ninto alphabetical order on a data-processing machine or are to be stored \nin a file in alphabetical order. Similarly, it might be used for the words of \na dictionary as a part of a language-translating machine, if it were \ndesired to preserve the conventional alphabetical order of dictionaries. \nIn addition to possible savings of memory space, it might be used to find \nentries in such a dictionary more quickly. Since the low redundancy of \nthis encoding causes the digits 0 and 1 to be used with more nearly equal \nfrequency and more nearly independently than in a fixed-length encod- \ning, the binary numerical value associated with each word would increase \nmore nearly as a linear function of distance progressed through the \ndictionary; hence, instead of searching for a given word by the method \nof successively halving the interval in which it is known to lie, linear \ninterpolation (or some rough approximation to it which might be done \nby a simpler circuit) could be used to speed up convergence. However, \nfor uses such as mentioned here, the particular alphabetical encoding \ngiven in Table I is not necessarily the optimum, since the frequencies of \noccurrence of letters in names or in dictionary entries are undoubtedly \ndifferent than they are in connected English text. However, the methods \ngiven in this paper would enable such an encoding to be obtained for \nany given probability distribution.\n\nWe will use the word /etter to refer to any symbol of some designated \nlist, including even the space symbol of Table I. By an alphabet we will \nmean a set of letters. We will usually require each member of an alphabet \nto have associated with it a probability of occurrence, and we will also \nusually require that some linear ordering relationship (which we will\n\ncall alphabetical order) be defined for the letters of this alphabet. So that\n\nwe may call any subset of the letters of an alphabet a subalphabet, and \nmay keep the same ordering and the same probabilities, we will require \nonly that the sum of the probabilities be less than or equal to one. All \nof the alphabets considered in this paper have only a finite number n \nof letters, but it might be advisable to allow countably infinite alphabets \nin certain further theoretical extensions of this subject.\n\n- which extends infinitely only into the future, not into the past. We \nwill consider a source which generates messages in which successive \nletters occur independently and with the given probabilities. However, \nin case the sum of the probabilities is less than one, we may imagine that \nthe probabilities are proportionately increased just enough that their \nsum becomes one, so that the associated source is more realistic.\n\nWe distinguish between code and encoding, both of which are often \nvalled codes by other writers. A code is a finite sequence of binary digits.\n\nAn encoding is a way of associating (or more formally, a function C \nwhich associates) a code C; with each letter L; of an alphabet.\n\nThe operation of enciphering (elsewhere often called encoding) con- \nstructs a sequence of binary digits which is made up of the code for the \nfirst letter of the message, followed immediately by the code for the \nsecond letter of the message, etc. Any message then produces a sequence\n\nof binary digits called the enciphered message. Any machine or circuit \nwhich does the operation of enciphering is called an enciphering machine \nor an enctphering circuit. The enciphered message of a finite message is \nobviously always finite.\n\nAn encoding will be said to be uniquely decipherable if, for each finite \nenciphered message, there exists exactly one original message which \ncould have produced it. If an encoding is uniquely decipherable, then \nthere is obviously a procedure for deciphering any finite enciphered \nmessage (by enumeration, for instance), and any machine or circuit \ncapable of doing this will be called a deciphering machine or a deciphering \ncircuit.\n\nFollowing Huffman,' we define a prefix of any sequence # of binary \ndigits to be any finite sequence which is either itself or is obtainable \nby deleting all of the digits after a given point of &. For example, the \nprefixes of 10110 are 10110, 1011, 101, 10, 1, and the null sequence, \nwhich has no digits. We will say that an encoding C has the prefix \nproperty if no code of C is a prefix of any other code of C.\n\nBy a presumed message we will mean a finite or infinite sequence \u00ae \nof binary digits such that every prefix of @ is a prefix of the enciphered \nform of some message. Then, at any given time while a presumed message \nis being sent into a deciphering machine, it is indistinguishable from a \nmessage, so it makes sense to allow presumed messages as well as mes- \nsages to be the class of sequences which can be sent into a deciphering \nmachine.\n\nConsider a discrete source S which uses the alphabet: space, A, B, \n--+ , Z (any other linearly ordered alphabet will also serve). An encoding \nof blocks of N letters into binary sequences will be called an alphabetical \nencoding if it is uniquely decipherable and the codes for the blocks in \nalphabetical (dictionary) order are themselves in numerical order. Here \nthe codes are imagined to be prefixed by binary points to convert them \ninto numbers in binary form. The alphabetical encoding of Table I is a\n\ncase with N = 1. It is a natural question to ask if a restriction to alpha- \nbetical encodings may not be severe for some sources S. In particular, \nare the results of Shannon\u2019s encoding theorem (Ref. 8, Theorem 9) \nstill obtainable with alphabetical encodings?\n\nShannon proved that the output of a discrete source having entropy \nH bits per character can be enciphered in a uniquely decipherable manner \ninto a sequence of binary digits so that the average number of digits \nused per character exceeds H by an arbitrarily small amount. Shannon\u2019s \nconstruction encodes blocks of N source characters into binary sequences, \nusing a cost (average number of binary digits per character) Hy which \nsatisfies\n\nHere, NGy is Shannon\u2019s notation for the information contained in a \nblock of N characters produced by the source; i.e.,\n\nNGy = \u2014 >, p; log pi, (2) \n1 \nin which the p; are the N-gram probabilities of the source. Then, since\n\nfollows from (1). Since NGy must be a lower bound on the average \nnumber of digits used to encode a block of N characters by any means \nwhatever, (1) shows that Shannon\u2019s construction is not far from the \nbest possible one for block encoding. We now give a similar theorem \nfor alphabetical encoding.\n\nTheorem 1: Let S be a source producing messages which may be ordered \n(alphabetically). Let Gy be computed from the N-gram probabilities p; of \nS by (2). There exists a uniquely decipherable alphabetical encoding of \nblocks of N characters of S into sequences of binary digits for which the \ncost, Hy , satisfies\n\nBy picking N large enough, Hy may be made arbitrarily close to the entropy \nH of S in bits per character.\n\nProof: The proof is adapted from Shannon\u2019s\u2019 proof of his Theorem 9. \nLet all possible blocks of N source characters be listed in alphabetical \norder, and let p; denote the probability of the ith block in the list (recall\n\nthat Shannon lists his blocks in order of probability rather than alpha- \nbetically). Let m; be the integer for which \ntoe. 2. \nAlso, let numbers A; , Az, A3, \u00ab++ be defined by \nA, = 2\n\nWe now construct an alphabetical encoding. The code for the ith block \nwill be the first m; + 1 digits of the binary expansion of the number A; . \nIn Shannon\u2019s encoding this same block has a code formed by expanding \na (different) number to m; places. Then our scheme uses only one more \ndigit than does Shannon\u2019s for each block, NHy = NH, + 1, and (4) \nfollows from (1). It remains now to show that our encoding is uniquely \ndecipherable; i.e., that the sequence of letters generated by S may be \nreconstructed from the binary digits.\n\nIt suffices to prove that our construction produces a list of codes which \nhave the prefix property. Then the enciphered message produced by \neach block of N letters may be deciphered as soon as all its digits have \nbeen received.\n\nTo prove that our list has the prefix property, consider any two blocks \nof letters, say the 7th and the jth with i < j. By (5),\n\nIf pi S p;, then m; = m;; but, by (6), the jth code cannot be identically \nthe same as the first 1 + m; places of the 7th code. Similarly, if p; = p,; \nthe ith code cannot be a prefix of the jth code. Thus, the prefix property,\n\nExcept in the case of an alphabet having only one letter, the prefix \nproperty is sufficient to insure unique decipherability, but it is not \nnecessary. For example, the list 0, 01, 11 does not have the prefix prop- \nerty; still it could be used. In a received message 00001111 --- there \nwould be no doubt about the first three 0\u2019s, and the fourth 0 would be \nrecognized as 01 or not according to whether an odd or even number of \n1\u2019s followed it.\n\nHowever, by a best alphabetical encoding we will mean an encoding \nwhich has the lowest cost among all alphabetical encodings which have \nthe prefix property. This insistence upon the prefix property will make \nit possible for us to prove Theorems 2 through 5 and give constructive \nmethods for finding these best alphabetical encodings.\n\ndeleting some digits which are obviously not needed. For example, the \nfirst few codes are those listed in Table II. Clearly the code 00110 for A \nis too long. As soon as the prefix 001 is received, A is the only possibility. \nThe final digits 10 may be deleted. Similarly, the other codes may be \nshortened, as indicated in Table II, until no code can lose a final digit \nwithout becoming a prefix for some other code. The cost is thereby \nreduced to 4.44 digits per character.\n\nA different encoding is obtainable using the same sort of construction \nbut with\n\nA; = 2 ae. \nThe same proof can be used, since (6) still holds. Since the code lengths \nare again the numbers m; + 1, the new encoding will have the same cost. \nThe numbers A; can now be computed with ease directly in the binary \nsystem, and much of the arithmetic needed for the first construction \nmay be avoided. However, the kind of shortening used in Table II does\n\nnot work as well with the new encoding. All codes (as numbers) are now \nless than\n\ni \nThis number need not be near 1 (typically it is about 2). The codes are \nthen cramped together in a range smaller than (0,1) and cannot be \nshortened as much. For the case of the English source with N = 1, the \nnew encoding can only be shortened to cost 5.02 digits per letter.\n\nWe will describe these results in terms of encoding single letters into \nbinary form; however, it is to be understood that blocks of N letters \nmay always be considered the single letters of a larger alphabet. By a \nprefix set of an encoding we will mean the set of all letters which have \ncodes beginning with a given prefix. For example, in the Huffman encod- \ning of Table I the prefix 011 has the prefix set consisting of letters B, G, \nJ, K, P, Q, V, X and Z. In an alphabetical encoding every prefix set \nmust consist of all letters lying between some two fixed letters in the \nalphabet.\n\nTheorem 2: In a best alphabetical encoding let S be a prefix set for a \nprefia m. Construct a shorter alphabet by replacing the letters of S by a \nsingle new letter, L', occupying their place in alphabetical order and having \nas its probability the sum of their probabilities. A best encoding of the new \nalphabet gives L' the code x and gives every other letter its old code.\n\nProof: Let C(L) denote the code for letter L in the original best \nencoding. Suppose, contrary to the theorem, that the new problem had \na better solution in which L, L' had codes C'(L) and C'(L'). One would \nthen obtain a better solution of the original problem by encoding L into \nC'(L). The code for a letter M in the prefix class would be C(M) with \nthe prefix + changed to C'(L').\n\nnonalphabetical encodings. The two letters of lowest probability must \nform a prefix set, and his result is used again and again, until there are \nonly two letters left and the problem is solved. When the encoding must \nbe alphabetical one cannot always find a prefix set easily. Some results \nin this direction are given by the following theorems. The symbols\n\nL, , Ly, +--+ are used to represent the letters of the alphabet in order; \nPi, Po, -*: Will be their probabilities; C(1:), C(Le2), --+ will be their \ncodes in the encoding C and N,, Ne, \u00ab++ will be the numbers of binary\n\ndigits in their codes. Also, if \u00ae is any code or any prefix, N(#) will be \nused to represent the number of binary digits in \u00ae.\n\nAn encoding will be said to be exhaustive if it encodes an alphabet of \ntwo or more letters in a uniquely decipherable manner and, for every \ninfinite sequence x = 2,22; --- of binary digits, there is some message \nwhich can be enciphered as x; or if it encodes an alphabet of one letter \nby using the null sequence.\n\nProof: Consider an encoding of an alphabet having two or more \nletters which is alphabetical and has the prefix property, but is not \nexhaustive. It will be shown that it is not a best encoding. Let x be an \ninfinite sequence of binary digits such that no message can be encoded \nas x. If any code of the encoding is a prefix of x, remove it from x, and, \nafter a finite number of repetitions of this process, an x will be obtained \nwhich has no one of the codes for a prefix. Let @ be the greatest prefix of \nx which is also a prefix of any one of the codes. Let C; be some code of \nwhich # is a prefix. We will use #0 to represent the sequence \u00a9 followed \nby 0. Then either 60 is a prefix of C; and #1 is a prefix of x, and #1 is \nnot a prefix of any code of this encoding; or else #1 is a prefix of C; and \n0 is a prefix of 2, and \u00a30 is not a prefix of any code of this encoding. \nWithout loss of generality, we assume the second one of these alterna- \ntives. Then consider the new encoding which agrees with the old one \nfor all codes not having \u00ae as a prefix, but which has a code 4 in place \nof each code of the form 16. The new encoding has a lower cost than \nthe old one, is still alphabetical and still has the prefix property. Hence \nthe original encoding was not a best alphabetical encoding.\n\nLemma 1: Let x be a prefix. In a best alphabetical encoding, if there is a \ncode with prefix 10 there is one with prefix w1. Conversely, if there is a \ncode with prefix 1, there is one with prefix 10.\n\nProof: If +O is a prefix, then by Theorem 3 the sequence 7111 \nmust have some code C; as a prefix. But by the prefix property, C; \ncannot be a prefix of 70; hence, C; has prefix 71. The converse is proved \nsimilarly.\n\nLemma 2: Let La be the letter of lowest probability. In a best alphabetical \nencoding, La , together with one of Lay; or La, must form a prefix set.\n\nProof: Suppose C(L,) ends in 0, say C(La) = 20, where mw stands for \nsome prefix. By Lemma 1, wl is a prefix of C(Lay1). If Chay) = xl, \nwe have the desired result. If not, +10 must be a prefix of C(La4:). \nBy Lemma | there exist codes with prefix 11. A better encoding (and \nhence a contradiction) may be had by the following changes: Lengthen \nC(La) from 70 to 700. Change all codes of the form rl0y to r01y. Shorten \nall codes of the form rlly to rly. Since the last change applies to at \nleast one letter (of higher probability than L,), there is a net decrease \nin cost.\n\nThe proof in the other case [(C(L.) ending in 1) is similar. If, as is the \ncase of the probabilities of Table I, the least probable letter is at the \nend of the alphabet, then this letter has only one neighboring letter and \nmust form a prefix set with it. Thus, as a first step in Table I, we can \nwrite\n\nwhere 7(Y,Z) is some unknown prefix. Then, using Theorem 2, the prob- \nlem is reduced to an encoding for a 26-letter alphabet in which Y and Z \nhave been replaced by a single letter L(Y,Z) of probability 0.0169. \nWhen this new problem is solved, #(Y,Z) will be found as the code for \nL(Y,Z). The new least probable letter is J or Q, both with the same \nprobability 0.0008; J, for example, can be in a prefix set with either I \nor K, but Lemma 2 gives no clue for deciding which one. One might \nhope that one can always pick the less probable neighbor, KX in this \ncase. However, it is easy to find counter-examples which disprove this \nconjecture. A weaker, but true, theorem is the following one. \nTheorem 4: Let La be the letter of lowest probability. Suppose that\n\nThen La and Lo, must form a prefix set in any best alphabetical encoding. \nSimilarly, if Par > Pa + Pasi, La and Lay, must form a prefix set. \nProof: Suppose (7) holds but that L, and L,_; do not form a prefix \nset. Then, by Lemma 2, L, and La, form a prefix set. The codes for L, \nand La,; must be of the form \nC(L.) = 20,\n\nFor, if C(Le-1) were p0, Lemma 1 would show that some code has prefix \npl and hence must stand for a letter between L,-; and ZL, in the alpha- \nbetical order, an impossibility. Lemma 1 now shows that some other \nletters have prefix pO.\n\nWe consider two cases determined by the numbers N (7) and N(p) of \ndigits in and p:\n\nCase 1 \u2014 N(mr) < N(p). An improved encoding can be made by changing \nC(L,) from 70 to 701, C(Le_1) from pl to 700 and all codes of the form \np0w to py. The last change, a shortening, affects some codes and so off- \nsets the lengthening of the least probable code.\n\nCase 2\u2014N(p) S N(x). An improvement can be made by shortening \nC(Las1) from 1 to x while changing C(L.) from 70 to pll and C(L._;) \nfrom pl to p10. That there is a net decrease in cost follows from (7).\n\nApplying Theorem 4 to our reduced problem of Table I, we obtain \nfurther reductions, producing new letters L(J,K) and L(P,Q) with prob- \nabilities 0.0057 and 0.0160. Now the lowest-probability letter has become \nX, and we need another kind of theorem.\n\nTheorem 5: If L; and L; (i < j) are two letters both of probability ex- \nceeding Pisi + Pisa +... + pj-r, then the intervening letters Lisi , Lix2 ,\n\nProof: Let denote the greatest common prefix of C(L;) and C(L;), \ni.e., a prefix such that 70 is a prefix of C(L,) while 71 is a prefix of C(L;). \nThe intervening letters have either 70 or wl as prefixes. Supposing that \nthere are some intervening letters with prefix 70, we assert that the \nintervening letters with prefix 0 form a prefix set. To prove this assertion, \nlet the intervening letters with prefix 70 be Lisi, ...Z., where C(L.41) \nhas prefix rl. Let 0p denote the greatest common prefix of C(L;) and \nC(L,). Then C(L,) must have prefix 70p1; otherwise, by Lemma 1, L.4; \nwould have prefix w0p, and hence 70. Also, C(L;) has prefix 20p0; other- \nwise, t0p1 would be a greater common prefix than 70p. The assertion re- \nquires only that we prove that C(Li,:) has prefix w0p1, for then the \nletters in question and no others have this prefix. If, on the contrary, \nC(Li41) has prefix 70p0, find the greatest common prefix r0p0c such \nthat 20p0c0 is a prefix of C(L;) and r0p0c1 is a prefix of C(Lis1). Now \nshorten all codes of the form x0p0cOy to rO0p0cy and lengthen all \nother codes r0py to r0ply. The shortened codes include the one for \nL;, which has more probability than the total probability of all the\n\nlengthened codes. The assertion is now proved, and likewise intervening \nletters with prefix 1 form a prefix set. \nBy our two assertions, each of C(Li4,:), ..., C(L;-1) has one of two\n\nprefixes, which we may call x0p1 and 170, while x0p0 is a prefix of \nC(L,) and wir is a prefix of C(L;). Again, one proves the theorem by \nmaking changes which put the intervening letters into a single prefix \nset. There are two cases:\n\nCase 1 \u2014 N(r0p) S N(rlr). Lengthen codes r0ply to r0p10y. Change \ncodes r170y to r0p11y. Shorten all codes rlrly to rlry. The intervening \nletters now form a prefix set with prefix r0p1 and the new encoding has \nsmaller cost.\n\nCase 2\u2014 N(rlr) S N(x0p). By changes similar to those of Case 1, one \nmay reduce the cost by making the intervening letters into a prefix set \nwith prefix 170.\n\nApplying Theorem 5 to Table I, we now recognize new prefix sets and \nreduce the problem by introducing new letters L(F,G) and L(U,V, \nW,X,Y,Z) of probabilities 0.0360 and 0.0668. Now L(J,K) becomes \nthe least probable letter, Theorem 4 applies, and we form a new letter \nL(J,K,L) of probability 0.0378. Next, Theorem 4 applies to letter B, and \nwe form a new letter L(B,C) of probability 0.0345. Again we are at an \nimpasse.\n\nTheorem 6: If px < ps, then L, and Lz form a prefix set in any best \nalphabetical encoding. Similarly, if L, is the last letter of the alphabet, \nL,-. and L,, must form a prefix set if Pa < Dn\u20142 .\n\nProof: If p, < p3 and L, and L, are not a prefix set, then C(1,), C(L2) \nand C(L3) may be shown to have the forms 70, rlp0 and rlply. Then \none could improve the encoding by changing C(L,) to 700, C(L2) to \n01 and all codes rlply to rlpy.\n\nThis theorem provides no further reduction of our example. Note, \nhowever, that it might have been applied following the creation of \nL(Y,Z) to prove that X,Y,Z, forms a prefix set. This information is \nhelpful when we must add the final digits to the prefix r(U,V, ..., Z) \nto form the codes for U, ..., Z. Using Huffman\u2019s encoding method, we \nfind, disregarding questions of alphabetical order, the best way of en- \ncoding four letters which have probabilities in the same ratio as our \nletters U,V,W and L(X,Y,Z). The solution gives each letter two digits. \nThen, an equally good alphabetical encoding gives these letters the code \n00, 01, 10, 11. We now know parts of the codes souglit, as summarized \nin Table III. The unknown prefixes 7(B,C), ... are'to be determined\n\nby finding a best alphabetical encoding of the 17-letier alphabet listed \nin Table IV.\n\nAgain we might try a Huffman encoding for Table IV. However, we \nnote in advance that M and L(P,Q) are much less probable than their \nneighbors. Then a Huffman encoding will give these letters such long\n\ncodes that there will be no alphabetical encoding which uses the same \nlength codes for every letter. To circumvent this difficulty we use Lemma \n2, first on L(P,Q) and next on M, and conclude that L(P,Q) must form \na prefix set with O or R and M must form a prefix set with L(J,K,L) or \nN. There are then four new alphabets to consider, and we have con- \nstructed Huffman encodings for each one. The one with smallest cost \nis the one in which J,K,L,M and P,Q,R were made into new letters. \nThe numbers of digits for the letters in Table IV which this Huffman \nencoding required are listed. We next look for an alphabetical encoding\n\nexists, and so we obtain the best alphabetical encoding shown in Table \nI. It must be admitted that we were somewhat lucky to be able to reduce \nthe problem to one in which one of the best possible encodings, disre- \ngarding alphabetical order, includes an alphabetical encoding. Undoubt- \nedly, minor changes in the probabilities in Table I might make the prob- \nlem much harder. In the next section we give an encoding method which \nwill apply in all cases.\n\nThe method which will be used in general builds up the best alpha- \nbetical encoding for the entire alphabet by first making best alphabetical \nencodings for certain subalphabets. In particular, the subalphabets \nwhich will be considered will be only those which might form a prefix \nset in some alphabetical binary encoding of the whole alphabet. Since \nonly those sets of letters consisting exactly of all those letters which lie \nbetween some pair of letters can serve as a prefix set, we will call such a \nset an allowable subalphabet.\n\nWe will denote the allowable subalphabet consisting of all of those \nletters which follow L; in the alphabet (including L; itself) and which \nprecede L; (again including L; itself) by (L; , L;). When referring to the \nordinary English alphabet of Table I we will use the symbol * for the \nspace symbol. Thus, ( # ,B) will be the subalphabet containing the three \nsymbols space, A and B, and (A,A) will be used to denote the subalpha- \nbet containing only the letter A.\n\nIf it were desired to find an optimum encoding satisfying certain kinds \nof restrictions other than the alphabetical one, different allowable sub- \nalphabets could be used, with the rest of the algorithm remaining analo- \ngous. This method of building up an encoding by combining encodings \nfor subalphabets is analogous to the method used by Huffman,' except \nthat he was able to organize his algorithms such that no subalphabets \nwere used except those which actually occurred as prefix sets in his \nfinal encoding. However, we consider all allowable subalphabets, in- \ncluding some which are not actually used as part of the final encoding.\n\nThe algorithm to be described takes place in n stages, where n is the \nnumber of letters in the alphabet. At the kth stage, the best alphabetical \nbinary encoding for each k-letter allowable subalphabet will be con- \nstructed and its partial cost will be computed. For k = 1, each subalpha- \nbet of the form (L; ,L,) will be encoded by the trivial encoding which \nencodes L; with the null sequence; it has cost 0, since the number of \ndigits in the null sequence is zero. For k = 2, each subalphabet of the \nform (L; , Li,1) will be encoded by letting the code for L; be 0 and the \ncode for Lis; be 1. The partial cost of this encoding is p; + pi4i:. In \ngeneral, the kth stage of the algorithm, in which it is desired to find the \nbest alphabetical binary encoding for each subalphabet of the form \n(L; ,Lisx-1) and its partial cost, proceeds by making use of the codes \nand the partial costs computed in the previous stages.\n\nFor each j between i + 1 and i + k \u2014 1, we ean define a binary \nalphabetical encoding as follows: Let C; , Cis, , . . . Cj-1 be the codes for \nL;, Lisa, ... Lj-1 given by the (previously constructed) best alphabeti- \ncal encoding for (1; ,L;-:), and let C; , Cas eee Fe be the codes for \nLj, Lisi, ..., Lise given by the (previously constructed) best alpha- \nbetical encoding for (L; , Li,x-1). Then the new encoding for L; , Lix:,\n\n, gay Eyy Daa, \u00ab+5 Deeps a Be Oi, Clas, 6.4 Oa, 1, \n1Cs41, ..., 1044-1. Such an encoding can be defined for each j, and \nthe encoding is exhaustive. It follows from Theorem 2 that the best \nencoding for this subalphabet is given by one of the k \u2014 1 such encod- \nings which can be obtained for the k \u2014 1 different values of 7. The \npartial cost of such an encoding made up out of two subencodings is the \nsum of the partial costs of the two subencodings plus p; + piyi +... + \nPisze-1- To perform the algorithm it will not be necessary to construct \nall of these encodings, but only to compute enough to decide which one \nof the k \u2014 1 different encodings has the lowest partial cost. This is \ndone by taking the sums of each of the k \u2014 1 pairs of partial costs of \nsubencodings and constructing the best encoding only.\n\nAfter the kth stage of this algorithm has been completed for k = 1, \n2,..., , the final encoding obtained is the best alphabetical encoding \nfor the entire original alphabet, and the final partial cost obtained is the \ncost of this best alphabetical encoding.\n\nIf the above algorithm were performed on a digital computer, the \nlength of time required to do the calculation would be proportional to \nn*. The innermost inductive loop of the computer program would per- \nform the operation mentioned above of computing sums of pairs of\n\nsince there are n \u2014 (k \u2014 1) different allowable subalphabets to be en- \ncoded in the kth stage, there are (k \u2014 1) [n \u2014 (k \u2014 1)] steps to be done \nin the kth stage. To find the total number of operations done in all of \nthe stages, we sum, and find that\n\nWe have already shown (Theorem 3) that every best alphabetical \nencoding is exhaustive. Another reason for considering exhaustive en- \ncodings to be of some general interest is given by the following theorem.\n\nProof: We prove by induction that each of the encodings for prefix \nsets arrived at during the steps of the algorithm of Huffman! is an ex- \nhaustive encoding. If this holds for the first k encodings constructed \nduring this algorithm, consider the prefix set L encoded at the (k + 1)th \nstep. Let \u00ab = ax rer; ... be any infinite sequence of binary digits. It \nsuffices to show that there is some letter whose code is a prefix of x. \nThe set L was made by combining two previous prefix sets of letters, \nL' and L\u201d\u2019, and it was encoded by prefixing the codes from their previous \nencodings by 0 and 1 respectively. Let L\u2019 be the set whose codes were \nprefixed by z, . Then if L\u2019 is a single letter, x, is its code, and hence its\n\ncode is a prefix of x. But if L\u2019 is a prefix set, then its previous encoding \nis exhaustive by inductive hypothesis, and hence there is a letter L\u2019\u201d\u2019\n\nwhose previous code is a prefix of xar3.... Then the new code for L \nis a prefix of x.\n\nSeveral of the properties of exhaustive encodings will be considered, \nsince both the Huffman encoding and the best alphabetical encoding \nare exhaustive, and it seems likely that exhaustive encodings might \narise from other types of optimizing problems. For instance, the short- \nening procedure used in Table II was essentially a way of making the \nencoding more nearly exhaustive.\n\nLemma 3: Whenever an encoding C has the property that for any infinite \nsequence & = 2X4XQt3... there is a code of C which is a prefix of x, then\n\nProof: Consider the set P of all finite sequences x having length exactly \nk, where k is some fixed integer longer than the longest code of C. Then \nthe property assumed in the hypothesis implies that each element of P \nhas at least one of the codes for a prefix. But P has exactly 2\u2018 elements, \nand for each code of length N; there are 2\u201c** elements of P of which \nit is a prefix. Hence,\n\nequivalent to having one of the two codes be a prefix of the other. \nTheorem 8: Every exhaustive binary encoding has the prefix property and\n\nProof: By Lemma 8 and the definition of exhaustive, (8) holds, but, \nby MeMillan,* unique decipherability implies\n\nThen we combine (8) and (10) to obtain (9). But, by Lemma 3, this im- \nplies the prefix property.\n\nLemma 4: For any exhaustive encoding of an alphabet, and any prefix \n& of this encoding, the new encoding of the prefix-set subalphabet which as- \nsociates the new code @ with each letter whose original code was 6 is an \nexhaustive encoding of this subalphabet.\n\nProof: Given any x, to find a letter whose new code is a prefix of \u00ab we \nconsider the letter LZ whose original code was a prefix of @x. Then, by \nthe prefix property, the original code of L cannot be a prefix of &, and \nthus the original code of L is of the form 6. Hence, L is in the subalpha- \nbet, its new code is 6, and @ is a prefix of \u00ab. To complete the proof that \nthe new encoding is exhaustive, note that it has the prefix property be- \ncause the original encoding does. Hence, the new encoding is either the \ntrivial encoding (of a one-letter alphabet) or is uniquely decipherable.\n\nLemma 5: For any exhaustive binary encoding of an alphabet having \nn letters, the total number of prefixes is 2n \u2014 1.\n\nLemma 6: In any exhaustive binary encoding of an alphabet having \nn letters, none of the codes consist of more than n \u2014 1 digits.\n\nTheorem 9: The cost of the Huffman encoding of an alphabet is a con- \ntinuous function of the probabilities of the letters.\n\nTheorem 10: The cost of the best alphabetical encoding of an alphabet is \na continuous function of the probabilities of the letters.\n\nThe last two theorems will be proved together, enclosing in parentheses \nthe changes which convert the proof of Theorem 9 into a proof for Theo- \nrem 10. In fact, what will be proved are the slightly stronger theorems: \nFor two alphabets A and A* having the same n letters, if p; is the prob- \nability of the ith letter of A, p;* is the probability of the 7th letter of A*, \nand if k and k* are the costs of the Huffman encoding (best alphabetical \nencoding) for A and A*, then\n\nIf we let B be the right member of inequality (11) and let k\u2019 be the \ncost of using the Huffman (best alphabetical) encoding of A* as an en- \ncoding for A, then, by Lemma 6 and the definition of cost, we can con- \nclude that | k\u2019 \u2014 k*| < B and, since from the definition of k we can \nconclude that k < k\u2019, we can combine these to obtain k* \u2014 k < B. \nBy a similar argument involving the use of k\u2019\u2019, the cost of using the Huff- \nman (best alphabetical) encoding of A as an encoding for A*, we obtain \nk \u2014 k* < B. Combining these, we obtain (11).\n\nTheorem 11: The Huffman encoding for a given alphabet has a cost which \nis less than or equal to that of any uniquely decipherable encoding for that \nalphabet.\n\nProof: This proof is essentially that of MeMillan.\u2019 Let us consider any \nuniquely decipherable encoding C. We will construct a new encoding C\u2019 \nwhich has the same cost as C, and which has the prefix property. How- \never, by its method of contruction, the Huffman encoding has a cost \nwhich is less than or equal to that of any encoding having the prefix \nproperty, completing the proof of the theorem. Let NV; be the number of \ndigits in the code which C associates with the 7th letter of the alphabet. \nLet the letters of the alphabet be renumbered in such a way that V; S \nNii. Then, as in the encoding theorem (Theorem 1 of this paper, or \nTheorem 9 of Shannon,\u2019 we let\n\nand we define C\u2019 to be the encoding which associates with the ith letter \nthe code C,\u2019 obtained by truncating A; after N; digits. Then it follows that \nthe digits truncated were 0\u2019s, and hence that each C;\u2019 agrees numerically \nwith the corresponding A;. By (10), each of the A; is less than 1. To \nshow that C\u2019 has the prefix property, we assume that C,\u2019 is a prefix of \nC;\u2019. Then i < j, by the renumbering. However, Ai,, = A; + 2-\u201d*, and \nhence A; 2 A; + 2 \u2018i Thus, A; cannot agree with the first NV; places \nof A;. Hence, the first N; digits of C;\u2019 are different from those of C;\u2019.\n\nThese theorems show how rapidly A, and 7\u2019, increase with increasing \nn. Since, by Theorem 3, A, would be the number of encodings to con- \nsider if it were desired to find the best alphabetical encoding by enumera- \ntion, Theorem 12 shows that the methods already given in this paper \n(even the general alphabetizing algorithm) are much faster than exhaus- \ntive enumeration. Similarly, Theorem 7 and Theorem 8 show how much \nslower exhaustive enumeration is than the algorithm given by Huffman.!\n\nEach of the A, alphabetical encodings may be converted into n! of \nthe 7, encodings by permuting its codes in all possible ways. It follows \nthat T,, = n!A, , and it suffices to prove Theorem 12. Consider for n = 2 \nan exhaustive alphabetical encoding of n letters. Some number k = \n1, ...,n \u2014 1 of these letters has a code with prefix 0. These k codes, \neach with its leading digit 0 removed, have been shown (Lemma 4) to \nform one of the A; exhaustive alphabetical encodings of k letters. Simi- \nlarly, the remaining n \u2014 k codes, minus their leading digits 1, form one of\n\nwhile A; = 1. To solve (14), construct the generating function a(x) = \nAye + Aor? + Azz? + .... By (14), a(x) = \u00ab + a(x); ie.,\n\nThe negative sign of the square root is needed to make a(0) = 0. The \nseries for a(x) is obtained using the binomial theorem with power 3. \nThe coefficient of \u00ab\u201d (which is A,) has the expression (12).\n\nSo far in this paper very little has been said about encodings without \nthe prefix property. For instance, we restricted the best alphabetical \nencoding to be the encoding having the lowest cost among all alphabetical \norder-preserving encodings having the prefix property. However, in view \nof the fact that the special encoding given in Table I is an alphabetical \nencoding and has cost 4.1801, it appears to be advantageous to dispense \nwith the prefix property requirement. However, not very much is known \nabout the properties of encodings lacking the prefix property, and, in \nfact, it is not known whether the special encoding given in Table I can \nbe further improved or not. In fact, it was not constructed on the basis \nof any general procedure, but was found by a heuristic method. The next \nfew paragraphs will give a few results which we have found about en- \ncodings without the prefix property, but will also give some examples of \nthe difficulties which it is possible to get into when using such encodings.\n\nIt should be noted that a message which begins with the letter Y in \nthe special encoding cannot be deciphered as soon as the Y has been \nreceived, but it is necessary to wait for further received digits in order to \ndistinguish it from a Z. In particular, in the case of the message enci- \nphered as 11111101111110 it is necessary to wait for the 14th received \nbinary digit before the first letter can be deciphered.\n\nIn general, we will say that the delay of a presumed message is d if it \nis necessary to wait for the receipt of the first d binary digits before the \nfirst transmitted letter can be recognized. We will say that the delay of \nan encoding is d if d is the least upper bound of the delays of all pre- \nsumed messages of that encoding. We will say that an encoding has the \nfinite delay property if the delay of that encoding is finite. For instance, \nthe special encoding of Table I has the finite delay property, and in fact \nhas delay 14.\n\nTheorem 14: If an encoding C has infinite delay, then there exists a pre- \nsumed message of C which has infinite delay.\n\nsequence of presumed messages M,, M,, M;, ... such that /; has \ndelay at least 7. Then either the set of those presumed messages M ; whose \nfirst binary digit is 0 or the set whose first binary digit is 1 is an infinite \nset. We thus can choose an infinite subsequence of presumed messages \nM,, Mz, M;,... such that M; has delay at least 7 and such that all of \nthe messages agree on the first binary digit. Proceeding by induction, \nwe can choose at the kth step a subsequence of presumed messages which \nall agree on the first k digits. Then the infinite presumed message whose \nkth binary digit is the Ath binary digit of all presumed messages re- \nmaining after the kth inductive step is a presumed message, and has \ninfinite delay.\n\nlor an encoding to be useful in practice, it seems likely that it must \nhave the finite delay property. This would permit a deciphering machine \nto be built having only a finite amount of memory, and it would permit \ntwo-way communication (as in telephony) to be almost instantaneous. \nHowever, in delayed communication systems (common in telegraphy) \nfor which a tape is used for storing messages, this tape might be used to \nprovide the unbounded amounts of memory needed to decipher an infi- \nnite delay encoding.\n\nTo investigate further the problems of designing an optimal-cost en- \ncoding of any sort (such as an alphabetical-order encoding), without \nrequiring it to have the prefix property, it should be remarked that the \nproblem is finite, but not necessarily easy to attack. That is, given an \nalphabet in which all of the letters have positive probability, and given a \nconstant K, there are only a finite number of encodings of this alphabet \nwhich have a cost less than K. For if m is the smallest of the probabilities, \nthere are not more than K/m digits in the longest code of any such en- \ncoding, and there are only a finite number of encodings of an n-letter \nalphabet in which each code has length less than K/m. However, this \nnumber would be astronomically large for any alphabet of reasonable \nsize.\n\nOne particular way of generating encodings which will be used in a \nfew examples below is of some general interest. The reversal of an en- \ncoding C is a new encoding (which will be called C* for the remainder \nof this paper) which is obtained by letting the code for each letter be \nwritten in the reverse order. This interchanges the direction of increas- \ning time, and changes many of the properties of the encoding, but it \ndoes preserve unique decipherability.\n\nTable V demonstrates many of the properties and complications of \nencodings, contrasting the one having the prefix property with three \nother encodings lacking this property. Each of the four encodings shown\n\npreserves alphabetical order, and each is uniquely decipherable. The \nfirst encoding has the prefix property, and in fact is the best alphabetical \nencoding in the sense used in this paper. However, it has an appreciably \nhigher cost than either of the other three encodings, none of which has \nthe prefix property. The reversals of each of the last three encodings have \nthe prefix property, but the reversal of the first encoding does not.\n\nThe second encoding of Table V has the lowest possible cost of any \nuniquely decipherable binary encoding by Theorem 11, since it is the \nreversal of a Huffman encoding. However, the second encoding has \ninfinite delay, since the presumed message OOL1L11 . . . has infinite delay. \nFurthermore, the second encoding, although it preserves the alphabetical \norder of individual letters, does not preserve the alphabetical order of \nwords made up out of these letters. For instance, the enciphered form \nof CE is a larger binary number than the enciphered form of DA, al- \nthough the latter occurs later in alphabetical order. The property of \npreserving alphabetical order of all words will be called the strong alpha- \nbetical property, and it has already been shown that alphabetical en- \ncodings having the prefix property have the strong alphabetical prop- \nerty. However, both the alphabetical encoding and the special encoding \nof Table I have the strong alphabetical property, and all of the en- \ncodings of Table V except the second encoding have the strong alpha- \nbetical property. There would be very little to be gained by employing \nan alphabetical order encoding for sorting or dictionary purposes unless \nit had the strong alphabetical property.\n\nThe third encoding lacks these defects of the second encoding, but it \nhas a special one of its own, about which more will be said in the next \nsection. This defect has to do with synchronizing, and it can be explained \nin this case by the observation that every code of the third encoding \nhas an even number of binary digits. Thus, if the deciphering circuit \nstarts up while it is out of phase, it can never get back in phase. The two \nphases correspond to the odd-numbered and the even-numbered binary\n\ndigits, and the deciphering machine, if it is out of phase, would never \nget back in. In this case, where there are certain codes which cannot \noccur, the defect could be remedied by designing the circuit to addition- \nally change phase if it ever receives a code 1011 or 1111, but this adds \nan extra complication to the circuit. However, the first and second \nencodings have the property that each of them will automatically get \nback in synchronism with probability 1, without the addition of any \nother codes or any other special features to the circuit.\n\nThe fourth encoding has none of these defects, and since its cost is so \nnear to the least possible, it would undoubtedly be a reasonably good \nchoice as a solution, if this particular alphabet had arisen in an actual \npractical problem.\n\nSo far in this paper, each example of an encoding with the finite delay \nproperty has had a delay equal to Nix , where Nimax is the number of \ndigits of the longest code of the encoding. This result does not hold in \ngeneral, as is illustrated by Table VI. The fifth encoding has Ninax = 6, \nbut it has delay 8.\n\nThe encodings having the finite delay property but not the prefix \nproperty, such as the special encoding of Table I and the fifth encoding \nof Table VI, provide counterexamples which contradict Remark II of \nSchiitzenberger (Ref. 5, page 55) and provide the example which is \nasked for in the sentence following Remark I of the same paper.\n\nAs an alternative to the above method of expressing quantitatively \nthe finite delay property, we may make the following definitions for use \nlater in this paper. We will say that the excess delay of a presumed mes- \nsage is e if it is necessary to wait for the receipt of e binary digits beyond \nthe end of the first transmitted letter of the presumed message before \nthis first letter can be recognized. We will say that the excess delay of an \nencoding is e if e is the least upper bound of the delays of all presumed \nmessages of the encoding.\n\nIf d is the delay of an encoding, e is its excess delay, and Nimin and Nmax \nare, respectively, the minimum and maximum numbers of digits of any \ncodes of the encoding, then we obviously have e + Nmin S d S \u20ac +\n\nexcess delay of that encoding is finite. Also, an encoding has the prefix \nproperty if and only if the excess delay of that encoding is 0.\n\nProblems of how to make a transmitting device and a receiving device \nbecome and remain synchronized with each other are important in the \nengineering design of many kinds of systems. Since the encodings dis- \ncussed in this paper are variable-length, it might seem that the syn- \nchronizing problem for enciphering and deciphering circuits would be \nespecially difficult. However, the synchronizing problem is very simple \nfor many variable-length binary encodings, because of a particularly \nfavorable property which they possess. These remarks can best be il- \nlustrated by an example. Suppose that (using the alphabetical encoding \nof Table I as an example) a message beginning 1110011110100111000. . . \nis received, and we wish to observe how a deciphering circuit would \ndecipher it. Since the encoding has the prefix property, the deciphering \ncircuit should first find a code which is a prefix of this message, and then \ndecode this to obtain the first letter T of this message. Proceeding with\n\nthe remaining part, it then finds the letter H, and then the rest of the \ndeciphered version shown in the first line of Table VII, where the sym- \nbol \u201c:\u201d is used to mark the divisions between those sequences of binary \ndigits which were deciphered as individual letters.\n\nNext suppose that the same sequence of digits had been received, but \nthat the deciphering circuit was not in synchronism with the enciphering \ncircuit. In particular, suppose that, when the deciphering circuit was \nfirst turned on, it was in the state that it would be in if it were partly \nthrough the operation of deciphering some letter, and that the initial | \nof the message was interpreted as the last digit of this letter. This de- \nciphering is indicated on the third line of Table VII. Once again, the \nsymbol \u201c\u2018:\u201d has been used to mark the divisions between letters. Then \nthese two decipherings are out of phase (i.e., out of synchronism) with \none another at the beginning of the message, but at the end of the re- \nceived message they are in phase with each other, as is indicated by the \nfact that the \u201c:\u201d symbols align with each other at the right end of Table \nVII. This means that the deciphering circuit would have automatically \nbecome synchronized, without any special synchronizing circuits or\n\nsynchronizing pulses being necessary. It was, of course, necessary for at \nleast two of the codes of the encoding to end in the same sequence of \ndigits, but this is very likely to happen for any variable-length encoding, \nunless special efforts are made to prevent it.\n\nHowever, if we had been using a fixed-length encoding, such as the \nsixth encoding of Table VI, in which all of the codes have a fixed length \nk, there would be exactly k different phases in which the deciphering \ncircuit might find itself, and the circuit could never make a transition \nbetween them. No pair of different codes can end in exactly the same \nsequence of digits, and so no two of these phases can become synchro- \nnized. Each of these phases will have all of the codes ending after 7 \ndigit times, and after k + j, 2k + j, ete., where j is the remainder ob- \ntained on dividing the position of the symbol \u2018\u201c:\u2019\u2019 by k, and hence j \ncan take on k different possible values.\n\nAlso, even in the case of variable-length encodings, if all of the code \nlengths are divisible by some integer k, then there will be at least k \ndifferent phases. For if the position of one occurrence of the symbol \u2018':\u201d\u2019 \nhas remainder 7 when divided by k, the position of all other occurrences \nof the symbol \u2018:\u201d\u2019 in this phase of decipherment will have the same re- \nmainder.\n\nThe above remarks apply strictly to exhaustive encodings, but may \nnot apply where there are certain sequences of digits which can never \noccur. For if such a sequence of digits does occur, this may be used by \nthe circuit as a special indication that it is out of phase, and hence it \nmay be possible to build auxiliary circuits which can cause resynchroni- \nzation, even when a fixed-length encoding is used. So a more complete \ntreatment of synchronization would allow such auxiliary circuits, but \nhere we will consider only self-synchronization, which is carried out \ninherently by the same means as is used for deciphering.\n\nTo speak more precisely about the self-synerhonizing properties, we \nwill make some definitions. Given any encoding C and any\n\nfinite sequences x and y such that x is not the \nenciphered form (with respect to encoding C) (16) \nof any message, and xy is a presumed message,\n\ncomplete enciphered messages, we will say that z is a synchronizing se- \nquence for x and y. As an example, we have seen in Table VII that \n011110100111000 is a synchronizing sequence for 1 and 110.\n\nGiven any uniquely decipherable encoding C which has some codes \nof length more than 1, exactly one of the three statements given below \nwill hold:\n\ni. For all (16), there is no z such that z is a synchronizing sequence \nfor x and y. The encoding C will then be said to be never-self-synchroniz- \ning.\n\nli. For each (16), there is a z which is a synchronizing sequence for zx \nand y. The encoding C will then be said to be completely self-synchronizing.\n\nili. For some (16), there is a synchronizing sequence for x and y, \nbut for other (16), there is no synchronizing sequence for x and y. The \nencoding C will then be said to be partially self-synchronizing.\n\nFurthermore, we will define a sequence z to be a universal synchronizing \nsequence for the encoding C if, for all (16), this same sequence z is a \nsynchronizing sequence for x and y.\n\nTheorem 15: Given an exhaustive encoding C, then C is completely self- \nsynchronizing if and only if there exists a z which is a universal synchroniz- \ning sequence for C.\n\nProof: A universal synchronizing sequence clearly satisfies the condi- \ntions of the definition of completely self-synchronizing, so it remains \nonly to construct a universal synchronizing sequence, given that there \nis a synchronizing sequence for each finite sequences x and y. By the \nexhaustive property, there is a code consisting entirely of 0\u2019s. We will \nassume that there are k 0\u2019s in this code. We will construct our z by \nstarting with Niax 0\u2019s, where Nax is the length of the longest code of \nC\u2019; after this, there are only k different phases in which the circuit could \nbe. Then we find a synchronizing sequence for two of these phases (for \ninstance, a synchronizing sequence for 00 and 0), and put this next after \nour sequence. Next we put on the sequence of Ninax 0\u2019s again. There are \nnow at most k \u2014 1 phases to synchronize, and, adding on sequences for \nthese one at a time, we eventually construct our desired universal \nsynchronizing sequence.\n\nThe alphabetical encoding of Table I can be shown by Theorem 15 \nto be completely self-synchronizing, since the sequence 010001011 is a \nuniversal synchronizing sequence for this encoding. The message AD \nhas this sequence as its enciphered form. In addition, there are many \nother short universal synchronizing sequences for this encoding, such \nas the enciphered forms of #Y, AY, BD, BY, EY, HI, ID, JO, JU, \nMW, NY, OW, PO, PU, TY, ete. Since just these digraphs listed here\n\nit can be seen that, if English text were transmitted by use of this \nencoding, it would be quite likely to synchronize itself very quickly. \nIn fact, it is easy to see that any exhaustive encoding which is com- \npletely self-synchronizing will synchronize itself with probability 1 if \nthe messages sent have the successive letters independently chosen with\n\nany given set of probabilities, assuming only that all of these probabilities \nare positive numbers. This will occur since the probability of a universal \nsynchronizing sequence occurring at any given time is positive, and, if \nwe wait long enough, this will have happened with probability 1.\n\nThe fact that this occurs with probability 1 does not make it quite \ncertain to occur, and, in fact, it is possible to choose arbitrarily long \nsequences of English words which do not contain a universal synchroniz- \ning sequence. An example of such a sequence for the alphabetical encod- \ning of Table I is\n\nBut such a sequence is extremely unlikely to continue indefinitely in any \npractical communication system or record-keeping system. Also, slight \ncomplications of the encoding could permit certain sequences which are \ncertain to occur in English text (such as a period followed by a space \nsymbol) to be universal synchronizing sequences.\n\nOne quality which might be worth comparing for various proposed \nencodings under consideration for possible use might be the average \nspeed with which they synchronize themselves, when carrying typical \ntraffic. This speed could be calculated from a sufficiently good knowledge \nof the statistics of the traffic, but it could more easily be measured \nexperimentally, either by the use of actual enciphering and deciphering \ncircuits, or by simulating their behavior on a digital computer.\n\nThe synchronization problem occurs not only when the equipment \nis first turned on, but also in transmission systems for which there is a \nnoisy channel. For if some digits of a message encoded in a variable- \nlength encoding are changed, the change may cause the circuits to get \nout of synchronism by the change of a short code into the prefix of a \nlong one, or vice versa. Also, of course, temporary malfunctions of the \nenciphering or deciphering circuit themselves might cause them to get \nout of phase.\n\nIt may be of interest to enumerate the known results about combina- \ntions of synchronizing properties and lengths of the codes of exhaustive \nencodings.\n\nIf an exhaustive encoding has a fixed length (all codes having length \nthe same integer /), then it must be\n\nVARIABLE-LENGTH BINARY ENCODINGS 961 \nsome integer k > 1, but these lengths are not all equal to k, then it \nmust be one of the following:\n\nIf an exhaustive encoding has the greatest common divisor of the \nlengths of its codes equal to 1, then it must be one of the following:\n\ncompletely self-synchronizing, (20) \npartially self-synchronizing, (21) \nnever-self-synchronizing. (22)\n\nOf the above six cases, (17), (19) and (20) occur very much more \ncommonly than the others. In fact, it is very difficult to construct \nexamples of the other three, unless you deliberately set out to do so. \nThe following theorems will give indications of the fact that cases (18) \nand (22) are hard to obtain.\n\nIt can be seen that, in the case of a fixed-length code, Q will be the \nlength. However, no one of the exhaustive encodings (except those \nhaving fixed length) listed so far in this paper has an integer value for \n(). Rather than give the full details of a rigorous proof of Theorem 16, \nonly the main ideas involved will be explained. The sum Q is the average \nlength of the codes obtained by deciphering a presumed message, if the \npresumed message was obtained by choosing 0\u2019s and I\u2019s as successive \ndigits by independent choices having probability one-half. If we put \nsuch a random presumed message into the deciphering circuit, we have \nseveral different phases in which it may be deciphered. By the never- \nself-synchronizing property no two of these phases can ever come to- \ngether.\n\nLet. H be the set of all prefixes of the presumed message. Then two \nof these prefixes will be said to be of the same phase if they are of the \nform 6 and 6@, where # is the enciphered form of a complete message. \nThe set H is subdivided by the equivalence relation \u201c\u2018being of the same \nphase\u201d into B distinct sets, where B is the number of phases. By sym- \nmetry, the probability that any two given members of H will be of the\n\nsame phase is equal, and, since each phase occurs with equal probability \nand the sum of all of them is 1, each phase occurs with probability 1/B, \nwhere B is the number of phases. However, Q was the expected difference \nin length between a given member of H and its next longer member; \nhence, we will have Q = B.\n\nTheorem 17: Given an exhaustive encoding C, C is never-self-synchroniz- \ning if and only if its reversal C* has the prefix property.\n\nSuppose that C is not never-self-synchronizing. By the definition of \nsynchronizing sequence, there exist finite sequences x, y and z such that \nx is not the enciphered form of a message, but yz is the enciphered form \nof message m, and xyz is the enciphered form of message me .\n\nlor some values of n the last n letters of m,; may agree with the last \nn letters of m,.. But, by the fact that x is not the enciphered form of a \nmessage, there is a largest value of n for which this is true. Let this \nlargest value be n\u2019, and let the letters which are n\u2019 + 1 from the end of \nm, and ms, respectively, be called L; and L.. Then C(L;) and C(Le) are \nboth suffixes of the same message (the previous part of xyz), and hence \nthe reversed form of one of them is a prefix of the reversed form of the \nother.\n\nThe converse follows more readily, since, if @ and 6@ are both codes \nof C*, then the reversed form of @ is a synchronizing sequence for the \nreversed form of @ and the null sequence.\n\nTo return to the problem of which of cases (17) through (22) can occur, \nit can easily be shown by the use of Theorems 16 and 17 that, among \nall exhaustive encodings in which not all codes are of the same length, \nthe only ones which are never-self-synchronizing and have fewer than \n16 letters in their alphabet are the encoding which encodes a nine-letter \nalphabet by using the list of codes (000, 0010, 0011, 01, 100, 1010, 1011, \n110, 111), and the reversal of this encoding. This encoding is due to \nSchiitzenberger.\u00ae\n\nIt is also possible to construct an example of case (18), but the one \nwe have found is too complicated to be worth presenting here.\n\nSome reluctance to use variable-length encodings has been based on \nthe opinion\u2019 that it is hard to build circuits to encipher or decipher\n\nDIRECTION OF SHIFT | | | \n[ \u2014\u2014 i ! \nHAS JUST BEEN \n} ENCIPHERED 1 1\u00b0) \u00b0 .@) 0 ie) ie) * 1?) ce) 1?) } NOT } \n4a \nSHIFT + \nREGISTER \nATE ENABLE \nTRANSL aes\n\nthem. Descriptions will be given below for one circuit for doing each \nof these, using principally just a shift register and a combinational \ntranslating circuit. Since using any code requires having a combinational \ntranslating circuit, and since presumably most devices using coded \nalphabetical information are likely to cause it to pass through a shift \nregister, the kind of circuit described below would add very little com- \nplexity to such machines, and would automatically give them the self- \nsynchronizing property, in the case of most variable-length binary \nencodings.\n\nThe enciphering circuit, shown in Fig. 1, contains a shift register \ncontaining the words \u201cHAS JUST BEEN ENCIPHERED\u201d followed \nby a binary digit 1 and a string of zeros as long as the longest code which \n\u201can occur in the variable-length encoding. We will assume that it is in \nsuch a state as to have the zeros as shown, although it can easily be seen \nthat it will get into this state if it starts in any other condition.\n\nThe circuit of Fig. 1 also contains an input reader (which can for \nconcreteness be thought of as a punched paper tape reader, although it \ncould be a buffer or other input device), which can read in one letter\n\nat a time whenever it is given a pulse on the lead labelled \u201cto advance \ninput\u201d\u2019.\n\nThe recognition circuit, which consists of a multiple-input OR circuit \nfollowed by a negation circuit, gives an output whenever there are as \nmany binary zeros present as there are in the illustration. This sends a \nsignal to enable the gate, letting the code corresponding to the next \nletter be read into the locations previously occupied by the 1 and all of \nthe zeros. However, the translating circuit, which translates the letters \ninto this encoding, instead of being designed to give directly the original \nvariable-length encoding, gives an encoding which differs from it by \nhaving an extra \u201c1\u201d added to the end of each code. The output of the \nrecognition circuit also goes to advance the input, reading in the next \nletter to be converted, after passing through a delay sufficient to be \nsure that the gate is now no longer enabled. This delay prevents the \nletter being translated from changing while it is being gated into the \noutput shift register.\n\nAs soon as the new code has been read into the shift register, it begins \nto be shifted along to the left in Fig. 1. The 1 at the end of the code \nserves to mark the end of the code during this shifting, but it will be \neliminated from the enciphered form of the message. The shift register \nis connected so that, when it is shifted, a 0 appears at the right end. \nAs soon as the 1 passes beyond the end of the recognition circuit, there \nwill be only zeros present, and hence the recognition circuit will again \nrecognize the end of a letter and repeat the cycle as given above.\n\nInstead of having a counter or a special sequential circuit to keep \ntrack of where the current letter ends, this has been done here by add- \ning a single binary digit to the code and adding one to the length \nof the required shift register.\n\nSimilarly, an analogous scheme can be used to decipher from a variable \nlength code into any other representation for letters, by using one special \nposition in the shift register, as shown in Fig. 2. This deciphering circuit \ncan be built only for encodings having the finite delay property, although \nthe enciphering circuit of Fig. 1 can be used for any binary encoding.\n\nThe shift register into which the digits to be deciphered are shifted \nis divided into two halves, which will be called the left half and the \nright half. The right half has e digit positions, where e is the excess delay \nof the encoding. The left half has Nmax + 1 digit positions, with the \nextra 1 being used to mark the end of those digits which already have \nbeen deciphered.\n\nto contain Ninax 0\u2019s followed by a 1. Next, the digits of the message to \nbe enciphered shift toward the left. Since the 1 precedes them, it marks \nclearly how many of these digits have been shifted into the left half. \nAs soon as all of the digits of the code of the first letter of the message \nhave been shifted into the left half, the translating circuit will then \ngive its outputs. It gives the translated codes for the letter, as well as \ngiving another output, w, which equals 1 only when the complete first \nletter is present. The translating circuit makes use of the inputs from \nonly the left half of the shift register, ignoring the digits in the right \nhalf, unless the code C present in the left half is a code which is also a \nprefix of another code. It makes use only of those digits from the right \nhalf which are necessary to distinguish between this code and the par- \ntially shifted-in code of which it is a prefix. It gives the output w = 1 \nwhenever the entire code for the first letter of the enciphered message \nhas been shifted over into the left half and, whenever only a prefix of \nthe code of the first letter is there, the output w will equal zero.\n\nThis output w will then cause the left half to clear back to its original \nstate, and, after a delay sufficient to allow the output to be received, it \ngives the \u2018\u201c\u2018to advance output\u201d signal to the output punch or buffer.\n\nINPUT TO CLEAR SHIFT REGISTER \nDIRECTION OF SHIFTING \n4 : | - 3 I : | I OF SHIFT REGISTER \n\u2014\n\nThe deciphering circuit then repeats the above cycle for the next letter \nof the message.\n\nThe translating circuit of this deciphering circuit must give the ap- \npropriate outputs whenever the complete code for the first letter is \npresent in the left half of the shift register, and must give w = 1 in these \ncases. It must also be designed to give the output w = 0 whenever an \nincomplete prefix of the first letter is present, but, since in general there \nmay be many states of the shift register which do not correspond to \neither a letter or a prefix, there may be many \u201cdon\u2019t cares\u2019\u2019 occurring \nin the design of this translating circuit, which will permit it to be simpler \nthan a completely specified function having this many inputs.\n\nThe time delay between the receipt of the beginning of an N-digit \ncode for a letter and the actual sending of this letter to the output punch \nor buffer will be N + e, which may sometimes be slightly longer than \nthe delay d of the message. However, the circuit for doing the deciphering \nin the minimum time would be more complicated, in that it would not \nalways clear the shift register to the same state, so it is not presented \nhere.\n\nHowever, in the enciphering circuit given in Fig. 1 there is only a \ndelay of one digit time, while the message is shifted through the one \nextra stage at the left end of the shift register. Hence, neither of these \ntwo circuits operates in quite the minimum possible time, since speed \nhas been sacrificed for simplicity of construction.\n\nThere are many further problems suggested by the ideas discussed \nin this paper, and which we have not been able to solve. Are there any \nbinary encodings which satisfy (9) other than the exhaustive encodings \nand their reversals? Are there any encodings C which satisfy (9) and \nsuch that both C and its reversal C* have the finite delay property \nwithout both C and C* having the prefix property? Given an encoding \nwhich is uniquely decipherable but which does not possess the finite \ndelay property, does the set of presumed messages having infinite delay \nalways form a finite set? Does it always form a set of measure zero? Is \nthere a simple polynomial in Na. and n which will be an upper bound \nto the delay of any encoding having the finite delay property? Are the \nencodings for which the algorithm of Sardinas and Patterson? fails to \nterminate precisely the same as the encodings having infinite delay? \nGiven any encoding having infinite delay, is there a Turing machine\n\nach) which can decipher any K-digit message in a length of time which \nis less than a constant times K?\n\nWe would like to express our thanks to T. H. Crowley for suggesting \nTheorem 7, and to 8. P. Lloyd for suggesting to us some of the complica-\n\n1. Huffman, D. A., A Method for the Construction of Minimum-Redundancy \nCodes, Proc. I.R.E., 40, September 1952, p. 1098.\n\n2. Sardinas, A. A. and Patterson, G. W., A Necessary and Sufficient Condition \nfor Unique Decomposition of Encoded Messages, I.R.E. Conv. Ree., 1953, \nPart 8, p. 104.\n\n3. MeMillan, B., Two Inequalities Implied by Unique Decipherability, I.R.E. \nTrans., IT-2, December 1956, p. 115.\n\n. Mandelbrot, B., On Recurrent Noise Limiting Coding, Proceedings of the \nSymposium on Information Networks, Polytechnic Institute of Brooklyn, \nApril 1954, p. 205.\n\n5. Schiitzenberger, M. P., On an Application of Semi-Groups Methods to Some \nProblems in Coding, I.R.E. Trans, IT-2, September 1956, p. 47.\n\n3. Michel, W. 8., Fleckenstein, W. O. and Kretzmer, E. R., A Coded Facsimile \nSystem, I.R.E.-Wescon Conv. Rec., 1957, Part 2, p. 84.\n\n. Dewey, G., Relativ Frequency of English Speech Sounds, Cambridge Univ. \nPress, Cambridge, Eng., 1923, p. 185.\n\n\u00a7. Shannon, C. E., A Mathematical Theory of Communication, B.S.T.J., 27, \nJuly 1948, p. 379; October 1948, p. 623\n\n. Brooks, F. P., Multi-Case Binary Codes for Non-Uniform Character Dis \ntributions, I.R.E. Conv. Ree., 1957, Part 2, p. 63.\n\nIn adapting the existing telephone network to high-speed digital data \ntransmission, an error control problem arises. Most of the circuits were \ndesigned primarily for voice-type signals and considerable attention \nwas given to control of thermal noise. Because of the high redundancy \nof speech, impulse noise on the lines is usually not even noticed by the \ntelephone users, and hence has not been a serious problem. On the other \nhand, high-speed digital data (especially numerical data) contain little \nredundancy, and the noise pulses may resemble the signal pulses and \nthus cause errors.\n\nThe deliberate introduction of redundancy to detect and correct \ntransmission errors has been used for some time. Early systems' used \nrepetition of characters and duplication of channels. There were two \nschemes which sent pictures of the characters using raster scans. By the \nlate 1930\u2019s a radio telegraph system? using a 3-out-of-7 code for error \ndetection had been patented and telephone apparatus using 2-out-of-5 \ncodes\u2019 was being designed.\n\nMost, if not all, of the recent work on error-detecting or error-correct- \ning codes stems from Hamming\u2019s Systematic Parity Check codes.\u2018 These \ncodes will correct a single error per block of digits. Since then, much work \nhas been done on codes for multiple errors (see Refs. 5 through 16). The\n\nassumption has usually been made that the errors are statistically in- \ndependent. On many communication channels, however, the errors are \nnot independent but tend to come in groups. For example, a lightning \nstroke may knock out several adjacent telegraph pulses. These groups \nof errors are called \u2018\u201c\u2018bursts\u201d. Codes for detecting and correcting bursts \nhave been proposed by Abramson,\" Gilbert,!\u00ae Hamming\" and Meyer.\" \nThe class of codes described here differs in that the block structure has \nbeen minimized; the resulting symmetry allows very simple mech- \nanization and also simplifies the synchronization problem. Since the \nblock size is small, the codes also fit very naturally into systems where \nthe data must be accepted and delivered continuously, rather than in \nbatches.\n\nBefore describing the general recurrent code we will give a particularly \nsimple example. Assume that we wish to correct bursts of length six or \nless. The simple code has every other digit a check digit, giving a re- \ndundancy of one-half. The encoder is illustrated in Fig. 1. It consists of \na shift register of length seven. The data digits enter from the left \n(Position 1) and are shifted through the register before being transmitted. \nFor each shift we generate a check digit so that the parity (number of 1\u2019s) \nof the check digit and the data digits in the first and fourth positions of \nthe shift register is even (zero or two). This check digit is transmitted \nbefore the data digit in the seventh position. Then a shift is made; the \ndata digit which was in Position 7 is transmitted, and a new check digit \nis calculated. This process is illustrated in Fig. 2; the successive lines are \none shift time apart. During this time interval one new data digit is \naccepted by the encoder and two digits, one data, one check, are trans- \nmitted.\n\nThe decoder is shown in Fig. 3. The received code enters the switch \nwhere the alternating data and check digits are separated, the check \ndigits going to the lower shift register and the data digits to the upper\n\none. There are two copies of the parity circuits, R and S, each one check- \ning the parity relation imposed by the encoder. The decoding rule is:\n\nWhenever both FR and S fail, change the data digit in Position 4 \n(0 \u2014 1, 1 \u2014 0) while shifting it to Position 5. If only one parity \ncheck fails, make no change.\n\nThe corrected data digits are available at Position 5 of the data shift \nregister. In a burst of length six or less, there can be at most three data \ndigits and three check digits wrong. The parity relation used in encoding \ninvolves digits which are spread far enough apart so that no burst of six \nor less will affect more than a single digit in any one parity group. \nAfter any burst of length six or less, a 20-digit errorless message is \nenough to completely refill the decoder shift registers. Hence, the next \nburst can be corrected without interference from a previous burst, if\n\nIf the message is to be retransmitted the check digits can be corrected \nat Position 10 of the check digit shift register (Fig. 3). The rule is:\n\nWhenever parity check R holds and parity check S fails, change \nthe digit in Position 10 of the check digit register.\n\nA data digit error cannot cause parity R to hold and parity S to fail, \nbecause this would require an error in Position 7 of the data register, \nand, since all data digit errors are corrected in going from Position 4 to \nPosition 5, this cannot happen.\n\nThis particular coding scheme fails first for a burst of length seven, \nconsisting of a check digit and another check digit six digits later. When \njust these two check digits are wrong, the decoder assumes that a data \ndigit is wrong and changes it.\n\nA demonstration device using this code has been built. It consists of a \npunched tape reader, an encoder, a transmission line, a decoder and a \ntape printer. The circuitry uses relays and can be operated fast, slow or \none step at a time. Digits in the encoder, transmission line and decoder \nare displayed on lamps. The transmission line has switches for inserting \nerrors in the encoded message. Other lamps are used to indicate parity \ncheck failures. An auxiliary circuit can be used for detecting overlong \nbursts, flashing a yellow lamp whenever the decoder has a burst and \nlocking up a red lamp whenever a detectable overlong burst occurs.\n\nThere is an extension of this code to correct bursts of any even length. \nWe merely spread out the parity check so that the burst can only effect \none term in any parity group. To correct bursts of length 2K or less \nrequires an encoding shift register of length 2K + 1. The decoding data \ndigit register has the same length, 2K + 1, and the check digit register \nmust be 3K + 1. The parity checks involve digits K apart in the registers. \nA clean message of length 6K + 1 will always be sufficient separation \nbetween bursts. Table I shows typical values.\n\nThe general (binary) recurrent code is constructed as follows: \nWe are given a message to be transmitted consisting of data digits.\n\nWe will add to this check digits to form the encoded message. The en- \ncoded message is divided into blocks of length b. One position in the \nblock is assigned to be a check digit? and the rest are data digits. Since \nthe block must have at least one data digit, the shortest block length is \nb = 2. (This is the value used in the example of Section II.) The data \ndigits are loaded into the data digit positions in the order received. The \ncheck digit is determined by a parity relation applied once for each \nblock. This parity relation extends over a selected set of the digits in p \nconsecutive blocks. (To be useful against bursts, p must be at least 2 and \nusually will be larger.) Fig. 4 shows a portion of the encoded message \nfrom the example of Section II. The data and check bits are indicated \nby D\u2019s and C\u2019s; the blocks are marked off with commas and the parity \nrelation is shown by lines having *\u2019s over the digits in a given parity \ngroup. Note that p for this example is 7; that is, any one of the parity \ngroups extends over seven blocks. Every parity group has three digits \nin it, two data and one check; thus, each data digit is in two parity \ngroups and each check digit is in only one parity group.\n\nP, , Ps, \u00ab++, Py . Consider p consecutive blocks. We form P, by observing \nthe first position of each block; if the digit is in this parity group we \nwrite 1, otherwise 0. Then P: depends on the second positions of these \np blocks, and so on. This is illustrated in Fig. 4. We have used the parity \ngroup indicated by the arrow and written the parity words so that the \ndigits fall under the corresponding blocks. Thus P; has 1\u2019s in the first \nand fourth blocks and P2 has a 1 only in the seventh block. (The num- \nbering of digits and blocks here and in Fig. 4 is from right to left. Fig. \n4 can be considered a \u201csnapshot\u201d of the encoded message on the trans- \n+ Codes with more than one check digit per block are possible, but it can be \nshown that, for a given efficiency and burst-correc ting \u00a2 vo ability, they always re\n\nquire more complicated encoding and dec \u2014 equipment than would the e quiva \nlent code with one check digit per block\n\nmission line. This is different from the numbering method used below, \nwhere the digits are considered to be flowing past a fixed point, and are \nlabeled with numbers which increase with time.) With this notation, \nthere is a simple correspondence between the 1\u2019s in the parity words \nand the connections to the shift registers of the encoder and decoder.\n\nwhere the constant is 0 or 1, \u00ae means sum modulo 2, k takes successive \nintegral values, b is the block length, and r, s, ---, w denote which digits \nenter into the parity group.\n\nThe requirements that every position in the block must be represented \nat least once implies that each of the integers 0, 1, ---, (b \u2014 1) must \noccur at least once as a remainder upon dividing r, s, ---, w by b.\n\nConsider an encoded message flowing through a communication chan- \nnel. A burst occurs and some of the digits of the message are changed. \nWe will describe the burst pattern by a binary word having a | for each \nchanged digit and a 0 for each correct digit. We require that the first \nand last digits of the word both be 1\u2019s, since there is no point in includ- \ning correct digits which are outside of the bursts. The length of the \nburst is the number of digits in the word. There are 2'~ different burst \npatterns of length J and 2'' different burst patterns of length J or less. \nThe latter are the odd binary numbers having / or fewer digits. For \nexample, the eight burst patterns of length 4 or less are: 1, 11, 101, 111, \n1001, 1011, 1101 and 1111.\n\nThe effect of a burst on the encoded message depends on the phase of \nthe burst pattern with respect to the block structure; hence, we will\n\ncode has a block length b. We will indicate particular bursts either by \nshowing a portion of the encoded message with the erroneous digits\n\nmarked with *\u2019s or by listing the erroneous digits with superscripts to \nindicate which block a particular digit occupies. For example,\n\nAt the decoder we will always have a circuit for checking the parity \nrelation imposed by the encoder. This circuit gives an output once for \neach block received. If the parity check fails, the output is a 1; other- \nwise, it is a 0. In a practical transmission system, there are usually no \nerrors and the check circuit has an output of all 0\u2019s. When a burst of\n\nerrors does occur, the check circuit will give a pattern of 1\u2019s and 0\u2019s. \nThis pattern will be used to identify the burst, and hence we shall call \nit the syndrome. Since the syndromes occur immersed in a string of 0\u2019s, \nonly binary words having 1\u2019s on both ends (odd numbers) can be used \nas syndromes and, as above, there are 2\u201c\"' possible different syndromes \nwith & or fewer digits.\n\nOur first problem is to choose the parity relation in such a fashion \nthat each burst of length / or less has a distinct syndrome.? A further \nproblem is to choose the parity relation so that, given a distinet syn- \ndrome, the correction of the burst which caused it is easily mechanized. \nThat is, we want a systematic scheme for correcting a burst, given the \ncorresponding syndrome, which is much better than having a table of \nall possible syndromes with the corresponding bursts.\n\nThe procedure for calculating the syndrome corresponding to a given \nburst is as follows:\n\n+ If our code has a block length b which is a power of 2, then it is possible for \nb2'-1 = 2-1. A close-packed recurrent code is one which has all possible syndromes \nof k or fewer digits in a one-to-one correspondence with all possible bursts of \nlength 1 or less. Since this is of more mathematical than practical interest, ex \namples are deferred to Appendix I.\n\nNumber the blocks, starting with 0 for the first block containing an \nerror, and continue the ihumbering far enough to inelude all blocks having \nerrors in the burst under consideration. (The direction of numbering\n\nlater times.) Write the parity word for the error in block number 0. \nUnder this write the parity words for any other errors in this block. \nNow write the parity words for the other errors, shifting each one (in \nthe direction of increasing time) the number of places equal to the block \nnumber in which the error occurs. The syndrome is the sum modulo 2 \nof these parity words. In the sample above we use superscripts on the \nparity words to indicate in which block each error occurred. This shows \nthe syndrome for the indicated burst of length 6, using the code of Sec- \ntion II. Note that there is never more than a single 1 in any column. \nBy spreading out the parity words with 0\u2019s sufficiently to prevent any \ninteraction of errors (in a burst not larger than the design maximum), \nwe allow the use of a simple circuit for recognizing the parity words and \ncorrecting the errors one at a time. In other words, the decoder for our \nexample of Section II is simple because we have a single circuit for cor- \nrecting a data-digit error, which is time-shared by every data digit. \nEach data digit is compared with four other digits, all far enough away \nfrom each other so that not more than one of these five digits can be in \nerror due to an allowable burst. Under these circumstances, it is an easy \nmatter to decide if the particular data digit needs correcting.\n\nWe can apply the same technique, spreading out the parity words \nwith 0\u2019s so as to avoid interactions between errors in a burst, to make \nthe redundancy as low as we wish and still have a relatively simple \ncorrecting mechanism. For instance, if we desire a code with a redun- \ndaney of one-quarter good for bursts of length 4, we choose the follow- \ning parity words (the digits are spaced to emphasize the method of\n\nNote that placing the code 100 to the extreme right allowed us to shorten \nthe parity words by dropping the last two columns, which were all 0\u2019s. \nIn assigning the parity words, the groups of 1\u2019s should be arranged to\n\ngo from upper left to lower right as shown above. That is, the order of \nthe groups of 1\u2019s in the parity words should agree with the order of the \ndigits in the block structure. If this is not done extra columns of 0\u2019s \nmust be inserted in the array of parity words, which would mean more \nshift register stages in the encoder and decoder. The difficulty is illus- \ntrated as follows:\n\n* * \n(The burst --- ABCDAB .--- is not allowed, since the above codes are \nfor bursts of length 4 or less.) If we wish to make a code of the same \nredundancy good for bursts of length 8 or less, we form the parity words \nby inserting 0\u2019s between each of the digits of the above code, giving:\n\nFig. 5(a) shows an encoder for this code. The data digits enter from the \nleft side and are cyclically switched to the three shift registers by the \ninput commutator. The buffers allow the shift registers to be stepped \ntogether. A check digit, calculated from the parity of the indicated posi- \ntions of the shift registers is transmitted with the digits from the last \npositions of the registers by the output commutator. Note the corre-\n\nregister comes from P, , the second from Ps , and so on. Each digit of \na parity word becomes a stage of shift register. The stages representing \n1\u2019s are connected to the parity circuit; those representing 0\u2019s are not. \nIf Pp , which has a single 1 at the right end, is assigned to the check \ndigit, no shift register is required at the encoder for this parity word. \n(However, one is needed in the decoder.)\n\nAt the decoder, Fig. 5(b), the incoming digits are commutated to the \nfour shift registers (synchronization must be maintained so that the\n\ndigits get in the proper registers.) As each block arrives at the decoder, \nthe parity relation is checked; if it fails, a 1 is put in the syndrome reg- \nister at the bottom of the figure. Suppose that a digit in the top register \nis wrong; it will cause parity failures as it goes through Positions 1, 3 \nand 5. When it is in Position 5 the syndrome register will have 1\u2019s in \nPositions R, S and T. This will enable the AND circuit, which will cor- \nrect the error as it shifts from Position 5 to Position 6. In a similar man- \nner, an error in the second register is corrected between Positions 11 \nand 12, and an error in the third register between Positions 17 and 18. \nWhenever a 1 reaches Position 7 of the syndrome register, any 1\u2019s in \nPositions R and S are cleared on the next shift. (If for some reason it \nshould be desirable to correct the check digits rather than discard them, \nthis can be done by adding the extension to the bottom register shown \ndotted.) Because of the way the taps for the parity circuit are spaced,\n\nany register can correct two adjacent errors, and the system is good \nagainst bursts of length 8 or less.\n\nIt takes 92 digits entering the decoder to completely refill all the \nregisters (including the syndrome register). Thus, a guard space of 91 \ngood digits between bursts is sufficient to assure that there is no inter- \naction between bursts.\n\nIn general, a procedure for constructing a code of redundancy 1/) \n(block length b) is as follows:\n\nTake the first b binary numbers and let L be the number of digits \nin the largest one. Form each of these numbers to a L-digit word \nby adding zeros to the right end. Now form a square array with b \nrows and b columns. The entries in the array are L-digit words. Put \nthe above-formed words along the main diagonal, with the word \nhaving a single 1 going in the lower right corner. The order of the \nother words on the diagonal is arbitrary. Fill in all remaining words \nwith zeros. Now replace the right-hand column of L-digit words with \nsingle-digit words; | in the bottom row, 0 elsewhere. (Strike out the\n\nThe rows of this array are the parity words of the desired code. The \norder from top to bottom is the (\u2018\u2018snapshot\u201d\u2019) order of occurrence of the \ncorresponding digits in the block structure of the message.* This code \nwill correct all bursts of length b or less. To make a code good for burst \nof length Kb or less, add K \u2014 1 zeros between each adjacent pair of \ndigits of the above parity words.\n\nIf the odd binary numbers were not increased to L digits as above, \ncertain otherwise allowable bursts could cause syndromes which would \nbe incorrectly interpreted by the decoder. For instance, 001 and 110 \nmight add to form 001110. The procedure given prevents this type of \ndifficulty.\n\nIf we design codes by the method indicated in the previous section, \nthe method is regular enough to allow us to give formulas for the shift \nregister stages and guard space. t\n\n* The bottom row is the parity word for the digit that is transmitted first in \nany block. See the direction of rotation of the output commutator in Fig. 5(a).\n\nt If the block length is not a power of 2 it may be possible to save a little from \nthese calculations by taking advantage of the fact that one or more of the odd\n\nnumbers is not used. For example, the burst-length 3, redundancy one-third de \ncoder shift registers can be reduced from 24 to 21 stages\n\nThe block length is b with one check digit; hence, the redundancy is \n1/b. The code is to be usable against bursts of length J or less, where \n1 = kb. L(b) is the smallest integer such that\n\nAny error-correcting system fails when the errors get beyond its cor- \nrecting capabilities. In some cases, it is desirable to detect that a burst \nhas occurred which the system cannot correct. In Section II we men- \ntioned that the code for that example failed on a burst consisting of two \ncheck-digit errors exactly six apart. The effect of this burst is to cause \nthe decoder to change the data digit which is common to the parity \ngroups containing these check digits. This is a fundamental difficulty of \nthe particular code and cannot be avoided, since such a burst converts \nour encoded message to what looks like a different encoded message \nwith a single data-digit error. In general, we cannot correct or even \ndetect bursts which convert one encoded message to another encoded \nmessage, or to another encoded message modified by an allowable burst \n(assuming we still wish to correct allowable bursts). For the example \nof Section II there are:\n\nwhich convert one encoded message to another encoded message mod- \nified by an allowable burst. These seven bursts are not detectable, but \nall other bursts of length 9 or less are detectable and, of course, all bursts \nof length 6 or less are correctable. In connection with the code demon- \nstrator described in Section II, a circuit which detects overlong bursts \nby monitoring the sequence of failures of the two parity circuits in Fig. \n3 has been built. All 512 bursts of length 9 or less have been tried on it, \nand it rings the alarm on all the uncorrected bursts except the seven \nlisted above.\n\nIn the code of Section II the syndrome for a single data error is the \nsame as the syndrome for a pair of check-digit errors six apart. To im- \nprove the error-detection capabilities of our code, we can always change \nthe parity words so that the first occurrence of two bursts giving the \nsame syndrome involves bursts longer than the correctable one.\n\nThis particular code permits a very simple overlong-burst-detection \nscheme. It corrects or detects all bursts of length 13 or less and corrects \nall bursts of length 6 or less. The encoder and decoder are shown in\n\n10 132 168 194 \n+ The decoder here is different from the one for Table I; this one has a syn \ndrome register.\n\nrig. 6. Note that, in the process of correcting an allowable burst, the \nthree parity-check circuits R, S and T cannot have either of the fail- \nure patterns 010 or 101. It happens that one or the other of these pat- \nterns occurs for every burst of length 13 or less that is not corrected by \nthe decoder.\n\nThe decoder here shows an alternative arrangement compared to \nFig. 5. Instead of the syndrome shift register, we have three copies of \nthe parity check circuit shifted so that Position 7 of the data register \nis the only one common to all three. If we were to make a circuit similar \nto Fig. 5, we would save the S and 7 parity circuits, the last five stages \nof the data register and the last six stages of the check register in ex- \nchange for a seven-stage syndrome register with its reset circuit.\n\nIn general, there are two synchronization problems with any binary \ncode, bit synchronization and block synchronization. For purposes of\n\nA amasel TT Tal Tel 1 | TI \nin Lett iet i iiei i. tit ENCODER \nCHECK SHIFT REG pent MESSAGE \net on ouT\n\n(8) \nRST RS'T R'sT\u2019 \nLib Lit Atl \nDATA SHIFT DATA \nREGISTER | ne OUT L_ a \n=F i ae 7 8 10 13 | \nt 1 1 1 1 1 1 1 1 | 1 \n=\u2014 qd J vom \n; ALARM | \nT PARITY CIRCUIT oe | | \nENCODER \nMESSAGE \nIN oA r _ \na ae S PARITY CIRCUIT ee \n\u2014 R PARITY CIRCUIT \nUl T T ! T r r ,@- y _e \n110 | 13 16 19 \n! \n(b) CHECK SHIFT REGISTER\n\nbit synchronization, it is desirable to have transitions from 0 to 1 or \n1 to 0 at some minimum rate. By proper choice of the number of terms \nin the parity relation and also whether the parity is odd or even we can \nprevent either of the codes 00000--- or 11111--- from occurring in the \nencoded message, regardless of what the input to the encoder may be. \nIt is probably also desirable to exclude these codes as possible encoded \nmessages since they are the most likely messages to be put out by an \nencoder with something stuck on or off. Table III shows which codes \ncannot occur.\n\nWith the redundancy one-half code, the block synchronization prob- \nlem is minimized, since there are only two phases that the decoder can \nhave. One possibility is to make a decoder with two equal shift registers \nand two copies of the error-correcting circuit, one wired in each of the \npossible phases. The fact that the wrong parity circuits fail half of the \ntime can be used to tell which phase to use.\n\nAll of the examples known to date are for burst length two. It is not \ntoo hard to show that there is no close-packed code of redundancy one- \nhalf good for burst length three (see Table IV).\n\n1. Storch, P., Evolution of Long Distance Type-Printing Traffic by Wire and \nRadio, Elek. Z., 65, 1934, pp. 109; 141.\n\n5. Plotkin, M., Binary Codes with Specified Minimum Distance, Research Div. \nRep. 51-20, Moore School of Electrical Engineering, Univ. of Pennsylvania, \n1951.\n\n7. Elias, P., Error-Free Coding, I.R.E. Trans., PGIT-4, 1954, p. 29; Coding for \nNoisy Channels, I.R.E. Conv. Rec., 1955, Part 4, p. 37.\n\n. Muller, D. E., Application of Boolean Algebra to Switching Circuit Design \nand to Error Detection, I.R.E. Trans., EC-3, 1954, p. 6. \n. Reed, I. 8., A Class of Multiple-Error-Correcting Codes and the Decoding \nScheme, I.R.E. Trans., PGIT-4, 1954, p. 38. \n. Slepian, D., A Class of Binary Signalling Alphabets, B.S.T.J., 35, 1956, p. \n203. \n. Lloyd, 8. P., Binary Block Coding, B.S.T.J., 36, 1957, p. 517. \n2. Ulrich, W., Non-Binary Error Correction Codes, B.S.T.J., 36, 1957, p. 1341. \nBrown, A. B. and Meyers, 8. T., Evaluation of Some Error Correction Meth- \nods Applicable to Digital Data Transmission, I.R.E. Conv. Rec., 1958, \nPart 4, p. 37. \n. Green, J. H., Jr., and SanSoucie, R. L., An Error-Correcting Encoder and \nDecoder of High Efficiency, Proc. I.R.E., 46, 1958, p. 1741.\n\n5. Kautz, W. H., A Class of Multiple-Error-Correcting Cale. Stanford Research \nInstitute, 1958.\n\n}. Sacks, G. E., Multiple Error Correction by Means of Parity Checks, I.R.E. \nTrans., IT-4, 1958, p. 145.\n\n17. Abramson, N. M., A Class of Systematic Codes for Nonindependent Errors, \nStanford Electronics Labs., Tech. Rep. No. 51, 1958.\n\n18. Gilbert, E. N., A Problem in Binary Coding, Symposium on Combinatorial \nDesigns and Analysis, Amer. Math. Soc., 1958 (to be published).\n\nA binary-decision program is a program consisting of a string of two- \naddress conditional transfer instructions. The paper shows the relationship \nbetween switching circuits and binary-decision programs and gives a set of \nsimple rules by which one can transform binary-decision programs to switch- \ning circuits. It then shows that, in regard to the computation of switching \nfunctions, binary-decision programming representation is superior to the \nusual Boolean representation.\n\nIn his 1938 paper,' Shannon showed how relay switching circuits can \nbe represented by the language of symbolic logic and designed and \nmanipulated according to the rules of Boolean algebra. This far-reaching \nstep provided an algebraic language for a systematic treatment of switch- \ning and logical design problems and provided a root system from which \nnew art can grow and flourish.\n\nWe may want to know, however, if there might not be other ways of \nrepresenting switching functions and circuits, and to compare such repre- \nsentations with the algebraic representation of Shannon. In this paper \nwe will give a new representation of switching circuits, and will call this \nrepresentation a \u201c\u2018binary-decision program.\u201d\n\nBinary-decision programs, as the reader will see, are not algebraic in \nnature. They are, therefore, less easily manipulated. A switching circuit \nmay be simplified not by simplifying its binary-decision program, but \nby essentially finding for it a better binary-decision program. A good \nbinary-decision program generally means one which is well-knit and \nmakes efficient use of subroutines; it is good in the sense then that a \ncomputer program is good. Binary-decision programs do not seek out \nseries-parallel circuits, but are more suited for representing circuits with \na large number of transfers. In these respects, binary decision programs \ntherefore differ very greatly from the usual Boolean representation.\n\nThe characteristic which sets binary decision programs still further \napart from Boolean representation and gave this study its initial stimu- \nlation is in the computation of switching functions. It is here that we will \ngive direct evidence of the superiority of binary-decision programs.\n\nIl. STRUCTURE OF BINARY-DECISION PROGRAMS \nA binary decision program is based on a single instruction \nT 2\u00ab:A,B.\n\nThis instruction says that, if the variable x is 0, take the next instruction \nfrom program address A, and if x is 1, take the next instruction from \naddress B. Every binary-decision program is made up of a sequence of \ninstructions of this kind. \nTake, for example, the switching circuit shown in Fig. 1. This circuit \nis described exactly by the following binary-decision program: \nBe \nT \nT \nwe \n5. T \nThe program is actually a sequential description of the possible events \nthat may occur. We begin at program address 1 by examining the vari- \nable x. If x should be 0, we go to address 2 and examine y. If y is 0, we \ngo to address 6; otherwise we go to address 3, and so forth. The symbols \n6 and J indicate whether the circuit output is 0 or 1. From a computer \nviewpoint, they can be the exit addresses once the circuit output value is \nknown.\n\nIII. CONSTRUCTION OF SWITCHING CIRCUITS FROM BINARY-DECISION \nPROGRAMS\n\nThe question that we will consider here is this: Suppose the logical \nrequirements of a switching circuit are given, when would it be possible\n\nIn various examples we have tried, this approach has given us a fresher \nlook at things and, in several instances, has given us rather good cir- \ncuits. The process of going from binary-decision programs to switching \ncircuits is very well defined, so that how good a circuit we get depends \nentirely upon how good a binary-decision program we can write. Roughly \nspeaking, if a problem has a fairly sizable set of logical requirements to \nbegin with, it would call for a well-organized array of subroutines in the \nbinary-decision program, which are called in as the need arises. Never- \ntheless, there are many exceptions, and it is very hard to say where \ningenuity ends and routine process begins.\n\nLet us now state the rules on how a switching circuit can be con- \nstructed from a binary-decision program.\n\nRule 1. Each address of the binary-decision program corresponds to a \nnode of the circuit.\n\nRule 2. If at address A the instruction is T \u00abx; B, C, a variable 2\u2019 \nshould be connected between nodes A and B and a variable x should be \nconnected between nodes A and C.\n\nRule 3. The node corresponding to address 1 is the input node. The \nnode corresponding to address J is the output node.\n\nA simple change in Rule 3 will enable us to get the negative of the \nswitching circuit. This is done by making the output node the node \ncorresponding to address @ rather than to address J.\n\nWe wish to design a circuit with six switching variables, a,b,c and \nx,y,z. Let M be the binary number abe and N be the binary number xyz. \nThen the output is to be 1 whenever M 2 N.\n\nThe problem says that two binary numbers M and N are to be com- \npared; these two numbers may be compared one bit at a time. We may \ncompare the most significant bits a and z first. If a = 0 and x l, \nthen M < N, so that there is no output. If a = 1 and x = 0, then \nM > N, and the output will be 1. If a = 0 and x = 0 ora = 1 and\n\nlastly, c and z, if necessary. The program instructions are \nAddress Instruction \nA a; Al, A2 \nAl x; A3, 0 \nA2 2: TAS \nA3 b; A4, A5 \nA4 y; AG, 0 \nA5 y; I, A6 \nA6 c; A7, I \nA7 pe Pe\n\nFollowing the three rules, we begin with the first instruction and let \nA correspond to the input node of the circuit. A branch labeled a\u2019 leads \nto the node Al and a branch labeled a leads to the node A2. Al and A2 \nthus become internal nodes of the circuit. From Al we need to put down \nonly the branch 2\u2019 leading to internal node A3, since a branch labeled \nx would give no output. Continuing in this way, we get all the paths \nfrom the input to the output; the addresses tell us where the interconnec- \ntions between these paths are to be made. The circuit for this example \nis given in Fig. 2. From this circuit it can be seen that the three circled \nvariables are superfluous and can be deleted.\n\nWe wish to design a switching circuit with eight variables, a,b,c,d and \nw,x,y,z. Let L be the number of the variables a,b,c,d which are in the \n0 state and let R be the number of the variables w,z,y,z which are in \nthe 0 state. Then the output is to be 1 whenever L 2 R.\n\nThe problem tells us that, if all of the variables a,b,c,d are 0, the \noutput would be 1 regardless of what w,a,y,z are; if exactly three of the\n\nrariables a,b,c,d are 0, then the output would be 1 whenever three or \nfewer of the variables w,z,y,z are 0; and so forth. To program this\n\nThe program is then completed by counting the number L of the \nvariables a,b,c,d which are 0. If LZ is 4, the output is made | directly; \nif L is 3,2,1 or 0, the program enters subroutine S1, S2, S3 or S4 respec- \ntively.\n\nWe will begin with the subroutine programs. The subroutine S1 is a \nsuccessive scan of the states of the variables w,x,y,z:\n\nThe subroutine S2 can be written likewise. A moment\u2019s reflection will \nshow, however, that S2 can make use of a portion of the instructions of \nS1. Similarly, S3 can make use of S2 and S4 can make use of S3. The \nsubroutine programs come out to be:\n\nThe main program which evaluates LZ and selects the appropriate \nsubroutine is\n\nFollowing the three rules of construction, the final circuit is given in \nFig. 3. To show how the subroutine circuits can be combined in stages, \nthe circuit for S1 is given in Fig. 4 and the combined circuit for Sl and \nS2 is given in Fig. 5.\n\nGenerally, we find that the switching circuits constructed from binary-\n\ndecision programs have several distinct characteristics. The construc-\n\ntion does not distinguish among series-parallel, bridge and nonplanar \ncircuits, but it is restricted to unidirectional flow of current in any\n\ntion, the program in most.cases gives bridge or nonplanar circuits and \nvery rarely gives series-parallel circuits. Again, because of the transfer \ncharacteristic of the instruction, the procedure tends to give circuits\n\nhaving a large number of transfers, causing unnecessary appearance of \nvariables in the circuits. On the other hand, the presence of the transfers \nprevents sneak paths, which are often a source of worry.\n\nThe problem that we wish to consider here is this: Suppose, in carry- \ning out a complicated task, a complex decision depending on many \nvariables is to be made and made repeatedly. Question: What procedure \nshould one follow so as to arrive at the decision quickly and without \nhaving to go through a large amount of computation?\n\nTo make the problem more tractable, let us say that the decision \nfunction is a switching function of n variables. The problem is to find \na good procedure for the computation of this function.\n\nThe first question one should ask is, perhaps, what are the choices? \nIf the switching function is, say,\n\nwhat alternatives in computation are there? \nThere are indeed many alternatives. One may, for instance, carry\n\nand 32 for the AND-OR-SUM procedure. On the other hand, the binary- \ndecision program is longer by one instruction.\n\n1. For an arbitrary switching function of n variables what is the \norder of magnitude of the number of instructions in its binary-decision \nprogram?\n\n2. Comparing specifically the binary-decision program approach with \nthe AND-OR-SUM procedure, which will in general need fewer instrue- \ntions and which will need less time to execute?\n\nQuestions of this nature but pertaining to the number of relay contacts \nor electronic components have been studied by Shannon? and Muller.* \nAs is the case with their investigations, we are not able to answer these \nquestions for individual functions but our answers apply to an over- \nwhelming fraction of switching functions of n variables.\n\nLet f be a switching function of n variables, and let u(f) be a number \nsuch that no binary-decision program representing f has fewer than u(f) \ninstructions. We will let u, be the smallest number of instructions suffi- \ncient to represent any switching function of n variables. That is,\n\nProof: Let N(n,p) denote the number of possible binary-decision \nprograms involving n variables with p instructions. Since each instruc- \ntion can be chosen from at most np\u2019 instructions, it follows that \nN(n,p) S (np*)\u201d and, in particular, N(n,u,) S (np,?)**.\n\nTo find an upper bound for yu, requires an interesting subroutine \ntechnique. Let a set of programs each of which computes a switching \nfunction be called a library. Let L(n) be the library of programs which\n\not . e \u00b0 \u00b0 . la hl \nrepresent all 2? switching functions of n variables. Then \nLemma 2: The library L(n) can be written so that it contains not\n\nTherefore, L(2) can be written in exactly 2? instructions. \nNow suppose the lemma is true for all n, 2 S n S m. Consider n =\n\n. . . . gmt on\u2122 \u00a2 . . \nof m + 1 variables. For each of the other 2? \u2014 2? functions of m + 1 \nvariables, the program can be written \n\u2018iM Lm+1 5 A, B,\n\nwhere A and B refer to addresses in the library L(m). Hence L(m + 1) \ncan be written with not more than \ngmt r o\u2122 oo \n(22 2\") +4\n\nProof: The lower bound was given by Lemma 1. To get the upper \nbound, let us write n = (n \u2014 j) + j, where j may vary from 0 to n. \nLet f be a switching function of n variables. Then f may be expanded \nabout n \u2014 j of its variables in its canonical expansion:\n\nAlso, by Lemma 2, we may construct a library L(n \u2014 j) with not more \non\" ae \u00b0 \u00b0 \nthan 2? ~ instructions. Hence f can be programmed with not more than \n\u2018 ee | 6 . . y \n2? + 2\u2019 \u2014 | instructions. Now set \nj =n \u2014 [loge(n \u2014 logs n)I, \nwhere [x] denotes the largest integer less than or equal to x. Then \nQn Qn Qn\n\nNow, by direct computation, we find uw, = 1, we. S 4 and yw; S 6. Hence \nfor all n, we have p, S 4 (2\"/n) \u2014 1, and the theorem follows. \nTheorem 2: Given any \u00a2,0 < \u00a2 < 1,a fraction 1 \u2014 2 2\u201d of switching \nfunctions of n variables will need at least 2\"(2n)-(1 \u2014 e) binary- \ndecision program instructions to program. \nProof: The number of possible binary-decision programs with not \nmore than 2\"(2n)-! (1 \u2014 e\u20ac) instructions cannot exceed\n\nwhich is less than 2?\u00b0\"-\u00ae, Therefore, the fraction of switching functions \nof n variables which need not more than 2\"(2n)~\"(1 \u2014 e) instructions to \nprogram cannot exceed 2-@\". Hence the rest must need at least 2\"(2n)~ \n(1 \u2014 e) instructions to program and the proof follows.\n\nThe procedure outlined in the proof of Theorem 1 yields for each \nswitching function of n variables a binary-decision program. We will \nvall this program the normal binary-decision program for that function. \nA close examination of this procedure will show that the number of \nprogram instructions executed in the computation of a particular value \nof any switching function of n variables never exceeds n. That is, in \nthe computation no variable is examined more than once. Therefore, \nwe have\n\nCorollary 1: The number of instructions which has to be executed in \nthe normal binary-decision program for the computation of each value \nof any switching function of n variables never exceeds n.\n\nThese results together give us a fairly good idea of how efficient it \nis to compute switching functions with binary-decision programs. For \nn = 20, for instance, practically all switching functions need more than \n25,000 instructions to program, although none needs more than 200,000 \ninstructions. The number of instructions that one needs to go through \nto compute a single value is never more than 20, however. We want \nnow to compare these results with the AND-OR-SUM procedure men- \ntioned earlier.\n\nBefore we consider the AND-OR-SUM procedure illustrated pre- \nviously, it might be well for us to show why this particular procedure \nis chosen for comparison. A switching function is commonly written in \nterms of its variables and their complements connected by AND and \nOR. Besides AND and OR, there are eight other binary operations, \ndenoted by 1, |, \u00ae,, D, C, Dp, and \u00a2, where we have called @ \nthe SUM operation. These can be written in terms of AND and OR \noperation :\n\nIn order not to be restrictive with our alternative computational \nprocedure, let us be allowed to use any of these 10 operations in a com- \nputation. The first thing we wish to show is that we lose nothing by \nthrowing away seven of these operations. In order to do this, let us \nvall any switching function expression involving the variables and their \ncomplements, in which any of the 10 operations may appear, a binary \nexpression. Let us also say that two binary expressions are equivalent if \nthey represent the same function. Then\n\nTheorem 3: Let f be a binary expression with r operations. Then there \nis an equivalent binary expression g having r or fewer operations such \nthat the only binary operations appearing in the expression g are AND, \nOR and SUM.\n\nin which no operation other than AND, OR and SUM appears. \nTo prove this theorem, we note that, if 9 is any binary-expression of \nr operations, r = 1, then g is expressible as\n\nwhere h and k are binary-expressions each of (r \u2014 1) or fewer operations \nand * is one of the 10 binary operations. Also,\n\ngj = (he ky) =h*' k, \nwhere +\u2019 is again one of the 10 binary operations. Therefore, if 9 is any \nbinary-expression with r operations, then its complement expression @\u2019 \nrequires not more than r operations.\n\nGoing back to Theorem 3, we note that the theorem is true for r = 1. \nNow suppose that the theorem is true for all r, 1 \u00bb p(ji) a= \n. n]} j=0 n\u2014-1+),\u2019\n\nwhere p(j:) represents the Poisson probability of j; arrivals in a service \ninterval, since, if the delayed call is not served at the first opportunity, \nany number of calls from zero upward may arrive during the next com- \nplete service interval. Extending this reasoning, one has for 7 > 0,\n\n\u2018Soull} Zurpfoy FT 09 dn sAvjap jo suonnquysiq \u2014 Zz \u201c31g \nJIWIL ONIDQIOH J9OVYESAV 4O SAITIdILINW Ni Av130 \nO% 6 8 Z 9 S\n\nEQUILIBRIUM DELAY DISTRIBUTION FOR ONE CHANNEL 1027 \ncomputationally to use a recursive formula for the probabilities. (This \nwas pointed out to the author by W. 8S. Hayward, Jr.) Let\n\nIt is clear that (6) is the solution of (7). The delay distribution, F'(), \nis obtained by substituting (6) into (5) and the latter into (3). The \nvalues of P,.; necessary for evaluating (3) are obtained recursively\n\nThe results of the calculations are shown as falling distributions of \ndelays for all calls. That is, A[1 \u2014 F(\u00e9)] is plotted rather than F(\u00e9), in \nkeeping with custom in the field of delay theory. The distributions are \nshown in Fig. 2 for delays up to 14 holding times and, in Fig. 3 on a \ncompressed scale, for delays up to 130 holding times.\n\nAs an example of the use of the curves, suppose a single marker whose \nholding time is 0.1 second serves calls at random and that it is desired \nto limit the probability of a delay greater than 2 seconds at this marker \nto 0.0001. It is required to find the permissible occupancy. Since a delay \nof 20 holding times is involved, Fig. 3 should be consulted. On this \nchart, the occupancy for a probability equal to 0.0001 of delay t/h = 20 \nis found to be just above 0.60, roughly 0.61. Thus, the marker can handle \na random input averaging 6.1 calls per second.\n\nIn some applications in which service is not precisely order-of-arrival, \nit may be presumed that the delay distribution will lie between those \nfor random and queued service. In such cases, the delay distributions \nwill fall in a band bounded by random service and queued-service \n(Crommelin) curves. Examples of such bands are shown on Fig. 4. It \nshould be noted that the bounding curves for any occupancy must cross, \nsince the average delay is independent of the queue discipline.\n\nIt is of some interest also to compare the random-service delay distri- \nbutions for constant and exponential holding times. It is conjectured \nthat a pair of such curves for a given occupancy defines a band containing \nall random-service delay distributions, for that occupany, where the \nholding-time distribution is of gamma type in which the coefficient of\n\n*soull} Zurpjoy OT 0} dn sAvjep jo suornqiuysiq \u2014 \u00a2 \u2018317 \n3WIL SNIGIOH 39vesAV 3O S3TdILINW NI Av730 = 4/2 \n06 oe OL 09 0S or\n\n\u201c@OTALOS ULOPUBL YIM \u201cSourry Zurploy jemueuodxea pues yUBISUOD JO uostiedwo >-\n\nvariation is not greater than unity. (In particular, the x? distributions \nwith two or more degrees of freedom are of this type.) Several such pairs \nof curves are shown on Fig. 5. (The exponential-holding-time curves are \nbased on Wilkinson.*) Here, of course, the curves do not cross \u2014 the\n\nThe extensive computations required for Figs. 2 through 5 were \nprogrammed by Miss Catherine Lennon, to whom the author expresses \nhis gratitude.\n\n1. Erlang, A. K., The Life and Works of A. K. Erlang, The Copenhagen Telephone \nCo., Copenhagen, 1948.\n\n2. Mellor, 8S. D., Delayed Call Formulae When Calls Are Served in a Random \nOrder, P.O.E.E.J., 36, 1942, p. 53.\n\n3. Vaulot, E., Delais d\u2019attente des appels t\u00e9l\u00e9phoniques trait\u00e9s au hazard, \nComptes Rend., 222, 1946, p. 268.\n\n5. Palm, C., Vantetider Vid Slumpvis Avverkad K6, Tekniska Meddelanden Fran \nKungl, Telegrafstyrelsen, Specialnummer for Teletrafikteknik, Stockholm, \n1946, p. 70. (Translated in Tele, English Edition, No. 1, 1957, p. 68.)\n\n, Kendall, D. G., Stochastic Processes Occurring in the Theory of Queues and \nTheir Analysis by the Method of Imbedded Markov Chains, Ann. Math. \nStat., 24, 1953, p. 338.\n\n8. Crommelin, C. D., Delay Probability Formulae When the Holding Times Are \nConstant, P.O.E.E.J., 25, 1932, p. 41.\n\nIn the development of solderless wrapped connections for telephone central \noffice applications, the general reliability objective has been that the connec- \ntions should remain mechanically secure and electrically stable during manu- \nfacture, shipment and installation and for 40 years thereafter in actual \nservice. Destructive mechanical tests have been used to evaluate the me- \nchanical properties of the connections. Combinations of elevated tempera- \ntures and mechanical disturbances have been used to accelerate the aging \nprocesses that tend to cause electrical instability. The results of such tests \nhave provided considerable assurance that properly designed and properly \nmade solderless wrapped connections will perform satisfactorily for 40 \nyears tn central office service.\n\nThe tangible and immediate results of solderless wrapping have been \ngratifying. For example, the use of solderless wrapping has reduced \nmanufacturing costs by speeding up many wiring operations and by re- \nducing troubles caused by wire clippings and solder splashes. Further- \nmore, since solderless wrapping avoids the risk of damaging heat- \nsensitive insulation by soldering operations, it has made widespread \nuse of plastic-insulated wire practicable, and this is leading to sub- \nstantial additional savings.\n\nIn the end, however, these savings could be illusory if the use of solder- \nless wrapped connections degraded telephone service or increased the\n\nmaintenance effort required in the telephone plant. The laboratory \nevaluation of solderless wrapped connections has been continued, there- \nfore, in order to assess the risk of deterioration in service and to provide \nguidance for the design of connections that are most likely to be reliable. \nThis work has revealed certain limitations of solderless wrapped connec- \ntions, but, at the same time, it has provided considerable assurance that \nproperly designed and properly made connections will be reliable in cen- \ntral office service.\n\nMany persons have inquired about the methods used for evaluating \nthe capabilities of solderless wrapped connections and about the results \nthat have been obtained since publication of earlier articles.?-* Since the \ninquiries continue undiminished year after year, it appears that there is \nsufficient interest in solderless wrapping to warrant another paper on the \nsubject. An attempt is made here, therefore, to bring the story on evalua- \ntion up to date.\n\nA solderless wrapped connection is made by wrapping a wire tightly \naround a terminal, and the connection is held together thereafter by the\n\nFor Bell System applications, a minimum of five turns of wire is speci- \nfied when No. 22 gauge wire is used, and a minimum of six turns is \nspecified when No. 24 gauge wire is used. The wire should be closely \nwound on the terminal, but turns of wire should not overlap.\n\nOnly solid copper wire has been approved for solderless wrapping. \nThe use of stranded wire presents a number of difficulties and has not \nbeen investigated in detail.\n\nThe general reliability objective in the development of solderless \nwrapped connections has been that the connections should remain \nmechanically secure and electrically stable during manufacture, shipment \nand installation and for 40 years thereafter in telephone central office \nservice.\n\nThe mechanical security objective cannot be defined in absolute terms, \nfor too little is known about the magnitudes and distributions of the\n\nobjective, however, solderless wrapping should not increase the occur- \nrence of broken wires and loose connections beyond the levels that now \nprevail with soldered connections.\n\nThe electrical stability objective can be stated more specifically. Not \nmore than one connection in 10,000 should exhibit resistance fluctuations \ngreater than 0.1 ohm in service. The electrical noise produced by re- \nsistance fluctuations of this magnitude is considered to be at the thresh- \nold of transmission impairment in the most critical transmission circuits \nnow in service.\n\nThe measurement of interest is the variation of resistance when the \nconnection is disturbed mechanically. The disturbance is created by \nplucking the terminal \u2014 that is, by slowly deflecting the free end of the \nterminal a predetermined distance and then releasing it abruptly, allow- \ning terminal and connection to vibrate freely. The resistance variation\n\n(AR) is the difference between the maximum and minimum resistance \nvalues observed during the disturbance.\n\nAlthough the moving-coil millivoltmeter is too sluggish to follow rapid \nfluctuations of resistance, the measurement is surprisingly sensitive. In a \nseries of measurements made by an appropriate electrical noise meter \nwhile connections were subjected to vibration of the sort encountered in \nservice, the measured noise levels consistently were lower than the levels \n\u2018alculated from the results of the simple AR measurements. It was con- \ncluded that the simple AR measurement would be adequate for routine \ndevelopment tests and, since it could be made far more rapidly than any \nof the more refined measurements that had been explored, it was adopted.\n\nA major problem in the evaluation, of course, has been to demonstrate \nby means of comparatively small samples that the probability of AR \nexceeding 0.1 ohm is no more than one in 10,000. The expense of testing \nlarge enough samples to determine the frequency distribution of AR in \nevery case would have been prohibitive. Over a period of years, however,\n\na moderately large number of tests were made on a few particular types \nof connections. The cumulative sample sizes in those cases, although still\n\nsmall compared with 10,000, were large enough to warrant attempts at \ncurve fitting.\n\nAs measured by the chi-square test, the expression that seems to fit \nthe observed distributions best is obtained by first grouping the AR data \nin cells as follows:\n\nThe arithmetic mean of the grouped distribution then is calculated as \nfollows:\n\nwhere N is the total number of connections in the sample. \nOnce the mean, m, has been calculated, the probability of finding a \nconnection in cell \u00ab can be expressed as\n\nBearing in mind that 0! = 1, the probabilities associated with the first \nfew cells become \nPo = \u201d he\n\nThe reader may recognize that (2), the general expression for P, , is \nthe same as the expression for the Poisson distribution. The physical \ninterpretation, however, is different. In the Poisson distribution, P, is \nthe probability that \u00ab defectives will occur in a random sample of size N \nif m is the expected average number of defectives in a sample of that \nsize. As a description of the AR distribution, however, P, is the probabil- \nity that AR, for a single connection chosen at random, will fall between \nthe limits defined by the cell number x. For a random sample of N con- \nnections, then, the number of connections expected to fall in cell number \nx willbe NP,.\n\nIn general, the agreement between (2) and observed AR distributions \nhas been best for the more stable types of connections \u2014 types in which \nhigh values of AR rarely occur and for which m is small. These, of course,\n\nare the types of connections that are desirable. For less stable types of \nconnections \u2014 the types that would be rejected as unreliable \u2014 the\n\nFig. 2 Ixamples of the AR distribution defined by (2). Shading indicates \ncells for which AR exceeds 0.1 ohm.\n\nagreement has been poorer. The dividing line between good agreement \nand poor agreement appears to be somewhere in the vicinity of m = 0.3.\n\nThe mean, m, is a convenient statistic to use in summarizing the re- \nsults of a group of AR measurements, and it will be used for that purpose \nin the discussion of accelerated aging tests. Qualitatively, low values of \nm indicate stable connections and high values indicate unstable connec- \ntions. Quantitatively, in those cases where m is less than about 0.3, m \ndefines the observed AR distribution very effectively.\n\nThe distribution corresponding to m = 0.086 (shown in Fig. 2) is of \nparticular interest. It represents the case for which there is one chance in \n10,000 that AR will exceed 0.1 ohm. Consequently, a value of m = 0.086 \nin service is the maximum value that will satisfy the stability objective \nfor central office use of solderless wrapped connections in the Bell Sys- \ntem,\n\nIairly early in the development of solderless wrapped connections, it \nwas concluded that electrical instability, if it occurred at all, would result \nprincipally from relaxation of stresses in the wire and terminal \u2014 the\n\nstresses that hold the connection together. Since that time, all aging \ntests employed in the evaluation of solderless wrapped connections have \nincluded elevated temperatures to accelerate the relaxation process. \nThe work of Mason? and others indicated that the stress in copper \nwire (measured with respect to its value one day after a connection was \nwrapped) would relax about 40 per cent in 40 years at room temperature. \nTo allow for some error in the room temperature prediction, and to allow\n\n55\u00b0C in some cases, it has been assumed that the stresses in solderless \nconnections wrapped with copper wire may relax as much as 50 per cent \nunder central office conditions. That has been the degree of stress relaxa- \ntion aimed at in the various accelerated aging tests.\n\nOne of the early tests consisted simply of baking the connections for \nthree hours at 175\u00b0C. (Mason had shown that the stresses in connections \nwrapped with copper wire would relax 50 per cent in about 23 hours at \n175\u00b0C, and the extra half-hour was needed to bring the specimens from \nroom temperature up to the oven temperature.) At the end of the heat \ntreatment, the connections were cooled to room temperature and then \nwere checked for electrical instability. The general experience was that \nany solderless wrapped connection which was stable before the heat \ntreatment still would be stable after the heat treatment.\n\nAlthough such results were encouraging, they were, at the same time, \ndisconcerting. For example, some of the connections that behaved so \nwell in the 175\u00b0C test were wrapped on terminals that scarcely could be \nconsidered good mechanical structures for supporting stresses over long \nperiods. The twin-wire terminal of the wire-spring relay, in particular, \nfell in the questionable category. At that time it consisted simply of two \nparallel nickel silver wires which were bonded together by being dipped \nin soft solder and then serrated. The parallel wires by themselves did not \nhave sufficient torsional stiffness to support the stresses that are required \nto hold a solderless wrapped connection together; and soft solder, be- \ncause of its cold flow properties, is a notoriously poor material for sup- \nporting stresses. It was doubtful that the soft solder, at room tempera- \nture, could maintain the stresses long enough at levels high enough for \nsolid state diffusion to occur. Since 175\u00b0C was not far below the softening \ntemperature of the solder, there was at least a suspicion that something \nakin to a soldered joint had been produced in the accelerated aging test.\n\nThere were questions, also, about the metallurgical behavior of the \ncopper wire at the elevated temperature. It was known, for example, that \nrecrystallization is more likely to occur in copper at 175\u00b0C than at lower \ntemperatures.\n\ndo more than accelerate the aging process: it might alter the physical \nnature of the aging process itself. If this were so, then the 175\u00b0C test \nmight give a false picture of the aging that would occur in actual service\n\nIt was decided, therefore, that some exploratory aging tests should be \nrun at a substantially lower temperature. For several reasons, a tempera- \nture of 105\u00b0C was chosen. It was well below the softening temperature \nof tin-lead solders; it was low enough so that there should be little likeli- \nhood of recrystallization occurring in the copper wire; yet it was high \nenough to produce the desired stress relaxation in a few months. Mason\u2019s \nwork had indicated that the stresses in the wrapped connections would \nrelax 50 per cent in about 150 days at 105\u00b0C, so the test period was set \nat 150 days, or approximately five months.\n\nAs compared with the desired service life of 40 years, the three-hour \n175\u00b0C test represented a 100,000:1 acceleration of the stress relaxation \nprocess. Since a five-month 105\u00b0C test would represent an acceleration of \nonly 100:1, it was expected to be a far more realistic aging test.\n\nFive months is a long time, however, to wait for test results. It was \ndecided, therefore, that the test connections should be measured peri- \nodically during the aging test, so that any instability would be detected \nas soon as it occurred. It is important to note that this decision intro- \nduced two more changes in the accelerated aging test: (a) it subjected \nthe connections to temperature cycling, for they were removed from the \noven and allowed to cool whenever they were measured, and (b) it sub- \njected the connections to mechanical disturbances while they were being \naged, for the terminals were plucked whenever resistance variations were \nmeasured.\n\non the solder-dipped twin-wire terminals described earlier. Connections \nof that type had survived the 175\u00b0C test without showing any evidence \nof instability. In the 105\u00b0C test, however, they soon began to exhibit \nmeasurable resistance fluctuations, and they grew more and more un- \nstable as the test continued. The history of that first group of connec- \ntions is plotted in terms of the statistic m in Fig. 3. It was evident that \nthe 105\u00b0C aging test with periodic cycling and measurement was more \nsevere than the undisturbed 175\u00b0C test.\n\nSubsequently an experiment was performed to compare the relative \neffects of temperature, temperature cycling and mechanical disturbance. \nOne group of connections was aged at 105\u00b0C, cooled to room tempera- \nture once each week and measured (plucked) while at room temperature\n\nFig. 3 \u2014 Effect of 105\u00b0C accelerated aging test on solderless connections wrap- \nped with No. 24 gauge copper wire on solder-dipped twin wire terminals of wire- \nspring relay. Sample size 48.\n\non alternate weeks. At the end of 150 days, the value of m for that group \nwas 2.1. \nA second group of similar connections was aged at 105\u00b0C and cooled\n\nto room temperature once each week, but was not disturbed by measure- \nments. After 150 days, m was 0.2.\n\nA third group was aged continuously at 105\u00b0C without either tem- \nperature cycling or mechanical disturbance. After 150 days, m was 0.04.\n\nA fourth group was maintained continuously at room temperature but \nmeasured every two weeks. After 150 days, m was 0.02.\n\nThree important inferences were drawn from the results of this experi- \nment:\n\ni. Although solid state diffusion may occur during undisturbed aging \nof solderless wrapped connections, thus tending to offset the detrimental \neffects of stress relaxation, repeated mechanical disturbances during the \naging process can impede diffusion and can lead to unstable connections.\n\nii. Since connections may be disturbed from time to time in service, \naccelerated aging tests should include periodic mechanical disturbances.\n\niii. Temperature cycling alone can produce a form of mechanical dis- \nturbance if the temperature coefficients of expansion of wire and terminal \nare not equal.\n\nAnother related experiment was performed to study the effects of the \nfrequency with which connections were disturbed during the 105\u00b0C aging \ntest. The more frequently the connections were disturbed, the sooner \nthey became unstable. A few of the test results are shown in Fig. 4 to \nillustrate the pattern.\n\nFig. 4 kiffeets of varying the frequency of disturbance in 105\u00b0C accelerated \naging test. Connections wrapped with No. 24 gauge tinned copper wire on 0.010 X \n0.062-inch flat nickel silver terminals. Sample size 48 in each case.\n\nsary to standardize an accelerated aging test so that the development \nof suitable terminals could proceed without further delay. The 150-day \n105\u00b0C test was adopted, primarily because it was the only aging test \nup to that time that had revealed highly significant differences among \nvarious types of connections \u2014 differences that usually were consistent \nwith qualitative analyses of the various mechanical structures. The con- \nnections were cooled to room temperature once each week, and their \nresistance variations were measured at room temperature every other \nweek. Each connection was plucked two or three times during the AR \nmeasurement. Eventually, a plucking amplitude of 3; inch was stand- \nardized.\n\nA standard procedure for the preparation of test specimens also \nevolved gradually. It has become the usual practice now, in preparing\n\neach group of test connections, to use two wrapping bits (one that wraps \nmore tightly than the average bit, and one that wraps less tightly), two \nwrapping tools (one power-driven and the other manually operated), \ntwo grades of wire (one comparatively hard and the other comparatively \nsoft) and two operators. All 16 combinations of the four parameters \nnow are included at least twice in each test.\n\nFig. 5 shows the results that were obtained with No. 24 gauge tinned \ncopper wire wrapped on terminals punched from several widely used \nthicknesses of nickel silver stock. The performance of the thinner ter- \nminals was considered to be unsatisfactory. Various types of longitudi- \nnal embossing were investigated to find means for improving the thin \nterminals, and the form shown in Fig. 6 finally was standardized. Al- \nthough this form is not necessarily optimum, it is a convenient form to \nmanufacture; and it has behaved well in the accelerated aging test, as \nshown in Table I.\n\nTasBLE I \u2014 Resutts oF ACCELERATED AGING TESTS ON SOLDERLESS \nCONNECTIONS WRAPPED WITH TINNED CopPpER WIRE \n175\u00b0C Screening Test\n\nFig. 5 Results of 105\u00b0C accelerated aging tests. All terminals flat nickel sil- \nver, 0.062 inch wide. Connections wrapped with No. 24 gauge tinned copper wire\n\nThe early single-wire terminal of the wire-spring relay was formed \nfrom a round wire by flattening, serrating on one side and solder-dip-\n\nping. Its performance was unsatisfactory, but it was improved simply \nby omitting the solder. Its present form is shown in Fig. 7.\n\nThe twin-wire terminal of the wire-spring relay was more of a prob- \nlem. Many designs were conceived and investigated, but most of the\n\nFig. 7 \u2014 Single-wire terminal of wire-spring relay. \ndesigns that showed promise from the solderless wrapping standpoint \nwere objectionable from the manufacturing standpoint. In the end, a \ncompromise design was adopted. The twin wires are twisted tightly \ntogether, then they are coined in a closed die which has a trapezoidal \ncross section. The resulting terminal is shown in Fig. 8.\n\nAlthough most of the 105\u00b0C tests have been made with No. 24 gauge \nwire, a number of tests have been made also with No. 22 gauge wire. As \nshown in Table I, the results indicate that No. 22 gauge connections on \nthe heavier terminals are as stable as No. 24 gauge connections, but that \nNo. 22 gauge connections on the lighter terminals are inferior.\n\nThe aging tests of No. 26 gauge connections are not completed yet. \nThe preliminary results indicate, however, that No. 26 gauge connec- \ntions, even when wrapped with as many as nine turns of wire, are less \nstable than six-turn No. 24 gauge connections on the same types of ter- \nminals.\n\nFor certain types of wiring in the Bell System, it has been standard \npractice to use untinned copper wire. Solderless connections wrapped \nwith untinned wire, however, tend to deteriorate sooner than connec- \ntions wrapped with tinned wire. Fig. 9 illustrates results obtained with \nuntinned wire.\n\nThe data that have been presented so far should be sufficient to pro- \nvide a bird\u2019s-eye view of the results that have been obtained in the\n\nFig. 9 Effect of 105\u00b0C accelerated aging test on connections wrapped with \nuntinned copper wire on electrotinned brass terminals. Sample size 32 in each \ncase\n\n105\u00b0C aging test. Other alleys and byways have been explored, but the \npicture would not be sharpened perceptibly by presenting more details. \nIt is more pertinent at this point to consider what use can be made of \nthe test results.\n\nThe purpose of the accelerated aging test, of course, is to distinguish \nbetween those types of solderless wrapped connections which are likely \nto satisfy the 40-year stability objective in service and those types which \nare not likely to satisfy the objective. The test results supply a reason- \nably clear picture of the relative instability of the several types of con- \nnections, but this by itself is not enough. Somewhere on the instability \nscale the development engineer eventually must draw a line and say, at \nleast to himself, \u2018I will approve the use of types of connections that fall \nbelow this line; I will not approve types that fall above it.\u201d In other \nwords, he must establish a criterion for acceptance.\n\nThe criterion for acceptance has not remained static as the develop- \nment of solderless wrapped connections progressed. Instead, it has been \nrevised several times as the aging test evolved and as the information \nobtained from aging tests expanded. Its present form has considerably \nmore meaning and is more convenient to use than some of the earlier \nforms.\n\nThe criterion for acceptance is based upon two premises: (a) that the \n105\u00b0C accelerated aging test does, in fact, produce at least as much \ninstability as 40 years of central office service will produce and (b) \nthat (2) is an adequate description of the AR distribution. Although \nfinal confirmation will not be available until about 1990, evidence that \nthese premises are valid is increasing year after year.\n\nIt was stated previously that the value of m should not exceed 0.086 \nin service if the resistance variation of not more than one connection in \n10,000 is to exceed 0.1 ohm. If the 105\u00b0C test is an adequate simulation \nof service conditions, then those types of connections which have values \nof m below 0.086 in the 105\u00b0C test should be acceptable. This would be \nthe criterion for acceptance if very large samples were tested. Where \nsmall samples are tested, however, it is prudent to make allowance for \nsampling errors.\n\nceptable if the mean, m, of a sample of N connections is less than the \nvalue of mo.o5 given by (5). The acceptance level is plotted as a function \nof N in Fig. 10.\n\nAs an aid to decision making, it also is possible to set up a criterion \nfor rejection. If a large number of samples of size N are drawn from a \npopulation whose true mean is m\u2019, then roughly 95 per cent of the sam- \nple means can be expected to fall below the value \n\u2018m\u2019\n\nFig. 10 \u2014 Criteria for acceptance and rejection in 105\u00b0C accelerated aging \ntest. Points are results of 105\u00b0C tests on approved types of solderless wrapped \nconnections.\n\nIn other words, the stability of the connections will be considered un- \nacceptable if the mean, m, of a sample of N connections exceeds the \nvalue of mo 95 given by (7). Further testing of that particular type of \nconnection is not very likely to be profitable, so it might as well be re- \njected.\n\nEstablishing a rejection limit that does not coincide with the accept- \nance limit provides a zone of uncertainty in which the connections are\n\nneither clearly acceptable nor clearly unacceptable. It recognizes the \npossibility that further testing of a marginal type of connection might\n\ndemonstrate that the type is acceptable. If the value of being able to \napprove that type of connection outweighs the cost of further testing, \nthen it may be worthwhile to continue.\n\nOn the average, the acceptance criterion of (5) is conservative. Not \nonly does it provide margin for moderate sampling errors, it also pro- \nvides some margin, on the average, for an error in the basic premise \nthat the 105\u00b0C test adequately simulates aging in service.\n\nAt the same time, the form of (5) is helpful to the experimenter, for \nit tells him the minimum sample size that can be used as the basis for \nacceptance. By setting moo, equal to zero in (5), the corresponding \nminimum sample size is found to be 32. If he tests 32 connections and \nm turns out to be zero, he is entitled to approve the connections without \nfurther testing. With a smaller sample, he would not be entitled to \napprove them even though m turned out to be zero.\n\nFrom a practical standpoint, it is prudent to test a larger sample \nwhen approval is needed in the shortest possible time. If AR for even a \nsingle connection exceeds 0.001 ohm in a sample of 32, then the con- \nnections cannot be approved, the test has to be expanded, and the final \ndecision is delayed. A practical compromise is to test a sample large \nenough so that four connections could exceed 0.001 ohm slightly without\n\ncausing m to exceed moo5. If \u00ab = 1 for the four connections, then \nm = 4/N and, from (5), the corresponding sample size is 104.\n\nAlthough the 105\u00b0C test appears to be quite effective in distinguish- \ning between stable connections and unstable connections, its slowness is \na practical disadvantage. In cases where a number of alternate terminal \ndesigns are being considered, for example, and where it is desirable to \nconcentrate development effort on a few of the most promising alter- \nnates, the five-month waiting period can be extremely inconvenient. \nThere is need, therefore, for a quick screening test that will serve to \nidentify those types of connections that are likely to pass the 105\u00b0C \naging test.\n\nEarly experience with the 105\u00b0C test suggested that addition of \nmechanical disturbances to the original three-hour undisturbed 175\u00b0C \ntest might make it capable of detecting potentially unstable connections. \nWithin limits, this proved to be so.\n\nIn the screening test that eventually was standardized, the solderless \nwrapped connections are baked in an oven for three hours at 175\u00b0C. \nThe three-hour period includes the warming up period of the oven and \nfixtures, which amounts to about one-half hour with the equipment that \nhas been used. During the entire three-hour period, each terminal is \nplucked automatically once per minute. The plucking mechanism deflects \nthe free end of each terminal ;'g inch, then releases it abruptly, allowing \nthe terminal and lead wire to vibrate freely. The opposite end of the \nterminal is supported rigidly, of course, and the unsupported length (on \nwhich the connection is wrapped) is }$ inch.\n\nIn the ordinary cases, where there is no soft solder in the connection, \nthe correlation between the results of this test and the results of the \n105\u00b0C test has been reasonably good. The principal discrepancy is that \nthe 175\u00b0C test is not as sensitive as the 105\u00b0C test; that is, the spread \nbetween stable and unstable connections tends to be smaller in the 175\u00b0C \ntest than in the 105\u00b0C test. This can be seen in Table I.\n\nuseful in conserving testing effort and in speeding up various phases of \nthe development program. Altogether, more than 16,000 solderless\n\nwrapped connections have been subjected to the 175\u00b0C test. On a few \noccasions, final approval of particular types of connections has been \nbased upon results of the 175\u00b0C test, although the usual practice is to \nwithhold final approval until the 105\u00b0C test is completed.\n\nEmpirically, it is possible to define acceptance and rejection limits \nfor the 175\u00b0C test that will correspond roughly to the limits for the 105\u00b0C \ntest. Although such limits actually have not been used in the past, it \nappears that limits based upon m\u2019 = 0.22 for the 175\u00b0C test would have \nled to essentially the same decisions that were made on the basis of \n105\u00b0C test results. For m\u2019 = 0.22, the limits for the 175\u00b0C test would \nbe\n\nThese limits are shown in Fig. 11, along with observed values for various \ntypes of connections that have been subjected to both the 175\u00b0C and \nthe 105\u00b0C tests. The symbols used for the values observed in the 175\u00b0C \ntest indicate how similar types of connections fared in the 105\u00b0C test. \nAs indicated previously, the limits for the 175\u00b0C test can serve as \nguides for making decisions. If m for a particular type of connection is\n\nFig. 11 Criteria for acceptance and rejection in 175\u00b0C screening test. Points \nare results of 175\u00b0C tests, but symbols indicate how similar connections behaved \nin 105\u00b0C tests.\n\nless than mo.o5, it probably is worthwhile to make tests at 105\u00b0C. If \nm is greater than mo.95 , it probably is not worthwhile. If m falls between \nMo.o5 and mos, the decision will have to be based upon additional \nconsiderations.\n\nThe sample size for which mo.o5 = 0 is about 13. The sample size for \nwhich mo.o5 = 4/N is about 41. A sample of 13, then, is the smallest \nsample that should be tested, and 41 is a more realistic minimum.\n\nwrapping bits for use in production, and the same tests have been made \nto qualify the bits used in the evaluation studies. Sample connections \nare wrapped on specified types of terminals, then two different types of \ntests are made on the sample connections. In the first test, the force \nrequired to strip the connection off of the terminal is measured. It is \nrequired that this stripping force be at least 3000 grams and that the \nmedian for any subgroup of five connections be at least 4200 grams. The \npurpose of this test is to provide assurance that the bit is capable of \nwrapping tight connections\n\nIn the second test, the wire is unwrapped from the terminal, the un- \nwrapping force being applied to the wire at least one-half inch from the \nterminal without the wire being restrained from twisting or bending \nback upon itself. It is required that the connection be capable of being \nunwrapped in this fashion without the wire breaking. The purpose of this \ntest is to provide assurance that the bit does not wrap too tightly \nso tightly that the wire would be weakened excessively.\n\nAssuming that the connections have been wrapped with qualified \nbits, it is of interest to consider what might happen to them subsequently \nin service. In general, this reduces to a consideration of mechanical \ntreatments that would tend to loosen the connection and break the wire.\n\nThe principal types of mechanical treatment that could loosen a \nwrapped connection are (a) squeezing the sides of the connection, (b) \npushing or pulling on the body of the connection and, of course, (c) \nunwrapping the connection.\n\nAlthough the squeezing forces that would be required to loosen con- \nnections have not been measured, it is evident that enough force could \nbe exerted with a pair of pliers to damage a connection. Wiremen and \nmaintenance men have been cautioned, therefore, not to squeeze the \nconnections \u2014 either with pliers or with test clips.\n\nFig. 12 \u2014 Effect of terminal thickness on stripping force. Connections wrapped \nwith No. 24 gauge tinned copper wire on flat nickel silver terminals 0.062 inch \nwide. Sample size 100.\n\nnarily is well above the minimum requirement of 3000 grams, ranging \nup to more than 10,000 grams in some cases. In general, the heavier \nterminals tend to give higher stripping forces than do the lighter termi- \nnals, and the heavier gauges of wire tend to give higher values than do \nthe lighter gauges. Figs. 12 and 13 illustrate the relationships.\n\nFig. 13 \u2014 Effect of wire size on stripping force. Connections wrapped with \ntinned copper wire on 0.0319 X 0.062-inch nickel silver terminals. Sample size 50 \nto 175.\n\nOrdinarily there is little risk that a connection will be unwrapped in \nnormal wiring or maintenance operations \u2014 unless, of course, the wire \nis unwrapped deliberately to remove the connection. It is possible, \nnevertheless, to unwind a connection by pulling steadily on the lead \nwire in the direction parallel to, and in line with, the terminal axis. On \nthe average, a force of about 825 grams is sufficient to unwrap one-half \nturn of a No. 24 gauge connection on a 0.0319 X 0.062-inch terminal, \nand a force of about 2300 grams will unwrap one full turn. The standard \ndeviations are about 15 per cent of these values.\n\nThe principal types of mechanical treatment that are liable to break \nwires in service are (a) tension alone, (b) repeated bending alone and \n(ec) repeated bending combined with tension. A number of tests have \nbeen made to compare the effects of these treatments on wires connected \nto terminals by solderless wrapping with the effects on wires connected \nby soldering.\n\nThe results of a few tensile tests are summarized in Table II. When \nthe wire was pulled radially (perpendicular to the terminal axis), almost \nthe full breaking strength of the wire was realized with the soldered \nconnections. The breaking strength with the solderless wrapped con- \nnections was about eight per cent lower, however, because the wire was \nindented where it had been wrapped around the corners of the rectan- \ngular terminal.\n\naxially. The soldered joint was broken in stages, and, in most cases, \nthe wire was completely unwrapped from the terminal before the force \nreached the breaking strength of the wire. With the flat terminals, the \nultimate strength of the solderless wrapped connections was significantly \nlower than that of the soldered connections. With the wire-spring relay \nterminals, on the other hand, the differences between the solderless \nwrapped and soldered connections were trivial. The serrations of the\n\nTaBLe I] \u2014 Mr&an ULTIMATE STRENGTH (IN GRAMS) OF CONNECTIONS \nMabe witu No. 24 GauGre Copper WIRE \nSolderless Wrapped Wrapped and Sol\n\nFig. 14 Iffects of repeated bending without tension. Connections made with \nNo. 24 gauge tinned copper wire on single-wire terminals of wire-spring relay. \nSample size 16\n\nsingle-wire terminal and the irregularities of the twisted and coined \ntwin-wire terminal were as effective as soldering in locking the wrapped \nwire in place.\n\nThe effects of repeated bending without tension are illustrated in Fig. \n14. The test was performed by bending the wire back and forth through \nthe angles indicated until the wire broke. The bending moments were \nlarge enough to exceed the elastic limit of the copper wire. In Fig. 14 \nconventional +3\u00a2 control limits (or confidence limits) are shown with \neach plotted point as a simple, graphic way of indicating that the per- \nformance of the solderless wrapped connections was significantly better, \non the average, than that of the soldered connections.\n\nVibration tests, of course, provide another method for measuring the \neffects of repeated bending without tension. Fig. 15 shows the results \nof a vibration test performed by the Western Electric Company on \nsmall equipment units wired with local cables. The +30 control limits \nin this case are based upon the observed breakage (\u2018\u2018fraction defective\u2019\u2019) \nof the soldered wires. The fact that the observed breakage of the solder- \nless wrapped wires consistently fell below the lower control limit for the\n\nsoldered wires indicates that the performance of the solderless wrapped\n\nThe effects of repeated bending combined with tension are shown in \nFig. 16. In this test, the wire was kept under tension continuously while \nit was bent from its starting position perpendicular to the terminal axis \nto a second position parallel to the terminal axis and then back to its \nstarting position. This cycle was repeated, always in the same direction \nfrom the starting position, until the wire broke. In Fig. 16, the +3e\u00a2 \ncontrol limits indicate again that the performance of the solderless \nwrapped wires was better, on the average, than the performance of the \nsoldered wires.\n\nconnection, so this limitation should be recognized in authorizing appli-\n\ncations of solderless wrapping. In its ability to withstand vibration and \nrepeated bending of the lead wire, however, the solderless wrapped \nconnection appears to be fully as good as, and probably better than, the \nsoldered connection.\n\nPresent approvals of specific combinations of terminals and wire are \nbased very largely upon the results of the accelerated aging tests that \n. owe > a)\n\nResults of vibration test on small equipment unit wired with local \ncable. Sample size 550 for each type of connection.\n\nFig. 16 Effects of repeated bending with wire under tension. Connections \nmade with No. 24 gauge wire on single-wire terminals of wire-spring relay. Sample \nsize 25 in each case.\n\nThe limiting dimension is the minimum diameter of the terminal hole \nin the bit used for wrapping No. 24 gauge wire. In order to be sure that \nNo. 24 gauge wire can be wrapped on any approved terminal, the maxi- \nmum dimensions of the cross-section are limited so that the terminal \nwill pass through a circular opening 0.073 inch in diameter.\n\nSolderless wrapping with No. 22 gauge tinned copper wire is approved \non terminals of rectangular cross section whose nominal thickness is at \nleast 0.030 inch and whose minimum diagonal exceeds 0.061 inch.\n\nSolderless wrapping with No. 24 gauge tinned copper wire is approved \non (a) terminals of rectangular cross section whose nominal thickness is \nat least 0.025 inch and whose minimum diagonal exceeds 0.059 inch, \n(b) embossed terminals of the form shown in Fig. 6 punched and formed \nfrom flat stock whose nominal thickness is at least 0.010 but less than \n0.025 inch and (c) the wire-spring relay terminals in Figs. 7 and 8.\n\nApproved terminal materials include nickel silver, brass, phosphor \nbronze and silicon copper. The best terminal materials for solderless\n\nwrapping have a high modulus of elasticity, a low rate of stress relaxa- \ntion and a temperature coefficient of expansion near that of the wire.\n\nIn general, a copper flash plus an electrotinned finish is required on \nbrass, phosphor bronze and silicon copper terminals, or they may be \npunched from either tin-coated or solder-coated stock. No finish is re- \nquired on nickel silver terminals, although any of the foregoing finishes \nis permissible and is specified in some cases to facilitate soldering. Solder \ndipping is not approved, because of the risk of obtaining abnormally \nthick coatings from time to time and the undesirable effect that this \ncould have upon the stability of connections wrapped on such terminals.\n\nThe use of untinned copper wire has been approved only in cases \nwhere the required service life of the connections is substantially less \nthan 40 years. Furthermore, such approvals are limited to the heavy \nterminals which are approved for use with No. 22 gauge wire.\n\nThere have been exceptions to some of the standards described in the \npreceding paragraphs. Solderless wrapping on solder-dipped terminals \nand on thin, flat terminals was approved on a limited basis early in the \ndevelopment program. Those connections, however, are in circuits \nwhere trouble, if it should occur, would be detected automatically, could \nbe located quickly and could be corrected easily by soldering the defec- \ntive connection. For future production, those terminals are being brought \ninto agreement with present standards.\n\nThe first field trial of solderless wrapped connections was installed in \n1950, and limited use of solderless wrapping in regular manufacture \nbegan a few years later. During the period 1950 to 1958, the service \nperformance of solderless wrapped connections appears to have been \nhighly satisfactory.\n\nA two-year survey of 411,000 solderless wrapped connections in five \ncentral offices showed a lower wire breakage rate than would have been \nexpected with soldered connections, and the difference was great enough \nto be considered statistically significant.\n\nThere has been no report of solderless connections being pulled off \nof terminals in service or of being partially unwrapped, and inspection \nof about 20,000 connections in two central offices revealed no sign of \npartial unwrapping.\n\nThe resistance variations of 135 connections were measured after two \nyears in service, and 160 more were measured after three and one-half\n\nyears of service. The highest value of AR observed was 0.0004 ohm, so \nthe value of m for the 295 connections still was zero.\n\nThe laboratory studies and field experience to date have provided \nconsiderable assurance that properly designed and properly made solder- \nless wrapped connections will perform satisfactorily for 40 years in cen- \ntral office service. The use of solderless wrapping is being expanded, \ntherefore, in the Bell System. Suitable terminals now are being provided \non many types of telephone apparatus. Design changes have been au- \nthorized to provide suitable terminals on a number of additional types \nof apparatus, although the changes have not been introduced yet in \nmanufacture. And design changes to provide suitable terminals on still \nother types of apparatus are being studied.\n\nSeveral hundred million solderless connections are being wrapped each \nyear in the Bell System now. The number will grow, but it is difficult to \npredict what the saturation level will be. Inevitably, the solderless \nwrapped connection is in competition with soldered connections, clinched \nconnections, welded connections and all the other types. In the end, the \nchoice of connections for any particular application is likely to be an \neconomic choice \u2014 based not only upon the cost of the labor involved \nin making a connection, but upon many other factors as well. The cost \nof modifying terminals, for example, is an obstacle to solderless wrap- \nping on existing apparatus. In some cases, the cost of modifying the \nterminals of a particular type of apparatus outweighs the potential sav- \nings of solderless wrapping. It is not likely, therefore, that solderless \nwrapping ever will displace other types of connections completely.\n\nThe present program for central office equipment in the Bell System \ncalls for modification of the terminals of existing types of apparatus in \nthose cases where the preparation expense clearly is outweighed by the \ndirect savings from solderless wrapping and the indirect savings from \nthe use of plastic insulated wire, which is made practicable by solderless \nwrapping. In other cases, modification of terminals will be deferred until \npresent manufacturing tools wear out and have to be replaced.\n\nthe trend is to provide terminals suitable for solderless wrapping at \nthe start. Furthermore, every effort is made to arrange the terminals in \nmodular arrays that will facilitate automatic wiring by machines. These \ntwo steps are opening a door to economical use of automatic wiring in \nmanufacture. It seems quite probable, therefore, that telephone switch-\n\ning systems of tomorrow will be well populated with solderless wrapped \nconnections.\n\npated in the development of solderless wrapped connections. Each of \nthose persons has played an important part in the development. In \nparticular, the author wishes to acknowledge the contributions of H. L. \nCoyne and R. H. Van Horn, who supervised the several phases of the \nevaluation program.\n\n1. Keller, A. C., A New General Purpose Relay for Telephone Switching Systems, \nB.8.T.J., 31, November 1952, p. 1023; Trans. A.I.E.E., 71, Part 1, January \n1953, p. 413.\n\n2. McRae, J. W., Mallina, R. F., Mason, W. P., Osmer, T. F. and Van Horn, R. \nH., Solderless Wrapped Connections, B.S.T.J., 32, January 1953, p. 523\n\n3. Mason, W. P. and Anderson, O. L., Stress Systems in the Solderless Wrapped \nConnection and Their Permanence, B.S8.T.J., 33, September 1954, p. 1093.\n\nBuck, T. M. and McKim, F. 8S. \nCertain Chemical Treatments and Ambient Atmospheres on Surface \nProperties of Silicon, Monograph 3191.\n\nCoutuins, R. J. and Tuomas, D. G. \nPhotoconduction and Surface Effects with Zinc Oxide Crystals, \nMonograph 3192.\n\nDova.ass, D. C. and McCatu, D. W. \nDiffusion in Paraffin Hydrocarbons, Monograph 3079.\n\n* Copies of these monographs may be obtained on request to the Publication \nDepartment, Bell Telephone Laboratories, Inc., 463 West Street, New York 14, \nN. Y. The numbers of the monographs should be given in all requests.\n\nStructure-Determined Gain-Band Product of Junction Triode Trans- \nistors, Monograph 3193.\n\nPlotting Experimental Data; and Control Charts for Log-Normal \nUniverses, Monograph 3194.\n\nThermal Expansion of Some Crystals with the Diamond Structure, \nMonograph 3197.\n\nConnections Made to Printed Circuit Boards Through Resistance \nFusing, Monograph 3200.\n\nDislocation Etch Pits in Tellurium and Apatite, Monograph 3088. \nMATREYEK, W., see Winslow, F. H. \nMcCatu, D. W., see Douglass, D. C. \nMcKim, F.S8., see Buck, T. M. \nMcMauon, W., Brrpsaui, H. A., Jounson, G. R. anp Camiuur, C. T.\n\nWau, A. J. \nAnalysis of Base Resistance for Alloy Junction Transistors, Mono- \ngraph 3204.\n\nWarner, R. M., Jr., Harty, J. M. anp Loman, G. T. \nCharacteristics and Performance of a Diffused-Base Germanium \nOscillator Transistor, Monograph 3205.\n\nWEISSMANN, G. F. AND Basineton, W. \nA High-Damping Magnesium Alloy for Missile Aplications, Mono- \ngraph 3206.\n\nWernick, J. H., GeLuer, 8. and Benson, K. E. \nConstitution of a Semiconducting Pseudo-Quaternary System, Mono- \ngraph 3081.\n\nTheory of Plasma Resonance in Solids, Monograph 3208. \nWotrstirn, K. and Futter, C. 8.\n\nComparison of Radio-Copper and Hole Concentration in Germanium \nMonograph 3209.\n\nPau. J. Burke, B.S., 1940, College of the City of New York; Ed.M., \n1950, Harvard University; Faculty, Vineland, N. J., High School, \n1943-45; Cooperative Test Service, 1945-48; Educational Testing \nService, 1948-49; Columbia University, 1950-53; Bell Telephone Labora- \ntories, 1953\u2014. He has been engaged in telephone traffic studies. Member \nOperations Research Society of America; Institute of Mathematical \nStatistics, American Statistical Association, American Association for \nthe Advancement of Science, Harvard Engineering Society, Phi Beta \nKappa, Phi Delta Kappa.\n\nSTANLEY J. Exvtiorr, B.S.E.E., 1937, and M.S.E.E.,. 1938, University \nof California; Bell Telephone Laboratories, 1938\u2014. Mr. Elliott was \nfirst engaged in fundamental contact studies. During World War IT he \ntook part in development work on airborne radars, fire control radar \nand other military projects. He later turned to development of glass- \nenclosed switches and relays and wire-spring relays. He was a coordinator \nfor Bell Laboratories with outside suppliers in development of apparatus \nfor guided missile systems. In 1953 he was named Switching Apparatus \nEngineer with responsibility for work on central office apparatus and \nsome military devices. In April, 1959 he was appointed Military Systems \nDevelopment Engineer. Member A.I.E.E., I.R.E., American Society \nfor Quality Control, Phi Beta Kappa, Sigma Xi, Eta Kappa Nu, Tau \nBeta Pi.\n\nE. N. Griipert, B.S., 1943, Queens College; Ph.D., 1948, Massa- \nchusetts Institute of Technology; M.1.T. Radiation Laboratory, 1944- \n46; Bell Telephone Laboratories, 1948\u2014. Mr. Gilbert has been engaged \nin studies of information theory and switching theory. Recipient M.1.T. \nApplied Mathematics Fellowship, 1946-48. Member American Mathe- \nmatical Society.\n\nDavin W. HaGeLBarGerR, A.B., 1942, Hiram College; Ph.D., 1947, \nCalifornia Institute of Technology; faculty, University of Michigan, \n1946-49; Bell Telephone Laboratories, 1949\u2014. His first work was with \nthe electron dynamics group on development of microwave tubes. Since \n1952 he has specialized in special purpose computers, automata and\n\nswitching research. He recently developed a new error-correcting code. \nMember I.R.E., American Physical Society, Sigma Xi.\n\nBeta JuLesz, Dipl. in Electrical Engineering, 1950, Budapest (Hun- \ngary) Technical University; Candidate in Technical Sciences, 1956, \nHungarian Academy of Sciences; Bell Telephone Laboratories, 1956 \nHe is engaged in studies of systems for reducing television bandwidth, \nwith emphasis on problems of pattern recognition. Member I.R.E.\n\nC. Y. Ler, B.E.E., 1947, Cornell University; M.S.E.E., 1949 and \nPh.D., 1954, University of Washington; John McMullen Regional \nScholar at Cornell, 1944\u201447; instructor, electrical engineering, University \nof Washington, 1948-51; Bell Telephone Laboratories, 1952\u2014. Mr. Lee \nhas been engaged in mathematical research in switching systems develop- \nment. He was a visiting member of the Institute for Advanced Study \nin the School of Mathematics during the academic year 1957-58. Member \nSigma Xi, Eta Kappa Nu.\n\nEpwarp F. Moors, B.S., 1947, Virginia Polytechnic Institute; M.S., \n1949, and Ph.D., 1950, Brown University; assistant professor, Univer- \nsity of Illinois, 1950-51; Bell Telephone Laboratories, 1951\u2014. He has \nbeen engaged in mathematical research on switching circuit design, \nautomata theory and information theory. Member American Mathe- \nmatical Society, Association for Computing Machinery, Association for \nSymbolic Logic, I.R.E., Sigma Xi, Phi Kappa Phi.\n\nH. Earte VauGuan, BS. in C.E., 1933, Cooper Union; Bell Telephone \nLaboratories, 1928\u2014. He was first engaged in work on voice operated\n\ndevices and studies of the effects of speech and noise on voice frequency \nsignaling systems. During World War II he worked on anti-aircraft \ncomputers, fire-control radar and other military projects. He was later\n\nconcerned with digital techniques and systems and electronic switching \nsystems. He was appointed Switching Systems Research Engineer in \n1955 and Director of Systems Research in 1957. Senior Member I.R.E.", "title": "The Bell System Technical Journal 1959-07: Vol 38 Iss 4", "trim_reasons": [], "year": 1959} {"archive_ref": "bitsavers_BellSystemJV31N04195207_11327836", "canonical_url": "https://archive.org/details/bitsavers_BellSystemJV31N04195207_11327836", "char_count": 219089, "collection": "archive-org-bell-labs", "doc_id": 482, "document_type": "journal_issue", "id": "bella-qwen-pretrain-doc482", "record_count": 406, "release_policy_version": "hf_public_v1", "rights_status": "public_domain", "selected_extraction_backend": null, "selected_extraction_score": null, "source_family": "archive_org", "source_url": "https://archive.org/details/bitsavers_BellSystemJV31N04195207_11327836", "split": "validation", "text": "Thirtieth Anniversary \u00ab6611 \nLee de Forest and William Shockley Discuss Electronics 612\n\nNetwork Synthesis Using Tchebycheff Polynomial Series \nSIDNEY DARLINGTON 613\n\nA Carrier Telegraph System for Short-Haul Applications \nJ. L. HYSKO, W. T. REA AND L. C. ROBERTS 666\n\nfficient Coding B. M. OLIVER 724 \nStatistics of Television Signals E. R. KRETZMER 751 \n\\\"xperiments with Linear Prediction in Television Cc. W. HARRISON 764\n\nPhotoelectric Properties of Ionically Bombarded Silicon \nEDWIN F. KINGSBURY AND RUSSELL S. OHL 802\n\nTHE BELL SYSTEM TECHNICAL JOURNAL \nPUBLISHED SIX TIMES A YEAR BY THE \nAMERICAN TELEPHONE AND TELEGRAPH GOMPANY\n\nFR. KAPPEL O. E. BUCKLEY \nH.S. OSBORNE M. J. KELLY \nJ.J. PILLIOD A. B. CLARK \nrR. BOWN D. A. QUARLES\n\nThirty years ago this month Tor Bretu System TECHNICAL JOURNAL \nbegan publication. Suggested by Dr. George A. Campbell, it had been \nunder discussion for some years. Dr. R. W. King, who had been one \nof its most active advocates, became its editor when the staff of the \nJOURNAL was established. Except for a six-year period following 1928, \nwhile he was in England, Dr. King continued as editor until he retired \nin 1949.\n\nBy July, 1922, when No. 1, Vol. 1 of the JourNAL appeared, research \nand development was a long established practice in the Bell System. \nThe high-vacuum electronic tube, which had already begun to revolu- \ntionize electrical communication, was itself a product of Bell System \nresearch. Since electrical communication was a still comparatively new \nfield of study, however, its publications were widely scattered. There \nseemed a need for a magazine that would serve the communication \nengineers exclusively, and it was largely to meet this need that THE BELL \nSystem TECHNICAL JOURNAL was launched.\n\nIn the thirty years since that time, the art and science of communica- \ntion has advanced and ramified beyond anything likely to have been \nthen foreseen. A very substantial part of this increase has originated \nwithin the Bell System, and this progress has been reflected in the pages \nof the TECHNICAL JOURNAL. There seems little reason to doubt that \nthe next three decades will witness-an advance at least comparable \nwith that of the past three, and it is planned to have the JouURNAL pre- \nsent the work of the coming years, with perhaps even greater effective- \nness than in the past. Abstracts or titles of all Bell System technical and \nscientific papers appearing in other publications are listed in the JouRNAL \nand reprints of many of these papers are available and may be obtained \nby subscribers. In one way or another, therefore, JouRNAL readers have \naccess to essentially all the technical papers published by the Bell \nSystem. With this increased coverage, it is hoped that the JouRNAL \nwill prove increasingly useful to a growing circle of readers.\n\nDr. de Forest is the inventor of the Audion from which the modern vacuum tube in \nits many forms and types has sprung. Dr. Shockley is the leader of the research \ngroup at Bell Telephone Laboratories whose members invented the transistor. Stand- \ning side by side these two men seem to epitomize the basic change in the pattern of \nour technical life which has taken place during the first half of the present century\u2014 \nthe change from the struggling individual inventor to the great industrial scientific \nlaboratory as the source of much of our technological advance.\n\nA general method is developed for finding functions of frequency which \napproximate assigned gain or phase characteristics, within the special class \nof functions which can be realized exactly as the gain or phase of finite \nnetworks of linear lumped elements. The method is based upon mantpula- \ntions of two Tchebycheff polynomial series, one of which represents the \nassigned characteristic, and the other the approximating network function. \nThe wide range of applicability is illustrated with a number of examples.\n\nNetwork synthesis is the opposite of network analysis\u2014namely, the \ndesign of a network to have assigned characteristics, as opposed to the \nevaluation of the characteristics of an assigned network. In general, \nthere are specifications on the internal constitution of the network, as \nwell as requirements relating to its external performance. A common \nform of the general problem is the design of a finite network of linear \nlumped elements, to produce an assigned gain or phase characteristic \nover a prescribed interval of useful frequencies. The present paper re- \nlates to this particular form.\n\nIn general, the restrictions on the network are such that the assigned \nperformance cannot be matched exactly. This gives rise to an approxi- \nmation or interpolation problem. For present purposes, the problem is: \nto choose a function of frequency which matches the assigned gain or \nphase to a satisfactory accuracy, from that special class of functions \nwhich can be realized exactly with physical finite networks of linear \nlumped elements. The function of frequency may be defined in terms \nof network singularities (natural modes and infinite loss points). The \n~~ + Presented orally, in briefer form, at the 1951 Western Convention of the \nInstitute of Radio Engineers, and at the Symposium on Modern Network Syn-\n\nthesis sponsored by the Polytechnic Institute of Brooklyn and The Office of \nNaval Research, New York City, April, 1952.\n\ninterpolation problem may then be regarded as solved when a suitable \nset of network singularities has been obtained; for quite different tech- \nniques are used to design actual networks with these singularities.\n\nThe interpolation problem may be attacked in a number of different \nways; and a variety of different techniques are, in fact, needed to cover \nthe wide diversity of practical applications. The present topic is a fairly \ngeneral way of attacking the problem, based upon manipulations of two \nseries of Tchebycheff polynomials. The two series represent expansions \nof two functions of frequency\u2014one, the ideal assigned gain or phase, \nthe other, the network approximation to the ideal. The interpolation \nproblem may be solved in this way because it is feasible, as will be \nshown, to determine network singularities from arbitrarily assigned \nvalues of coefficients in the corresponding Tchebycheff polynomial series.\n\nThe techniques to be described were derived originally from studies \nof the so-called potential analogy; but they can now be developed most \neasily without reference thereto.{ In a sense they may be regarded as \nextensions of familiar filter theory, using Tchebycheff polynomials, to \nmore general gain and phase functions. The extensions, however, depend \nupon a number of new principles. Extensions of the filter theory applied \nto more general problems have been noted in published papers; but \nthose noted have not used the specific general approach employed here.{ \nThe wide applicability of this general approach will be illustrated by \nspecific examples.\n\nIt will be sufficient for our present purposes to limit the discussion to \nthe general 4-pole shown in Fig. 1. The 4-pole may be active or passive, \nbut it must be a stable finite network of linear lumped elements. HE and \nV are steady state ac voltages, H the driving voltage and V the response. \nThe gain a and phase @ are here defined as the real and imaginary parts \nof log V/E.\n\nt For the most part, they have used the potential analogy, in such a way that. \nTchebycheff polynomials do not appear at all in general applications. For ex- \namples, see methods of Matthaei?, Bashkow\u2019, and Kuh\u2018.\n\nThe \u201cfrequency variable\u201d p represents, of course, tw. The zeros De of \nthe rational fraction are those values of p at which there is infinite loss. \n\u2018The poles p, are the so-called natural modes, or values of p at which \nresponse V can exist in the absence of driving voltage 7. The scale \nfactor K determines the average level of transmission. The zeros, poles, \nand scale factor together determine the gain and phase completely.\n\nFor a physical stable network, the zeros and poles must meet certain \nwell known restrictions, which are commonly stated in terms of loca- \ntions in the complex plane for frequency variable p. Within these re- \nstrictions, the zeros and poles can be subject to arbitrary choice, say \nfor purposes of network synthesis.\n\nThe symmetries required by the physical restrictions permit a and 8 \nto be represented separately as follows:T\n\nThese expressions hold at all real frequencies, but only at real fre- \nquencies. .\n\nActually, the definitions must vary with the nature of the useful fre- \nquency interval. For the present, however, it will be assumed that the \nuseful interval extends from w = 0 to w; or more precisely, from \nw = \u2014w, to +w, (in accordance with the symmetries of gain and phase \nfunctions). Useful intervals which do not include w = 0 require changes \nin the definitions, which will be taken up in Section 28.\n\nFor our present purposes, Tchebycheff polynomials 7; may be defined \nas follows:\n\nThe first equation defines an auxiliary angle variable, \u00a2, in terms of \nwhich 7; is especially simple. The imaginary scale factor 7, associated \nwith polynomials of odd order, simplifies later analysis. In addition, it\n\nis especially appropriate for general network applications, because the \nodd ordered polynomials contribute to the imaginary parts of complex \n~ network functions\u2014such as 78 in a + 7b.\n\nIt is apparent from (3) that the Tchebycheff polynomials become \nsimply Fourier harmonics, if they are plotted against a distorted fre- \nquency scale\u2014that is, against \u00a2. This means that they must be ortho- \ngonal, over that particular range of frequencies which corresponds to \nreal values of \u00a2. From the relation between \u00a2 and \u00bb, it is clear that real \nvalues of \u00a2 cover the frequency interval between \u2014w, and +w,, which \nis our useful interval. In other words, the interval of orthogonality coin- \ncides with the useful frequency interval. The corresponding interval of \np is of course p = \u20141a, to +tu..\n\nIf a given function is plotted against \u00a2, instead of w, it may be ex- \npanded in a Fourier series. Each term in the series may be replaced by \na Tchebycheff polynomial, to obtain an expansion of a given function \nin terms of polynomials, for the specific useful interval w = \u2014w, to \n+w,. Established techniques are available for expanding experimental, \nor other numerical data, in Fourier series, as well as actual analytic \nfunctions.\n\nIn Fig. 2, some of the Tchebycheff polynomials are plotted against w. \nThe frequencies \u2014w, and +a, are also indicated. Frequencies between \nthese limits correspond to real values of the angle variable \u00a2. If this \npart of the frequency scale is stretched, in the proper non-uniform way, \nthe various \u201cloops\u201d not only have the same maximum values, but also \nthe same shapes. In other words, they become periodic. More specifically, \na stretch which changes the frequency scale into a @ scale changes the \nplots into sin k\u00a2 or cos k\u00a2.\n\n\u00a2 by . \nz= e* (4) \nSubstituting z in the exponential equivalent of sin \u00a2, in the first equa- \ntion of (8), gives an alternative definition of z directly in terms of p,\n\n+ A small change in the definition of \u00a2 would bring the definitions closer to \nconvention, by replacing both sines by cosines (without altering 7, as a function \nof p). This however, would complicate our later analysis.\n\nSubstitutions in the exponential equivalents of the other sine and cosine \nin (3) give: \nDal \n(< + a k even \n2\n\nNetwork applications depend upon the nature of the relationship be- \ntween the variable p, and the variable z. The relationship is illustrated \nin Fig. 3, which indicates corresponding contours in the p and z planes.\n\nSince angle \u00a2 is real in the useful interval, z, as defined by (4), has \nunit magnitude. In equivalent conformal mapping terms, the unit circle \nin the z plane maps onto a segment of the axis of real frequencies in \nthe p plane\u2014namely the segment extending from p = \u20141w, to +m, . \nHereafter, we shall say merely that the useful interval in the z plane is \nthe unit circle, or |z| = 1. The real frequency intervals outside the \nuseful interval map onto the imaginary axis in the z-plane.\n\nz-plane circles with radii other than unity map onto p-plane ellipses, all \nwith foci at p = +2, . This is reminiscent of filter theory using Tcheby- \ncheff polynomials, and in fact such a filter may be obtained by spacing \nz-plane mappings of natural modes uniformly around such a circle. f\n\nt The filter theory is developed in detail in a monograph by Wheeler\u2019, which \nalso includes an extensive bibliography.\n\nz-plane mappings of network singularities are also an essential part \nof synthesis applications. The mapping 2, of a typical zero or pole 7, is \nillustrated in Fig. 4. From (5), the analytic relation must be:\n\nBy its quadratic nature, there must be exactly two values of z, , corre- \nsponding to one p,. The relation is such that replacing z, by \u20141/z. \nleaves p, unchanged; and hence the two values of z, must be negative \nreciprocals, each of the other. Thus, one mapping of 7p, falls outside the \nunit z-plane circle, and the other inside.\n\nA unique definition of z, may be obtained by requiring that z, must \nbe the mapping outside the unit circle. Then | z, | > 1 by definition, and \nthe complete definition of z, may be:\n\nThis definition is unique provided network singularities p, are excluded \nfrom that very special line segment of the real frequency axis which \ncorresponds to the useful frequency interval, \u2014w. << w < +w, (where \n| z. | would be exactly 1).\n\nWe are going to solve the interpolation problem by choosing the z, \nfirst, instead of the p-plane singularities p, , after formulating the inter- \npolation problem in suitable z-plane terms. For this, however, we must\n\nknow what further conditions must be imposed upon the z, , so that \nthe corresponding p, will meet the special conditions necessary for \nphysical networks. A simple analysis of the definition (8) of z,, and of \nthe well known restrictions on the p, , leads to the following assertion; |\n\nIt is obvious, for example, that conjugate complex z, are necessary \nfor conjugate complex p, . Also, because | z,| > 1, 2, dominates \u20141/z, . \nThen the sign of Re p, is the same as that of the Re z, , and p, with \nnegative real parts require z, with negative real parts, and so on.\n\nThus the direct choice of z, is restricted in exactly the same way as \nthe choice of p,., except for the additional general requirement | z, | > 1. \nThe last condition imposes no important restriction on the corresponding \np,. Initially, it was adopted to make z, unique for any p, (not at a \nuseful real frequency); but this condition does also play an essential \nrole in the z-plane formulation of the interpolation problem.\n\nA first step in the z-plane formulation of the interpolation problem is \nthe formulation of the network gain and phase functions, (1) and (2), in \nterms of z. This is most usefully examined as a transformation of func- \ntional form, rather than as a conformal mapping.\n\nThe gain and phase function (1) transforms as follows: The analytic \nrelation between p and z is regular in the neighborhood of the singular- \nities p, of the network function. Therefore, there will be similar singu- \nlarities of the transformed function at the z-plane mappings of p, , \nwhich are z, and \u20141/z, . These singularities, and also suitable behavior \nat infinity, are exhibited by the following expression for a + 76 as a\n\n[] is used here to designate a product of factors of the type following it.f \n+ The expression is readily confirmed in the following very elementary man- \nner: For every factor (a _ 2) , in (9), there is also a factor (1+ = . The\n\nEquation (13) holds at all values of p and z, while (14) holds at all \nreal frequencies. Simplifications of (14) should be noted, good for the \nuseful interval only. When |z| = 1, 1/z = 2*. Recalling also that log \n| x |\u2019 is 2 log | x |, and similar elementary relations, one obtains from (14):\n\nOur applications to network synthesis depend upon a correspondence \nwhich may be shown to exist between certain functions of z and certain \npower series in z. The functions of :z may be formulated in terms of \nnetwork singularities. The power series in zg may be derived from the \n-Tchebycheff polynomial series in p representing the corresponding gain \nand phase.\n\nThe Tchebycheff polynomial expansion of a gain and phase function \nmay be written:\n\nIf a + 78 corresponds to a finite network, it may be represented by the \nfunction of z in (13). At the same time, 7, may be represented by the \nfunction of z in (6). With these changes, (16) becomes:\n\nThe logarithm of the product of the two rational functions, in z and \n\u20141/z respectively, may be written as the sum of two logarithms. The \nseries in sums of 2\u201d and (\u20141/z)* may be written as the sum of two series. \nThen\n\nThe above expression equates the sum of two similar functions, in z \nand \u20141/z respectively, to the sum of two power series, also respectively \nin zg and \u20141/z. The theorem on which the synthesis methods are based \nasserts that the functions and power series in z and \u20141/z may be equated \nseparately, throughout the useful interval. That is:\n\nThe transformation from variable p to variable z \nconverts an expansion in Tchebycheff polynomials \nim p into an expansion in a power series in 2.\n\nThus, by working with the z, , in place of the p,, one may use a \npower series sort of analysis in calculating, or in choosing, the coeffi- \ncients C;, in the Tchebycheff polynomial series.\n\nThe relations (20) refer to the combined gain and phase function. \nExactly similar relations can readily be obtained, however, for gain and\n\n1 As defined in (8), | #e) > 1. In the useful interval, | z| = 1. Hence | 2/z,| < 1. \nIt follows that log (1 \u2014 z/z,) has a power (MacClauren) series expansion in posi- \ntive powers of z, convergent on and within the circle | z | = 1. Finally the first \nlogarithm in (19) may be expressed as a sum of logarithms of this simple type, \neach of which may be expanded separately. Substituting \u20141/z for z maps the \nunit circle onto itself. It follows that the second logarithm in (19) has an expan- \nsion in positive powers of \u20141/z, in the useful interval, provided the first loga- \nrithm has an expansion in positive powers of z; and the coefficients in the two \nseries will be the same.\n\n(The absence of factors } in >, Cyz\", as compared with (20), reflects the \nfactors 2 associated with a and @ in (14).)\n\nLet & + 78 be any function of p which has the following properties: \nIt must be analytic throughout the useful interval. Further, there are \nto be no singularities within a (p-plane) distance e of the useful interval, \nwhere e\u00a2 is finite (but may be small). Finally, at real frequencies, & and \niB are to equal respectively the even and odd parts of & + 7.\n\nUnder the conditions stated, a + 78 may always be expanded in \nterms of our Tchebycheff polynomials 7. Let >. C,7', be the expansion. \nTo obtain a parallel to (20), we may form (arbitrarily) a power series \n> 40,2\". Then we may define a function R(z) by identifying log R(z) \nwith the power series. All this adds up to the following, comparable to \n(20):\n\nThe functions of z have the following properties: Because of the mild \nrestrictions, which we have imposed on the singularities of & + 78, the \nseries >, C,z\" defines a function which is analytic within, and on the \ncircle |z| = 1. Then A(z), also, is analytic within, and on the circle. \nFurther, 2(z) has no zeros anywhere in the same region. (R(z), however, \nmay be more general than the rational fraction in (20).) Finally, because \nof the even and odd symmetries, required of & and 7B, (22) may be \nbroken into the following parallels of the equations (21):\n\nIn some applications, it is possible to express R(z) in closed form. In \nall applications, it is possible to expand #(z) as a power series, convergent \nin the region |z| S 1. The same is true of 1/R(z), since there are no \nzeros in the region. Coefficients of either series (#(z) or 1/R(z)) may \nreadily be calculated by means which we shall examine a little later. For \nthe present we shall say merely that R(z) is a known function, corre- \nsponding to an assigned & + 76.\n\nWhen the gain and phase function, a + 78, is to approximate @ + 78, \nthe error in the approximation is (a \u2014 &) + i(8 \u2014 @). The error may \nbe expressed in terms of z by taking the difference of corresponding \nequations in (20), (22). The difference of the logarithms may be ex- \npressed as a single logarithm of a ratio. Alternatively, and also more \nconveniently for our later purposes, it may be expressed as the negative \nof the logarithm of the reciprocal ratio. When this is done,\n\nConsider the following arbitrary requirement, as a design criterion: \nThe series >> C,T;, is to match exactly the series >) C.7;, through\n\nterms of order m. If both series have converged to small remainders: \nwhen k = m, this criterion will surely make a + 78 a good approxima- \ntion to a + 78.+ In terms of the coefficients, the criterion requires:\n\nIf (25) is applied to the second equation of (24), the power series is \nzero through terms of order m. In other words, the logarithm, equated \nto the series, will approximate zero in the power series, or \u201cmaximally \nflat\u201d? manner, to order m. The logarithm is zero when the expression in. \nbrackets is unity. Further, the logarithm will approximate zero in the \nmaximally flat manner when, and only when the bracket approximates \nunity in the maximally flat manner. Thus a condition which is equivalent. \nto (25) is the following:\n\nZz \n, u (1 Tg ) . \nee ie a eee? (27) \nK, 2 \nII l- 7 \nbe \nwhere = is used to indicate equality through power series terms of \norder m.\n\nWhen (27) is applied to network synthesis, the singularities z, , and \nscale factor K, are the unknowns, while R(z) is known. If m is equal to \nthe total number of z, , (27) will determine the network function com- \npletely. When m is smaller, (27) will furnish m + 1 relations between \nthe network parameters (including the zero order condition), which \nmay be combined with specifications of other sorts. Since (27) is equiv- \nalent to (25), this procedure amounts to the determination of network \nparameters which will yield assigned values of the coefficients, C. = C;. , \nk < m, in the Tchebycheff polynomial expansion of a + 78.\n\nEquation (27) applies when both gain and phase are to be approx- \nimated. For approximation to gain only, or to phase only, similar rela- \ntions may be derived from (21) and (23). Only even ordered Tchebycheff \n~~ + When both residues are relatively large, the approximation may still be\n\ngood, for the remainders may be quite similar, and the error will be their differ- \nence. In practical applications, this is a not uncommon situation.\n\npolynomials contribute to gain. The following condition turns out to be \nthe equivalent of Cyn = Cx,k < m:\n\nwhere = means approximation in accordance with a power series of \neven ordered terms, through order 2m. Correspondingly, only odd \nordered Tchebycheff polynomials contribute to phase. The following \ncondition is equivalent to Co.1 = Cx1,k = 1 tom:\n\nIn all cases, unity is approximated with one of the functions appear- \ning in (27), (28), (29). It will be convenient to use H(z) to represent the \nerror in the approximation, or departure from unity. When gain only is \nof interest, the function in (28) is used, and H(z) is defined by:\n\nThe example which has been chosen for detailed discussion is the \nequalization of the gain distortion produced by two resistance-capacity\n\ntype cut-offs. The equalization is to be accomplished with a network \nwhich has n natural modes, but no finite frequencies of infinite loss. \n(This is simply one of the arbitrary specifications which define this \nproblem.)\n\nThe two natural modes would be cancelled completely by two infinite \nloss points at the same location in the p plane. A network with two \ninfinite loss points, however, is not physically possible unless it has also \nat least two natural modes; and the natural modes will have to introduce \ndistortion of their own. Thus no finite network will give perfect equali- \nzation of unwanted natural modes. Sometimes it is desirable, in practice, \nto use an equalizer configuration which produces no finite frequencies of \ninfinite loss, the entire equalization being accomplished by a suitable \nchoice of its n modes. Configurations of this sort are illustrated in Fig. \n6. Thus, our simple illustrative problem, though chosen to introduce \nprinciples, is also of some practical interest.\n\nThe exclusion of finite frequencies of infinite loss simplifies the repre-\n\nFig. 6\u2014Configurations which produce no finite frequencies of infinite loss.\n\n(For convenience, z, has been written for z, , and K, has been redefined \nto avoid the 1/K, required if it is defined as in (21).)\n\nThe assigned gain & is even more special. In this particular problem, \na has most of the properties of a network gain a. Specifically, it is the \nnegative of the gain to be equalized, which in fact corresponds toa \nfinite network. As a result, R(z) of (22) may be expressed in closed \n(rational) form. (Later on, we shall modify the methods appropriate for \nthis very special situation, so that R(z) need be representable only by \nseries. )\n\nThe specific representation of our present & may be very similar to \nthe representation of a in (31), as follows:\n\nThe constant % is the z-plane mapping of the assigned unwanted \nnatural modes at p = jo, and may be calculated therefrom by (8). In \n(32), Z determines the Cy, , which in turn determine &. The constants \n2\u00a2, in (31), are the z-plane mappings of the arbitrary natural modes of \nthe equalizer. They are to be adjusted to make a approximate a. Then \nthe network natural modes p, may be calculated from them, by means \nof (8).\n\nTaking the difference of corresponding equations in om and (82) \ngives the following, analogous to (24):\n\nwithout regard to phase. It reflects the more specific functional forms of \nour present a and @.\n\nThe formulas show that the coefficients in the Tchebycheff poly- \nnomial expansion of our present a \u2014 & are fixed by the logarithm of a \npolynomial in z\u2019, of degree n + 2. Since the Tchebycheff polynomial \nseries is simply one representation of the function or &, this means \nthat a \u2014 & itself is determined by the polynomial in z\u2019. Out of the n + 2 \nzeros, in terms of z\u2019, n are subject to arbitrary choice, but the other two \nare required to be at z= %.\n\nTo arrive at a useful choice of the zeros, one may start with the ex- \npanded form of the polynomial, which replaces the second equation of \n(33) by:\n\nAll but two of the coefficients K;, may be assigned arbitrary values, pro- \nvided the remaining two are then adjusted to give the required two \nzeros at 2 = 2). The corresponding zeros 2; may then be found by \nordinary root extraction methods.\n\nThe coefficients may be chosen in such a way that the complex poly- \nnomial approximates unity, when | z| = 1. Then the logarithm approx- \nimates zero, the coefficients in the power series (34) are small, and since \nthese are also the coefficients in the Tchebycheff polynomial series in \n(33), a \u2014 wis small.\n\nA special choice of coefficients, which meets these requirements fairly \nwell, is the choice determined by (28), with m = n. The function on the \nleft side of (28) is here the polynomial in (34). For our present purposes, \ntherefore, (28) becomes:\n\n{Ko + Kz +. Kysae } = 1 (35) \nThis requires K, = 1, and K, = 0 fork = 1 ton. Then Kasi and Kn4. \nmust be adjusted to give the two required zeros at z\u2019 = 2) . This gives:\n\nIn accordance with Section 9, this special choice of coefficients corre- \nsponds to a match of Tchebycheff polynomial series, a to a, through \nterms of order 2n:\n\nA sample plot of a \u2014 & is shown in Fig. 7. This corresponds to an \nequalizer of four natural modes, compensating for an initial loss which \nrises to about 8 db at the top useful frequency, or a distortion of +4 db \nabout the median loss. Residual errors are order of --0.06 db.\n\nA little later we shall return to the question of accuracy, to take up . \nmethods of estimating what can be done with other numbers of arbi- \ntrary natural modes, and other values of the assigned modes. First, \nhowever, we should investigate whether the network singularities z, \ndetermined by (36) meet the other necessary conditions.\n\nIn the first place, | z,| must be >1. Otherwise, the function of z in \n(31) will have no power series expansion over the useful interval | z | = 1; \nand (31) will not, in fact, determine the gain a over the useful interval. \nIt turns out, however, that the condition does not give trouble in the \nsynthesis of natural modes, when there are no arbitrary frequencies of \ninfinite loss. This may be demonstrated by the argument outlined below.\n\nThe z, are zeros of the polynomial in (84), which we have given the \nspecial form (36), by applying (35). A function theoretic test for | z,| <1\n\nmakes use of the contour in the complex plane for the polynomial, corre- \nsponding to the z-plane circle | z| = 1. (This is like a Nyquist diagram \nexcept that the contour for the variable, z, is different.) There will be \n|z,| < 1 if and only if the contour for the polynomial encloses the \norigin.\n\nNow the polynomial in (34), and (85), is merely a special case of the \nfunction on the left in (28), and (80). For this special case (30) becomes\n\nThe polynomial cannot enclose the origin without passing through some \nnegative real value. But this requires an | H(z) | > 1, at some point on \nthe contour in question, | z| = 1, which happens to be also our uscful \ninterval. On the other hand, \u00ab \u2014 a = 0 when >, Riz\u201d = 1, and H(z) \nis in the nature of a correction term, which is small in the useful interval \nwhen a \u2014 & is small.\n\nThe conclusion is: There will be no | z,| < 1 unless the approxima- \ntion, a to &, is so poor that a \u2014 & exceeds several db in the useful inter- \nval. .\n\nBesides the requirement | z,| > 1, the z, must meet physical restric- \ntions, which we found to be the same as those limiting the natural \nmodes p, . The z, may be calculated as follows: The z; are roots of the \npolynomial in (35), in terms of z\u2019. All the roots in terms of 2 are 2; , \nexcept the two required roots at 2) , which correspond to assigned gain @. \nEach z, is a square root of a 2;. There are two possible square roots, \nhowever, differing only as to sign. As far as gain @ is concerned, either \nchoice of sign is permissible; for a depends only on z?. For a physical \nnetwork, however, the choice must be such that Re z, < 0. This choice \nis possible if, and only if +~/z? has a finite real part. A pure imaginary z, \ncorresponds to a negative real z; , and thus negative real roots in terms \nof 2\u201d are excluded by physical considerations.\n\nTable I lists both z2 and z, for a number of values of n. When 7 is \neven, all roots are physical. On the other hand, when n is odd, one root \nis always non-physical. In a sense, an odd n is not really appropriate \nfor the present illustrative problem, with any physical design. An odd n \nmust necessarily bring in a real natural mode, which merely increases \nthe sort of distortion we are trying to equalize\u2014that is the distortion \ndue to unwanted real modes.\n\nThe following argument substantiates the suggestion, and also illus- \ntrates manipulations of a sort which are frequently useful in more gen- \neral applications: The highest order coefficient in (34), Kn42, may be \nset aside for adjustments to satisfy physical requirements. The rest of\n\nthe coefficients may then be chosen to eliminate terms from the series \n> (Co, \u2014 Co.)T ox , representing a \u2014 &, subject to the previous condi-\n\nIf n is odd, all the roots z, can be physical only if Ky42 is negative. \nOn the other hand, any finite negative K,4. leads to a larger error, \na \u2014 a, than Kay. = 0. Reducing K,+2 to zero is the same as reducing \nthe degree of the polynomial by one, which amounts to reducing n by 1, \nfrom an odd to the next smaller even integer. In other words, a physical \n_ design with an odd number of natural modes is less effective, for the \npresent application, than a simpler network, with the next smaller even \nnumber of modes.\n\nNote that the z, in Table I are proportional to Z% . This means that \nroot extraction methods need be used only once for each value of n, \nafter which the roots may be quickly adjusted for any value of %, \ncorresponding to any assigned value of the two identical modes, fin .\n\nThe accuracy of a completed design can be checked by calculating a \nfrom the natural modes p, , and comparing a with a. It is important, \nhowever, to have at least some information about accuracy in advance\n\nof the detailed calculation of the p, . Otherwise, it may be necessary to \ncarry out several designs, in all detail, in order to obtain one satisfactory \ndesign.\n\nThe needed information about accuracy can in fact be obtained from \nthe error function H(z), which we formulated for general gain applica- \ntions in (30), and for the present application in (38). The analysis \nwhich yields (15) may be used to obtain a very similar expression for \na \u2014 &, in which R(z)R(\u2014z) appears in combination with the rational \nfunction of z from (15). It may be expressed in terms of the error func- \ntion H(z) of (30), as follows:\n\nWhen H(z) is zero, \u00ab \u2014 wis zero. When H(z) is small, a \u2014 & depends \non phase H(z) as much as on | H(z) |. When H(z) is a positive real, \na \u2014 ais negative. When H(z) is imaginary, a \u2014 @ is very small. When \nH(z) is a negative real, a \u2014 ais positive. When H(z) is complex, | a \u2014 @ | \nis always smaller than with a real H(z) of the same magnitude. The last \nstatement may be expressed as follows:\n\nThe left hand relation is an equality when phase H(z) is an even num- \nber of a radians; the right hand side, when it is an odd number of + \nradians.\n\nphase of H(z) varies by (n + 1) radians, which means that H(z) is \nsuccessively positive real, imaginary, negative real, imaginary, through \nn + 1 half cycles. This accounts for the oscillatory nature of the a \u2014 @ \ncurve, illustrated in Fig. 7.\n\nThe amplitudes of the oscillations are fixed by | H(z) | , which varies \nrelatively slowly. Specifically, the two logarithms in (41) determine\n\nenvelopes, between which the actual error curve oscillates. Theseare \nthe dashed lines in Fig. 7.\n\nThe maximum error, in the useful interval, is determined by the \nmaximum value of the envelopes, i.e.,\n\nThis function is plotted in Fig. 8, for various values of n. The abscissae \n\u201cdistortion before equalization\u2019? represent distortion relative to the \nmedian loss in the useful interval, or one half the total variation in the \ninterval. (This is a function of the top useful frequency w, , relative to \nthe assigned natural mode ; and (7) makes w,/fo a simple function of \n2.) The figure is convenient for estimating the values of n needed for \nspecific applications.\n\nThe various ripples in a \u2014 & do not all have the same amplitude, (43). \nFor some values of \u00bb and %, the amplitudes are almost uniform; for \nothers they are quite variable. A measure of the variability in ripple\n\nFig. 8\u2014Distortion before and after equalization\u2014n natural modes equalizing \n2 identical natural modes.\n\nThe above analysis suggests a way of improving the design deter- \nmined by (87) (or the equivalent, (36)). An optimum a \u2014 & is commonly \none which has the following properties, in the useful interval:\n\n(This usually minimizes the largest departure in the useful interval, \nthereby yielding an \u201capproximation in the Tchebycheff Sense.\u2019\u2019) Since \nthe variation in phase H(z) determines the number of ripples, while \n| H(z) | determines the amplitudes of the ripples, the above conditions \nwill be met if H(z) has the following properties, in the useful interval:\n\nThese conditions may be regarded as alternative design criteria, re- \nplacing Co, = Cx, . They can in fact be applied to our special example, \nand also to certain other special problems which will be noted later. \nFor more general applications, a suitable H(z) can be defined, but no \nreasonably simple procedure has yet been found for calculating the re- \nquired constants. (The difficulties will be particularized in a later \nsection.)\n\nFor the present example, (88) may be used to replace (84), and hence \nalso the second equation of (83), by:\n\n(33) requires H(z) to be a polynomial in 2\u2019, of degree n + 2, with two \nzeros of [1 + H(z)] at 2 = 2%. The object is to find an H(z) of this \nsort, which also satisfies (45), at least to a good approximation.\n\nThe function is a polynomial because the factor [1 \u2014 J\u201d\"/2\u00b0\"*\") is \ndivisible by (1 \u2014 J/z\u2019). The constants J and G are to be chosen to\n\ngive the required double zero of [1 + H(z)] at 2 = %. One value of J ; \nso determined, is real and of order 1/2) . This is the appropriate solution. \nThen | J\u00b0**/z2\u2019\"\u2122* | is of order 1/25\"** , when | z| = 1. This suggests the \nfollowing approximation in place of (47):\n\nThe approximation is at least as good as 1/%\u201d\"**, compared with \nunity, both in the useful interval and in the neighborhood of the singu- \nlarities % , and z,. This means that the approximation can be used: in \nestimating the error a \u2014 & (in the useful interval), in calculating J and \nG, and in finding the roots 2, .\n\nIn the useful interval, |z| = 1, and therefore 1/2 = 2*. Then \n(1 \u2014 J/z\u2019) is (1 \u2014 Jz\u2019)*; and their ratio has magnitude unity. Thus \n| H(z) | = |G@|, in the useful interval, to order of 1/%\u201d** compared \nwith unityt. With | J | <1, phase H (2) varies over the useful interval \nto the same extent as the phase of 2\u2019\u201d*\u201d.{ Fig. 9 illustrates the difference \nin a \u2014 &, as determined by (42) and (48). These curves, however, are \nfor single values of n and % ; and the improvement obtained by using \n(48) would be different with different values of n or % .\n\nThe values of J and G, determined from (48), and the requirement \nthat [1 + H(z)] must have two zeros at 2\u2019 = % , turn out to be:\n\nt This is the most we can expect, when we have n singularities, which can pre- \nvent the dominance of only lower order terms, through 2\u201d.\n\nFig. 9\u2014Comparison of design procedures\u2014four natural modes equalizing two\n\napproximating network gain is generalized, by introducing arbitrary \nfrequencies of infinite loss, in addition to the arbitrary natural modes. \nThe methods are also modified for approximation to an assigned phase, \ninstead of gain, or to phase and gain simultaneously. Finally, the anal- \nysis is modified to permit useful intervals of the \u201chigh-pass\u201d type, or \n(in the case of gain simulation) of the \u201cband-pass\u201d type.\n\nIf we now permit the assigned gain @ to be general, in the sense of \nSection 8, we must return to the formulation:\n\nIf we retain simulation with a network which has 7 natural modes, and \nno frequencies of infinite loss, we must retain the formulation:\n\na= \n: (51) \nE Cus\" = \u2014tog K211(1 - 5), o=I1,-+-,n \nThe corresponding formulation of the error is (in place of (83)): \na-a= >) (Cx \u2014 Cx)To \n(52)\n\nNow the reciprocal of &(z)R(\u2014z) has a power series expansion, in the \nregion of interest. (Recall Section 8.)\n\nIt follows that (53) may be multiplied by this quantity, without \ndamaging the equality of power series coefficients. In other words (53) \nis equivalent to:\n\nLet Ky, be the coefficient of z\u201d* in the polynomial expansion of the left \nhand side; and let K;, be the coefficient of 2\u201d in the infinite series ex- \npansion of the right hand side. Then,\n\nThese relations are directly applicable to network synthesis, provided\n\n640 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1952 \nthe coefficients K;, can be calculated. Formulae for their calculation \nmay be derived in the following way: \nIf (55) is substituted in (50), the result is:t \n= 7 . > Co.T ox (58) \n> Gio = log > K,2\"\" \nWhen z = 0, the second equation reduces to:\n\nIf the functions of z are differentiated, a simple rearrangement gives: \nD> kK? = [\u2014D kCae\u201d [D> Kie\u2122] (60)\n\nThe right hand side may be expanded as a single power series, and then \nlike powers on the two sides may be equated separately. The result is:\n\nSynthesis calculations may now be carried out in the following stages. \nThe assigned gain & is expanded as a Tchebycheff polynomial series, to \ndetermine coefficients Cx, , say through order k = n. The equations (61) \nare then used to calculate coefficients K; , also through order n. Each \nsuccessive coefficient is computed in terms of those previously deter- \nmined. Note that the K,, k < n, are fixed by the same number of \nCo,\u2014that is, orders k S n.\n\nEquation (57) is now applied to identify K, with K,, k < m. If all \nthe network degrees of freedom are to be used to get Cx = Cy, , index \nm = n, and (57) determines the polynomial in (55) completely. Other- \nwise, m < n, and coefficients K 41 to K, are to be adjusted in accord- \nance with specifications of other kinds. When all the K; have been \ndetermined, the singularities z, are found by root extraction methods, \napplied to the right hand side of the first equation of (55).\n\nThe previous example might have been carried out in these terms, \nbut happened to be simpler in the terms used. If (32) is regarded as a \nspecial case of (50), and if (32) is simplified (for purposes illustration) \nby using K, = 1, the corresponding R(z)R(\u2014z) becomes simply\n\n| We may think of these equations as defining an infinite network, with na- \ntural modes only, which would match the assigned gain & exactly.\n\nIf these K; are used to evaluate the polynomial on the left hand side of \n(53), in accordance with (55), and if the polynomial is then multiplied \nby the above special R(z)R(\u2014z), the result is exactly (36). :\n\nIf (64) is used to express (53) in terms of H(z), a \u201c1\u201d may be sub- \ntracted from each side of the relation, to get\n\nWhen m = n, this requires an H(z) of the following form, in terms of \nthe coefficients K;, derived from R(z)R(\u20142z):\n\nAs in the previous example, | z,| > 1 when the approximation, a to \n, is at all reasonable. The z, are again zeros of 1 + H(z); but now \nH(z) is defined by (64). If | H(z) | < 1, when |z| = 1, there will be \nthe same number of zeros of 1 + H(z) as poles, in the region | z| < 1. \nAny poles would have to be poles of R(z)R(\u2014z). In Section 8, we noted \nthat this function is regular in the region | z| < 1. Hence, there will be \nno poles, and there will be no | z,| < 1, under ordinary accuracy con- \nditions.\n\nditions, provided none are pure imaginaries. Since an imaginary 2, Is a \n: 2 \nnegative real z, :\n\nThere will be no negative real 2} if the polynomial >> Kz\u201d in (55) is \nnon-zero at all negative real z\u2019. If the requirement is violated, initially, \none or more K;, of the highest orders, must be modified. Graphical \nmethods are likely to be useful for this, combining plots of the original \npolynomial, and proposed changes. An approximation of the form \nCo, = Cx, k S m, will still be realized, but with m > K./z2\u201d] is [D> Kiz\u2122]*. Hence the polynomials \nin z and 1/z have identical magnitudes, in the useful interval; and, \nsince also |z| = 1, | H(z)| = |G@| in (75). The phase variation, over \nthe useful interval, is the same for H(z) as for 2\", which yields the same \nnumber of ripples in a \u2014 & as an ordinary Tchebycheff filter of like \ndegree. t\n\nThe constant G is arbitrary, except that its sign must be properly \nchosen to avoid non-physical natural modes. Increasing G increases the \nfilter selectivity, but also increases a \u2014 @ in the useful interval. G and n \nare to be chosen together, to realize an assigned selectivity within an \nassigned limit on distortion.\n\nThe above analysis may be related to the following filter problem: \nRequired to design a filter which has flat gain, in the useful interval, \nbut which has m assigned frequencies of infinite loss, in addition to n \narbitrary natural modes (m S n). The n arbitrary natural modes may \nbe regarded as compensating for gain variations due to the assigned \nfrequencies of infinite loss, in the useful interval, while reinforcing their \neffects at other frequencies. Compensation of effects of the infinite loss \npoints is the same as s\u00a2mulation of the effects of natural modes at the \nsame (assigned) frequencies. The approximation in the useful interval \n+ This assumes an @ with the general characteristics described in Section 8,\n\nwhich are such that the numerator and denominator of the fraction in (75) will \neach have a net phase shift of zero, across the useful interval.\n\nis to be no better than necessary, so that there may be a maximum \nreinforcing of losses at other frequencies. In these terms, (58), and \n>> Ky2\"\" in (78), correspond to the assigned natural modes (at the \nsame locations as the assigned frequencies of infinite loss). Then the \nideal >> Kz\u201d is itself a polynomial, of degree m < n, and (74) is exact, \nrather than an approximation to (73). Then (76) determines the n \narbitrary modes in such a way that the net filter gain approximates \nzero in. the Tchebycheff sense, over the useful interval.\n\nEquation (75) may be related to work of Bashkow\u2019. The (arbitrary) \namplitude of the (equal) maxima of | a \u2014 @|, computed from H(z) of \n(75), depends only on | G | . The frequencies at which the maxima occur \ncorrespond to phase H(z) = sz, which is independent of | G|. Thus, \nthe locations of the maxima are invariant to the arbitrary amplitude, \nwithin the range where (75) applies. (75) applies only when (74) may be \nused in place of (73). Generally, (74) only approximates (73), and the \napproximation introduces small variations in the maxima of |a \u2014 @| \n(when \u00ab corresponds to (76)). If the maxima themselves are sufficiently \nsmall, the small variations will be large percentage variations; and the \nadjustments to compensate for the variations will yield significant \nshifts in the location of the maxima. In other words, the locations of \nthe maxima of |a@ \u2014 @|, required for equal amplitudes, are largely \ninvariant to the magnitude of the equal amplitudes, but only to an \napproximation which becomes worse as the amplitudes are decreased.\n\nBashkow states the invariance of the frequencies of maximum \n| a \u2014 &|, as a more or less empirical conclusion, based on a quite dif- \nferent approach to the same synthesis problem.\n\nEquation (75) may be related also to work of Kuh.\u2019 The natural \nmodes 2, are zeros of 1 + A(z). In other words, H(z,) = \u20141. Using the \nH(z) of (75) gives the following:\n\n- Jt must be remembered, however, that this formulation is permissible \nonly if the approximations, inherent in (75), are justified when z = z, \n(as well as in the useful interval). Taking the logarithm of each side \ngives: \nlog {Ko + +++ Knze\"} \n2 K,\\ (78) \n= log (\u2014G) + 2n log z, + log, Ko + --:> om \nEquation (58) may now be applied, to replace the logarithms by \npower series, provided the truncation of the series is again justified, and \nprovided the convergence of >> C22\u201d is also proper, at both z = z, and \nz= 1/z,. This gives\n\n(Summations >> are all with respect to k; and there is one equation for \neach o.) This is a suitable rule, for obtaining an |a \u2014 &| with cqual \nmaxima, whenever the approximations are in fact unimportant. It is \nnot at all clear, however, just when the approximations become sig- \nnificant.\n\nKuh uses the potential analogy approach for the same sort of syn- \nthesis problem. He spaces the natural modes along a p-plane contour \ndefined in fairly complicated potential analogy terms. It can be shown, \nhowever, that mapping his potentials from p plane to z plane leads to \n(79).\n\nWhen the network is to approximate & in the useful interval, but is \nnot required to supply selectivity at other frequencies, the approxima- \ntion (74) is usually untenable. It is generally necessary to retain the \nexact formulation (73).\n\nWhen selectivity is not required, the phase excursion of H(z), in the \nuseful interval, can usually be increased to that of 2\u00b0\u201d* (as in (67), \ncorresponding to Co, = Cx, k S n). As a step toward meeting the first\n\ndesign constants are the Q, . They are to be small enough so that they \ndo not affect the total phase excursion H(z), when |z| = 1. Their \nspecific values are to make | H(z) | approximately constant, when \n|z| = 1. In general the (required) series in 2\u201d in the numerator makes \nit extremely difficult to determine the required values for the Q,;. No \nreasonably simple general procedure has yet been found.\n\nThe preceding sections were devoted to the approximation a to &, \nusing \u201d arbitrary natural modes, but no arbitrary frequencies of in- \nfinite loss. Similar techniques may be used when there are n\u201d arbitrary \nnatural modes and n\u2019 arbitrary frequencies of infinite loss. As the appli- \ncations become more involved, however, routine calculations must be \nsupplemented increasingly with an element of art.\n\nFor simultaneous design of natural modes and frequencies of infinite \nloss, we must go back from (81) to the a formulation in (21). This we \nshall now write:\n\nThe functions N and D are polynomials. The coefficients will be defined \nas follows:\n\nBy comparison with (21), the zeros of N, in terms of 2\u2019, are the 2,\u201d. \n(Note the minus sign in 81.) The zeros of D are then the z,\u201d. For physical \nnetworks, n\u201d = n\u2019.\n\nEquations (50), describing &, may be retained as they stand. Com- \nbining (50) and (81) gives, in place of (52):\n\nThe function R(z)R(\u2014z) is exactly the same as before. The reciprocal \nof the function will still be >) Ki.z\u201d, with the K; related to Cx by (58), \n(59), (61). The new rational fraction N/D will appear where previously \nwe had the polynomial Ky + --: K,2\u201d.\n\n- This condition may be used to determine the coefficients K; : Ky, of \nN and D (in combination with conditions of other sorts, when \nm n\u201d. There- \nfore (85) requires zero coefficients in the expansion of the right hand \nside, from order n\u201d + 1 to order n\u201d + n\u2019. Equating these coefficients \nto zero gives n\u2019 linear equations in the n\u2019 unknown K; . Solving for the \nK;, determines polynomial D. The values calculated for the K; may \nthen be used in lower order coefficients of the expansion of the right \nhand side of (85), which are exactly the coefficients K;, of N.\n\nWhen n\u201d \u2014 n\u2019 = 0 or 1, a continued fraction method is likely to be \npreferable. Various established techniquest may be used to convert the \nseries >) K.2\" into a continued fraction of the form: \ncor 1 \nSs Kz\u201d = a +\n\n{ See, for example, Fry\u2019s applications of continued fractions to network de- \nsign.\u00ae\n\nIf the continued fraction is truncated after the term of order m, and is \nrearranged as a rational fraction N/D, it will obey equation (84). The \ndegrees of N and D will be such that n\u201d + n\u2019 = m, and n\u201d \u2014 n\u2019 = 0 \nor 1. The continued fraction may be associated with the hypothetical \nladder network shown in Fig. 10, with variable impedance shunt branches \nproportional to 2\u2019. The impedance of the (truncated) ladder is N/D.\n\nThe accuracy of match, a \u2014 @, may again be evaluated from the \nfinal network singularities; or by (41), with H(z) as in (80), before the \nsingularities have been determined from roots of N and D. A rougher \nestimate may again be obtained from the error in the first unmatched \nterm in the Tchebycheff polynomial series. As before, (equation (72)), \nthis is equal to the leading term in H(z), with 2\u00b0\u201d\"\u201d\u201d replaced by \u2014Tom4.2 .\n\nH() 7 (a1a2 oes Om) OmyrK a (88) \nThe corresponding mismatch in Tchebycheff polynomial terms is: \n7 Cae as \nCompe T Comte = (a1d2 nee Am) Omyrko (89)\n\nWhen frequencies of infinite loss are to be chosen, as well as natural \nmodes, the situation in regard to | z, | < 1 is somewhat less favorable.\n\nIt is still true that 1 + H(z) will have the same number of zeros as \npoles in the region | z| < 1, so long as a \u2014 @ is reasonably small in the \ninterval |z| = 1. In equation (87), however, the poles of 1 + H(z) \ninclude the zeros z, of D (the arbitrary infinite loss points), as well as \nthe poles of R(z)R(\u2014z). When the coefficients of D are to be chosen as \nin the previous section, the contour rule merely says that any z, and z, \nin the region | z| < 1 will occur in like numbers.\n\nFortunately, the frequent occurrence of | z,| < 1 is softened by the \nfollowing curious circumstance. Almost always, any | 2, | and | 2 | <1 \nare so nearly identical that factors (\u00a2 \u2014 z,) and (z \u2014 z,) may be can- \ncelled out without any important effect on H(z), or a \u2014 &. Cancellations \nof this sort were encountered a number of times before an explanation \nwas discovered. Actually the explanation is quite simple.\n\nAt any zero of 1 + H(z), H(z) = \u20141. On the other hand, A(z) is \nsmall when | z| = 1. Generally, it is much smaller in most of the inter- \nval |z| < 1. For instance, when Cy, = C2, through k = m, H(z) is pro- \nportional to 2\u00b0\u201d*\u2019, in the neighborhood of z = 0. As a result, | H(z) | \nrarely becomes as large as 1, in the region |z| < 1, except in the very \nclose proximity of a pole. In other words, in the region | z| < 1, any \nzero 2, is usually very close to a pole 2,\u2014usually so close that the \ncorresponding factors z \u2014 z, may be cancleled out without significant \neffect on a \u2014 &.\n\nThe occurrence of non-physical natural modes (Rez, = 0) is the same \nas before; but adjustments to correct for these, in an efficient manner, \nare much more complicated. In addition, there may be non-physical \ninfinite loss points, 2. To correct for non-physical singularities, the \nsimplest procedure would be to change one or both of the highest order \ncoefficients in N and D of (82), that is Ky, and K\u2018,,. This would be \ninefficient, however, for it would spoil the match of C,,, to Car, or Cn \nto C,, . The unmodified design, defined by (84), can match terms through \norder n\u201d -++ n\u2019, and it is desirable to change only the highest order terms \nin adjusting the design.\n\nMore efficient adjustments are in fact feasible. They sometimes re- \nquire an increased element of art; but the art may be based on specific \nprinciples. Some particularly useful principles are described in the next \nsection. These apply to various other corrections besides correction of \nnon-physical zeros and poles. Examples are reduction in phase to make \ntwo-terminal realization possible, and increase in shunt capacity in \ntwo-terminal designs. In general, they offer a means of making \nm ) Kz\u201d, \nof the order indicated :f\n\nThe left hand side of (92) may be used as N/D in (84), to match \nCox to Cx, through k = m. Adjustment of the function F may be used to \nsatisfy other requirements, in addition to accuracy specifications.\n\nFrequently, Ni/D,; may be the rational fraction corresponding to \ntruncation of the continued fraction, (86), after the term in dyr4n-. \nThen N2/Dz is likely to be a truncation of order m < n\u201d + n\u2019. The \ncorresponding F is likely to be proportional to 2, or at most a simple \npolynomial in 2\u2019. When F is a constant, and m = n\u201d + n\u2019 \u2014 1, the \nuse of these particular rational functions in (92), to determine N/D, \ncorresponds to matching Cy, to Cx through k = n\u201d + n\u2019 \u2014 1, but \nleaving Con+4n\u2019) Subject to adjustment. Specificially, Cocn++4n) depends \non the choice of /, which may hinge upon such special conditions as \nthe elimination of non-physical singularities.\n\nProblems which call for more complicated combinations are by no \nmeans uncommon. Skill may be needed in the choice of specific com- \nbinations which will solve specific problems. Computations may be\n\n(If only natural modes are to be used, the suitable replacement for the \nfirst equation or (55) is here obtained merely by using D = 1, and K., \n2, 2\u00a2, in place of their squares.)\n\nA comparable expression is needed for the assigned gain and phase \na + 76. In place of (50), we now repeat (22), and redefine the coeffi- \ncients K; in accordance with\n\nThe definition of K, has been changed in such a way that it is now \nrelated to C;,/2 exactly as it was previously (in 58) related to Cy, . \nEquations (59), (61) may be applied to calculating the K;, by merely \nsubstituting therein a C,/2 for every Cx .\n\n} For example, a simple recursion formula may be used to assemble the poly- \nnomials N and D which correspond to truncation of the continued fraction (86)\n\nis either N or D and P, corresponds to truncation of the sontmued fraction after \nthe term in a, . The formula holds for n 2 2.\n\nEquations (84), (85), (86) may now be modified, for the new N, D \nand. K,, by merely using z in place of 2\u2019 wherever it occurs (including \nz\" in place of 2\u201d).| The modifications of equations (84), (85), and the \ntruncation of (86) after am now lead to C, = C,, k S m, instead of the \nprevious Cx, = Cy . This means that m must be twice as great to match \ncoefficients out to the same actual orders. This is to be expected since \nnow one half of our design parameters are used to approximate phase \nB, leaving only half for approximating gain a. Equation (89) must be \nchanged not only in regard to the orders of C,, C; , but also in regard \nto the factors $ in (94), (96). This gives\n\nThe most important change is in regard to the zeros and poles z, . \nThe polynomials N and D now determine z, and z, directly, instead of \ntheir squares. There is no opportunity to adjust the sign of Re z, by \nchoosing the correct sign of +~/2/2. When non-physical singularities ap- \npear, adjustments of high order coefficients may be tried. Section 23 \napplies provided z\u2019 is replaced by z. If the specification of the problem \npermits added delay, linear phase may be added to @ + 78 to increase \nthe probability of physical singularities{t. (Addition of linear phase \nchanges only C,, in >> O.7;. A negative change in C, increases the \ndelay.)\n\nSometimes it is required to approximate an assigned phase, without \nregard to gain. More commonly, it is required to approximate an as- \nsigned phase, using an \u201c\u2018all-pass\u201d network, which has a theoretically \nzero gain. These two problems, however, are very nearly identical, due \nto circumstances explained at the end of this section.\n\nFor approximation to phase only, we go back to the 6 equation in \n(21). As before, products of factors (\u00a2 \u2014 2.) are replaced by polynomial\n\nft The well known relation between the gain and phase of any physical network \n(See for instance Bode) may give some information regarding the reasonable- \nness of 8. It must be remembered, however, that departures of network gain a, \nfrom the assigned gain &, outside the useful interval, may affect the permissible \nphase 8, within the interval.\n\n\u00a7 Up to the present, applications to phase problems have not been developed \nto the same extent as for gain. Techniques have been explored, however, to deter- \nmine how such applications may in fact be carried out.\n\nUsing n to represent n\u201d + n\u2019, the total number of network singularities, \nwe may write N and D as follows, in place of (82) or (95):\n\nTo arrive at a design procedure most easily (but not the simplest \ndesign procedure), one may express the assigned gain 8 in the following \nway (comparable to (58) and (96)):\n\n>> Cra\u00ae = \u2014log > Biz\" \nCoefficients K;, may again be calculated by a modification of (61). This \ntime Cx, is replaced by C,, wherever it appears in (61), and then all \neven ordered C; are made zero (since only odd terms appears in >, C,2\" \nof (101)). Note that even ordered K; are not usually zero, even though \neven ordered C;, are. \nThe degrees of N and D, in (99), are such that we can make C;, = C; \nthrough terms of order k = 2n. This requires merely:\n\nAs stated, the condition applies to C; of both even and odd orders. \nSince even ordered C; are zero, it means that at least n even ordered \nC;, will be zero, in addition to the match between n odd orders. (102) \nis sufficient to determine an N and a D without reference to (100). If \nthe (equal) degrees n of (99) are assumed, however, the N and D deter- \nmined by (102) will be found to obey (100) automatically (provided \n>> Kiz* corresponds to an odd series >) C2\", as here assumed).\n\nof the known relation (100), connecting N and D. Let EF and O be re- \nspectively the sums of even and odd terms in N. Then N is L + O and \n(100) requires D to be EF \u2014 O. The ratio O/E may be related to >> C,2\" \nof (98) as follows:\n\nLet coefficients K; be defined by: \nE+0= >> Ke | (105) \nThen H and O are respectively the sums of the even and odd terms. \nThe complete series may now be related to the (odd) series >) C,z\" as \nfollows: \n> 2Cyz = \u2014log > Kye\" (106) \nThis fixes the K; of Z + O in terms of the C;. \nTo make C, = C;, through m odd orders, (102) is now replaced by \noO\u201d O .\n\nmo \nThe symbol = designates equality of power series through m odd orders. \n(All even terms are now zero on both sides.) The right hand side may be \nexpressed as a continued fraction of the following form, comparable to \n(86):\n\nThe coefficients of O and EH may be calculated by an appropriate \nmodification of (61). (Calculate like K, of (101), after dividing all C, \nby 2). After O and EF have been evaluated, by truncating the continued \nfraction (108), their sum gives polynomial N of (99).\n\nThe natural modes and frequencies of infinite loss are determined \nfrom the zeros of the polynomial N. By (21), each zero is either a (z- \nplane) natural mode, z, , or the negative of an infinite loss point = ae \nIf gain variations are inconsequential, there is likely to be some latitude \nin designating each zero as az, , or asa \u2014Z,.\n\nA zero of N with a positive real part would make a non-physical natural \nmode, and hence it must be a \u2014z,, corresponding to an infinite loss \npoint. A zero of N with a negative real part can be a natural mode z; , \nbut this may not be required. It may be either a z, or a \u20142, , provided \nconjugate zeros are assigned in the same way, and provided the total \nnumber of \u2014z, does not exceed the total number of 2, . The latter con- \ndition requires:\n\nThe continued fraction (108) shows how many zeros will have nega-\u2019 \ntive real parts, before any zeros have been calculated. The following \ntheorem makes this easy:\n\nThe number of zeros of N which have negative real parts \nis equal to the number of positive coefficients in the trun- \ncation of the continued fraction (108) which determined N.\n\nWhen gain is not to be disregarded, but is to be exactly zero, the \nsynthesis technique needs few changes. The phase of an \u2018\u2018all-pass\u2019\u2019 net- \nwork is related to the natural modes z, as follows:\n\nCuz I \u00a2 7 *) \nDy, \u2014\u2014 = \u2014log \u2014\u2014_*4 (109) \n(+2) \nThis may be regarded as a special case of (20) for a = 0 (which makes \nC,, = O for k even, and also happens to require z, = \u2014z,). In functional \nform however, it is more like 78 of (21). It differs in only two regards. \nIn the power series in z, each C;, is divided by two. In the rational frac- \ntion in 2, all the zeros correspond to natural modes, and the poles cor- \nrespond to frequencies of infinite loss; but the poles are also exactly the \nnegatives of the zeros, as in the 78 equations of (21).\n\nAccordingly, the phase synthesis technique which ignores gain varia- \ntions may be applied to the zero gain form of the problem by cutting\n\nevery C; in two. All zeros of N = E + O must be construed as natural \nmodes z, . Finally, the network must have as many infinite loss points \nas natural modes, such that 24, = \u2014z, . (Integer 7 is now the number \nof natural modes, rather than the total number of singularities.)\n\nFor physical networks, all the first n terms of the continued fraction \n(108) must now be positive. To meet this condition it may be necessary \nto add linear phase to the assigned phase (by adding a negative cor- \nrection to C,). It appears that sufficient linear phase will always lead \nto a physical design, provided the number of modes n is increased to \nretain a reasonable accuracy.\n\nWhen the assigned phase \u00a3 is linear, the calculations are relatively \nsimple.\n\nIf a delay D is to be approximated over a frequency interval extending \ntow = a,\n\nIf delay D is to be realized without regard to gain variations, the ap- \npropriate O/E is\n\nA known continued fraction expansion of tanh X may be applied to \n(111), to obtain the coefficients of (108) without bothering with (105).t \nThe result may be arranged as follows:\n\nTruncation of the continued fraction gives O/E, and then O + EH. The \nzeros 2, turn out to be proportional to 5 , and therefore root extraction \ntechniques are required only for one D, for each n. The zeros are tabu- \nlated for sample n\u2019s, in Table IT.\n\n+ For the expansion of tanh X, reference may be made to a text on continued \nfractions by Wall!\"!, page 349, equation 91.6.\n\nThe error in the first mismatched Tchebycheff coefficient is a rough \nmeasure of accuracy. It may be shown to be\n\nConga ct Cons = \nThis measure of accuracy is plotted in Fig. 11, for various numbers of \nnatural modes n. A sample detailed curve of 8 \u2014 8 is shown in Fig. 12, \nwith dotted lines corresponding to the estimated error (113).\n\nIf delay D is such that the error is reasonable, all the zeros may be \nnatural modes. If these are combined with a like number of infinite \nloss points, such that <4, = \u2014z,, , an all-pass network will be obtained, \ninstead of one which approximates D without regard to gain. The all \npass network will produce twice the delay, and twice the nonlinearity \nof phase. In other words, for an all pass network, both co\u00e9rdinates in \nFig. 11 must be doubled.\n\n10 20 30 40 5060 80 100 200 300 400 600 1000 \nPHASE ANGLE IN DEGREES AT TOP USEFUL FREQUENCY \n(MULTIPLY BY 2 FOR ALL-PASS NETWORKS)\n\nFig. 12\u2014Error when six natural modes approximate a linear phase, with a \nslope giving 402\u00b0 at top useful frequency.\n\nThe singularities Z, , % correspond, of course, to the network singu- \nlarities which are to be boiled down. If only @, or only \u00a3, is to be ap- \nproximated, suitable modifications are readily derived from (21). \nThe boiling down is accomplished by requiring \nae al 115) \nDD | ( \nwhere N/D is of lower total degree than N/D. If m = n+ n\u2019, and \nn\u201d \u2014 n\u2019 = 0 or 1, the continued fraction method can again be used. \nThis requires expansion of N/D in continued fraction form, instead of \nDS Kiz\".\n\nAll the previous analysis applies to a useful frequency interval \u2014w, < \nw < +w.. Its important characteristics are as follows: It is a single \ncontinuous interval, with \u00bb = 0 at its center. Useful intervals with other\n\nWith this transformation, the whole of the previous z-plane analysis \nmay be applied at once to high-pass useful intervals, except where \nlinear phase is involved.\n\nThe situation is more complicated in regard to \u201c\u2018band-pass\u201d\u2019 intervals. \nIf the useful interval includes the frequencies between w.. and w., the \ncomplete useful interval (p-plane mapping of |z|= 1) must include \nalso the \u201cimage\u201d frequencies, between \u2014w. and \u2014w.. Otherwise, \nconjugate complex z-plane singularities z, will not lead to conjugate \nnetwork singularities p, . When there are two disjoint parts of the use- \nful interval, the appropriate relation between p and z is relatively com- \nplicated. Up to the present, no corresponding technique has been dis- \ncovered for approximating assigned phases over band-pass intervals, \nin Tchebycheff polynomial terms. Gain approximations can be handled, \nhowever, and for a quite simple reason. Gain functions are even func- \ntions, and behave in the p\u2019 plane much as gain-and-phase functions \nbehave in the p plane. In the p\u2019 plane, \u2014w and +w are identical, and a \nband-pass useful interval is a single segment of the w\u201d axis.\n\nThe three coefficients, a, b, c are subject to two conditions, stemming \nfrom the requirement that the interval |z| = 1 must map onto the \ninterval w?1 < w\u2019 < we. This leaves one arbitrary degree of freedom. \nIts choice may be related to ordinary least squares approximations in \nthe following way:\n\nIf a = >> CxT'x, , the first n terms approximate a in the least squares \nsense. In other words, the integrated square of the error is a minimum, \nrelative to all possible choices of the first n coefficients Cs, , provided \nthe integration extends over the useful frequency interval,.and in- \ncludes an appropriate \u201cweight function\u201d. When (117) relates z to p, \nthe arbitrary degree of freedom in the choice of the constants a, b, \u00a2 \npermits selection of any one of a family of weight functions. Conventional\n\nIn applying least squares analysis, it must be borne in mind that the \nnetwork gain a does not approximate the assigned gain & in the simple \nleast squares sense. When Cy, = Cy, for k S n, a \u2014 & depends upon \ntwo least squares approximations. The first n terms of > CxT'x, represent \na least squares approximation to a, and are made identical with the \nfirst n terms of >> Cx,7'x, , Which represent a least squares approximation \nto &.\n\nAn additional singularity, 2} , is also needed, corresponding to the finite \npoles of (117). It may be defined as follows:\n\nWhen p; \u2014 p\u2019, in a of (2), is expressed in terms of z and z, , (117) \nintroduces denominator factors (1 \u2014 2\u2019/z3) and (1 \u2014 1/z0z\u201d). As a re- \nsult, a of (21) must be changed to the following, for band-pass intervals:\n\nWhen definite values have been chosen for a, b, \u00a2 of (117) (in order \nthat the C, may be calculated), (1 \u2014 2\u2019/z5) in (120) is not subject to \narbitrary adjustment. This situation can be handled by defining N/D \nas the rational fraction in the a equations of (21), as before, but re-\n\n+ For general discussions of orthogonal functions and least squares approxi- \nmations, see Courant and Hilbert\u00ae, and also a short text by Jackson.??\n\nFig. 14 illustrates an application of the technique to the simulation of \na coaxial cable attenuation (which is nearly proportional to +~/w).\n\nFig. 14\u2014Simulation of a coaxial cable attenuation\u2014Attenuation at top useful \nfrequency = 46 db; Network = four constant-resistance sections.\n\nnetwork singularities. This makes it possible to apply power series ap- \nproximation methods, in terms of z, to obtain approximations based on \nTchebycheff polynomial series, in terms of frequency.\n\n\u201cMaximally flat\u2019? approximations in terms of z may be used to match \nthe first m terms in the Tchebycheff polynomial series representing net- \nwork gain or phase to the corresponding terms in the series representing \nassigned gain or phase. In this way, a Tchebycheff polynomial type of \nleast squares approximation to the network function is made identical \nto the corresponding least squares approximation to the ideal function. \nThe overall error, network function minus ideal function, is then the \ndifference between the two least squares errors.\n\nThe z-plane analysis may also be manipulated, in a quite different \nway, to approach an equal ripple type of approximation (which usually \nrepresents approximation in the Tchebycheff sense). The complications \nare such that applications have been limited to problems of certain \nquite special types. On the other hand, analysis of this sort has been \nfound useful in clarifying various other ways of seeking equal ripple \napproximations.\n\n1. S. Darlington, \u2018\u2018The Potential Analogue Method of Network Synthesis,\u2019\u2019 Beil \nSystem Tech. J., 30, pp. 315-365, Apr. 1951.\n\n2. G. L. Matthaei, \u2018\u2018A General Method for Synthesis of Filter Transfer Func- - \ntions as Applied to L-C and R-C Filter Examples,\u201d Stanford University \nElectronics Laboratory Technical Report No. 39, Aug. 31, 1951 (for Office of \nNaval Research, NR-078-360).\n\n3. T. R. Bashkow, \u2018\u201c\u2018A Contribution to Network Synthesis by Potential Anal- \nogy,\u2019\u2019 Stanford University Electronics Laboratory Technical Report No. 26, \nJune 30, 1950 (for Office of Naval Research, NR-078-360).\n\n. B.S. Kuh, \u2018A Study of the Network-Synthesis Approximation Problem for \nArbitrary Loss Functions,\u2019\u2019 Stanford University Electronics Laboratory Tech- \nnical Report No. 44, Feb. 14, 1952 (for Office of Naval Research, NR-078-360).\n\n. R. Courant and D. Hilbert, Methoden der Mathematischen Physik, Vol. I, \nChap. 2, Julius Springer, Berlin, 1931.\n\n. C. Lanczos, \u2018\u201cTrigonometric Interpolation of Empirical and Analytic Func- \ntions,\u2019\u201d\u2019 J. of Math. and Phys., 17, pp. 123-199, 1938-39.\n\nH. A. Wheeler, \u2018\u2018Potential Analog for Frequency Selectors with Oscillating \nacre Wheeler Monograph No. 15, Wheeler Laboratories, Great Neck, \n. Y., 1951.\n\n. T. C. Fry, \u201cUse of Continued Fractions in Design of Electrical Networks,\u201d \nAmerican Math. Soc. Bulletin, 36, pp. 463-498, July-Aug., 1929.\n\ntrand Co., New York, 1945. \n11. H. 8. Wall, Analytic Theory of Continued Fractions, D. Van Nostrand Co., \nNew York, 1948.\n\ndesigned for application in large groups at telegraph central offices and \nfor trunk-service operation over toll telephone circuits employing stand- \nard levels. It has proved very economical in this field. However, the \nvery features which make for economy in large installations (such as \namplitude modulation, common carrier supply and testing equipment, \nand standardized operating conditions) cause this equipment to be \ncostly when it is applied a few channels at a time in outlying offices; \nthese may not be equipped with either telegraph battery supplies or \ntelegraph boards. Moreover, the 40Cl equipment, being a carrier-on- \nfor-mark and carrier-off-for-space system, does not lend itself to the \nprovision of TWX toll subscriber line supervision identical to that of \nlocal stations without the addition of rather complex and expensive \nsupervisory applique circuits. Where TWX supervision is involved these \nsupervisory circuits are required to generate and recognize supervisory \nsignal patterns capable of being distinguished from transmission space \nsignals and communication breaks, which are long space signals.\n\nConsequently, it was decided to develop a new carrier telegraph \nsystem especially aimed at the needs of fringe areas. One of the problems \nto which much thought was given concerned the choice between ampli- \ntude-modulation and frequency-shift operation. A frequency-shift sys- \ntem provides some reduction in the effect of noise and other interference \non transmission and it is also less affected by rapid level changes. Al- \nthough these advantages were attractive, it was not clear that they were \nsufficient to justify the added complexity and cost entailed by the \nadoption of this type of transmission, in view of the quiet and stable cir- \ncuits encountered in the Bell System plant. What finally swung the bal- \nance to a frequency-shift system was its advantage in handling TWX \nsupervisory signals. With transmission accomplished by shifting the car- \nrier frequency, supervisory signals could be sent by turning the carrier \non and off. A cheap and simple circuit might then be used to distinguish \nbetween transmission and supervision.\n\nFrom the foregoing discussion it will be evident that during the twelve \nyears since the 40Cl system was developed the needs of the Bell System \nhave changed. Fortunately, the designer\u2019s art has concurrently made \ngreat strides in making available new miniature apparatus and elec- \ntronic techniques such as have been exploited so successfully in the \n143A type electronic telegraph regenerative repeater,\u2019 the V3 telephone \nrepeater\u2019 and the N-1 carrier telephone system. As a result, the \nchannel terminal of the new 43A1 carrier telegraph system, being small, \ninexpensive, self-contained and all-electronic with no electro-mechanical\n\nThe 43A1 system provides two groups of channel-frequency alloca- \ntions, as follows:\n\na\u2014A three-channel high-frequency allocation, using frequencies be- \ntween the upper edge of the voice-frequency band and the lower edge of \nthe type-C carrier telephone band. This allocation is primarily for opera- \ntion on open-wire lines but can also be operated on cable circuits where \nthe loading provides a suitably high cut-off.\n\nb\u2014A voice-frequency allocation capable of providing six channels \non two-wire circuits or twelve channels on four-wire circuits. The chan- \nnels of this allocation are for operation over telephone speech channels \non any of the standard facilities, including broad-band carrier and cable \nor open-wire physical circuits.\n\nThe present frequency allocations are shown in Fig. 1. The voice- \nfrequency system is based on twelve nominal midband frequencies \nspaced 170 cycles apart from 595 cycles to 2635 cycles, omitting 1615 \ncycles. The carrier frequency is shifted +35 cycles about midband, and \neither the higher or the lower frequency may be used for marking sig-\n\niii 9 ee. ee ars \n= re) 9 o oO iy) \nVOICE FREQUENcy .2@ \u00a9 @ 2 & Y o @ XS wu t+ \u00a9 \n\u00a3 35VSHIFT + as et ee ee ae \nSMSMSMSMSMSM SMSMSMSMSMS5M \nCHANNEL NUMBER 2 3 4 5 6 7 9 10 1 12 13 14 \ne 2 @ 2@ 2@ @ Sa a \n2-WIRE n 2 2 mH 4 9 fo oo 8 9 \nVOICE FREQUENCY 4 XL o@ 2 \u00a5 r gx VN YT \u00a9 \n\u2014 | | | | | | Tae \nSMSMSMSMSMSM SMSMSMSMSM SM \nCHANNEL NUMBER 2 3 4 5 6 7 a3 4\u00b058 & 7 \nR58 e ee \nHIGH FREQUENCY 8 2 8 &\u00ae 2 8 \no _ \u201d 9) \u00a9 \u00b0o \na) vt v vt vt Wy)\n\nnals. The high-frequency system is based on six midband frequencies \nspaced from 200 to 240 cycles apart. The frequency shift ranges from \n+40 cycles in the lowest channel to -+-50 cycles in the highest. These \nwider spacings and shifts were adopted to ease the problem of designing \ninexpensive filters and oscillators for the higher frequencies.\n\nChannel 1 of the high-frequency system employs adjacent frequency \nassignments for the two directions of transmission. The lower frequency \npath employs a downward shift for marking signals and the higher- \nfrequency path an upward shift for marking signals. In half-duplex \noperation this minimizes interference from the strong signals at the \ntransmitter output to the weak signals at the receiver input. The steady \nmarking frequency, which is being sent against the flow of traffic, is \nshifted away from the band over which the message is passing.\n\nror) \nRECEIVE SUPERVISORY SIGNALS = \n(IN SWITCHBOARD TERMINATION ONLY): ehariniy ree \nit LOOP tid \n\u201c+t \ni a P+130V I Ee \nMODULATOR ru . Lt \nSUPERVISORY | o--\u2014-* 1 ie \nTRIODE | I ~T \nREVERSING POR Ste ae \nSWITCH SENDING \nTRIODE 5\n\ndownward transformation (7500:600) from the impedance of the buffer \namplifier to that of the line so that no amplifier output transformer \nis required.\n\nHither unity-ratio line coils or a hybrid coil may be used to connect \nthe unbalanced sending and receiving filters to a balanced line. The \nhybrid coil is used with a two-wire line when the send and receive \nfrequencies occupy adjacent bands.\n\nWhen the channel is used in TWX service as a toll subscriber line, \nthe subscriber calls the operator to initiate a call by closing the power \nswitch on his teletypewriter. This connects power to the teletypewriter \nmotor, closes the transmission circuit to the teletypewriter and applies \nplate battery voltage to the transmitting oscillator in the channel ter- \nminal, resulting in the transmission of carrier current over the line. \nAt the distant (switchboard) terminal the receipt of carrier current \nenergizes a supervisory signal receiving circuit which is responsive to \ncarrier-on and carrier-off conditions in the receive band. In this circuit, \ncarrier voltage appearing at the plate of the limiter tube is rectified \nand applied to the grid of the supervisory triode. The operation of a \nrelay in the plate circuit of this tube causes a line lamp at the switch- \nboard to light.\n\nA disconnect signal is sent by the subscriber at the end of a call by \nopening the teletypewriter power switch. This removes the oscillator \nplate voltage. At the central office, the receipt of the resulting no-carrier \nsignal de-energizes the supervisory receiving circuit and causes the super- \nvisory lamp in the operator\u2019s cord circuit to light steadily. To recall \nthe operator during a call the subscriber opens and recloses his power \nswitch. This causes the cord lamp at the switchboard to flash.\n\nAn Rc circuit slows the rise of current in the supervisory receiving \ntube to guard against false operation of the switchboard line lamp due \nto noise impulses during the carrier-off, that is, the idle condition.\n\nOn the de side of the channel terminal, provision is made for optional \nwiring arrangements to connect to the circuits of the various telegraph \ntest boards, service boards and TWX switchboards, as well as to local \n- teletypewriter loops, using telegraph voltages of either 130 or 48 volts. \nIn offices where a negative 130-volt battery is not provided, operation \nwith a single positive 130-volt battery is possible.\n\n(a) shows a conventional open-and-close circuit and the wave shapes \nwhich it produces at the central office end and at the far end of a capaci-\n\nIn half-duplex operation, one de loop at each channel terminal serves \nfor both sending and receiving. The central office end of this loop is \nconnected to the grid of the sending triode and to the plates of the re- \nceiving tetrodes. If a marking signal is being received from the carrier \nline while the teletypewriter contacts in the loop are closed, the receiving \ntubes conduct, current flows in the loop and the teletypewriter in the \nloop receives a marking signal. Under this condition the office end of \nthe loop is positive with respect to the cathode of the sending triode; \nhence this tube passes a marking signal toward the carrier line. When a \nspacing signal is received from the carrier line the tetrodes are cut off, \nthe loop current is reduced practically to zero, the teletypewriter re- \nceives a spacing signal and the voltage at the office end of the loop be- \ncomes more positive. Hence a marking signal continues to be transmitted \nto the line during the receipt of either mark or space signals from the \nline.\n\nWhen the subscriber opens the loop at the teletypewriter to break \ntransmission coming from the distant terminal, a clean-cut space should \nbe transmitted to the line regardless of any incoming signals. The re- \nsistor shunted between the plates and cathodes of the receiving tubes \ncauses the central office end of the open loop to assume the same potential \nas the tetrode cathodes. This insures that a steady spacing potential \nwill be applied to the send tube even though the tetrodes are cut off \nby an incoming space. This provides a rapid, clean break. However, if \na large leakage exists across the loop conductors, the resistor will not be \nable to keep the sending tube in a cut-off condition and a break by the \nsubscriber will result in the incoming transmission being reflected in an \ninverted condition to the distant carrier terminal. In such a case the \ndistant sending subscriber would be broken by a \u201cbust-up\u201d of local \ncopy or by operation of the keyboard break lock. This would normally \nbe caused only by a trouble condition in cable loops.\n\nOn quiet circuits, total distortion per section averages 1 to 2 per cent \nat 60 words per minute and about 5 per cent at 100 words per minute. \nPlots of received signal distortion versus level of received carrier are \nshown on Fig. 6 for both signaling speeds.\n\nThe channel terminal employs a formed sheet-metal framework and \noccupies a space 103 inches high, 5} inches wide and 7? inches deep over- \nall. Fig. 7 shows a 43A1 channel terminal. It is plug-terminated, and \nhence removable for maintenance or repair at a bench.\n\nThe basic portion of the channel terminal is common to all frequency \nallocations. The oscillator network and send filter, which constitute the \nelements determining the transmitted frequency, form a plug-termi- \nnated sub-assembly 7% inches high, 53 inches wide, and 13 inches deep. \nThe receive filter and discriminator, which select the received frequency, \nform a plug-terminated sub-assembly of the same size.\n\nA rear view of the channel terminal with the send frequency unit \nremoved is shown in Fig. 8. With both frequency units in place, the \nrear of the channel terminal is almost completely enclosed. When they \nare removed, the wiring and apparatus terminals of the basic channel \nterminal are readily accessible for test and repair.\n\nTube sockets, potentiometers, test points, switches and the inductor \nof the low-pass filter are mounted on the front panel. Small resistors, \ncapacitors, and germanium diodes are assembled on a plastic \u201cladder\u201d \nwhich is mounted vertically in the space between the frequency units.\n\nAs shown in Fig. 9, three channel terminals may be mounted abreast \non a welded metal frame which is fastened to any of the standard bay \nframeworks designed to accommodate 19-inch mounting plates. The \nunit mounting frame carries the multicontact receptacles into which the \nchannel terminals are plugged. Twenty-four channel terminals may be \nmounted on an 114-foot relay rack, with line coils and certain auxiliary \nequipment.\n\nWhere arrangements for switching between half and full-duplex opera- \ntion are required, duplex switches for a number of channel terminals \nare mounted on a narrow plate between the channel terminal mounting \nframeworks.\n\nLoop rheostats, when required, may be mounted adjacent to the \nchannel terminals or in a loop pad bay along with other loop rheostats \nthat may be associated with electronic loop repeaters. The latter arrange-\n\nment concentrates the heat dissipated. by these rheostats at a place \nwhere it will not be harmful.\n\nof the sending tube at the central office terminal, actuates the station \nringer, which is connected to the local loop whenever the teletypewriter \npower switch is in the OFF position. .\n\nA channel terminal dissipates about 25 watts. Tube heaters consume \nabout half an ampere at 24 volts and the remainder \u2018of the channel term- \ninal, exclusive of its loop-terminating portion, consumes 50 ma at 130 \nvolts. The loop terminating portion dissipates 20, 30 or 62.5 ma at 80 \nvolts, depending upon the type of local circuit employed.\n\nThe 43A1 system is capable of working with a great variety of line \nlevels. The send level may be adjusted for any value from +6 dbm \ndownward: The receiving equipment operates satisfactorily with \u201445 \ndbm or even \u201450 dbm. But the levels actually used are controlled by \ncrosstalk and noise conditions in the line.\n\nReceiving levels are normally limited by lightning interference on \nopen wire and by noise on cable circuits. The minimum tolerable levels \nare about \u201440 dbm on open wire, \u201445 dbm on four-wire cable circuits \nand \u201435 dbm on two-wire cable.\n\nIn Fig. 11, a comparison is made of the effects of static on the 43A1 \nsystem and on the 40C amplitude-modulation system. It gives the \nresults of simultaneous tests on the 2465-cycle bands of the two systems, \nusing the static from a record made at Madison, Florida. The 48A1 \nchannel could tolerate about 4 db stronger static than the 40C.\n\nA typical circuit layout of the 43A1 system working in the frequency \nband between the voice and type-C carrier on an open-wire line is shown \nin Fig. 12. The telegraph circuits extend from 48A1 channel terminals \nlocated in a central office, at the left, to 180B1 sets in subscriber stations, \nat the right. In the central office, the send and receive paths of the chan- \nnel terminal are combined in a hybrid coil. With the moderate degree of \nbalance provided by the network of this hybrid coil, the allowable dif- \nference between send and receive levels of the middle channel may be\n\nTIME, AS MEASURED IN A 10 KC \nBAND BY A METER HAVING A 10 \nMILLISECOND INTEGRATION TIME \nCIRCUIT.\n\n1 \n-24 -22 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 \nSIGNAL-TO- INTERFERENCE * RATIO IN DECIBELS \nFig. 11\u2014Comparison of amplitude and frequency shift modulation with static\n\n35 db or more. The telegraph channels are next combined. with the voice \nfrequency circuit by means of a 150A filter, and are connected to the \ncomposite set and line through the low-pass section of the 121A (type \n-C) carrier line filter. As a result of the cut-offs of the 150A high-pass \nand 121A low-pass filter components, the pass band of the telegraph is \nabout 3.7 to 5.4kce. At the outlying terminal of the open-wire line, the \ntelegraph is separated from the voice and type-C carrier circuits by \nsimilar filters and connected to the individual subscriber stations by a \nbranching network and branch lines.\n\nThe typical arrangement on a two-wire circuit in the voice feouisaey \nrange is shown in Fig. 13. Six channels are available, using six of the \ntwelve frequency bands for transmission east to west and the other six \nbands west to east. As in the high frequency case, a branching network \nand branch lines at the outlying end connect the circuits to the sub- \nscribers. Fig. 14 shows a layout in which branch lines are connected at \nintermediate points in the telephone circuit. At these intermediate points \nthe impedance of the branching network is made high, in order to keep \nthe balance at the telephone repeater from being harmed excessively. \nThough the network attenuates greatly the signals through it, the tele- \ngraph level is usually sufficiently high so that this loss can be tolerated.\n\nThe branching network at the outlying terminal has low impedance. \nTaps on the transformers in the network permit the impedance ratios \nto be adjusted to suit the line impedances between which the network \noperates. Since several circuits may pass through this network, a short- \ncircuit on one branch should not be capable of degrading transmission \nin the other branches. To prevent this, resistances are inserted in series \nwith each branch of such a value that a short circuit will not cause more \nthan 3 db excess loss in other channels. It has been shown by tests that,\n\npatch. Obviously echo suppressors must be disabled when a message \ncircuit is used for telegraph.\n\nWhen the telegraph circuit contains one or more branches at inter- \nmediate points, it would be difficult and often impractical to use an \nordinary message circuit to replace the telegraph stem in emergencies. \nThe branching location frequently will not be manned and so no one \nwill be available to patch the branch line to the message circuit. In such \ncases each intermediate branch circuit may be made good over a separate \nmessage circuit which is individual to it. Fig. 16 shows this arrangement. \nA patch trunk is provided between the 43A1 channel terminal at the \ncentral office and the telephone switchboard. At the switchboard which \nis nearest to the intermediate branch subscriber, the branch line is\n\nSWITCHBOARD SWITCHBOARD \nFig. 16\u2014Emergency circuit for intermediate branch.\n\nIt is expected that the field of application of the 48A1 system will be \nbroadened by further development over the next few years. More fre- \nquencies will be provided, both in and above the voice band. Means will \nbe designed for passing TWX supervisory signals over a direct-current \nloop from a subscriber station to a channel terminal installed in a nearby \ncentral office. The built-in supervisory arrangements of the 43A1 equip- \nment will be exploited to gbtain inexpensive straightforward trunks \nfor use both between TWX switchboards and from switchboards to \nLine Concentrating Units. The supervisory feature will also be employed \nin private line service to provide an open circuit alarm.\n\n1. R 8. Caruthers, H, R. Huntley, W. E. Kahl, L. Pedersen, \u2018\u2018A New Telephone \nCarrier System for Medium-Haul Circuits,\u2019\u201d\u2019 Elec. Eng., 70, pp. 692-697, Aug. \n1951.\n\n2. B. P. Hamilton, \u201cCarrier Telegraphy in the Bell System,\u201d\u2019 Bell Labs. Record, \n26, pp. 58-62, Feb. 1948.\n\n3. J. A. Duncan, R. D. Parker and R. E. Pierce, \u2018\u2018Telegraphy in the Bell System,\u201d\u2019 \nA.LE.E. Transactions, 68, pp. 1032-1044, 1944.\n\n4. B. Ostendorf, Jr., \u2018\u201cNew Electronic Telegraph Regenerative Repeater,\u201d Elec. \nEng., 69, pp. 237-240, March, 1950.\n\nO \nNEGRASKA OE \nTOWAL DAVENPORT \nj CITY xe - \u2014\u2014s \n, O D CHICAGO \nDENVER . ~\\ROCK \n(coL) ; /MUSCATINE. ISLAND\n\nMEPREGIONAL CENTER BURLINGTON \nO O O MT. PLEASANT \nA SECTIONAL CENTER SHENANDOAH CLARINDA CORYDON , \n@ PRIMARY OUTLET \u2014 = Ne \no TOLL CENTER \n\u2014 TOLL CABLE ST. JOSEPH YIKEOKUK \n---- FUTURE TOLL CABLE MS a Re Ted \n\u2014 OPEN WIRE KANSAS CITY\n\n< \nyn\u201d \nn \n(0) \n9) \nisa} \n< \nVv \n5 \nNORTHWESTERN BELL TELEPHONE CIRCUITS \nI TOTAL NUMBER OF CIRCUITS = 2720 \nY) TOTAL NUMBER OF CIRCUIT MILES = 86,400 \n> END OF 1949 \noO \na \n1S) \nWw \nre) \n= \nz \nWw \n16) \nry \nao oO 20 40 60 80 100 120 140 160 180 200 \nOPEN-WIRE LENGTH IN MILES \nFig. 2\u2014Distribution of circuit lengths in Iowa in 1950. \nio \n90\n\nThe type-O carrier system followed the type-N system closely in \ntime, and, in effect, covers the same range of circuit lengths for open \nwire lines that N provides for cables. It was both natural and expedient \nthat many of the N features were carried over directly into the O design. \nIt was necessary, however, to make important distinctions as well. These \nsimilarities and differences will be discussed in some detail.\n\nThe transmitting and receiving voice frequency subassemblies are \nreused with substantially no modification. This provides the O system \nwith the same compandor and the same 3700 cycle signaling system as \nused in N.\n\nAn important difference between the two systems is concerned with \nthe use of single sideband in the O rather than double sideband as in \nthe N. This choice is an economic one. The double sideband system is \nrelatively easier to design and less expensive than the single sideband \narrangement. The use of double sideband in cables is practicable in \nmany cables because of the relative abundance of conductors as com- \npared with open wire pairs. In some cases the use of single sideband in \ncables may be attractive as compared with the cost of new outside plant \nfor certain length ranges.\n\nAnother distinction between the two systems is the provision of cir- \ncuits in smaller groups in O. In N the basic group is 12, although systems \nmay in some instances be partially equipped. In O, the desire to furnish \nsmaller circuits groups resulted in the choice of a basic four-channel \ngroup. The full complement per pair for O, including a channel replacing \nthe voice circuit, is sixteen channels.\n\nto provide sufficient regulator range to accommodate line variations due \nto wet or icy lines. The repeater and receiving group regulator range \ncommon to four channels is in the order of 40 to 50 db, or approximately \nfour times the regulating range of an N repeater. The range of the \ntwin-channel regulator is comparable to the N individual channel regu- \nlator, but the O regulator is shared by two channels forming adjacent \nsidebands of the same carrier.\n\nThe use of a single sideband imposes more severe requirements on \nchannel band filters. The use of a material called ferrite, in combination \nwith a crystal, affords an efficient channel band filter in a small space \nwhen compared to previous single sideband channel filters employing \nair-core coils. Ferrite coils are employed in a coil-condenser type of filter \nto provide separation for the various four-channel groups. While the N \nsystem employs only receiving channel band filters, O has filters in \nboth the transmitting and receiving terminals.\n\nThe O system employs the double modulation principle for all groups. \nThis arrangement. permits the use of only four channel band filter de- \nsigns for all of the 32 channel frequency allocations. The frequency range \nfor these basic channel bands has been selected to provide the most \neconomical overall filter design.\n\nThe use of die-castings has been extended in a number of ways. No- \ntable among these is a die-cast framework, used in both the terminal \nand the repeater. The plug-in technique has been expanded to provide \nplug-in filters for channel and group band filters.\n\nThe O modulation plan is shown on Fig. 5. The single-sideband chan- \nnel filters for all groups are in the frequency range from 180 to 196 ke.\n\nBy the use of different group carrier frequencies the several four-channel\n\n5, high and low group assignments are used for the two directions of \neach four-channel system. A repeater is provided for each four-channel \nsystem and, except in the case of OA, the high and low frequency groups \nare \u2018frogged\u201d\u2019 at each repeater, as in the N system.\n\nFigure 6 shows a block diagram of a complete O system. On this figure, \nand in general on other figures showing filters, a letter code is assigned \nto designate the kind of filter, with a subscript letter to indicate the \nparticular system in which the filter is used. The several filter designa- \ntions and number codes are collected for reference in Table I. Much of \nthe apparent complexity of the system, particularly as regards filters,\n\narises out of the use of a single pair for both directions of transmission.\n\n| MODULATOR | \nOB SYSTEM OB SYSTEM \n40-76 KC 40-76 KC \n4 Cp, | GROUP INEL \nCHANNELS Cc | OSCILLATOR | B CHAN Ss \n(180-196 KC) S Ca UNIT | (180-196 KC) \n| MODULATOR | \nOC SYSTEM OC SYSTEM \n80-116 KC 80-116 KC\n\nGROUP \nCHANNELS Cc Co pew nnn nm en wn wn a rr nr ee ee Co Cc CHANNELS \n(180-196 KC) \u00b0 Gg \u00a2 | UNIT | Wg0-196 Kc)\n\nGROUP GROUP \nCHANNELS Cop Cp pee enn en em own a ee -- Cp , CHANNELS \n(180-196 Kc) } UNIT UNIT | (1g0-196 KC)\n\nLine filters (G) are provided to separate the OB, OC, and OD Systems \nfrom the OA frequency ranges. Because of the lower attenuation and \nslope in the OA frequency range, and the better line coupling factors, \nthe repeaters do not \u201cfrog\u201d the high and low groups.\n\nA block diagram of a typical carrier terminal is shown on Fig. 7, \nin this case the OB terminal. The terminal is comprised of four channel \nunits, two twin-channel units, group transmitting and receiving units, \nand a group oscillator. An oscillator in each of the twin channel units \nsupplies carrier to the transmitting channel modulators. The same oscil- \nlator supplies transmitted carrier for two associated sidebands. The \noriginal carrier is balanced out in the transmitting modulator. This \nmethod results in a more accurate control of the transmitted carrier. \nlevel. The group oscillators supply the necessary frequencies to the\n\nTaBLeE I \nFilter Codes for Each System \nLocation and Function Filter Symbol) \nCommon OA OB oc | OD \nTERMINAL ONLY \nTransmitting low pass..... None 168F \nReceiving low pass........ None 169G \nCarrier pickoff (184ke)..... Fi 532A \nCarrier pickoff (192kc)..... F2 532B \nSignal pickoff............. None 169A \nChannel band pass........ None 529A \nChannel band pass........ None 529B \nGroup transmitting........ E. 540A* \nGroup receiving........... A+ D 530J | 531B | 5380C | 530F \nGroup receiving........... B+D 531F | 5381C | 530D | 530G \nTERMINAL AND REPEATER.... \nDirectional................ C 5380H | 580A | 530B | 5380E \nG2 219St \nLINC ie ose re ehoaetelox wets G 5Gl 5387At \nGl 538A \nREPEATER ONLY \nAVRINATY o% (cx Beaiey eee A+B 531A | 531D | 531E \nA 530K \nB 530L\n\n* Except OA system. f Cut-apart region between 36 and 40 ke. tf Cut-apart \nregion between 30 and 40 ke. 538A is a 587A filter with housing and protectors \nfor pole mounting.\n\n; \n| \nMODU- \nLATOR \n! I \nHYBRID & | \n| | NETWORK \n| ! \nl \n| BAND FILTER | \n1 | (PLUG IN AND! \nHersh Sees e Ses ere em Rena somal Rae See ae | REVERSIBLE | \na ee ar IS a Poca Se ene Pe epee Ieee PEE ee SN ats | 529A OR 529B! \nEXPANDOR SUB-ASSEMBLY ! | ! \ni I | { | \n<\u2014 _|ExPANDOR I | \n[or | \nONTROL ba DEMODU- 1 \n1 | LATOR | 192-196 KC \n1 | ' \\(OR 180-184 KC) \nVARIO LPF rg | REC <\u2014_ \nH LOSSER (3100) tf ! BPF a \n1 | \n] toy ! I \n{ toy ! | \n, ted ee 1 \n| MERCURY RECT & BPF \nRELAY DELAY a LIMITER < (3700) [1 | \n! # ! \n' i | ' \n1 , | i \n| { | i\n\nplug-in filter reversible in its socket, this grouping can be made to serve \ntwo channels as follows: \neee ees 4 eae oS \n192-196 Receiving 1) 180-184. Receiving \nA similar paired filter serves \nae \u2014\u2014 d eae eas \n. (188-192 Receiving 184-188 Receiving \nThus only two basic kinds of paired channel band filters are required, \nrather than four kinds. In these filters, as well as the reversible group \nfilters, the filter designations are so arranged that when the filter is in \nplace the proper filter designation is in view.\n\nLINE FREQUENCIES IN KILOCYCLES FREQUENCIES IN KILOCYCLES \nFOR EACH CHANNEL FOR EACH CHANNEL \n44 52 184 192 \n40 48 56 180 188 196 \n1 2 3 4 \nLOW fee 8 \nGROUP 4 3 2 1 fence \n236 \nGROUP \nCARRIER \n64 72 \n60 68 76 256 \nGROUP \nCARRIER \nHIGH more S=sTort \nGROUP t, \u201c2 3 4 s\u2014\u2014\u2014.J \"> \n4 3 2 1 \n180 188 196 \n184 192\n\npicked off by a narrow band crystal filter. This same carrier is supplied \nto the receiving side of the channel units for demodulating the associated \nsidebands.\n\nThe OB group transmitting unit is shown on Figure 11. It receives the \nfour sidebands and two transmitted carriers and places thein in the \nproper high or low line frequency assignment. The transmitting group \nunit, depending on the optional connection to the group oscillator (Fig. \n11), can be either a high group transmitting unit or a low group trans- \nmitting unit.\n\nFor convenience the noise generator is contained in the group trans- \nmitting unit. On very quiet circuits this noise source provides a means of \nmasking crosstalk. In ordinary usage the noise thus provided is not \nnoticeable on the circuit, but is sufficient to reduce the chance of hearing \nintelligible crosstalk to a small value.\n\nCARRIER SUPPLY OSCILLATOR TRANSMITTED \nTO TRANSMITTING <= 184 KC CARRIER \nMODULATORS (OR 192 KC) \n<_\n\nfier, and operates principally on the two received carriers, although the \nsidebands are fed back also.\n\nFROM == REC UNIT \n40-56KC \n i \namid | 256 236 3700 | \n| KC KC CYCLES | \n| \n| THER LGR \np bese \\ \ney (eerie eee eee fees: 4 \nTO GROUP | TO KEYING \n; REC UNIT } CIRCUITS\n\n= \nREG LINE \nAMPLIFIER AMPLIFIER \n' TO OC AND \nOD SYSTEMS \n| \neee [to pati \nCONTROL \n| AMPLIFIER \n| \n| RECTI- \n! FIER \n| \nx* \n| LINE \ni osc \nFILT -- \n(116 Kc) les \n] \n! \np--------------------}--------------+-+------ \nLINE REG \n| AMPLIFIER \n1 \n| \nt \nf | \nt 1 \nt 1 \n| 1 \nCONTROL TO OA SYSTEM \nAMPLIFIER OR TO TYPE C \n: | CARRIER AND \n! 'VOICE FACILITIES \n| \n| i] \n| ' \nbe beste one eee ae Ae ek Se eee Se ee a eee ee ee\n\n* FILTERS ARE PLUG-IN AND REVERSIBLE ** BASIC AMPLIFIER USED FOR OB, OC AND OD FOR \nREPEATERS AND GROUP RECEIVING UNITS\n\n60 \n-60 -55 -50 -45 -40 -35 -30 -25 -20 -15 +10 -5 O 5 10 \nCOMPRESSOR 1000-CYCLE INPUT IN DBM (AT ZERO LEVEL) \nFig. 16\u2014Typical over-all channel load characteristic.\n\nwith repeaters will not result in a substantial change of the net loss \nvariation, assuming the repeater section losses do not exceed the range \nof the regulators.\n\nThe line regulator is assisted by the twin channel regulator, for which \na characteristic is shown on Fig. 19. This regulator is similar to the \nindividual channel regulator of N, and serves two channels having a \ncommon carrier. This fact alone does not materially change the effective-\n\nit controls in any case. There are other important differences, however, \nbetween N and O channel regulators. In N the channel regulator follows \nthe channel band filter and thus tends to compensate for its flat trans- \nmission variations. Also the N regulator is controlled from the demodu- \nlator de output and thus compensates in some degree for demodulator \nvariations. In O, the twin-channel control is ahead of both the channel \nband filter and the channel demodulator, and therefore does not make \nup their variations.\n\nA statement might be interpolated at this point to emphasize that \nthe relative advantages of single-sideband and double-sideband trans- \nmission are by no means easily listed and evaluated, since the differences \nare many and devious, some necessarily and some fortuitously. An ex- \nample worthy of note is that in N it is necessary to be concerned about \nrelative phase shift of the sidebands and in the instances of longer cir-\n\ncuits, perhaps to equalize this phase shift in order to prevent serious \nreduction of signal output, or variation in channel net loss with fre- \nquency. No such concern applies to O.\n\nIn regard to filter characteristics, it seems obvious that complete \ncoverage is not feasible in this description. Instead typical curves only \nwill be shown.\n\nFig. 20 shows the general characteristics of filters for separating the \nwanted sideband from the carrier and unwanted sideband. The trans- \nmitting and receiving filters have similar shapes. The carrier pick-off \nfilter characteristic is shown in the same figure. Fig. 21 shows the filter \ncharacteristics for separating the voice and signaling (3700 cycle) func- \ntions.\n\nAnother filter case of interest is the line filter for separating, for ex- \nample, the OA system from the OB system, and from the OC and OD \nsystems, as well, if they are employed. Fig. 22 shows the configuration \nand loss characteristics of the G1 (537A or 538A) filter. A Cg directional \nfilter (580A) characteristic is shown on Figure 23. This filter assembly \nincludes two filters to accommodate the OB high and low group assign-\n\n4 3 2 1 Oo 4 \nFREQUENCY IN KILOCYCLES PER SECOND (FROM CARRIER) \nFig. 20\u2014Typical channel band and carrier pick-off filter characteristic.\n\nments. Similar characteristics apply to the Ag + Bg auxiliary filter \n(531A). The A and B characteristics are used in the group receiving \nfilters Ag + Dg , (5381B) and Bg + Dg, (531C). The D filter is a band- \npass filter with relatively gradual cutoff to pass the 180-196 band for \nthe channel filters, and has peaks at the group carrier frequencies of \n236 ke and 256 ke. These filter characteristics are not shown.\n\nand a crystal with the necessary fixed and adjustable capacitors. The \nsmall size is made possible partly by the high Q ferrite coil, and partly \nby the circuit configuration employing it. As compared with filters em- \nploying air-core coils and having comparable cutoffs, the reduction in \nsize of these filters is very striking.\n\nThe group receiving unit is shown with its plug-in filters on Fig. 31. \nThe filters are held in place by stud screws and nuts. The arrangement \nshown on Fig. 31 is also used with different filters for the repeater ampli-\n\nPREGUENEY IN Recs: PER econ \nFig. 22\u2014Typical line filter characteristics (G1, 537A or 538A).\n\nplug-in units. Since there is no interference between plug-in units in \ninserting and removing them, can covers have been eliminated. This \nfact, and the somewhat wider distribution of units having a high con- \ncentration of vacuum tubes, result in a relatively low temperature rise \nfor O as compared with N. Blower facilities are not provided in the \nterminal.\n\nplug-in group oscillators, which are also shown in the photograph, to- \ngether with fuses, alarm lamps, etc.\n\nPole mounted repeaters are housed in a cabinet, similar to that used \nfor N. Such a cabinet, equipped with four repeaters is shown on Fig. 37.\n\nSince a maximum of four repeaters would have to be supplied by one \npair of wires, it is not feasible to transmit power for the repeaters over \nline pairs. Instead the cabinet contains rectifiers and a line voltage \nregulator for obtaining 130 volts de from commercial ac supply. For \nreserve power supply, a cabinet is available containing a 24-volt storage \nbattery and a dynamotor to supply 130 volts de to two repeaters (or \ntwo dynamotors to supply four repeaters) in case of power failure.\n\nFig. 38\u2014Tes \ntheir being held during the interval of failure; and second, to make all \ncircuits busy at both terminals, to prevent false seizure by operators or \nautomatic switching equipment. Since many O systems may be em- \nployed in situations where one terminal is unattended, facilities are \nincluded whereby, after failure, the system can be tested from either \nend, through the use of one of the signaling channels. If it is indicated\n\nthat the system is operable it can be placed in service again without the \nnecessity of a trip to the unattended terminal.\n\nArrangements are provided by which two O circuits can have their E \nand M signaling control leads interconnected without the use of the \nsignaling converter, which is otherwise required. This feature is employed \nwhen two circuits are connected together on a permanent or semi-per- \nmanent basis to form a single trunk.\n\nTo facilitate testing at terminal points a test stand (Fig. 38) has been \nprovided which supports an O, or N, channel unit during test and \nadjustment. By a patch cord, the channel unit can be connected to its \noriginal framework if desired. Built in pin jacks permit bridging meas- \nurements to be made at selected points in the transmission circuit.\n\nThe term coding, as applied to electrical communication, has several \nmeanings. It means the representation of letters as sequences of dots \nand dashes. It means the representation of signal sample amplitudes as \ngroups of pulses having two or more possible amplitudes as in pulse \ncode modulation. Lately, it has also come to be the generic term for \nany process by which a message or message wave is converted into a \nsignal suitable for a given channel. In this usage single-sideband modula- \ntion, frequency modulation and pulse code modulation are examples of \nencoding procedures, while microphones, teletypewriters and television \ncameras are examples of encoding devices.\n\nThis is a nice concept, but it is useful to distinguish between two classes \nof encoding processes and devices: those which make no use of the \nstatistical properties of the signal, and those which do. In the first class, \nthe encoding operation consists simply of a one-to-one conversion of \nthe message into a new physical variable, as a microphone converts sound \npressure into a proportional voltage or current, or of the one-to-one \nremapping of the message into a new representation without regard to \nprobabilities, as by ordinary amplitude, frequency or pulse code modula-\n\ntion. In ordinary PCM for example, the message samples are converted \ninto groups of on-or-off pulses. The particular combination of pulses \nin any group depends only upon the amplitude of the particular sample, \nnot upon any other property of the message, and the same time is allotted \nto each group, regardless of the probability of that group or of the \namplitude it represents. Almost all the processes and devices used in \npresent day communication belong to this first class. In the second class, \nthe probabilities of the message are taken into account so that short \nrepresentations are used for likely messages or likely subsequences, longer \nrepresentations for less likely ones. Morse code, for example, uses short \ncode groups for the common letters, longer code groups for the rare ones.\n\nProcesses of the first class we may call non-statistical coding processes, \nor simply modulation or remapping processes. The time of transmission \nis the same for all messages of the same length, and all messages are \nhandled by the system with equal facility (or difficulty). These processes \nrequire no memory and have a small and constant delay. They are \ninefficient in their use of channel capacity.\n\nProcesses of the second class we may call statistical encoding proc- \nesses. These processes in general require memory. The time of trans- \nmission .of messages of the same length may be different so that if \nmessages are to be accepted and delivered by the system at constant \nrates, variable delays may be necessary at the sending and receiving \nends. They are more efficient in their use of channel capacity. It is with \nthis second type of process that this paper is concerned, although pro- \ncesses of the first type may be used as component steps. Thus we con- \nsider systems of the type shown in Fig. 1, with the accent on the word \n\u201cefficient\u201d\u2019.\n\nSIGNAL= EFFICIENT DESCRIPTION OF MESSAGE \nFig. 1\u2014Reversible statistical encoding.\n\nstatic discharges. The best type of signal for one channel may be very \npoor for another.\n\nIn the following sections it is assumed that the channel transmission \ncharacteristic is flat in amplitude and delay over a definite band and \nzero outside. It is also assumed that the channel has a definite peak signal \npower limitation, and that the noise is white gaussian noise. Such a \nchannel is no mere academic ideal. It is in fact quite closely approached \nin practice by many circuits. Moreover, the conclusions based on these \nassumptions can usually be modified or extended to other actual cases, \nsuch as that of noise with non-uniform spectral distribution (as for \nexample the coaxial cable).\n\nIf the bandwidth of the channel is W, we can (using single sideband \nmodulation, if necessary) transmit over it without distortion from fre- \nquency limitation signals containing frequencies from 0 to W (or \u2014W \nto W in the Fourier sense). Such a wave can assume no more than 2W \nindependent amplitudes per second. Any set of samples of the wave \ntaken at regular intervals sa serves to specify the wave completely. \nThe wave may be thought of as a series of (sin x)/2 pulses centered on \nthe samples and of proportional height, and indeed the wave may be \nreconstructed from the samples in this fashion. This is the well-known \nsampling theorem\u2019. Thus a message source of bandwidth W can supply \nat most 2W independent symbols (samples) per second, and this same \nnumber can be transmitted as overlapping, but independently dis- \ntinguishable pulses by a circuit of bandwidth W.\n\nSince, as will appear later, channels which are to transmit signals \nresulting from efficient statistical encoding must be relatively invulner- \nable to noise, we shall assume that the pulses on the channel are quan- \ntized. This allows regenerative repeatering to be used to eliminate the \naccumulation of noise\u2019. If there are b quantizing levels, and if the levels \nare sufficiently separated so that the probability of noise causing in- \ncorrect readings is negligibly small, then the capacity of the channel in \nbits/sec is\u201d\n\nSuch a circuit talks in an alphabet of b \u201cletters\u201d and uses a language \nin which all combinations of these letters are allowed. There are no for- \nbidden or impossible \u2018\u2018words\u201d. The circuit has a vocabulary of b one- \nletter words, b\u201d two-letter words, b\u201d n-letter words. The basic ineffi- \nciency in present day electrical communication is that we build circuits \nwith unrestricted vocabularies and then send signals over them which\n\nin which C is the capacity in bits/sec, W is the bandwidth and P/N the \nratio of average signal power to average noise power. This capacity can \nonly be approached, never exceeded, and is only reached when the sig- \nnal itself has the statistics of a white noise. The expression sets a limit \nfor practical endeavor, and also gives the theoretical rate of exchange \nbetween W and P/N.\n\nA practical quantized channel, operated so that the loss of informa- \ntion due to incorrectly received levels is negligible requires about 20 \ndb more peak signal power than the average signal power of the ideal \nchannel to attain the same capacity\u2019. However, bandwidth and signal- \nto-noise ratio are still exchanged on the same basis. For example, a satis- \nfactory television picture could be sent over a channel with, say, 100 \nlevels. This would require a (peak) signal to rms noise ratio of some 40 + \n20 = 60 db. The bandwidth could be halved by a sort of reverse PCM: \nby using one pulse: to represent two picture elements. But there are 10,000 \ncombinations of two samples each of which can have any of 100 values. \nHence the new combination pulse would need 10,000 distinguishable \nlevels and this would require a signal to noise ratio of 80 + 20 = (2 xX \n40) + 20 = 100 db.\n\nIt is evident that while bandwidth compression by non-statistical or \nstraight signal remapping means is not an impossibility, it is neverthe-\n\nless impractical when the signal to noise ratios are already high. What \nwe should really try to do is make our descriptions of our messages more \nefficient so that less channel capacity is required in the first place. The \nsaving can then be taken either in bandwidth or in signal-to-noise ratio, \nwhichever fits the requirements of our channels best.\n\nMessages can either be continuous waves like speech, music, or tele- \nvision; or they can consist of a succession of discrete characters each with \na finite set of possible values, such as English text. Because a finite band- \nwidth and a small added noise are both permissible, continuous signals \ncan be converted to discrete signals by the processes of sampling and \nquantizing\u2019. This permits us to talk about them as equivalent from the \ncommunication engineering viewpoint. Since many of the principles \nwhich follow are easier to think of with discrete messages and since \nquantization of the channel is assumed for reasons already stated, we \nshall think of our messages as always being available in discrete form.\n\nThen if all the message samples were independent and if all quantizing \nlevels were equally likely, the information per sample would be\n\nand the message would use the full capacity of a channel with \u00a2 quan- \ntizing levels, and bandwidth S/2. Or by remapping k message samples\n\n(with the \u00a2 possible levels) into (85) k samples, a channel with b levels \nand bandwidth W = S/2 (75) could be loaded to full capacity.\n\nHowever, it is not true that the successive samples of typical messages \nare independent, nor is it true that the various sample amplitudes are \nin general equiprobable. If these things were true, speech and music \nwould sound like white noise, pictures would look like the snowstorm\n\nwhere VN = number of message sequences of length n. If the successive \nsymbols of the message are independent but not equiprobable, then a long \nsequence will contain x; symbols of type 1, x2 of type 2, etc. The number \nof possible combinations of these symbols will be\n\nn! \nN ~ II x;! , \n7 \nso that log N = log n! \u2014 >> log 2;! \n7 \nFor large enough n, all the x; will be large also and we may write, by\n\nBut since >) x; = n, and since for large n, x, > p(j)n where p(j) is the \nprobability of the j symbol, we have\n\nwhich is the expression Shannon derives more rigorously\u2019. H; is a maxi- \nmum when all the p(j) are equal to 1/\u00a2. Then Hi = log, \u00a2 = Hy. The \nmore unequal the p(j), i.e., the more peaked the probability distribution, \nthe smaller H, becomes.\n\nIf the successive samples are not independent, the message source will \npass through a sequence of states which are determined by the past of \nthe message*. In each state there will be a set of conditional probabilities \ndescribing the choice of the next symbol. If the state is 7 and the condi- \ntional probability (in this state) of the next symbol being the j\" is p,(j), \nthen the information produced by this selection is\n\nThe average rate of the source is then found by averaging (6) over all \nstates with the proper weighting; thus\n\nThe greater the correlation between successive symbols or samples of a \nmessage, the more peaked the distributions p,(7) become on the average, \nand this results in a lower value for H. As Shannon points out, the in- \nformation rate of a source, as given by (7), is simply the average un- \ncertainty as to the next symbol when all the past is known. But in a \nproperly operating communication channel the past of the message is \navailable at both ends, so that it should be possible to signal over the \nchannel at the rate H bits/message symbol, rather than Hy as we now \ndo. In present day communication systems we ignore the past and \npretend each sample is a complete surprise.\n\nBy completely efficient statistical coding it should be possible to re- \nduce the required channel capacity by the factor H/H>. Whether or not \nthis improvement can be actually reached in practice depends upon the \namount of past required to uniquely specify the state of the message \nsource. If long range statistical influences exist, then long segments of \nthe past must be remembered. If there are m symbols in the past which \ndetermine the present state and each symbol has \u00a2 possible values, \nthere will be \u00a2\u201d states possible (although only 2\u201d\u201d of these are at all prob- \nable for large m). If m is large the number of possible states becomes fan-\n\n* In a philosophical sense the state of a message source may be dependent on \nmany other factors besides the past of the message. If the source is a human being, \nfor example, the state will depend on a large number of intangibles. If these could \nreally be taken into account the resulting H for the message might be quite low. \nIf the universe is strictly deterministic one might say that H is \u2018\u2018really\u201d\u2019 always \nzero. When we describe the drawing of balls from the urn in terms of probabilities, \nwe admit our ignorance as to the exact detail of the mixing operation which has \noccurred in the urn. Likewise the information rate of a source is a measure of our \nignorance of the exact state of the source. From a communication engineering \nstandpoint, the knowledge of the state of the source is confined to that given by \nthe past of the message.\n\ntastically large and complete statistical encoding becomes an economic \nimpossibility if not a technical one.\n\nLet Bi be a particular combination (the i) of k symbols in the past \nof the message. Each of these combinations at least partially determines \nthe state of the system. Hence we can write an approximation to (7):\n\nIF, > H,ask\u2014 o. If only m symbols in the past influence the present \nstate, then k need only be as great as m, in order that F,, = H. In any \ncase the sequence Ff, , F,, --- F, is monotone decreasing. Naturally \none should always pick the k symbols in the past which exert the great- \nest effect upon the present state, ie. which cause ps*(j) to be as highly\n\npeaked as possible, on the average. In English these would be the im- \nmediately previous letters; in television, the picture elements in the im- \nmediate space-time vicinity of the present element.\n\nSuppose we break the message up into blocks of length k. Each of these \nblocks may be considered to be a character in a new (and huge) alpha- \nbet. If we ignore any influences from previous blocks, i.e. if we consider \nthe blocks to be independent, then the information per block will be \nsimply\n\nSince there are / symbols per block, the information per symbol, G; is \n1 , \nGe = \u2014 7 2 p(Bi) log p(Bi). (10)\n\nAs k > \u00ab, G, \u2014 H, since the amount of statistical influence ignored \n(between blocks) becomes negligible compared with that taken into \naccount.\n\nIf d is the number of binary digits required to specify a message n \nsymbols long, then as n > \u00ab, d/nH \u2014 1. For large n there are thus \n2\u201d\"\" messages which are at all likely out of 2\"\u201d\u00b0 = \u00a2\u201d possible sequences \n(in an \u00a2 letter alphabet). The probability that a purely random source \nwill produce a message (i.e., a sequence with all the proper statistics) is \ntherefore\n\nfor large n. Even if Hp \u2014 H is small, p \u2014 0 rapidly for large n. This is \nwhy white noise never produces anything resembling a picture on a \n-television screen, for instance. For in television signals, Hj) \u2014 H > 1\n\nAs given by (11), p, also represents the fraction of the possible signals \non a channel of \u00a2 levels which are likely ever to be used by messages of \nlength n without statistical encoding. |\n\nSince a sequence of binary digits can be remapped by a non-statistical \nprocess into a channel with b quantizing levels, or indeed into a wide \nvariety of other signalling alphabets, it suffices to consider statistical \n~ coding processes and codes which reduce the message to a sequence of \nbinary digits. An efficient code is then one for which the average number \nof binary digits, H., per message symbol lies between Hp and H. As the \nefficiency increases H/H, \u2014 1, so this ratio may be taken as an efficiency \nindex. With highly efficient processes, the sequences of binary digits \nproduced will have little residual correlation, i.e., they will be nearly \nrandom sequences. Since the encoding process must be reversible the \nreceiver must be able to recognize the beginnings and ends of code groups. \nSince we have at our disposal only zeros and ones, the divisions between \ncode groups must either be marked by a special code group reserved for \nthis purpose, or else the code must have the property that no short code \ngroup is duplicated as the beginning of a longer group.\n\nA code which satisfies this latter requirement and which is capable of \nunity efficiency is the so-called Shannon-Fano code, developed inde- \npendently by C. E. Shannon of Bell Telephone Laboratories and R. M. \nFano of the Massachusetts Institute of Technology. This code is con- \nstructed as follows: One writes down all the possible message sequences \nof length & in order of decreasing probability. This list is then divided \ninto two groups of as nearly equal probability as possible. One then \nwrites zero as the first digit of the code for all messages in the top half, \none as the first digit for all messages in the bottom half. Each of these \ngroups is again divided into two subsets of nearly equal probability \nand a zero is written as the second digit if the message is in the top \nsubsets, a one if it is in the bottom. The process is continued until \nthere is only one message in each subset. Fig. 2a shows the code which \nresults when this process is applied to a particularly simple probability \ndistribution p(B) = (1/2)*. Here each code group is a series of ones \nfollowed by a zero. The receiver knows a code group is finished as soon \nas a zero appears. Although the longer groups contain mostly ones, their \nprobability is less and on the average as many zeros are sent as ones.\n\nFig. 2\u2014Shannon-Fano codes for three different distributions. The successive \nbisections are indicated by the dashed lines and the number gives the step at \nwhich that bisection took place.\n\nIf the successive message segments are independent, the code will gen- \nerate a random sequence of zeros and ones. Fig. 2b shows the code which \nresults with another distribution. Here the termination of each code \ngroup is more complicated but the non-duplicative property exists so \nthe receiver can still identify the groups. Fig. 2c shows the code which \nresults when all the p(Bj) are equal. It is the ordinary binary code.\n\nThe length of each code group is equal to log 1/p(B%), for the cases \nshown in the figures. This is true in general so long as it is possible to \ndivide the list into subgroups which are of exactly equal probability.\n\nWhen this is not possible, some code groups may be one digit longer \nas Shannon shows. The average number of digits per message symbol \nusing this code is therefore given by\n\nFor large k, H, \u2014 G, \u2014 H and the efficiency approaches unity. With \nsmall k, H, increases both because the smaller list of messages cannot be \nso accurately divided repeatedly into equal probability subsets (so- \ncalled \u201c\u2018granularity\u201d\u2019 trouble), and also because more statistics are ig- \nnored between the shorter blocks.\n\nThe ordinary binary code provides a stabauoal match between mes- \nsage source and channel only if the various message blocks Bi have \nequal probability p(Bj) = 1/2\", and are mutually independent. With \nk = 1, p(B) = p(y) and the \u201cblocks\u201d are merely the successive symbols.\n\nThe application of the Shannon-Fano code to a block of k symbols of \na message in an \u00a2 letter alphabet requires that \u00a2* different codes be used. \nThe receiver must be able to recognize each of these and to regenerate \nthe proper message block when a particular code is received. If f is on \nthe order of 10 to 100 as is typically the case, we very quickly run out of \nroom to house the receiver and money to build it with. On the other \nhand, if k is small, say on the order of 1 to 3, considerable statistical \ninformation between blocks is ignored. These considerations led to the \ndevelopment of a class of encoders known as n-grammers. The name \nstems from the fact that they operate on the n-gram statistics of the\n\nmessage, to produce a reduced signal having more nearly independent \nsymbols, but (in return) a highly peaked simple probability distribution \nwhich allows savings with Shannon-Fano coding on a symbol-by-sym- \nbol (k = 1) basis. .\n\nThe simplest member of this class is the monogrammer. It is basically \nmerely a re-ordering device. The operation may be best understood by \nthe following example. Suppose someone supplied us with English text \nencoded into a quantized pulse signal as follows:\n\nThe device shown in Fig. 4 will accomplish this translation. The orig- \ninal signal is applied to the vertical deflecting plates of a cathode ray \ntube. The rest position of the spot corresponds to \u201c\u2018space\u2019\u2019, i.e. no pulse. \nA pulse one unit high deflects the spot to A, a pulse two units high de- \nflects the spot to B, etc.\n\nNow in front of these spot positions we place a number of light at- \ntenuating filters. In front of the \u2018\u201c\u2018space\u201d\u2019 position we place an opaque \nmask. Hence when the spot is deflected to \u2018\u2018space\u201d\u2019 the photocell receives \nno light and no pulse is sent. In front of the \u2018\u2018E\u201d\u2019 position we place a \nmask having one unit of transmission. So although F is received as a \npulse 5 units high, it is sent as a pulse of unit height. In front of the\n\n\u201cT\u201d position we place a mask with two units transmission, and so on. \nThe signal amplitudes as received are thus re-ordered in the desired \nfashion.\n\nThe resulting signal has lower average power and this can sometimes \nbe an advantage, particularly if several such signals are to be sent over \na common channel by frequency division. In this case the extreme rarity \nof occurrence of high peak powers on all channels simultaneously means\n\nthat the system can be designed to have a lower peak power capacity. \nThe signal out of the monogrammer can be remapped into binary digits \nusing a Shannon-Fano code, pulse by pulse. However, this could have \nbeen done equally well with the original signal merely by rearranging the \ncode groups in the coder tube. It is when we extend the principle to di- \ngrams and trigrams that the potentialities of the system become evident.\n\nWe can easily take account of the influence of the preceding message \nsymbol. To do this we apply the signal to the vertical plates as before, \nand to the horizontal plates we apply the signal delayed by an amount \nequal to the time between successive pulses as shown in Fig. 5. Thus the \nbeam is deflected vertically by the present message symbol, and horizon- \ntally by the previous message symbol. Whereas before we used a single \ncolumn of optical filters chosen in accordance with the simple probabil- \nities of the letters, we now have 27 columns, one for each letter and one \nfor the space. The filters in each column are chosen in accordance with \nthe conditional probabilities which apply when the corresponding letter \nwas the previous symbol. For example, in the \u2018\u2018Q\u201d column (last letter \nQ), and the \u2018\u2018U\u201d\u2019 row (present letter U) the mask would be opaque, since \nU is most common after Q. In general, the transmission of cell 77, in the \ni column and j\" row, is proportional to the rank of the entry for p;(7) \nwhen the entire distribution (conditioned on 7) is ordered in a monotone \ndecreasing sequence. The amplitude distribution of the output pulses\n\nfrom the digrammer will be more peaked toward zero amplitude than \nthat of the monogrammer. This is illustrated by the signals in the figures. \nAt the receiver the same type of device, but with an inverse mask can be \nused to convert the signal back to its original form.\n\nThe digrammer can, with a little assistance, supply all the data re- \nquired to prepare the encoding mask. If typical signals from the message \nsource are applied to the cathode ray tube (without mask) for a long \ntime, and a time exposure is made of the face of the tube, a lattice of \nspots will be obtained on the film. These spots will be dense where the \nhigh probability combinations occur and less dense elsewhere. The order \nof decreasing density in each column is noted, and the filter transmis- \nsions are arranged in the same order.\n\nIt is, of course, not necessary to use a phosphor, optical filters, and a \nphotocell. An array of targets each of which connects to the appropriate \ntap on a load resistor might be simpler and more efficient. The cathode \nray tube itself can be replaced with an appropriate diode switching net- \nwork. Relay networks could be used for low-speed operation.\n\nAt the digrammer level we run out of new dimensions to use in the \ncathode ray tube. The principle can, however, be extended to trigram- \nming and genera] n-gramming. For example, tetragramming could be \naccomplished by using a bank of \u00a2 digrammers all in parallel, and all \ndeflected by the present and previous samples. Only one of these tubes \nwould be turned on at a time however. Which one this was would depend \non the other two previous symbols of the tetragram. These (by addi- \ntional delays) would be applied to the deflecting plates of a master switch- \ning tube having an array of target plates in place of a mask. Depending \non the particular combination of signal samples applied to this tube, \nthe beam would strike a particular target. The target current would then \nbe used to turn on the beam of a particular digrammer tube, namely the \none with the proper mask for that particular combination of two past \nsymbols.\n\nThe complete array of equipment is admittedly rather staggering, but \nthen, rather efficient coding should result. In practice it would probably \nbe found that the masks of many of the tubes would be so similar that \nlittle gain resulted from differentiating between them. That is, the state \nof the message source might be nearly equivalent for several past com- \nbinations. In these cases, the group of tubes could be replaced with one \nhaving the best average mask, and the corresponding targets on the \nswitching tube then tied together. This compromise would be particu- \nlarly warranted for those tubes which were rarely used anyway. By these\n\ntricks it should be possible to keep the growth of equipment down to \nsomething approaching 2\u201d\u201d rather than \u00a2\u201d.\n\nThe output signal from the n-grammer will be, as we have seen, a series \nof pulses with an amplitude distribution very peaked toward zero and \nsmall pulses. If \u00a2 ,the alphabet, is large, these pulses can be efficiently \nencoded into a Shannon-Fano code. For small alphabets, granularity \ntrouble can be reduced by remapping the output pulses two-by-two \ninto pulses of base \u00a2\u2019, and then encoding these into the Shannon-Fano \ncode.\n\ndictive-subtractive coding. In an actual system the reduced signal \nwould ordinarily be encoded into Shannon-Fano code groups before \ntransmission over the channel.\n\nIf so is the present sample amplitude, and s; , s: , 83 \u00ab++ S, are previous \nsample amplitudes we compute a predicted value, s,, for the present \nsample which is given by\n\nwhere 6 < 3 quantizing level. If the conditional probability distribution \nfor the present sample is p,,...s,(80), then the difference, or output, or\n\n\u201cerror\u201d signal, \u00a2, will have the conditional distribution p,,...s,(\u20ac + sp) \nfor this particular case. The simple distribution is then the weighted \naverage over all cases, 1.e.\n\nPredictive-subtractive coding has especial merit when a simple func- \ntion can be used for computing s, . This is often the case. When the \nfunction is simply a weighted sum of the past sample amplitudes, i.e. \nwhen\n\nwe have what is known as linear prediction. Of course, linear prediction \ncan always be used, but it may not be good enough with some types of \nmessages.\n\nAs Wiener has shown the coefficients a, b, c --- which minimize \n\u00e9 are readily computed. For simplicity, assume only two message sam- \nples, s; and Ss , from the past are to be used. We then have\n\nwhere Ao , Ai , and Az are the values of the auto-covariance of the mes- \nsage wave at displacements of 0, 1, and 2 sampling periods. Thus\n\nThe autocorrelation (normalized auto-covariance) is given by \u00a2; = a : \n0 \nA\u00bb is proportional to the average power in the message wave, so the \n= \nratio p = *\u2014 is the ratio of the power in the error signal to the power \n0\n\nIf \u00a2. = \u00a2;, then the expressions simplify to \na=, b= 0, p=1- 1. \nAs can easily be shown, if \u00a2(x) = e \u201c|, then all the coefficients except\n\na are zero, and a has the value e *. In other words, if the autocorrela- \ntion function is of exponential shape, the previous sample alone is needed\n\n* From the preceding expression for p, we see that p = 0 (i.e., perfect predic- \ntion is possible) if:\n\nIf \u00a2. = 1, the message samples alternate between two independent but constant \nvalues. For this case a = 0, b = 1. If $2 = 26, \u2014 1 the autocorrelation is a cosine \nwave so the message consists of samples of a sinusoid. In this case a = 2\u00a2,, b = \n\u20141. If \u00a2 is nearly unity, the sinusoid is of low frequency, and the prediction \napproaches \u2018\u2018slope\u2019\u201d\u2019 prediction (i.e. extrapolation of a straight line through the \nlast two samples).\n\nIn any case where perfect prediction is possible the wave is periodic and there- \nfore H = 0.\n\nPower reduction is an index of merit when many reduced signals are \nto be sent by frequency division over one channel, as we have said. \nWhen the object is to reduce the channel capacity required for a single \nmessage source, then it is the upper bound entropy of the reduced signal \nwhich should be minimized, not the power. That is we want \u2014>.; p(J) \nlog p(j) to be minimized. For certain types of signals this requires the \nmodes to be shifted to zero, although this is by no means a general rule. \nShifting the modes to zero may actually increase the entropy of the \n\u201creduced\u201d signal over that of the original message, by adding too many \nnew symbol levels, as the example in the last section shows.\n\nIf the original message has \u00a2 quantizing levels, the reduced message \nafter predictive-subtractive coding will in general contain more than \nlevels since an error of more than : can be made in either direction. \nAn n-gramming operation, on the other hand, never increases the al- \nphabet.\n\nQQ \n| | | ] ee \nNe > \n\\y 2) OF \nAy yd oe \n9 \nas ee pee Vee \nFIRST ORDER ROWS THEN NaS \nADD COLUMNS FOR J \nDIGRAMMER DISTRIBUTION YP \nVv\n\nFig. 8\u2014Joint probability distribution (divide all coefficients by the sum over \neach array).\n\nThus the most likely level is that of the previous sample. A camule \ndiffering by one level is 1/a times as likely, one differing by m levels \nis a\u201d times as likely. Figure 8 shows a plot of the relative values of \np(t, 7) (neglecting the factor K). For \u00a2 = 4, the total array would be \nthe 4 x 4 portion enclosed by the dashed line. This sort of distribution \nis:rather similar to those of typical television signals, as shown by pre- \nliminary measurements, although typical values of a have yet to be \ndetermined. With no statistical coding, the required channel capacity is\n\nH, may be computed from the array of relative coefficients by adding \nthe rows to form the sums\n\nSince, with the assumed distribution, the S; are all nearly equal very \nlittle reduction in channel capacity is achieved by this step.\n\nWith linear prediction, the modes of the distributions (\u00a2 = 7) could \nbe centered at zero merely by sending the difference between the present \nand previous sample (previous value prediction). This would give a \nreduced signal whose distribution may be found by adding the array \nalong the diagonals. The required channel capacity is then given by:\n\nThe distribution of the signal from a digrammer is found by rearrang- \ning each row of the table in order of decreasing probability and then \nadding the resulting columns. Call these sums Sz . The digrammer out- \nput will thus require a channel capacity:\n\nH = \u2014 7 p(t) D2 pj) log ps(j) \nu ] \n1 tek \n= \u2014\u2014H 2h \nloge i+ > me k lag a \nValues for the above quantities were computed for a = zg and n =\n\n2, 3, 4, 6, 8, 16, 32, \u00a9. For the case of a = 2, we find that \nK = [8-401 \u2014 2\u00b09]\u00b0 \nand that as f\u2014> o, \nH,, Hp , H > $ + loge 3 = 2.918 bits. \nThe results are shown in the Table I and also are plotted in Fig. 9. \nWhile Hy and H; increase without limit as \u00a2 is increased, H, , Ho,\n\nand H quickly approach a definite limit. This limit exists because we \nassumed that the decrease in joint probability as a function of number\n\n(These figures were computed by slide rule so the fourth figure is not very \nsignificant.)\n\nof levels off the diagonal was the same regardless of \u00a2. In typical signals \nthis is not true. The decrease is more apt to depend on amplitude differ- \nence and the finer the quantum step, the more levels a given difference \nrepresents. As a result, the probability will fall off less per level off the \ndiagonal, and doubling \u00a2 will in general add one bit to H.\n\nOn the other hand, doubling the sampling rate will not in general \ndouble the required channel capacity, for the closer spaced samples will\n\nWe have seen in the last two sections how it is possible to convert \na message for which H \u00ab Hy as a result primarily of intersymbol correla- \ntion, into a reduced signal for which H \u00ab Hy as a result primarily of a \nhighly peaked probability distribution in the individual symbols (i.e. \none for which H, \u2014 H). Since the operations are reversible, the true \ninformation rate, H, is preserved. In the original signal it was the \nconditional distributions which were peaked, while the simple distribu- \ntion was relatively flat. In the reduced signal the simple distribution is \npeaked.\n\nThe result is that whereas a Shannon-Fano code would only have been \neffective on the original message if applied to blocks two or more symbols \nin length (and then it would ignore correlation between blocks), in the \nreduced signal the code will be effective on a symbol to symbol basis.\n\nl=s8 \na side a lies Perera (a) Original, (b) After linear modal pre- \ndiction, (c) After digramming.\n\nThe encoding of the reduced signal into binary digits presents no \ntheoretical difficulties. A PCM type coder tube* with the appropriate \nShannon-Fano groups built into it is all that is needed. The biggest \npractical complication arises out of the fact that the code groups are of \ndifferent length. Some messages, such as written text, can be fed into \nthe system as fast as it can handle them. The transmission time will \nthen vary with the message complexity. Others, such as television are \ngenerated and must be accepted and delivered at a constant rate. One \nsolution is then to take the binary digits in big and little batches \u2018as they \ncome from the coder and store the surplus in a sort of pulse \u2018\u2018surge tank\u201d \nbefore they are sent over the channel at a regular rate. At the receiver, \na similar sort of storage register is necessary as the pulses arrive over \nthe channel at a regular rate and are used by the decoder at a varying \nrate. Devices which will perform this variable delay function satisfacto- \nrily for signals with relatively slow sampling frequency are available, \nand as the art progresses there is every reason to believe that high speed \nsampled signals like television can be handled also. :\n\nIt will be noticed that the digramming or prediction operation, while \nit involves memory, does not introduce appreciable transmission delay. \nEach symbol of the reduced signal appears the moment the correspond- \ning message sample is applied. The total transmission delay required \nfor statistical coding thus depends upon how much variation is required \nin the variable delay units. This in turn depends upon the degree of \nstationarity in the \u201clocal information rate\u201d of the message. For example, \nin television, if each line could be described (by the n-grammer and \nsubsequent coder) in the same total number of binary digits, then the \ntotal delay variation and total delay would be less than one line time. \nSince this is not true, we either must have enough channel capacity to \nsend in one line time the number of digits corresponding to the \u201cworst\u201d \nline, or enough variable delay to average the existing rate over many \nlines.\n\nProbably the most practical solution is to provide sufficient channel \ncapacity and variable delay to take care of all but a small fraction of \nthe possible message sequences. Then when an unusual stretch of message \ncontinues long enough for the variable delay to be nearly all used up, the \nsystem should fail in some relatively harmless way. In television, the \nsampling rate could be momentarily reduced, for example. This would \ndegrade the resolution in rare situations, but a small amount of this \ncould be tolerated in return for transmission savings.\n\nTf long blocks of the message are efficiently encoded as a group, then \nan error in transmission may cause the whole block to be reproduced\n\n1. Oliver, Pierce, and Shannon, \u2018\u2018The Philosophy of PCM,\u201d Proc. Inst. Radio \nEngrs., Nov. 1948.\n\n2. C. E. Shannon, \u2018\u2018A Mathematical Theory of Communication,\u201d Bell System \nTech. J., July and Oct. 1948; Shannon and Weaver, \u2018\u2018The Mathematical \nTheory of Communication,\u2019\u2019 University of Illinois Press, 1949.\n\n3. C. E. Shannon, \u2018\u2018Prediction and the Entropy of Printed English,\u2019\u2019 Bell System \nTech. J., Jan. 1951.\n\n4. R. W. Sears, \u2018\u2018Electron Beam Deflection Tube for Pulse Code Modulation,\u201d\u2019 \nBell System Tech. J., Jan. 1948; W. M. Goodall, \u2018\u201cTelevision by Pulse Code \nModulation,\u2019\u2019 Bell System Tech. J., Jan. 1951.\n\nOne of the teachings of information theory is that most communica- \ntion signals convey information at a rate well below the capacity of the \nchannels provided for them. The excess capacity 1s required to accom- \nmodate the redundancy, or repeated information, which the signals \ncontain in addition to the actual information. Removal of some of this \nredundancy would reduce the channel capacity required for transmission, \nthus opening the way for possible bandwidth reduction. In order to \nremove redundancy, one must first understand it; the amount and nature \nof the redundancy can be completely defined in terms of various statis- \ntical parameters characterizing the signal.\n\nIt has been pointed out that the existence of redundancy is particularly \nevident in the case of television; moreover, its elimination is highly de- \nsirable because of the large bandwith presently required for transmis- \nsion. Evidence of redundancy is found in the subject matter of televi- \nsion\u2014the average scene or picture. Knowing part of a picture, one can \ngenerally draw certain inferences about the remainder; or, knowing a \nsequence of frames, one can, on the average, make a good guess or pre- \ndiction about the next frame. In either case, knowledge of the past re- \nmoves uncertainty as to the future, leaving less actual information to be \ntransmitted.\n\nAnother way of looking at this is to visualize the picture as an array \nof approximately 210,000 dots, 500 vertically, 420 horizontally, cor- \nresponding, respectively, to the 500 scanning lines and 420 resolvable\n\npicture elements per line of the standard television raster. Each dot can \nhave, say, 100 distinguishable brightness values in a good-quality pic- \nture. The number of possible combinations is therefore approximately \n10077\"? or 10\u00b0 At the usual rate of 30 frames per second it would \ntake approximately 10\u00b0\": years to transmit all these \u201cpictures,\u201d which \nour present television system is fully prepared to transmit! The vast \nmajority of these \u201cpictures\u201d will, of course, never be transmitted in this \nage because the average picture statistics virtually preclude the pos- \nsiblity of their occurrence.\n\nIf all of the redundancy alluded to in the preceding paragraph were \nto be expressed in terms of statistics, the array of data would be stagger- \ning.* Redundancy encompassing even a small part of a single frame \nimplies statistics of enormously high order because of the large number \nof possible past histories. The initial attention should therefore be \nfocused on local redundancy, encompassing only a few adjoining pic- \nture elements. Accordingly, measurements have been made of the fol- \nlowing statistical quantities.\n\n1. Simple probability distribution of signal amplitudes corresponding \nto picture brightness. This encompasses only a single picture element, \nrevealing the relative probabilities of this or any element\u2019s assuming \nthe various possible brightness values, in the absence of any past-his- \ntory information.\n\n2. Simple probability distribution of error amplitudes resulting from \nlinear prediction of television signals. Only the simplest type of linear \nprediction is considered here, so-called previous-value prediction, which \npredicts each picture element to have the same brightness value as the \npreceding one. The prediction error signal is simply the difference be- \ntween the picture signal and a replica delayed by one Nyquist interval \n(one-half the reciprocal bandwidth or the time interval corresponding \nto the spacing between picture elements). The distribution of this error \nsignal encompasses tio picture elements (past history of one element) \nand therefore is a condensed version of the family of first-order joint \nprobability distributions.\n\n3. Autocorrelation of typical pictures. This statistical quantity is\u2019 an \neven more streamlined version of various families of different-order \njoint probability distributions. Each family corresponds to just a single \npoint on the autocorrelation curve; the ordinates of the curve represent \nthe average correlation between picture elements spaced by various\n\n* Complete statistics extending, say, over one frame period, would comprise \none conditional probability distribution per picture element for each possible \npast history. With the approximate figures cited above, the number of distribution \ncurves (many of which would be similar) is 210,000 X \"10 419,999 op 10420,004.3,\n\ndistances. This correlation, say, between horizontally adjoining elements \nis simply the average product of the two brightness values of each pair \nof neighbors, relative to the average square of all brightness values.\n\nThe three quantities enumerated above contain a great deal of sta- \ntistics in very compact form, but these statistics are essentially of a local \nand linear nature. They do not include the bulk of the large-scale re- \ndundancy, which is of a far-flung and nonlinear nature.\n\nAUTOCORRELATION \nFor a function of time, f(t), the autocorrelation can be expressed as\n\naveraged over all time, for various values of the time shift 7. In the case \nof a picture transparency, the optical transmission is a function of two- \ndimensional space, expressible in polar coordinates as 7'(s/\u00a2), and the \nautocorrelation can be expressed in analogous fashion. The time variable \nt is replaced by the space coordinate s/\u00a2, and the correlation time shift 7 \nis replaced by a space shift As/@, so that the new expression is\n\nFig. 3\u2014Close-up view of slide holding assembly and shifting mechanism of \npicture autocorrelator.\n\nThe apparatus used to measure autocorrelation is shown in Figs. 1 \nand 2. The chamber at the bottom contains a light source of very \nconstant intensity and a convex lens to collimate the light. The middle \npart, made of accurately machined aluminum, holds the two identical \nslides of the picture under test, and an aperture exposing a large circular \narea of the slides. The top chamber contains a collector lens and a photo- \nmultiplier tube which (on a microammeter not shown) gives a sensitive \nindication of the total light transmitted through the slides. Fig. 3 \nshows a close-up view of the slide-holding assembly. Two close-fitting \ngraduated aluminum rings permit accurately determined rotation of \nboth slides or one slide, and the micrometer drive permits translational \ndisplacements measurable to within one mil (moving the two slides by \nequal and opposite amounts); the separation between picture elements \nis approximately 7.5 mils horizontally and 5 mils vertically (for the \n23\u201d by 34\u201d slide size used).\n\nThe light transmission is always a maximum when the two slides are \nin precise register (As = 0). For large shifts the transmission fluctuates . \nabout a nonzero asymptote. The nonzero asymptote results from the \nfact that the average transmission is always positive, and the fluctuation \nfrom the fact that large displacements introduce substantial amounts of \nnew picture material into the aperture. Since these components tend to\n\nobscure the correlation effects, it is useful to make additional measure- \nments which enable us to subtract them out completely. This leaves us \nwith a \u2018pure\u2019 autocorrelation A(As/@), which is then normalized so as \nto have a peak value of unity. It is given by\n\nwhere 7, (a /2) is the transmission through the two cascaded slides \nshifted by equal and opposite amounts = at an angle @ with the hori-\n\nSCENE C \"SCENE D \nFig. 4\u2014Test pictures whose statistics are included in this article.\n\nSTATISTICS OF TELEVISION SIGNALS 757 \nSHIFT, AS, NUMBER OF VERTICAL PICTURE ELEMENTS \n~-100 -80 -60 -40 ~20 ie) 20 40 60 80 100\n\nFig. 6\u2014Contours of constant autocorrelation for Scene A. In general there are \nno preferred directions of correlation.\n\nFig. 7\u2014Plots of autocorrelation for small shifts. Ai is the autocorrelation for \na shift of one horizontal elemental distance, Azo for two horizontal elemental dis- \ntances, and Ao, for one vertical elemental distance. Alternatively Aio may be\n\nA probability distribution of amplitudes is generally shown as a plot \nof probability density versus signal amplitude. Probability density, say, \ncorresponding to amplitude x1, is the probability of finding the signal \namplitude between 21 and x1 + dz, divided by the differential amplitude \nincrement dx. Conversely, the probability of finding the signal ampli- \ntude between 7 and x; + dz is given by p(x,)dx, p(x) being the proba- \nbility density corresponding to amplitude 2.\n\nIf a cathode-ray spot is deflected, say horizontally, by the signal in \nquestion, its average dwell time at any point is directly proportional to \nthe corresponding probability density. In the optical system shown in \nFig. 8, a cylindrical lens maps each point into a vertical line which is\n\nUNDEFLECTED DEFLECTED \nIMAGE *, /|MAGE \n5XP it f \\ ! \nCATHODE LOW Sy \nRAY TUBE TRANSMISSION, | \nCONVEX \\ AE \nLENS\\, aS | \nao \n_UNDEFLECTED LA a \nSPOT f \u201c1 \n_DEFLECTED ee | \nSPOT aa \nCYLINDRICAL\u2019 re \nLENS OPTICAL \nDENSITY \n1SIGNAL WEDGE SIGNAL\n\nthen tapered in intensity by an optical density wedge before reaching a \nhigh-contrast photographic film. Depending on the dwell time at any \namplitude level, the corresponding tapered line has enough average \nintensity to blacken the film up to a certain level. This level is pro- \nportional to log p(x), since the density wedge is tapered exponentially \nso that the intensity of each tapered line of light reaching the film \ndiminishes, say, by a factor of ten for each inch we travel up the line. \nThe film in effect traces out a contour of constant exposure.\n\nTwo or three iterated photographic printings increase the effective \ngamma, sufficiently to yield a contour of ample sharpness. This contour \nis then changed to a sharp line by a simple dark room trick: while the \nfilm is in the development tray, already fully developed, it is momentarily \nexposed to light. The blackened portion of the film is unaffected, the \nclear portion is fully blackened, while the transition contour, being \npartly opaque, is not fully blackened. By printing from this film we then\n\nobtain a well-defined black-on-white curve of p(x) versus x on a loga- \nrithmic probability scale. The logarithmic scale has the advantage of \nmaking the curve shape independent of exposure length and giving uni- \nform relative accuracy over the entire range.\n\nFig. 9 shows some typical results obtained by means of the \u201cproba- \nbiloscope.\u201d The two small curves are distributions of two different still \npictures. The left-hand end corresponds to black, the right-hand end to \npeak white; the blanking intervals (slightly blacker than black)\u2019 cause \nthe peaks at the extreme left. (The signals did not contain any synchro- \nnizing pulses.) The tall and slender curve at the right of Fig. 9 is the \ndistribution of errors resulting from previous-value prediction of one \nof the pictures in Fig. 4. The peak corresponds to zero error which is \nseen to be most probable, as it should be if the prediction criterion is \ngood. Increasingly larger errors are increasingly improbable or rare. \nThe six decades of probability density spanned by the curve were ob- \ntained in three separate exposures and subsequently joined, since stray\n\nFig. 9\u2014Typical probability distributions as obtained from the probabiloscope.\n\nCurves at left are for video signals; right-hand curve is for difference between \nvideo signal and delayed replica.\n\n-where p; is the simple probability of the signal\u2019s falling into the zth \nlevel. Since the 64 p,\u2019s are unequal, Hmax is necessarily less than 6 bits. \nFor all available data the average value of Hmax turns out to be ap- \nproximately 5 bits, indicating a one-bit redundancy. The latter figure \nis essentially independent of quantization.\n\nThe prediction error signal still contains all the useful picture in- \nformation. The maximum possible information content per sample (max- \nimum in that all samples are assumed to be completely independent) \nis still given by (4) but in this case the 64 values of p; are obtained \nfrom the peaked error distribution. The average* result from all available \ndata turns out to be approximately 3.4 bits below the 6-bit ceiling, show-\n\n* This average was computed by averaging the various redundancy values ob- \ntained for the individual pictures, rather than averaging all statistical data and \nthen finding one corresponding average redundancy. The average computed here\n\nis more favorable and can be realized only if, optimum coding is performed on a \nshort-term basis rather than on the basis of one set of long-term statistics.\n\ning that the original signal must have contained at least 3.4 bits of \nredundancy.\n\nThe autocorrelation can also furnish a lower bound to the redundancy, \nas has been pointed out by P. Elias in his Letter to the Editor of the \nProceedings of the I.R.E. for July, 1951. If, for example, the correlation \nAi, between horizontally adjoining picture elements, is high, the cor- \nresponding lower-bound redundancy is very roughly equal to\n\nAlternatively, taking the Fourier transform of the autocorrelation yields \nthe power spectrum P(f), from which we can find the lower-bound re- \ndundancy through the relation\n\nUsing either method, one obtains approximately 2.4 bits for the \naverage* of the available data. This is an approximate bound, in that . \nit applies strictly only to functions having gaussian amplitude distri- \nbutions.\n\nSuppose, then, that we have exposed an average redundancy of at \nleast 3 bits per sample. This means a potential 3-bit reduction in the \nchannel capacity required for television transmission. In a 6-bit system \n(64 amplitude levels) this means a 50 per cent reduction, and hence a \npotential halving of the bandwidth with the aid of an ideal coding scheme. \nIt is true that the decorrelated signal is somewhat \u201cfrail,\u201d i.e., vulner- \nable to interference, so that it might be desirable to use a \u201crugged\u201d \nsystem of the PCM variety for transmission. Thus, if a Shannon-Fano \ncode were used, the 3-bit decorrelation should enable us to send tele- \nvision by an average of 3 on-off pulses per picture sample rather than \n6. This represents a two-to-one saving over the usual PCM bandwidth. \nMore spectacular reductions are likely to be achievable only by tap- \nping the large-scale redundancies mentioned earlier.\n\nwhere 7\u2019:2 is the optical transmission of frames 1 and 2 in cascade, 7\u2019; is the average \nof the individual transmission of frames 1 and 2, and 71: is the average of the \ntransmissions of two cascaded slides of frame 1 and two cascaded slides of frame \n2, respectively. In all cascade transmission measurements, the two frames must \nbe in precise register.\n\nThe correlation present in a signal makes possible the prediction of the \nfuture of the signal in terms of the past and present. If the method used for \nprediction makes full use of the entire pertinent past, then the error signal\u2014 \nthe difference between the actual and the predicted signal\u2014will be a com- \npletely random wave of lower power than the original signal but containing \nall the information of the original.\n\nOne method of prediction, which does not make full use of the past, but \nwhich 1s nevertheless remarkably effective with certain signals and also \nappealing because of tts relative simplicity, is linear prediction. Here the \nprediction for the next signal sample is simply the sum of previous signal \nsamples each multiplied by an appropriate weighting factor. The best values \nfor the weighting coefficients depend upon the statistics of the signal, but \nonce they have been determined the prediction may be done with relatively \nsimple apparatus.\n\nLinear prediction is perhaps the most expedient elementary means of \nremoving first order correlation in a television message. Before discussing \nthe advantages and disadvantages of linear prediction, it might be well \nto consider what is generally meant by correlation in a television pic- \nture and why it should be removed.\n\nAlmost every. picture that has recognizable features contains both \nlinear and non-linear correlation. Each type of correlation helps in \nidentifying one picture from another; however, linear prediction is only \neffective in removing linear correlation, and for this reason, future ref- \nerences to correlation will refer only to its linear properties. With tele- \nvision, a signal is obtained as the result of scanning; hence, the cor-\n\nrelation is evident in both space and time. Briefly, correlation is that \nrelation which the \u2018next\u2019? elemental part of the signal has with its past.\n\nTo leave correlation in a message is to be redundant, and this effec- \ntively loads the transmission medium with a lot of excess \u2018words\u2019 not \nnecessary to the description of the picture at the receiving end. It is\u2019 \nthen more \u201cefficient\u201d to send only the information necessary to identify \nthe picture, and to restore the redundancy at the receiver.\n\nThe more efficient we are in sending pictures over a, given transmission \nline, the more alarmed we become at the increasing amount of equipment \nthat is required at the transmitting and receiving terminals. Certainly \nthe design will be a compromise between the complexity of apparatus and \nthe efficiency achieved. The ingenuity of engineers will be taxed along \nthese lines for years to come; however basically, the general form of \nthese systems will be similar to that shown in Fig. 1. Although not \nalways separable, four essential operations are required-namely, decor- \nrelating, encoding, decoding and correlating. The transmitting decor- \nrelator and the encoder encompass the principal design problems, since \nthe decoder and correlator at the receiving end perform the reverse \noperations which interpret the code and add in the redundancy that was \nremoved.\n\nDecorrelation involves prediction, and as the predictors are more \nnearly made to predict the future of the signal, the more the output \nsignal from the decorrelator resembles random noise. The essential \npicture information is still present, which means that our original picture \nsignal can be obtained at the receiving end without theoretical degrada- \ntion. The basic job of the encoder is to match the picture information \nout of the decorrelator to the channel over which it is to be transmitted. \nThere are several encoding operations. The first concerns the rate of \ninformation into the encoder, and that required out of it. In the case \nof television, there are flat, highly correlated areas as well as areas \ncontaining more concentrated detail. This means that the information\n\nTRANSMISSION \nMEDIUM \nFig. 1\u2014Block diagram of an efficient transmission system employing reversible \ndecorrelating and encoding means.\n\nrate varies when the picture is scanned at the conventional uniform scan- \nning rate. The output of the encoder feeds a transmission line that has \na definite channel capacity, and if maximum efficiency is to be obtained \nfrom this transmission medium, then the rate of information into it \nmust be held relatively uniform at a value near the channel capacity. \nIt is the job of the encoder to take the varying rate of information from \nthe decorrelator and feed it to the channel at a constant rate. At the \nreceiving end, the decoder must take the constant rate of information \nand deliver it to the correlator at the variable rate as originally fed into \nthe transmitter\u2019s encoder. Thus, to perform this task, a variable or \nelastic delay to run ahead or behind, depending on the information con- \ntent of the picture being scanned, is an important part of the encoder. \nOver a long period of time, the variable delay would average out to \nsome fixed value. This variable delay must never run out, even when the \ndetail is concentrated. There are instances when this condition could \nnot be met, such as an extended reproduction of a snow storm; however, \nwith good design the system should fail \u2018\u2018safe\u2019\u2019\u2014a slight degradation of \npicture quality. This condition can be made infrequent enough to cause \nlittle concern.\n\nThe encoder design must also account for noise as well as bandwidth \nof the channel and must consider the ultimate effect of an error that \nmay be introduced by noise along the transmission line. As more re- \ndundancy is removed to get at the \u201cessence\u201d of the picture signal, the \nmore important it is to guard this \u2018\u201c\u2018essence,\u201d\u2019 as mistakes presented to \nthe receiver will propagate themselves longer in the absence of correla- \ntion. Errors can be minimized by rugged systems of modulation such \nas PCM, where the signal-to-noise ratio of the transmission line deter- \nmines the base of the PCM system selected. In any event, the encoder \nmust send the information so that the effect of errors will not appreciably \ndisturb the picture.\n\nFig. 2 illustrates, in a general way, a means of decorrelating the sig- \nnal, S,(\u00e9). For purposes of explanation, the encoder and decoder have \nbeen omitted, and the transmission between the receiving and sending \nterminals, idealized. The predictors, P, are identical, and base their \nprediction, S,(t), on the signal\u2019s past history. In this way, the output \nof the computer represents the discrepancy between the actual value of \nthe signal sample and the predictor\u2019s prediction. By this means we are \nsending only our mistakes\u2014the amount by which the next picture ele- \nment surprises us. For example, if the computer is so designed that it\n\nFig. 2\u2014Decorrelator and correlator showing reversible nature of this method \nof removing redundancy.\n\nbases its prediction on the \u2018\u2018previous frame,\u2019\u201d\u2019 and we are transmitting \na \u201cstill,\u201d there will be no surprises after the first frame and consequently \nno output signal. Certainly it is redundant to send the same picture \nmore than once.\n\nLinear prediction provides an easily instrumented means of removing \nredundancy. With linear prediction the next signal sample is simply \nthe sum of the previous signal samples, each multiplied by an appropriate \nweighting factor. The best values for these weighting coefficients de- \npend on the statistics of the signal.\n\nFig. 3 is a block diagram of a decorrelator employing linear predic- \ntion. The delayed versions of the input signal can be obtained from \ntaps along the delay line. The weighting coefficients for each of the \ndelayed signals are selected by loss in their respective paths as shown \nby the amplitude controls. The polarity of each signal can be determined \nby the switches. The output is simply the sum of these weighted signals.\n\nIf we consider the signal on a continuous basis (not quantized or \nsampled), linear predictors can be characterized as ordinary linear \nfilters used to predistort the frequency spectrum of the signal. As such, \nthey can be designed in the frequency or time domain. However as will\n\nFig. 3\u2014General block diagram of decorrelator employing linear prediction. \nLinear prediction bases its prediction on the weighted sum of previous signal \nsamples.\n\nbe shown, it is much easier to recognize circuit configurations that \nreduce \u2018redundancy in the time domain. To this end, and for purposes \nof encoding, the signal is thought of as signal samples uniformly spaced \nat Nyquist intervals. Thus, amplitude values obtained by sampling \na 4.0 me picture signal at $ microsecond intervals serve to specify the \nsignal completely. Fig. 4 shows a small portion of a television raster where \nthe signal is represented by signal values spaced at Nyquist intervals, \n+. The coordinates shown are designated with respect to the \u201cpresent \nvalue\u201d of the signal, Spo . The positive coordinate directions are shown \nby the arrows. The past is represented by positive coordinates\u2014the future \nby negative coordinates. In this way, the previous value of the signal\n\nx \n_ Fig. 4\u2014A small portion of a television raster showing geometrical location of \nsignal samples with relation to the \u201cpresent value\u201d of the signal, So,o.\n\ntaken one Nuquist interval before Soo is designated by S15 \u2014 the previous \nline samples by So,1, etc.\n\nAs previously stated, with linear prediction the next signal sample, \nS,(t), is simply the sum of the previous signal samples each multiplied \nby an appropriate weighting factor. Thus,\n\nrepresents the weighted sum of all the previous signal values. The error \nsignal, e, as shown in Fig. 2, is represented by the difference between the \npresent vaue of the signal, So and the predictor\u2019s prediction.\n\nther explanation \u2014namehs \u201cprevious value, previous line,\u201d\u2019 \n\u201cplanar\u201d and \u201ccircular.\u201d\n\nTIME \nFig. 5\u2014Example of \u2018\u2018previous value\u2019\u2019 prediction, where the error signal is the \ndifference between the actual value of the signal and the previous value.\n\nIt is of interest to mention that \u201cslope\u201d prediction is equivalent to \ntwo \u201cprevious value\u201d\u2019 predictors in tandem. Three or more \u2018previous \nvalue\u201d predictors in tandem are equivalent to a binomial weighting \nof the previous values of the signal to form a predicted signal.\n\nFor example, the prediction for three \u2018\u2018previous value\u201d predictors in \ntandem is given by\n\nTIME \nFig. 6\u2014Example of \u201c\u2018slope\u2019\u2019 prediction. Here the next signal value is assumed \nto lie on a straight line that intersects the two previous signal values.\n\n\u201cPlanar\u201d prediction, shown in Fig. 8, is effectively tandem operation \nof \u201cprevious value\u201d and \u2018previous line\u201d prediction. Planar prediction \nmay also be thought of as the value represented by a plane above the \npresent value of the signal when passed through three adjacent signal\n\nSe = Soy \n\u20ac = Soo -Soy \nFig. 7\u2014Example of \u2018\u2018previous line\u2019\u2019 prediction. Here the error signal is the\n\ndifference between the actual value of the signal and the value of the signal on \nthe line directly above.\n\nFig. 8\u2014An example of \u2018 planar\u2019\u2019 prediction. Here the prediction is represented \nby a plane that has been passed through three adjacent signal values.\n\nvalues, namely Si, So,1 and S:i,1. The predicted signal is given by \n. Sp = S10 + Sor \u2014 Sia. \nThe filter characteristic is given by\n\n2 2 \nThe peak error amplitude for \u201cPlanar\u201d prediction can be four times \nthat of the input signal.\n\n\u201cPlanar\u201d prediction has several good characteristics. For example, \nif S11, and Si, were white and So,1 black, then So would be predicted \nto be black. Thus a change horizontally from white to black would \nproduce no errors. Similary, if Si,1and So,, were white and Sj black, \nthen So, would be predicted to be black. This indicates that a change \nvertically from white to black would be predicted correctly. In this \nmanner, all vertical and horizontal contours in a picture are deleted. This \nphilosophy can be extended to include other directions as well.\n\n\u201cCircular\u201d prediction, illustrated in Fig. 9, is an extension of planar, \nsince it deletes horizontal, vertical and 52\u00b0 contours as well. A total of \n190.5 microseconds of delay is required, making the required equipment \nmore elaborate. Also, as more delay is required, more noise is added.\n\nFig. 9\u2014Past signal samples required for \u201ccircular prediction\u2019\u2019\u2014a type of \nprediction which removes horizontal, vertical, and +52\u00b0 straight line picture \ncontours.\n\nTherefore, indefinite extension of this straight line contour deleting \nphilosophy is not a paying means of prediction, at least not at the present \nstate of the art of wide band delay lines. Furthermore, the increasing \ndiameter of the circle for extension of circular prediction would decrease \nits accuracy for finely concentrated detail.\n\nFig. 10 shows the relative position of picture elements nearest So, \nif a wide band field delay were available. The methods of prediction dis-\n\nFig. 10\u2014Small portion of television raster showing signal samples, including \nthose of previous field, which would enable time extrapolation-space interpolation \nas a method of prediction. \ncussed have been essentially an extrapolation in space; however, with a \nfield delay, interpolation in space, and extrapolation in time would also \nbe possible.\n\nExperimentally, those types of predictors that involve only a few \nNyquist intervals of delay are easiest to mechanize. Fig. 11 shows a \nsimplified schematic of a decorrelator that enables an evaluation of \nlinear prediction schemes having error signals given by @\u00a2 =. do,oSo,o + \n@1,091,0 -\u2014 Q2,0Se0. This enables an evaluation of \u2018\u2018previous value\u201d and \n\u201cslope\u201d prediction. The signal is fed into a terminated delay line having \ntaps at Nyquist intervals. Each of these signals is individually attenuated \nby the potentiometers in the cathode circuit of the cathode followers. \nEach output is then fed to its respective polarity switch. The D.P.D.T. \nswitch determines to which side of the differential amplifier, V,, the \nparticular signal is sent. Since more than one signal may require the \nsame polarity, the signals are combined through \u2018\u2018L\u201d type resistance \nattenuators to prevent interaction between signals. The D.P.D.T. \nswitches are so arranged that the other signals are unaffected when a \npolarity switch is reversed. The differential amplifier, V4, is a cathode \ncoupled circuit having the advantage of two identical grids which pro- \nduce opposing effects in the output. The output is then matched to the \nline by the cathode follower, V;. In this way we can transmit (1) the\n\nFig. 12\u2014Block diagram of experimental apparatus used to investigate methods \nof prediction involving combinations of previous signal values along a line with \nthose on the line directly above. \nfrequency of 54.0 mc. The over-all video bandwidth is flat (- 0.1 db) to \n5.0 mc. Nonlinear distortion is approximately one percent when the \npeak-to-peak signal to r.m.s. noise is 58 db. To give an idea of its com- \nplexity, two such units with their associated power supplies require a \nseven-foot relay rack for housing. The signal at J1 represents the input \npicture signal, even though it may be delayed by a small fraction of a \nNyquist interval from the actual input signal. The signal at Jo is the \nsame signal as found at Ji but delayed by one line time. Each of these \nsignals is fed into terminated delay lines to enable additional signal \nsamples to be obtained. The geometrical location of these signal sam- \nples is illustrated in the upper right section of Fig. 12. Here, six signals \nare obtained instead of three as were required for \u2018\u201c\u2018previous value\u201d and \n\u201cslope\u201d prediction. These signals are weighted and polarized in the same \nmanner as the three signals shown in Fig. 11. The output is the sum of \nthese weighted signals and is given by\n\n\u20ac = ,0S0,0 + 41,0S1,0 + 2,0S2,0 + A180 + 41,1811 + 2821. \nThe coefficients may assume positive or negative values. \nMEASUREMENTS\n\nIt is obvious that if we are able to predict the value of most signal \nsamples closely (which we will be able to do if there is a large amount of \ncorrelation in the picture), then the average amplitude of our mistakes\n\nwill be much less than the average amplitude of the original signal. \nThus, by using the decorrelator alone, we can send a message over a \nchannel with the same bandwidth as before but with less average power. \nAt first, this might sound like a worthwhile saving; however this lower \naverage power is accompanied by an even higher peak amplitude which \nmakes any direct saving less attractive. Furthermore, the low frequency \nattentuation of the decorrelator makes the signal vulnerable to low \nfrequency disturbances, since the correlator must restore (emphasize) \nthese low frequency components.\n\nA proper but no\u00e9 entirely adequate method of evaluating the effective- \nness of a predictor is by measuring the ratio of signal power to error \npower. This is called \u2018\u201c\u201cPower Reduction\u201d and is generally expressed in \ndb. Power reduction simply provides a scale by which we can weigh a \nlinear predictor\u2019s capabilities. The \u201cnot entirely adequate\u201d refers to \nthe fact that minimum error power may not provide simultaneously the \nlowest amount of redundancy for that given type of prediction.\n\nAs an example, Fig. 18 shows the power reduction for the relative \nweighting of the previous horizontal signal sample as compared to the \npresent value of the signal, for three pictures-later to be described as \nScene A, Band C. The top-most curve is for Scene B, which is a \nsimple, soft picture that contains very little detail. For this picture, \nthe minimum error power coincides (within measurable limits) with the \nminimum redundancy. For Scene A and particularly Scene C, mini- \nmum error power is considerably different than that for minimum re- \ndundancy. This difference between minimum error power and minimum \nredundancy also applies to decorrelators using other types of predictors \nas well. Minimum redundancy may also be a misleading criterion of a \npredictor\u2019s performance, since the. value of the prediction must depend \non the particular type of encoder used, and some types of encoding will \nrequire certain types of redundant information to be retained.\n\nThe following pictures are representations of the error signal as photo- \ngraphed from a 10-inch laboratory monitor. The signals were band \n_ limited to 4.3 me. Fig. 14 represents the \u2018\u2018original\u201d\u2019 for three scenes called \nA, B and C. These pictures represent, to a first approximation, the \ngamut of pictures normally expected to be transmitted. They are by \nno means the best or the worst pictures than can be imagined; how- \never any system should be able to reproduce these pictures without \nappreciable distortion. For example, Scene C should be capable of \nbeing sent continuously without the elastic delay running out, etc. _\n\nFig. 15 shows how the error signal appears for \u201cprevious value\u2019\u201d\u2019 pre- \ndiction. \u2018\u201c\u2018Previous value\u201d prediction is excellent for flat white or dark\n\nFig. 13\u2014Power reduction for various weighting coefficients for the previous \nhorizontal sample.\n\nareas as can be observed in the background of Scene A. Where the \nseparation of a white to black area is made, the error signal is large. It \nis this large error signal that informs the receiver of this change in bright- \nness, and until another change occurs, the error output is again zero. This \ntype of performance produced the flat grey appearance of the back- \nground. In this way, the picture represents only changes in brightness\u2014 \na first difference type of picture.\n\nIt may be noted that horizontal contour lines have vanished leaving \nonly vertical contours which pertain to the brightness changes that . \nhave occurred. This effect is especially evident in Scene C. The \npower reductions given in the lower left hand corner of these pictures \nare consistent with their complexity.\n\nFig. 16 shows the error signal appearance for \u2018\u2018slope\u2019\u2019 prediction. \nWhen compared to the error signal for \u201cprevious value\u201d prediction \na finer vertical granularity is observed, and this is attributed to sudden\n\nFig. 14\u2014Three pictures as photographed from the face of a kinescope. Scene \n\u2018fA\u2019\u2019 is a picture of average complexity. Scene \u2018\u2018B\u201d\u2019 is a simple, rather soft picture. \nScene \u2018\u2018C\u2019\u2019 is a complex, highly detailed picture. Roughly, these pictures represent \nthe gamut of pictures normally expected to be transmitted.\n\nFig. 15\u2014Three pictures showing the appearance of the error signal when using \n\u201cprevious value\u201d\u2019 prediction. Note the absence of horizontal contours.\n\nFig. 16\u2014Three pictures showing the appearance of the error signal when using \n\u2018slope\u2019\u2019 prediction.\n\nFig. 17\u2014Three pictures showing the appearance of the error signal when using \n\u201cprevious line\u2019\u2019 prediction. Note the absence of vertical contours.\n\nFig. 18\u2014Three pictures showing the appearance of the error signal when using \n\u201cplanar\u201d prediction. Note the absence of horizontal and vertical contours.\n\nchanges in brightness. In the case of \u2018\u2018previous value\u201d prediction a sudden \nchange in brightness produces only one error, where for \u201cslope,\u201d two \nerrors result. This, to some extent, accounts for the lesser amount of \npower reduction measured for these scenes.\n\nFig. 17 shows the appearance of the error signal for \u2018previous line\u201d \nprediction in the three scenes. Where vertical contour lines are pre- \ndominately left after \u2018previous value\u201d prediction shown in Fig. 15, \nhorizontal contours, are more prevalent now. It can be noted that the \npower reduction for \u2018previous line\u2019\u2019 prediction is less than that for \u201cpre- \nvious value\u201d prediction. This is due principally to the increased distance \nof the previous line sample from So,o. If the closest horizontal sample \nwas taken at the same distance from the present value of the signal as \nthe previous line sample, then the power reduction using these signal \nvalues individually for prediction would be essentially the same for most \npictures.\n\nFig. 18 shows the error signal appearance for \u201c\u2018planar\u2019\u2019 prediction. \nHere, vertical as well as horizontal contours are deleted. In Scene A \nthe tree trunk has almost completely vanished. In Scene B the picture \nhas an extremely flat appearance. Scene C exhibits the lack of hori- \nzontal and vertical contours best, since only sloping contours are left. \nThe power reduction figures at the lower left hand corner also show values \nfor minimum error power. For most pictures, the error power can be \nreduced by a factor of one-half again over the planar coefficients by \nmodifying the weighting coefficients. The coefficients for this modified \nplanar case are given by\n\nThese coefficients generally produce an error signal with less power than \nthe coefficients used for \u201cplanar\u201d prediction.\n\nWhile all pictures contain redundancy, the error signals from these \nsimple linear predictors shown in Figs. 15, 16, 17 and 18 can visually \nbe noted still to contain large amounts of redundancy. The contours of \nthe models and of the various objects are readily identifiable. Were all \nredundancy removed, the picture would be completely chaotic and would \nappear very much like random noise, although greater efficiency in \ntransmission would be achieved. For richer rewards, more sophisticated\n\nThe author wishes to acknowledge with grateful appreciation the in- \nvaluable guidance of Dr. B. M. Oliver. It was principally through his ef- \u00a9 \norts that this study was made possible.\n\nwhere M and J are the densities of magnetic and electric polarization \ncurrents.\u201d\n\nand yp, \u20ac are constants (not necessarily those of vacuum). If M and J \nwere given, they would act as sources exciting various modes of propa- \ngation in a homogeneous, isotropic waveguide. If M and J are functions \nof H and E, they can still be considered as the sources, acting on power \nborrowed from the wave, of the various modes. Thus M and J will \nprovide the coupling between the modes existing in a homogeneous, \nisotropic waveguide.\n\nwhere x is the separation constant and e;, @ are the scale factors in \nthe expression for the elementary distance\n\nIn the case of TM waves the 7\u2019-function must vanish on the boundary \nof zero impedance. This boundary condition restricts x to a doubly in- \nfinite set of values xmn with the corresponding functions 7m, . In the \ncase of TE waves the normal derivative of the 7-function must vanish \non the boundary of zero impedance. Since we have to consider both \ntypes of waves simultaneously, we shall distinguish between them by \nenclosing the subscripts in parentheses for TM waves and in brackets \nfor TE waves. The double subscript designation of various modes has \nbeen standardized only for rectangular and circular waveguides. For \nwaveguides of other shapes the standard is to use a single subscript by \narranging the modes in the order of their cutoff frequencies. For con- \nvenience, we shall use this convention in the general case and denote \nTM modes by 7'ta)(u, v), and TE modes by 7'n(u, v). The correspond- \ning cutoff constants will be xq) and xn). In what follows it is under- \nstood that whenever the 7-functions should be designated by double \nsubscripts, our single letter subscripts should be conics as symbols \nfor ordered double subscripts.\n\nThe transverse field components may be derived from the potential \nand stream functions,\u2019 V and Il for TM waves and U and W for TE \nwaves. Thus\n\nThe 7-functions corresponding to the various modes of the same va- \nriety are orthogonal; that is, the following integrals over the cross-section \nvanish,\n\nSimilarly the gradients of the 7-functions of the same variety as well as \nthe fluxes, are orthogonal,\n\n/ i (grad Tey) +(grad Tem) dS = i if (flux Toy): (flux Tom) dS \n: (9) \n= i / (grad Tm) + (grad Tym) dS = i (flux Tiny) \u00ab (flux Tm) dS = 0,\n\nif m \u00a5% n. The following gradients and fluxes of the 7-functions are ortho- \ngonal for all m and n,\n\nOn the other hand, grad T'tm; and flux 7;,; are not, in general, orthogonal. \nIf all modes are present, the potential and stream functions are \u00a9\n\nwhere the tensor summation convention is used: whenever the same \nletter subscript is used in a product, it should receive all values in a \ngiven set and the resulting products should be added. The negative \nsigns have been inserted in order to avoid a preponderance of negative\n\nsigns in later equations. Substituting in (9), we have, \ni; = Vin) grad Tees + Vin flux Tn] ; (12) \nH, = \u2014T flux T (n) + LItnj grad T tn) .\n\nThe 7-functions for the various modes are determined by equation \n(4) and the boundary conditions except for arbitrary factors related to \nthe power levels of the modes. If we choose these constants in such a \nway that\n\nthen the complex power carried by the wave is given by an expression \nsimilar to that in an ordinary transmission line,\n\nHence, the V\u2019s and J\u2019s correspond to the voltages and currents in coupled \ntransmission lines. \nIn an expanded form equations (12) are\n\nTo these we add the following expansions for the longitudinal compo- \nnents of H and H\n\nEquations of this form satisfy automatically the boundary conditions \non EF, and H, . The multipliers x, have been inserted arbitrarily in order \nto make the physical dimensions of the second factors to correspond to \nthose of voltage and current.\n\nMultiplying (18) by [\u20149T (m/e2 dv] dS, (19) by [AT (m/e, du] dS, adding, \nand integrating over the cross-section, we obtain\n\nIn the first term the summation convention should be ignored. Multiply- \ning (18) by [07 {m/e: du] dS, (19) by [0T{m/e2 dv] dS, adding, and in- \ntegrating we find\n\nSubjecting the right column of (17) to a similar treatment, we obtain \nthree additional equations. Summarizing, we have\n\nIn the last terms of equations (25) and (28) the summation convention \nshould be ignored.\n\nIf the components of B and D are linear functions of the components \nof H and E respectively, then with the aid of (15) and (16) they can be \nexpressed as linear functions of Vay, Vin, Ia, Lt, Ven, Lem - \nSolving (29) for Vz,\u00a2n) and J.,:.; and making the appropriate substitu- \ntions in (25), (26), (27), (28), we obtain the generalized telegraphist\u2019s\n\ndV, ) \u00a5 ig \nFg Zemomlign \u2014 SomimZin \u2014 \u201cTeme Very \u2014 Lome V in \ndl ) I - \nae Tx Ym) (n) Vay \u2014 YG) [n] Vinl \u2014e Dm) inl (ny = Dm) tml ta] , \ndV \nus 7 \nae = \u2014Zimitnyl tn) \u2014 Zimmliny \u2014 Tmt Viny \u2014 Timmy \ndL tm) q I \nDi = \u2014VimimVing \u2014 YemaVoy \u2014 Ttmintiny \u2014 TT pmimlon -\n\nThe transfer impedances Z, the transfer admittances Y, the voltage \ntransfer coefficients \"7, and the current transfer coefficients \"T between \nvarious modes are in general functions of z. They are constants if the \nproperties of the waveguide are independent of the distance along it; \nin this case the problem of solving the generalized telegraphist\u2019s equa- \ntions reduces to solving an infinite system of linear algebraic equations \nand the corresponding characteristic equation.\n\nSimilar equations may be derived for spherical waves either in an un- \nlimited medium or in a medium bounded by a perfectly conducting coni- \ncal surface of arbitrary cross-section. If the latter is circular and if the \nflare angle is 180\u00b0, we have a plane boundary. Hence, the case of spheri- \ncal waves in a non-homogeneous medium is included. In the spherical \ncase we shall use the general orthogonal system of coordinates (r, u, v) \nwhere r is the distance from the center and (u, v) are orthogonal angular \ncoordinates. In this system the elements of length ds and area dS are \ngiven by . \u2018\n\nThe transverse field components may be expressed in a form similar \nto that for waveguides\n\nwhere grad and flux of a typical scalar function are defined by equations \n(10). Instead of (11) we have\n\nwhere the T-functions satisfy equation (4) and appropriate boundary \nconditions. These functions, their gradients and fluxes are orthogonal.\n\nThey are assumed to be normalized as follows \n[[(erad 7)- (grad 7) do = 32 [[ravet, (34) \nwhere dQ is an elementary solid angle. Hence, equation (14) will again\n\nrepresent the complex power flow in the direction of propagation. \nThe various field components may then be expressed as follows\n\nIt should be noted that the physical dimensions of V;,\u00a2,) and I,,tnj are \nnot those of voltage and current. Substituting in Maxwell\u2019s equations \nand using transformations similar to those in the case of plane waves, \nwe find\n\nReturning to the plane wave case and assuming the following general \nlinear relations\n\nIf we solve the last two equations for I,,tm) and V.,.n) and substitute \nin the preceding four equations, we shall obtain the telegraphist\u2019s equa- \ntions in their final form (30). Thus, let\n\n\u201cZm\\tn] = / / Jomeex tn T'tnj T'tm BS, \n(45) \n\u201cYom (ny = | jooesx(nyT (my Tom AS. \nFrom these coefficients we obtain another set \n*Zinitm) = normalized co-factor of *Zpmjtnj , \n*Zcn)(m) = normalized co-factor of *Y (myn - \nThen,\n\nBefore substituting in equations (39) to (42), the summation index m \nin (47) should be changed to avoid conflict with m in the former equa- \ntions. It does not seem necessary to make these final substitutions in \ntheir most general form. The results are\u2019 very complicated and in prac- \ntice the various coefficients are not independent. Some coefficients may\n\nvanish; others may be small. In isotropic media, pun = boo = be = \nBy \u20acuu = \u20ac\u00bb = \u20acz = e\u20ac and the mutual coefficients vanish. In gyromag- \nnetic media subjected to a strong magnetic field in the z-direction, the \npermeability coefficients of superposed ac fields are\u00ae\n\nIf the entire waveguide is filled with such a medium, assumed to be \nhomogeneous, equations (48) and (44) become\n\nIn view of the orthogonality of the T-functions and the normalization \nconditions (13), we have\n\nwhere the summation convention is waived. In this case all the transfer \ncoefficients in equations (30) vanish,\n\n8 C. L. Hogan, \u2018\u2018The Ferromagnetic Faraday Effect at Microwave Frequencies \nand Its Applications\u2014The Microwave Gyrator, Bell System Tech. J., Jan. 1952,\n\nIn rectangular waveguides we choose cartesian coordinates; \nthene:=@=1, w= 2,0 = yand\n\nSome of the mutual impedances vanish; thus \nZooey = O, (55) \nif either p + sorg +t is even. If p + 8s, as well as q + \u00a2, is odd,\n\n. 2 2 \nSe \nSimilarly \noe Ztpatst) = 9, (57) \nif either p + s org + tis even, provided p ~ sandq \u00a5 t. If p + s, as \nwell as q + \u00a2, is odd, \nA-Ipgla(pt? \u2014 q\u2019s)jupay (58)\n\nConsider now the set of modes which includes TEj10}.. This set in- \ncludes TE, modes and all the other modes which are coupled to either \nof these modes. Noting that there are no TM\u00bb) and TM @,) modes, we \nobtain the following table in which those modes which do not belong \nto the set are marked with a bar:\n\nThe principal effect of the gyromagnetic medium on the TEj19) and TEjoy \nmodes may be understood by taking into account their mutual coupling \nbut ignoring their coupling to other modes. The equations of propaga- \ntion become\n\ndV : i \n\u2014\u2014 = \u2014Jjoplyo \u2014 jopey(8/r')Lio 5 \nal r \npl = \u2014 (joe + saicat) Yom \nZ JOM \ndV op \nra = jops,(8/ p10) \u2014 jou on , \naI 01} - \u00a9 a) \nao Jue as V tor} - \nFor exponentially propagated waves we have \nVio = Vane, Vion = Vine\u2122, 62)\n\nWhen the mutual permeability is zero, we have two independent modes \nwhose phase constants are\n\n(8\u00b0 \u2014 Bor)L oy = FhBOF 110) \u00ab i \nMultiplying term by term, we obtain the characteristic equation \nB* \u2014 (Bio + Ba)8\u00b0 + (L \u2014 K\u2019)Bio801 = 0. (67) \nSolving, we have \nB\u00b0 = 4(Bio + Bor) = 4[(Bi0 \u2014Bor)\u201d + 4KBio801)\"\u201d. (68)\n\nThe effect of coupling is to increase the larger phase constant and de- \ncrease the smaller one; that is, to make the slower wave slower, and the \nfaster wave faster.\n\nLet us assume a > 6; then 61 > 8. Taking the upper sign in (68) \nand substituting in the second equation of the set (66), we have\n\nV 101 Bor Tt10) p+ (p? + ky)? \u00b0 \nHence, the ratio of the power carried in the TEjoy mode to that in the \nTE} mode is\n\nIf the phase constants of the uncoupled modes are equal, then p = 0 \nand Po. = Pi for all values of the coupling coefficient. In this case (68) \nbecomes\n\nThe cutoff frequencies of both normal modes are seen to be independent \nof either the transverse permeability or the mutual permeability. Since\n\nHzy 1S a pure imaginary, it effectively increases the transverse permeabil- \nity for one mode and decreases it for the other.\n\nTo evaluate the effect of higher order TE and TM modes on wave \npropagation we may substitute from (68) in all terms of the character- \nistic equation for telegraphist\u2019s equations except the first two diagonal \nterms and recalculate the 6\u2019s. Alternatively we may replace TE; and \nTE,o1 modes by the normal modes just obtained, recalculate the cou- \npling coefficients, and evaluate the effect of the mode with the greatest \ncoupling to the modes under consideration.\n\nThe approximate location of the natural barrier found in early melts \nis shown in Fig. 1. The barrier was generally located in the melt per- \npendicular to the axis of the melting crucible or more accurately to the \ndirection of the temperature gradient. Plates and rods containing sec- \ntions of the photoactive barrier, Fig. la, were cut from the melt and \nmounted on convenient supports for laboratory tests. Fig. le shows a \nmagnified section of one of these barriers.\u201d\n\nFig. 1\u2014(a) Drawing of melt showing position of photovoltaic barrier and photo \ncells with natural barrier. (b) Drawing of melt showing surface type photo cell \nmade from natural barrier. (c) Magnified, etched section of slowly cooled silicon \nshowing the transition between p and n silicon forming the barrier which consists \nof intermeshed striae of these two varieties.\n\n-6 -5 -4 -3 2 - oO 14 \nVOLTS (Cc) \nFig. 2a\u2014Spectral response of internal barrier in silicon. \nFig. 2b\u2014Voltage and current photosensitivity of internal barrier in silicon. \nFig. 2c-\u2014Rectification characteristic of internal barrier, dark and illuminated.\n\nThat ion velocity has a profound effect on the voltage current char- \nacteristic of bombarded surfaces is shown in Fig. 5. These characteristics \nwere obtained by placing a tungsten point contact under 10 gm of force,\n\nFhe 5\u2014Liffect of bombardment voltage on the rectification of the intermediate \ncells.\n\nFig. 6\u2014Photocurrent at a constant illuminance versus the bombarding voltage.\n\non the photo active surfaces of the medium size cells whose spectral \nresponse js given in Fig. 8. However, in order to show the rectifying prop- \nerty of the barrier without the complication of a point contact, a disc of \nhyper-purity silicon 13\u201d in diameter and about 0.025\u201d thick was given \nan optical polish on both faces. One face was bombarded with 30-kv ions.\n\nFig. 7\u2014Photovoltage at a constant illumination versus temperature of the \nbombarded silicon surface.\n\nFig. 8\u2014Spectral response of the intermediate size cells at various bombarding \nvoltages.\n\nElectrodes 14\u201d in diameter of evaporated rhodium metal were applied in \nlike manner to each surface. Contact was made to the collector electrodes \nby means of tin discs. Fig. 4 gives the forward and backward log voltage- \nlog current relation of this large cell. Without bombardment such an \narrangement shows ohmic conductivity so it is evident that the treat- \nment is responsible for the development of a potential barrier beneath \nthe surface. It is believed from the high dark resistivity of the bom- \nbarded layer that the intrinsic properties of the silicon are developed \ntherein. Thus an intrinsic -p type potential barrier is produced similar \nto a degree to the n-p junction. One would expect the depth of this bar- \nrier to be related to the velocity of the ions. Consequently a study has \nbeen made of the effect of ion velocity on the photoelectric properties.\n\nThe photoelectric current at constant illuminance for a series of cells \nprepared by bombardment with ions of different energies is shown in \nFig. 6. It is remarkable how quickly and completely the current sensi- \ntivity saturates at approximately 500 volts.\n\nThe photoresponsiveness improves as the total bombarding charge is \nincreased until it has reached about 600 microcoulombs per sq. em. \nFurther bombardment produces no appreciable improvement. In certain \nexploratory tests a total charge of about 9000 microcoulombs at 30 kv \nhas been applied. Under these severe conditions the surface may show \nsmall areas having a slightly etched appearance.\n\nNo extensive tests have been made to determine the effect of the rate \nof application of the bombarding charge. The apparatus was designed \nfor use at a rate of about 5 microamperes per sq. cm. It is known how- \never, that between the limits of about 2.5 and 10 microamperes per sq. \ncm. the effects are subject only to the total charge or the total number \nof ions which strike the silicon surface.\n\nSix spectral curves are shown in Fig. 8 which illustrate the result ob- \ntained with the intermediate size cells over the bombardment voltage\n\nrange previously mentioned. The peak of the lowest voltage cell is \ndefinitely toward the blue compared with the other five whose maximum \nis constant at about 0.725 pu.\n\nOne objective in this study was to obtain evidence relating to the \ndepth of the barrier below the silicon surface as a function of the energy \nof the bombarding particles. The higher the velocity of the particles the \nfurther beneath the surface one would expect the barrier to be located \nand as a result there might be a shift in the spectral characteristic toward \nthe red with increasing depth of the barrier due to the relatively greater \nabsorption at the blue end. There is however, a selective or secondary \nmaximum at the peak which sharpens it and nullifies the effect of the \nwarping of the entire curve. The blue to red shift can be shown as in \nFig. 9 by plotting the ratio of the responses in Fig. 8 at 0.50 \u00bb and 1.0 pz. \nThus at low voltage the blue to red ratio is high and decreases as the \nbombarding potential is raised.\n\nIn the spectral curves it will be noted that there are a number of \nsecondary humps located near the top of the curves and extending down \non the\u2018blue side. There is a strong tendency for them to occur at definite \nwavelengths and to beevenly spaced regardless of the bombarding voltage.\n\nSPECTRAL MEASUREMENTS ON THE LARGE CELLS AND THE EFFECT OF \nMATERIAL COMPOSITION\n\nFor the large cells, two grades of silicon were used peu niente by \npyrolytic reduction of SiCl, and called \u201chyper-pure\u201d. These will be\n\nLOGig\u2014VOLTS = \nFig. 9\u2014Ratio of blue to near infra-red response versus bombarding voltage.\n\ndesignated B and C, the former being from the same source as \u201c\u2018silicon \nB\u201d referred to in the paper by Scaff et al.\u201d A typical analysis is given \ntherein. The C silicon was from another source and a spectroscopic analy- \nsis indicated it was somewhat more impure than B thus agreeing with \nobserved differences in its electrical and optical characteristics. An opti- \ncal variation of considerable interest is shown in Fig. 10 where the \nspectral transmittance of the two grades of silicon is compared in the \ninfra-red for polished plates each 0.0195\u201d thick.\n\nThe transmittance of B decreases a little with increasing wavelength \nbut C goes down much more. Both however, start to get transparent at \nabout the same point, 1.14 and also show corresponding absorption \nbands superimposed on the main curve. Briggs\u2019 has compared the trans-\n\nWAVELENGTH IN MICRONS \nFig. 10\u2014Spectral transmittance of B and C grades of silicon, polished plates, \n0.0195\u201d thick.\n\nmittance from 2 \u00bb to 12 uw of the A and B silicons in Scaff\u2019s paper where \nthe former was much more impure than the C grade. The absorption \nof the A silicon increased so rapidly out in the infra-red that a much \nthinner sample was used for the measurements than for the B material. \nIf this difference in thickness is allowed for, the effect of impurity is \nvery striking.\n\nThe spectral response of large area cells made of the B and C materials \nand bombarded with 1000-volt helium positive ions is shown in Fig. 11. \nThe two curves are similar in shape except the one for C silicon is some- \nwhat narrower and in addition is shifted toward the blue. Both have \nsome of the secondary humps noted previously.\n\nAll the cells shown in this paper have indicated a long wave limit of \nabout 1.2 u. Actually some response can usually be detected out to about \n1.3 \u00bb. Measurements made some years ago on the internal barrier units \nalso gave a limit around 1.3 \u00bb but relatively more response at 1.2 \u00bb with \npeaks close to 1.10 4. This difference is reasonable because light was\n\nprojected along the barrier plane and not normal to it as in the latest \nunits, so that with the rapidly increasing transparency in this region, \nless infra-red radiation was lost. However, the blue was rapidly at- \ntenuated.\n\nWhen illuminated by tungsten light of 2848\u00b0K color temperature, the \nlarge B cells gave 2160 microamps per lumen and the C unit 638. Cor- \nrecting for a surface reflectance of 0.385, the net sensitivities would be \n3510 and 1040. These measurements were made with between 4- and \n5-footcandles illuminance on the cells, a region in which the response is \nproportional to the intensity. At much higher values of illuminance there \nwas some falling off of response so that the effective sensitivity was a \nlittle lower. The above measurements were made on a ten ohm microam- \nmeter which is too low a resistance to affect the linearity. The inter- \nmediate cells ran approximately 3000 microamps per lumen in the most \nsensitive region of bombardment without correction for surface reflec- \ntion and at 10- to 20-footcandles for the same tungsten lamp using a \nmeter of 76 ohms.\n\nThese experiments have served not only to introduce us to some of the \nphenomena involved in semiconductor barriers but have also yielded \nphoto cells having desirable properties. These cells have a high degree of \nstability and will stand treatment ruinous to most other cells. They have \na very high current sensitivity to tungsten light and daylight. They re- \nquire no associated battery and can be made in large areas. Unlike the \nmaterial used in many types of photo cells, silicon does not have the \ndisadvantage of scarcity. All tests to date indicate that an indefinitely \nlong life may be expected even under extreme illumination. Fig. 11 sug- \ngests that it may be possible to control to some extent the spectral re- \nsponse in the region from the deep blue into the infra-red. The long wave \nlimit is set by the edge of the absorption characteristic.\n\n1. U. S. Patent No. 2,402,839, Filed Mar. 27, 1941. \nU. S. Patent No. 2,402,662, Filed May 27, 1941. \nU. S. Patent No. 2,443,542, Filed May 27, 1941. \n2. J. H. Seaff, H. C. Theuerer and E. E. Schumacher; also W. G. Pfann and J. H. \nSeaff, Trans. A. I. M. E., 185, pp. 383-392, 1949. \n3. R. S. Ohl, Bell System Tech. J., Jan., 1952. Also see this paper for more details \nregarding the method of preparing silicon. \n4. H. B. Briggs, Phys. Rev., 77, pp. 727-728, Mar. 1, 1950.\n\nAbstracts of Bell System Technical Papers* \nNot Published in This Journal\n\nMechanical Properties of Discrete Polymer Molecules. W. O. Baxer\u2019, \nW. P. Mason\u2019 and J. H. Huss\u2019. J. Polymer Sci., 8, pp. 129-155, Feb., \n1952. (Monograph 1937).\n\nPost-War Achievements of Bell Laboratories: IJ. O. E. Bucxury\u2019. \nBell Tel. Mag., 30, No. 4, pp. 224-237, 1951-1952.\n\nA Portable, Direct-Reading Microwave Noise Generator. Kh. L. CxHin- \nnock\u2019. Proc. Inst. Radio Engrs., 40, pp. 160-164, Feb., 1952. (Mono- \ngraph 1939).\n\nConcerning the early years of this fundamental concept of modern physics\u2014 \nhow Max Planck formulated it at the turn of the century and how others en- \nlarged it up to 1923.\n\nResults of tests at 10 and 60 me with resistive terminations of 75 to 1000 \nohms. Low terminating impedance values yield wide bands but involve higher \ninsertion losses.\n\n* Certain of these papers are available as Bell System Monographs and may \nbe obtained on request to the Publication Department, Bell Telephone Labora- \ntories, Inc., 463 West Street, New York 14, N. Y. For papers available in this \nform, the monograph number is given in parentheses following the date of pub- \nlication, and this number should be given in all requests.\n\nEcho Distortion in the FM Transmission of Frequency-Division Mul- \ntiplec. W. J. ALBERsHEIM\u2019 and J. P. Scuarer\u2019. Proc. Inst. Radio Engrs.,\n\nThe composite multiplex signals generated by frequency-division methods \nlong standard in telephone communication can be transmitted by the new trans- \ncontinental broad-band FM radio relays. Signal intermodulation by echoes must \nbe minimized. Such intermodulation is investigated in this paper experimentally \nand analytically. Two types of echoes are considered: (1) weak echoes with de- \nlays exceeding 0.1 microseconds, caused mainly by mismatched long lines; and \n(2) powerful echoes with delays shorter than 0.01 microseconds, caused by multi- \npath transmission, and leading to selective fading. By use of random noise sig- \nnals, the distortion is evaluated as a function of various parameters of the echo, \nthe base-band, and the rf modulation.\n\nExperiments have been made on a sample of FeO, cut from a single crystal \nin such a way that its ferromagnetic domain pattern includes an individual \ndomain wall whose motion can be studied. This sample has a permeability which \nis high (about 5000) at low frequencies and drops off rapidly above 1000 cycles. \nA hysteresis loop and data on wall velocity vs applied field were also taken. \nThe data are discussed in terms of recent developments in the theory of the \nferromagnetic domain wall. It appears that this theory explains our data satis- \nfactorily, and that in using it to explain our data we determine some of the \nfundamental magnetic constants of Fe;O4. We are also able to gain some insight \ninto domain wall motion in ferrites generally in this way.\n\nThe Drift Mobility of Electrons in Silicon. J. R. Haynes\u2019 and W. C. \nWestpnar. Phys Rev., 85, p. 680, Feb. 15, 1952.\n\nFormulas for the Group Sequential Sampling of Attributes. H. L. \nJones\u2019, Ann. Math. Statistics, 23, pp. 72-87, March, 1952.\n\nSome Fundamental Properties of Transmission Systems. F. B. \nLumwettyn. Proc. Inst. Radio Engrs., 40, pp. 271-283, March, \n1952. ;\n\nThe problem of the minimum loss in relation to the singing point is investi- \ngated for generalized transmission systems that must be stable for any combina-\n\ntion of passive terminating impedances. It is concluded that the loss may ap- \nproach zero db only in those cases where the image impedances seen at the ends \nof the system are purely resistive. Moreover, in such cases, the method of over- \ncoming the transmission loss, whether by conventional repeaters or by series and \nshunt negative impedance loading, or otherwise, is. quite immaterial to the ex- \nternal behavior of the system as long as the image impedances are not changed. \nThe use of impedance- -correcting networks provides one means of insuring that \nthe:-phase of the image impedance of the over-all system approaches zero. Gen- \neral relations are derived which connect the image impedance and the image \ngain of an active system with its over-all performance properties.\n\nA Recurrence Relation for Three-Line Latin Rectangles. J. RIORDAN\u2019. \nAm. Math. Monthly, 59, pp. 159-162, March, 1952.\n\nCapacitors and Communications. Inductive Coordination of Lines. A. \nR. WarHNER\u2019 and W. E. Broecker\u2019. Elec. Light and Power, 30, pp. 105-\n\nANTENNAS: THEORY AND Practice. By Sergei A. Schelkunoff and \nHarald T. Friis, 689 + xxii pages, John Wiley and Sons, Inc., New York\n\nSrpney Daruineton, B.S., Harvard University, 1928; B.S. in E.E., \nMassachusetts Institute of Technology, 1929; Ph.D., Columbia Uni- \nversity, 1940. Bell Telephone Laboratories, 1929-. Dr. Darlington has \nbeen engaged in research in applied mathematics with emphasis on \nnetwork theory.\n\nPaut G. Epwarps, B.E.E., Ohio State University, 1924; E.E., Ohio \nState University, 1929. Western Union Telegraph Company, 1919-22; \nAmerican Telephone and Telegraph Company, 1922-34; Bell Telephone \nLaboratories, 1934-. His main concern in the Laboratories has been \nwith toll transmission problems, including voice frequency and carrier \nsystems. Member of the I.R.E., A.I.E.E., Sigma Xi, Tau Beta Pi, and \nKta Kappa Nu.\n\nC. W. Harrison, BS. in E.E., Purdue University, 1938; M.S., Lehigh \nUniversity, 1940. Bamberger Broadacasting Company, 1939-41. Bell \nTelephone Laboratories, 1941~-. Mr. Harrison is a member or the tele- \nvison research group. He formerly designed radio receivers and, later, \nmicrowave relay repeaters. Member of the I.R.E.\n\nJoHn L. Hysxo, B.S. in E.E., Cooper Union, 1921. U. S. Army, \n1918-19. Bell Telephone Laboratories, 1919-. Mr. Hysko\u2019s principal \nactivities in the Laboratories have been in the development of amplitude- \nmodulation and frequency-shift carrier telegraph systems for land line, \nradio teletypewriter and submarine cable applications.\n\nEpwin F. Kinessury, B.S., Colgate University, 1910. United Gas \nImprovement Company, 1910-18. U.S. Army, 1918-19. Eastman Kodak \nCompany, 1919-20. Bell Telephone Laboratories, 1920-51. Mr. Kings- \nbury retired in 1951 after a career which was primarily concerned with \ntelevision research and development, especially that part dealing with \nphotoelectric and electrooptical problems. Member of the Franklin In- \nstitute, the Optical Society of America, and Phi Beta Kappa; Fellow of \nthe American Physical Society and the American Association for the \nAdvancement of Science.\n\nErnest R. Kretzmer, B.S., Worcester Polytechnic Institute, 1944; \nM.S., Massachusetts Institute of Technology, 1946; Sc.D., Massachu- \nsetts Institute of Technology, 1949. As a member of the Electrical En- \ngineering Department at Massachusetts Institute of Technology, Dr. \nKretzmer taught from 1944-46 and conducted research there from \n1946-49. Bell Telephone Laboratories, 1949-. He works in the televison \nresearch group, where he has been principally concerned with decor- \nrelation of television signals. Member of I.R.E. and Sigma Xi.\n\nL. R. Montrort, E.E., University of Virginia, 1926; American Tele- \nphone and Telegraph Company 1926-34; Bell Telephone Laboratories, \n1934\u2014. Mr. Montfort has been concerned with the engineering of carrier \nsystems. This has included field work with new systems and field tests \nprior to the design of new systems. During the end of World War II \nand for a short time thereafter, he assisted in the engineering and test- \ning of microwave radio systems. Member of A.I.E.E., Tau Beta Pi, \nTheta Tau, and Sigma Phi Epsilon.\n\nRusset 8. Out, B.S. in Electro-Chemical Engineering, Pennsylvania \nState College, 1918; U.S. Army, 1918 (2nd Lieutenant, Signal Corps); \nVacuum tube development, Westinghouse:-Lamp Company, 1919-21; \nInstructor in Physics, University of Colorado, 1921-1922. Department of \nDevelopment and Research, American Telephone and Telegraph Com- \npany, 1922-27; Bell Telephone Laboratories, 1927-. Mr. Ohl has been \nengaged in various exploratory phases of radio research, the results of \nwhich have led to numerous patents. For the past ten or more years he \nhas been working on some of the problems encountered in the use of \nmillimeter radio waves. Member of American Physical Society and Alpha \nChi Sigma and Senior Member of the I.R.E.\n\nB. M. Ottver, B.A., Stanford University, 1935; M.S., California \nInstitute of Technology, 1936; Ph.D., California Institute of Technology, \n1939. Bell Telephone Laboratories, 1939-52. During World War II, \nDr. Oliver was engaged in radar research and the rest of his employ-\n\nment before leaving the laboratories was in the television research group. \nMember of I.R.E. and Phi Beta Kappa.\n\nWitton T. Rua, B.S., Princeton University, 1926; American Tele- \nphone and Telegraph Company, 1926-34; Bell Telephone Laboratories, \n1934\u2014. Except for the years 1941-45, when he worked on military pro- \njects. Mr. Rea has been principally concerned with telegraphy. As Tele-\n\ngraph Development Engineer, he is in charge of the development of tele- \ngraph and telephotograph systems. Senior member of I.R.E. and member \nof A.I.E.E. and Phi Beta Kappa.\n\nL. C. Rosrrts, A.B., Harvard University, 1916; B.S. in E.E., Harvard \nUniversity, 1919; B.S. in E.E., Massachusetts Institute of Technology, \n1918; American Telephone and. Telegraph Company, 1917-34; Bell \nTelephone Laboratories, 1934\u2014. Mr. Roberts has been primarily concerned \nwith the development of de and carrier telegraph except during World \nWar II when he worked on multichannel and single-channel radio tele- \ntypewriter developments. Member of A.I.E.E.\n\nS. A. ScHeLKunorr, B.A., M.A. in Mathematics, The State College \nof Washington, 1923; Ph.D. in Mathematics, Columbia University, \n1928. Engineering Department, Western Electric Company, 1923-25; \nBell Telephone Laboratories, 1925-26. Department of Mathematics, \nState College of Washington, 1926-29. Bell Telephone Laboratories, \n1929-. Dr. Schelkunoff has been engaged in mathematical research, \nespecially in the field of electromagnetic theory.", "title": "magazine :: Bell System Technical Journal :: BSTJ V31N04 195207", "trim_reasons": [], "year": 1952} {"archive_ref": "bitsavers_BellSystemJV53N02197402_9013471", "canonical_url": "https://archive.org/details/bitsavers_BellSystemJV53N02197402_9013471", "char_count": 266759, "collection": "archive-org-bell-labs", "doc_id": 617, "document_type": "journal_issue", "id": "bella-qwen-pretrain-doc617", "record_count": 486, "release_policy_version": "hf_public_v1", "rights_status": "public_domain", "selected_extraction_backend": null, "selected_extraction_score": null, "source_family": "archive_org", "source_url": "https://archive.org/details/bitsavers_BellSystemJV53N02197402_9013471", "split": "validation", "text": "Losses and Impulse Response in Parabolic Index \nFibers With Square Cross Section\n\nTransverse Coupling in Fiber Optics\u2014Part |: \nCoupling Between Trapped Modes\n\nPerformance Models of an Experimental \nComputer Communication Network\n\nPeak-Load Traffic Administration of a Rural \nMultiplexer With Concentration \nTime Domain Analysis and Synthesis\n\nOn the Behavior of Minimax Relative Error \nFIR Digital Differentiators\n\nInterframe Picturephone\u00ae Coding Using \nUnconditional Vertical and Temporal \nSubsampling Techniques\n\nSimultaneous Measurements of Depolarization \nby Rain Using Linear and Circular \nPolarizations at 18 GHz\n\nF, T. ANDREWS, JR. J. M. NEMECEK \nS. J. BUCHSBAUM B. E. STRASSER \n|. DORROS D. G. THOMAS \nD. GILLETTE W. ULRICH\n\nTHE BELL SYSTEM TECHNICAL JOURNAL is published ten times a year by \nthe American Telephone and Telegraph Company, J. D. deButts, Chairman \nand Chief Executive Officer, R. D. Lilley, President, J. J. Scanlon, Executive \nVice President and Chief Financial Officer, F. A. Hutson, Jr., Secretary. Checks \nfor subscriptions should be made payable to American Telephone and Telegraph \nCompany and should be addressed to the Treasury Department, Room 1038, 195 \nBroadway, New York, N. Y. 10007. Subscriptions $11.00 per year; single copies \n$1.50 each. Foreign postage $1.00 per year; 15 cents per copy. Printed in U.S.A.\n\nExplicit expressions are derived for the phase constant, the speczfic- \ngroup-delay constant, and the rms width of the impulse response for two- \ndimensional or square media having a transverse variation of index of \nrefraction according to n = ni(1 \u2014 faye\" \u2014 40,2\"), in which x ts the \ntransverse dimension, au and a, are constants with |a,| <> pmin; thus\n\nThe effect on transmission system performance is approximately the \nsame for various shapes of the impulse response if the rms width is \nthe same ;! this applies in the region where the fiber impulse response \ndegrades the system signal-power requirements by only 1 or 2dB. We\n\nWe now give the results for the index distribution according to \neq. (1). The guide has width 2a. We specify that at x = a, f(x) =\u2014A, \nleading to eq. (2) and\n\nEquation (29) can be used to eliminate the last factor in (36). For \nthe first term of (34), representing the major response due to a,x\u201d in \n(1), the maximum value of \u00a2 is\n\nFor the second term of (34), representing the perturbing term a,a* \nin (1), the maximum value of \u00a2 is\n\nEquation (34) is not valid for u = 2; for the later case the impulse \nresponse is \n4096(1 \u2014 6)r/4mt/2.,\n\nLetting wu = 2 in the equations of the preceding section yields the \nnear-parabolic index distribution. As shown by (35), the impulse \nresponse has zero width when a, = 0 in the approximation made here. \nIn the cylindrical fiber there is no index distribution which gives zero \ndelay distortion among all the various modes. There is a distribution \nof index which minimizes the delay distortion, and we now evaluate \nthis condition. We can use the above theory to evaluate the cylindrical \nwaveguide by noting the two limiting conditions already known for \nlow dispersion. Take the form\n\nin which R is the radial transverse coordinate. In two earlier papers*8 \nit has been pointed out that the value of b; must be different to produce \nno dispersion for meridional rays versus skew rays; the difference in \nbs was found to be $. Kawakami and Nishizawa\u00ae found that b, must \nbe 3 to give no dispersion for skew rays and must be 3 to give no dis- \npersion for meridional rays. We can visualize minimizing the dis - \npersion for one ray type, and thus experiencing a maximum dispersion \ncorresponding to a change in b, of 4. We do this in the approximation \nused here by setting u = 2, r = 4, and making\n\n(31), and (41) we find for this \u201cideal\u201d index distribution in the round \nfiber the specific group delay\n\nThis agrees reasonably well with the value \u2014n,A?/8c arrived at by \nGloge and Marcatili!\u00ae using an entirely different analysis for an \noptimum index distribution defined differently.* The rms width of \nthe impulse response corresponding to (41) and (42) is\n\nIn contrast with this, the simple step-index fiber [represented by \na, = 0 and n \u00a9 in (1) ] has an rms impulse response width of \n1 Ni \n\u00a2=\u2014=\u2014A., 45 \nae (45) \nThus the \u2018ideal,\u2019 corresponding to (42) and (43), is smaller by a \nfactor of 0.264. Since A ~ 0.01 the ideal graded-index fiber has an \nimpulse response narrower by a factor of about 400 than that for the \nconventional fiber. \nThe fourth-order term represented by (41) corresponds to\n\nThis is very little different from the simple parabola\u2014not enough to \nsee on Fig. 1 where curve @ represents both 6 = 0 and (46) for \nA ~ 0.01. More importantly, (46) and (41) imply that the fourth- \norder term decreases in size relative to the second-order term as A \ndecreases. The inaccuracies of material processing are likely to prevent \nthis as A becomes small. A more probable limit is a fixed value of 6 \nin (25) as A changes. This results in a specific group delay\n\n* If instead of minimizing the delay distortion for either the skew rays or meridional \nrays we had minimized the delay distortion for an index equation (40) at the mean \nof the index values giving minimum distortion for the skew and meridional rays\u2014i.e., \nat b = 5/12\u2014then the maximum departure in b for any mode corresponds to a \nchange in b = +1/12. This corresponds to a, = +1/6a?, leading to\n\nin place of (42). The coefficient 0.13 corresponds almost exactly to the result of \nGloge and Marcatili,\u00b0 but the present analysis indicates twice the total delay spread \npredicted by Gloge and Marcatili due to the + sign.\n\nFig. 1\u2014Normalized index of refraction versus transverse coordinate (x/a) for the \nfollowing parameters in eqs. (1) and (25): curve @, u = 2, 6 = 0; curve @, u = 2, \nr = 4,6 = 0.05; curve \u00a9, u = 4, 6 = 0; curve @, u = 4,7 = 2,5 = \u2014 1; curve \u00a9, \nu = 8,6 = 0; curve \u00a9 u = ~,5 =0.\n\nFor 6 = 0.05, \u00ab becomes 0.00591 niA/c which is narrower than for the \nstep-index fiber by a factor of about 50 independent of A.\n\nWe note from (39) that the impulse response for the ideal index \ndistribution perturbed by a fourth-order term (r = 4) is a rectangular \npulse, shown as curve () in Fig. 2. However, if the perturbation were \nsixth order, r = 6, the impulse response would vary as t\u2014?. Other values \nof r give other impulse-response shapes, which we discuss further in \nthe next section.\n\nFinally we note from (47) that the impulse response due to the \nfourth-order perturbation of the ideal distribution may either lead or \nlag the impulse at +r = ni/c, depending on whether 6 is positive or \nnegative [see (1) and (25) ]. Similar effects due to the sign of 6 are\n\nFig. 2\u2014Impulse response P(t) versus t/tmax where t = +r \u2014 ni/c and 7 is given by \n(31) and (33). The conditions are the same as defined under Fig. 1.\n\nfound for perturbations of the nonideal index distributions and may \nbe seen in (31).\n\nIn Section VI there is a discussion of Fig. 8 which shows the effects \nof perturbing the parabolic index distribution in several ways.\n\nIn this section we discuss the distributions obtained by setting \na, = 0 in (1) which mean 6 = 0 in (24) and (25).\n\nThe total spread in specific group delay for all modes tmax,u 1S given \nby (87), which gives a null value when u = 2. As already discussed, \nthis is a simplification in the vicinity of the \u2018\u2018ideal\u2019\u2019 distribution. \nHowever, (37) gives a valid representation as u departs significantly \nfrom the value 2. Figure 3 shows the variation in fmax,. Versus Uw. \nThe behavior in the vicinity of u = 2 is a form of singularity. For \n5-percent error in uw from the ideal, tmax,u 2% 0.025n,A/c. This com- \npares with 0.0244n,;A/c for the modal delay spread from (47) for \n5-percent (at \u00ab = a) fourth-order perturbation of the ideal. We con- \nclude that it is not particularly important how the ideal is perturbed.\n\nThe value of tmax,. from (37) and plotted in Fig. 3 is not very \nsensitive to the value of u at values removed from u = 2. The reduction \nin rms width of the impulse response is illustrated in Fig. 4. For wu = \u00a9 \n(the conventional step-index fiber) the value of o/(n1A/c) is 1/V\u00a512 or \n0.289. This is reduced by a factor of 2 for u near 6, and by a factor \nof 4 for u near 3.5. These results are identical to those of Gloge and \nMarcatili.\u00b0\n\nThe shape of the impulse response, given by (39) for wu = 2 and \nby (34) for u away from 2, is plotted in Fig. 2 for several cases of \ninterest.\n\nThe number of modes which can propagate, given by (28) for the \nsquare fiber, is plotted as a function of uw in Fig. 5. For comparison \nthe corresponding quantity for the round fiber from Ref. 10 is also \nplotted. The ratio is 4/7 at wu = \u00a9, and near 2 for u = 2. The approxi- \nmations made here are seen to be good, though not perfect.\n\nWe discuss now some of the results for the perturbed index distribu- \ntions, eq. (1). We recall the solutions have been obtained assuming \n|a,| Ka,or |6| <1.\n\nThe solutions for the specific group delay, given in (31) and (83), \ncontain the quantity Q as a factor in the perturbing term. The factor\n\nQ, given by (82), contains the principal effect of the exponents wu and \nr on specific group delay. Figure 6 shows how Q varies with r for the \nspecial case u = 2. The region very near r = 2 is in question since we \nknow the \u2018\u2018ideal\u2019\u201d\u2019 index distribution differs slightly from u = 2. Else- \nwhere, the results should be significant and may be used in (34), \n(31), and (33).\n\nMore general curves for Q are given in Fig. 7. We observe that \nwhen r > 0 the maximum value of Q is not very dependent on u but \nthe most sensitive region of r (giving largest Q) does depend somewhat \non u. An intuitive feel for the changes in the index distribution which \ncorrespond to some of the curves in Fig. 7 can be obtained by examina- \ntion of Fig. 8. Figure 8 shows the normalized index n versus transverse \ncoordinate (a/a). The curve labeled r = 2 corresponds to the pure \nparabolic distribution. The other curves correspond to 6 = 0.05 with \nvarious values of r in the perturbing term and u always equal to 2.\n\nWe note in I'ig. 7 that, at wu = 2, the value of Q at r = 10 is much \nlarger than at r = \u00a9. This may seem surprising, since a step-index \nchange occurs at (z/a) = 1.0 when r=. Below (2/a) = 1 the \nr = \u00a9 curve in Fig. 8 corresponds to a pure parabolic gradient between \nthe ordinate equal zero and \u20140.95A.\n\nWe also note in Figs. 8 and 7 that dips in the index distribution \nnear (x/a) equal zero (curves for r = \u20140.4 and \u20140.1) yield values of \n|Q| comparable to those for r in the range 4 to 20.\n\nThe above analysis provides an approximate solution for the delay \ndistortion to be expected in a wide variety of graded-index fibers, \nrepresentable by (1) with |a,| \u00ab du.\n\nIn general, gradual tapering of the index between the center of the \nfiber and the outer support provides reduced delay distortion. Only \nin the vicinity of the near-parabolic distribution is the performance \nhighly sensitive to the exact index distribution. The \u2018ideal\u2019 near- \nparabolic distribution provides a potential reduction in delay distortion \nof several hundred times compared to the step-index distribution of \nthe conventional clad fiber. With an accuracy of the order of 5 percent \nin achieving the \u201c\u2018ideal\u2019\u2019 distribution, the reduction in delay distortion \nis on the order of 50.\n\nFig. 8\u2014Normalized index versus transverse coordinate (z/a) for several per- \nturbations of the parabolic index distribution.\n\nIt is a pleasure to acknowledge fruitful discussions with E. A. J. \nMarcatili and D. Gloge.\n\n1. S. E. Miller, U. S. Patent No. 3,434,774, \u201cWaveguide for Millimeter and Optical \nWaves,\u201d issued March 25, 1969. \n2. Nippon Selfoc Co., Ltd., \u201cLight-Conducting Glass Fibers or Fiber Structures \nang ereue on Thereof,\u201d Japanese Patent No. 1,266,521, issued March 8, \n3. T. Uchida, M. Furukawa, I. Kitano, K. Koizumi, and H. Matsumura, \u201cA Light \nFocusing Fiber,\u2019\u2019 IEEE J. Quan. Elec. (Digest of Technical Papers), QE-5, \nJune 1969, pp. 25. \nE. A. J. Marcatili, \u2018\u201cModes in a Sequence of Thick Astigmatic Lens-Like \nFocusers,\u201d\u2019 B.S.T.J., 43, No. 6 (November 1964), pp. 2887-2904.\n\n. S. Kawakami and T. Nishizawa, \u201cAn Optical Waveguide with the Optimum \nDistribution of the Refractive Index with Reference to Waveform Distortion,\u201d \nee Trans. Microwave Theory and Tech., MTT-16, October 1968, pp.\n\n. D. Gloge, EB. L. Chinnock, and K. Koizumi, \u201cStudy of Pulse Distortion in Selfoc \nFibers,\u2019\u2019 Elec. Letters, 8, October 1972, pp. 526-527.\n\n. C. A. Burrus, E. L. Chinnock, D. Gloge, W. S. Holden, T. Li, R. D. Standley, \nand D. B. Keck, \u201cPulse Dispersion and Refractive-Index Profiles of Some\n\n. BE. L. Chinnock, L. G. Cohen, W. S. Holden, R. D. Standley, and D. B. Keck, \n\u201cThe Length Dependence of Pulse Spreading in the CGW-Bell-10 Optical \nFiber,\u2019\u201d\u2019 Proc. IEEE, 61, October 1973, pp. 1499-1500.\n\n. D. Gloge and E. A. J. Marcatili, \u201cMultimode Theory of Graded-Core Fibers,\u201d\u2019 \nBS.T.J., 52, No. 9 (November 1973), pp. 1563-1578.\n\n. D. Marcuse, \u2018\u201cThe Impulse Response of an Optical Fiber With Parabolic Index \nProfile,\u201d B.S.T.J., 62, No. 7 (September 1973), pp. 1169-1174.\n\n. S. D. Personick, \u2018Receiver Design for Digital Fiber Optic Communication \nSystems,\u201d B.S.T.J., 52, No. 6 (July-August 1973), pp. 843-886.\n\n. E. G. Rawson, D. R. Herriott, and J. McKenna, \u201c\u2018Analysis of Refractive-Index \nDistributions in Cylindrical Graded-Index Glass Rods Used as Image Relays,\u201d\u2019 \nAppl. Opt., 9, March 1970, pp. 753-759.\n\nCopyright \u00a9 1974 American Telephone and Telegraph Company \nTue BELL SysTeM TECHNICAL JOURNAL \nVol. 53, No. 2, February 1974 \nPrinted in U.S.A.\n\nLosses and Impulse Response in Parabolic \nIndex Fibers With Square Cross Section\n\nMode coupling is studied in a parabolic index fiber with a lossy boundary \nand square cross section. Statistical deviations of the fiber axis from perfect \nstraightness and random changes of its width are considered as causing \nmode coupling. The excess loss caused by these mode coupling mechanisms \nand the loss penalty incurred for a certain degree of narrowing of the \numpulse response are estimated.\n\nMultimode optical fibers whose cores have parabolic distributions \nof the refractive index,!\u00b0\n\nare of great practical interest for light transmission over long distances, \nsince their delay distortion is much less serious than that of con- \nventional clad fibers.\n\nSince no optical fiber can ever be produced free of random imper- \nfections, it is important to know how statistical irregularities of the \nfiber affect its performance. Random irregularities of the fiber axis \nand random changes of the effective width of the fiber cause coupling \namong its modes. The mode losses are functions of the mode number. \nAbsorption losses tend to affect all modes in the same way. However, \nif we assume that the fiber boundary either consists of an absorptive \nmaterial or is a rough surface that scatters light, we must expect that \nhigher order modes, whose fields reach strongly into the neighborhood \nof the fiber boundary, suffer much higher losses than lower order \nmodes that are confined to the vicinity of the fiber axis. Coupling of \nthe low-order modes to the high-loss, high-order modes increases the\n\noverall waveguide losses. One objective of our study of the effect of \nwaveguide irregularities is thus the determinabion of the excess losses \ncaused by mode coupling.\n\nThe second objective of this study of waveguide irregularities con- \nsists in determining the impulse response of the fiber. In the absence \nof coupling, each mode transports a fraction of the total power at its \ncharacteristic group velocity. Since the group velocities of different \nmode groups are not identical, pulse distortion results.2* Mode \ncoupling has the beneficial effect of improving the impulse response of \nthe fiber. It is thus of interest to determine how much reduction of \nmultimode pulse distortion can be achieved by random bends and \nrandom width changes of the fiber.\n\nThe effect of random bends on parabolic index fibers with circular \ncross section has been estimated in an earlier paper.* Pure diameter \nchanges of a fiber with circular cross section leave modes with different \ncircumferential symmetries uncoupled. Statistical irregularities are \nunlikely to result in pure diameter changes without distorting the \ncircular fiber cross section. However, an analysis of more general \ndistortions of a fiber with nominally circular cross section is difficult \nto perform. For this reason we discuss a fiber with parabolic index \ndistribution (1) but with square cross section. It seems reasonable to \nexpect that the performance of a fiber with square cross section is \nsimilar to that of a fiber with circular cross section. We expect to find \nthe correct order of magnitude of the losses and impulse response of \nthe round fiber by examining its close relative, the fiber with square \ncross section. In particular, it should be possible to assess the relative \neffect of random axis deformations as compared to random width \nchanges. In a square fiber, changes of only one set of opposing walls \nleave groups of modes uncoupled from each other. This situation \ncorresponds to the circular fiber with pure diameter changes that \nleave modes of different azimuthal symmetry uncoupled. By allowing \nboth sets of opposing walls to change their separation randomly, we \nare sure that all modes are coupled to each other. This model corre- \nsponds to a nominally round fiber whose cross section is deformed in \nan arbitrary way that does not conserve the circular symmetry.\n\nll. THE MODES OF THE PERFECT FIBER WITH SQUARE CROSS SECTION \nThe modes of an infinitely extended medium with the distribution\n\nThe parameter a is an arbitrary constant that, in conjunction with A, \ndetermines the transverse dependence of the refractive index distribu- \ntion. However, in the round fiber it is convenient to associate a with \nthe radius of the fiber boundary so that A is the relative difference \nbetween the values of the refractive index on axis and at the fiber \nboundary.\n\nThe square of the refractive index distribution (2) does not follow \nprecisely from (1). However, if one equation is regarded as the precise \ndistribution of the corresponding quantity, the other holds approxi- \nmately provided A is small and we limit r to the range r S a. H, and \nH, are Hermite polynomials of degree p and q, and P is the power \ncarried by the mode. The parameter w is defined as\u00ae (& = wvVeouo)\n\nnok lA \nand determines the radius of the field distribution with p = q = 0. At \nr = w the field has decayed to 1/e of its value on axis. Epq represents \nthe transverse component of the electric field vector. The longitudinal \nfield components are relatively much weaker and are not being con-\n\nsidered. The field (3) is only an approximate solution of Maxwell\u2019s \nequations. The propagation constant of the mode is given as\u00ae\n\nThe modes of the square-law medium are mutually orthogonal and \nsatisfy the relation\n\nSo far, the fiber boundary has been ignored. The mode field (8) is an \n(approximate) solution of the guided-wave problem if we assume that \nthe distribution (2) extends to infinity. However, each mode decays \nvery rapidly outside of a certain region. For a given value of p the\n\nfield oscillates as a function of x passing through p zero crossings. The \nshape of the function\n\nthe oscillatory behavior of the function changes to a rapid decay. \nIf x\u2019 < a the presence of the wall does not interfere appreciably with \nthe field distribution. However, if x\u2019 >a the field distribution is \nseverely altered by the presence of the wall. Since we are assuming \nthat the interaction of the field with the wall causes power dissipation \neither by absorption or by radiation, we consider those modes whose \nfields reach the vicinity of the wall with high field intensity as being \neffectively cut off. By replacing x\u2019 in (9) with a we obtain the condition \nfor the maximum value of p that can be allowed for low-loss modes.\n\nThe coupling coefficients between two modes are defined by the \ngeneral expression\u00ae7\n\nWe assume that f and g are both random functions of z and that \nf/a and g/a are small quantities. The deflection of the optical axis of \nthe square-law medium has a far more important effect on the modes \nthan the corresponding deviation of the fiber boundary. The deflection \nof the fiber boundary that results from the random bends of its axis \nis neglected.\n\nAll other coupling coefficients vanish. The two choices (1 or 0) that \nare indicated under the square-root sign in (14) and (15) belong to \nthe corresponding upper or lower sign of the subscript on the left-hand \nside. Random deformations of the fiber axis couple only neighboring \nmodes.\n\nFor small values of f/a and g/a we can write this expression approxi- \nmately as follows:\n\nAll other coupling coefficients vanish. There are nonvanishing diagonal \nelements in this case. However, diagonal elements couple each mode \nonly to itself. This self-coupling is of no importance if f(z) and g(z) \nhave Fourier spectra with no zero (spatial) frequency component.\n\nP, is the average power carried by the mode labeled \u00bb, \u00bb, is its group \nvelocity, and a, its power loss coefficient. The mode label \u00bb is used as \nan abbreviation for the set of labels p, g. The power coupling coefficient \nhy, is defined as follows :\u00ae\n\nThe coefficient K,, is the factor of the function f(z) or g(z) appearing \nin eqs. (14), (15), (18), and (19). The spatial power spectrum of the \nfunction f(z) [or g(z) ] is defined as\n\nSince the random processes considered here tend to couple each \nmode only to one of its neighbors on either side (in mode label space) \nthe equation system (20) can be converted to a partial differential \nequation whose variables are not only the length coordinate z and \ntime \u00a2 but in addition the two mode labels p and q.? If the number of \nmodes below the effective cutoff value is very large, the set of discrete \nmodes can be regarded as a quasicontinuum. We write\n\n= hog. prdv.a(P prapia =e P 5q) ar hog. p\u2014dn.a(P p_an.a a P 5q) \nSid hog.piatda(Pp,atAq \u2014- P pq) ae hing, p.a\u2014ha(P p,g\u2014ag \u2014 P 5q)\n\nThe last step follows by considering the discrete mode labels as con- \ntinuous variables and replacing differences by differentials. The nota- \ntion h(p) and h(q) serves as a reminder that, according to (14) and \n(15), the coupling coefficients depend only on p if q is held fixed, and \n(18) and (19) show that they depend only on q if p is held fixed. We \nthus obtain the approximate partial differential equation\n\nThe average mode power P is now regarded as a continuous function \nof z, t, p, and g. The group velocity v is a function of p and g. We have \nomitted the loss term. We consider the modes as lossless if the vari- \nables p and g remain below the cutoff values (10) and (11) and as \nhaving infinitely high loss if cutoff is exceeded. This fact can be incor- \nporated into the theory as a boundary condition by requiring\n\nIt has been shown in Ref. 8 how the pulse propagation problem can be \nsolved by means of a perturbation method if the solutions of (24) for \nthe time-independent case are known. We thus consider the trial \nsolution\n\nWe separate this equation into two ordinary differential equations by \nintroducing the separation constant x?:\n\nThe equation system (28) and (29) together with the boundary \ncondition (25) (and an additional one to be discussed later) defines \nan eigenvalue problem. The lowest order eigenvalue oi; has the \nphysical meaning of the steady-state loss of the statistical power \ndistribution.* This quantity is of interest since it determines the \nadditional losses that are caused by the statistical irregularities of \nthe fiber.\n\nFor random deformations of the fiber axis we obtain the power \ncoupling coefficient h(p) from (14) and (21).\n\nWe assume that f(z) and g(z) have identical power spectra so that \nh(q) follows from h(p) by replacing p with g. According to (6) the \ndifference of the propagation constants of adjacent modes can be \napproximated as\n\nThis approximation is independent of the mode numbers. This means \nthat only one spatial frequency (or actually a very narrow range of \nspatial frequencies) of the power spectrum F(Q) is responsible for \nmode coupling. For random axis deformations we have\n\nThe choice of the Bessel function instead of a Neumann function, \nthat would also solve (84), is dictated by an additional boundary \ncondition. Since the partial differential equation (24) can be regarded \nas a diffusion process, we must require that no power diffuses into the \nlowest order mode p = 0 from negative values of p. This requirement \nmeans that dP/dp = 0 at p = 0. The solution (85) satisfies this \ncondition. The solution of (29) is similarly\n\nSince the eigenvalues depend on the labels v and yu, we attach these \nlabels to \u00ab and obtain from (37) and (388) (note, pe = qe)\n\nThe steady-state power loss, the lowest order eigenvalue o1, follows \nfrom (5), (10) (neglecting the term 4), (31), and wi = 2.405\n\nFor random diameter changes we obtain from (18), (21), and (31), \nconsidering that the spacing (in f-space) between adjacent coupled \nmodes is now twice as large,\n\nd { ,dU a _ \ndp E = | sd uw KM) U=0. (43) \nThe solution of this differential equation is \n1 \nU = \u2014 cos (p, np+ \u00a2, 44 \na5 (op, In p + \u00a2) (44) \nwith \na x 1 \nP= Alok KOM) 4 =) \nThe solution of (29) is correspondingly \n1 \nv= A (o, Ing + \u00a2,) (46)\n\nThese solutions have a singular behavior at p = 0 or q = 0. However, \nwe must keep in mind that p and q are really discrete quantities. \nConsidering them as continuous variables is an approximate procedure \nthat can work only for very large values of p or q where the relative \ndifference between adjacent discrete values becomes small. Since \nIn p = 0 for p = 1, we allow p and q to vary only between 1 and p.. \nThe requirement that no power diffuses across the lower limit of the \nrange of the variables imposes the conditions\n\np, as well as p, are solutions of this equation with integer values of \u00bbv. \nSince the values of p, are now known, we obtain the eigenvalue g,, \nfrom (45) and (47)\n\nFor the lowest order eigenvalue, that is, for the steady-state power \nloss coefficient, we obtain with the help of (5) and (81)\n\nThe solution of (51) is not a constant. It depends on the waveguide \nparameters through its dependence on p, = (a/w)?. A plot of pi as a \nfunction of p, is shown in Fig. 2.\n\nThe width of the impulse response of a multimode fiber that is \nlong enough for the steady-state distribution to establish itself is \ngiven by the formula :\u00ae\n\nand V is by definition the difference between the inverse group velocity \nof the modes minus the inverse of the maximum group velocity.\u2018\n\n(p + q). (56) \nThe expression in parenthesis is an abbreviated way of writing \nGu, VG.) = fap [dgGuVG,, (57)\n\nThe integrals extend over the entire range of p and q variables from \neither 0 or 1 to the cutoff value p, = q. Requiring the normalization\n\n2 2 \u20144 \nAig =| Inve + ea [|e + ea || (61) \nThe integrals (57) have the following solutions. For axis deforma- \ntions (u # 1): \n(Gu, VG@1,) = (Gu, V@u1) \n_\u2014- 82Apuu, | 2ui\u20141 6(ui + uf)\n\nEvaluation of (54) with the help of (62) and (63) yields, for random \ndeformations of the fiber axis,\n\nEquation (66) determines the pulse width of an impulse after it has \ntraveled a distance L (LZ must be large enough so that the pulse has \nsettled down to steady state) in the presence of random deformations \nof the fiber axis. The pulse width for uncoupled modes is obtained \nfrom (56)\n\nThe relative improvement of the width of the impulse response caused \nby mode coupling is characterized by the ratio\u00ae\n\na ten \nAT VLK(Q) w \nMode coupling not only shortens the width of the impulse response, \nbut it also leads to excess loss. In order to find out how much excess\n\nloss is associated with a given improvement of the width of the impulse \nresponse, we form the product of (41) with the square of (68)\n\nFor random axis deformations, the product of the square of the im- \nprovement factor with the excess loss is independent of the waveguide \nparameters and the statistics of the random axis deformations.\n\nWe have derived expressions for the steady-state loss and the loss \npenalty of graded index fibers with square cross section for the case of \nrandom axis deformation and random width changes. The most\n\nconspicuous difference between these two types of fiber imperfections \nis the fact that, whereas the Fourier components of the function f(z) \n(describing the fiber axis) at the spatial frequency Q are instrumental \nin the mode mixing process, the Fourier components at twice the \nspatial frequency, 20, determine the mode mixing process in case of \nrandom changes of the width of the fiber. This behavior can easily be \nunderstood. Consider a Gaussian beam of arbitrary width that is \ninjected into the fiber off axis. The beam undulates periodically \naround the fiber axis and also changes its width periodically. The \nundulations around the fiber axis have a period!\n\nwhile the width changes repeat themselves with half that period or at \ntwice the spatial frequency.!! Random displacements of the fiber axis \ncouple to the deflections of the beam from its on-axis position. This \ndeflection is driven by a Fourier component at the spatial frequency\n\n(74) \nThe beam width changes are correspondingly driven by changes in \nthe gradient (width) of the parabolic index medium. It is thus clear \nthat they respond to twice the spatial frequency.\n\nIn order to be able to associate specific rms deviations of the fiber \naxis or rms width changes with fiber loss we have to consider a par- \nticular statistical model. We choose (arbitrarily) a Gaussian correlation \nfunction\n\n& is the rms deviation of the function f(z) and D its correlation length. \nThe power spectrum of f(z) is known to be!\n\nAt \\ = 1 yum wavelength we have a/w = 6.3 or p. = 39.7. The \ndifference between the propagation constant of adjacent modes is, \naccording to (32), 2 = 34.5 cm7!. With 6 = Q we calculate the excess \nloss values at the peak of the power spectrum at the value of the \ncorrelation length given by (78), Dn = 0.041 cm. For random devia- \ntions of the waveguide axis we obtain from (41), (77), and (79) \n(\u00a2 in cm)\n\nIn order to keep the excess loss below 10 dB/km = 2.3 10-> cm\u2122 we \nmust keep the rms deviation of the fiber axis below \u00a2 = 2 X 107\u00b0 cm. \nHowever, this stringent tolerance requirement results from our as- \nsumption that the correlation length of the random irregularities of \nthe fiber axis assumes its worst possible value (78). If, for example, \nthe correlation length happens to be D = 0.5 cm we obtain instead \nof (80)\n\nso that we can now tolerate \u00a2 = 6 X 10\u00b0 cm in order to keep the excess \nloss below 10 dB/km. This example shows that it is impossible to \npredict the excess loss to be expected from a practical square-law fiber \nunless the statistics of its irregularities are known precisely.\n\nFor reasons of comparison we state the corresponding value for \nrandom width changes. In this case the spatial frequency that is \ninstrumental in providing mode coupling is 20 = 69 em~. The worst \npossible correlation length is now Dm = 0.02 cm. From (53) and Fig. 2 \nwith p. = 40 we obtain (\u00a2 in em)\n\nThe tolerance requirements of random width changes appear a little \nless stringent than those of random axis deformations. However, we \nhave already pointed out that the excess loss value depends critically \non the actual statistics of the fiber. Since the excess loss caused by \nrandom axis deviations depends on a different spatial frequency than \nthe excess loss caused by random width changes, a loss comparison \nof the two effects is not possible.\n\nNext we discuss the loss penalty that is incurred for a given im- \nprovement of the width of the impulse response of coupled mode \noperation compared to uncoupled mode operation. The equations (69) \nand (72) show that the loss penalty is independent of the statistics of \nthe fiber irregularities. This feature makes the loss penalty a useful \nquantity. In case of random variations of the fiber axis, the loss penalty \nis even independent of the fiber parameters and is simply a dimension- \nless number. Let us assume that we want to achieve a ten-fold improve- \nment of the width of the impulse response compared to the impulse \nresponse of uncoupled multimode operation. In this case we have \nR = 0.1 and obtain from (69) for random deviations of the fiber axis\n\nThe length L needed to incur this loss and at the same time to achieve \nR = 0.1 depends on the statistics of the irregularities. However, eq. \n(83) tells us that it costs 14 dB in excess loss to achieve a ten-fold \nrelative pulse width improvement.\n\nFor random width changes, the situation is slightly different. Here \nthe loss penalty depends somewhat on the fiber parameters. For the \nvalues used earlier we find from Fig. 4 with p. = 40,\n\nFiber irregularities can be introduced intentionally in order to \nimprove the impulse response. In the conventional fiber with a round \ncore of constant refractive index that is surrounded by a cladding \nwith constant index, the loss penalty for pulse distortion improvement \ncan be reduced (in principle avoided) by tailoring the shape of the \npower spectrum carefully. The reason that the shape of the power \nspectrum has an influence on the loss penalty is explained by the \nobservation that the spacing (in 6-space) between adjacent modes of \nthe conventional fiber is dependent on the mode number, so that a \nband of spatial frequencies of the power spectrum takes part in the \nmode coupling process.\n\nIn case of the parabolic index fiber, only one spatial frequency \n(or actually a narrow range of spatial frequencies) is responsible for \nmode coupling. The shape of the power spectrum is thus immaterial, \nonly its value at the spatial frequency \u00a9 enters into the picture. The \nexpressions (69) and (72) show that the loss penalty of the parabolic\n\nindex fiber is independent of the power spectrum. No loss advantage \nis to be gained by using especially shaped power spectra. One might \nthink that an advantage could be gained by departing from the \nsquare-law index profile in order to change the mode spacing and \nsample more of the power spectrum. But as soon as the index distribu- \ntion deviates slightly from the parabolic profile the uncoupled impulse \nresponse becomes much broader. The mode coupling mechanism would \nnow have to work against a far less favorable (uncoupled) impulse re- \nsponse so that it seems unlikely that an advantage can be gained \nin this way.\n\nFinally, we consider an example of pulse width reduction by random \nirregularities. We can introduce intentional deviations of the fiber \naxis from perfect straightness in order to cause mode coupling. Since \nthe coupling process must be random, we could use deformation func- \ntions f(z) and g(z) that are sinusoidal in shape but have a random \nphase. This introduces a power spectrum centered around the spatial \nfrequency of the sinusoidal process having a finite width. Instead of \npursuing this idea further, we assume that we have somehow created \nan axis deformation whose power spectrum reaches beyond the fre- \nquency 2 of (32). For simplicity, and to have a definite case in mind, \nwe choose\n\nThis power spectrum is flat from zero spatial frequencies to a cutoff \nvalue of 6 = 20 and zero for 6 > 20. The rms deviation \u00a2 of the fiber \naxis from a straight line appears in (85). Using the fiber parameters \n(79) we obtain from (68) (\u00a2, LZ in cm)\n\nA ten-fold improvement of the width of the impulse response \n(compared to the uncoupled case), R = 0.1, over a length of \nL = 1 km = 10\u00b0 cm requires an rms deviation of the fiber axis of \n& = 2.2 X 10-* cm. We already know that we pay for this improve- \nment of the impulse response with a loss penalty of 14 dB. Very slight \nrandom deviations from perfect straightness are already very effective \nin providing mode coupling and improving the width of the impulse \nresponse.\n\nFor random width changes we have to allow for a wider power \nspectrum. Letting the power spectrum again extend twice as far as \nthe effective spatial frequency, 2Q in this case, forces us to divide \n(85) by 2. We thus find from Fig. 3 and (71)\n\nDz \nH= n(x). (90) \nThe quantum mechanical treatment of this problem leads to an ex- \npression for the \u201cenergy\u201d EF of the ray that has the form\"\n\nE=- ae (91) \nWe define the \u2018turning point\u2019\u2019 of the light rays associated with the \nwave field (88) by the condition that p,, which is proportional to the \nslope of the light ray, must vanish. That means that the ray trajectory \nis tangential to the optical axis as the rays turn back in their path \nleading them away from the axis. Using p, = 0 and equating (90) \nand (91) we find the following condition for the turning point:\n\nSubstitution of (89) and (98) into (92) leads with the help of (5) to \nthe formula (9) for the turning point.\n\nThe physical argument advanced here serves the purpose of defining \nthe range in which the Hermite polynomial has an oscillatory behavior. \nThis range is given by\n\nOutside of this range the Hermite polynomial grows monotonically to \ninfinite values. However, since the Hermite polynomial enters the \nmode field (88) only as a product with a Gaussian function, the mode \nfield decays rapidly without oscillation outside of the range given \nby (94).\n\n1. S. E. Miller, U.S. Patent No. 3,434,774, \u2018\u201c\u2018Waveguide for Millimeter and Optical \nWaves,\u201d issued March 25, 1969. \n2. D. Gloge and E. A. J. Marcatili, \u2018\u2018Multimode Theory of Graded-Core Fibers,\u201d\u2019 \nB.S.T.J., 52, No. 9 (November 1973), pp. 1563-1578.\n\n3. D. Marcuse, \u2018The Impulse Response of an Optical Fiber With Parabolic Index \nProfile,\u201d B.S.T.J., 52, No. 7 (September 1973), pp. 1169-1174.\n\nD. Marcuse, \u201cLosses and Impulse Response of a Parabolic Index Fiber with \nRandom Bends,\u201d B.8.T.J., 62, No. 8 (October 1973), pp. 1423-1437.\n\n. A. W. Snyder, \u201cCoupled Mode Theory for Optical Fibers,\u201d J. Opt. Soc. Am., \n62, No. 11 (November 1972), pp. 1267-1277.\n\nD. Marcuse, \u201cCoupled Mode Theory of Round Optical Fibers,\u2019\u201d\u2019 B.S.T.J., 52, \nNo. 6 (July-August 1973), pp. 817-842.\n\nD. Marcuse, \u201cPulse Propagation in Multimode Dielectric Waveguides,\u2019\u2019 B.S.T.J., \n61, No. 6 (July-August 1972), pp. 1199-1232.\n\nCopyright \u00a9 1974 American Telephone and Telegraph Company \nTue Be. SysteEM TECHNICAL JOURNAL \nVol. 53, No. 2, February 1974 \nPrinted in U.S.A.\n\nTransverse Coupling in Fiber Optics \nPart I: Coupling Between Trapped Modes\n\nTwo perturbation formulas have been proposed to evaluate the coupling \nbetween parallel optical waveguides, one involving a line integral and the \nother a surface integral. They are shown to be identical. The former \nexpression 1s preferred because of its greater simplicity. The case of two \nparallel lossy dielectric slabs is discussed as an example.\n\nThere has been a renewed interest during the last few years in the \nevaluation of the transverse* coupling between two parallel open wave- \nguides in connection with integrated optics circuitry? and long- \ndistance optical communication by bundles of glass fibers.\n\nThe coupling between two open waveguides can be obtained by \nreplacing the field of one waveguide by an equivalent current and \nevaluating the perturbation caused by this current on the other \nwaveguide.\u2018 A more direct and slightly more general (but essentially \nequivalent) derivation, based on Lorentz\u2019s reciprocity theorem, is given \nin this paper. A related result, applicable only to lossless fibers, has \nbeen used to evaluate the coupling between dielectric rods with circular \ncross section.\u00ae The perturbation formula derived in this paper involves \nan integral along a contour located between the two waveguides. A \nseemingly different perturbation formula has been recently proposed \nthat involves a surface integral over the cross section. The two \nformulas are shown to be in fact identical. We will not discuss in \ndetail other coupling formulas such as the ones proposed in Refs. 7 \nor 3. In Ref. 7, the coupling is obtained by applying the Rayleigh-Ritz\n\n\u201cThe word \u201ctransverse\u201d is used here to distinguish the problem of two dielectric \nwaveguides lying side by side, where the transfer of power takes place in transverse \ndirections, and the axial coupling between two waveguides placed end to end, where \nthe transfer of power takes place along the z axis (the later arrangement is discussed, \nfor instance, in Ref. 1).\n\noptimization technique to a variational expression. The formula ob- \ntained by this method involves surface integrals and is rather com- \nplicated. In Ref. 3, analytic expressions were obtained for the coupling \nbetween two identical rectangular fibers that agree well with numerical \ncalculations based on the exact field equations. The approach, how- \never, is restricted to fibers with a particular geometry.\n\nLet the time dependence of the sources be denoted exp (\u2014xt). \nMaxwell\u2019s equations are, in a source-free region with scalar permit- \ntivity \u00ab and permeability u,,\n\nVv X E = KUoH, (la) \nV XH =\u2014x\u00abeE. (1b) \nAny two solutions (E, H) and (E,, H,) of eq. (1) satisfy the relation \nV-J =0, (2a)\n\nIntegrating over a volume V, Lorentz reciprocity theorem is obtained \n[, XH - EX H,)-d8 = 0, (2c)\n\nwhere S denotes the surface enclosing V, and dS a vector normal to \nS pointing outward with magnitude dS. Let the medium be uniform \nalong z, that is, e be independent of z. If\n\n(E, H) = (E., Ex, H., Ht) exp (yz) (3) \ndenotes a solution of Maxwell\u2019s equations, then \n(E*, H+) = (\u2014E,, Ey, Hz, \u2014 Hk) exp (\u2014 72) (4)\n\nLet us now consider two open waveguides a and b uniform along \nthe z-axis, and let S be the surface S, + Sz; + Cadz shown in Fig. 1. \nThe field (E,, H.) in eq. (2) is taken as the field of a trapped mode on\n\nwaveguide a in the absence of waveguide b. The dependence of (E., H.) \non 2 is denoted exp (y.z). The field (E+, H*) is the adjoint field of a \ntrapped mode of the two coupled waveguides, with an exp (\u2014TIz) \ndependence on z. Letting the spacing dz between S; and S, tend to \nzero, eq. (2) becomes\n\na \nwhere dC, is a vector perpendicular to the contour C., pointing out- \nward. Proceeding similarly for waveguide b we obtain \n(\u00bb\u2014 1) f (By x HY \u2014 BY x Hh) -dS, \nb \n= = (E, X H+ \u2014 E+ X H;)-dCs. (5b) \nCo\n\nBecause the coupling between the two waveguides is small, we can \nassume that the field E, H at plane z = 0 is the sum of the fields of \nthe two waveguides, that is,\n\nSubstituting these expressions, eqs. (6), in eqs. (5a) and (5b) we \nobserve that the cross terms can be neglected on the left-hand sides \n(l.h.s.) because (Es, Hz) is small when (E,, H.) is large, and vice \nversa. On the right-hand sides (r-h.s.), on the contrary, only the \ncross terms remain, as we can verify by applying Lorentz reciprocity \ntheorem to each waveguide. Multiplying together the l.h.s. and r.h.s. \nof eq. (5a) and (5b) the desired equation for I is obtained.\n\nBecause the coupling takes place only if yz ~ ys, the coupling c \n(resp. cy) is independent of the choice of the contour C, (resp. Cy) as \nlong as it surrounds only one waveguide. By choosing the two contours \nas coincident in the region where the fields of the two trapped modes \nhave a significant intensity and using eq. (4), we find that c, is equal \nto cy. It is shown in the appendix that our result, eq. (6), can be \nexpressed in the form given in Ref. 6. The expression, eq. (6), however, \nis simpler to evaluate.\n\nLet us now assume that the contours C., Cy coincide with the y \naxis and are closed at infinity where the fields vanish. The general \nexpression, eq. (6), becomes\n\nLet us specialize eq. (7) to symmetrical stratified dielectric wave- \nguides such as the slabs shown in Fig. 2. The fields are assumed to \nbe independent of y. For TE waves the electric field has only one\n\nthe fields H, and E, of the uncoupled waveguides being evaluated at the \nsame point between the two waveguides.\n\nIf the waveguides are homogeneous dielectric slabs of thickness 2d \nand complex permittivity \u00ab we have\n\nwithin the slabs (obvious changes in the origin of the x axis were \nmade). In eqs. (10a) and (10b) we have defined\n\n(See, for instance, Ref. 6.) Substituting EH from eqs. (10a) and (10b) \nin eq. (9) we obtain, using eq. (12),\n\nwhere D denotes the spacing between the slabs. This expression \ncoincides with the result given in Ref. 6 when appropriate changes of \nnotation are made.\n\nLet us now make a general comment. The coupling formula, eq. \n(6), rests on the existence of a divergenceless quantity, the vector J \nin eq. (2a). Coupling formulas similar to eq. (6) can be derived from \nother wave equations. For the case of the scalar parabolic wave \nequation\u00ae applicable to the propagation of radio waves in atmospheric \nducts,* the vector J has components\n\nThe above expression for J can be obtained by analogy with the \nequivalent quantum mechanical problem.\u00b0\n\nIn conclusion, we have derived a simple coupling formula which is \nmore general than previous similar expressions\u2018:> because it is appli- \ncable to lossy fibers. In order to evaluate explicitly the coupling, one \nneeds to know the normalized field of each waveguide, in the absence \nof the other, along some line located between the two waveguides. \nFor slabs and rods with circular cross section, exact solutions are \navailable. In general, however, we have to resort to numerical tech- \nniques or to measurements made at a convenient wavelength on a \nscaled version of the open waveguide. In asecond part of this paper,\u201d \nwe will apply eq. (6) to mode-selecting systems.\n\n* A similar equation is applicable to anisotropic fibers that have small transverse \nvariation of permittivity.\u2019 Note that, in this approximation, a curvature of the fiber \naxis is equivalent to a constant gradient of refractive index.\n\nThe purpose of this appendix is to show that for lossless fibers the \ncoupling formulas given in Refs. 4 and 6 coincide. \nLet (E, H) denote a field in free space\n\n1 \nV X H = \u2014x\u00abe,E, (14) \nand (Es, Hs) a field in a dielectric with permittivity e(r) \nV X Es = \u00abuoHs, \nX Eo = kyuoHs (15)\n\nin any source-free volume V bounded by S. Let now the surface S \nbe the surface S, + S; + Csdz shown in Fig. 1, (Es, Hs) be the field \nof a trapped mode of waveguide 6 with an exp (yz) dependence on a, \nand (E, H) be the adjoint field (Ez, Hz) of a trapped mode of wave- \nguide a, with an exp (\u20147az) dependence on z. The field (Ez, Hi) \nsatisfies eq. (14) inside the surface S that we have just defined. If the \ntwo trapped modes are degenerate, that is, if yz = yo, the contribu- \ntions of the two surfaces S; and S; on the l.h.s. of eq. (16) cancel out. \nTherefore, letting dz tend to zero, eq. (16) becomes\n\nA similar relation can be obtained for waveguide a. Our coupling \nequation, eq. (6), can therefore be written in the form given in Ref. 6, \nexcept for the fact that in eq. (6) E and E, represent fields at the \nsame frequency. In Ref. 6 the field E7 is defined at the opposite \nangular frequency \u2014x, that is, EZ is replaced by Ez\u201d, where the asterisk \ndenotes complex conjugation. For lossless fibers this difference is \nunimportant because E7 can be assumed real.\n\n3. E. A. J. \u2019 Mavontili \u201cDielectric Rectangular Waveguide and Aaa a \nfor Integrated Optics,\u201d B.S.T.J., 48, No. 7 (September 1969), p\n\n4, J. A. Arnaud, \u201cGeneral Properties of Periodic Structures,\u2019 Sections B and E, in \nCrossed Field Microwave Devices, Vol. 1, E. Okress ed., New York: Academic \nPress, 1961.\n\n.R. Vanclooster and P. Phariseau, \u201cThe Coupling of Two Parallel Dielectric \nFibers,\u2019 Physica, 7, June 1970, pp. 485 and 501.\n\nD. Marcuse, \u2018The Coupling of Degenerate Modes in Two Parallel Dielectric \nWaveguides,\u201d B.S.T.J., 50, No. 6 (July-August 1971), pp. 1791-1816.\n\n. M. Matsuhara and N. Numagai, \u201cCoupling Theory of Open-Type Transmission \nLines and its Application to Optical Circuits,\u201d Electron. Commun. Japan, 564, \nApril 1972, p. 102.\n\nJ. A. Arnaud, tBierehowonality Relations for Bianisotropic Media,\u201d J. Opt. Soc. \nAm., 63, February 1973, p. 238.\n\n. Vv. A, Fock, \u201cTheory of Radio-Wave Propagation in an Inhomogeneous Atmo- \nsphere for a Raised Source,\u201d\u2019 Bull. Acad. Sciences de l\u2019URSS, s\u00e9r. phys. 14, \nNo. 1, p. 70 (1950). In Russian. Translation in V. A. Fock, \"Electromagnetic \nsean and Propagation Problems, Oxford: Pergamon Press, 1965, Chapter\n\n10. J. at Arnaud, \u201c\u2018Transverse Coupling in Fiber Optics, Part II,\u2019\u2019 to appear in \nBS.T.J., 66, No. 4 (April 1974).\n\nCopyright \u00a9 1974 American Telephone and Telegraph Company \nTue Bet System TECHNICAL JOURNAL \nVol. 53, No. 2, February 1974 \nPrinted in U.S.A.\n\nPerformance Models of an Experimental \nComputer Communication Network\n\nThis paper reports the results of a performance study of an experimental \ncomputer communication network. The network is currently being designed \nand butlt in order to test concepts and techniques that may find future \napplication. The network consists of synchronous digital transmission \nlines connected in loops to a Central Switch. User traffic enters the system \nthrough multiplexers connected to the synchronous lines. The Central \nSwitch has the two-fold function of routing and controlling traffic.\n\nTwo multiplexing techniques were examined, Demand Multiplexing \n(DM) and Synchronous Time Division Multiplexing (STDM). In both \ntechniques, user messages are blocked into fixed size packets, prior to \nmultiplexing on the line. The synchronous line can carry these packets at a \nmaximum rate of 4000 packet slots per second. In STDM each terminal \nas assigned a packet slot which recurs periodically. In contrast, for DM, \npackets are multiplexed on the line asynchronously into unoccupied packet \nslots. Alternative implementations of the DM technique were studied, one \nwhere each terminal transmits and receives at a maximum rate of 4000 \npackets per second and another where the maximum rate is 2000 packets \nper second.\n\nAs part of its message-handling function, the Central Switch buffers \nmessages in transit. This allows User Terminals to transmit and receive \nmessages with a degree of independence from one another. However, the \nterminals\u2019 strategy affects the amount of storage required in the Central \nSwitch. In order to prevent the loss of information when there is insufficient \nbuffering, there ts a mechanism to inhibit traffic from User Terminals \nwhen the Central Switch buffer ts near overflow. Due to thts control of \ntraffic, there ts a relationship between the amount of data that flows through \nthe switch and the amount of buffering in the switch.\n\nSimulation results showed that there was little difference in delay \nperformance between the two implementations of DM. However, an analysis\n\ncomparing DM and STDM showed a great difference in performance for \nall but the very heaviest line loadings. This difference increases as the \nnumber of terminals sharing the T1 line increases.\n\nOur study concentrated on two aspects of buffering in the Central Switch. \nWe examined the relationship between throughput and the amount of \nstorage available in the switch. The results of a simulation study showed \nthat throughput can be quite high for all but minimal storage in the switch. \nMoreover, a strategy that dedicates buffers does quite well compared to \ncommon buffering. The second aspect of the study concentrated upon the \nUser Terminal\u2019s strategy. Since each terminal acts tndependently, there \nmay be strategies that make particularly high demands upon storage \ncapacity in the Central Switch. An analysis showed that at the loadings \nwhere the system would be expected to operate, the user strategy in trans- \nmitting and receiving messages has little effect.\n\nAn experimental computer communication network is currently \nbeing designed and built. The function of this network is to provide a \nflexible communication medium between computers, users, and pe- \nripheral devices. The network can accommodate sources with varying \ninput-output rates and varying activity. Many of the components of \nthe system employ techniques that are new. In order to gain insight \ninto the operation of these components and thereby aid in design \ndecisions, mathematical models were developed. The study of these \nmodels involved both analysis and simulation. The results are pre- \nsented in the form of sets of curves.\n\nThe system under study consists of several T1 carrier lines,* con- \nfigured as loops, connected to a Central Switch (see Fig. 1). The \nsystem is accessed through Terminal Interface Units (TIU) connected \nbetween User Terminals and the T1 line. In addition to forming an \ninterface between the user and the T1 line, the TIU also does signaling. \nThis signaling plays a role in switching calls and controlling the \ntraffic flow.\n\nThere may be a wide variation of users accessing the system, ranging \nfrom Teletypes' to high-speed computer systems. The switch receives \nmessages from all terminals and delivers messages to all addressed \nterminals so that any terminal in the system may communicate with\n\n\u201cThe T1 carrier line is a digital synchronous short-haul transmission system \noperating at 1.544-Mb/s rate.\n\nany other terminal. All data pass through the switch even when two \nterminals are on the same T1 line.\n\nThe T1 line operates at a rate of 1.544 X 10\u00ae b/s. For purposes of \nsynchronization and timing, the bit flow is divided into frames of 193 \nbits, with a flow of 8000 frames per second. The multiplexing arrange- \nment in the system under study is such that a \u201cnetwork frame\u2019 \nconsists of two adjacent T1 frames. Figure 2 indicates schematically \nhow the 386 bits of the pair of T1 frames are allocated. The 50 bits \nrequired for framing and timing are part of the operation of the T1 \ncarrier system. The assignment of the remaining 336 bits in the net- \nwork frame is peculiar to the system under study.\n\nUser data are blocked into 256-bit packets and multiplexed on the \nline. Twenty-four bits of header information are attached to these \ninformation packets. (In the sequel we shall use the term \u201c\u2018packet slot\u201d \nin referring to this 280-bit block assigned to data and header.)\n\nTwenty-four of the 336 bits are used to carry signal packets. Signal \npackets convey control and routing information between the TIU and \nthe switch. The remaining 32 bits of the frame pair are used for error \ndetection in order to insure the integrity of the information in the \nsignal and data packets.\n\nFrom the foregoing we see that the information-carrying capability \nof the T1 loop is 4000 packets per second, each packet bearing 256 \ndata bits, yielding a total information capacity of 1.024 Mb/s. There \nare many strategies that can be used to divide this capacity among \nthe terminals connected to the loop. We shall evaluate the performance \nof two strategies, Synchronous Time Division Multiplexing and \nDemand Multiplexing. In Synchronous Time Division Multiplexing \n(STDM), each User Terminal is assigned a particular packet slot \nwhich recurs periodically. The terminal may multiplex data into its \nslot and receive data only in this same slot. For example, if there are \nten terminals on the Tl loop and each terminal receives the same \nservice, a particular terminal may multiplex packets on the line at a \nmaximum rate of 400 packets per second. The time between packet \nmultiplexing for these terminals is a constant 1/400 second.\n\nIn Demand Multiplexing (DM), packet slots are not assigned to a \nparticular terminal. If a terminal has a packet to transmit to the \nswitch, it inserts the packet into the first slot that is empty. Thus, \nunlike the STDM system, the flow of packets into the switch has no \nparticular ordering as to originating terminal. So that the switch can \nsort packets according to their originating terminal, each packet has \nan address label in its 24-bit header. Similarly, information packets \ngoing from the switch to the terminal are not ordered and a header \nis required for each packet. Furthermore, each TIU must be able to \nrecognize packets addressed to it. As we shall see, the number of bits \nrequired for addressing is relatively small.\n\nOnce a packet has been multiplexed on the loop either from the \nswitch or from a terminal, it has priority over incoming traffic until\n\nit reaches its destination. A terminal must wait for an empty data \npacket slot before it can place a waiting packet onto the line. As in \nthe STDM, the implementation also allows a terminal to place an \noutgoing packet into a slot from which it is removing an incoming \npacket.\n\nWe consider two implementations of the DM system, which corre- \nspond to the maximum speed at which terminals can transmit or \nreceive. In the adjacent slot seizure implementation, terminals can \ntransmit and receive at a 4000-packet-per-second rate. We consider \nan alternate implementation where the terminal is constrained to \noperate at a 2000-packet-per-second rate. In this case, a terminal can \nonly write into or read from alternate packet slots.\n\nA major component of the system is the Central Switch. The function \nof the switch is to route and control the flow of information. All \nmessages generated at User Terminals pass through the switch where \nthey are passed on to their destination terminals. Now the operation \nof the system (see Section V) is such that, as it may not be possible to \ndeliver a message to its destination immediately, messages are tempo- \nrarily stored in the switch. Also, destination terminals have some \ncontrol over the way that these stored messages are read out of the \nswitch\u2019s buffer.\n\nThe storage capability of the switch is not unlimited; therefore, \nthe flow of information packets into the switch must be controlled. \nThe switch does this by informing terminal TIU of the amount of \nstorage currently available in the switch. The terminal does not \ntransmit information packets when there is no room in the switch, \nbut holds them until storage is available.\n\nAs mentioned earlier, models of the system were studied in order to \ngain insight into performance and thereby guide design decisions. The \nmodels studied are approximations to actual system operation. We \nfelt that the study of more exact, hence more complicated, models \nwould have involved far more time and effort, without a corresponding \nincrease in insight.\n\nWe study the performance of multiplexing techniques on the loop \nas measured by message delay. In the switch we study packet storage \nrequirements from two points of view, throughput and user strategy. \nSince the switch inhibits the flow of information when the storage in \nthe switch is used up, there is a relationship between throughput and \nstorage capacity. We also study the effect of different user readout \nstrategies on switch storage requirements.\n\nAs a guide to the reader, we pause to summarize the main body of \nthe paper before plunging into details. In Section III, analytical and \nsimulation approaches to the loop multiplexing problem are presented. \nSection IV is devoted to a discussion of our results on loop multiplexing. \nThe relationship between storage capacity in the switch and through- \nput is considered in Section V. The results of a simulation study of \ncapacity and throughput are presented in Section VI. In Section VII \nwe consider the effect of a user\u2019s strategy on storage requirements in \nthe switch. The results of this study are presented in Section VIII.\n\nAlthough the analytical and simulation techniques used in our study \nare not restricted to a particular message distribution, we concentrated \non the case where 30 percent of the messages are 32 packets long \n(8192 bits) and the remaining messages are one packet in duration \n(256 bits). This message distribution was our best guess at the actual \ndistribution of messages in the system and reflects the fact that most \nterminals will, in fact, be computers. In the sequel we use the term \nvariable message length to designate this distribution. The case where \nall messages are one packet in duration was also studied to some \nextent. In referring to this latter distribution we use the term constant \nmessage length.\n\nThe results of our studies of loop multiplexing are presented in \nSection IV. Simulation results for Demand Multiplexing indicate \nlittle difference in performance between alternate and adjacent slot \nseizure (see Figs. 6 and 7). The simulation was carried out for the \nvariable message length distribution which consists of a large propor- \ntion of long messages. One would expect this distribution to be es- \npecially sensitive to the minimum time required to transmit and \nreceive these long messages. In contrast, for the constant message \nlength distribution, these maximum speeds, 2000 packets per second \n(alternate slot seizure) or 4000 packets per second (adjacent slot \nseizure), should have much less effect since the time to transmit a \nsingle packet is the same for both.\n\nAnalytical results show, not unexpectedly, that Demand Multi- \nplexing yields better performance than Synchronous Time Division \nMultiplexing (see Fig. 8). Further, as the number of terminals served \nby a loop increases so also does the advantage of Demand Multiplexing \n(see Fig. 9). However, as the loading for a particular loop configuration \nincreases, the difference in performance between DM and STDM \ndecreases (see Fig. 8).\n\nResults on information storage in the switch are presented in \nSections VI and VIII. Our results indicate that, for all but minimum \nstorage allocation, storage in the switch does not markedly affect \nthroughput (see Figs. 12 and 13). The study also showed that, for the \nmessage distributions we considered, little is gained by dynamically \nallocating storage in the switch, as it is needed, holding nothing in \nreserve. Indeed, in certain circumstances, a static storage assignment \ndoes better simply because a static assignment insures reserves in \nthe switch.\n\nOur study showed that, for the loadings under which the system \nmay be expected to operate, the effect of user strategy on switch \nstorage requirements is not pronounced (see Figs. 14 and 15).\n\nTwo techniques for multiplexing data on the line are under con- \nsideration, Synchronous Time Division Multiplexing and Demand \nMultiplexing. In this section we shall present models designed to \nevaluate the performance of each of these techniques. These models \nare studied using both mathematical analysis and simulation. Simula- \ntion is necessary in situations where mathematical analysis is not \npossible.\n\nA basic consideration in the design of the system is the response \ntime to interactive users. An important component in this response \ntime is message delay. We define message delay to be the time elapsing \nbetween the arrival of a message at a User Terminal and the departure \nof the last packet of the message from the terminal. Message delay is \nthe criterion that we use to evaluate the multiplexing techniques \nunder study.\n\nWe assumed that messages arrive at the User Terminals at a Poisson \nrate, and that the entire message arrives instantaneously. One would \nencounter this sort of behavior when a computer outputs directly \nfrom its memory to the loop, since the operation of the computer is \nat a much higher speed than the operation of the loop.\n\nIn both of the system configurations under study, the message delay \nmay be broken up into two components, queuing delay and multi- \nplexing delay. Recall that messages arrive at the station at a Poisson \nrate. Since it takes a nonzero amount of time to multiplex each message, \nthere is a nonzero probability that when a message arrives at the \nstation it must wait until previously arrived messages have been \nmultiplexed onto the line. Once all prior messages have been multi- \nplexed it takes additional time to multiplex the newly arrived message.\n\nThe problem of determining message delay for Synchronous Time \nDivision Multiplexing and Demand Multiplexing with adjacent slot \nseizure is mathematically tractable. In order to study message delay \nin the DM case with alternate slot seizure, simulation is required.\n\nA sketch of the loop model is shown in Fig. 3. N terminals are \nconnected to the loop. The flow of data is unidirectional around the \nloop and is shown as counterclockwise in Fig. 3. The first terminal \nafter the switch is labeled terminal number 1, the second terminal \nnumber 2, and so on. Messages arrive for multiplexing at a terminal \nat a rate of \\ messages per second. We also assume that messages \nflow from the switch to each terminal at a rate of \\ messages per \nsecond. The result is that the volume of traffic flow around the loop \nis symmetric. The total traffic flow from the switch to the terminals \non the loop is NA messages per second. In the case of Demand Multi- \nplexing this flow of return messages affects the operation of the loop. \nWe shall ignore the interaction between the loop and the rest of the \nsystem by assuming that return message flow is Poisson. This assump- \ntion makes analysis possible and considerably simplifies simulation. We \nshall return to a consideration of this assumption after we present \nour models.\n\nAs we have seen, the bit flow on the T1 loop is formated so that \nslots, into which information packets can be inserted, flow at a rate of \n4000 per second. For Synchronous Time Division Multiplexing, each \nof these packet slots are assigned to particular terminals on a periodic \nbasis. If there are N terminals connected to the T1 loop and each \nterminal is accorded equal treatment, then a packet slot is available \nevery T. = NT, seconds, where T, is the duration of a packet slot. \nIn the sequel we shall refer to 7\u2019. as the cycle time. For each terminal, \nwe take the end of one cycle and the beginning of the next to be the \nend of the packet slot assigned to that terminal. We assume that a \nterminal may always write into its assigned slot even if it is simul- \ntaneously reading from the slot.\n\nIn order to develop an expression for the delay encountered by a \nmessage, let us assume that a message consisting of mzi1 packets \narrives at a terminal whose buffer is empty, i.e., all previously arriving \nmessages have been transmitted. If the message arrives w seconds \nbefore the end of a cycle, then a total of w + (mz41 \u2014 1)T. seconds \nelapse before the entire message is transmitted. Now if previous \nmessages have not been transmitted, a newly arrived message suffers \nqueuing delay as well as this multiplexing delay. For the purposes of \nanalysis we categorize the packets of previously arrived messages into \ntwo classes: packets held over from previous cycles and packets that \nhave arrived during the present cycle in the time interval T, \u2014 w. \nWe may write the total delay queuing and multiplexing as:\n\nIn eq. (1), gis the number of packets remaining from previous cycles, \nLis the number of messages arriving in the interval T, \u2014 w, and m; \nis the number of packets in the ith of these L messages. The mean \nvalue of d; is shown in the appendix to be\n\nd= T.(m 5) tag ar (2) \nwhere m is the average message length in packets. Higher moments of \nd; can be found since, in eq. (1), the terms g7., Te )o#41 mi + w, and \n(mr41 \u20141)T. are independent random variables whose moment- \ngenerating functions can be calculated (see the appendix). Expressions\n\nfor the moment-generating function of di and for the mean-square \nvalue of d; are given in the appendix.*\n\nWe now consider two implementations of Demand Multiplexing, \nadjacent slot seizure and alternate slot seizure. With adjacent slot \nseizure, a typical sequence of information slots leaving the switch \nmight look as shown in Fig. 4. For purposes of explanation in Fig. 4 \nwe assume messages are either three packets long or one packet long. \nThe numbers in the slots correspond to the destination of the packet. \nNo number in a slot indicates that it is empty. When the first three \nslots shown in Fig. 4 pass terminal 1, it is blocked. Terminal 1 may \ninsert an information packet into slot 4 and into successive slots up to \nslot 10 when it is again blocked until slot 11. Terminal 1 also removes \npackets from slots 7 and 9. Terminal 2 removes the packets from slots \n1, 2, and 3 and may insert information packets into these slots. \nTerminal 2 will be blocked when slots 10, 13, 15, 16, and 17 pass. \nTerminal 2 will also be blocked by terminal 1, if terminal 1 multiplexes \npackets onto the lines. The same rules apply to all of the other termi- \nnals on the loop. A terminal is free to insert data into empty slots and \nslots from which it removes data. Once an information packet has \nbeen inserted into an empty slot, it has priority over any other incom- \ning packets.\n\nAlternate slot seizure is similar except in one important respect. \nSince the terminal cannot receive nor transmit on adjacent information \nslots, it is limited to a maximum rate of 2000 packets per second. A \ntypical flow of information is indicated in Fig. 5. Terminal 1 is blocked \nin slots 1, 3, and 5 but may transmit in slots 2 and 4. If terminal 1 \nbegins by inserting a packet in slot 8, the next slot that is available to \nit is slot 11. These same rules apply to all of the other terminals in \nthe loop.\n\nThe problem of message delay for Demand Multiplexing with \nadjacent slot seizure has received considerable attention recently.?~+ \nExpressions for message delay that are relevant to our study can be \nfound in Ref. 5. In order to make clear the assumptions that led to \nthese expressions we shall sketch the analysis.\n\nBasic assumptions of our study are that each terminal on the \nloop receives as much traffic as it transmits (see Fig. 3) and may \nwrite into slots containing packets addressed to it. Therefore, each\n\nterminal \u201csees\u201d the same traffic volume, (N \u2014 1)\\ messages per \nsecond. The flow of traffic past each terminal consists of alternate \nbusy and idle periods. Messages are multiplexed into line idle periods \nand are blocked by busy periods.\n\nThe probability distribution of message delay depends upon the \ndistributions of the line busy and idle periods. In order to find these \ndistributions, a basic assumption about the nature of the traffic flow \nout of the switch is necessary. We assume that the line busy and idle \nperiods out of the switch are caused by the Poisson arrival of messages \nat the switch. This is not difficult to justify when there is light loading \non the loops connected to the switch. Under light loading, messages \narriving at User Terminals encounter little blocking and are conveyed \nimmediately to the switch. Message arrival at the terminals is Poisson. \nFor the message lengths and loadings we shall consider, the time \nbetween message arrivals is large compared to a slot time so that the \ndiscretization of message flow on the loop has little effect. As loading \nincreases, the situation is less clear. However, messages arrive from all \nof the loops connected to the switch, tending to randomize \nmessage flow.\n\nA line busy period at the output of the switch is initiated by a \nmessage arrival, which under the Poisson assumption is instantaneous. \nThe busy period is lengthened if another message arrives while the \nprevious message is being transmitted. The duration of a busy period \nis the same as the duration of the busy period of an M/G/1 queue\n\nfor which results are well known.* Furthermore, under the Poisson \nassumption, the interval between message arrivals has a negative \nexponential distribution. Since each terminal sees (NV \u2014 1)\\ messages \nper second, the duration of a line idle period, as seen by a TIU, is \nnegative exponential with mean [(N \u2014 1)A]}7.\n\nWe assume that the statistics of line busy and idle periods are the \nsame for all terminals on the loop. The removal of messages from the \ndata stream may affect this assumption. Also, strictly speaking, these \nstatistics also depend upon the multiplexing strategy of the switch. \nFurther work involving simulation must be done to verify this \nassumption.\n\nMessages are multiplexed packet-by-packet into empty slots. The \nmultiplexing is interrupted by the advent of a busy period and is \nresumed when the busy period is over. Armed with the statistics of \nthe line busy and idle periods, the message delay can be found. In \nthe language of Queuing Theory, the model is that of a server that \nsuffers periodic breakdowns. The results of the analysis appear as sets \nof curves that will be discussed presently.\n\nFrom the foregoing we have an analytical approach for the calcu- \nlation of delay in the case of Demand Multiplexing with adjacent \nslot seizure. There are inherent difficulties that preclude an analytical \nsolution in the case of alternate slot seizure. The basic difficulty lies in \ncalculating the durations of line busy and idle periods. For alternate \nslot seizure a terminal is blocked only if there are two or more inter- \nfering terminals. Thus a line idle period is terminated when a terminal \nbegins transmitting, if there is at least one other terminal already \ntransmitting.\n\nMessage delay in the case of alternate slot seizure was studied by \nmeans of simulation. The simulation program also could be used to \nstudy adjacent slot seizure. Although adjacent slot seizure can be \nanalyzed, it was simulated primarily as a check.\n\nIn order to insure that the basic assumptions that underlie our \nmodel are understood, we outline the basic structure of the simulation \nprogram. The number of terminals on the loop is an input variable \nto the program. Input variables also determine the rate of message \narrival, the length of long messages in packets, and the mixture of \nlong and short messages. The simulation was carried out for the \nvariable length message distribution. The basic time unit of the \nprogram corresponds to the duration of a packet slot, 1/4000 second. \nDuring each time unit a message may arrive to be multiplexed on the\n\nline. The random message arrival is simulated by comparing the \noutput of a pseudorandom number generator to a threshold. If the \ntest indicates that a message has arrived, the length of the message \nand the terminal to which it arrived are chosen randomly. A basic \nassumption here is that during a packet slot time no more than one \nmessage arrives at all N terminals. For the loadings of interest, this is \nnot a restrictive assumption.\n\nFor each of the N terminals in the loop simulation, numbers are \nstored indicating the current number of packets and messages in the \nterminal buffer. In each basic time unit, terminal buffers 1, 2, --- , N \nare examined in succession until a nonempty buffer is found. If adjacent \nslot seizure is being simulated, a packet is removed from the first \nnonempty buffer. In the simulation of alternate slot seizure, a packet \nis removed from the first nonempty buffer from which a packet was \nnot removed in the previous time unit. After either a packet has \nbeen removed from a buffer or all buffers have been examined, the \nprogram shifts to the next basic time unit and the cycle repeats \nbeginning with message arrival.\n\nOur interest is in the Nth terminal as it sees traffic from N \u2014 1 \nother terminals. The line busy and idle periods seen by this terminal \nare measured. The program also measures the number of messages \nremaining in terminal N\u2019s buffer immediately after an entire message \nhas been removed from the buffer. This measurement was not made \nevery time a message departs, but periodically. The length of the \nperiod between measurements was varied from run to run. The reason \nfor this is to guard against high correlation between measurements, \nthereby insuring independent samples.\n\nResults of the simulation and the analysis of the previous section \nare shown as curves which show the mean and the standard deviation \nof delay as a function of loading. From these curves we draw con- \nclusions about the relative merits of the systems under study.\n\nOn Fig. 6 are shown plots of average delay measured in the simula- \ntion as a function of loading for 5- and 20-terminal loops. The line \nloading is the portion of the time that the line is occupied. For com- \nparison the results of the theoretical calculation of average delay is \nalso shown in Fig. 6.\n\nThe simulation also yielded estimates of the standard deviation of \nmessage delay. Results are shown on Fig. 7, where the standard devia- \ntion of delay is shown as a function of loading. As in Fig. 6, the results \nof analysis for adjacent slot seizure calculations are shown.\n\nIn all of the curves the message distribution is the variable length \nmessage distribution defined earlier. The resulting average message \nlength is 10.3 packets per message. The message arrival rate at each \nstation in the loop in terms of loading, p, is p/(10.3N) messages per \nslot time. (Each slot time is 1/4000 second.) Thus for 0.103 loading \non a 20-terminal loop, messages arrive at a rate of 0.0005 message \nper slot time or 2 messages per second at each terminal.\n\nO ADJACENT SLOT SEIZURE \u2014 5 TERMINALS \n4 ALTERNATE SLOT SEIZURE \u2014 5 TERMINALS \nX ADJACENT SLOT SEIZURE \u2014 20 TERMINALS \n\u00a9 ALTERNATE SLOT SEIZURE \u2014 20 TERMINALS\n\n4 ALTERNATE SLOT SEIZURE \u2014 5 TERMINALS / \nX ADJACENT SLOT SEIZURE \u2014 20 TERMINALS / oO \n\u00a9 ALTERNATE SLOT SEIZURE \u2014 20 TERMINALS\n\nequilibrium had been reached. The duration of runs and the random \nsequences used in the simulation were varied. The standard deviation \nof the estimates of the mean values of delay shown on Fig. 6 can be \nestimated. We assume that the measured standard deviations are the \ntrue standard deviations. The standard deviation of the mean is then \nthe measured standard deviation divided by the square root of the \nnumber of samples. The results indicate that the standard deviation \nof the mean is small compared to the mean value. The standard \ndeviation is largest relative to the mean at light loadings on the \n20-terminal loop where it is approximately 5 percent of the mean.\n\nThere is a basic difficulty in making measurements at light loadings \non a 20-terminal loop. Due to the relatively low departure rate, fewer \nindependent samples can be gathered. Except for the lighter values \nof line loading on the 20-terminal loop there is good correspondence \nbetween the results of simulation and theory. Even at these lighter \nloadings the results of simulation are not so far from theory as to cast \ndoubt on the simulation.\n\nThe simulation results show that adjacent slot seizure yields some- \nwhat better delay performance than alternate slot seizure. For almost \nall values of line loading, adjacent slot seizure gives lower values of\n\nmean delay and standard deviation of delay. Moreover, measurements \nmade on loops with 2, 10, and 64 terminals, not shown here, yield much \nthe same result.\n\nThe reader will notice, however, that for most values of line loading, \nthe difference between alternate and adjacent slot seizure is not large. \nThe difference is small enough so that ease of implementation should \nprobably determine the choice between the two.\n\nBecause of pressures of time we did not compute message delay \ndistributions. However, estimates of the distribution of message delay \ncan be calculated from the simulation values of mean and standard \ndeviation. From the Tchebychev inequality we have\n\nwhere y is the mean and o the standard deviation of the delay. On a \n20-terminal loop with alternate slot seizure this inequality shows that \nat 0.515 loading 90 percent of the messages suffer delays of less than \n83 milliseconds. However, the Tchebychev inequality often gives a \nrather loose bound. Under a rather tenuous assumption about the \ndistribution of delay, one obtains a more optimistic result. If we \ncompare means and standard deviations of delay we see that, for the \nsame line loadings, the means and the standard deviations are roughly \nthe same. For an exponentially distributed random variable the mean \nand the standard deviation are equal. If we assume that delay is \nexponentially distributed we find\n\nwhere 1/a is the standard deviation. For 0.515 loading on a 20-terminal \nloop, 90 percent of the messages have delay less than 50.5 milliseconds.\n\nA second phase of our work on loop multiplexing was devoted to a \ncomparison of Synchronous Time Division Multiplexing and Demand \nMultiplexing. In order to simplify analysis we have ignored the fact \nthat for DM information packets must contain the address of the \ntransmitting terminal. No such addressing is required for STDM. \nHowever, such addressing information is a negligible part of an \ninformation packet. For example, for a 64-terminal loop, only 6 bits \nare necessary to specify the address of a terminal. We feel that the \nsmall improvement in accuracy that could be attained by considering \naddressing did not justify the complications introduced into the \nanalysis.\n\nFig. 8\u2014Average delay versus loading in DM and STDM (30 percent of messages \nare 32 packets long).\n\nTypical results are shown on Fig. 8 where delay in both packet \ntimes and milliseconds is shown as a function of line loading for the \nvariable length message case. As the curves show, DM is clearly \nsuperior to STDM. This superiority is more pronounced at the lighter \nloading, where the multiplexing time is the strongest component of \ndelay. In the absence of interfering traffic, the time required to multi- \nplex a message in DM is an average of 10.3 slot times. In contrast, \nfor an STDM system with N terminals, the average time required to \nmultiplex a message is 10.3 X N slot times. As the loading increases, \nthe difference between the two systems decreases. Line traffic in the \nDM system interferes with message multiplexing and as the load \nincreases so does the interference.\n\nSimilar results have been obtained for the constant length message \ndistribution. Computations of the standard deviation of delay for \nboth constant and variable length message distributions also show the \nsame basic pattern.\n\nAnother view of the performance is indicated on Fig. 9 where average \ndelay is shown as a function of the number of terminals in the loop\n\nFig. 9\u2014Message delay versus number of stations (30 percent of messages are \n32 packets long).\n\nfor fixed values of loading. In Fig. 9 the dependence of delay in the \nSTDM system on the number of terminals in the loop is marked. \nThere is little of this dependence in the case of DM. However, DM \nis more sensitive to changes in load than STDM. Notice the large \njump in delay from 0.5 loading to 0.9 loading in the case of DM. \nAlthough we have not shown them, similar results obtain for the \nconstant length message distribution.\n\nThe second phase of our work involved a study of buffering in the \nswitch. Streams of data enter the switch from the loops connected to \nit. In the DM implementation entering packets are labeled as to \noriginating terminal. In the STDM implementation each terminal has \nan assigned packet slot recurring periodically. System operation is \nsuch that, at any given time, each terminal in the system transmits to \nand receives from only one other terminal in the system. Information \non which pairs of terminals are linked together is stored in the switch.\n\nTherefore, given the origin of an information packet, the switch \ndetermines its destination by looking in a table.\n\nA terminal can rapidly change the destination of the packets that \nit transmits. Stored in the Central Switch is a list of up to 64 possible \ncorrespondent terminals for each terminal. A terminal that is trans- \nmitting to terminal A, for example, may select a new destination, say \nterminal B. By means of signal packets (see Section I) the Central \nSwitch is notified of this change in destination. After the change all \ninformation packets transmitted from the originating terminal are \nrouted to terminal B. A terminal can select only from the list of its \n64 correspondent terminals stored in the switch. However, this list \ncan be altered by the originating terminal when it wishes to make \nconnection with a new terminal or drop connection with an old. Again, \nsignal packets are used to communicate between the terminal and \nthe switch. The process of altering the list requires much more time \nthen switching between terminals already on the list.\n\nAt a given instant of time, a terminal transmits to and receives from \nthe same terminal. Further, each terminal in the system acts indepen- \ndently in selecting the correspondent terminal that is the destination \nof its packets. Thus a terminal may select a destination terminal that \nis, at that point in time, corresponding with a third terminal. In this \nevent the packets that are transmitted are stored temporarily in the \nCentral Switch. The Central Switch, again using signal packets, \nnotifies the destination terminal that packets from a particular originat- \ning terminal are waiting to be delivered. It may happen that, for a \nparticularly busy terminal, there may be messages from several \ndifferent originating terminals stored in the switch waiting to be \ndelivered. The receiving terminal is free to choose the order in which \nthese messages are read out of the switch buffer.\n\nIn connection with this routing and selection procedure we use the \nterm virtual channel as a notational shorthand. As we have seen, each \nUser Terminal has stored in the switch a list of as many as 64 corre- \nspondent terminals. When a terminal selects the 7th correspondent on \nthis list, we say that the terminal selects the zth virtual channel. \nWhen we say that a terminal transmits and receives over virtual \nchannel 7 we mean that the terminal transmits to and receives from \nthe zth correspondent terminal on the list stored in the Central Switch.\n\nAs we have indicated, it may be necessary to store information \npackets in the switch before they can be delivered. As a practical \nnecessity, the amount of storage in the switch is finite and under \nheavy loading conditions storage may be used up. In this situation the\n\nswitch sends signal packets to User Terminals which inhibit transmis- \nsion until storage is available in the switch.\n\nOur study of packet storage capacity in the switch focused on two \naspects of the problem, throughput and user strategy. Given the \nrandom nature of the message flow in the system, there will be occa- \nsions when all of the storage assigned to a channel is used up and the \ntransmitting terminal is inhibited. If this condition occurs often \nenough, there will be a significant effect on the total throughput of \ndata. Secondly, the user through his virtual channel selection strategy \ncan affect the amount of storage that is required in the Central Switch. \nAs we have noted earlier, a certain amount of time is required for a \nUser Terminal to switch from one virtual channel to another. During \nthis switching time, the terminal cannot read packets out of the \nswitch. If User Terminals pursue a strategy calling for frequent \nswitches, demands on switch storage may be too large.\n\nIn order to study throughput and the effect of user strategy on \nbuffer requirements, a simplified model was constructed. The model is \nshown in Fig. 10. N independent data streams carrying \\ messages per \nsecond flow into N buffers. These data streams represent traffic from \ncorrespondent terminals flowing over different virtual channels to the \nsame destination terminal. The destination terminal\u2019s changing of \nvirtual channels is represented by the switch in Fig. 10 moving from \nbuffer to buffer. In the model the time required to switch buffers is \ntaken to be either zero or eight packet times (1/4000 second).\n\nA good deal of previous work on buffer occupancy has been based \non a Poisson arrival model for messages in the input data stream. In \nthe Poisson model, messages arrive instantaneously with an ex-\n\nponentially distributed interval of time between messages. A more \nrealistic model, for our study of throughput, is one in which messages \narrive over a time interval proportional to the message length with \nthe time between the beginning of one message and the end of the \nprevious message being exponentially distributed. This latter model is \nmore appropriate to buffering in the switch where the arrival and \ndeparture of messages is over T1 lines and the read-in and write-out \nrate of messages is the same. In Section VIII, results based on the \ncontinuous arrival model will be compared with the Poisson arrival \nmodel.\n\nThe model used in our study is indeed something of a simplification. \nBecause terminals share the same T1 loop, messages are likely, \nespecially in heavy loading, to be broken up when they are multiplexed. \nIn our model we do not take this effect into account. For example, in \nour model a message with 32 packets would occupy 32 successive \npacket slots on the input line. In the actual system, there may well \nbe gaps in these messages. Similarly, we assume that messages going to \na particular destination terminal have sole access to the T1 line, when \nin fact the line is shared. Thus we assume that messages can be read \nout of buffers at will. Fortunately, these two effects tend to cancel out. \nIn our model we read in faster and read out faster than reality. Also, \nwe are not looking at absolute measures of performance, but are\n\ncomparing different implementations. We felt that a more complicated \ninput output model would not improve this comparison significantly.\n\nEven this simplified model was not amenable to analysis and a \nMonte Carlo simulation program was written. The basic functions of \nthe program is to measure the throughput as a function of storage \ncapacity and to measure the average occupancy of the buffers. Input \nvariables to the program determine the amount of storage available, \nthe number of input lines and buffers, the time required to switch \nbetween buffers, and the probability of message arrival.\n\nThe program is easily changed to handle either common or dedicated \nbuffering. For common buffering, an input variable is the total storage \navailable. When a packet is inserted in a buffer, this number is reduced \nby one. For dedicated storage, the storage for each line\u2019s buffer is an \ninput variable. As a packet is inserted in a buffer, the amount of \nstorage available for that buffer is reduced by one.\n\nThere is a simple relationship between the probability of message \narrival and load. Let p be the probability that a message is generated \nin a slot. It can be shown that the portion of the slots on each input \nline that are busy is given by the expression\n\n| ee 16 aa \npm +1 \u2014p\u2019 \nwhere 7m is the mean length of a message in packets. The assumption \nhere is that there is no limitation on the content of the buffer into \nwhich the input line feeds. N input lines feed into the buffers, conse-\n\nFig. 11\u2014Line load as a function of the probability of message arrival (80 percent \nof messages are 32 packets long).\n\nquently the maximum occupancy of the line carrying messages out of \nthe buffers is \n_ pNm\n\n= DET p \u201d) \nThe output line will attain this maximum occupancy if no time is \nrequired to switch between buffers. The relationship between loading, \nL, and the quantity pN, which we designate as the probability of \nmessage arrival, given in eq. (3) is plotted in Fig. 11.\n\nrequired by a User Terminal to select a new virtual channel. When a \npacket is removed from a buffer, the amount of storage available is \nincreased by one up to some fixed amount.\n\nIn successive simulation runs the amount of packet storage available \nwas varied with all other parameters held constant. For very large \namounts of storage, there is always room in the buffers. As the amount \nof storage is decreased, it is increasingly likely that packet flow from \nan input line is inhibited. For relatively low amounts of storage, it will \noften happen that there is no room in the buffer. In this case, the flow \nof messages will be halted frequently and the number of packets flow- \ning into the buffers per unit time will be reduced.\n\nIn the measurement portion of the program, the main focus was on \nthroughput. Programs were run for 20,000 cycles, and the total number \nof packets that were fed into buffers were measured. By varying the \ntotal amount of storage available, with all other parameters fixed, one \nobtains the relationship between throughput and storage. Simulation \nruns were made for the constant and variable length message dis- \ntributions. Measurements were also made of the total number of \nmessages in the buffers. The results of these latter measurements will \nbe considered in a later section dealing with user strategy.\n\nTypical results of simulation are shown on Figs. 12 and 13 for 5 \nand 20 input lines, respectively. In obtaining the results shown on both \nfigures the variable length message distribution was used. The switch- \ning time is 8 packet slots. If the line rate is 4000 packets per second, \nthe time required to switch is 2 milliseconds. The curves show nor- \nmalized throughput as a function of the total packet storage with \nmessage arrival probability as a parameter. For each loading the \nthroughput is normalized to the throughput measured at very large \nstorage capacity.\n\nThe basic configuration of the curves is as one might expect. As the \nstorage capacity decreases, the throughput decreases. Further, the \nnormalized throughput decreases faster for the larger values of loading.\n\nThe results show that, even for a limited amount of storage, the \nthroughput is high. For example, if there are two packet slots for each \nbuffer, the throughput is over 70 percent even for high loading. Results \n(not shown) for the case of zero switching time show that for this \nsame amount of storage the throughput is over 90 percent.\n\nA surprising result shown on Figs. 12 and 13 is that dedicated \nstorage shows better performance than common storage when there is\n\nFig. 12\u2014Throughput versus packet storage for 5 input lines (switching time is \nequal to 8 slot times).\n\na limited amount of buffering available. A combination of factors \nproduces this result. First of all, even though storage may be held in \ncommon, it is committed to input lines (virtual channels) in a specific\n\nFig. 13\u2014Throughput versus packet storage for 20 input lines (switching time is \nequal to 8 slot times).\n\nway that may be far from optimum. The preponderance of traffic \nis contained in messages that are 32 packets long. If the amount of \nstorage held in common is limited, one channel may absorb all of the \nstorage that is available in the switch. We have also simulated models \nwhere all messages are one packet long. In this case common storage \nis superior to dedicated. However, even in this case the difference \nbetween common and dedicated storage is not great.\n\nIn the foregoing, messages are generated regardless of whether there \nis room in the switch or not. We have also examined an implementation \nwhere messages are not generated until there is buffer space available. \nThe results of a simulation study of this implementation are essentially \nthe same as the results presented here.\n\nBefore concluding this section let us consider the reliability of the \nforegoing results. First of all, a good many simulation runs were made \nwhose results are not shown here. In these runs, the number of chan- \nnels, the starting points of the random sequence used in the Monte \nCarlo technique, and the running time of the simulation were varied. \nAll of the results were in conformity with the results presented in \nthis paper.\n\nRecall that an input parameter to the program was the probability \nof message arrival. In Fig. 11 the theoretical relationship between \nloading and this quantity is shown. Also shown on Fig. 11 is the \nloading obtained in the simulation. As seen on Fig. 11, the results of \nsimulation are within 5 percent of the theoretical values. This is \nadditional indication that the simulation runs were long enough to \nobtain representative data sequences.\n\nEstimates of the standard deviation of the throughput were made. \nThis was done on each simulation run by measuring the throughput \nevery 1000 cycles, obtaining a sequence of 20 points. (Recall that the \nsimulation runs were 20,000 cycles long.) The mean, yu, and the vari- \nance, o\u201d, of these points was calculated, giving an estimate of the \nmean and standard deviation of the throughput in 1000-cycle intervals. \nThe sum of these points is the total throughput for the simulation \nrun. If we assume that the throughputs for successive 1000-cycle \nintervals form a sequence of independent, identically distributed \nrandom variables, the variance of the throughput for a 20,000-cycle \nrun is 2002. The coefficient of variation or the ratio of the standard \ndeviation to the mean for a 20,000-cycle run is\n\nOur measurements show that in all cases the coefficient of variation is \nless than 0.1 and in many cases it is less than 0.05. This result means \nthat with different starting points in the random sequences we would \nexpect a relatively small variation around the points we have plotted \non Figs. 12 and 13.\n\nAt any given point in time, a User Terminal knows which virtual \nchannels have messages waiting to be delivered. A terminal is free to \nselect these virtual channels in any order. We assume that a terminal \nwill not interrupt the reading out of a message in order to switch to a \nnew channel. Since the channel selection procedure is entirely in the \nhands of the User Terminal, we studied the effect of different strategies \non system storage requirements. Accordingly, a calculation of buffer \noccupancy statistics for different user strategies was performed.\n\nAs in the study of throughput we use the model shown on Fig. 10. \nAgain, input lines correspond to virtual channels and switching \nbetween buffers corresponds to the selection of new virtual channels. \nIn order to make the analysis tractable, we assume that messages \narrive at a Poisson rate of ) messages per second over each input line. \nFurther, we assume that eight packet slot times are required to switch \nbuffers. In order to calculate bounds, we also consider the case where \nno time is required to switch.\n\nWe analyze the buffer occupancy of the 1-by-1 and the random \nstrategies by using the theory of the M/G/1 queue. Messages arrive \nat all buffers at a Poisson rate NA messages per second. If the time \nrequired to switch between buffers is zero, we can take the service\n\ntime in both strategies to be either 1 slot time or 32 slot times, depend- \ning on whether a message is long or short. An upper bound on storage \nrequirement for the 1-by-1 strategy can be found by assuming that \nafter each message is read out one always switches to a nonempty \nbuffer. We can analyze this situation by adding the switch time to the \ntime required to read out each message. Thus we have read out times \nof 9 slot times for short messages and 40 slot times for long messages. \nThis is an upper bound because there is a nonzero probability that \nall of the messages are in the same buffer and there is no reason for \nthe station to select a new virtual channel.\n\nFor the random strategy the service time is slightly different than \n1-by-1. With probability 1/N no switching takes place and the service \ntime is simply the time required to multiplex a message.\n\nLet b be a random variable denoting the number of slots required \nto read a message out of a buffer, including switching time. We write \nb = (m+ w)T,, where w is the time required to switch in slot times. \nThe random variable w is independent of m. If, in the case of random \nswitching, 8 slot times are required to switch between buffers, the \nprobability that w = 8 is 1-1/N and the probability that w = 0 is \n1/N. From the analysis of the M/G/1 queue,\u00ae it can be shown that \nthe mean number of messages in all N buffers is\n\n(4) \nwhere b? is the 7th moment of b and ) is the average message arrival \nrate in messages per second. The mean-square number of messages in \nthe buffer is\n\nOur primary interest is in the number of data packets in switch \nbuffers rather than in the number of messages. It can be shown that \nthe mean and the mean-square number of packets in all N buffers is \ngiven respectively by\n\nThe foregoing considers packet storage requirements in all of the \nbuffers in the switch. We shall focus our attention on the number of \npackets in individual buffers assigned to virtual channels. The mean\n\nIn the sequel we shall consider the time to switch between buffers, \nw, as fixed; therefore, \u00a9 = w and w*? = w*. The quantities mT, and \nmT? denote the first two moments of the time required to read a \nmessage out of a buffer. The mean number of messages in the buffer is\n\nAn expression for the mean-square number of packets in each buffer \ncan be derived from the work presented in Ref. 6. This expression is \nrather lengthy and provides little insight; therefore, we shall omit it.\n\nResults of computation using this expression will be presented in \nthe sequel.\n\nThe results of computations using the formula derived in the fore- \ngoing are shown in Figs. 14 and 15 for 5 and 20 buffers, respectively. \nIn these figures the average occupancy of each buffer is shown as a \nfunction of load, which is the product of the message arrival rate and \nthe average time required to read out a message, NAm. As expected, \nthe lowest buffer occupancy occurs in the case where no time is re- \nquired to select a new virtual channel. When an 8-slot-time channel \nselect time is required, the technique with the lower occupancy \ndepends upon the loading. At light loading, the \u201cempty before switch\u201d\u2019 \nstrategy shows poorer performance because time is wasted stopping at \nempty buffers. It must of course be remembered that this is only an \nupper bound for the \u201c\u201cempty before switch\u201d that selects only nonempty \nbuffers. As the loading increases, there are fewer empty buffers and \nthe performance of the \u201cempty before switch\u201d strategy improves \nrelative to the l1-by-1 strategy.\n\nFig. 14\u2014Average number of packets in each buffer for 5 buffers (380 percent of \nmessages are 32 packets long).\n\nFig. 15\u2014Average number of packets in each buffer for 20 buffers (30 percent of \nmessages are 32 packets long).\n\nIn the previous section we considered an \u2018\u2018empty before switch\u201d \nstrategy that skipped empty buffers. As we have mentioned, the \nproblem of calculating occupancy statistics for this technique is \nintractable. However, the results shown on Figs. 14 and 15 form \nbounds on the skipping empty technique. The shaded areas in the \nfigures indicate the areas in which the statistics for this method lie.\n\nIf the system is operated below 0.5 loading, the difference between \nthe different channel switching strategies is not very large. For example, \nfor 20 channels and 0.4 loading (see Fig. 15) the average occupancy for \n1-by-1 rotating strategy is 1.1 packets. For the \u201c\u2018empty before switch\u201d \nstrategy skipping empties, the average occupancy is between 0.4 and \n1.0 packet. As the load increases beyond 0.5 loading, the 1-by-1 \nstrategy leads to saturation and the cyclic system is clearly superior.\n\nResults for the standard deviations of buffer occupancy have been \nobtained. These results support the foregoing conclusions.\n\nThe simulation program discussed in the previous section computed \nmeans and standard deviations of buffer occupancy for an \u201cempty \nbefore switch\u201d strategy with skipping of empty buffers. The results \nare shown on Figs. 14 and 15. A comparison of analysis and simulation\n\nindicates that for the most part the analysis gives upper bounds to \nthe simulation. This is not unexpected since, in the simulation pro- \ngram, messages arrive over an interval of time, whereas for the Poisson \narrival model used in the analysis, messages arrive instantaneously.\n\nEquation (1) of the text is the following expression for the delay \nin Synchronous Time Division Multiplexing:\n\nThe delay, d,, is the sum of the three mutually independent random \nvariables qT... T. Di1 mi + w, and (mz41 \u2014 1)T.. Thus the moment- \ngenerating function for di is the product of the moment-generating \nfunction for these three variables. In this appendix we shall calculate \nthe moment-generating functions of each of these.\n\nRecall that in STDM dedicated packet slots are available to each \nterminal cyclically every 7\u2019, seconds. We take the end of one cycle \nand the beginning of the next to be the end of a dedicated packet slot.\n\nLet gq; be the number of packets remaining at the end of the jth \ncycle and let a; be the number of packets arriving during the jth \ncycle. We can write\n\nwhere U(zx) is such that U(x) = 1 for xz > 0 and U(x) = O forz < 0. \nTaking expectation on both sides of (14) and assuming equilibrium \n(i.e., Eqj41 = Eq;) we find that \nElu(q; + aj41)] = ELaj41]. \nBut \nElu(q; + aj+1)] = P-La; + aiz1 > 0].\n\nIf we assume equilibrium has been reached, we may define \nQ(s) = ELe~*% ] \nfor all 7. From (16) after some manipulation we have\n\nwhere A(s) = E[e~**]. Since messages arrive at a Poisson rate i, \nit can be shown that \nA(s) = e>Pell\u2014M(a)) | (18)\n\nwhere M(s) is the generating function of the messages. \nBy successive differentiation it can be shown that the first two \nmoments of q are\n\nwhere 4, a\u2019, and a are the first three moments respectively of the \nnumber of packets arriving in a cycle 7',. By successive differentiation\n\nwhere 7, m2, and m3 are respectively the first three moments of the \nnumber of packets in a message.\n\nWe turn now to the second term in (1), f Aw + TT. Diei1m; A \nmessage arrives at random during a cycle, w seconds before the end \nof a cycle. In the time interval T.. \u2014 w, L messages arrive, all of which \nhave priority over the newly arrived message. Since message arrival \nis random, the quantities L and w are mutually dependent random \nvariables. Conditioned on w, the probability that L messages arrive \nin the interval T, \u2014 w is \nM(T. \u2014 w)t\n\nThe random variable w is uniformly distributed in the interval (0, 7\u2019). \nLet r(t) be the density function of the random variable T.m;. We may \nwrite\n\nwhere r)(t) is the Z-fold convolution of r(t). The Laplace-Stieltjes \ntransform of this can be shown to be\n\nThe first two moments of f can be found by successive differentiation \nof (23):\n\ngenerating function of the message is M(s), the generating function of \nthis term is easily shown to be\n\nThe mean value of delay is the sum of the terms q7., f, and g. The \nvariance of the delay can be calculated by summing the variances of \nqT, f, and g.\n\n1. A. G. Kohneim, \u201cService Epochs in a Loop System,\u201d presented at the 22nd Int. \nSymp. Computer-Communications Networks and Teletraffic, Polytech. Inst. \nBrooklyn, Brooklyn, N. Y., April 1972.\n\n. J. F. Hayes and D. N. Sherman, \u201cTraffic Analysis of a Ring Switched Data \nTransmission System,\u201d B.S.T.J., 50, No. 9 (November 1971), pp. 2947-2978.\n\n. R. R. Anderson, J. F. Hayes, and D. N. Sherman, \u201cSimulated Performance of a \nRing Switched Data Network,\u2019 IEEE Trans. Commun., COM-20, No. 3 \n(June 1972), pp. 576-591.\n\n. B. Avi-Itzhak, \u2018\u201cHeavy Traffic Characteristics of a Circular Data Network,\u201d \nB.S.T.J., 50, No. 8 (October 1971), pp. 2521-2549.\n\n. J. F. Hayes and D. N. Sherman, \u2018\u2018A Study of Data Multiplexing Techniques and \nDelay Performance,\u201d B.S.T.J., 51, No. 9 (November 1972), pp. 1983-2011.\n\n. A. G. Fraser, \u201cInterconnecting Computers and Digital Equipment,\u201d internal \nreport available upon request.\n\nCopyright \u00a9 1974 American Telephone and Telegraph Company \nTue Bey System TEcHNIcCAL JOURNAL \nVol. 53, No. 2, February 1974 \nPrinted in U.S.A.\n\nPeak-Load Traffic Administration of a Rural \nMultiplexer with Concentration\n\nA procedure is proposed for estimating the main-station capacity of an \nSLM* (Subscriber Loop Multiplexer) system by observing the traffic load \nwhen the system ts partially filled. The procedure is intended to be usable \nin unattended offices, and requires only one measurement per week and \nvery few calculations. In contrast to the usual practice of measuring load \nin a time-consistent busy-hour, we work with weekly peak loads, and so \nour method is based upon the statistical theory of extreme values. The \nvalidity and precision of the procedure have been investigated by applying \nat to data from a study of rural traffic and by a Monte Carlo study of tts \nbehavior. Use of this administrative procedure should give the average \nSLM _ system a capacity of about 120 rural residential customers, in \ncontrast to the limit of 80 that would be necessary in the absence of traffic \nmeasurements.\n\nI TN PRODUCTION 6440 ).ccuwesd dy Sa Ge eee sal ee ree ers hss 262 \nHo THE \u2018BASIC: PROCH DUR s iss hy bee Sire NBs ahaa es oe ee hs 263 \nIJI. THE DISTRIBUTION OF WEEKLY PEAK TRAFFIC LOADS... 265 \nIV. THE MATHEMATICAL MODEL..................0...00 000005: 265 \nV.. THE SERVICE: CRITBRION 54; caccs Oona ibe Fauna ek vate 267 \nVi\" THE MONTE: CARLO STUDY. oc) oo vine jin 35-4 Seca ents 270 \nVII. DISCUSSION OF ASSUMPTIONS............... 0.00.00 0 000 e eee 273 \nVIII. SUMMARY AND CONCLUSIONS............... 0002200002000 5. 275 \nDx ACKNOWLEDGMENT sce direitos dike sae ended Sok hia s 276\n\nAPPENDIX A\u2014Number of Candidate Busy-Hours and Their Load \nDDUSEP ID ULBON os. 2.6 5 2s 5 see RRR Sa Aste Soaps cape odeeed Ba gesclos spl Aba t Wqen pode eh eae 276 \nAPPENDIX B\u2014Rules for Traffic Administration............0.. 000000002 278\n\nThe SLM (Subscriber Loop Multiplexer) system is a digital carrier \nand switching system that was developed to provide economically for \nmain-station growth and upgraded service on long rural cable routes. \nIt is capable of serving 80 lines, all sharing 24 channels. Each of the \n80 lines can be used for single- or multi-party service. (For a detailed \ndescription of the SLM system see Ref. 1.) For the purposes of this \npaper, which is concerned with traffic, the SLM system may be viewed \nas a remote line-concentrator serving 80 lines on 24 full-access channels.\n\nThe quality of service given to SLM subscribers should be kept \nwell above levels that might lead to complaints, and to the need for \nhasty rearrangements that would interfere with the orderly growth of \nsubscriber plant. Hence, service for these subscribers should not be \nnoticeably different from that for customers served by physical pairs \nto the central office. This service objective will be met if blocking \nexceeds one-half percent in no more than a few hours per year. (It is \npossible to imagine a distinct service, for sparsely populated rural \nareas, in which a less stringent service objective would be appropriate.)\n\nThe Rural Line Study,?\" a study of subscriber line usage in rural \nareas, has confirmed that rural residential subscribers like those studied \nin the territory of South Central Bell can almost always be served on \none SLM system with essentially no blocking in groups of 80 main \nstations or more. (In fact, as shown below, most rural systems should be \nable to serve many more than 80 main stations.) However, the load per \nmain station does vary greatly from place to place and from customer \nto customer. Thus even 80 main stations will in a few cases generate \nenough load to cause undesirably frequent blocking in excess of one- \nhalf percent. Some means of monitoring the traffic performance of \nSLM systems are therefore necessary.\n\nOne such means is a register which records the total amount of a \nsystem\u2019s all-channels-busy time since the register was last read and \nreset to zero. But such a register, which can indicate by its readings \nwhen a system is overloaded, cannot be used to foresee an overloaded \ncondition until too many lines have already been assigned to the \nsystem. When the register\u2019s readings exceed a specified threshold, the \nadministrator\u2019s response must be to remove lines from the system and \nto serve them on other facilities.* Because of the long lcad-times \ninvolved in cable planning and installation, a major goal of the work \nreported here was to avoid this situation.\n\nSince some additional traffic-monitoring capability was necessary, \nit seemed best to provide a measurement which could be used to \npredict the ultimate main-station capacity of a system, and thus to \nguide the loading of the system and the planning of relief facilities. \nThe natural quantity to measure is carried load; and the system\u2019s \nsecond traffic register, which was also chosen to minimize the volume \nof data to be taken and processed, records peak hourly carried load\u2014 \nthat is, the highest hourly carried load that has occurred since this \nregister was last read and reset to zero. As shown below, it is sufficient \nto take readings once a week. This frequency is compatible with a \nnormal schedule of visits to unattended offices. Note that the time \nthat this peak traffic occurred is neither recorded nor of importance \nto the procedure to be described, so that the usual time-consistent \nbusy-hour is not identified.\n\nWeekly peak load measurements can be used whenever 40 or more \nmain stations are assigned to an SLM system. We begin with N weekly\n\npeaks, 11, --- , ty. (N is normally equal to 4.) We simply calculate \nthe mean, \nSe tide 1 \nr= ve Liy ( ) \nand the variance, \n1 4 a ; \np= yh wo (2)\n\nFig. 1\u2014Estimated main-station capacity as determined by mean and variance \nof weekly peak loads.\n\ncurrently working main stations, we find the point defined by the \ncoordinates \u00a3 and v. This point will fall in one of the regions labeled \n40, 45, --- , 160. The label of that region is the estimated main-station \ncapacity of the SLM system.\n\nFor example, let us say we have 80 working main stations. We \nobserve four weekly peaks and calculate a mean of 260 CCS and a \nvariance of 1400 (CCS)?. Figure 1 is the chart corresponding to 80 \nworking main stations. The point (260, 1400) falls in the region \nlabeled 120. This is the estimated main-station capacity for the system \nin question. Repeating this estimation procedure four times (using \ndata from 16 weeks of operation) and calculating the weighted mean \nof the estimates, using the respective numbers of working main \nstations as weights, we obtain the predicted capacity of the system in\n\nmain stations. Some precautions which must be observed in drawing \nconclusions from this process are summarized below.\n\nwhich is sometimes referred to as \u2018\u201cGumbel\u2019s first asymptotic distribu- \ntion.\u2019\u2019 It has been shown\u2018 that, for the so-called \u2018\u2018exponential\u2019\u2019 class \nof distributions, the largest value of a random sample of size n will be \nasymptotically distributed (as n \u00a9) according to (8). The exponen- \ntial class includes most well-known distributions with an infinite tail \nto the right, such as the normal, lognormal, and gamma.\n\nGumbel suggests that wu and @ be estimated by replacing E(x) and \nV(x) by their sample values, (1) and (2) respectively, and solving \n(5) and then (4) for a and u:4\n\nWith J main stations served by an SLM system, the weekly peaks \nwill have an extreme-value distribution with parameters u; and ay. \nIf we increase the number of main stations from J to K, the weekly \npeaks will have a new extreme-value distribution with parameters ux \nand ax. In this section we describe a method for estimating ux and \nax when J and K are known and u, and a; have been estimated from \nmeasurements. That is, we want to know what the distribution of \nweekly peaks will look like for K main stations when we have observed \nthis distribution with only J main stations being served.\n\nSuppose that, during any week, there are n hours in which the \nweekly peak traffic load may occur. We know from experience that \nthe weekly peak can occur during almost any waking hour.? However, \nfor any given week, n will be much smaller than the number of waking \nhours. (In Appendix A we show that n = 10 seems to be an appropriate \nchoice for our purposes.) We call these n hours (whose actual times of \noccurrence are not specified) the candidate busy-hours.\n\nWe now assume that each main station generates a load with mean \npw and standard deviation o during each of the candidate busy-hours. \nIf customers behave independently, the load distribution in candidate \nbusy-hours must have mean Ju and standard deviation ovVJ. Let this \ndistribution be F, with density f = F\u2019. The weekly peak will then be \nthe maximum value in a random sample of size n from the distribution \nF. If F is in the exponential class of distributions, the distribution of \nthis maximum can be approximated by the extreme-value distribution \n(3). Gumbel! shows that the parameters wu and a@ are given approxi- \nmately by\n\nSince the candidate-busy-hour loads are the sums of the loads from \nJ main stations, it seems reasonable to assume that F is normal,\u201d as \nsuggested by the central-limit theorem. (As mentioned above, we \ntake J and K to be at least 40.)\n\nLet \u00ae be the standard unit-normal distribution function and \u00a2 = \u00ae\u2019 \nthe corresponding density. Define v by the relation\n\nThen \u00bb is the 1 \u2014 (1/n) quantile of the unit-normal distribution, for \nwhich tables and computer subroutines are available. Then from (8) \nand (9) it is readily seen that\n\nIf the K \u2014 J subscribers to be added come from the same population \nas the J subscribers already being served, the candidate-busy-hour \nload distribution for K main stations will be normal with mean Ku \nand standard deviation oVK. The weekly-peak-load distribution will \nhave parameters defined by (11) and (12) with J replaced by K. From \nthe four equations (11), (12), and the corresponding equations for K \nmain stations, the variables \u00bb and o can be algebraically eliminated to \nyield these expressions for ux and ax in terms of u,; and a;:\n\nHere C,, = nvd(v), a function of n only. Hence, for a given n, we \ncan estimate the parameters of the weekly-peak-load distribution for \nK main stations by observing the weekly peaks generated by J(.\n\nThe transient response of a notch filter followed by a low-pass \nfilter is of interest. However, (25) is restricted to a particular low-pass \nfilter with a high-frequency cutoff in the vicinity of the notch fre- \nquency, and will not be considered further.\n\nThe special case ag >, treated previously for the unit step re- \nsponse, can be obtained from (26) and is in agreement with the result \nobtained by performing the integration directly by using (17).\n\nFor az \u2014>* and m = 0, 1, 2, a comparison was made between the \nexact solutions and the approximate solution (26). The comparison \nshowed the same accuracies as for the unit step response.\n\nThe time response due to a stepped cosine excitation can be ob- \ntained by differentiating (26) and dividing by w,. It readily follows\n\nthat, within the accuracy of (26), the same expression is obtained but \nwith sin w,t replaced by cos wz.\n\nIt is noted that (26) gives the correct value for t = 0. This value \ncan be obtained by using the initial value theorem of Laplace \ntransforms.\n\nGraphs of e~*L8(x) are shown in Fig. 3 for n = 0, 1, 2. These graphs \ngive the envelope of the transient response (26) for ag \u2014\u00ab. The \neffect of finite values of a, can be deduced from the graphs. For \nexample, for a: negative the arguments of the Laguerre functions \nincrease reaching maximum values of (6t)/a, for a1 = \u2014a\u00bb. Therefore, \nfor the same ft the spacing between the zeros would decrease and \nthe maximum values increase. For positive a2 the opposite would be \nthe case.\n\nIt has been shown above that the transient response of notch filters \ncan be obtained from the Hankel transform of the low-pass impulse \nresponse. This property can be used to deduce the qualitative charac- \nteristics of notch filters derived from conventional low-pass filters of \nthe Bessel, Butterworth, and Tschebyscheff type. The impulse re- \nsponse of conventional filters, with transfer function polynomials of \nthe same order and approximately the same bandwidth, has similarities \nto the impulse response considered. Therefore, the graphs shown in \nFig. 3 are also representative of the transient response of notch filters \nderived from conventional filters.\n\nThe transient response of notch filters can be kept arbitrarily low \nat large times, such times being defined after the first zero of the \nenvelope, t,. The time \u00a2, can be kept small by the choice of the number \nof sections m, and/or by choosing 8/a: large. However, for the interval \n0 St St, these methods are not effective. In fact, it has been shown \nabove from the initial value theorem (27) that, at \u00a2 = 0, the envelope \nof the response is unity independent of the filter parameters. A low- \npass filter combined with a notch filter would cause the transient \nresponse to be zero at \u00a2 = 0, and behave, for small t, as \u00a2*\u2014 if k is the \norder with which the transfer function goes to zero as s > \u00a9. However, \nwith a given low-pass filter the transient response may not be reduced \nto a desired level at small t. An additional method of reducing the \nresponse by the use of phasing sections is discussed subsequently.\n\nTo illustrate some of the properties of notch filters, numerical \ncomputations for a three-section filter (m = 2), with the parameters \ngiven in Table I, have been performed. Figure 4 shows the filter \nresponse to a step function and Fig. 5 the response to a stepped cosine \nfunction. The computed results are essentially in agreement with \nthose obtained based on the approximate method. Figure 6 shows the \ntransient response of this filter followed by a C-message weighting \nfilter, when excited with a stepped cosine function. A comparison of \nFigs. 5 and 6 shows that the C-message filter reduced, as expected, \nthe first lobe of the response, affected only slightly the second lobe \nand increased the subsequent lobes. Increasing 8 and hence the 3-dB \nbandwidth of the notch is not very effective in reducing the second \nlobe. This led to the investigation of phasing sections as a means of \nreducing the transient response.\n\nFig. 6\u2014Response of notch and C-message weighting filters to stepped cosine \nfunction.\n\nV. TRANSIENT RESPONSE OF PHASING SECTIONS \nThe transient response of a phasing section is considered when\n\nPols) = Fes + \u00e9 o \nand the Laplace transform of the damped sine function, Fa(s), by \nFa(s) = ge ye pe Las + 8 (29)\n\nThe first term in (82) is the damped sine function and the other two \nterms are introduced by the phasing section. In order that the last \ntwo terms be of significance, it is necessary that these terms be com- \nparable to the first term. This will be the case for d = b, for which \n(32) reduces to\n\n= a\u2014- Cw, \nIf, in addition, (a/2)? \u00ab b? and (c/2)? \u00ab d*, (37) simplifies further \nand, for (a/2 \u2014 c/2)t \u00ab1, (37) is approximately given by\n\nEquation (88) contains the damped sine function but modified by \nthe term (1 \u2014 ct). This term can be used to introduce a zero in the \ntime vicinity where the damped sine function assumes a maximum \nvalue.\n\nTo illustrate the above, a phasing section is introduced to modify \nthe impulse response of a C-message weighting filter. The computed \nimpulse response of the filter is shown in Fig. 7 and has relatively \nlarge values in the time vicinity of 0.4 ms. The impulse response \nmodified by a phasing section is shown in Fig. 8. The phasing section \nparameters are c = 2-10 and d = 108. These parameters have been \nchosen on the basis of the above analysis. It is evident the large values \nof the response have been reduced, but the modified response has\n\nappreciable values for a much longer time duration than the initial \nresponse. This behavior can be explained on the basis of Parseval\u2019s \ntheorem,\" since the absolute value of the Fourier transform of the \nresponse is the same with and without the phasing section.\n\nFig. 8\u2014Impulse response of C-message weighting filter with phasing section.\n\nTable !I\u2014Two-section filter with phasing section \n(3-dB bandwidth 390 Hz, 30-dB bandwidth 80 Hz)\n\nPhasing sections can be used to reduce the overshoot of the response \nof a notch filter followed by a low or bandpass filter and excited with \na stepped trigonometric function at the notch frequency. Such sections \nare of particular importance where the transient response has to be \nmodified without affecting the amplitude of the frequency response or \nwhere a modification is needed at times shortly after the beginning of \nthe response. However, such sections may also introduce considerable \ndistortions of the unit step response.\n\nAs an example, the performance of a 1010-Hz notch filter with \nand without a phasing section is considered. The transfer function, \nT(z), of the filter and phasing section can be written as\n\nThis filter was derived from a Tschebyscheff low-pass filter, and \nan operational amplifier version was synthesized and built. Figures 9a \nand 9b show the computed response to a stepped cosine of the filter \ncombined with a C-message weighting filter without and with the \nphasing section. Figures 9c and 9d show photos of the corresponding \noscilloscope displays obtained with the actual filters. Good agreement \nwas obtained between the computed and measured response. The \neffect of the phasing section on the response is evident in this figure. \nAbout a 4-dB reduction in the overshoot was obtained with the \nphasing section.\n\nThe transient response of a class of notch filters which are derived \nfrom low-pass filters by a frequency transformation was investigated. \nGeneral expressions for the transient response due to a unit step\n\nFig. 9\u2014Computed and measured response of notch filter with C-message weighting \nfilter to a stepped cosine: (a) and (c) without phasing section, (b) and (d) with \nphasing section.\n\nfunction and a stepped trigonometric function have been obtained in \nterms of the low-pass impulse response.\n\nThe transient response of certain types of notch filters can be formu- \nlated approximately in terms of Laguerre functions. These filters have \nbeen examined in detail and some general properties of the notch \nfilter response have been deduced from this formulation.\n\nNotch filters may considerably distort short time pulses (time \nduration less than one-half notch frequency period). The amount of \ndistortion depends on the notch depth.\n\nThe response of notch filters to stepped trigonometric functions can \nbe kept at low levels only after a certain time interval from the begin- \nning of the response. The length of the time interval depends on the \nfilter parameters.\n\nA method of reducing the transient response at short time intervals \nby the use of phasing sections was presented. This method may prove\n\nparticularly useful in applications where it is necessary to modify the \ntransient response without affecting the frequency response.\n\nThe author wishes to express his gratitude to E. R. Nagelberg for \nhis critical reading of the manuscript and for his helpful comments \nand suggestions, Mrs. A. M. Franz for the computational assistance, \nMrs. E. Y. McBride for the synthesis of the operational amplifier \nversion of the notch filter and phasing section, and R. R. Redington \nwho built the filter and measured its charactcristics.\n\nThe relationship between the step response of the notch filter and \nthe impulse response of the low-pass filter from which the notch filter \nis derived is given by (6) of the text,\n\nAfter interchanging the order of the Rance and expanding the \nexponential function, (40) can be written\n\nEquation (41) contains a sum of inverse Laplace transforms of a \ntabulated form !>16\n\nEquation (42) is of its own interest, since it may be used to obtain \nthe step response of a bandpass filter derived from a low-pass filter by \na frequency transformation. A direct derivation of (42) follows.\n\nAfter interchanging the order of integration and expanding the \nexponential function in a power series, (43) can be written\n\nThe inverse of each term in (44) is zero for a negative exponential \nargument. For a positive argument u S \u00e9, the inverse is readily ob- \ntained ; hence,\n\n~ | gu) Py m! (m + 2v)! \nThe summation of the terms in (45) gives a Bessel function \" of order \n2v, and hence (42). Using (42), (41) can be written \nn n\u20141 \nfast) =f\" faotaut f\u00b0 fay fo bw\" er\n\nThe series in (46) can be summed yielding a Bessel function of \norder one; hence,\n\nThe integration with respect to u can be interpreted as a Hankel \ntransform of the low-pass impulse response. For an impulse response \nwhich is not very oscillatory, and for 6 \u00ab w., the Hankel transform \nwill be a slowly varying function in comparison to the Bessel function. \nUnder these conditions an approximation to (47) can be obtained by \nusing the method of stationary phase.\n\nThe stationary phase method!* approximates integrals, 7, of the \nfollowing type:\n\nwhere & is large and g(x) is a slowly varying function. The approxi- \nmation considers only contributions from the vicinity of stationary\n\npoints where (dy)/dx = 0, and is of order (1/k). The approximate \nvalue of the integral (48) is\n\nTo bring (47) to a form suitable for evaluation with the stationary \nphase method, the Bessel function is expressed in terms of modulus \nand phase.!9\n\n(2) = 2\u2014 4 + d0(2), (51) \nwhere 6,(z) and M,(z) are slowly varying functions for large z with \nlim, \u00ab0 5o(z) = 0 and lim,... M,(z) = V2/ (2).\n\nWith z = 2wovix \u2014 22, the integral in (47) has a stationary point at \nx = t/2. The approximate value of (47), obtained by using (49), is\n\nFor large values of \u00a2 such that M,(z) and 6,(t) can be approximated \nwith their asymptotic values,\n\nIt is of interest to note that the stationary phase method gives the \ncorrect value for the integral\n\nThis integral can be evaluated exactly by using (42) with \u00bbv = 0 and \ng(u) = 1.0. The left-hand side of (42) is readily inverted yielding (54).\n\nComparison of Exact and Approximate Solutions \nConsider a notch filter transfer function\n\nThe Laplace transform of the time response due to a unit step \nfunction is\n\nA comparison of (57) with (19) shows that both are of the same \nform but w is replaced by w,. Hence, the approximation is of order\n\n. Members of the Technical Staff, Bell Laboratories, Transmission Systems for\n\nM.E. Van Valkenburg, Introduction to Modern Network Synthesis, New York: \nJohn Wiley, 1960, pp. 479-486. \nP. M. Morse and H. Feshbach, Methods of Theoretical Physics, Part I, New York: \nMcGraw-Hill, 1953, p. 944. \nW. T. Howell, \u201cOn a Class of Function Which are Self-Reciprocal in the Hankel \nTransform,\u2019\u2019 Phil. Mag., 25, Series 7, April 1938, pp. 622-628. \n. A. Erdelyi, et al., T'ables of Integral Transforms, Vol. 2, New York: McGraw-Hill, \n1954, p. 43. \n. E. A. Guillemin, Synthesis of Passive Networks, New York: John Wiley, 1957, \np. 489. \n. Ref. 3, p. 348.\n\n. Ref. 6, Vol. 1, p. 175. \n. I. S. Gradshteyn and I. M. Ryzhik, Tables of Integral Series and Products, New\n\n. Ref. 4, p. 456. \n. Ref. 6, Vol. 1, p. 1383. \n. N. W. McLachlan, Modern Operational Calculus, London: The MacMillan Com-\n\nCopyright \u00a9 1974 American Telephone and Telegraph Company \nTue BELL SystEM TECHNICAL JOURNAL \nVol. 53, No. 2, February 1974 \nPrinted in U.S.A.\n\nThe purpose of this paper 1s to make comparisons between optimum, \nlinear phase, finite impulse response (FIR) digital filters and infinite \nimpulse response (IIR) digital filters which meet equivalent frequency \ndomain specifications. The basis of comparison is, for the most part, \nthe number of multiplications per sample required in the usual realiza- \ntions of these filters\u2014t.e., the cascade form for IIR filters, and the direct \nform for FIR filters. Comparisons are also made between group-delay \nequalized filters and linear phase FIR filters. Considerations dealing \nwith finite word-length effects are discussed for both these filter types. A \nset of design charts 1s also presented for determining the minimum filter \norder required to meet given low-pass filter specifications for both digital \nand analog filters.\n\nAlthough a great deal is known about the properties of different \ntypes of digital filters, very little has been done to relate the various \ndesigns as to performance and complexity of realization. Thus the \nfilter designer must learn the details of several design procedures \nbefore being able to make a wise decision on a suitable filter for his \nspecific application. It is the purpose of this paper to add insight into \nsome of the problems that have been encountered by filter designers \nby: (2) presenting new and useful design curves for digital and analog \nlow-pass filters, and (27) making several comparisons between optimum \n(quasi-equiripple), linear phase, FIR low-pass filters and equiripple \n(elliptic) IIR filters which meet equivalent frequency domain specifica- \ntions. Although these results are presented for low-pass filter designs, \nthey are easily extended to the case of bandpass, bandstop, and high- \npass filters by the well-known frequency band transformations.\n\nThe organization of the paper is as follows. After defining the \nterminology to be used, the design relationships between the FIR \nfilter parameters are reviewed. The design relationships for the IIR \nfilter parameters are developed and a novel graphical interpretation \nof these relations is presented in the form of useful filter design charts \n(applicable to both digital and analog filters). Using the design rela- \ntionships, the filter orders required to achieve equivalent performance \nare compared for different ranges of filter parameters.\n\nThe design procedures for the two general classes of digital filters, \nFIR and IIR, have essentially progressed along independent paths. As \na result, the terminology used in specifying the filter performance is \ngenerally not quite the same. Thus it is instructive to define the most \ncommonly accepted definitions of the filter parameters for these two \nclasses of filters. The relations between these parameter sets for \nequivalence are then established. Figure la shows the amplitude \nresponse of a typical optimum FIR low-pass filter and Fig. 1b shows \nthe magnitude response of a typical elliptic low-pass filter. For the \nFIR case the amplitude response in the passband (0 S f S F,)* \ngenerally oscillates between 1 + 6; and 1 \u2014 61, where 6; is the passband \nripple. In the stopband (Ff, S f S 0.5) the amplitude response oscil- \nlates between +6, and \u2014\u00e9_2 where 62 is the stopband ripple. For the \nelliptic case the magnitude response is constrained to always be less\n\n* Throughout this paper the frequency scale has been normalized with respect to \nthe sampling frequency. Thus the normalized sampling frequency is 1.0 and the \nfrequency range graphed is 0 < f S 0.5 or, equivalently, 0 Sw Sx.\n\nthan 1.0. Thus, in the passband (0 S f S F,) the magnitude response \noscillates between 1 and 1 \u2014 6,. In the stopband the magnitude re- \nsponse oscillates between 62 and 0. It is straightforward to relate 44, \n52, 61, and 4 so the resulting magnitude characteristics are equivalent. \nIf the FIR amplitude characteristic is scaled by 1/(1 + 6;) and the \nmagnitude of the resulting amplitude response is taken, then the \nfollowing relationships are obtained:\n\nAt this point it is convenient to define the additional filter terms \u00a3, \nATT, and 7 as\n\nfilter. The parameter 7 has been shown to be a basic analog filter \nparameter! which will be used in the filter design curves given in a \nlater section.\n\nThe five basic FIR filter parameters are Fy, F;, 61, 52, and N, the \nduration of the filter impulse response in samples. For the general \ncase of optimum, linear phase, low-pass FIR filters, there exist no \nsimple analytical relationships between these five filter parameters, \nexcept in special cases, e.g., one passband or one stopband ripple. \nHowever, an approximate empirical relationship between the filter \nparameters has recently been obtained? which accurately satisfies \nknown design results for a wide range of values of the filter parameters. \nThe relationship is of the form:\n\nEquation (10) can generally predict the value of N required to meet \nspecifications on 61, 62, Fp, and F, to within +2. In the cases where \nF\u2019, is very close to 0, or F; is very close to 0.5, eq. (10) tends to over- \nestimate the required N. It should be noted that eq. (10) shows the \nestimate of N to be independent of specific values of F, or Fy, but \ninstead is dependent only on the transition width, (Ff, \u2014 Fp).\n\nThis expression is a modification of the design relationship for FIR \nfilters designed by windowing techniques (where 6; = 62). See Ref. 3, \npp. 237-238.\n\nOne of the most general procedures for designing IIR digital filters \nis through the bilinear transformation of an appropriate continuous\n\nfilter. There are two equivalent techniques for obtaining the desired \ndigital filter using the bilinear transformation and these are illustrated \nin Fig. 2. The technique of Fig. 2a begins with an analog low-pass \nfilter with normalized passband cutoff frequency of 1 radian per second, \nand analog stopband cutoff frequency of Q, radians per second. This \nfilter is bilinearly transformed\u2018 to give a \u2018\u2018normalized\u2019\u2019 digital filter \nwith passband cutoff frequency 7/2 radians per second (or f = 0.25 on \nthe normalized scale) and stopband cutoff frequency 4,. The relation \nbetween the frequency variables Q and @ is given by\n\nThus Q, and 4, are simply related by eq. (15) with Q = Q,, and 6 = 4,. \nFinally, a digital all-pass transformation\u00ae is used to give the desired \ndigital low-pass filter with passband cutoff frequency w, and stopband \ncutoff frequency w,. The relation between the frequency variables w \nand @ is given by\n\nThe second technique (shown in Fig. 2b) begins with the identical \nanalog low-pass filter as in the first technique and immediately per- \nforms a low-pass\u2014to-low-pass transformation to give an analog filter \nwith passband cutoff frequency 2, and stopband cutoff frequency Q,. \nThe relation between the frequency variables Q and 2 is\n\nThe resulting low-pass filter is then transformed to a digital filter using \nthe bilinear transformation, giving the same end result as in the first \ntechnique (Fig. 2a). The relation between frequency variables w and Q is\n\nIn the case where the prototype normalized analog filter is an elliptic \nfilter, it is relatively easy to derive a design formula relating the various \nfilter parameters, both in the analog and digital cases. For either the \nanalog or digital case the order, n, of the elliptic filter is related to \nthe remaining filter parameters by the equation\n\nDISCRETE \nCONTINUOUS NORMALIZED \nNORMALIZED BILINEAR LOW-PASS FILTER ALL\u2014PASS pr eal oe \nLOW-PASS TRANSFORMATION TRANSFORMATION a \nFILTER \nFILTER \n1 \u201c 1 \n1-8, 1-8 1-84 \n3 s 4 \n2 2 2 \n0 a 0 A) 0 w \n0 ~ 0 7/2 Gs 7 0 Wy Ws 7 \n(a) \nCONTINUOUS CONTINUOUS \nNORMALIZED LOW-PASS-\u00bbLOW_PASS LOW-PASS FILTER BILINEAR iG et \nLOW-PASS TRANSFORMATION TRANSFORMATION \nFILTER \nFILTER \n1 1 1 \n& A \n1-9) 1-8, 1-6; \nA A A \n52 52 A 62 \n0 o 0 - ~ 0 0 a \n0 1 0, 0 Op Q, 0 Mp Ws 7\n\nFig. 2\u2014T wo techniques for transforming a continuous normalized low-pass filter to a digital low-pass filter.\n\nh=n= (22) \nThus eq. (20) relates filter order, n, to the parameters F\u2019,, , [through \neq. (21) ] and 6; and 62 [through eq. (22) ].\n\nFor the case when the prototype filter is a Chebyshev filter (either \ntype I\u2014equiripple passband, monotone stopband, or type I]\u2014maxi- \nmally flat passband, equiripple stopband) the design equation becomes\n\nand 7 and k are defined as eqs. (21) and (22). Finally for a prototype \nButterworth filter (maximally-flat magnitude, all pole) the design \nequation is\n\nAlthough eqs. (20) through (25) completely describe the design\u2019 \ncurves for both analog and digital filters, it is generally quite helpful \nto see the relationships between filter parameters displayed in a \nmeaningful way. Since, in general, there are five filter parameters \nthere is no simple way of presenting these relationships on a single \nplot, even in terms of well-known nomograph procedures.* There is, \nhowever, a simple and straightforward way of including all design \nrelations for both digital and analog filters, for any prototype filter, \nusing a sequence of three charts.\n\nThe first chart(s) relates the filter design parameter n to the pass- \nband and stopband ripple specifications 6; and 62 or their equivalents. \nThe second chart(s) graphs the filter design equation relating filter \norder n, design parameter n, and transition ratio k. The third chart(s) \nrelates transition ratio k to passband cutoff frequency F\u2019, and transition \nbandwidth \u00bb.\n\nFigures 3a through 3d show four possibilities for Chart No. 1. The \ngraphs of Figs. 3a and 3b correspond to digital filters with 6, as a param-\n\nFig. 3\u2014Plots of 7 versus stopband specification, with parameter passband specifi- \ncation for low-pass filters.\n\neter (Fig. 3a) or 20 logio (1 + 61)(dB) as a parameter (Fig. 3b). The \ngraphs of Figs. 3c and 3d correspond to analog filters with absolute rip- \nple 6; as a parameter (Fig. 3c) or total ripple 20 logio [1/(1 \u2014 6) ](dB) \nas a parameter (Fig. 3d).\n\nChart No. 2 represents the design relations particular to the proto- \ntype filters, i.e., eq. (20) for elliptic filters, eq. (23) for Chebyshev \nfilters, and eq. (25) for Butterworth filters. For these graphs the param- \neter 7 is plotted versus transition ratio, k, with filter order, n, as the \nparameter. Figures 4a through 4c show the resulting graphs for elliptic \nfilters, Chebyshev filters, and Butterworth filters, respectively. The \nhorizontal scale on each of these graphs is a nonuniform scale which \nwas chosen to provide a reasonably good spacing of the curves for the \nvarious values of n. The actual nonlinear scale used is represented by \nthe equation\n\nwhere x is the z-axis coordinate (0 S$ x S 1) and k is the transition \nwidth. Thus, the scale is linear for small values of k and highly non- \nlinear near k = 1.0.\n\nChart No. 3 represents the relation between the transition ratio and \nthe filter cutoff frequencies [eq. (21) ]. For these graphs the passband \ncutoff frequency, F\u2019,, is plotted versus transition ratio, k, for various \nvalues of normalized transition width, v, defined as\n\nfilters. The scale for transition ratio is identical to the seale used for \nChart No. 2.\n\nTo illustrate how to use the set of charts of Figs. 3 through 5, con- \nsider the determination of filter order n required to meet the following \nspecifications:\n\n6; = 0.01 (} +0.086-dB passband ripple) \n52 = 0.0001 (80-dB stopband loss) \npassband cutoff frequency = 480 Hz \nstopband edge frequency = 520 Hz \nsampling frequency = 8000 Hz.\n\nFor the determination of filter order n for a digital filter of the \nelliptic type, the charts of Figs. 3a, 4a, and 5a are used (Fig. 4a special- \nizes the design to the elliptic type). To obtain the value of 7 on Fig. \n3a, we use the curve 6; = 0.01 and find its intersection with the line \n52 = 0.0001 which yields a value of 7 approximately equal to 2 X 10-5. \nTo obtain the transition ratio, we use Fig. 5a by finding the intersection \nof the curve v = F, \u2014 F, = 0.005 with line F, = 0.06; this yields a \nvalue of 0.923 for the transition ratio (this agrees nicely with \nF,/F, = 0.06/0.065 = 0.923, an alternate way of arriving at the same \nresult). Finally, the filter order, n, can now be determined from Fig. 4a \nby finding the intersection of the lines 7 = 2 X 10-5 and transition \nratio = 0.923; thus the required theoretical elliptic filter order is \n11.5. In order to meet specifications on all four parameters, a \n12th-order filter must be used.\n\nHowever, there are several tradeoffs possible for the final filter \nspecifications. For example, if 7 is held fixed at 2 X 10-5 and the \ntransition ratio is changed to approximately 0.94 to lie on the n = 12 \ncurve, then either F, or F, can be varied to match this new value of \ntransition ratio. The tradeoffs here are obtained from Fig. 5a. If the \ntransition ratio is held fixed, then for n = 12 we find 7 is 1.0 X 107-5; \nfrom Chart No. 1 (Fig. 3a) we can observe the tradeoff as 6, and 6, are \nvaried for this new value of 7. Finally, both transition ratio and 7 \ncan be varied, e.g., to 0.93 for transition ratio and 1.5 X 10-5 for , \nso as to make their intersection remain on the n = 12 curve; now all \nfour filter parameters can be varied to match the new values of 7 \nand transition ratio.\n\nIt is interesting to note that if a Chebyshev or Butterworth filter \ntype is specified in place of the elliptic, the designer need only substi- \ntute Figs. 4b or 4c for Fig. 4a as Chart No. 2 and proceed as before. \nIn both cases of the example given, the required filter order consider- \nably exceeds the maximum limit of 20 of the curves; thus the \u201ceffi- \nciency\u201d\u2019 of the elliptic design is clearly seen.\n\nClearly, this design procedure presents a tremendous amount of \nflexibility to the designer\u2014more so than is generally available in most\n\nFig. 4\u2014Plots of 7 versus transition ratio as a function of filter order n for elliptic, \nChebyshev, and Butterworth low-pass filters.\n\nprograms for filter order determination. Furthermore, the insight into \nthe design problem afforded by this graphical technique allows the designer \nto get a feeling for the way in which small changes in filter specification \naffect the required filter order. Quite often the designer is willing to \nchanges his ideas on \u201crequired\u201d\u2019 specifications, especially if it reduces \nthe filter order necessary to meet his specifications.\n\nBased on the design formulas of the preceding sections, it is possible \nto make some comparisons between optimum FIR low-pass filters and \nequivalent elliptic filters. The main basis of comparison will be the \nnumber of multiplications per input sample* required in the most \nstandard realization of each filter type, i.e., the direct form for the \nFIR case and the cascade form for the elliptic case.\u2019 Direct realization \nof an N-point impulse response filter with linear phase requires\n\n*The number of multiplications per input sample is a useful measure of the com- \nputational complexity of the filtering operations as it represents the number of \nmultiply-add operations required for a software implementation of the algorithm as \nwell as for a general hardware implementation.\n\nFig. 5\u2014Plots of passband cutoff frequency versus transition ratio as a function of \ntransition width for discrete and continuous low-pass filters.\n\n[(N + 1)/2] multiplications per sample, whereas cascade realization \nof an nth-order elliptic filter (all zeros on the unit circle) requires \n[(8n + 3)/2]* multiplications per sample where [- ] denotes \u201cinteger \npart of.\u201d\n\nThus, one basis of comparison between equivalent filter designs (i.e., \nboth meeting the same specifications on 61, 52, F,, and F,) is in terms \nof the efficiency of the respective realizations, i.e., which structure \nrequires fewer multiplications per sample. Equivalence between struc- \ntures is attained when the condition\n\nUsing the appropriate filter design formulas, we have measured the \nquantity N/n as a function of n for a large range of values of Fp, 41, \nand 62. Figure 6 shows two typical sets of curves which were obtained. \nFigure 6a shows data for the case F, = 0.15, 6; = 0.1, 62 = 0.1, 0.01, \n0.001, 0.0001, and Fig. 6b shows data for F, = 0.35, 6: = 0.00001, and \nthe same range of 62 as in Fig. 6a. Also shown in these plots is the line \nN/n = 3 for showing where the data lie with respect to the fixed \nportion of eq. (29). As seen in this figure, for certain values of F\u2019y, 41, \nand 62, the ratio of N/n falls below the equivalence level of eq. (29), \ni.e., the FIR filter is more efficient than the elliptic filter. However, in \ngeneral, the elliptic filter is more efficient than the optimum FIR \nfilter, and, in the case of high-order elliptic designs, the ratio of N/n \nis often in the hundreds or thousands.\n\nBased on our examination of large amounts of data, the following \ngeneral observation can be made: the most favorable conditions for \nthe FIR design are large values of 6;, small values of 62, and large \ntransition widths (i.e., small transition ratios). One also observes the \nfollowing behavior:\n\n(c) For values of F, = 0.3, the ratio N/n always exceeded 3 + 1/n \nfor all values of 61, 52, and n. \n(22) For values of n 2 7, the ratio N/n always exceeded 3 + 1/n \nfor all values of 61, 62, and Fp.\n\n\u201cThis number of multiplications per sample for the IIR filter assumes that any \nscaling between sections is an integer power of 2 and is performed entirely by shifts \nof the data. If finer scaling multipliers are included between each cascade section, \nthe realization requires [(4n + 3)/2] multiplications per sample.\n\nFig. 6\u2014Plots of the ratio N/n as a function of n for optimum FIR filters and elliptic \nfilters meeting identical specifications on 61, 52, Fy, and F,.\n\n(it) The smaller the value of F\u2019,, the larger the range of 61, 62, and \nn for which N/n was less than 3 + 1/n.\n\nSince the design formula for N for the optimum FIR case is not \nexact but only an estimate, measurements were also made of the \nrequired theoretical value of n (elliptical filter order) to meet the \nspecifications of optimum FIR filters which had already been designed. \nTypical results of these measurements are shown in Fig. 7. Figure 7a \nshows the theoretical order n (n need not be an integer) required to \nmatch specifications on F,, F,, for 6; = 0.1, 52 = 0.1, 0.01, 0.001, \n0.0001, and 0.00001, as a function of F, for a set of optimum FIR \nfilters with N = 21. (It should be noted that as F\u2019, varies, F; also \nvaries so as to achieve the desired specifications on 6; and 62.) Figure \n7b shows similar measurements for N = 41. In Fig. 7a the theoretical \npoint of equivalence is n = 6.3, whereas in Fig. 7b it is n = 13. From \nthis figure it is seen that for these cases the elliptic filter is always \nmore efficient than the equivalent FIR filter, as anticipated by the \ndiscussion in the preceding paragraphs. :\n\nIn summary, elliptic filters are generally more efficient in achieving \ngiven specifications on the frequency response than optimum FIR \nfilters. However, the FIR filters have the additional useful property \nthat their phase is exactly linear, i.e., there is no group delay distortion. \nFor the elliptic filter, however, there is generally a large amount of \ngroup delay distortion (concentrated primarily near the band edge). A \nquestion of both theoretical and practical importance is whether, in \ncases when the additional requirement of a flat delay is specified, it is \nmore desirable to equalize the delay of an elliptic filter or to use the \nequivalent optimum FIR filter (with its constant group delay). In the \nnext section we discuss various aspects of this question. It should be \nnoted that the above alternatives are not the only possibilities for \nobtaining a digital filter which meets frequency domain specifications \non both magnitude and group delay responses. For example, a filter \ncan be designed, using modern optimization procedures, where the \nnumber of poles and zeros are unequal. In such cases, the comparisons \nbetween FIR and IIR filters are quite distinct from those to be dis- \ncussed in the next section.\n\nVil. COMPARISONS OF OPTIMUM FIR FILTERS AND DELAY-EQUALIZED \nELLIPTIC FILTERS\n\nRecently developed optimization procedures\u2019 make it possible to \ndesign an all-pass equalizer which can equalize the group delay of any\n\nFig. 7\u2014Theoretical order of elliptic filters required to meet given specification on \n51, 52, F,, and F\u2019, as a function of F\u2019, for various values of 52. Optimum FIR filters \nwith N = 21 meet the specifications for all filters of (a), whereas N = 41 is re- \nquired for all filters of (b).\n\ndigital filter to any desired accuracy over a restricted band of fre- \nquencies. As an example of the use of this procedure, Fig. 8 shows \nplots of the group delay of a 6th-order (unequalized) elliptic filter \n(with parameters 6; = 0.01, 6: = 0.0001, F, = 0.24163, F, = 0.34842) \nand the equalized group delay using a 10th-order all-pass filter. The \nrelative error in the equalized delay curve is 3.6 percent of the average \ndelay in the passband. In this case the equalized elliptic filter requires \n20 multiplications per sample, whereas an optimum FIR filter which \nachieves the same specifications requires only 11 multiplications per \nsample.\n\nThe difficulty with trying to equalize the group delay of a filter \nlies in the fact that the equalized filter must have a total delay greater \nthan the largest delay in the unequalized filter which always occurs \nnear the passband cutoff frequency. Thus, in the example of Fig. 8, \neven though the delay throughout most of the passband is between \n2 and 6 samples, the delay at the edge of the band is about 15 samples. \nIt can be shown that an all-pass equalizer of degree n, has the\n\nFig. 8\u2014The group delay of an unequalized and an equalized elliptic filter. The \nequalizer is of 10th degree and the elliptic filter is of 6th degree.\n\nwhere 7,(w) is the equalizer group delay and the integral is taken over \nhalf the sampling interval (0 S w S zm). Since 7,(w) = 0, i.e., group \ndelays add, to justify eq. (30) it is sufficient to show that a first-degree \nall-pass equalizer has the required property. The z-transform of a first- \ndegree all-pass equalizer is \nkee /e\n\nH(z) = i ae (31) \nwhere a is the pole position and 1/a is the zero position in the z-plane. \nThe group delay is commonly defined as\n\nfor the first-degree equalizer. Integrating eq. (33) from 0 to w and \nnormalizing by 27 gives\n\nThe significance of eq. (30) is that one can estimate the minimum- \norder equalizer required to equalize a given group delay characteristic \nby determining the area between the line 7 = 7max and the curve \n7,() and dividing by 7, where tmax is the maximum value of 7,(w) \nin the passband. Thus in the example of Fig. 8, the estimated order of \nthe equalizer is approximately (13 X w/2)/m = 6.5. Of course, the \nrequired order of the equalizer must be greater than the estimate given \nabove, since this estimate assumes the delay of the equalizer exactly \ncompensates the delay of the unequalized filter. As the degree of the \nequalizer is increased over the estimate, the peak error of approxima- \ntion decreases monotonically.\n\nWe have used the above algorithm, along with initial estimates of \nequalizer order, to equalize three sets of elliptic filters. The data for\n\nTable |\u2014 Comparisons between optimum FIR and equalized \nelliptic digital filters\n\n_ * Ni is the number of multiplications per sample for the optimum FIR filter; N2 \nis the number of multiplications per sample for the equalized elliptic filter.\n\nthese three sets of filters are given in Tables I through III. Included \nin the table are the filter specifications (61, 62, Fp, F,); the required \nelliptic order n; the required FIR filter duration N; the equalizer \norder n.; the average passband delay, 7, (in samples), of the equalized \nfilter; the percentage ripple, r, in the passband group delay of the \nequalized filter; and a comparison between the number of multiplica- \ntions per sample required in both the optimum FIR filter and the \nequalized elliptic filters. The data in these tables indicate that to \nachieve equalization to within about a 3-percent error requires on the \norder of 30 percent more multiplications per sample for the equalized \nfilter than for the optimum FIR design, although in most cases the \nunequalized elliptic filter was more efficient than the optimum FIR \ndesigns. Thus it would appear that, at least for these restricted results, \nif constant group delay is required in addition to the equiripple magni-\n\nTable I|\u2014 Comparisons between optimum FIR and equalized \nelliptic digital filters\n\n* N, is the number of multiplications per sample for the optimum FIR filter; N2 \nis the number of multiplications per sample for the equalized elliptic filter.\n\ntude characteristics, then the optimum FIR filter is always more \nefficient than an equalized elliptic filter. It should also be noted that \nthe delay of the optimum FIR filter [(N \u2014 1)/2 samples] was always \nless than the delay of the equalized elliptic filter.\n\nThe examples of Tables I through III considered filters where the \norder of the unequalized elliptic filter was six or less. It can be argued \nthat, for higher-order elliptic designs, the relative efficiency of the \nelliptic filter over the optimum FIR filter is far greater than for lower- \norder designs; hence in these cases perhaps the equalized filter may \nstill be more efficient than the optimum FIR design. This conjecture \nturns out to be untestable because high-order elliptic filters have a \npeak passband delay timax which is much larger than for low-order \nfilters, hence the order required for the equalizer becomes extremely \nlarge and thus is not even practical to consider if equalization over \nthe entire passband is required. To illustrate this point, Fig. 9 shows \nthe group delay of a 10th-order elliptic low-pass filter with F, = 0.25. \nUsing eq. (30) to get an estimate of n. we arrive at a value of n, = 45. \nSince this value of n, is only an underbound on the actual order of the\n\nTable II! \u2014- Comparisons between optimum FIR and equalized \nelliptic digital filters\n\n* N; is the number of multiplications per sample for the optimum FIR filter; N2 \nis the number of multiplications per sample for the equalized elliptic filter.\n\nequalizer, it is clear that it is not practical to try to obtain such a \nhigh-degree equalizer.\n\nAnother interesting question which arises when one considers the \nidea of equalizing an IIR filter is how does the cascade combination \nof an elliptic filter and an all-pass equalizer compare to the optimum \nIIR filter which best approximates both the desired magnitude and \ngroup delay characteristics? It is clear that the optimum IIR filter can \nbe no worse than the cascade; the question remains as to how much\n\nbetter it can be. There is no clear-cut answer to this question. However, \nbased on our experience with equalized elliptic filters, several observa- \ntions can be made. (We shall use the z-plane pole-zero plot of a typical \nequalizer filter, shown in Fig. 10, to aid in understanding the nature of \nthe equalized filter.)\n\n(17) The zeros of the equalizer lie outside the unit circle to give \npositive delay.\n\n(iz) The poles of the elliptic filter are constrained by the transition \nwidth requirements of the low-pass filter.\n\n(iv) The poles of the equalizer lie approximately on a circle of fixed \nradius, and are approximately equally spaced in the passband.\n\nIf the zeros of the optimum filter are not constrained to lie on the \nunit circle, then each second-order section will require four multipli- \ncations per sample, rather than the three multiplications for each \nsecond-order section of the elliptic design and the two multiplications \nfor each second-order section of the all-pass equalizer. Based on the\n\nabove observations, it seems unlikely that there is much to gain by \nusing the optimum IIR filter over the equalized filter.\n\nIn this paper we have considered only one basis for comparison \nbetween optimum FIR filters and equivalent IIR designs, that mea- \nsure being the number of multiplications per sample required in the \nstandard method of realization for each of these filter types. The \njustification for this measure is that in hardware (and generally in \nsoftware) the number of multiplications per sample is an excellent \nmeasure of the complexity required in the implementation as well as \nthe factor which determines the maximum throughput rate of the \nsystem.\u00ae However, there are many other ways for comparing these \nfilter types when one takes into consideration the various finite word- \nlength effects which occur in a practical design situation. In this section \nwe review several of these design issues.\n\nAmong the various finite word-length effects are roundoff noise, \nboth uncorrelated and correlated (e.g., limit cycles), and coefficient \nquantization sensitivity. For direct-form FIR realization, the peak \nroundoff noise can easily be made to be less than 4 of the least signifi- \ncant bit by accumulating partial sums in an extended length register \nand then rounding the final result. For cascade IIR filters realized \nwith fixed-point arithmetic, the roundoff noise problem is inherently \nrelated to the dynamic range problem,\u2019 and involves the concepts of \npole-zero pairing and section ordering. Jackson\u201d has shown that with \nreasonable pairing and ordering the uncorrelated roundoff noise vari- \nance can be minimized. However, even in the best of situations, the \nroundoff noise is equivalent to several bits. In terms of correlated \nroundoff noise, i.e., limit cycles, the direct-form FIR realization has no \nzero-input limit cycles (because no feedback is present), whereas the \ncascade IIR realization will generally exhibit zero-input limit cycles. \nKaiser! has extensively studied these limit cycles and has developed \nbounds and estimates for their amplitude and frequency.\n\nThe coefficient quantization problem is one of the most difficult \nfinite word length effects to treat analytically. Rounding of infinite \nprecision filter coefficients to a fixed number of bits alters the overall \nfrequency response of the filter in a complicated manner. Avenhaus\u201d \nhas shown that straight rounding of the infinite precision filter co- \nefficients is generally inferior to optimizing the filter performance over \nthe finite set of fixed precision filter coefficients. However, there are\n\nno general procedures for performing this optimization, nor are there \nany guarantees of convergence of the existing methods. Furthermore, \nin many cases the advantage of optimizing finite precision coefficients \nover straight rounding of the infinite precision coefficients is small. \nThus for the case of coefficient quantization neither direct-form \nrealization of FIR filters nor cascade realization of IIR filters seems \nto offer a relative advantage here.\n\nThus it is difficult, if not impossible, to be quantitative in comparing \nFIR and IIR filters based on anything other than number of multipli- \ncations per sample. This is why we have used this measure throughout \nthis paper.\n\nIn this paper some comparisons were made between equivalent FIR \nand IIR digital filters based on the number of multiplications per \nsample required to realize these filters. In the case of low-pass filters \nwith quasi-equiripple magnitude characteristics, IIR elliptic filters \ncould generally be realized more efficiently than equivalent linear phase \nFIR filters. When the additional requirement of constant group delay \nin the passband was added to the specifications, comparisons showed \nthe linear phase FIR filters to be more efficient than group-delay- \nequalized elliptic IIR filters.\n\nAdditionally, a novel set of design charts for determining the \nminimum filter order required to meet given filter specifications for \nboth digital and analog elliptic, Chebyshev, and Butterworth low- \npass filters was presented. Explanation of how to use these charts to \ngain insight into the various filter parameter tradeoffs was also given.\n\n2. O. Herrmann, L. R. Rabiner, and D. 8S. K. Chan, \u2018\u2018Practical Design Rules for \nOptimum Finite Impulse Response Low-Pass Digital Filters,\u2019 B.S.T.J., 52, \nNo. 6 (July-August 1973), pp. 769-799.\n\n. J. F. Kaiser, \u201cDigital Filters,\u2019\u2019 in System Analysis by Digital Computer, edited \nby F. F. Kuo and J. F. Kaiser, New York: John Wiley and Sons, 1966.\n\n. R. M. Golden and J. F. Kaiser, \u2018\u2018Design of Wideband Sampled Data Filters,\u201d \nB.S.T.J., 43, No. 4, Pt. 2 (July 1964), pp. 1533-1546.\n\n. A. G. Constantinides, \u201cSpectral Transformations for Digital Filters,\u2019\u2019 Proc. IEE, \n117, No. 8, 1970, pp. 1585-1590.\n\n. E. Christian and E. Eisenmann, Filter Design Tables and Graphs, New York: \nJohn Wiley and Sons, 1966.\n\n. L. B. Jackson, \u201cOn the Interaction of Roundoff Noise and Dynamic Range in \nDigital Filters,\u201d B.S.T.J., 49, No. 2 (February 1970), pp. 159-184.\n\n. A. G. Deczky, \u201cSynthesis of Recursive Digital Filters Using the Minimum \np-Error Criterion,\u201d IEEE Trans. Audio and Electroacoustics, AU-20, No. 4 \n(October 1972), pp. 257-263.\n\nB. Jackson, J. F. Kaiser, and H. S. McDonald, \u2018\u2018An Approach to the Imple- \nmentation of Digital Filters,\u2019 IEEE Trans. Audio and Electroacoustics, \nAU-16, No. 3 (September 1968), pp. 413-421.\n\nB. Jackson, \u2018\u2018Roundoff-Noise Analysis for Fixed-Point Digital Filters Realized \nin Cascade or Parallel Form,\u2019? [EEE Trans. Audio and Electroacoustics, \nAU-18, No. 2 (June 1970), pp. 107-122.\n\nF. Kaiser, \u201cAn Overview on Digital Filters,\u2019\u2019 Newsletter of IEEE Circuit \nTheory Group, 6, No. 1 (March 1972).\n\nAvenhaus, \u2018On the Design of Digital Filters with Coefficients of Limited \nWord Length,\u2019 IEEE Trans. Audio and Electroacoustics, AU-20, No. 3 \n(August 1972), pp. 206-212.\n\nCopyright \u00a9 1974 American Telephone and Telegraph Company \nTue BELL SysTeEM TECHNICAL JOURNAL \nVol. 53, No. 2, February 1974 \nPrinted in U.S.A.\n\nOn the Behavior of Minimax Relative Error \nFIR Digital Differentiators\n\nOptimum (in a minimax relative error sense) linear phase FIR digital \ndifferentiators can be designed in an efficient manner using a Remez opti- \nmization procedure. This paper presents data on wideband differentiators \ndesigned with even and odd values of N, the filter impulse response dura- \ntion in samples. Based on these data, several interesting observations can \nbe made, including:\n\n(i) Differentiators with even values of N have peak relative errors which \nare approximately one to two orders of magnitude smaller than identical \nbandwidth differentiators with odd values of N, and with the same number \nof multiplications per sample in a direct convolution realization.\n\n(22) The smaller the bandwidth of the differentiator, the faster the de- \ncrease of the peak relative error with increasing N.\n\n(iz) The larger the value of N, the faster the decrease of the peak relative \nerror with decreasing bandwidth.\n\nThese observations lead to the conclusions that the bandwidth of a \ndifferentiator should be made as small as possible, and that even values \nof N should be used whenever possible. Complete tables of values of the \nimpulse response coefficients are included for several wideband dtffer- \nentiators for even and odd values of N.\n\npart of many practical systems,\u2018 it is the purpose of this paper to \npresent new data on the characteristics of optimum FIR differentiators, \nas an aid in making informed decisions concerning their use.\n\nA differentiator is a system whose output is the derivative of its \ninput. The frequency response of a differentiator is purely imaginary \nand is proportional to frequency. A sequence of samples of the deriva- \ntive of a band-limited signal can be obtained by filtering a sequence \nof samples of the signal with a digital filter that approximates the \nideal frequency response of a differentiator over the bandwidth of the \nsignal. Therefore, digital filters having this type of frequency response \nare also called differentiators.\n\nThe frequency response of the ideal digital differentiator with a \ndelay of 7 samples is\n\nThe impulse response corresponding to eq. (1) is obtained as the \ninverse Fourier transform of eq. (1) and is given by\n\nThe impulse response of eq. (5), which corresponds to an ideal differ- \nentiator with zero delay, is of infinite duration and obeys the symmetry\n\nThe impulse response of eq. (6), which corresponds to an ideal differ- \nentiator with one-half-sample advance, is of infinite duration and obeys \nthe symmetry condition\n\nIn Ref. 2 it was shown that the frequency response of an ideal \ndifferentiator with zero delay had a discontinuity at half the sampling \nfrequency [i.e., w = 7 in eq. (1) with 7 = 0], whereas the frequency \nresponse of an ideal differentiator with a one-half-sample advance had \nno discontinuity at w = 7. The frequency response of a half-sample- \nadvance differentiator has a slope discontinuity at w = 7 but, as we \nwill see, slope discontinuities are much easier to approximate than \nfunction discontinuities. It should be noted that the output of a one- \nhalf-sample-advance differentiator is the derivative of the input signal \nevaluated midway between input samples. For numerical analysis appli- \ncations where one desires the derivative at the sample point rather \nthan midway between samples, the use of differentiators with zero \ndelay is required. For most signal processing applications, either type \nof differentiator is generally appropriate.\n\nWe have only considered 7 = 0 and r = \u2014 3 as possible delays for \nthe ideal differentiator. It can be seen from eq. (4) that these are the \nonly values of (\u2014 1 < 7 S$ 0) such that the impulse response has desir- \nable symmetry properties.\n\nIn order to obtain a causal approximation to the ideal differentiator \nwhich has no phase distortion (other than that corresponding to \ndelay), it can be shown that an FIR approximation is required.\u00b0\u00ae \nTherefore, consider a causal FIR filter with impulse response h(n), \n0 Zl. The result, eq. (154), is again quite\nsimple.\nII. PRELIMINARY CONSIDERATIONS\n\nFor a smooth waveguide, there is a simple relation between the\npropagation constant {3 of a mode and the waveguide diameter, but no\nsuch simple relation exists in the case of a corrugated waveguide [see eq.\n(20)]. For this reason, the properties of the corrugated waveguide modes\ncannot generally be determined as simply as in the case of a smooth\nwaveguide. Also, the field configuration of each mode varies with\nwaveguide diameter. There is, however, an important exception. When\nthe radius a of the corrugated waveguide is sufficiently large, the propagation constant {3 for some of the modes is simply given by\n{3 = V(ka)2 - u6m'\n\n(1)\n\nwhere UO m is the m th zero of the Bessel function J 0 of order zero,\n(2)\n\nFor all the other modes except one (for this special mode (3 is independent\nof a; see Appendix B) one has\n{3 =\n\nv (ka)2 - u~m ,\n\n(3)\n\nwhere U2m is the m th root of the Bessel function of order two,\nJ 2(U2m) = o.\n\n(4)\n\nEquations (1) and (3) are valid provided a \u00bb A, a condition which is\nsatisfied to a good approximation by most feed apertures. Thus, the\ncase\nka\u00bb 1\n\n(5)\n\nis of considerable practical interest. One finds that as ka -- 00, the\nproperties of a mode become independent of the surface reactance Xs\nof the corrugated walls, except for the mode of Appendix B. Thus, the\nfield distribution over the aperture of a feed illuminated by a single mode\nwill be little affected by the surface reactance Xs (which varies fairly\nrapidly with frequency) provided ka is sufficiently large. This result, first\npointed out by Thomas,8 is very important for it implies that the aperture field distribution becomes frequency independent for large ka. The\nmain purpose of this section is to determine the asymptotic behavior of\nthe hybrid modes for large ka. It is shown that if ka ~ 00 there is over\nthe aperture of a feed a certain undesirable cross-polarized component,\neven if the aperture is illuminated by a single mode, unless of course Xs\n838\n\nTHE BELL SYSTEM TECHNICAL JOURNAL, JULY-AUGUST 1977\n\n=\n\nCX).\n\nA simple expression for the amplitude of this component is\n\ngiven.\nIII. ASYMPTOTIC BEHAVIOR FOR LARGE ka\n\nConsider a disk-loaded waveguide centered around the z-axis, as in\nFig. 1, and assume its parameters a, b, and h are independent of z. Let\nr, \u00a2, z be cylindrical coordinates defined by x = r cos\u00a2 and y = r sin\u00a2.\nThe separation of the disks, which occupy the region a < r < b, is assumed to be much smaller than a wavelength A,\nkh \u00ab 1.\n\n(6)\n\nThe region between two consecutive disks forms a radial line whose input\nreactancejX at r = a is a function of the radial length l = b - a; for ka\n\u00bb 1, one has approximately\n\njX = jZo tankl,\nwhere Zo = vi}la/Eo' For a finite number of teeth per wavelength, the\nvalue of l must be corrected. * Because of condition (6) the effect of the\ndisks can be accounted for adequately by introducing an effective surface\nreactance 5 ,12,19\n\njXs = jX ( 1 - ~),\n\n(7)\n\nwhere t is the thickness of the disks, and by requiring that the field for\nr < a satisfy the boundary conditions\n\nE 1> -0\n'\"\n\n} for r = a,\n\n(8)\n\nH ;:;:;_ Ez\n1>\n]'Xs\nwhere E 1>, H 1>, E z are the \u00a2 and z components of the electric and magnetic\nfield.\nLet (3 be the propagation constant in the z direction,\n(3 = k cost'h,\n\n(9)\n\nand assume (h is real, so that (3 < k. The case where (h is imaginary is\nconsidered in Appendix B. Assume the \u00a2 dependence of E z is given by\ncos\u00a2. Then, the field components of a mode that propagates in the z\ndirection with propagation constant (3 are eiven by\n(10)\n\n* See Ref. 17 for the effect of a finite number of teeth per wavelength, which causes a\nreduction of the effective depth, l.\n\nCORRUGATED FEED PERFORMANCE\n\n839\n\n(11)\n(12)\n\n(13)\n(14)\n(15)\n\nwhere\nK\n\n= k sinOl.\n\nThe boundary conditions (8) give l2\nu\n\nJ;(u)\n\n'Y=-----\n\n(16)\n\nCOSOl 1\n1 J;(u)\ny=---+---sinOl u 'Y sinOl J 1 (u) ,\n\n(17)\n\nCOSOl Jl(u) ,\n\nwhere\n\nu = ka sinO!,\ny = -\n\nZo\nXs'\n\n(18)\n\nand 'Y is the ratio between the TM and TE components of the hybrid\nmode,\nA\n(19)\n'Y =-.\nB\nBy eliminating 'Y from eqs. (16) and (17), one obtains the eigenvalue\nequation\n(20)\n\nwhich is eq. (10) of Ref. 12.\nThe solutions of this equation are now studied for large ka. Both u and\nyare assumed to be finite. Then, in the limit as ka --- 00, eq. (20) reduces\nto\nJ'l(U)\n( Jl(u)\n840\n\nu)2 _1 = o.\n\nTHE BELL SYSTEM TECHNICAL JOURNAL, JULY-AUGUST 1977\n\n(21)\n\nWe distinguish two cases:\nJ'l(U)U =\n\n-1\n\nJ 1 (u)\n\n(22)\n\nand\n\nJ; (u)u = 1.\nJdu)\n\n(23)\n\nAccording to eq. (16) (with COS01 ~ 1, since 01 - - 0 as ka -- co), these two\ncases correspond respectively to\n1'=1\n\n(24)\n\n1'=-1.\n\n(25)\n\nand\n\nUsing well known recurrence relations between the Bessel functions and\ntheir derivatives, and using conditions (22) and (23), we find\n(26)\n\nand\n(27)\n\nWe conclude that for large ka, eq. (20) possesses the two sets of solutions\nu ~ UO m (m = 1, 2, etc.)\n\n(28)\n\nu ~ U2m (m = 1, 2, etc.),\n\n(29)\n\nand\n\nUO m and U2m being respectively the mth root of Jo(u) and J 2 (u). Solutions (28) and (29) are characterized by l' ~ 1 and l' ~ -1; the corresponding modes will be designated, * respectively, HElm and HE;m.\nAsymptotic series for u and l' in terms of\n\n1\nka'\n\n(30)\n\n* This mode classification differs from the one by Clarricoats 12 and it was chosen for the\nfollowing reason. Here, and in Ref. 17, we are interested in horns whose inner radius a varies\ngradually with z, while the wall susceptance y is approximately constant, as in Fig. 1, from\nZ2 to Zl. Consider therefore a mode propagating in Fig. 1 from Z2 towards Zl. Clarricoats'\nclassification assigns in some cases a different name to this mode in different regions of\nthe horn, even though there will be no discontinuous variation of the mode-field configuration, as it propagates in the horn. On the other hand, our classification based on the\nBessel function roots UO m and U2m, assigns a single name everywhere in the horn. If instead\nthe frequency is gradually changed the mode of a waveguide of given dimensions will retain\nthe same name with Clarricoats' classification, whereas this is not always true with our\nclassification. To understand better these considerations, see also Ref. 25.\nCORRUGATED FEED PERFORMANCE\n\n841\n\nare derived in Appendix A under the assumption y ~ co. For the HElm\nmodes, characterized by 'Y - 1 as ka - co, it is found that\nU\n\n=Um = UO m 11 - ~\n\n(k1J'\n1\n+ ~ [ 1 - ~; (7U 6m + 1)] (k a)\n\n:a -t[1- ~ +\n(1\n\nU6m)]\n\n3 \u2022\u2022\u2022 )\n\n(31)\n\n3 \u2022\u2022\u2022 ).\n\n(32)\n\nand\n\"V\n\n= 1-\n\n1\n\nU2\n\nOm\n\n{y2 ka1 y28 (4 + u (1)2\nka\n- -\n\n-\n\n2 )\n\n-\n\nOm\n\n-\n\n- ~ [ 1 - ~ U5m - ~ (3U6m + 2)]\n\nCJ\n\nFor the HE~m-modes, characterized by 'Y - -1, u is given by\n(33)\nand\n'Y = -1 -\n\nu~m {~ :a ... }.\n\n(34)\n\nThe x and y components of the electric field are now derived. First\nconsider the HElm modes. One finds from eqs. (10) to (15), with cosO 1\n= 1 and 'Y given by eq. (32), that for large ka the transverse component\nof E is given by\n\nE t ;=:; - j k: A [ J 0 (~u ix\n\n)\n\n+ 1:. u2 L J 2 (!... u) (cos2\u00a2 ix + sin2\u00a2 i y )],\n4\n\nka\n\na\n\n(35)\n\nomitting the factor e - j(3z. Amplitude A is determined by power P carried\nby the mode. From eq. (67) with du/dy given by eq. (92) and YJi = A\n\nIAI ;=:;.!VZo~u2_I_\na\n\n7r\n\na{3 ka Jr(u)\n\n(36)\n\nif P = %.\nFor the HE~m modes with 'Y ;=:; -1, on the other hand,\nE, ;v j k: A [ J, (~u) (cos2q, ix + sin2q, iy) + ... ],\n842\n\n(37)\n\nTHE BELL SYSTEM TECHNICAL JOURNAL, JULY-AUGUST 1977\n\nwhere the dots represent terms that vanish as ka - 00. The amplitude\n1A 1 for P = %is still given by eq. (36). *\nAn important property of the field distribution (35) is that Ey - 0 as\nka - 00. Thus, in the limifas ka - 00, the field becomes polarized in one\ndirection, regardless of the value of the surface reactance Xs (unless,\nof course Xs = 0). From eq. (35), the amplitude of Ey is porportional to\nthe ratio\n\nl\n\n(38)\n\nka\n\nTherefore, in order that Ey be negligible over the aperture of a feed, it\nis sufficient that the aperture diameter be large and the thickness t of\nthe disks (see Fig. 1) be small compared with their separation.t The far\nfield of an aperture illuminated by the fundamental mode, the HEn\nmode given by eq. (35) for u = UOl = 2.4048, is discussed in Ref. 17. From\na comparison of the radiation patterns of Ex and E y, we find that the\nratio C2 between the maximum value attained by 1Ey 12 and 1Ex 12 (which\noccurs on axis) is given by\n\nC2 = 0.14 ( -Y\n\nka\n\n)2 =\n\n0.14\n[ (1 - t/h)ka tan 7r W]2\n2 Wo\n\n,\n\n(39)\n\nwhere Wo denotes the frequency for which y = o. One can easily verify\nusing this formula that C2 remains less than 0.000316 (-35 dB) over a\nfrequency range WI < W < 1.93 WI, provided ka > 10 and t/h < 0.1.\nThus, good performance over a wide frequency range is possible,\nprovided all the power incident at the input of the feed is converted to\nthe HEn mode. If, however, some of the input power is converted into\nsome of the HE~m modes, then, according to eq. (37), the field over the\nfeed aperture will contain a cross-polarized component whose amplitude\nis essentially independent of the ratio y/ka. The resulting cross-polarized\ncomponent of the far field is discussed in Ref. 17. If WI < W < W2 denotes\nthe frequency range over which only the fundamental mode (HEn)\npropagates, it is pointed out in Ref. 17 that the largest value that W2/WI\ncan assume is 1.6839; this value is attained for b/a = 1.8309. Cutofffrequency formulas are derived in Appendix D.\nIn Appendix B, the properties of a surface-wave mode that can exist\nin a corrugated waveguide, in addition to the modes of eqs. (35) and (37),\nare briefly described.\n* In eqs. (35) and (37), only the leading terms for the symmetrical, asymmetrical, and\ncross-polarized components are retained.\nt Note that from eqs. (7), (8), and (18), y increases with t/h.\n\nCORRUGATED FEED PERFORMANCE\n\n843\n\nIV. COUPLING COEFFICIENT BETWEEN TWO MODES\n\nSuppose the electric field El at the input of a corrugated waveguide\nis known, and we want to determine the resulting amplitude of one of\nthe modes excited in the corrugated waveguide. We have to evaluate a\nsurface integral of the form\n\nf Is\n\n(E 1 X H;) . iz dxdy,\n\n(40)\n\nwhere H2 is the magnetic field of the mode whose amplitude is to be\ndetermined. This integral, identical to that involved in determining the\nfar field radiated in a given direction by an aperture containing the field\nEll is in general difficult to evaluate. However, in many cases, we can\nassume that\nOEl_ . E\n02\n-]{31 1,\n\n(41)\n\nf'oJ\n\nwhere {31 is a constant. This condition is approximately satisfied, * for\ninstance, in the case of a feed aperture illuminated by a single mode\npropagating in the 2 direction with propagation constant {31. We will show\nthat the above surface integral can be reduced to a line integral which\ncan be evaluated straightforwardly. We use the symbol (Ell H 2 ) for the\nintegral (40), and call it the scalar product of the two modes El and\nH 2\u2022\nIf Ell HI and E 2, H2 are two solutions of Maxwell's equations, in free\nspace,20\n(42)\n\nin the absence of sources. Now, let the 2 dependence of the two solutions\nbe given by\n(43)\n\nThen, in eq. (42)\n(44)\n\nv = Vt - j({31- (32)iz,\nwhere v t is the transverse part of V. Therefore eq. (42) gives\n\nvdEl X H; + E; X HI) = j({31 - (32)[(E 1 X H;) . iz + (E; X HI)\u00b7 izl.\n(45)\n\nNext, consider a new solution E~, H~ with propagation constant {3~ =\n-{31 and with 2 components given by\n(46)\n\n* Of course, condition (41) is satisfied exactly by a mode in a cylindrical waveguide.\n844\n\nTHE BELL SYSTEM TECHNICAL JOURNAL, JULY-AUGUST 1977\n\n(47)\n\nThen the x, y components of E;, H; simply coincide 21 with the x, y\ncomponents of Eb -HI,\n\nH;x = -H lx ,\n\nE;y = Ely,\n\n(48)\n\nH;y = -H ly .\n\n(49)\n\nTherefore, replacing in eq. (45) (31, Eb HI with -(31, E;, H; and making\nuse of eqs. (48) and (49), we obtain\n\"'V t \u2022 (E; X H; + E; X H;) = -j((31 + (32)[(E I X H;)\n\n- (E; . HI)] X i z .\n\n(50)\n\nBy adding eq. (45) to eq. (50), we obtain\n(51)\n\n(E I X H;) . iz = \"'V t \u2022 F,\nwhere\n\nWe now integrate eq. (51) over a finite area S of the plane z = 0, making\nuse of the divergence theorem,\n\nJ Is\n\n(E I X H;) . iz dxdy =\n\nfc F\u00b7 ds,\nn\n\n(53)\n\nwhere C is the contour of Sand n is the outward normal. To determine\nF . n, let T be a unit vector tangent to C,\nT = iz X\n\nn.\n\n(54)\n\nThen, if A and B are two arbitrary vectors,\n(A X B) . n = ArBz - AzB n\n\n(55)\n\nwhere An Br are the components of A and B in the direction of T.\nTherefore, from eq. (52), taking into account eqs. (46) to (49),\n\nF\u00b7 n = -j\n\nA\n\n(31 - (32\n\n[ElrH;z + E;rHlz]\n\n+j\n\nA [E 1z H;r + E;zHlr]. (56)\n(31 - (32\n\nCORRUGATED FEED PERFORMANCE\n\n845\n\nFinally, from eqs. (53) and (56), we obtain the desired result,\n\nSIs\n\n(E I , H 2 ) =\n\n(E I X H;) . iz dxdy\n\n= -j\n\nA\n\nrI:' (ElTH;z + E;THlz)ds\n\n{31 - {32 ~ C\n\nA\n\n+j\n\nrI:' (ElzH;T + E;zH IT)ds.\n\n{31 - {32 ~ C\n\n(57)\n\nThus, the scalar product (coupling coefficient) of two modes EI and\nE2 can be determined straightforwardly from the values of EI and E2\non the contour of the aperture S. This result has a number of applications. It can be used, as already pointed out, to determine the far field\nradiated by an aperture S with known field distribution El, in which\ncase H2 is the magnetic field * of a plane wave with propagation vector\nk and eq. (57) gives, except for a constant independent of k, the field\ncomponent radiated in the direction of k with the polarization of H 2 \u2022 In\nthis article, we are interested in the special case where S is a circular area\nof radius a, in which case we can replace in eq. (57) T with \u00a2, since\nT =\n\nif/>.\n\nIf Ei, Hi (i = 1, 2) represents a mode of a corrugated waveguide of radius\n\na, so that for r = a\nEif/> = 0,\n\nZoHif/> = - jYiEiz,\n\n(58)\n\nthen eq. (57) simplifies to\n(E I , H 2) = -\n\n~\n\nA\n\nZo {31 - {32\n\n(Y2 - YI)\n\nrI:' ElzE;z ds.\n\n~C\n\n(59)\n\nSince the modes are characterized for z = 0 and r = a by\nEiz = 7'JiJI(ud cos\u00a2,\n\n(60)\n\nwhere 7'Ji is the coefficient A of the ith mode, then\na7r\n{31\n*\n(El, H 2) = - Zo {3r _ {3~ (Y2 - YI)7'J17'J2 J I(Ul)JI (U2).\n\n(61)\n\nNote that\n(62)\n\nIf we assume\nY2 = YI + dy,\n\n(63)\n(64)\n\nk.\n\n* There are two cases (two polarizations) that must be considered, for each value of\n\n846\n\nTHE BELL SYSTEM TECHNICAL JOURNAL, JULY-AUGUST 1977\n\nfrom eq. (61) we obtain for the power carried by the mode EI\n3\n\np = 1: (E H) = _ ~ f3la dy TJ2J2(U ).\n1\n\n2\n\nb\n\n2Z0 2UI dUI\n\n1\n\n1 1\n\n(65)\n\n1\n\nThe derivative dy/duI, which appears in this expression, is calculated\nin Appendix C. In the following sections, we choose\n(66)\nin which case from eq. (65)\n.. / 2Z o Ui\n\nITJd = 'V a 2 f3i a\n7r\n\nI dUi I\ndy\n\n1\n\nJi(ud\u00b7\n\n(67)\n\nThese results are now applied to the problem of a junction between two\ndifferent waveguides.\nV. JUNCTION BETWEEN TWO WAVEGUIDES OF DIFFERENT SURFACE\nREACTANCE\n\nLet two waveguides of different surface reactance, but the same diameter, be jointed at z = o. Assume a single mode incident on the plane\nof the junction from the region z < 0 and let E t , H t denote the transverse\nfield components. To determine the amplitudes of the reflected and\ntransmitted modes, we expand E t and H t on either side of the junction\nin an infinite series of modes, and then require continuity of E t and H t\nat the junction. A simple solution for the amplitudes of the scattered\nmodes is then obtained assuming the difference in surface reactance is\nsmall. This result will be extended in Section VI to the more general case\nof two waveguides of slightly different diameter.\nLet the transverse fields for z < 0 be represented by a superposition\nof the modes of the waveguide occupying the region z < 0,\n00\n\nE t = Alel-j/hz + I: Rieiejlhz,\n\n(z < 0)\n\n(68)\n\n(z < 0),\n\n(69)\n\n1\n00\n\nH t = Alhle-j/hz -\n\nI: Rihiei/hz,\n1\n\nwhere\n\nare the transverse field components of the incident mode, and\n\nare those of the reflected modes.\n\nCORRUGATED FEED PERFORMANCE\n\n847\n\nSimilarly, for z > 0,\n\nf: Tie~e-j{3iz, (z > 0)\n\nEt =\n\n(70)\n\nI\n\nHt =\n\nf Tih~e-j{3iz, (z > 0),\n\n(71)\n\nwhere Ti are the amplitudes of the transmitted modes.\nWe assume that ei, hi are normalized so that\n\nSimilarly,\n(73)\nSince (ei, hi) represents twice the power carried by the ith mode ei, this\npower becomes imaginary if the mode is cutoff, in which case eq. (73) for\ni = 1 should be replaced with\n(ei, hi) = j.\n\nHowever, in this article the calculation of R i , Ti is restricted to the modes\nthat are not cut off by the two waveguides.\nFrom eq. (61) with 11i, 11k given by eq. (67),\n~--------~------\n\n( r. h') - ~\n\ne,\n\nn\n\n-\n\n{3i\n(\n') ~ /\nUiU~\na2 {3[ _ {3~2 Y - Y V I(3i{3~(dy/dui)(dy' /du~) I\u00b7\n\n(74)\n\nand\n(75)\n\nwhere (ei, h~) and (e~, hi) are scalar products defined as in eq. (72)\nand\n(76)\na being the radius of the two waveguides. In eq. (74) 1/y and 1/y' are the\n\nnormalized surface reactances of the two waveguides.\nN ow assume y' - y is very small and let\nby = y' - y.\n\n(77)\n\nTo determine Ri, T i, we require continuity of E t and H t for z = 0,\n\n848\n\nAIel +\n\nf Rnen = Tle~ + f Tne~.\n\n(78)\n\nAlh l -\n\nfI Rnhn = Tlh~ + f2 Tnh~.\n\n(79)\n\nI\n\n2\n\nTHE BELL SYSTEM TECHNICAL JOURNAL, JULY-AUGUST 1977\n\nTake the scalar product of the first equation with h~ and of the second\nwith e~. One obtains, taking into account eq. (73) and assuming that the\nmode e; is not cutoff, so that (3; is real,\nAl (eI, h;) + Rdei, h;) +\n\nL\nn~I,i\n\nAI(e;, hI) - Ri(e~, hd -\n\nL\nn~I,i\n\nRn (en, h) = T i,\n\n(80)\n\nRn(e;, h n ) = T i .\n\n(81)\n\nNow, assume for the moment that y, y' ~ 00. Furthermore assume none\nof the modes under consideration is at cutoff. Then\n(en, h~),\n\n(e;, h n )\n\n(i ~ n)\n\n(82)\n\nare small quantities of the same order of oy. Furthermore, as we show\nbelow, this is true also for Rn. It follows that the two sums involving Rn\nin eqs. (80) and (81) are of order higher than oy. Therefore, subtracting\nthese two equations and neglecting terms of order higher than oy,\nRi = -AI (eI, h~) - (e~, hI).\n(ei, hi) + (e i,hd\n\n(83)\n\nAdding eqs. (80) and (81), and neglecting terms of order higher than\noy and solving for T i , we obtain\nTi = Al (eI, h~) + (e;, hI) .\n\n(84)\n\n2\nUsing eqs. (74) and (75), we rewrite eqs. (83) and (84) in the form\nRi = -AI (3i - (3~ yU I (3i\n(31 + (3i\nui(31\n\nYI\n\ndy/dui\ndy/dul\n\nI'\n\n1\n1\n(\n') ~ lUlu;\n1\nTi = Al a2 (31 - (3; y - y 'V (31(3; I(dy/duI) (dy' /du;) I .\n\n(85)\n(\n\n)\n86\n\nThe derivatives dy/dul and dy' /du; are derived in Appendix C.\nIt is interesting to note from eq. (85) that the reflection coefficient for\nthe mode i = 1 is simply\n\nR1\n(31 - (3~\nPI = Al = - (31 + (3~ ,\n\n(87)\n\nwhich coincides with a formula derived by Brown I8 from a principle of\nconservation of momentum. However, that derivation is not applicable\nto the present problem, which involves hybrid modes. Measurements\nof PI described in Ref. 17 show that this formula, although derived assuming y' ~ y, is quite accurate even for relatively large differences between y and y'.\nCORRUGATED FEED PERFORMANCE\n\n849\n\nIt is also interesting to note that the following interpretation can be\ngiven to eq. (86). If E t for z = were known, we could determine Ti\nsimply using the formula\n\n\u00b0\n\nTi = (E t , h~),\n\n(z = 0),\n\n(88)\n\nwhich follows from eq. (70), in view of the orthogonality relations (73).\nNow, if y - y' ;::;:; 0, E t does not differ much from AIel and, therefore, we\nmight be tempted to write in eq. (88) E t ;::;:; AIel, in which case we would\nget\nTi;::;:; AI(et, h}\n\n(89)\n\nAlternatively, since from eq. (71) we also have\nTi = (e~, H t )\n\nfor z = 0,\n\n(90)\n\nwe might be tempted to assume H t ;::;:; Alh l for z = 0, in which case\nTi ;::;:; Al (e~, hI)'\n\n(91)\n\nN either of the two formulas is correct* even if by ;::;:; 0. However, according\nto eq. (84), a correct expression for small by is obtained by taking the\naverage of the two formulas. We now treat two special cases.\n5.1 Limiting case ka\n\n\u00bb 1\n\nAssume that both y and y' are finite, but the radius a is very large,\nka \u00bb 1,\na condition which is often satisfied near the aperture of a feed. From eqs.\n(31) and (33)\n. du\n1 u\nhm - = - - - .\nka-oo dy\n2 ka\n\n(92)\n\nFurthermore, for large ka,\n1u2\n\n{3a ;::;:; ka -\n\n2. ka '\n\n(93)\n\nsince ({3a)2 = (ka)2 - u 2. Therefore,\n,\n_\n1 u? a{3i - a{3i '\" - 2.\nka\n\nU[ _1 (Ui)2\n'\" 2. ka\n\nby,\n\n(94)\n\nsince from eq. (92)\n(95)\n\n* They are often used, however.22\n850\n\nTHE BELL SYSTEM TECHNICAL JOURNAL, JULY-AUGUST 1977\n\nUsing these results, from eqs. (85) and (86) we obtain\nT. = -A\nl\n\nUIUi\n(y' 2\n2\nk\nUi - Ul\n\n1\n\ny)\n\na\n\n(96)\n\n'\n\nR. = A .! UiUl y' - Y\nl\n14 (ka)2 ka .\n\n(97)\n\nOne can show that these formulas are valid even if oy is not small, provided both\n\nL'\nka\n\nand\n\ny\n\n-\n\nka\n\nare small.\nAn application of eq. (96) is considered in Section 7.1.\n5.2 Case 1/y = 0\n\nAt the input of the feed of Fig. 1, the corrugated waveguide is connected to a smooth waveguide (l/y = 0) of the same diameter. We now\nwish to calculate the reflection and transmission coefficients of such a\njunction. Thus, assume y ~ 00 for z < O. For y ~ 00, there are two types\nof modes: TE modes, in which case 'Y ~ 0, and TM modes, in which case\n'Y ~ 00. In the former case, from eq. (179) of Appendix C\n. dy\nhm - = _y2(u 2 - 1)\n\ny_oo du\n\nkau\n(ka)2 - u 2 '\n\n('Y ~ 0).\n\n(98)\n\nIn the latter case, from eq. (180)\ndy\nU\n~ - y2\ndu\nka\n\n('Y ~ (0).\n\n-\n\n(99)\n\nNow let the incident mode be a TEll mode. We distinguish two cases\ndepending on whether the i th mode is a TM mode or a TE mode. In the\nformer case, from eqs. (85) and (98)\n\n\u00b7\n\n11m\ny_oo\n\n.!. '\n\u00b7V (Ul{3i{31\n2\n- 1) k\n\nR\u00b7 = -A {3i - {3; ... /\nl\n\n1\n\n{31 + {3i\nI\n\n(100)\n\nwhere Ul is the first root of J~ (Ul) = 0,\nUl = 1.8411.\n\n(101)\n\nIf, on the other hand, the ith mode is also a TE-mode, from eqs. (85)\nand (99),\n(102)\n\nCORRUGATED FEED PERFORMANCE\n\n851\n\n10\nPl\n\n-0-0- P2\n- - - - t2\n\nm\n\n20\n\nITI\n----.t...\nb\nI\n\na\n\n-T-l..\n\n_~~b-'\n\n30\n\n~ = 1.83\na\n\n40\n\n50\n0.5\n\n1.4\n\nwlw c\n\nFig. 2-Reflection, transmission, ~nd coupling coefficients for input junction of Fig. 1.\n\nFrom eq. (86) we obtain, using eq. (98),\n\n-\n\nhm\n\nT\n\ni\n\n= AI\n\ny-oo\n\n1\n.. /\n(hu~\n, 'V\n'2\na{h - a{3i\nka{3i(ul - 1)\n\n1\n'\ndy~ \\\n\nV\\\n\n(103)\n\ndUi\n\nwhere dy' /du~ can be determined using eq. (178), unless y' \u00bb 1, in which\ncase we can use eq. (98) or (99) with y,u replaced by y',u~.\nEquations (100) to (103) have been used to calculate the behavior of\na junction with b = 1.8309a. Consideration has been restricted to the\nTEn mode and the TMn mode of the smooth waveguide, and the corresponding modes (HEn and HE~l) of the corrugated waveguide. The\nresults are shown in Fig. 2, where i = 2 refers to the TMll mode (or the\nHE~l mode),\n\n_\\RI\\2\n\nPI2 -\n\n(104)\n\nAl\n\nis the input reflection,\n\nR2\\2\n\nP~ = \\Al\n852\n\n(105)\n\nTHE BELL SYSTEM TECHNICAL JOURNAL, JULY-AUGUST 1977\n\ngives the power converted into the TMl1 mode, and\n(106)\ngives the power converted into the HE~I mode. In Fig. 2, We is the frequency at which y' = 00. The corrugated guide at this frequency behaves\nlike a smooth guide and, hence,\n(107)\n\nPI = P2 = t 2 = O.\n\nThe curves of Fig. 2 are useful in determining the practical bandwidth\nof the junction of Fig. 1.\nVI. JUNCTION BETWEEN TWO WAVEGUIDES OF DIFFERENT DIAMETER\n\nFor some applications, to minimize the input reflection of a corrugated\nfeed, it may be convenient to choose for the smooth waveguide a diameter\ndifferent from that of the corrugated waveguide. In this section, the\nanalysis of Section V is extended to the general case of a junction between\ntwo corrugated waveguides of different diameter. Let a and a' be the two\ndiameters for z > 0 and z < 0, respectively, and assume again a single\nmode is incident on the junction, from the region z < O.\nIf E t for z = 0 were known, then the transmission coefficients Ti which\nappear in eqs. (70) and (71) could be determined at once using the formula*\nTi =\n\nf Ss,\n\n(E t X h;) . i z dS,\n\nfor z = 0,\n\n(108)\n\nwhich follows directly from eq. (70) in view of the orthogonality of the\nmodes e~, h~ [see eq. (73)]. In eq. (108) S' denotes the circular area\n\n0< r < a'.\nNow, for z = 0, E t is given by eq. (68) inside the area\n\n0< r < a,\n\n(109)\n\nand it vanishes for a < r < a'. Therefore, eqs. (108) and (68) give\n00\n\nTi = AI(el, h;) + L Rn(e n, h;),\n\n(110)\n\nn=1\n\nwhere\n(en, h;) =\n\nf Ss\n\n(en X ht) . iz dS,\n\n(111)\n\nS being the circular area (109), which corresponds to the waveguide of\nthe region z < o.\n* Here we are only interested in calculating Ti and R for {3i > 0, {3; > O.\n\nCORRUGATED FEED PERFORMANCE\n\n853\n\nEquation (79), which was obtained by requiring continuity of H t for\nz = 0, must be satisfied over the area S. By multiplying this equation\nwith en and integrating over S, we obtain for n ~ 1\n00\n\n-Rn = L Ti(e n, h)\n\n(n ~ 1).\n\n(112)\n\nI\n\nIf the coefficients Ti in this relation are expressed in terms of the coefficients Ri using eq. (110), we get for n ~ 1\n-Rn = (AI + R I )\n\nf (eb h;)(e n, h;) + Rn f: (en, h;)2\n\ni=1\n\ni=1\n\n00\n\n+ L\n\nRs L (es , h;)(e n , h}\n\n(113)\n\ni=1\n\nsr\"n,1\n\nFor n = 1, the second sum of the right-hand side should be omitted and,\nfurthermore, -Rn should be replaced with Al - R I .\nWe have thus obtained a system of equations in the unknowns R I , R 2 ,\netc. We solve* them in the limiting case where both a' - a and y' - yare\nvery small, in which case\n(en, h~) NO\n\nfor n ~ s\n\nRi NO\n\n}\n\n(en, h~) - I N O\n\n(114)\n\n'\n\nand therefore the first two terms of the right-hand side of eq. (113) for\nn ~ 1 are respectively equal to\nAr[(e n , h~) + (eb h~)]\n\nand Rn. The last term can be neglected. Therefore, eq. (113) gives for\nn~1\n\n(n ~ 1).\n\n(115)\n\nRI N! [1 - (er, h~)2]AI N [1 - (er, h~)]AI'\n2\n\n(116)\n\nSimilarly, for n = 1,\n\nThe transmission coefficients can now be determined using eq. (110).\nWe find for n ~ 1\nTn N -1 [\n(er, '\nh n ) - (en, hI) AI.\n2\nI\n\n]\n\n(n ~ 1),\n\n(117)\n\nwhich is a generalization of eq. (84).\n* This derivation is not rigorous, for we neglect to examine the question of convergence\nof the summations in eq. (113). However, the validity of the results appears to be confirmed\nby the experimental results.\n854\n\nTHE BELL SYSTEM TECHNICAL JOURNAL, JULY-AUGUST 1977\n\nThe coefficients (ei, h~) can be calculated using eq. (57). Ify' - yand\na l - a are very small, we can proceed as follows. The field components\nen and h n of the nth mode are considered to be functions of the coordinates r,c/> and of the two waveguide parameters a,Y. Therefore,\nohn\noa,\n(118)\nOa\nwhere hn, ohn/oy and ohn/oa are evaluated for a l = a, yl = y, and oy\nare oa denote yl - Y and a l - a. a similar relation can be written for e~.\nIt follows from eq. (118) that (ei, h~) for i =P n is a sum of two terms,\n,\n\n_\n\nI\n\nI\n\nh n - h n (r, C/>, a , y)\n\nN\n\nhn +\n\noh n\n\nOy\n\noy +\n\n(119)\nsince (ei, h n ) = O. The first term is simply the coefficient (ei, h~) calculated for a' = a; it corresponds to a junction between two waveguides\nof the same radius, but different surface reactance. The second term can\nbe interpreted as the coefficient (ei, h~) relative to a junction between\ntwo waveguides having the same surface reactance but different radii\na and a'. Since the term has already been treated in Section V, only the\nlatter need be considered. If one sets\noh n\nOen\noh n =-oa\noe n =-oa\n(120)\nOa\n'\nOa\n'\nand if the c/> variations of both modes are of the type considered in Section\nI, then, taking into account that ei4> = 0 for r = a, using eq. (57) we\nget\noh~z + Oe ~p hiz ) rjJ=90\n(ei, oh n ) -_ 7raoa [.!3n\n-] ~ _ 2 ( ei4> !31\n!3 n\nOa\nOa\nr=a\n0\n\n+]. 2 !3i\n\n2\n\n!3i - !3n\n\n( eiz oh ~p + Oe~z hi4>) rjJ=O\u00b0'\n]\nOa\nOa\nr=a\n\n(121 )\n\nAs an application, consider y = 00, in which case (ei, h~) can be interpreted as the coefficient (ei, h~) relative to a junction between two\nsmooth waveguides of radii a and a l = a + oa, respectively. Assume ei\nis a TE mode and en is a TM mode, so that for r = a\noh~z\n\nei4> = eiz = - - = 0,\nOa\n\n(122)\n\nwhere the last term vanishes because h n is a TM mode. Then eq. (121)\ngives\n(e u. 0hn) - 7raoa\n\n2\n\n1\n\n2\n\n!3i - !3n\n\n[_.]!3n (~.)\nh lZ rjJ=90\u00b0\n\nOa\n\nr=a\n\n(123)\n\nCORRUGATED FEED PERFORMANCE\n\n855\n\nSimilarly, interchanging n ~ i in eq. (121) and taking into account that\nfor r = a\n(124)\n\nwe obtain\n(en, Ohi) =\n\no.\n\n(125)\n\nNow, the two modes are characterized by\nhiz =\n\n;0 1(~Ui)\n71i J\n\nj\n(3i a\nhi1> = - -Z 71i\n\nr\n)\nJ 1 ( -U'\na I\n\nui\n\no\n\nsinet>,\n\nr\n-ui\na\n\ncoset>,\n\n(126)\n\n(127)\n\nand\nenz = 71n J 1 (~Un) COSet>,\n\n.\n\ne n 1> = J71n\n\n(3n a\n\nr\n)\nJ 1 ( -Un\na\nr\n\nUn\n\n.\nsmet>,\n\n(128)\n\n(129)\n\n-Un\n\na\n\nwhere the amplitudes 71i and 71n are, because of the requirement (72),\ngiven by\ny\n71i =\n\n2Zo 1 U[\n1\n1\ny-17ra ~ ~ vur=I IJ 1 (Ui)1\n(ka) .\n\n\"'\" /2Zo 1 Un\n71n ='V 7ra ~ V{3;;\n\n1\n\n(130)\n\n~ /-1-\n\nIJ 1 (u n )1 V (ka)'\n\n(131)\n\nFrom eqs. (123) and (126) to (131), taking into account that J 1 (u n ) = 0,\nwe obtain the final result\n(ei, oh n ) = 2\n\nka\n\n1\noa\n.~\n.\nva{3ia{3n v U[ - 1 a\n\n(132)\n\nNote that in deriving this relation it has been assumed that oa is sufficiently small so that\n\n856\n\nTHE BELL SYSTEM TECHNICAL JOURNAL, JULY-AUGUST 1977\n\nIf this condition is not satisfied, we should replace {3n with {3~ in eq.\n\n(132).\nOf special interest is the case where ei and en represent the TEll mode\nand the TMll mode, respectively. In this case Ui = 1.8411 and, letting\ni = 1 and n = 2 for these two modes, we get\n\nka\noa\nva{31a{32 a\n\n(eI, oh 2) = 1.2937 ---.;::===~\n\n(133)\n\nFrom eqs. (115), (117), (125), and (133) we then obtain for the conversion\ncoefficients T 2 and R 2\n\nka\noa\nX AI,\n(134)\nva{3Ia{32 a\nwhere IArl2, IT212, and IR212 represent the incident power, and the\npowers transmitted and reflected in the TMll mode. We can verify* that\nT 2 is smaller by a factor of 2 than the conversion coefficient given in Ref.\n22, which is due to the fact that the assumptions of Ref. 22 imply\n\nT 2 ;;:;:; -R 2 ;;:;:; 0.646\n\nTn;;:;:; (er, h~),\n\n(135)\n\nrather than eq. (117).\nNote that for {32 -- 0, we have a{3~ -- u2voa/a , and therefore\n\nT 2 ;;:;:; 0.646\n\nVa{31U2 (oa)a\n\n3/4.\n\n(136)\n\nNote T2 remains finite even when the TMll mode approaches cutoff\nin the first guide.\nVII. MODE CONVERSION IN A NONUNIFORM WAVEGUIDE\n\nTypically, a corrugated feed is made of one or more sections of nonuniform waveguide whose surface reactance and radius are functions\nof z. Since a nonuniform waveguide does not in general possess a natural\nmode of propagation, an incident mode will be scattered in forward and\nbackward modes. This is true even for a conical waveguide of constant\nsurface reactance (except when y = 0 or y = co). The analysis of Sections\nV and VI gives the differential scattering parameters which allow the\nlocal coupling into forward and backward modes to be determined at any\npoint in a uniform waveguide. We can thus obtain a set of differential\nequations, whose coefficients are given by the above scattering parameters, and which can be solved, at least in principle, for the mode am* In Refs. 22 and 23, the TMll mode was cut off to the left of the junction, and for this\nreason there is poor agreement between those measurements and eq. (134), which is not\napplicable in this case. However, numerical calculations by Masterman and Clarricoats\nagre well with eq. (134) at frequencies well above the cutofffrequency of the TMu mode,\nas we may verify from Fig. 11 of Ref. 24.\n\nCORRUGATED FEED PERFORMANCE\n\n857\n\nplitudes. We confine ourselves to a first-order treatment assuming the\ntotal scattered power is much less than the incident power, since this is\nthe most interesting case if the feed is well designed. It is convenient to\nassume for the moment that only y varies with z, in which case the\nwaveguide can be approximated by a succession of junctions of the type\nconsidered in Section V. Let the HEll mode be incident at the input (z\n= ZI). We wish to determine the resulting amplitude T 2 (z) of the HE~1\nmode for z = Z2. If the variation ofy is sufficiently slow, we can neglect\nreflections and determine T2 assuming the amplitude Al of the HEll\nmode is nearly constant. The transverse field of the fundamental mode\nis then\n(137)\n\nwhere\nd1>1 _ (.J\n\ndz - 1-'1\u00b7\n\n(138)\n\nThe effect on the HE~l mode of a small variation oy at z = ~ is to produce\nat z ;;;:; Z2 a component\n(139)\nwhere\nd1>2 _ (.J\n\ndz - 1-'2,\n\n(140)\n\nand from Eq. (86),\n( ) =\nt2~\n\n~ / UIU2\n1\n'v-.\n2\na(31 - a(32\na (31(32 I(dy/du l)(dy/du 2) I\n\n-1\n\n(141)\n\nNote that both (31 and (32 are functions of z. From eq. (139), integrating\nfrom ZI to Z2,\n\n(142)\n\nwhich assumes a very simple form when ka \u00bb1, as discussed in the following section.\n7. 1 Conical horn with ka\n\n\u00bb 1\n\nSuppose the radius a varies linearly with z, as shown in Fig. 1 for z >\nz 1, that the flare angle a is very small, and\n858\n\nTHE BELL SYSTEM TECHNICAL JOURNAL, JULY-AUGUST 1977\n\nka(z) \u00bb 1\n\nfor Z1 < z < Z2. It was shown in Section III that for ka \u00bb 1 the properties\nof a mode are entirely determined * by y /ka and, therefore, a mode will\npropagate without variation of its transverse field distribution if y/ka\n= constant. For this reason, it is reasonable to assume that mode conversion will be negligible if\nb\n\n(:a) = O.\n\n(143)\n\nUnder this assumption, the effect on the amplitude of the HE~l mode\nfor z = Z2 of a small variation b(y/ka) occurring at z = ~ can be expressed\nin the form\ndT 2 =\n\nT2(~)b\n\n(:a) A e1\n\ne\n\nj IW -j[2(Z2)\n\n~1U2 2\nU2 -\n\nUl\n\nr Z2 e j [IW-2Wld (L).\n\nJZI\n\n(147)\n\nka\n\nNote that, since ka \u00bb 1,\na{3i ~ ka -\n\n1 u~\n\n2k~ .\n\n(148)\n\nTherefore, from eqs. (138) and (140)\nd\nk u~ - uf\ndz [4>1(Z) - 4>2(Z)] = 2 (ka)2 .\n\n(149)\n\nNow, a varies linearly with z,\na = (z - zo) tana,\n\n(150)\n\n* Since now we are dealing with a conical waveguide, each mode is a spherical wave\ncentered at the apex A of the waveguide, and the field distribution over a spherical\nwavefront is given to a first approximation (small a) byeqs. (35) and (37). To obtain the\nfield distribution over a plane z = constant, we must therefore introdce in eqs. (35) and\n(37) a factor of exp (-j1/;), 1/; = k(x 2 + y2)/2R, R being the distance of the plane from the\napex.\n\nCORRUGATED FEED PERFORMANCE\n\n859\n\nwhere Zo is the value of z at the apex of the waveguide. Therefore, from\neqs. (149) and (150)\n1 u~ - uf y\n-.\n2 y tana ka\n\ndz) - 4>2(Z) = - -\n\n(151)\n\nOf particular interest is the case\ny = constant.\n(152)\nThen eq. (147) can be readily integrated. Taking into account eq. (151),\nwe obtain\n2 22t\n\nana\nIT 2 12 = IA I 12 UIU2Y\n(2 _\n2)4\nU2\nUI\n4\n\n2\n\nl\nX 1 - exp [ ]. -1 u~ - uf y ( 1 - -a ) ] 12 ,\n2 Y tan a kal\na2\n\n1\nwhere ai = a (Zi). Therefore,\n\nIT 2 12 :s- IA 1 12\n\n2 2 2 t\n2\n16 UIU2Y\nana\n\n(2\n\nU2 -\n\n2)4\nUI\n\n'\n\n(153)\n\n(154)\n\nwhere it is recalled that U2 = 5.1356 and Ul = 2.4048. For a = 4\u00b0, which\nis the value chosen in the experiment of Ref. 17, this inequality gives for\n\ny=l\n\n:~::: ;2 0.663610-<, (-41.8 dB),\n\n(155)\n\nwhich is a very small value for most aplications. For a = 16\u00b0, on the other\nhand, we obtain -29.8 dB, which may no be negligible.\nNote that 1 T212 and IAll2 are, respectively, the powers carried by the\nHE~1 mode and the HEll mode.\nVIII. SUMMARY\n\nIn the feed of Fig. 1, when a TEll mode is incident at the input, some\nof the incident power is in general reflected. Furthermore, some power\nmay be converted to unwanted modes if the corrugated waveguide\nsupports more than one mode at the input. Additional mode conversion\nmay take place inside the feed if the variation of the radius and of the\nsurface reactance is not gradual enough. As a result, a feed will have a\nnonzero input reflection and, at some frequencies, unwanted modes may\nilluminate the aperture of the feed. The consequences of these unwanted\nmodes on the radiation characteristics-e.g., enhanced cross polarization-are pointed out in Section III and in Ref. 17, where the theory is\ncompared with experiment.\nThese effects can be evaluated to good accuracy using the expressions\nderived in this article, as highlighted below. For large ka, eq. (35) ex860\n\nTHE BELL SYSTEM TECHNICAL JOURNAL, JULY-AUGUST 1977\n\npresses the field shape for all copolarized hybrid modes of various radial\nharmonics with the same \u00a2 dependence, while eq. (37) corresponds to\nthe cross-polarized modes. Equation (36) gives the mode amplitudes\nrequired to normalize the power carried by the modes.\nA property of corrugated feeds is that the aperture field distribution\ndoes not remain constant with frequency, as in the case of a feed with\nsmooth walls, but varies because of the frequency dependence of the\nsurface reactance Xs. Thus, although the desired mode has no crosspolarized component at the resonant frequency of the corrugations, at\nother frequencies the desired mode does radiate some cross polarization.\nThe ratio, C2, between the maximum value of the cross-polarized power\nin the radiation pattern and the maximum value of the copolarized power\n(which occurs on axis) is given by eq. (39). From eq. (39), it follows that\nwith large ka and thin disks one can maintain low cross-polarized power\nin the radiation pattern from the desired mode over an octave or\nmore.\nAt a junction between waveguides of the same diameter but of different surface reactance, eq. (85) gives the general expression for the\nmode coupling coefficient to modes reflected from the transition, and\nEq. (86) gives that for modes transmitted forward from the transition.\nEquations (97) and (96) are simplifications of eqs. (85) and (86), respectively, which apply for ka \u00bb 1. When the input waveguide is smooth,\nthe mode coupling coefficient is given by eq. (100) for reflected TM\nmodes, by eq. (102) for reflected TE modes, and by eq. (103) for hybrid\nmodes transmitted forward from the transition. Since the transition from\nsmooth to corrugated waveguide is a major source of unwanted modes\nin a corrugated horn, eq. (103) is very useful in determining mode purity.\nAnother important formula is eq. (87), which determines the reflection\ncoefficient of the dominant mode (return loss) for any transition in Xs\nand any ka.\nAnother source of generation of undesired modes is the mode conversion occurring along the conical taper of a corrugated horn. Equation\n(154) gives the mode-coupling coefficient for the transmitted undesired\nmode due to a conical taper.\nIn some cases a step in diameter may be used to match transitions\nbetween different surface impedances; eq. (134) determines the modecoupling coefficients at a step in diameter.\nAPPENDIX A\n\nAsymptotic Series for u and 'Y in Terms of lIka\n\nWe determine the asymptotic series for u and 'Y in terms of\n1\nka'\n\nCORRUGATED FEED PERFORMANCE\n\n(156)\n861\n\n(167)\n\nF(uo m ) = -1,\n\nwe obtain for the derivatives appearing in eq. (166),\n= -UO m\n( dF)\ndu U=UOm\n\n(~:~)\nd3F)\n3\n\n( du\n\nU=UOm\n\n(168)\n\n= -3.\n\n_ - 2 1 + U6m , etc.\n\nU=UOm\n\nUO m\n\nSubstituting eqs. (165), (167), and (168) in eq. (166) one obtains F as a\nseries of powers of l/ka; the coefficients of this series are algebraic expressions in UO m and aI, a2, etc. Similarly, by developing dF/du in a\nTaylor series about the point U = UO m , and then using eqs. (165), (167),\nand (168), we obtain dF/du as a series of powers of l/ka. Substituting\neq. (165) and the above series expansions of F and dF/du in eq. (164),\nwe can solve for the coefficients aI, a2, etc. We obtain eq. (31). Substituting eq. (31) in eq. (166) we obtain an expansion of F in powers of l/ka.\nUsing these results, from\n\nF\n\nl' = - - - = -\n\ncos8,\n\nF,\n\n-=======\n\nVl- (:J\n\n(169)\n\n2\n\n'\n\nwe get eq. (32).\nEquations (31) and (32) have been obtained assuming eq. (165), which\ncorresponds to the limiting case of eq. (28). If, instead of assuming eq.\n(165), we assume\n\nu= u~ =\n\nU2m\n\n[1 + (k1a) + (k1a) + ... ],\n{3l\n\n{32\n\n2\n\n(170)\n\nwe obtain eqs. (33) and (34).\nAPPENDIX B\n\nSurface Wave Mode\n\nIn addition to the modes considered in Section III, there is a mode for\nwhich {3 > k. Thus, since for this mode cos fh > 1, it is convenient to replace 01 with Fh in eqs. (16) and (18). Since\ncos jO = cosh fh\n\nsin~Ol ~\n\n= sinh Ol},\nJl(jx) =]Il(x),\n\n(171)\n\nJ~Ux) = I~(x),\n\nCORRUGATED FEED PERFORMANCE\n\n863\n\nwhere II (x) is the modified Bessel function of order 1, we obtain from\neqs. (16) and (17)\nI~(u)\n\n')'=---\n\nu\n\nI 1 (u) cosh (h '\n\n(172)\n\n!.1:.]\n\n.:L = _ [.!J'I(U) + cosh 01\nka\n\nul 1 (u)\n\n(173)\n\n')'u'\n\nU\n\nwhere u = ka sinh 01 \u2022 We can verify from these two equations that u 00 as ka 00. Now, for large u,\neU\nI~(u);;::; I 1 (u);;::; _;r.--.\n(174)\nV 27ru\nTherefore eq. (172) gives\n')' -\n\n00,\n\nas ka -\n\n00.\n\nFrom eq. (173), for large u and ka,\n\nL;;::;_!.\nka\nu\n\n(175)\n\nTherefore, since u = ka sinh 01 ,\n\n. h 0 ;;::; - -1.\nsm\n1\n\n(176)\n\ny\n\nWe now examine the behavior of the field components for ka - 00.\nTaking into account eq. (171), from eqs. (10) to (15), after replacing 01\nwith ifh, we find for,), = - 0 0 (i.e., for B = 0) that the only nonzero component of the magnetic field is H \u00a2 and\n\nr)\n\n1\n, ( u - cos\u00a2 e- JfJZ \u2022\n-ZoH\u00a2 = -.--AI\nI\nsmh 01\na\nOR\n\nTherefore, for kr \u00bb y\n\n-ZoH\u00a2;;::; A' V~ cos\u00a2 exp[k(r - a) sinh 01 - j,Bz],\nr\n\nwhere A' is a constant. This shows that the field is confined to the near\nvicinity of the wall, decaying approximately exponentially from the\nwall.\nWe can show that ka > 1.81, the surface wave mode in combination\nwith the HElm and HE~m modes comprise the complete set of propagating modes whose Ez azimuthal dependence is cos\u00a2.\nAPPENDIX C\n\nDerivation of dy/du\n\nFrom eq. (163),\n864\n\nTHE BELL SYSTEM TECHNICAL JOURNAL, JULY-AUGUST 1977\n\nAPPENDIX D\n\nCutoff Frequencies of the Modes of Equations (35) and (37)\n\nFrom eqs. (16) and (17) we get\n')'2\n\n+ ')'w - 1 = 0,\n\nwhere\nyu 2\n\nw=\n\nka cosfh\n\nTherefore, either\n')'=\n\n-w+Vw2-=i=4\n2\n\n(181)\n\nor\n')'=\n\n-w-Vw2-=i=4\n\n(182)\n\n2\n\nrespectively, in the two cases of eqs. (35) and (37) (which correspond,\nrespectively, to ')' - 1 and')' - -1 for ka - 00 ). At cutoff {3 - 0; i.e., cos(h\n- 0. For COSOl NO, Y :;6: 0, we have Iwl - 00 and, therefore, from eq.\n(181)\n\n')' -\n\n\u00b0\n{\u00b0 ify>\nif < \u00b0'\n00\n\ny\n\n(183)\n(184)\n\nwhereas from eq. (182)\n\n\u00b0\n\nif y > .\n0, ify <\nIf ')' = 0, the mode is of the TE type. Now, for a TE mode at cutoff, the\nonly nonzero component of the magnetic field is Hz and therefore the\nsurface reactance Xs has no effect on the cutoff frequency. This means\nthat the cutoff frequency can be determined by replaci~g the corrugated\nwall with a smooth wall of radius a, and therefore the cutoff frequency\nis determined by the condition:\n- ')'- {\n\n00,\n\n\u00b0\n\nJ~(ka) = 0.\n\nIf ')' = 00, on the other hand, the mode is of the TM type and the only\nnonzero component of the electric field at cutoff is E z \u2022 It follows that if\nthe disks are very thin (t \"\"' 0), they can be removed without affecting\nthe field. Thus, the cutoff frequency can in this case be determined by\nreplacing the corrugated waveguide with a smooth waveguide of radius\nb. It is thus determined by the condition\n866\n\nTHE BELL SYSTEM TECHNICAL JOURNAL, JULY-AUGUST 1977\n\nCopyright (c;) 1977 American Telephone and Telegraph Company\nTHE BELL SYSTEM TECHNICAL JOURNAL\n\nVol. 56, No.6, July-August 1977\nPrinted in U.S.A.\n\nCharacteristics of a Broadband Microwave\nCorrugated Feed: A Comparison Between\nTheory and Experiment\nBy C. DRAGONE\n(Manuscript received December 14, 1976)\n\nA corrugated feed with nearly ideal radiation characteristics from\n17 GHz to 29 GHz has been built using a novel fabrication technique.\nThe bandwidth of single-mode operation was maximized by properly\nchoosing the input parameters of the feed. As a result, only the fundamental mode can propagate at the input from 19 GHz to 28.8 GHz.\nIn this frequency range, the far field is essentially polarized in one\ndirection. At frequencies higher than 28.8 GHz, there is a cross-polarized component caused by an unwanted mode. An approximate calculation of the power in this mode is given. A simple formula for the\ninput reflection coefficient is provided. Results are included that show\nhow to compute mode conversion in a conical taper, cross polarization\nfrom a corrugated horn, including contributions from spurious modes,\nand the reflection coefficient from the smooth-guide to corrugatedguide transition. Comparison of theory and experiment shows good\nagreement.\nI. INTRODUCTION\n\nIt has been shown by Thomas! that under certain conditions the field\nover the aperture of a corrugated feed is virtually constant over a very\nwide frequency range. For this behaviour to occur, the radius a of the\naperture must be much larger than a wavelength, i.e.,\n\nka \u00bb 1(k = 2;)\n\n(1)\n\nand furthermore, the aperture must be illuminated by a single mode. If\nboth conditions are satisfied, we can show that the field distribution is\nessentially independent of the surface reactance of the corrugated horn\nwall, X s , and, as a consequence, it is little affected by the variation of\nXs with frequency. This result is very important, for it implies that it\n869\n\nx\n\na = 4\u00b0\n\n(z)\n\n--- --z=o\nala) = 0.629 em\nb(a) = 1.161 em\na(z2) = 3.144 em\n\nb(Z2) - a(z2);;;:;:\\/4 AT 22.9 GHz\n\nz, = 45.7 em\nz2 = 78.7 em\n\nFig. I-Dimensions of the corrugated horn.\n\nis possible to design a feed so that its radiation pattern is circularly\nsymmetric and polarized in one direction over a very wide frequency\nrange I- 3 (an octave or more). The most difficult condition to satisfy to\nobtain such large bandwidth is the requirement that a single mode be\nexcited in the feed. This requirement is discussed in a separate article. 4\nHere, after summarizing certain results of that article, we describe the\nresults of an experiment. A long feed, with a flare angle of only 4 0 , was\nfabricated using a special technique described in Appendix D. At the\ninput of the feed, which is shown in Fig. 1, the waveguide dimensions (the\ncorrugated depth I and the radius a; see Fig. 1) were optimized so as to\nmaximize the bandwidth of single mode propagation. As a consequence,\nunwanted modes were cut off (at the input) over the frequency range\nWI < W < 1.6839wI,\n\n(2)\n\nwhere WI = 19 GHz and 1.6839wl = 28.8 GHz. The input reflection and\nthe far field were then measured from 17 GHz to 35 GHz. The input reflection agrees very well with a simple formula given in eq. (42) and derived in Ref. 4. Over the frequency range (2), the far field is essentially\npolarized in one direction. At frequencies higher than 28.8 GHz, however,\na strong cross-polarized component is caused by an unwanted HE~I\nmode, which is excited primarily at the input of the feed. A simple expression for the power converted into this mode is given in Ref. 4.\n870\n\nTHE BELL SYSTEM TECHNICAL JOURNAL, JULY-AUGUST 1977\n\nII. PRELIMINARY CONSIDERATIONS\n\nIn the experiment described in Section V, the feed is excited at the\ninput by a linearly polarized TEn mode. Therefore, consideration will\nbe restricted to the modes arising for this particular excitation. 2- 8\nConsider a disk-loaded waveguide centered around the z axis as in Fig.\n1, and let r, \u00a2, z be cylindrical coordinates defined by x = rcos\u00a2 and y\n= r sin\u00a2. Assume for the moment that the waveguide parameters h, a,\nb, and t are independent of z. The separation h of the disks, which occupy the region a < r < b, is assumed to be much smaller than a wavelength A\nkh \u00ab 1.\n\n(3)\n\nThe region between two consecutive disks forms a radial line whose input\nreactance jX at r = a is a function of the radial length l = b - a; for ka\n\u00bb 1,\njX ~ jZo tankl,\n\n(4)\n\nwhere Zo = vi PO/EO. Because of condition (3), the effect of the disks can\nbe adequately accounted for by introducing an effective surface reactance 2\n\n.\n\n. ( t)\n\n}Xs =}X 1 - h '\n\n(5)\n\nwhere t is the thickness of the disks, and by requiring that the field for\nr < a satisfy the boundary conditions\n\nE cp\n\n~o\n\n} forr=a,\n\n(6)\n\nEz\n\nHcp~- .X\n}\n\ns\n\nwhere Ecp, Hix + sin24>iy )e-j {3z.\n\n(13)\n\nThe absence of a z component in eqs. (12) and (13) is due to the fact that\nthis component vanishes like l/ka, as ka -- 00.\nThe HElm modes, which are given by eq. (12), have the important\nproperty that the electric field is polarized in one direction. Of special\ninterest is the fundamental mode (m = 1) characterized by\nu = Ul = 2.4048.\n\n(14)\n\nNote that both eqs. (12) and (13) are frequency independent.\nThus, over the frequency range in which both conditions (1) and (7)\nare satisfied, the field distribution of an aperture illuminated by the HEll\nmode is essentially frequency independent. 1 ,2 If, however, only condition\n(1) and not condition (7) is satisfied, then we must add 4 to the right-hand\nside of eq. (12) a component of the type (13), so that\nE;:;;:; J o (~U) ix - I' - 1 J\na\n1'+1\n\n(cos24>ix + sin24>iy),\n2(~U)\na\n\n(15)\n\nwhere the factor e - j{3z has been omitted. Both I' and U are functions of\nka and X s , and, therefore, they vary with frequency. If one develops 1',\n872\n\nTHE BELL SYSTEM TECHNICAL JOURNAL, JULY -AUGUST 1977\n\nU\n\nin power series of y and l/ka one finds 4\nU = Urn { 1 -\n\n'Y =\n\n~ y (k~) ... }\n\n1- u;( ~ k~ - ~ u~ (4+ u~) (k1J .. -J.\n\n(16)\n(17)\n\n2.2 Mode conversion in a conical horn 4\n\nConsider a conical horn of constant surface reactance and flare angle\na, as shown in Fig. 1, from z = Zl to Z = Z2. If a is sufficiently small, and\nif the input of the horn is excited in the HEll mode, then the resulting\nfield inside the horn is very nearly a spherical wave 1 ,3 originating from\nthe apex of the horn and given by\n\nEe- ihR ,\n\n(18)\n\nwhere E is given by eq. (15) and R is the distance from the apex of the\nhorn. Since a is small,\nr2\n\nR-;:;::;z+-\n\n(19)\n\n2z'\n\nr being the radial distance from the axis and z the axial distance measured from the horn apex. From eq. 17, the parameter 'Y which appears\nin eq. (15) is a function of both y and ka; assume Iyl ~ 00, O. Then, since\nka increases with z, we have from eq. (17) that 'Y varies with z, and\ntherefore the field distribution (15) does not remain constant with z. This\nvariation is accompanied by generation of unwanted modes, an effect\nthat will be negligible only if a is sufficiently small.\nTo determine how small a should be, consider the special case ka (z 1)\n\u00bb 1 treated in Ref. 4. Let Pc be the total power converted from the desired mode into the HE~l mode and let Po be the power incident at the\ninput. Then, we find that for z = Z2\nPc = Po X 3.393 (10-3)y2 tan 2all - e N 12,\n\n(20)\n\nt/; = 10.295 - y - (1 _ a(zl))\n\n(21)\n\nwhere\nytanaka(zl)\n\na(z2) .\n\nTherefore,\n(22)\nwhere the equality sign is attained for t/; = (2n + 1)7r. In the experiment,\na = 4 0 , in which case for y = 1 we find Pc ~ 6.636 X 10- 5 (-41.8 dB),\nwhich is negligible for most practical purposes.\nCORRUGATED FEED EXPERIMENT\n\n873\n\nIII. RADIATION CHARACTERISTICS2,6,7\n\nLet the aperture of the horn be of sufficiently large diameter that the\nfar field is simply proportional to the Fourier transform F of the aperture\nfield. Also let a be so small that we can neglect the phase variation caused\nover the aperture plane by the variation of R in (18). Then, by taking the\nFourier transform of eq. (15), we obtain for the field distribution at a\ngreat distance D from the aperture, for example, using the contour integral method of Ref. (4),\nF = No(u,v)ix +\n\nI'1'+1\n- I N2 (u,v) (cos2ix + sin2iy),\n\n(23)\n\nv = ka (Z2) sinO,\n\n(24)\n\nwhere\n\nand , 0 are spherical coordinates defined by x = D sinO cos, y = D sin\n\nosin. Equation (23) gives, except for a factor independent of ,0, the\nfar-field pattern. For small y/ka we have\nU\n\n= Ul = 2.4048.\n\nIn this case, from eqs. (23) to (25) the cross-polarization ratio C between\nthe maximum value of lEy I, which occurs for v = 3.67, and the maximum\nvalue of lEx I, which occurs for v = 0, is given by\nC2 == lEy I:ax = (0.26)2\n\nlEx Imax\n\n(I' - 1)2.\nI' + 1\n\n(26)\n\nFrom eq. 17, the asymptotic value of C2 for large ka is\nC2 -- 0.14\n\n(:a)\n\n2.\n\n(27)\n\nIf ka \u00bb 1, but y/ka is not small, C2 has the behaviour of Fig. 2.\nEquation (23) assumes that the aperture of the horn is illuminated\nby the HEu mode. If, in addition to this mode, there is also some HE~l\nmode of power Pc, then we have in addition to the component in (23),\na component4\n\n\"./,\n\n-eJ'I\"\n\n'\" /PcJ\u00a5(u)\n)(.\n.. )\nX 'V\n2 _\nN 2(U,V COSlx + slnly ,\nP OJ 1 (u)\n\n(28)\n\nwhere Pc, Po are the powers carried by the two modes and t/; is their difference in phase for z = Z2. For ka \u00bb 1,\nU r;:; U ~ = 5.1356.\n874\n\n(29)\n\nTHE BELL SYSTEM TECHNICAL JOURNAL, JULY-AUGUST 1977\n\n-10.-----------------------------------------------~~\nUl\n-l\nW\n\nen\n\nU\n\nw\n\no\n\n~\n\n\u00ab\n~\n\nz\n\no\nI\u00ab\nN\n\na:\n\n\u00ab\n-30\n-l\n\nf2\nI\nUl\nUl\n\no\n\na:\n\nu\n\n-40\n0.30\ny/ka\n\nFig. 2-Cross-polarization peak versus normalized surface susceptance.\n\nTherefore, from eq. (25) with J 2 (u) = 0,\n\nNi (u,v) = (v2a~uu2J2(V)Jr(u))2\n\n(30)\n\nwhose maximum value occurs for v;:;;;:; 4.356 and is\n(31)\nBecause of the component (28), we have for 'Y = 1 that the ratio C2 between the maximum value of lEy 1 2 , which now occurs for v = 4.4 and\nthe maximum value of lEx I is\nC2 = 0.194 Pc .\n\n(32)\n\nPo\n\nNote from eq. (23) that the normalized radiation pattern of the HEll\nmode for ka \u00bb 1 is simply given by\nP(O) =\n\n[u 2 uJo(v)v ]2\n2 -\n\n2\n\n(33)\n\nwith u = u 1 = 2.4048 and v = ka sin O. If 01 and O2 denote the values of\n8 for which P(O) = 0.5 and P(O) = 0.1, then from eq. (33)\nka sin 01 = 2.078 (3-dB point)\n\n(34)\n\nand\nCORRUGATED FEED EXPERIMENT\n\n875\n\n(35)\n\nka sin ()2 = 3.597 (10-dB point),\n\nres pecti vel y.\nIV. FEED DESIGN 2 ,4,9\n\nThe feed of Fig. 1 is now described. Its measured characteristics are\ndiscussed in Section V. Let \\W2, wl1 be the frequency range over which\nonly the dominant mode, the HEll mode, propagates at the input (z ~\n0). Let Wo be the frequency at which the surface reactance is infinite at\nthe aperture; then\n(36)\nAt the input, the ratio between the radii b and a is optimized for maximimum W2/Wl' This is shown in Appendix A to require\nb(O) = 7.0155 = 1.8309.\na(O) 3.8317\n\n(37)\n\nThen*\nW2 = (W2)\n= 1.6839,\nWI\nwI MAX\n\n(38)\n\nand the surface reactance can be shown to vanish for W = W2,\nY = 00 for z = 0, at W = W2.\n\n(39)\n\nIn the experiment, the frequency WI was chosen equal to 19 GHz, which\ngives W2 = 28.8 GHz, a(O) = 0.556 cm, and b(O) = 1.161 cm, as we obtain\nfrom eqs. (37) and (38) and the condition\nkb = 7.0155 at W = W2,\n\n(40)\n\nshown by Fig. 9 of Appendix A.\nFrom Fig. 1 the feed consists of two parts joined at z = ZI. From z =\no to z = ZI, the outer radius is kept constant, so the cutoff frequency of\nthe HE~l mode remains constant, as shown in Appendix A, where the\nrelations between a, b and the cutoff frequencies of the various modes\nof eqs. (12) and (13) are derived. Note that from z = 0 to z = ZI the radius\na increases, which implies that at any given frequency the surface reactance decreases with z. The importance of this requirement was first\nrealized by Bryants. From z = z 1 to the aperture, the surface reactance\nremains constant with z. The frequency Wo at which it is infinite was\nchosen in the experiment\n* To put this ratio in perspective, the highest frequency of the 6-GHz (TH) common\ncarrier band is 1.732 times the lowest frequency of the 4-GHz (TD-2) band; similarly, for\nthe 18- and 30-GHz band3, the ratio is 1.695.\n876\n\nTHE BELL SYSTEM TECHNICAL JOURNAL, JULY-AUGUST 1977\n\n(41)\n\nWo = 1.21 WI.\n\nOver the frequency range IwI, w21 only the HEll mode is excited at the\ninput, other modes being cut off. Therefore, since the variations of a (z)\nand b (z) from the input to the aperture in Fig. 1 are sufficiently gradual\nto ensure negligible generation of unwanted modes, we have that the\naperture is essentially illuminated by a single mode, the HEll mode, over\nthe above frequency range. The radiation characteristics for WI < W <\nW2 are, therefore, given accurately by eq. (23) with a = a (Z2) and u given\nby eq. (16) for m = 1.\nFrom eq. (39), the input surface reactance vanishes at W2. Therefore,\nsince the corrugated waveguide is connected at the input to a smooth\nwaveguide of the same diameter, the input reflection is essentially zero\nat W = W2. For W ~ W2, however, there is a reflection which, as we shall\nsee in Section V, is given accurately by\n2\n2 = ({31 - (3'l)\n{31 + {3; ,\n\n(42)\n\n1P 1\n\nwhere {31 is the propagation constant of the TEll mode and (3; is that of\nthe HEll mode. Equation (42) is derived in Ref. 4.\nAt frequencies higher than W2, some of the incident power is converted\ninto the HE;l mode. If Pc denotes the converted power and Po denotes\nthe incident power, then\n\nPc _ [\n1\nPo '\" a ({31 - {3~)y\n\n]2(3~(u{3I2 -\n\n1) ,\n\n(43)\n\nwhere u = 1.841 and {3~ is the propagation constant of the HE;1 mode.\nSome of the incident power is also converted into the TMll mode of the\nsmooth waveguide. If P~ denotes this power, which is reflected by the\njunction, we have 4\nP~ _ ({32 - {3~)2 {32{3I 1\n(44)\nPo '\" ({31 + {3~)2u2 - 1 k 2 '\nwhere (32 is the propagation constant of the TMll mode. The above\ncoupling equations are derived in Ref. 4 assuming Iyl \u00bb 1.\nIn the experiment described in the following section, the corrugated\nwaveguide is connected at the input to a smooth waveguide whose radius\ngradually increases from a relatively small value a' to the final value a(O).\nThe initial value a' is sufficiently small so that the TMll mode is cut off\nand, as a consequence, the power P~ is reflected back towards the junction where it is converted into the HE;1 mode of the corrugated waveguide. The total power converted into the HE;lmode is thus in general\ndifferent from Pc. It varies approximately between the two values\n\nCORRUGATED FEED EXPERIMENT\n\n877\n\no~------------------------------------------------~\n\n(f)\n\n...J\nW\n\nOJ\n\nU\n\n~ -20\n~\n\n(f)\n(f)\n\no\nz -30\n\n...J\n\na:\n\n:J\nIw\n\na:\n\n-40\n\nFREQUENCY IN GIGAHERTZ\n\nFig. 3-Return loss of corrugated horn of Fig. 1 vs frequency.\n\ndepending on the phase angle of the TMu mode incident on the junction.\n\nv. EXPERIMENT\nA corrugated feed of the dimensions shown in Fig. 2 was built using\na technique described in Appendix C. Its measured reflection coefficient\nagrees* very well with eq. (42), as shown in Fig. 3. Its radiation characteristics are shown in Figs. 4 through 6. From 17.5 GHz to 32 to GHz, the\nradiation patterns are in good agreement with eq. (33), as shown in Fig.\n4, which compares eq. (33) with two measured patterns of lEx 12 in the\nplane \u00a2 = 45\u00b0. Furthermore, from 17.5 GHz to 32 GHz, there is little\ndifference between the patterns of lEx 12 in the two principal planes (\u00a2\n= 0 and \u00a2 = 90\u00b0) and the pattern for \u00a2 = 45\u00b0. The difference is altogether\nnegligible at Wo = 23 GHz, which is the frequency for whichy = 0 at the\naperture. Figures 5 and 6 show a few examples of patterns measured in\nthe two principal planes. The variations with frequency of the beamwidths 2(h and 28 2 (respectively, the 3-dB and 10-dB beamwidths) agree\nvery well with eqs. (34) and (35), as shown in Fig. 7, where the measured\nbeamwidths in the plane \u00a2 = 45\u00b0 are compared with the calculated\nvalues.\nFinally, the cross-polarized component Ey is very small over the frequency range of eq. (2), as shown in Fig. 8. For w > 28.8 GHz, however,\n* Note that the measured reflection coefficient includes a small reflection due to a\ntransition from rectangular to circular waveguide, which was connected at the input of\nthe feed during the measurement.\n878\n\nTHE BELL SYSTEM TECHNICAL JOURNAL, JULY-AUGUST 1977\n\no~--------------------------------------------------~\n\n10\n\n. - -CALCULATED [EO. (37)]\n15\n\n/'\n\n20\n\n25\n\n30\n\n---17.5GHz\n35\n\n40\n\n45\n\n5~~----------~--------~--~~~L---~~~----------~20\nka sin e\n\nFig. 4-Calculated and measured radiation patterns vs normalized angle at \u00a2 = 45\u00b0.\n\nthe normalized peak C2 of Ey increases rapidly with frequency as expected because of the HE~l mode, which is excited at the input for w >\n28.8 G Hz. The solid curves and the dashed curves in Fig. 8 correspond\nto eqs. (27) and (43), respectively. The agreement with the measurements\nis satisfactory, taking into account that eq. (43) is not expected to give\nexactly the total power converted into the HE~l mode, for several reasons.\nIn the first place, eq. (43) assumes a very large number of disks per\nwavelength,\n\nh\u00ab A,\nCORRUGATED FEED EXPERIMENT\n\n879\n\nwhereas in the experiment, h ~ 0.137A at 30 GHz; the effect of a finite\nnumber of teeth is briefly discussed in Appendix B. In the second place,\neq. (43) assumes that only the TEu mode is incident at the input,\nwhereas in practice also the TMu mode is incident, for the reason\npointed out in Section IV. The total power carried by the TMl1 mode\nis approximately given by eq. (44).\no~--------------------=-~--------------------~\n- - \u00a2=oo\n\n- - - 9=90\u00b0\n\n-10\n\n-20\n\n-30\n\nBEAMWIDTH (0) IN DEGREES\n\nFig. 5-Measured radiation patterns at 1> = 0\u00b0 and 1> = 90\u00b0 (principal planes).\n\nNote, finally, that even if the total power converted into the HE~l mode\nis calculated accurately, to determine the resulting cross-polarization\npeak C2, the difference in phase between the HEu and HE~l modes must\nbe determined.\n880\n\nTHE BELL SYSTEM TECHNICAL JOURNAL, JULY-AUGUST 1977\n\nO~----------------------~-----------------------.\n\n-10\n\n-20\n\n-30\n\n-40\n\nBEAMWIDTH (0) IN DEGREES\n\nFig. 6-Measured radiation pattern at \u00a2 = 0\u00b0 and \u00a2 = 90\u00b0 for 32 GHz (effect of HE~l mode\non pattern symmetry is evident at upper frequency limit of operation).\n\nVI. CONCLUSIONS\n\nUsing a novel fabrication technique, described in Appendix C, which\ncan be applied at very high frequencies, a corrugated feed of small flare\nangle was fabricated. Its input reflection, found to be given accurately\nby the simple formula\n\n11P 2=({3I-{3~)2\n{3I + {3~ ,\nremained less than -30 dB from about 24 to 32 GHz. Over the frequency\nrange WI < W < W2, the far field was essentially polarized in one direction;\nCORRUGATED FEED EXPERIMENT\n\n881\n\n20~----------------------------------__----------~\n\nrilw 15\na:\n\n19\nw\n\no\n\n~\n(f)\n\nI\n\nI-\n\no\n\n~\n\n~\n<{\n\n~ 10\n\n5~\n\n16\n\n______\n\n~\n\n__\n____________\n__________\n20\n25\n~\n\n~\n\n~\n\n__\n\n~\n\n____\n\n~\n\n30\n\nFREQUENCY IN GIGAHERTZ\n\nFig. 7-Calculated and measured 3-dB and lO-dB beamwidths.\n\nits pattern is simply given by\n\nAt frequencies higher than 28.8 GHz, the far field contained a crosspolarized component, as predicted by the theory of Ref. 4.\nIt was shown that a maximum bandwidth, expressed as the ratio W2/Wl,\nof about 1.68 can be achieved for the type of corrugations considered\nhere. By using the corrugations of Ref. 10, which, however, are difficult\nto realize at high frequency, greater values of W2/Wl may be achieved.\nBoth the input reflection and the cross-polarization ratio can be improved by increasing the thickness t of the disks at the input. Curves of\n1p 12 and C2 as a function of frequency for different values of t /h are given\nin Fig. 2 9f Ref. 4. In the experiment, t /h was kept constant for reasons\nof simplicity, since our main concern was to verify the results of Sections\nII through IV and of Refs. 1 and 4, and to demonstrate the feasibility of\nthe fabrication technique described in Appendix D.\n882\n\nTHE BELL SYSTEM TECHNICAL JOURNAL, JULY-AUGUST 1977\n\nUl\n-.J\nW\n\na:J\n\nU -10\nw\no\n~\nN\n\nU\n\n::,,: -20\n\n:5\n\"-\n\nCALCULATED\n(HE'll )\n\nz\no\n\nf-\n\n~ -30\na:\n O'}.\nTM mode, if y < 0,\nCORRUGATED FEED EXPERIMENT\n\n(48)\n\n883\n\nBOTH HE\" AND\nHE'\" PROPAGATE_ .........\n.........\n\n'\" '\"\n7.0155\n(TM'2\n\nREGION WHERE ONLY\nTHE HE,,- MODE\nCAN PROPAGATE\n\n....... BOTH THE HEll - MODE\n\n3.8317\n(TM,,)\n\nAND THE \"SURFACE WAVE\"\n\n- - - - - --!'=-F'-'=:J;,,=::::;;\"\n\nMODE PROPAGATE\n\nI\n\nf\nb\n\n:t=1111111I111111I1\n\nT-r-----I\n\n1\n\nI\n\n1111111111111111\n\n1\n\n(TE\" )\nka\n\nFig. 9-Region where only the HEll mode propagates. Note: As w varies for a given a, b,\na point ka,kb moves along a straight line through the origin.\n\nIn the former case, since the only nonzero component of the magnetic\nfield of a TE mode near cutoff is Hz, we have H 1> = 0, and therefore the\nsecond of the two boundary conditions (6) can be ignored, which implies\nthat Wcm is independent of y. The corrugated waveguide can be replaced,\ntherefore, with a smooth waveguide of the same diameter whose cutoff\nfrequencies for the TE modes are given by the roots of J~(ka),\nJ~(ka) =\n884\n\n\u00b0for =\nW\n\nWcm\n\n(y > 0).\n\n(49)\n\nTHE BELL SYSTEM TECHNICAL JOURNAL, JULY-AUGUST 1977\n\n(b)\n\n(a)\n\nI\n\nf\n~\n\nI\n\n1\nl\nI\n\n1\nl\n\n~\n\n~\n\n(e)\n\n(d)\n\n(e)\n\nI\n\n\\\n\nFig.lO-Aluminum and brass disks assembled on mandrel. (a) Before machining. (b) After\nmachining exterior surface. (c) With electroformed wall of copper. (d) After machining\ninterior surface. (e) After etching away aluminum disks.\n\nIn the latter case, y < 0, the only component of the electric field for\nis Ez and, therefore, the very thin disks can be removed without\naffecting the field. The cutoff frequencies therefore coincide with those\nof the TM modes in a smooth waveguide of radius b, and are given by\nthe roots of J1(kb),\n(50)\nJ1(kb) = for W = w cm , (y < 0).\n4\nAnalogous considerations are valid for the HEimmodes, except that\nnow, instead of the rules (48),\n\nW N Wcm\n\n\u00b0\n\nTM mode, if y > O,}\nTE mode, ify < 0, '\n\n(51)\n\nand therefore the cutoff frequencies w~m are given by the conditions\nJ~(ka) = 0 for W = w~m' ify <\nJ1(kb) =\n\n\u00b0\n\n\u00b0for = w~m' ify > 0.\n\n(52)\n\nW\n\nCORRUGATED FEED EXPERIMENT\n\n885\n\n(e')\n\n(b')\n\nFig. II-Modification of assembly to obtain strong attachment to teeth of electroformed\nwall.\n\nThese results are illustrated by the diagram of Fig. 9 showing in the ka,kb\nplane the region* where only the HEll-mode can propagate. We can see\nthat W2/Wl is maximum when b/a = 7.0155/3.8317 = 1.8309, in which case\nW2/Wl = 1.6839, as pointed out in Section I before eq. 2.\n\nAPPENDIX B\n\nEffect of a Finite Number of Teeth Per Wavelength\n\nIn Section IV, we assumed an infinite number of teeth per wavelength-i.e.,\n\nh\u00ab >..,\na condition which seldom holds in practice. For instance, in the experiment\n\nh > 0.13716>..\nfor W > 30 GHz. The effect of a finite number of teeth is not difficult to\nevaluate approximately if\nka \u00bb 1,\n\nIn this case, in fact, the field in the vicinity of the corrugations can be\nconsidered to be locally the field of a plane wave reflected by a corrugated\nplane tangent to the actual corrugated surface. The angle of incidence\n* In Fig. 9 we have not indicated a region for kb < 3.8317 where mode propagation can\noccur, since that region is of no interest to us here. (The HEn mode is cut off for kb <\n3.8317).\n886\n\nTHE BELL SYSTEM TECHNICAL JOURNAL, JULY-AUGUST 1977\n\nis 90\u00b0 - (h, where\n{31\n\ncos 81 = k.\nThus, from Ref. 9, we find that a corrugated waveguide of radius a \u00bb\n'A with a finite number of teeth is equivalent to one with h \u00ab 'A, but with\nslightly larger inner radius a',\nIn2\n\na';:;:;a+-h,\n7r\n\nand the same outer radius b. Although this result is strictly valid only\nif a \u00bb 'A, measurements l l have shown that it is valid approximately even\nfor ka;:;:; 4.\nAPPENDIX C\nFabrication Technique\n\nEven if the aperture of a feed is illuminated by a single mode, the far\nfield contains a cross-polarized component with amplitude proportional\nto [eqs. (4), (5), and (27)]\n\nILl\n= I\n1\nI\nka\n(1 - t/h) ka tankl .\n\n(53)\n\nTo minimize this cross-polarized component, it is important that the\nthickness t of the disks be much smaller than their separation h,\n\nt\u00ab h.\n\n(54)\n\nSince h is always appreciably smaller than 'A/4, and since typically the\ndepth l of the grooves is not much different from 'A/4, condition (54)\nimplies\n\nt \u00ab 'A/4\n\n(55)\n\nt \u00ab l.\n\n(56)\n\nCorrugated feeds are difficult to fabricate. When a corrugated feed\nis electroformed, a mandrel of aluminum or other material is first prepared, and then the corrugated feed is electroformed around the mandril,\nwhich is then removed with a solvent. However, at high frequencies, say\nat frequencies higher than about 10 GHz, condition (55) demands that\nt be very small (much less than 0.318 em). Then, taking into account (56),\nthe above technique cannot be used.\nFigures 10 and 11 illustrate a technique that can be used at very high\nfrequencies, as high as 100 GHz, and which allows very small thicknesses\nt to be realized. First a set of disks of aluminum and brass is assembled,\nas shown in Fig. lOa, to form a single block whose outside surface is then\nCORRUGATED FEED EXPERIMENT\n\n887\n\nCopyright IC) 1977 American Telephone and Telegraph Company\nTHE BELL SYSTEM TECHNICAL ,JOURNAL\n\nVol. 56, No.6, July-August 1977\nPrinted in U.S.A.\n\nAcoustic Properties of Longitudinal\nDisplacement in Vocal Cord Vibration\nBy K. ISHIZAKA and J. L. FLANAGAN\n(Manuscript received January 12, 1977)\n\nWe examine the acoustic significance of longitudinal displacement\nin the self-oscillatory behavior of the vocal cords, and inquire into the\nneed for representing this detail in speech synthesis. We use computer\ntechniques and a previously derived model of the vocal cords to study\nthe contribution of longitudinal displacement to the total acoustic\nvolume velocity generated at the vocal cords. This volume velocity is\nthe effective sound source for production of voiced speech. From computational results, and from speech sounds synthesized by the programmed model, we find that the contribution of longitudinal displacement is not significant perceptually, and is not essential for\nmodeling the dominant acoustic properties of voiced speech.\nI. VOCAL-CORD MODEL\n\nIn earlier work I ,2 we derived an analytical model for the self-oscillatory\nmotion of the human vocal cords. We consider the displacing tissue of\neach cord to be approximated by two stiffness-coupled masses (see Fig.\n1). For normal (nonpathological) conditions of phonation, the oscillator\nis bilaterally symmetric, and the mechanical constants of the opposing\ncords are identical. The left-hand mass pair (denoted mI, m;) constitutes\nthe bulk of the firm cord tissue, while the smaller right-hand mass pair\n(m2, m~) represents the more flaccid mucous membrane covering of the\nfirmer tissue. Each mass has associated with it a restoring stiffness and\na resistive loss. All the stiffnesses and resistances are substantially\nnonlinear,l and in the original work, these elements act to oppose lateral\nmotion (x-direction) only. The restriction to lateral motion still permits,\nof course, phase differences in the motion of the coupled masses. Lateral\ndisplacement of each mass pair determines the cross-sectional area of\nopening at each position. If the length of the cords, or glottal opening,\nis taken as f g, then the cross-sectional glottal areas are taken as rectangular shapes whose areas are Agi = 2fgXi, i = 1, 2, where the factor\n889\n\nI.---\n\nVOCAL __\nCORDS\n\n-J\n\nFig. 1-Two-mass model of the vocal cords. Translational displacement is permitted in\nlateral (x) and longitudinal (y) directions_\n\n2 arises from the bilaterally symmetric cord configuration. These\ncross-sectional areas determine the acoustic properties of the glottal\nvolume current UgS ' which enters the cord orifice (from the subglottal\nsystem), and that which leaves it Uge (to pass into the larynx tube). The\nlatter volume velocity is the effective sound source for all voiced speech\nsounds. The air pressure just to the left of (beneath) the vocal cords is\nthe subglottal pressure PSg, and the pressure just to the right of (above)\nthe cords, at the entrance to the vocal tract, is Pt. The differential\npressure (Psg - P t ) is the potential that creates the glottal volume currents.\nThe resulting volume currents depend upon serial acoustic impedances\ndictated by Agl and Ag2 and, hence, upon the cord motion, which, in turn,\nis conditioned by the intraglottal pressure distribution in the orifice and\nby the transglottal pressure (Psg - P t ). These serial acoustic impedances\nalso are nonlinear (and flow dependent), and represent the mass (inertance) of air contained within the glottal orifice and the associated\nresistive flow losses. 1\nAdditionally, there is another potential influence upon the glottal flow,\nnamely, the volume of air displaced by the vibrating mass pairs. In\ngeneral, this volume displacement can have components associated with\nlateral and longitudinal motion. In the original work, components of\n890\n\nTHE BELL SYSTEM TECHNICAL JOURNAL, JULY-AUGUST 1977\n\nr\n\noz\n\nTRACHEA\n\nGLOTTIS\n\nVOCAL\n\nTRACT\n\nG)\n\n=i\n\no\nZ\n\u00bb\nr\no\n\nRc\n\n---'U g\n\n- U g2\n\n- Ugl\n\nc\n\nRV1/2\n\nLgl/2\n\nLgl/2\n\nRvl/2\n\nR12\n\nRv2/2\n\nLg2/2\n\nLg2/2\n\nRv2/2\n\nRe\n-Ugi\n\n- U gs\n\nen\n\"'U\nr\n\n\u00bb\n\n()\n\nm\n$:\n\nm\nZ\n\n-i\n\nZ\n\nPsg\n\nUY2 (\n\n+\n\no<\n\u00bb\nr\n\n()\n\n()\n\na\n:::0\no\n<\n05\n\n1\n\nAgl\n\ni\n\nAg2\n\n:::0\n\n\u00bb\n-i\n\n(5\nZ\n\nco\nCD\n\n\"\"\"\"\n\nFig. 2-Equivalent acoustic circuit including lateral and longitudinal displacement-volume\nvelocities.\n\nt\n\nPt\n\nTable I -\n\nValues of impedance components of Fig. 2\nR\n\nc\n\n= 137 ~,I U~l1l\n\u2022\n\nP (\n\nR 12 ='2\n\n2~'\n\nSerial\nImpedances\n\nLongitudinal\nComponents\n\nLateral\nComponents\n\n1\n1 )\nAT-AT\nIUg2\ng2\ngl\n\n1\n\ng2 ) I I\nAR e =P- -2- - ( 1 Ug\n2 Ag2Al\nAl\nRu1 = 12~\u00a3lddA2h\nLg1 = pdd gl,\n\nRu2 = 12~\u00a3ld2/A22\nLg2 = pd 2/ g2\n\ndy\nUy1 = 2t'g(d 1 + d 2) dt'\n\ndy\nUy2 = 2t'g(d 1 + d 2) dt\n\nd\nUx1 = d 1 dt (Agt>,\n\nd\nUx2 = d 2 dt (A g2)\n\n= 2t'gd 1 dx/dt,\n\n= 2t'gd 2 d x2 (dt\nCg2 = Ag2d 2/pC 2\n\nCg1 = Ag1ddpc 2\nG - S 1] -1\n1 1 pc2\n\nV\n\nAWo\n\n2c p p'\n\nSl = 2(\u00a3g + 2X1)d1\n\nG -S\n2 -\n\n2\n\n1]-1~\n2c p\n\n---;;G2\n\np\n\nS2 = 2(fg + 2X2)d 2\n\np = 1.14 X 1O-3gm/ cm3, air density\n\nConstants\n(for vocal\nsystem,\nmoist air\nat body\ntemperature) *\n\n~\n\n= 1.86 X 1O- 4dyne-sec(cm 2 , kinematic-coefficient of viscosity.\n\nc = 3.5 X 104 cm/sec, sound velocity\n1] = 1.4, adiabatic constant\nA = 0.055 X 1O-3cal/cm-sec-deg, coefficient of heat conduction\nWO = 27r(1000), mid audio range radian frequency\n\ncp = 0.24 cal/gm-degree, specific heat at constant pressure.\n\n* From J. L. Flanagan, Speech Analysis, Synthesis and Perception, second edition,\nNew York: Springer Verlag, 1972.\n\nglottal current corresponding to rate of volume displacement (both\nlateral and longitudinal) were neglected.\nII. ACOUSTIC CIRCUIT\n\nRecognizing that the cord dimensions are very small compared to\nsound wavelengths at the frequencies of interest, and that all mechanical\nvelocities are small compared to the sound velocity, we derive a onedimensional equivalent circuit for the acoustic quantities involved. Its\ncomplete form is shown in Fig. 2. The values of all impedance elements\nare given in Table 1.\nThe serial elements (top branch in Fig. 2) are identical to those of our\noriginal work!, and relate to time-variation of the acoustic impedance\nof the glottal opening.\n892\n\nTHE BELL SYSTEM TECHNICAL JOURNAL, JULY-AUGUST 1977\n\n-Ugl\n\n- U gs\n\nFig.3-Simplified equivalent acoustic circuit, including longitudinal displacement\ncurrents.\n\nAll shunt elements relate to rate of displacement of air volume by the\nmoving cord masses. The time variation of all shunt quantities is also\ndetermined by the motion of the cord masses.\nLateral motion of the cord masses (normal to the direction of glottal\nflow) displaces air volume at the rate of\nUxi = 2fg d i -dXi cm 3/'\ns, l = 1, 2,\ndt\nwhere Xi is the lateral displacement and d i is the depth (thickness) of\nthe cord element (mass). Again, the factor 2 arises from the two bilaterally opposing cords. The acoustic compliances, C 1 and C2, represent\nthe compressibility of the small air volumes contained between the opposing cords and the conductances G 1 and G 2 represent the heat-conduction loss at the tissue surfaces of the cords.\nLongitudinal motion of the cord masses is assumed to occur cophasically and to be translational only. In this regard, consider the y- motion\nof the locked masses to be opposed by a nonlinear spring and loss similar\nto that of hI and rl. The effective surface area exposed to the transglottal\npressure difference is taken to be the product of cord length and total\ncord thickness, fg(d 1 + d 2 ). No cavity compliances or losses are associated with the longitudinal motion, and the longitudinal contribution to\nthe total volume velocity is\nUyi = 2fg(d 1 + d 2 )\n\n~~ , i = 1,2.\n\nIn other words, Uy1 and Uy2 are equal and oppositely poled.\nNotice that in the earlier formulation,I,2 the absence of the shunt elements imposes the constraint U ge = U gs = U g. The presence of the\nshunt elements (all time-varying with displacements that are determined\nby the equations of motion for the mechanical system which, in turn, is\nforced by the intraglottal and transglottal pressures to close the feedback\nloop of the oscillator) makes the input flow Ugs and the output Uge\ntypically different.\nLONGITUDINAL DISPLACEMENT IN VOCAL CORD VIBRATION\n\n893\n\n15\n/a/\n\nX,\n\n10\n\n0\n-5\n\n~\n\n15\n\nN\nI\n\nX2\n\na\n\n~\n\n10\n\nIZ\n\nw\n\n:2:\nw\n\nu\n\n0\n\nc..\n\n-5\n\n\u00ab-.J\n~\n\n0\n\n15\nY\n10\n\n/ ..... Ps = 8 em H2O\n\n,. ,._---1-----,/\n\n,/\n,/\n\n0\n-5\n0.3\nAg\n\n1\u00ab\n\n0.2\n0.1\n\nw\n\na:\n\n\u00ab\n\n0\n-0.1\n0\n\n10\n\n20\n\n30\n\n40\n\n50\n\n60\n\n70\n\n80\n\nTIME IN MILLISECONDS\n\nFig. 4-Computed mechanical behavior of the vocal-cord/vocal-tract model. The vowel\nconfiguration is /a/.\n\nA recent related study3 examined the influence of the Uxi upon Ugf .\nThe present study considers separately the effects of the Uyi . For this\npurpose, the circuit of Fig. 3 is a simplification of Fig. 2.\nIII. PURPOSE OF PRESENT STUDY\n\nIn the original work,1,2 we made estimates of the volume displacement\ncurrents, based upon long-wave assumptions and one-dimensional sound\npropagation, together with what we believed to be reasonable physiological estimates of cord velocities (compared with volume velocities\nresponsive to transglottal pressure). We concluded that displacement\ncurrents are of second order, and in the original work we chose to neglect\nthem in favor of elucidating dominant principles. The original formulation, therefore, treated only lateral displacement as it affects the serial\nglottal impedances. As a matter of completeness, we more recently have\n894\n\nTHE BELL SYSTEM TECHNICAL JOURNAL, JULY-AUGUST 1977\n\nCORD\nMIDLINE\n\nOSCILLATION\nBUILDUP\n\nI\n\n/34\n\n35\n\n/a/\n\n33\n\nCORD\nMIDLINE\n\nI\nI\n31\n\n30\n8\n\n,\n\nm2\n\n,\n\n/\n\nI\n\n,~Jd2\nI\ndl\n\nc;:J\n\nI,\n\nI\n\n,\n\nml\n\n\\\n\n~\nI\n\n6\n\ny=Omm--~--~~~----L-----L-----~----4-----~____~\n\no\n\nFig. 5-X- Y trajectories for initiation of oscillation. Trajectories are for pellet positions\nshown in insert.\n\nreturned to a quantitative examination of these assumptions. A first\nstudy,:3 now completed, considered the importance of the shunt branches\nthat represent the lateral components of volume velocity generated by\nthe displacing masses-that is, from the volume current sources Ux1 and\nUx2 . The results of the study support the original assumptions, and show\nthe lateral components to be second order by comparison to the currents\nactuated by the pressure difference acting across the glottal opening.\nThe present study examines the contributions of the longitudinal\ndisplacement to the total glottal volume velocity (specifically, the contributions of U y1 and Uy2 ) and the importance of longitudinal displacement to the self-oscillatory dynamics of the cord model and to\nsound perception.\nWe take the longitudinal restoring stiffness ky typically to be the same\nas the lateral restoring stiffness kI, namely 80 kdynes/cm. The longituLONGITUDINAL DISPLACEMENT IN VOCAL CORD VIBRATION\n\n895\n\nCORD\nMIDLINE\n\nOSCILLATION\nSTEADY STATE\n\nI\n\nI\n\nI a/\n\n(Fa = 125 Hzl\n\nI\n\no\n\n/ TIME IN ms\n/\n\n/\n\ny = 3.8 mm----\n\n3\n\n5~\n\n6\n\nCORD\nMIDLINE\n\nI\n\nm2\n\nI I\nI\nIt::::\u00b1::::r...1.d2\n\nIQ\nI \\ 1\nI m,\n\nd,\n\ny=Omm\n\nFig. 6-X- Y trajectories for steady-state oscillation of the cord model.\n\ndinalloss (or damping ratio) is also taken to be similar to the lateral one,\nnamely (y = (1 = 0.2 These values are based upon clinical observations. 9\nWe examine these choices subsequently. Further, since the longitudinal\nand lateral motions of the cord masses are considered to be translational\nonly, no rotational behavior is included. Still further, while the lateral\ntranslations of the coupled masses ml and m2 can have large (and\nphysiologically natural) phase differences, their longitudinal translations\nare considered to be cophasic, and the internal coupling stiffness is assumed to act only for lateral motion. The lateral and longitudinal motions are, therefore, coupled only through the acoustic variables that\ndetermine the oscillator forcing functions. In the course of our discussion,\nwe will indicate comparisons to actual physiological data to assess the\nrealism of these assumptions.\n896\n\nTHE BELL SYSTEM TECHNICAL JOURNAL, JULY-AUGUST 1977\n\n10\n\n/ a/\n\nPI\n\n0\n-5\n-10\n20\n0\",\nI\n\n15\n\n\u00a7\nw\n\na:\n\n10\n\n:::J\n(J)\n\nw\n\na:\n~\n\n0\n20\nPsg\n\n15\n\n./ Ps (8 em H2 O)\n/\n\n/ __ t __\n\n10\n\n\"\n0 \"\"\n>-\n\n'=\n\nu\n\n\"\"\n\n1500\n\n0\n\n1000\n\n>'\"\n\n500\n\nUg\n\n....Jw on\n\nw E\n22\n:::J\n....J\n\n0\n\n0\n\n>\n\n-500\n0\n\n10\n\n20\n\n30\n\n40\n\n50\n\n60\n\n70\n\n80\n\nTIME IN MILLISECONDS\n\nFig. 7-Computed acoustic qualities for the vocal-cord/vocal-tract model. The vowel\nis /a/.\n\nIV. RESULTS OF COMPUTER SIMULATIONS\n\nThe vocal-cord model, as represented by Fig. 3, was combined with\na transmission-line formulation of the vocal tract that we have used\npreviously in speech synthesis studies. 4 The programmed vocal tract\ncontains 20 sections which, in addition to the classical acoustic elements,\nrepresents the yielding soft walls of the tract and sound radiation from\nthe yielding walls. This formulation is based upon measurements of\ntissue impedances that we reported earlier.5 Also included for the present\nstudy is a transmission-line representation of the subglottal system. Six\nsections of line represent the trachea, bronchi and lungs, as previously\ndescribed. 6 We implemented the entire system in terms of difference\nequations programmed on a laboratory computer by techniques we have\ndescribed in detail previously.l,2\nLONGITUDINAL DISPLACEMENT IN VOCAL CORD VIBRATION\n\n897\n\n/::.:::'~-'PARTICLE 2\n\nAPPROXIMATE\nMIDLINE\n\nf~\n\n\"'PARTICLE 1\n\n\\\n\n\"'- - - PARTICLE 3\n\n4\n\nzo\n\n6 ~ - - - - TIME IN 1.25 ms INCREMENTS\n\n(JJ\n\n:::o\n\nFO=100HZ\n)\n( Ps = 8 CM H 2 0\n\nE\nE\n\n::.\n>\n\no\n\n~\n6\n\n1\n\n2\n\n4\n\n3\n\n5\n\n(AFTER BAER)\n\nx (1 mm/DIVISION)\n\nFig. 8-X- Y trajectories observed from excised larynx of dog (after Baer).\n\nMost of the data reported here are for the vocal tract configured in\nthe shape for the neutral (schwa) vowel I a/. Some data are also included\nfor the vowels Iii and la/.\nA first step is to ascertain if the cord oscillator, so arranged for longitudinal motion, performs realistically when compared with observations\non the human larynx. A second step, then, is to determine the acoustic\nsignificance of the volume displacement current arising from longitudinal\nmotion.\nThroughout these calculations, the laryngeal parameters are set to\nthe \"standard\" values used earlier for phonation by a man's voice in the\nchest registerl (i.e., neutral glottal area Ago = 0.05 cm 2 , cord tension\nparameter Q = 0.78, d 1 = 0.25/Q cm, d 2 = 0.05/Q cm). Recall that the\nQ parameter scales the values of mass and stiffness and, hence, also the\nvalues of the d i . Phonation is initiated by raising the lung pressure P s\nsmoothly from zero to the standard value of 8 cm H 2 0. The pressure is\nelevated in a lO-ms interval.\n4.1 Mechanical behavior\n\nAs the lung pressure is elevated, the model commences a buildup of\noscillation. After four or five transient swings, the oscillation settles into\n898\n\nTHE BELL SYSTEM TECHNICAL JOURNAL, JULY-AUGUST 1977\n\nTIME IN MILLISECONDS\n\nFig. 9-Subglottal pressure variation measured on a human subject (after Sawashima).\n\na steady state behavior with a fundamental frequency (pitch) determined\nby the model parameters (the tension parameter Q has the dominant\neffect on pitch 1 ). The initial 80 ms of this synthetic phonation is illustrated in Fig. 4 for the mechanical variables.\nThe top two curves show the displacements x 1 and x 2 of mass pair m 1\nand mass pair m2, respectively. The first collision of each mass pair is\nindicated by the first flat, negative-going portion of the displacement\nwaveforms. For the Af,'() = 0.05 cm 2 value, this occurs for Xi = -0.0178\ncm. Note, too, that x 1 leads X2 in phase by the order of 60\u00b0, which is\n25\nky = 40 kdyne/ em\n\n20\n\n/a/\n\n[x~y TRAJECTORIES]\n\nI\n\n15\n\n10\n\n0\n\n1 20\n\nN\n\nI\n\na\n\nky= 80kdyne/em\n\n~\n\n15\n\nI-\n\nz\n\nw\n\n10\n\n~\n\nw\nu\n\n\u00ab\n\n.J\nc..\n\n~\n\n0\n\n0\n20\nky = 120 kdynel em\n\n15\n10\n\n0\n0\n\n10\n\n20\n\n30\n\n40\n\n50\n\n60\n\n70\n\n80\n\n90\n\nTIME IN MILLISECONDS\n\nFig. lO-Effect of longitudinal restoring stiffness ky upon the longitudinal displacement,\ny. Data show oscillation buildup for a lung pressure\" Ps that is raised smoothly from zero\n\nto 8cm H 2 0.\n\nLONGITUDINAL DISPLACEMENT IN VOCAL CORD VIBRATION\n\n899\n\n10\nky = 40kdyne/cm\n\nPt\n\n/a/\n\n0\n\n-5\n-10\n10\n\n0\n\nky = 80kdyne/cm\n\nN\n\nI\n\n]\nw\n\n0\n\ncr:\n::J\n(f)\n(f)\n\nw\n\n-5\n\ncr:\n\nc..\n\n-10\n10\nky = 120 kdyne/c m\n\n0\n-5\n-10\n0\n\n10\n\n20\n\n30\n\n40\n\n50\n\n60\n\n70\n\n80\n\n90\n\nTIME IN MILLISECONDS\n\nFig. ll-Effect of ky upon Pt.\n\nconsistent with observations from high-speed motion pictures of the\nhuman vocal cords. The third trace shows the longitudinal displacement,\ny, which bulges upward as P s is raised. The y motion is roughly sinusoidal. The lower trace shows the net area of glottal opening Ag (namely\nthe rp.inimum of AgI and A g2 ). The y-displacement is seen to lead in\nphase the Ag wave, again consistent with the upward, rolling motion seen\nin high-speed photography of the real cords.\nAn x-y plot of the buildup transient portrays the behavior perhaps\nmore graphically. Figure 5 shows the Xl vs y and the X2 vs y values with\ntime as the parameter. Imagine pellets fixed to the lower and upper inner\nedges of one simulated cord, shown by the inserted anterior-posterior\nview of Fig. 5. The trajectories of the two pellets are plotted for the oscillation buildup. The y-axis is broken and re-originated at y = (d l +\nd 2 ) = [(2.5 + O.5mm)/Q] = 3.8 mm. The flat portion of the tracks, along\nthe vertical midline, reflect collision with the opposing vocal-cord\nmass.\nAfter several initial swings, the oscillator settles into a steady-state\nbehavior. One cycle of this trajectory is shown in Fig. 6. The steady-state\npitch frequency in this case is Fa = 125 Hz, or a period of T = 8 ms.\n4.2 Acoustical behavior\n\nThe corresponding acoustical parameters, calculated for the same\nbuildup period, are shown in Fig. 7. The acoustic pressure at the input\n900\n\nTHE BELL SYSTEM TECHNICAL JOURNAL, JULY-AUGUST 1977\n\no\n\n4\n\n02::1\n\nOmm ____\u0001L--Lt~~-----J----~-----L----~I____~I__--.. x\n-~ O.2mm ~-\n\nFig. 12(a)-Steady-state X- Y trajectory for ky = 40 kdyne/cm.\n\nto the vocal tract P t is shown in the top trace. It reflects strongly the\neigenfrequency structure of the tract, in this case configured for /a/ and\nhaving formant frequencies of approximately 500 Hz, 1500 Hz, 2500 Hz\n... The transglottal pressure (Psg - Pd, which is the forcing function\nfor the y- motion and the pressure potential for the volume flow through\nthe glottal opening, exhibits a pronounced pitch-synchronous variation.\nIts peak values, in fact, approach twice the lung pressure value of P s =\n8 cm H 2 0. Recall that Ps is the lung pressure input to the simulated\nLONGITUDINAL DISPLACEMENT IN VOCAL CORD VIBRATION\n\n901\n\n6\n5\n4\n\no\n\n~\nI\n\n0.2 mm\n\ni\nOmm----L-~~~\n\n__\n\n~\n\n____\n\n~\n\n____\n\n~\n\n____\n\n~----~----+\n\nFig. 12(b}-Steady-state X- Y trajectory for ky = 80 kdyne/cm.\n\nsubglottal system, representing trachea and bronchi. But notice that\nthe mechanical y-displacement (Fig. 4) does not respond with this detail.\n(Neither do the x 1 and X2 displacements respond to high-frequency detail\nin their forcing functions-that is, the mechanical system, being masscontrolled, filters out this detail.)\nThe sub glottal pressure Psg (the pressure just beneath the vocal cords)\nalso exhibits a pitch-synchronous fluctuation, but of somewhat less\namplitude, namely about \u00b120 to \u00b130 percent of the mean subglottal\npressure. Its positive peaks correspond to the closing epochs of the glottal\nport. The calculated volume velocity passing the glottal opening Ug\n(bottom trace) appears as a traditionally shaped, pulsive waveform. This\nwave is similar to that calculated in previous work (without longitudinal\nmotion) but differs in that its values are modified by the effects that U y1\nand Uy2 couple into the pressure variables. That is, Uy1 and Uy2 can\ninfluence Psg and P t and, hence, Ugl . The latter three variables, in turn,\nclose the oscillator feedback loop by constituting the forcing functions\n902\n\nTHE BELL SYSTEM TECHNICAL JOURNAL, JULY-AUGUST 1977\n\ny\n\n5\n4\n\no\n\nI\n\n0.2 mm\n\ni\nOmm----~--~+_----~----~----~----+_----+_----x\n\nFig. 12(c}-Steady-state X- Y trajectory for ky = 120 kdyne/cm.\n\nfor the lateral displacement. As was the case in the mechanical variables,\nthe VI! flow does not reflect a temporal fine structure comparable, say,\nto the (PsI! - P t ) waveform. The resistive and inertive components of\nthe glottal impedance (i.e., the serial components in Fig. 3) act effectively\nas a low-pass filter. It is not unusual, however, to see pronounced temporal structure that corresponds to the lowest eigenfrequency of the vocal\ntract, especially for low, back vowels (such as /a/), or for tightly articulated sounds.\nA next question, then, is how do these mechanical and acoustical\nquantities, resulting from the model with longitudinal displacement,\ncompare with physiological data.\n4.3 Comparisons to physiological observations\n\nOne qualitative comparison can be made for the mechanical displacement behavior. Baer 7 performed studies on the excised larynx of\nLONGITUDINAL DISPLACEMENT IN VOCAL CORD VIBRATION\n\n903\n\nCORD\nMIDLINE\n\ny\n\nOSCILLATION\nBUILDUP\n\nI\nI\n\n22\n\n/a/\n(NO SUBGLOTTAL SYSTEM)\n\n2~\n\n32~-~-.l-\n\n31\n~-+-_~ 36\n9\n\n29\n\n37\n\n8\n\n23\n22\n\n30\n\ny=Omm----~~~--~----~----~----~----~----~x\n\nFig. 13-0scillation buildup without subglottal system.\n\na dog in which he fixed pellets to the displacing tissue and made optical\nobservations under stroboscopic illumination. While his pellet positions\ndo not correspond exactly to our mass-pair corners, we can roughly\ncompare his observations with our data. Figure 8 shows x-y trajectories\nfor one set of conditions for the dog larynx that approximates values used\nin human phonation (namely P s = 8 cm H 2 0, Ug = 275 cm 2 /s, and Fo\n= 100 Hz). Particles (pellets) 2 and 3 are of interest. While the vibratory\nexcursions of the excised dog larynx are larger than those we calculate\nwith the model, the qualitative motions are gratifyingly similar. One\nquestion that arises is how much does the longitudinal (vertical) displacement depend upon the choice of longitudinal stiffness constant.\nWe shall examine this question in more detail subsequently.\nAnother comparison can be made in the acoustic domain-namely,\nto the subglottal pressure variation Psg shown previously in Fig. 7. Sawashima 8 has measured the subglottal pressure during phonation in a\n904\n\nTHE BELL SYSTEM TECHNICAL JOURNAL, JULY-AUGUST 1977\n\nCORD\nMIDLINE\n\nOSCILLATION\nSTEADY STATE\n\nI\n\n/a/\n(Fo= 123 Hz)\n\n1\n5\n\n(NO SUBGLOTTAL SYSTEM)\n\n4\n\n~\n\n__\n\n~O\n\n/TIME IN ms\n./\n\n3.8mm-----\n\nI\n\n6;?\n\n4\n\n3\n\nI~f---+----~\n12\n\nI\nI\n\nrr\n\n0.2,mm\nI\n\ny=Omm--~--~~----~----~----~----~I----~I-----..x\n-,../\n\n0.2 mm\n\nh-\n\nFig. 14-Steady-state oscillation without subglottal system.\n\nhuman subject. One of his results is shown in Fig. 9. The qualitative\ncorrespondence to the model calculation appears relatively good, and\nthe acoustic interaction among the simulated cords, vocal tract, and\nsubglottal system is realistic.\n4.4 Effect of longitudinal stiffness constant\n\nIn view of uncertainties in the measurement of the stiffness constants\nin physiological preparations, it is important to examine how critical the\nvalue of ky (the longitudinal restoring stiffness) is to the oscillatory behavior of the model.\nFor the bulk of our studies, we have taken ky equal to our typical\n\"standard\" value of kI, namely 80 kdynes/cm.I We have also used the\nstandard value for the damping ratio, y =\n= 0.2. This choice is based\nupon the physiological measurements on cord tissue conducted by Ka-\n\nr rl\n\nLONGITUDINAL DISPLACEMENT IN VOCAL CORD VIBRATION\n\n905\n\n20r---~-----------------------------------------------.\n\n/a/\n\nY - DISPLACEMENTS\n\n15\n\nx - Y TRAJECTORIES\nI\n\n10\n\no~=-~~\n\n__\n\n~\n\n____\n\n~\n\n____\n\n~\n\n____\n\n~\n\n____\n\n~\n\n____\n\n~\n\n__\n\n~~\n\n__\n\n~~\n\ng 20r----------------------------------------------------.\n\n<\"\n\nI\n\no\n\n15\n\n~\n\n10\n\n!a/\n\nill\n\n:2\"\nill\n\nu\n\n5\n\n- 600\n~\n\nu\n0\n\n-l\nW\n\n400\n\n> 200\nw\n::::;\n\n:)\n\n-l\n\na\n\n0\n\n>\n\n40\n20\n0\n-20\n-40\n0\n\n4\n\n8\n\n10\n\nTIME IN MILLISECONDS\n\nFig. 22-Glottal volume velocities calculated with y-displacement (refer to Fig. 3).\n\nof the difference for this condition is on the order of 10 cm3 /s, or about\nl/fiO of the peak value of the total Uge . This result is not just peculiar to\nthis range of volume velocity, but rather it scales comparably at louder\nand softer phonation. For example, if the lung pressure Ps is doubled\nsay to 16 em H 2 0, the longitudinal displacement current increases because the transglottal pressure and the longitudinal displacement increase. But the Ug flow also increases and remains far and away the\ndominant quantity.\nThe amplitude spectra of these quantities provide convenient correlation with auditory percepts. The spectra for Uge and Ug are shown in\nFigs. 23a and b. A close comparison shows the differences to he less than\n2 dB, an amount that is not significant perceptually. The more relevant\ncomparison is obtained when the effect of y- motion is eliminated (by\nremoving U y1 and U y2 ). The corresponding glottal waveform for no ydisplacement is illustrated in Fig. 24. It is denoted Ug ;. Also reproduced\nis the Uge with y~displacement. Further, the difference between the\nlongitudinal displacement and lateral-only conditions (Uge - Ug ;) is\nshown on an XI0 enlarged scale. During the glottis-closed time, this\ndifference is identical to the (Uge - Ug ) difference of Fig. 22, because\nU g = O. During the glottis-open time, the (Uge - Ug ;) difference differs\nfrom the (Uge - Ug ) difference. In other words, Ug differs from Ug ;\nLONGITUDINAL DISPLACEMENT IN VOCAL CORD VIBRATION\n\n913\n\no~--------------------------------------------~\n\nUgl\n\n/a/\n\n-10\n\n-20\n\n(f)\n\nuj -30\nCD\n\nu\n\nw\n\no\n\nz\n\n~\n\no\n\n-40\n\n~\n\n~\n...J\n\n~ -50\n-60\n\n-70\n\no\n\n8\nTIME IN MILLISECONDS\n\n-80L-____L -_ _ _ _L -_ _ _ _L -_ _ _ _L -_ _ _ _L -_ _ _ _\n\no\n\n~\n\n____\n\n~\n\n__\n\n~\n\n3\n\n4\n\nFREQUENCY IN KILOHERTZ\n\nFig. 23(a}-Amplitude spectrum of U/: e. which includes the effects of y-displacement.\n\nessentially by the influence that Uy1 and Uy2 have upon the transglottal\npressure difference (Psg - P t ).\nAgain, the more perceptually relevant comparison is to the amplitude\nspectrum. The spectrum of Ug ; is given in Fig. 25. A close comparison\nto the Uge spectrum of Fig. 23 shows the differences to be less than about\n2 dB. Auditory assessment of the output synthetic vowels shows them\nto be indistinguishable even in close comparison.\nVI. CONCLUSION\n\nIn view of these results, we conclude that realistic acoustic behavior\n(which is needed in speech synthesis) can be obtained in the cord model\nwithout the additional complexity of longitudinal displacement. Longitudinal displacement is not necessary for realistic self-oscillation of\nthe model. The important vertical phase differences in the two-mass\nmotion are adequately duplicated by lateral displacement only, as is the\nsignificant acoustic interaction between vocal tract and vocal cords.\nFurther, the rate of volume displacement owing to longitudinal motion\n914\n\nTHE BELL SYSTEM TECHNICAL JOURNAL, JULY-AUGUST 1977\n\n-80~--------------------------------------------~\n\nlal\n-70\n\n-60\n\nVl\n\nuj -50\nCD\n\n~\no\nz\no\n\nill\n\n-40\n\n::J\nf-\n\n::i\n\n~ -30\n\n~ 1:::~\n\n-20\n\n~\n\n~ 200\n\nOL-______\n\n-10\n\n!l\n~\n\n________\n\n~\n\no\n\n8\nTIME IN MILLESECONDS\n\nOL-____L -_ _ _ _\n\n~\n\n____\n\n~\n\n____\n\n~\n\n____\n\n~\n\n____\n\no\n\n~\n\n____\n\n~\n\n__\n\n~\n\n3\n\n4\n\nFREQUENCY IN KILOHERTZ\n\nFig. 23(b)-Amplitude spectrum of Ug calculated with y-displacement.\n\nis clearly perceptually not significant and need not be represented with\nadded detail.\nThese conclusions about the mechanical and acoustic behavior have\na corollary in a comp~nion study on the rate of displacement of air volume owing to lateral motion only. 3 This contribution was examined by\nmaking use of the shunt branches in Fig. 2 that include U x1 , U x2 . Calculations and computer simulations showed that the contribution to\nglottal volume velocity of the air extruded from the glottal port by lateral\ntissue displacement is barely discriminable in a differential auditory\ncomparison. In fact, the perceptual effect for the lateral volume displacement is just slightly larger than for the longitudinal displacement.\nBoth are quite second-order in importance.\nWe have found in the present study that proper acoustic and oscillatory behavior of the model does not depend significantly upon longitudinal displacement. The longitudinal motion is relatively insensitive to\nacoustic loading and to changes in longitudinal stiffness. The longitudinal motion influences fundamental frequency only slightly. What,\nLONGITUDINAL DISPLACEMENT IN VOCAL CORD VIBRATION\n\n915\n\n700\n\n/a/\n600\n400\n200\n\n\"'5\n\n0\n40\n\n~\n\n>-\n\nf0-\n\n20\n\nG\n\n0\n\n...J\nW\n\n0\n\nw\n\n-20\n\n>\n\n::?:\n\n'WITHOUT V-DISPLACEMENT\n\n::J\n\n...J\n\n0\n\n>\n\n-40\n600\nUg \u00a3\n\n400\n\nWITH V -DISPLACEMENT\n\n200\n0\n-200\n0\n\n2\n\n4\n\n6\n\n8\n\nTIME IN MI LLiSECONDS\n\nFig. 24-Comparison of waveforms for Uf{f' which includes y-displacement current,\nand UI:;' which is calculated without y-displacement.\n\nthen, are the critical and sensitive parameters of the cord model? In other\nwords, what parameters are most influential upon the perceptual attributes of Uge , since the end product-the output sound-depends\ndirectly upon Uge ? The results of our earlier work can be combined with\nthe insights obtained here to consider this question.\nThe original study showed that the intra-glottal pressure distribution,\nand the fluid flow laws used to deduce it, are quite important to proper\noscillatory behavior, to proper generation of the Uge flow, and to realistic\nacoustic interaction between the vocal tract and vocal cords. To a large\nextent this pressure distribution determines how the pitch frequency\nvaries with subglottal pressure and with articulatory configuration. The\nmass-stiffness product (i.e., the natural frequency of the mechanical\nsystem) is quite dominant in determining pitch range. Subglottal pressure, assuming it to be above an initiation threshold of several cm H 2 0,\nis primarily correlated with sound intensity, a relatively noncritical factor\nfor voiced sounds. Mechanical parameters such as cord thickness,\ndamping ratio, and nonlinearity are relatively noncritical except as they\ninfluence duty factor and \"flow chopping\" at collision (which yields a\nbroad-spectrum Uge function). None of the mechanical variables, lateral\nor longitudinal, reflects the temporal fine structure of the acoustic\nvariables, but both must and do reflect the open-close cycles of the vi916\n\nTHE BELL SYSTEM TECHNICAL JOURNAL, JULY-AUGUST 1977\n\nO~----------------------------------------------,\n\nfa /\n\n-10\n\n-20\n\n'WITHOUT DISPLACEMENT CURRENTS\n\nen\n\nLd -30\n\nCD\n\nU\nw\n\no\nz\n-\n\nw\n\n-40\n\no\n\n:)\n\nf-\n\n::::i\n\n~ -50\n\n~ ~:::~\n\n-60\n\n~ ~20t\n\n-70\n\nnl\n\n~.\n\n\u00b00~------~--------~8\nTIME IN MILLISECONDS\n\n-80~\n\n____~____~____~____~____~____~____~__~\n\no\n\n3\n\n4\n\nFREQUENCY IN KILOHERTZ\n\nFig. 25-Amplitude spectrum of Ug ;, the glottal volume velocity without y-displacement.\n\nbrating cords. The realistic phase differences in motion of the upper and\nlower edges of the cords (m2 and ml in the model) allow phonation\nsmoothly over a wide range of input impedances to the vocal tract (both\ninductive and capacitive), and this behavior can be obtained satisfactorily by permitting lateral displacement only of the stiffness-coupled\nmasses. The computational complexity of anything more detailed does\nnot seem necessary from the standpoint of duplicating realistic acoustic\nbehavior, which is the objective in speech synthesis.\nOn the other hand, if the objective were a detailed study of tissue deformation (as might be the case in simulations for clinical diagnosis or\nfor representing pathological conditions) then the computational complexity of longitudinal displacement might be considered. In such a case,\nthe vocal-cord model should be treated as a more distributed system.\nFor the representation and synthesis of normal speech, however, these\ndetails do not appear perceptually significant and are not needed to\nrepresent the dominant properties of vocal-cord vibration.\nLONGITUDINAL DISPLACEMENT IN VOCAL CORD VIBRATION\n\n917\n\nCopyright \u00a9 1977 American Telephone and Telegraph Company\nTHE BELL SYSTEM TECHNICAL JOURNAL\n\nVol. 56, No.6, July-August 1977\nPrinted in U.S.A.\n\nFaulty-Trunk Detection Algorithms Using\nEADAS/ICUR Traffic Data\nBy J. s. KAUFMAN\n(Manuscript received November 1, 1976)\n\nA class of algorithms for detecting abnormally short-holding-time\ntrunks has been developed that utilizes individual trunk data available\nin EADAS/ICUR (Engineering and Administrative Data Acquisition\nSystem/Individual Circuit Usage Recorder). This data consists of a\ntwo-dimensional statistic that compresses the raw trunk measurements-the state of the trunk (busy or idle) sampled every 100 or 200\nseconds-into a manageable form. Because this data is essentially a\nsufficient statistic for the stochastic process used to model the (unobservable) trunk state measurements, one of the algorithms developed\nis Wald's sequential probability ratio test. Two of the algorithms developed have been implemented in ICAN (Individual Circuit Analysis\nProgram), and are currently being used to test trunks associated with\nthe No.1 crossbar, No.5 crossbar, crossbar tandem (lXB, 5XB, XBT),\nand step-by-step switching machines. The focus in this paper, however,\nis on the modeling and analysis aspects of the problem, and only slight\nattention is paid to the various trade-offs and real-world constraints\nencountered in implementing the algorithms.\nI. INTRODUCTION\n\nA message trunk, the basic connecting link in the switched telephone\nnetwork, provides the communication path between switching machines\nas well as certain call setup capabilities, such as supervision, signaling,\nand ringing. For an important class of trunk faults that cause call failure,\nthe trunk is released by the switching system upon customer abandonment and is again available to fail another call. As a result, a single undetected faulty trunk of this type can fail a significant fraction of the\noffered attempts to a group and will characteristically have an abnormally short holding time.\nBecause of their potential service impact, significant efforts have been\nmade to understand and quantify the impact that such abnormally\n919\n\nshort-holding-time trunks have on central office and network service. 1- 4\nIt is now widely understood as a result of these studies that this generic\ntrunk fault results in a fraction of service attempts \"killed,\" which is out\nof all proportion to their number in the trunk population. Consequently,\ntraffic data available from new and existing traffic data-acquisition\nsystems has been viewed in the light of increasing interest in trunk-fault\ndetection. In particular, with the advent of the Bell System EADAS/ICUR\n(Engineering and Administrative Data Acquistion System/Individual\nCircuit Usage Recorder) system,5 it was natural to ask whether the new\nindividual trunk data available could be used to detect such \"killer\"\ntrunks.*\nThis paper discusses the theoretical aspects of a class of killer-trunk\ndetection algorithms that utilize the individual trunk traffic data\navailable in EADAS/ICUR. These algorithms were designed for, and\npractical versions of them are presently implemented in, the ICANt\nportion of the EADAS/ICUR system. We focus here, however, on the\nproblem formulation, modeling, and analysis aspects of the algorithms\nwithout bringing in many of the diverse factors and trade-offs encountered in the actual implementation.\nBecause the holding time of a trunk affects the statistical properties\nof the trunk data in EADAS/ICUR, it is natural to formulate the killertrunk detection problem as a problem in the testing of statistical hypotheses. In this context our modeling effort is basically an attempt to\nprecisely define the state of a trunk (normal or killer) and expose the\nrelevant underlying distributions. Well-known aspects of the theory of\nhypothesis testing are then applicable and immediately suggest a number\nof different tests. Sequential tests are naturally considered since the\nEADAS/ICUR data evolve sequentially in time. Questions about the robustness of the models, and the structure and performance of statistical\ntests, are addressed using standard analytic tools.\nThe material in this paper has been organized into six major sections,\nwhose content we briefly describe. After considering the data available\nin EADAS/ICUR (Section II), we proceed to model a trunk (Section 3.1),\nmotivate an appropriate set of statistical hypotheses suitable to our\nproblem (Section 3.2), and briefly review several classical tests for deciding between statistical hypotheses (Section 3.3). With these preliminaries out of the way, we develop individual trunk algorithms based\nsolely on individual trunk data. Proceeding in a heuristic manner, we\nuse the individual trunk data to \"derive\" an ad hoc killer-trunk-detection\n* The term killer trunk has been widely adopted in referring to a faulty switchingmachine-accessible trunk in a group whose average holding time is substantially smaller\nthan the average group holding time.\nt Individual circuit analysis program-a software program that analyzes much of the\nEADAS/ICUR traffic data and maintains the system data base.\n920\n\nTHE BELL SYSTEM TECHNICAL JOURNAL, JULY-AUGUST 1977\n\nalgorithm (Section 4.1). Although the insight gained in proceeding in\na heuristic fashion is significant, we shift our emphasis in Section 4.2 and\nrigorously derive an optimal test statistic. It is interesting to find that\nthe ad hoc statistic is essentially one of two symmetric statistics which\ncomprises the optimal test statistic. The relationship between these\nindividual trunk statistics is further explored in Section 4.3.\nIn Section V we factor grouping information (which essentially\nidentifies all trunks common to a trunk group) into the picture, and\ndevelop detection algorithms tailored to trunks associated with the\nNo. 5 crossbar switching machine. This development necessitates\nmodeling the 5XB trunk-group selection procedure, and several results\ndue to Forys and Messerli 2 are utilized. In Section VI we shift our discussion to the performance of the 5XB group algorithms, deriving approximate expressions for the mean statistic update and mean detection\ntime in Sections 6.1 and 6.2, respectively. The paper concludes in Section\n6.3 with an approximate analysis of the false-alarm probability of the\n5XB group algorithms.\nII. EADASIICUR DATA\n\nThe structure of a killer-trunk detection algorithm is largely dependent on the type of individual trunk measurements available. * In\nEADAS/ICUR, the raw (unobservable) data consists of the state of each\ntrunk (busy or idle) every 100 or 200 seconds. Fortunately, the data accumulations available essentially summarize all the relevent information\nin the raw data.\n2. 1 Switch-count and transition data\n\nThe data available from the EADAS/ICUR system, which can be used\nto distinguish between normal and killer trunks, is obtained by sampling\nindividual trunks at 100 or 200 second intervals. This data consists of\nperiodic accumulations (typically hourly, two-hourly, or three-hourly)\nof both the Busy states, and the State transitions. The busy state accumulation is usually referred to as the switch count. For the 200-second\nsampling option with a one-hour accumulation period, the switch-count\nis an integer between 0 and 18. A state transition occurs whenever the\nstate of a trunk (busy or idle) is different at two successive scans. For the\n200-second sampling option with a one-hour accumulation period, the\nnumber of state transitions is an integer between 0 and 17.\nIf we denote the ith scan during an accumulation period in which m\nscans occur by Xi, and let 0 and 1 correspond to trunk idle and trunk\n* Until very recently, almost all trunk-traffic measurements were obtained on a group\nrather than on an individual trunk basis.\nTRUNK-DETECTION ALGORITHMS\n\n921\n\nTRUNK- 1\nSTATE\n\n0\n\n0\n\no }S SWITCH COUNTS\n3 TRANSITIONS\n\nIn\n0\n\n0\n\nIn I\n\n400\n\n800\n\nCALLS ON NORMAL\nTRUNK\n\n1200\n\n1600\n\nSECONDS\n\n0\n\n0\n\n0\n\n0\n\n0\n\n0\n\no } 25WITCH COUNTS\n3 TRANSITIONS\n\nSAMPLING-e\nEPOCHS\n\nn ~~ n 0 0\nI\n\n0\n\n400\n\nCALLS ON KILLER\nTRUNK\n\nI\n\n800\nSECONDS\n\n1200\n\n1600\n\nFig. I-leUR data.\n\nbusy, respectively, the available data may be written\nm\n\n(i) n (m) = L Xi (switch count)\ni=l\nm\n\n(ii) t(m) = L IXi - xi-d (state transitions).\ni=2\n\nThus, the raw (unavailable) data in the form of a binary sequence,\n\nis compressed into the two statistics n(m) and t(m).\nBecause the holding time of a killer trunk is generally on the order\nof a few tens of seconds, it should have substantially more state transitions than a normal trunk, for a given switch count. Figure 1 illustrates\nthe sampling process on both a normal and killer trunk. * For the purposes of this figure individual calls are represented by rectangles, call\ndurations correspond to the width of the rectangles, and a half-hour\naccumulation period with the 200-second sampling option is used.\nWe note in passing that for the 200-second sampling option, very little\ninformation is lost by \"compressing\" the raw data Xm = (Xl, . \u00b7,x m ) into\nthe two statistics n(m) and t(m). Thus, normal conversation lengths tend\nto be in the vicinity of 3 to 4 minutes and, hence, with the 200-second\nsampling option, we expect that only adjacent samples are significantly\n* The realizations shown in Fig. 1 are more or less typical for a 5XB trunk group with a\nmean group holding time of approximately 4 minutes operating at about 40-percent occupancy, and having a killer trunk with a mean holding time of approximately 1 minute.\n922\n\nTHE BELL SYSTEM TECHNICAL JOURNAL, JULY-AUGUST 1977\n\ncorrelated. If Ixd~l is Markovian, then [n(m),t(m)] is almost a sufficient\nstatistic ([n(m),t(m),xl,x m ] is sufficient) for Xm (see Section 4.2). Note\nalso that for a trunk in the killer state, succesive samples should be essentially independent (for both sampling options).\n2.2 Grouping information\n\nIn addition to the switch-count and transition data available from the\nEADAS/ICUR system, we are also able to utilize a system map to identify\n\n(i) all trunks common to a trunk group, and (ii) the trunk-selection\nprocedure* associated with the trunk group. It turns out that using this\ngrouping information,t in addition to the switch-count and transition\ndata, enhances the detection potential considerably.\nThus, we divide the class of algorithms into two types according to\nwhether or not grouping information is utilized. The first type, which\nuses only switch-count and transition data is referred to as an individual\ntrunk algorithm. These individual trunk algorithms are applicable to\nall trunks-including two-way trunks-independent of the type of\nswitching machine they are associated with. They do however assume\nknowledge of the trunks nominal holding time. The second type of algorithm uses the grouping information in addition to the switch-count\nand transition data and is referred to as a group algorithm. Group algorithms are \"tailored\" to a specific kind of trunk-selection procedure\nand, hence, apply to trunk groups associated with specific switching\nmachines. For the purposes of this paper, the trunk-selection procedure\nconsidered is random selection of idle trunks. This procedure models\nthe selection procedure of trunk groups associated with the 5XB\nswitching machine. Group algorithms generally apply only to one-way\ntrunk groups.\nIII. PRELIMINARY CONSIDERATIONS\n\nIn attempting to quantify the intuitive notion that a killer trunk will\nexhibit more transitions than a normal trunk (see Fig. 1), for a given\nswitch count, it is natural to consider the transition probabilities:\nP1,o = PIXt+T = O/Xt = 11\nand\n\nPO,l = PIXt+T = l/xt = 01,\n* The map in EADAS/ICUR indicates the type of switching machine that the trunk group\nis associated with, and this allows us to model the trunk-selection procedures (see\nRef. 2).\nt We will consistently use \"grouping information\" to refer to both the identification\nof all trunks common to the group and the trunk-selection procedure associated with the\ngroup.\nTRUNK-DETECTION ALGORITHMS\n\n923\n\nwhere Xt denotes the state of a trunk at epoch t and r denotes the sampling interval. Of course, to evaluate these transition probabilities, we\nmust be concrete about how we model a trunk.\nBefore tying ourselves down to any specific model, however, it is useful\nto view these conditional probabilities in a canonical form. Thus, suppose\nwe begin by assuming only that the binary valued process Xt is stationary.\nWe have then the following simple result:\nLemma 1: Let Xt be a binary valued, stationary random process and let\np and R(\u00b7) denote its mean and covariance function, respectively.\nThen,\n(l) P1,o(p,r) = (1 - p) 1 - R(O)\n\n.\n\n{\n\nR(r)}\n\n(1)\n\n(ii) pP1,o(p,r) = (1 - P)Po,l(p,r).\n\n(2)\n\nProof: Part (i) is a consequence of the definition of R(\u00b7). That is,\nR(r) = E(XtXt+T) - p2\n= P(Xt = 1,xt+T = 1) - p2,\n\nwhere\np = E(xt) = P(Xt = 1).\n\nPart (ii) follows from the two identities:\np = pP1,1(p,r) + (1 - p)Po,dp,r)\n\nand\n1 = P1,dp,r) + P1,o(p,r).\n\nA consequence of this result is that uncorrelatedness and independence\nare equivalent:\nCorollary 1: For the process in lemma 1, Xt,Xt+T are independent if and\nonly if R(r) = o.\n\nNote that the dependence of R (.) on p has been suppressed for convenIence.\n3. 1 Modeling an individual trunk\n\nA particularly simple way to model a trunk is as the server in a single\nserver loss* system with a Poisson arrival process and an exponential\nservice time distribution. This model is commonly denoted by\nM/M/1-10ss. 6 Let x t denote the state of the server:\n* In a loss system, customers who are blocked depart without waiting.\n924\n\nTHE BELL SYSTEM TECHNICAL JOURNAL, JULY-AUGUST 1977\n\n_ {I\nXt 0\n\nif server is busy at epoch t\nif server is idle at epoch t\n\nand R{o) the covariance function of Xt. It is easily shown 7 that for the\nM/M/1-10ss system,\nR{r) = R{O) exp \\-(A + ~hj,\n\nwhere Aand ~ are the mean arrival and service rates, respectively. Thus,\nP1,o(p,r) may be written as:\nP1,o{p,r) = (I - p) {I - exp (1-~:) },\n\n(3)\n\nwhere the trunk occupancy p is equal to A/{A + ~). Throughout this paper\nwe will be concerned with r = 100 or 200 seconds and a nominal holding\ntime 1/~ in the vicinity of 3 minutes. The mean holding time of a killer\ntrunk 1/~* will always be expressed as l/r~ with r typically in the range\n5 to 15. Thus, if we denote ~r by S, we may write the transition probability P\\xt+r = O/Xt = 1j for a trunk with mean occupancy pas\nP1,o(p,r) = (1 - p) [ 1- exp\n\nC-~SJ\n\nl\n\n(4)\n\nwhere r = 1 corresponds to a normal trunk. (Since P1,o = 1 - p implies\nthat XnX2n\u00b0 \u00b0 \u00b0 are independent, we will assume independence for r\nsufficiently large in subsequent sections.)\nFigure 2 is a plot of P1,o vs p corresponding to S = 10/9 (200-second\nsampling and a 3-minute mean holding time) for several values of r. P1,o\nis essentially equal to 1 - p for r ~ 5. Figure 3 is a similar plot of P1,o vs\np corresponding to 100-second sampling and a 3-minute mean holding\ntime (8 = 5/9)~ In this figure P1,o is essentially equal to 1 - p for r ~\n\n7.5.\nBefore putting too much emphasis on the transition probabilities in\nFigs. 2 and 3, it is prudent to consider the effect of factoring more realistic\nassumptions into the single server loss model. Thus, while the Poisson\narrival process assumption is probably a reasonable assumption for a\ntrunk in a 5XB trunk group (random selection of idle servers), it poorly\nmodels the overflow nature of the traffic offered to trunks in a 1XB/XBT\ntrunk group. t In the latter case, it is more appropriate to model the input\nstream to a trunk as a peaked process. 6 Figure 4 is a plot of P1,o vs p\nparameterized by the peakedness (z) of the input stream. This figure\nis based on an expression for P1,o derived for a GI/M/1-10ss modelt with\nt The trunk-selection procedure for lXB and XBT trunk groups is essentially a twosided ordered hunt. 2\nt GI/M/l-loss denotes a single server loss system with a renewal process input stream\n(GO and an exponential (M) service time distribution.\n\nTRUNK-DETECTION ALGORITHMS\n\n925\n\n1.0~---------------------,\n\nGI/M/l - LOSS MODEL\n\n- - KILLER TRUNKS (r = 5)\n\nfl- 1 = 180 SECONDS\n\nZ = 1,2,5\n\nT= 200 SECONDS\n\n0.8\n\nZ= PEAKEDNESS\n\n0.6\na\nc...\n\n0.4\n./\n\nNORMAL TRUNKS~~-/\n\n0.2\n\nOL-_ _\n\no\n\n~\n\n___\n\n20\n\n~\n\n___\n\n40\n\n~\n\n___\n\n60\n\n~\n\n___\n\n80\n\n~\n\n100\n\nMEAN TRUNK OCCUPANCY IN PERCENT\n\nFig. 4- I -- 0 transition probability for the GI/M/I-loss model with a switched Poisson\narrival process-~OO-second sampling option.\n\na switched Poisson input stream (commonly used to model overflow\ntraffic).8 Appendix A contains several details on the model and derivation. It is clear that the effect of peaked traffic on the transition probability is very small (z = 1 corresponds to a Poisson stream).\nRecent data 9 indicates that the service time distribution of a normal\ntrunk has a coefficient of variation significantly greater than 1 (the exponential case). Thus, in Appendix A we derive the covariance function\nof the server process Xt for an M/G/I-Ioss! model with a mixed exponential\ntype of service distribution. Figure 5 is a plot of P1,o vs p parameterized\nby the coefficient of variation of the mixed exponential service distribution. We see that increasing the coefficient of variation has a noticeable\neffect on the transition probabilities, but the effect is to increase the\ndiscrimination between the normal and killer-trunk transition probabilities.\nThus, it would appear that the transition probabilities based on the\nM/M/l-Ioss model are reasonably robust to perturbations in the trunk\nmodel. In addition, one suspects that using these transition probabilities\nin a detection scheme, which exploits the basic differences between killer\nand normal trunk transitions, might lead to a conservative design.\nt M/G/I-loss denotes a single server loss system with a Poisson (M) input stream and\na general (G) service time distribution.\n\nTRUNK-DETECTION ALGORITHMS\n\n927\n\n1.0.r---------------------,\nM/G/l - LOSS MODEL\n\nfL -1 = 180 SECONDS\n\n7KILLER TRUNKS\n(r = 10)\n\nT = 200 SECONDS\n\nc = COEFFICIENT OF\nVARIATION\n\n0.8\n\n0.6\n\n0.4\n\n0.2\n\nO~\n\n___\n\no\n\n~\n\n___\n\n~\n\n___\n\n40\n\n20\n\n~\n\n___\n\n~\n\n80\n\n60\n\n___\n\n~\n\n100\n\nMEAN TRUNK OCCUPANCY IN PERCENT\n\nFig. 5- 1-- 0 transition probability for the M/G/1-lossmodel with a mixed exponential\nservice time distribution-200-second sampling option.\n\n3.2 Testing statistical hypotheses-a basic idea\n\nSuppose a trunk has constant mean occupancy p (EXt = p) and we\nobserve it for h seconds during which n switch counts and t 10 1 - 0 state\ntransitions accumulate. We may write\n\u00b7m\n\nn =\n\n:L Xhr\n\nk=l\n\nand\nm\n\nt10 =\n\n:L [Xkr - X(k-l)r]-,\nk=2\n\nwhere\nm = ~ and z- = {O\nT\n1 z T j , decide that the trunk is a killer, otherwise decide that\nthe trunk is normal. [tlO is not directly available (see Section 2.1), but\nit may be estimated by t/2.]\nIf the trunk occupancy were known and fixed, this scheme would appear to be very reasonable. The analogy to the usual scheme suggested\nfor deciding between a fair and a biased coin is clear: no is the number\nof (hopefully) independent experiments (analogous to the number of\ncoin tosses), with each experiment having just two possible outcomes:\nthe scan which follows the switch count is either 0 or 1. Thus, each switch\ncount is associated with a 1-- 0 state transition (\"heads\") or a 1--1 state\ntransition (\"tails\").\nFrom the point of view of statistical hypothesis testing, we are thinking\nof two underlying states:\n\nNull hypothesis H o: P 1,0(p) = P trunk normal\nAlternate hypothesis HI: P 1,0(p) = p* trunk killer\nThus, our intuition suggests that a threshold test of the type sketched\nabove is natural for distinguishing between H and HI. We will see\n(Section 4.1) that a (nonoptimal) test of this form arises naturally from\npursuing the coin tossing analogy further.\n\n\u00b0\n\n3.3 Problem formulation-sharpening the focus\n\nTo simplify matters, assume to begin with that\n(i) The nominal mean holding time 1/J.L is known.\n(ii) The trunk occupancy P is known and constant.\n(iii) The switch-count and transition data accumulations n(m) and\nt(m) are continuously available (scan by scan).\n\nWith these assumptions, it is an easy matter to conceptually describe\nTRUNK-DETECTION ALGORITHMS\n\n929\n\nthe \"optimum\" scheme for deciding between the two simple hypotheses,\n\nH 0: Trunk normal (mean holding time 1iJ.t)\nHI: Trunk killer (mean holding time l/rJ.!),\n\nwith it understood that \"trunk\" refers to one of the specific models described in Section 3.1 (for concreteness assume the M/M/1-loss\nmodel).\nLet Xm = (Xl,' ',x m ) be the sequence of trunk states up to and including the mth scan, and let the available data be (as before)\nm\n\nm\n\ni=1\n\ni=2\n\nn(m) = LXi, t(m) = L IXi - xi-II\u00b7\n\nLet\nPim(n,t) = P(n(m) = n,t(m) = t/Hd i = Oar 1\n\nand let\nfm(n,t) = Plm(n,t).\nPOm(n,t)\n\nThe joint probability distributions P im (n,t), i = 0,1, are well defined\nfor any specific trunk model, but they may be nontrivial to derive. f m (. ,.)\nviewed as a function of the vector random variable [n(m),t(m)] is referred to as the likelihood ratio statistic and plays a central role in the\ntheory of statistical hypothesis testing. More specifically, the optimum\ntest (in a variety of senses) for deciding between two simple hypotheses\ninvolves suitably comparing f m to a threshold (or thresholds) in order\nto make a decision.\nWe briefly review two optimum tests, the Neyman-Pearson (fixed\nsample) test lO and Wald's sequential probability ratio test (SPRT), using\nnotation appropriate to our (discrete) problem.\n3.3. 1 The Neyman-Pearson test\n\nSuppose a and {3 denote the type 1 and 2 errors* of the test,\nChoose HI if f m ~ T\nChoose Ho if fm < T,\nand suppose a' and {3' denote the type 1 and 2 errors of any other test\n(requiring m samples) for deciding between Ho and HI. Neyman and\n* The type 1 and 2 errors, (\\' and {3, are often referred to as the probability of false alarm\nand the probability of miss, respectively ((\\' = probability of choosing HI given H is the\ntrue state, (3 = probability of choosing H 0, given HI is the true state.)\n\n\u00b0\n\n930\n\nTHE BELL SYSTEM TECHNICAL JOURNAL, JULY-AUGUST 1977\n\nPearson's classical result is: if a' ~ a, then {3' ~ {3. Thus, of all tests requiring m samples and having a false-alarm probability not exceeding\na, the likelihood ratio test achieves the minimum probability of miss\n(maximum probability of detection). Since a = P( f m > T /H 0), choosing.\na sample size m and threshold T to achieve a ~ ao requires knowledge\nof the (conditional) distribution of f m' Similarly, having chosen m and\nT, calculating (3 = P(f m < T/H 1 ) requires the distribution of fm (conditioned on HI). Note also that with such a fixed sample test, we decide\nin advance to accumulate exactly m samples before making a decision.\nIn many contexts, data accumulates sequentially in time, and rigidly\nrequiring m samples-independent of the particular realization that is\nunfolding-is not an optimal strategy.\n3.3.2 Wald's sequential probability ratio test\n\nUsing Wald's SPRT,10,11 we continue to update fk' k = 1,2,\u00b7\u00b7\u00b7 and\ndefer a decision as long as fkdT o,T1). We make a decision the first time\nfk falls outside the interval (T o,T1 ). Thus,\nif To < fk < T1\n\nk = 1,2,\u00b7\u00b7\u00b7,m-1\n\nand fm ft (To,T1 ),\nthen choose HI if f m ~ T 1\nand choose H o if fm ~ To.\nClearly the stopping time m of the SPRT is a random variable, and the\nmean of m (given either hypothesis) is a measure of the time it takes to\nreach a decision. (Under a wide variety of circumstances, the SPRT terminates with probability 1.) Let Edm) (i = 0 or 1) denote the mean\nstopping time, given that hypothesis i is in effect. Given a SPRT with type\n1 and 2 errors a and (3, and with mean stopping times Eo(m) and E 1(m),\nconsider any other test (sequential or not) with type 1 and 2 errors a'\nand (3', and with mean stopping times E~(m) and E~(m). The SPRT has\nthe following optimal character10\nif a' ~ a and {3' ~ (3,\nthen E~(m) ~ Eo(m) and E~(m) ~ E1(m).\nThus a SPRT is superior to a fixed sample test, if both tests have the same\ntype 1 and 2 errors, in the sense that on the average it reaches a decision\nmore quickly (under either hypotheses).\nIn sharp distinction to the fixed sample test, the thresholds To and\nT 1 required to approximately achieve specified type 1 and 2 errors are\ntrivially determined.!l On the other hand, even determining the mean\nand variance of the stopping time is often a difficult chore.\nTRUNK-DETECTION ALGORITHMS\n\n931\n\nIn Section 4.2, we explicitly calculate the SPRT* for the simple hypothesis testing problem described at the beginning of this section.\nBefore looking at this optimum test, however, we describe an ad hoc\nalgorithm which is very robust and consequently attractive from a\npractical point of view.\nIV. INDIVIDUAL TRUNK ALGORITHMS\n\nA basic underlying assumption in this section is that the normal mean\nholding time of a trunk is known. Thus, if the algorithms in this section\nare designed relative to a normal mean holding time of 3 minutes, they\nwill not discriminate between normal trunks having a mean holding time\nin the vicinity of 40 seconds,t and an actual killer trunk with the same\nmean holding time-both of these trunks will be detected as killer\ntrunks.\nThe rationale for studying this type of detection problem is two-fold:\nfrom the practical point of view the simplicity of implementation and\ngeneral applicabilityt of these algorithms is attractive, and EADAS/ICUR\ncan flag trunk groups which should not be studied by the killer trunkdetection algorithms (thus preventing false alarms on normal shortholding-time trunks). From the theoretical point of view, it was natural\nto consider this problem before factoring group information into the\npicture.\nAnother modeling assumption used in this section (as well as in subsequent ones) is that the arrival process is stationary within data accumulation intervals, but the mean arrival rate may change arbitrarily from\none accumulation period to another. Since we use equilibrium analysis\n(e.g., in calculating PI,o) we assume, in effect, that equilibrium is achieved\ninstantaneously.\n4. 1 An ad hoc algorithm\n\nThe essential idea of the test suggested in Section 3.2, is to decide on\nthe state of a trunk by comparing the number of 1 -- 0 state transitions\n(t1O) to some threshold Tr, conditional on having accumulated a fixed\nnumber of switch -counts. We heuristically* proceed to derive such a test,\nusing a standard likelihood ratio formulation, and explicitly take into\naccount the time-variability of traffic.\nLet Xm = (xv\u00b7 \u00b7,x m ) correspond to the (unobservable) binary se* Based on the M/M/l-Ioss model for a trunk.\nt Trunks in special-purpose trunk groups (credit checking, weather, etc.) will typically\n\nhave mean holding times in the vicinity of 40 seconds.\nt The individual trunk algorithms can be used to test any trunk-regardless of the type\nof switching machine the trunk is associated with.\n* The distributional assumptions made in this section are intuitively motivated, but\ncannot be rigorously justified. We examine these assumptions carefully in Section 4.3.\n\n932\n\nTHE BELL SYSTEM TECHNICAL JOURNAL, JULY-AUGUST 1977\n\nquence of trunk states during an accumulation period in which m scans\noccur. Let t lO (m) and n(m) be the number of 1- 0 state transitions and\nswitch counts associated with X m . Denote the conditional probability\nP(tlO(m) = tln(m) = n)\n\nfor a normal and killer trunk by P(tln) and P*(tln), respectively. These\nconditional distributions depend, of course, on the trunk's occupancy\nand on the particular trunk model we have in mind. [p* (tin) also depends on the killer parameter r.] However, for the purposes of the heuristic development of this section, we do not precisely define which trunk\nmodel we have in mind.\nSince each switch count is associated with either a 1 - 0 or a 1 - 1\nstate transition with probabilities PI,o and PI,1 = 1 - PI,o, respectively\nfor a normal trunk, and since we expect successive transition events on\na trunk to be essentially independent, * it seems reasonable to assume\nthat P[tlO(m) = tln(m) = n] for a normal trunk is binomially distributed\nwith parameters nand PI,o. This same argument applies to a killer trunk.\nDenote the binomial distribution with parameters nand p by b (k ;n,p)\nk = 0\" . ',n, where\nb(k;n,p) = (~) pk(l - p)n-k.\n\nThus, we may think of a trunk with occupancy p during an accumulation\nperiod as having a conditional distribution\nP[tlO(m) = tln(m) = n] = b[t;n,PI,o(p,r)],\n\n(6)\n\nwith r = 1 and r = ro corresponding to the normal and killer states of the\ntrunk. (Recall that PI,o(p,r) is essentially independent of r for r ~ ro with\nro = 7.5 and 5.0 for 100- and 200-second sampling, respectively.) With\nthese assumptions, we may think of testing the two simple hypotheses:\nHo: P(tln) = b(t;n,PI,o)\n\nPI,o = P I ,o(p,l)\n\nHI: P(tln) = b(t;n,P~,o)\n\nP~,o = PI,o(p,ro).\n\nIf the 1 - 0 transition and switch -count accumulations for two successive\n\nand contiguous accumulation periods are (tl,nl) and (t2,n2) respectively,\nwe assume that\nP(tI,t2I n l,n2) = P(tr!n l)P(t2In 2)'\n\nThe idea here is that the only dependence between the two successive\n* The idea is that if significant correlation extends only one or two scans back, then\nsuccessive transition events (events \"triggered\" by switch counts) should be essentially\nindependent.\nTRUNK-DETECTION ALGORITHMS\n\n933\n\nbit streams x~ = (Xl, \u2022 \u00b7,x m ) and x~ = (Xm+l,\u00b7 \u00b7,X2m) is essentially due\nto the dependence between Xm and Xm+l.\nThus, if we denote the transition and switch-court accumulations for\nthe ith accumulation period (in which mi scans occur) by [tlO(mJ,n(mi)]\nduring which the trunk has occupancy Pi, we have\nP[tlO(ml) = tv\u00b7 \u00b7,tlO(mk) = tk \\n(ml) = nv\u00b7 \u00b7,n(mk) = niJ\nk\n\n=\n\nrr b[ti;ni,PI,O(Pi,r)],\n\n(7)\n\ni=l\n\nwhere Pi i = 1,.\u00b7 \u00b7,k are the occupancies for the k accumulation periods.\nIf tk = (tv\u00b7 \u00b7,tk) and nk = (nl, . \u00b7,nk) consider the likelihood ratio:\nn(\n\n\u00a3\n\n~\n\n/\n\nnk\n\n) _ rrk b[ti;ni,PI,O(Pi,rO)]\n.\ni= I b [ti;ni,P1,O(Pi, 1)]\n\n(8)\n\nDenote the log likelihood ratio t log f(tk/ nk) by i(tk/ nk) and note\nthat\n\nwhere\n\n\"'( ./ .) - 1 b[ti;ni,P1,O(Pi,rO)]\nog [\n].\n\nf tc nc -\n\nb ti ;ni,P1,O(Pi, 1)\n\nThe expression i(tJni) can be written as\ni(tJnd = a(Pi)ti - a(pdni\n\nwith\na ()\nP = 1og\n\n1 - PI o(p,l)\n\n,\n1 - PI,o(p,ro)\n\n(9a)\n\nand\na(p)=a(p)+log\n\nPIO(p,ro)\n, (\n).\nPI,o p,l\n\n(9b)\n\nThus, we have\n(9c)\nUnfortunately, the occupancy in the ith accumulation period (Pi) is\nunknown and hence equation (9c) cannot be used as a test statistic. One\nobvious \"fix\" is to estimate Pi by Pi = nJmi, where ni and mi are the\nt I > Tiff g(e) > g(T) if g is monotone increasing, so the tests! > T and g(f) > g(T)are\nequivalent.\n\n934\n\nTHE BELL SYSTEM TECHNICAL JOURNAL, JULY -AUGUST 1977\n\nswitch count and the number of scans, respectively, during the ith accumulation period. In stationary traffic, the estimate\n\nPi = .Li nj / .Li mj\n)=1\n\n)=1\n\nwould be used [a-{pd == I/Vl a-{pd if mj = m for allj].\nCorresponding to the sequence of accumulations, {t1,ni,mJ i = 1,2,.\nwe define ri and Ri, i = 1,2,. by\n0\n\n0\n\n0\n\n0\n\n(lOa)\n\nand\n\nRi = R i- 1 + ri with Ro = o.\n\n(lOb)\n\nThus, we arrive at the sequential test:\n(i)\n\nCompute R i , i = 1,2,.\n\n0\n\n0\n\nand defer making a decision as long as To\n\n< Ri < T 1.\n\n(ii) If i = k corresponds to the first accumulation period for which\nRi ft (T o,T 1), then\nRk ~ To ==> Trunk normal\nRk ~ T 1 ==> Trunk killer.\nIf we ignore the fact that we are estimating Pi by Pi, and by assuming that\nthe various assumptions made are valid (see Section 4.3), we identify the\nabove test as Wald's SPRT and as such To and T1 can be calculated as\nrefollows:l1 to approximately achieve type 1 and 2 errors, a and\nspectively, a + < 1, choose\n\n/3,\n\n/3\n\nTo = log\n\n(_/3_)\nI-a\n\n(10c)\n\nT1 = log\n\n(1 : /3).\n\n(10d)\n\nand\n\nThroughout this section, we have assumed that the 1 ~ 0 transitions\n(t 10) are available when, in fact, only the total transitions (t) are available.\nIt should be clear that tlO can differ from t/2 by at most \u00b1%. To be precise, let tlO{m), tOl (m) be the number of 1 ~ 0 and 0 ~ 1 state transitions\ncorresponding to a bit stream Xm = (Xl,\nxm). If n{m) is the switch\n0\n\n0\n\n0,\n\ncount corresponding to X m , then we have\n\n= tlO{m) + tl1{m) + Xm\n\n(lla)\n\nn{m) = tor(m) + tl1{m) + XI,\n\n(lIb)\n\nn{m)\n\nand\n\nTRUNK-DETECTION ALGORITHMS\n\n935\n\nwhere t 11 (m) is the number of 1 -- 1 state transitions. Therefore\ntlO(m} + Xm = tOI(m} + Xl,\n\nwhich together with t(m} = t01(m} + tlO(m} yields\ntlO(m} = ~ t(m} + (Xl ~ Xm)\n\n(I2a)\n\ntOI(m} = ~ t(m} _ (Xl ~ Xm).\n\n(12b)\n\nand\n\nThus, we can write the statistic update (eq. lOa) as\na\n\ni-an +\n\n(X I ~ Xm) a.\n\n[It is easy to show that E[(XI - xm}a(p)] = 0.]\nWe conclude this section with an interpretation of the statistic update.\nRewriting the statistic update as\nr = (a - a)tlO - a(n - tlO)\n\nand using eq. (I1a), we obtain\nr = (a - a}tlO - at11 - ax m.\n\n(13)\n\nNow, from eqs. (9a) and (9b), it is clear that a > a > o. Thus, each 1 --\n\notransition is weighted positively (evidence of a killer) while each 1-1 transition is weighted negatively (evidence of a normal trunk). This\n\nis an intuitive explanation of the fact that the random walk (eq.\n(lOb\u00bb\nRk = Rk-l\n\n+ rk\n\nhas a positive drift if the trunk is a killer and a negative drift if the trunk\nis normal.\nThe fact that the update assigns a negative weight (-a) whenever the\nlast bit (xm) is 1 uncovers a modeling deficiency. Recall that in eq. (6)\nwe assumed\nP(tlO(m} = t/n(m) = n} = b(t;n,P lO },\n\neven though Xm = 1 can not contribute to an observable 1 -- 0 transition.\nIn this way we effectively modeled in a bias towards making \"trunk\nnormal\" decisions. We can easily correct eq. (6) by conditioning on\nwhether Xm = 0 or 1, obtaining:\nP(tlO(m) = t/n(m) = n) = (1 - p)b(t;n,PlO) + pb(t;n - I,P IO }.\n\nNow, proceeding as before in formulating the log likelihood ratio yields\n936\n\nTHE BELL SYSTEM TECHNICAL JOURNAL, JULY-AUGUST 1977\n\na statistic Rk , where\n\nand\n\nwhere rk is defined by eq. (lOa),\n\nqk = 1og\n\n1+ (~)(1-~)(\n1 )\n1 - Pk\nnk\n1 - P ,O(Pk,rO)\n1\n\n(14)\n\nC~kpJ (1 - ~:) C_ 0(Pk,l))\n1\n\n1+\n\nPl\n\n\u00b0\n\nand Pk, tk, and nk are the trunks occupancy estimate, 1 -- state transitions, and switch count, respectively, during the kth accumulation\nperiod.\nThus, we obtain our original test statistic with the correction term qk\nadded on. Note that qk ~ 0, qk -- as Pk -- 0, and qk -- a as Pk -- 1,\nwhich is just the type of behavior expected, to offset the bias term in\n\n\u00b0\n\nrk\u00b7\n\nHaving heuristically developed an ad hoc sequential algorithm that\nis intuitively appealing and easily implementable, it is natural to ask:\nhow does it compare to the optimum sequential algorithm? In the following section, we rigorously develop an optimum sequential test.\n4.2 An optimal algorithm\n\nConsider the two simple hypotheses:\nHo: Trunk normal (mean occupancy p, mean holding time I/Jl)\nHI: Trunk killer (mean occupancy p, mean holding time l/roJl).\nThe optimum test for deciding between the two hypotheses-in the sense\nof minimizing the mean decision time-for given type 1 and 2 errors, is\nWald's SPRT (see Section 3.3), and it is based on the likelihood ratio\nstatistic fm(t,n) given by\n/J\n{,m\n\n(\n\nt,n\n\n)\n\n= P*(t(m) = t,n(m) = n) .\nP(t(m) = t,n(m) = n)\n\n(15)\n\nThus, it is clear that the ad hoc test described in Section 4.1 is not optimal, based as it is on an assumed conditional distribution,\nP(tlO(m) = t/n(m) = n).\n\nBefore proceeding to study eq. (15), we must define the trunk model\nprecisely. In the developments that follow, we model a trunk as the server\nin an M/M/1-loss system (see Section 3.1). The model implies that the\nsequence of trunk states Xt, t = k T, k = 1,2,\u00b7 .. is Markovian. Note that\nTRUNK-DETECTION ALGORITHMS\n\n937\n\nalthough this appears to be a reasonable model for a normal trunk with\n200-second sampling, it ignores the conditional dependence \"2 samples\nback,\" which is more important for 100-second sampling-e.g., Xt given\nXt-r is independent of Xt-2r for the M/M/1-loss model. Taking this dependence into account in a trunk model would not be useful however,\nsince the data needed to implement dependence \"two scans back,\" is not\navailable.\nSince we are modeling the sequence of trunk states as a binary valued\nMarkov process Xkn k = 1,2,.\u00b7 \u00b7,in equilibrium,iit is clear that this process\nis characterized by 8 = (PI,O,PO,I), where PI,o and PO,1 are the transition\npro babilities\nP(Xt+r = O/Xt = 1) and P(xt+r = l/xt = 0),\n\nrespectively. (In general, a binary valued Markov process Xkn k = 1,2,.\u00b7\u00b7\nin equilibrium, can be characterized by any two of the three quantities\np, PI,O,PO,I. For our special Markov process (based on the M/M/1-loss\nmodel), both PI,o and PO,1 and hence the process itself is determined by\np alone.) Now having observed any m-tuple of the samples, which we\ndenote by Xm = (XI,\"\u00b7 \u00b7,x m), it is trivial to show that the statistic\n\nis a sufficient statistic for O. Thus, except for the initial and terminal\nstates (Xl and x m ), the transition and switch-count accumulations\nsummarize all the \"relevant information\" in X m .\nOur hypothesis-testing problem can now be formulated as follows:\nXt,X2,\u00b7\u00b7 is a binary-valued Markov chain in equilibrium with parameter\no= (PO,I,PI,O) or 0* = (P~,I'P~,O). That is, our two states are\nH o: Ixil Markovian, characterized by 0 = (PO,I,PI,O)\nHI: Ixi! Markovian, characterized by 0* = (P~,bP~,O).\n\nNow, because (t(m),n(m),xI,x m) is a sufficient statistic for 0, we know\nthat the likelihood-test statistic based on the raw (unobservable) data\nXm = (XI,\"\u00b7 \u00b7,x m) will be expressible in terms of t(m), n(m), Xl and Xm\nonly. Thus, instead of studying eq. (15), we proceed (for simplicity) to\nstudy the likelihood-ratio statistic:\nP*(Xm )\nf(x m) = log P(Xm) .\nA\n\n(16)\n\nIn Appendix B we study i m(t,n) and find that it differs from 1(xm) only\nin an end-effect term . .In l(xm ) this term depends on Xl and X m , whereas\nin 1m (t,n) the corresponding term is a function of t and n.\nSince\n938\n\nTHE BELL SYSTEM TECHNICAL JOURNAL, JULY-AUGUST 1977\n\nm\n\nP(Xm ) = P(Xl) II P(XdXi-l),\ni=2\n\nwe may write\nSO\n\n(1 -\n\nP*(Xl)\nP~o\nP~O)\nf(xm) = log-(-) + tlolo g -p + tulog\nP\nP Xl\n10\n1 - 10\nA\n\n+ tOl log -P~1 + too log\nPOI\n\n(1 - P~1) . (17)\n1 - POI\n\nNote that a trunk with mean occupancy p is busy and idle with probability p and 1 - p respectively, independently of the state it is in (normal\nor killer). Thus,\n\nP*(Xl)\n.\nlog - - - = 0 and eq. (17) can be WrItten\nP(Xl)\ni(x m ) = [(a - a)tlO - atul + [(iJ - b)tOl - btoo],\n\n(18)\n\nwhere the parameters band iJ are defined by\n\nI (11 -- POI)\np*\n\n(19a)\n\niJ = b + log -P~1) ,\n\n(19b)\n\nb = og\n\n01\n\n(POI\n\nand the parameters a and a are defined as in Section 4.1 (eqs. (9a) and\n(9b)). P~,1 and P~,o correspond to PO,l(p,r) and Pl,o(p,r) with r = roo\nBefore discussing the symmetric structure of the optimum statistic\n[eq. (18)], we examine the PO,l characteristics for the M/M/1-loss model.\nUsing eqs. (2) and (3), we can obtain Po'! vs mean-trunk occupancy p for\na normal (r = 1) and killer (r = ro) trunk. Figures 6 and 7 are plots for\nthe 200- and 100-second sampling option, respectively, with a mean\nholding time of 180 seconds. It is clear from Fig. 6 that a 0 -- 1 transition\nis just marginally more likely to occur on a killer trunk than on a normal\ntrunk with a 200-second sampling rate. Although, the difference in the\no -- 1 transition probabilities between a normal and killer trunk increases substantially with the 100-second sampling rate, it is clear that\nthese differences are still quite small-compared to the spread between\nthe PI,o and P~,o plots (see Figs. 2 and 3). Note that eqs. (2) and (4) show\nthat\n-ros\n1- exp-P~,1 __\n1- P\n(19c)\n- - - - - > 1 for ro > 1\nPO,I\n-s\n1- exp--\n\n1-p\n\nTRUNK-DETECTION ALGORITHMS\n\n939\n\nand, hence, we have {3 > b > O. Using eqs. (4) and (19c), we see that\nP~,dPO,1 = P~,O/PI,O and, therefore,\n(19d)\n\n{3-b=o:-a\n\nEquation (18) shows that the optimum statistic is the sum of two\nsymmetric statistics:\n(i) The statistic [(0: - a)tlO - atllL which is essentially the ad hoc\nstatistic (see eq. (13) and related discussion).\n(ii) An additional statistic [({3 - b)tOl - btoo], which weights 0 ~ 1\ntransitions positively (evidence of a killer) and 0 ~ 0 transitions negatively (evidence of a normal trunk).\n\nNote that by interchanging the role of 0 and 1 in either of these two\nstatistics, we obtain the other-b is obtained from a and (3 is obtained\nfrom by replacing PI,o with PO,I.\nBy using eq. (1Ia) and the analogous equation\n\n0:\n\nm - n(m)\n\n= too(m) + tOI(m) + x~, (x~ = 1 - xm)\n\n(20)\n\nin eq. (18), the optimum statistic can be written\nl(xm ) = [o:tlO(m) - an(m)] + [(3tOl(m) - b(m - n)] + el(x m ),\n\n(21)\n\nwhere the end-effect term edxm) is given by\nel(x m ) = aXm + bx~.\n\nTo implement l(xm ) with only t(m) and n(m) available, necessitates\nestimating both tlO(m) and tOl(m) by t(m)/2. That is, using eqs. (12a)\nand (12b) in eq. (21) yields.\ni(xm ) = [ IX t(;) - an(m)] +\n\nIp t(;) - b[m - n(m)]) + e(x\"xm),\n(22a)\n\nwhere\n\nb) (Xl + xm) + b\n\na = ( -2-\n\nt\n\n(22b)\n\nor\n\n(0: (3)\n\n+ - t(m) - (a - b)n(m) - bm + e(xl,x m ).\nf(x m ) = - 2\nA\n\nt Recall that a -\n\n(23)\n\n{3 = a - b [eq. (I9d)].\n\nTRUNK-DETECTION ALGORITHMS\n\n941\n\nIn the development of the ad hoc algorithm, we assumed that the\nstatistics corresponding to successive accumulation periods are independent. We conclude this section by examining the independence assumption and with some remarks on implementation.\nThus, turning to multiple accumulation periods, suppose x~, i =\n1,2,. . \u00b7,k are the (unobservable) bit streams for k successive (and contiguous) accumulation periods, where x~ = (X(i-l)m+l,\"\u00b7 \u00b7,Xim). Assuming stationary traffic, and noting that Ixd?:I is Markovian, we can\nwrite\n\nand, therefore,\n\ni(x~,\" . .,x~) =\n\nt i(x~) + kf.1log {P*(Xim+l/Xim)/P*(Xim+l)}, (25)\n\ni=l\n\ni=l\n\nP(xim+dxim)/P(Xim+l)\n\nwhere P(.) and P* (.) denote the distribution under H 0 (trunk normal)\nand HI (trunk killer), respectively. But, as we have seen,\n\n-roS}\n\nP*(xim+dxim) = 1 - exp {- P*(Xim+l)\n1-p\n\n--~----'----....:..;..;.'--\n\n(26)\n\nand hence Xim+ 1 and Xim are essentially independent for ro sufficiently\nlarge. Therefore,\nP*(Xim+l/Xim) = P*(Xim+l)\n\nand, hence, eq. (25) may be written as\n....\n\nk\n\nk-l\n\nk.....\n\nf(x m,\" \u2022\u2022, x m ) = L f(x~) - L I(Xim;Xim+l),\ni=l\ni=l\n\nwhere\n(27)\n\nis recognized as the mutual information random variable, which plays\na central role in information theory.1 2 -1t is well known 12 that (under Ho)\nEII(xim;xim+l)1 is non-negative, and hence to ignore the end-effect\nterm\nk-l\n\nL I(Xim;Xim+l)\n\ni=l\n\nby implementing the statistic\nk\n\n.\n\nL i(x~)\n\ni=l\n942\n\nTHE BELL SYSTEM TECHNICAL JOURNAL, JULY-AUGUST 1977\n\nwould tend to make a normal trunk look more like a killer trunk on the\naverage. In Appendix C, however, we show that the mean end effect\nEII(xim;xim+l)} is negligibfe compared to the mean statistic update\nEll(x~}.\nThe \"optimal\" sequential algorithm is implemented in the same\nmanner as the ad hoc algorithm (see eqs. (lOa) and (lOb)) except that\nnow, corresponding to the sequence of accumulations (ti,ni,mdi =\n1,2,\u00b7 .. , we define ri by\nri =\n\n(ex ; (3) ti - (a - b )ni - bmi.\n\nThe term ti denotes the total number of transitions in the ith accumulation interval. As is the case for the ad hoc algorithm (which corresponds\nto b = f3 = 0), the weights are functions of the trunk occupancy estimate\nPi = nJmi. In a practical nonstationary environment, no claims of optimality are made or implied. The term \"optimal\" is applicable only in\nthe context of the equilibrium (e.g., stationary) model with known trunk\noccupancy.\n4.3 The ad hoc algorithm reviewed\n\nThe assumption that tlO(m) conditioned on the switch count n(m)\nis binomially distributed, is the basic assumption in the development\nof the ad hoc statistic. Although this assumption is incorrect (as we will\nsoon see), the ad hoc statistic is essentially (except for an end-effect term)\none of two symmetric statistics whose sum is the optimum statistic. Our\npurpose in this section is to examine the binomial assumption and to\nexplain the relationship found between the ad hoc and optimal statistics.\nSince the optimal statistic was developed for a trunk modeled as a\nserver in an M/M/1-loss system, it is natural to examine the binomial\nassumption (eq. (6)):\nP[tlO(m) = t/n(m) = n] = b[t;n,P1,o(p,r)],\n\n(28)\n\nwhere P1,o(p,r) is given by eq. (4) in this context. Consider a killer trunk\nwith r sufficiently large and suppose Xm = (XI,\" \u2022 \u2022,x m ) is the bit stream\nfor a killer trunk during some accumulation period. Then, for all practical\npurposes [see eq. (26)], the trunk states Xi i = 1,2,\u00b7\u00b7 \u00b7,m are independent\nand identically distributed Bernoulli random variables:\nP(Xi = x)\n\n= {P\n\n1- p\n\n~f x = 1\n\nlfx = O.\n\nThus, it is clear that the switch-count distribution on a killer trunk is\nthe binomial:\nTRUNK-DETECTION ALGORITHMS\n\n943\n\nP(n(m) = n) = b(n;m,p).\n\n(29)\n\nNow suppose Am{t,n) denotes the number of binary m-tuples having\n1 -- 0 transitions and n ones. If Xm = (Xl,\u00b7 \u00b7,x m ) is a seexactly t\nquence of trunk states for a killer trunk with n(m) = n, it is clear that\neach such sequence has probability\nP(xm ) = pn(l - p)m-n\n\nand therefore\nP(tlO(m) = t,n(m) = n) = Am (t,n)pn(1 - p)m-n\n\n(30)\n\nfor a killer trunk (with r sufficiently large). Equations (29) and (30) show\nthat for a killer trunk,\n\n(31)\n\nwhere we have used the fact that\n(32)\n\nIt is interesting to note that while our assumed distribution for a killer\ntrunk (28) differs from the correct distribution (31)-note that (31) is\nindependent of p-there are some interesting similarities. For example,\nthe assumed distribution peaks in the vicinity of (n + 1)(1 - p) and has\nmean equal to n(l - p)t whereas the true distribution peaks in the vicinity of (n + 1)[1- (n/m)] and has mean equal to n[l- n/m]. Note that\nfor \"typical\" realizations (Xl, \u2022 \u00b7,x m ), we have\n\n-mn =p\nand, hence, the two distributions have the same general location and\nscale. [In fact, expression (31) is a hypergeometric distribution, which\nconverges to (28) as m -- 00 if n = pm (Ref. 13).] Thus, although incorrect, the binomial distribution approximates the true distribution of the\nkiller trunk.\nThe following result helps to put the relationship between the ad hoc\nand the optimal statistics in perspective.\nLemma 2: If lxi/ is a binary state stationary Markov chain with transition probabilities PO,1 and PI,o, and if Xm = (Xl,\u00b7 \u00b7,x m ), then we\nt P1,o(p,r) -- 1 - p as r -- roo\n\n944\n\nTHE BELL SYSTEM TECHNICAL JOURNAL, JULY-AUGUST 1977\n\nhave\nP(Xm ) = b(tlO;n,P 1,0) x b(tO,l;m-n,PO,l) x q,\n\n(33a)\n\nwhere\n(33b)\n\nProof:\nm\n\nP(Xm ) = P(X1) II P(XdXi-1)\ni=2\n\n= P(X1) PL~o P~V P~~l P~~oo\n= PLloo (1 - P 1,0)t ll P~~l (1 - P O,l)t oo X P(X1).\nUsing eqs. (IIa) and (18) to express t11 and too in terms of tlO and tOb\nrespectively, yields the result.\nThus, given a binary state stationary Markov chain lxii, it is clear from\nthe above lemma that the log likelihood ratio\nfi(\n{, Xm\n\n) - I\n-\n\nP*(xm )\n\nog P(x\n\nm\n\n)\n\nformulated for the two hypotheses\nH o: Ixd Markovian, characterized by (P O,1,P 1,0)\n\nH 1: IXi I Markovian, characterized by (P~,bP~,O)\n\nis the sum of three terms:\nfi(\n\n{, Xm\n\n) = I og b(tlO'n\n\"p~,0) + I og b(t01;m - n,P~ ,1) + I og (q*)\n- .\nb(t1O;n,P 1,0)\nb(t01;m - n,PO,l)\nq\n\nThe first term is the ad hoc statistic (O'tlO - an), the second term is the\nadditional statistic [(3t01 - b(m - n)], and the third term is an end-effect\nterm (ax m + bx~).\nlog (q*) = ax\nq\n\nm\n\n+ b XCm + log P*(X1)\n= ax + bx c\nP(xd\nm\nm,\n\nsince, P* (x d = P(x 1) = p.\nThe ad hoc algorithm, although based on the approximate binomial\ndistribution, is very attractive for a number of practical reasons:\n(i) For the 200-second sampling option, it is essentially optimum in\na practical sense, since the P O,l characteristics for a normal and killer\ntrunk are not far enough apart to exploit (see Fig. 6).\n(ii) When we exploit the grouping information for the 5XB trunk\nTRUNK-DETECTION ALGORITHMS\n\n945\n\ngroup in Section V, it will become obvious that the additional part of the\noptimum statistic is quite sensitive to the trunk occupancy and, hence,\nto the trunk-selection procedure modeled. (The sensitivity of the \"additional\" statistic to trunk occupancy stems from the fact that PO,1 is\n\"almost\" proportional to p.) On the other hand, we will see that the ad\nhoc 5XB algorithm is relatively robust to minor perturbations in the\ntrunk occupancy (and therefore to the trunk-selection procedure) and\nhence might be expected to perform well in a rea15XB environment.\nV. THE 5XB TRUNK-GROUP ALGORITHMS\n\nIn addition to utilizing individual trunk switch-count and transition\naccumulations the 5XB group algorithms exploit the following:\n(i) The identity of all trunks common to a group.\n(ii) The trunk-selection procedure.\n\nThe resulting 5XB group algorithms typically are faster* than their\nindividual trunk counterparts and are also less sensitive to the groups\nnominal holding time.\n5.1 The 5XB trunk-group model\n\nFor the purposes of this paper, we model a 5XB trunk group (with all\ntrunks normal) as an M/M/N-loss model with random selection of idle\ntrunks. 2 The same assumptions apply if the group contains one or more\nkiller trunks, but in this case we assume that killer trunks have a mean\nholding time equal to 1/r that of the normal mean holding time. In addition to being convenient theoretically, this idealized model has also\nbeen very useful in developing the 5XB group algorithms presently\nimplemented in leAN.\nIf all N trunks are normal, the random selection rule implies that all\ntrunks have the same mean occupancy. In Ref. 2, the birth and death\nequations for the above model with a single killer trunk were solved in\nclosed form, and in Ref. 14 this was generalized to an arbitrary number\nof killer trunks. These analytic results turn out to be quite useful, and\nin what follows we will need the following results derived in Ref. 2.\nTheorem 1: For the above 5XB trunk group model having a single killer\ntrunk with parameter r and an offered load of a erlangs, the blocking\nprobability B(N,a, r) and the mean occupancy p; (N,a,r) of the killer\ntrunk are given by:\n* For given type 1 and 2 errors, the group algorithms typically have a considerably\nsmaller mean decision time than their individual trunk algorithm counterparts.\n946\n\nTHE BELL SYSTEM TECHNICAL JOURNAL, JULY -AUGUST 1977\n\n(i) B(N,a,r) =\n\nNB(N,a)\nNr - (r -l)a[l - B(N,a)]\n\n(34a)\n\n(ii) p;(N,a,r) =\n\n1\nrN\n1 + - - r[l - B(N - 1,a)]\na\n\n(34b)\n\nwhere B(N,a) is the usual erlang B blocking associated with an MI\nMIN-loss system with all trunks normal and an offered load of a\nerlangs.\n\nIt is easy to see that the occupancy Pr of each of the N - 1 normal\ntrunks must satisfy the conservation equation:\nrp; + (N - l)Pr = a[l - B],\n\n(34c)\n\nand the trunk-group occupancy \u00a2; is defined by:\n*\n\n\u00a2r =\n\nP; + (N - l)Pr\nN\n.\n\n(34d)\n\n(For a 5XB trunk group having a killer trunk with parameter r: P; and\nPr denote the mean occupancy for a killer and normal trunk and \u00a2; denotes the mean group occupancy.)\nAlthough eqs. (34a) through (34d) define an implicit relationship\nbetween p;(N,a,r) and \u00a2;(N,a,r), it will be very useful to have a simple\nexplicit relationship. If the blocking term in eq. (34b) is ignored and if\nwe \"associate\" \u00a2; with alN, an approximation suggested is:\n* .\n\nPr =\n\n\u00a2;\n\n*.\n\nr - (r - l)\u00a2r\n\n(35a)\n\nThis approximation, although quite good for large N, is rendered obsolete by the following exact result:\nTheorem 2: Consider a 5XB trunk-group model with all trunks normal\nand mean-group occupancy \u00a2. (We will let \u00a2 denote the (mean) group\noccupancy for a 5XB trunk group with all trunks normal.) If one of the\ntrunks is replaced by a killer with parameter r, then\nP; = p(\u00a2,r),\nwhere,\np(\u00a2,r) = r - (r - 1)\u00a2\n\n(35b)\n\nOf course\na[l - B(N,a)]\n\u00a2 = --=--------=N\n\nTRUNK-DETECTION ALGORITHMS\n\n947\n\nwhere B(\u00b7 , .) is the usual erlang B blocking expression.\nThis surprising result, which follows easily from eq. (34b), is proved\nin Appendix D. As a consequence of this theorem, \"5XB group occupancy\" will be used to denote the occupancy of a 5XB group with all\ntrunks normal.\nThe mean occupancy of the normal trunks in a 5XB trunk group\nmodel having a single killer trunk no longer is given exactly by 1>. But\nthe following result, derived in Appendix D, shows that 1> is a good approximation.\nTheorem 3: Consider a 5XB trunk group model with N trunks having\na single killer trunk with parameter r ~ 1. The mean occupancy (Pr)\nof the N - 1 normal trunks satisfy\nr -\n\n1> ~ Pr ~\n\n{\n\n(~) (r - 1)1>}\nr _ (r _ 1)1>\n\nX 1>,\n\n(36)\n\nwhere 1> is the mean-group occupancy with all trunks normal.\n\nTheorems 2 and 3 are proved in Appendix D, where an exact expression\nfor Pr is also derived. These results are special cases of general results\nobtained for the random selection model. 14\n5.2 Exploiting the 5XB Grouping Information\n\nTo simplify matters, we assume that a trunk in a 5XB group* with\nmean-group occupancy 1> has mean occupancy p(1),r) given by\np(1),r) = r - (r - 1)1> '\n\n(37a)\n\nwhere r = 1 corresponds to a normal trunk. Thus, if a group has no killer\ntrunks, all normal trunks satisfy P = 1> and eq. (37a) with r = 1 yields the\ncorrect occupancy. If, however, the group has a killer trunk, then all\nnormal trunks satisfy inequality (36) so eq. (37a) with r = 1 is an approximation that increases in accuracy with the size of the group. Of\ncourse eq. (37a) is exact for a (single) killer trunk in a 5XB trunk\ngroup.\nIt is clear from eq. (37a) that\np(1),l)\np(1),r) = r - (r - l)p(1),l)\n\n(37b)\n\n* We use \"5XB group\" and our idealized model of a 5XB trunk group interchangeably.\n948\n\nTHE BELL SYSTEM TECHNICAL JOURNAL, JULY-AUGUST 1977\n\nand hence p(4),r) is typically much smaller than p(4),l). (For 4> = 0.50 and\nr = 10, p(4),r) = 2/11 p(4),l). Thus, it would appear that considering the\n1 ~ 0 transition probability as a function of the 5XB group occupancy\nwould effectively \"spread\" the Pl,o characteristics in Figs. 2 and 3 further\napart. That is, for a given 4>, we propose comparing\nP l ,o[p(4),l)] and P~,o[p(4),r)]\n\n[rather than Pl,o(p) and P~,o(p), as in Section IV].\nDenoting the composition P l ,o[p(4),r)] by P l ,o(4),r), we have\n\nP1,o(q\"r) =\n\n(1 - p(q\"r\u00bb (1 - exp (1 --;~,r\u00bb))'\n\n(38)\n\nwhich is plotted in Figs. 8 and 9 for the 200- and 100-second sampling\noptions, respectively. The normal holding time used in these figures is\n180 seconds, and the killer-trunk characteristics are drawn for r = 5,10,\nand 15.\nThe increased \"spread\" between normal and killer Pl,o characteristics\nobtained in this way is simply a consequence of exploiting the distinctly\ndifferent occupancies of a normal and killer trunk in a 5XB trunk group.\nFigure 10 is a three-dimensional sketch of the composition of Pl,o and\np. Because all normal trunks in a 5XB group have the same mean occupancy, we see that a single Pl,o vs 4> characteristic suffices to describe\n1.or:::::::~;;;;;;;;;;===---------l\n\nKILLER TRUNKS--0.8\n\n0.6\na\nCl.\n\n0.4\n\n5XB TRUNK GROUP MODEL\n(RANDOM SELECTION OF IDLE TRUNKS)\n\n0.2\n\nW1 = 180 SECONDS\nT=200SECONDS\n\nO~\n\no\n\n____\n\n~\n\n______\n\n20\n\n~\n\n40\n\n______\n\n~\n\n____\n\n~\n\n60\n\n______\n\n80\n\n~\n\n100\n\nMEAN GROUP OCCUPANCY IN PERCENT\n\nFig. 8- 1 - 0 transition probability for the 200-second sampling option.\n\nTRUNK-DETECTION ALGORITHMS\n\n949\n\nl.\u00b0r~~::.:::::::::::==-------------'\n\nO.B\n\nKILLER TRUNKS---\n\n0.6\n0\n\na:0.4\n\n5XB TRUNK GROUP MODEL\n(RANDOM SELECTION OF IDLE TRUNKS)\n\n0.2\n\n\",,-1 = lBOSECONDS\nT = 100 SECONDS\n\n0\n0\n\n20\n\n40\n\n60\n\n100\n\nBO\n\nMEAN GROUP OCCUPANCY IN PERCENT\n\nFig. 9- 1-+ 0 transition probability for the IOO-second sampling option.\n\nP1.0 'P PLANE:--MiMil - LOSS\nMODEL\n\n)rooo::~------T--\u00a2\n\n/\n\n/\n\n/\n\n//\n\n~7L __ - p.\u00a2PLANE: 5XB GROUP\n//\n\nMODEL\n\np(\u00a2.r)\n\nFig. lO-Sketch of the composition of P1,o(p) with p(\u00a2,r).\n\nall normal trunks. This fact allows us to translate the individual trunk\nalgorithm's development to this 5XB context with essentially only notational changes.\n950\n\nTHE BELL SYSTEM TECHNICAL JOURNAL, JULY-AUGUST 1977\n\n1.0 ~:::::::~;;;;;;;::===---------I\n\n0.8\n\n0.6\na\n\n--------\n\nNORMAL TRUNK\n(r = 1)\n\n..........\n\nNORMAL TRUNK .............\nFOR A GROUP\n........ ,\nWITHP.-l = 180 SECONDS)\n................\n\na.\n\n.......\n\n0.4\n\n0.2\n\n\"\n\n-.;:\n\n5XB TRUNK GROUP MODEL\n(RANDOM SELECTION OF IDLE TRUNKS)\np.-l = 45 SECONDS\nT = 200 SECONDS\n\nMEAN GROUP OCCUPANCY IN PERCENT\n\nFig. 11- 1 -- 0 transition probability for the200-second sampling option (mean group\nholding time = 45 seconds).\n\nFigures 11 and 12 are plots of eq. (38) drawn for a normal group mean\nholding time of 45 seconds. * The normal trunk characteristic corresponding to 180 seconds is shown in dashed lines. We see that with 5XB\ngrouping information factored into the picture, considerable discrimination exists between both normal trunk characteristics as well as between the normal trunk having a holding time of 45 seconds and the killer\ntrunks. The discrimination that exists between the normal trunks permits us to make the 5XB group algorithm adaptive to the group mean\nholding time. [Although we will not pursue this topic, the basic idea is\nthat L.jtlO(j)/L.jn(j) (sums are over all trunks in the group) is an estimate\nof Pl,O and can be used to decide which (of several) normalpl,O characteristics constitutes H 0.]\n5.3 The ad hoc and the optimal 5XB group algorithms\n\nWe assume that the mean group holding time is known and consider\nformulating a hypothesis-testing problem similar to that in Section 4.l.\nThus, we denote P(tlO(m) = t/n(m) = n) by P(t/n) and consider the two\nhypotheses:\n* For normal holding times in the vicinity of 45 seconds, a killer parameter r in the range\n3 to 5 probably is typical. An r of 10 or 15 in this context is unrealistic.\nTRUNK-DETECTION ALGORITHMS\n\n951\n\n1.0 r~~;;;;;;;===---------I\n\n0.8\n\n0.6\na\n\nNORMAL TRUNK\nFOR A GROUP WITH\np..-l = 180 SECONDS\n\ncC\n0.4\n\n-----------..._..\n\n---- --\n\n-- ......\n\n' ......\n\n5XB TRUNK GROUP MODEL\n(RANDOM SELECTION OF IDLE TRUNKS)\n\n0.2\n\n\"~\n\nJL -1 = 45 SECONDS\nT = 100 SECONDS\n\no~\n\no\n\n____\n\n~\n\n______\n\n20\n\n~\n\n40\n\n______\n\n~\n\n______\n\n60\n\n~\n\n80\n\n____\n\n~\n\n100\n\nMEAN GROUP OCCUPANCY IN PERCENT\n\nFig. 12- 1 --. 0 transition probability for the 100-second sampling option (mean grouping\nholding time = 45 seconds).\n\nH o: P(t/n) = b[t;n,P I ,o(\u00a2,l)]\nHI: P(t/n) = b[t;n,PI,o(\u00a2,r)],\n\nr ~ roo\n\n(39)\n\nThere are two differences between this formulation and the one in\nSection 4.1:\n(i) The trunk occupancy p in Section 4.1 is replaced by the group\noccupancy \u00a2.\n(ii) The alternate hypothesis HI is composite since PI,o(\u00a2,r) for r ~\nro are distinct.\n\nThe approach taken in dealing with (ii) is a natural one often\nadopted;l1 since PI,o( \u00a2,r) is monotone increasing in r Ithis follows from\neq. (38) upon noting that r/[1 - p(\u00a2,r)] = r + \u00a2/(1 - \u00a2)I, then testing\nbetween H and the simple alternate hypothesis\n\n\u00b0\n\nHI: P(t/n) = b[t;n,PI,o(\u00a2,ro)],\n\nsay with type 1 and 2 errors a and {j, respectively, implies that if the true\nstate of nature is H I with r = r~ > ro the resulting type 2 error will not\nexceed {j. With this approach, we can simply translate the ad hoc algorithm results developed in Section 4.1 to this 5XB group context by\nmaking the appropriate changes in notation.\n952\n\nTHE BELL SYSTEM TECHNICAL JOURNAL, JULY-AUGUST 1977\n\nThus, the ad hoc 5XB group algorithm can be described as follows:\ncorresponding to the sequence of data accumulations (t{,n{) i = 1,2,\u00b7 ..\nfor the jth trunk in a group of N trunks, where t{ and n{ are the 1 - 0\ntransition and switch-count accumulations, respectively, during the ith\naccumulation period in which mi scans are made, define sf and S{ i =\n1,2,\u00b7 ..; j = 1,\u00b7 .. ; N by\n(40a)\n\nand\n\nS{ = S{-I + s{ with Sb = 0,\n\n(40b)\n\nwhere \u00a2i is the group's occupancy during the ith accumulation period.\nThe sequential test for the jth trunk in the group, j = 1,\u00b7 . \u00b7,N is defined\nby\n(i) Compute Sf, i = 1,2,\u00b7 .. and defer making a decision as long as To\n\n< sf < T 1.\n\n(ii) If i = k corresponds to the first accumulation period for which\n\nS{ rt (To,T I ),\nthen\n\nS{ ~ To ~ trunkj is normal\nS{ ~ TI ~ trunk j is a killer.\nThe weights a(\u00a2) and a(\u00a2) are defined by\na ()\n\u00a2 = I og\n\n1 - PI o(\u00a2,I)\n,\n\n1 - P1,o(\u00a2,ro)\n\n(41a)\n\nand\n(41b)\n\nwhere PI,o(\u00a2,r) is defined by eq. (38).\nJust as in the individual trunk algorithm, the actual occupancy required to choose the weights a and a is unknown and must be estimated.\nThus, the group occupancy \u00a2i during the ith accumulation period is\nestimated by\n1 N\n.\n\u00a2i = N L ni/mi\nA\n\n(42)\n\nj=l\n\nNote that \u00a2i is a \"better\" estimator than Pi = nJmi (the estimator used\nin the individual trunk algorithm) in the following sense: given a 5XB\ngroup with all trunks normal and mean-group occupancy \u00a2 (in equilibrium), we have\nTRUNK-DETECTION ALGORITHMS\n\n953\n\n(i) E(P) = p = cp\n(ii) E(\u00a2) = cp\n(iii) var(\u00a2) < var(p).\n\nIn addition to the better occupancy estimate available on a group basis,\nthe fact that the group P 1,0 characteristics are \"flatter and broader\" then\nthe individual trunk P 1,0 characteristic implies that the group algorithm\nmore faithfully tracks the required weights, than does the individual\ntrunk algorithm.\nThe ad hoc 5XB group algorithm has the same pleasant intuitive interpretation that the ad hoc individual trunk algorithm had (see eq. (13)\nand related discussion). It is also easy to show how the optimal individual\ntrunk algorithm development of Section 4.2 carries over to the 5XB\ngroup context.\nThus, consider the two states of a trunk to be described by:\n\nH o: \\xi/ Markovian, characterized by 0 = (P O,1,P1,0)\nHI: \\xi/ Markovian, characterized by 0* = (P~,l'P~,O)'\n\nwhere P1,0 = P 1,0(,I), P~,o = P 1,0(cp,ro), and [see eq. (2)]\nP\n\n(A.)\np(cp,r) P (A. )\n0,1 'P,r = 1 _ p(cp,r) 1,0 'P,r\n\n(\n\n43\n\n)\n\nwith p(cp,r) defined by eq. (37a). The assumptions that lead to a consideration of these two statistical hypotheses as a model of the normal\nand killer states of a trunk can be found in Section 4.2.\nProceeding as in Section 4.2 leads us to the optimum statistic l(xm )\nfor distinguishing between the two simple hypotheses under consideration:\nP*(X1)\nf(x m ) = [(a - a)tlO - atl1] + [btoo - ({3 - b)tod + l o g - - ,\nP(X1)\nA\n\n-\n\n-\n\n-\n\n(44)\n\nwhere the parameters a and a are defined by eqs. (41a) and (41b) and\nthe parameters b and ~ are defined by\n- I 1 - Po ,l(cp,rO)\nb = og\n1 - P O,l(cp,l)\n\n(45a)\n\n~ = b + log P O,l(cp,l) .\n\n(45b)\n\nand\nP O,l(cp,rO)\n\nAs in eq. (39), the alternate hypothesis is really composite since\n[P O,l(cp,r), P 1,0(cp,r)] for r ~ ro are distinct. Since P O,l(cp,r) is monotone\ndecreasing in r, the approach discussed earlier of treating HI as a simple\n954\n\nTHE BELL SYSTEM TECHNICAL JOURNAL, JULY-AUGUST 1977\n\nhypothesis with r = ro is followed. The parameters 6 and ~ are defined\na bit differently than were the parameters band {J for the optimal individual trunk algorithm (see eq. (20a) and (20b)) in order to obtain nonnegative weights. Thus, in the individual trunk algorithm context, we\nhad P~,l > PO,l (eq. (19c)), but in the present 5XB group context we have\nPO,l > P~,l. The reason for this \"flip-flop\" is easy to see: for a given group\noccupancy \u00a2, we are now contrasting the 0 -- 1 transition probability\nfor two trunks which differ, not only in their hang-up rates but also in\ntheir occupancies as well. Thus, the difference in the two occupancies\ndominates the effect that the hang-up rates alone have. Roughly\nspeaking, the 0 -- 1 transition probability of a trunk is approximately\nequal to its occupancy (conditioning on the last scan has little effect)\nand hence since p(\u00a2,ro)\u00ab p(\u00a2,I) it is clear that we shmlld have PO,l(\u00a2,r)\n< P o,r(\u00a2,I). Figures 13 and 14 are plots of PO,l(\u00a2,r) for the 200- and\n100-second sampling options, respectively. In both figures, the killer\ntrunk characteristics have been plotted for r = 5, 10, and 15 and a normal\nmean holding time of 180 seconds is assumed. These figures are very\ninsensitive to the assumed normal mean holding time, since they essentially reflect eq. (37a), which is independent of the mean group\nholding time.\nThe \"additional\" statistic which appears in eq. (44),\n\nbtoo - (~ - b )tOl\n1.0r-----------------------\"\"\n5XB TRUNK MODEL\n(RANDOM SELECTION OF IDLE TRUNKS)\n\np.-1 = 180 SECONDS\nT = 200 SECONDS\n0.8\n\n0.6\n\n0.4\n\n0.2\n\n20\n\n40\n\n60\n\n80\n\n100\n\nMEAN GROUP OCCUPANCY IN PERCENT\n\nFig. 13- 0 -- 1 transition probability for the 200-second sampling option.\nTRUNK-DETECTION ALGORITHMS\n\n955\n\n1.0.-----------------------,.,\n5XB TRUNK GROUP MODEL\n(RANDOM SELECTION OF IDLE TRUNKS)\n\nf.L- 1 = 180 SECONDS\nT= 100SECONDS\n\n0.8\n\n0.6\no\u00b7\n\na..\n\n0.4\n\n0.2\n\n0~~\u00a75====~\n\no\n\n20\n\n____\n\n-L____-L____~\n\n40\n\n60\n\n80\n\n100\n\nMEAN GROUP OCCUPANCY IN PERCENT\n\nFig. 14-0 -- 1 transition probability for the 100-second sampling option.\n\nshows that 0 -- 0 transitions are weighted positively (evidence of a killer\ntrunk*) and 0 -- 1 transitions are weighted negatively (evidence of a\nnormal trunk). This additional statistic is strongly influenced by the\noccupancy of a trunk, and only slightly by its hang-up rate.\nNote also that the term log P*(XI)/P(XI) is nonzero in the 5XB context\nSInce\n1\n\nr\n\n-(r:\n\n1)\",\n\n{\nr - (r - I)\n\nif Xl = 1\nif Xl = O.\n\nVI. PERFORMANCE OF THE 5XB GROUP ALGORITHMS\n\nIn common with all sequential detection algorithms, the time required\nby the killer-trunk detection algorithms to reach a decision (trunk normal or killer) is a random variable. In this section, we obtain an approximate formula for the mean time required by the 5XB group algorithms to reach a decision. This result is used to contrast the performance\n* Killer trunks in the 5XB group model have very low occupancy, and hence 0 -- 0\ntransitions are likely.\n956\n\nTHE BELL SYSTEM TECHNICAL JOURNAL, JULY-AUGUST 1977\n\nof the ad hoc and optimal algorithms as well as to point out the considerable effect that the sampling rate has on each. In addition, we also\nobtain an approximate expression for the false-alarm probability of the\n5XB group algorithms. The analysis for the individual trunk algorithms,\nalthough differing in several respects from the group algorithms, involves\nthe same sort of considerations and is omitted.\nThe analysis in this section assumes a server system in equilibrium\nand, therefore, the mean trunk-group occupancy \u00a2 is assumed constant.\nIn addition, to simplify the analysis, we assume that \u00a2 is known; an approximate analysis which does not require this assumption is sketched\nin Section 6.1. A consequence of this assumption is that the algorithm\nweights are treated as constants rather than random variables. This\nassumption is not unreasonable because for multiple-hour accumulation\nperiods var(1)) is quite small (1) is the switch-count estimate of \u00a2). (Var(1\u00bb\nhas been derived for an M/M/N-Ioss system.1 5 )\n6. 1 Mean statistic update\n\nCorresponding to a sequence of trunk states Xl,X2, \u2022 ',Xm in an accumulation period with m scans, define a sequence of transition updates\nZ2,' ',Zm by\n\n6\n\nZn =\n\n(~\n\nif\n\n{- 6) if\n(a - a)\nif\n\n-a\n\nif\n\n(Xn-bXn) =\n\n(0,0)\n(Xn-bXn) = (0,1)\n\n(46)\n\n(Xn-l,X n ) =\n\n(1,0)\n(Xn-l,X n ) = (1,1)\n\nThe optimum 5XB statistic (eq. (44)) may therefore be written:\n\"\n\nm\n\nP*(x m )\n\nt=2\n\nXm\n\nf(x m ) = .L Zi + log P(\n\n)\n\n(47)\n\nIn practice the end-effect term cannot be implemented and all the\ntransitions in eq. (44) must be estimated in terms of t(m), n(m), and m.\nThus, if we denote the implementable version of eq. (44) by Sm(\u00a2,ro), t\nuse eqs. (11), (12), and (20) in eq. (44), and drop all end-effect terms we\nobtain\n\n(48)\n\nt ro is the value of the killer parameter used in defining the alternate hypothesis and\nhence the algorithm weights (see eqs. (41) and (45\u00bb.\n\nTRUNK-DETECTION ALGORITHMS\n\n957\n\nNow using eqs. (11), (12), and (20) once again, we see that 8 m (cp,ro) may\nbe written\n8 m (cp,ro) = ~ Zi + (bx~ - aXm) + (ex + ~) (Xl - Xm).\ni=2\n2\n\n(49)\n\nSince the 5XB group is in equilibrium, Z2, \u2022 \u00b7,Zm are identically distributed and it is easily verified that their common mean is given by\nE(z) = (ex PI,o - a)p + (b - Po,I~)(1 - p).\n\n(50)\n\nWe recall that p (eq. (37a)) as well as the transition probabilities (eqs.\n(38) and (43)) are functions of the group occupancy \u00a2 and the state r of\nthe trunk. The weights a, ex, b and ~ are only functions of cp for a specified\nchoice of the parameter (ro), which characterizes the alternate hypothesis. Thus, the mean statistic update for the optimum 5XB statistic and\nits \"implementable version\" is given by:\n\n\" m )} = (m -1)E(z) +E {l oP*(xd}\nE{e(x\ng-P(XI)\n\n(51a)\n\nE{8 m (cp,ro)} = (m - I)E(z) + b(1 - p) - ap.\n\n(51b)\n\nand\n\nNote that it is easily shown that\n\n\u00a2\\\n\nE {IOgP*((XI)} = -log [ro - (ro -1)cp] + r(~ log ro\nP Xl)\nr - r - 1 cp\n\nwhich is negative for r = 1 and positive for r ~ roo\nAlthough the increments (transition updates) defined in eq. (46) are\nidentically distributed, they are not independent. In fact, since the state\nsequence {xd has been modeled as a Markov chain (see Section 4.2), it\nis easy to see that the sequence {zd defined by (46) is also a Markov chain.\nRelabeling the four natural states,\n\nb, -(~ - b), (ex - a), -a,\nof the chain {Zi} by\n0,1,2,3,\nrespectively, it is easily seen that the one-step transition matrix 7r for\nthis chain is given by\n7r =\n\n958\n\n(1 -:0\" P~,j P~,o 1_\u00b0Pj,O)\n1 - Po, I\n\nPo, I\n\no\n\n0\n\n0\nPI,o\n\n0\n1 - PI,Q\n\n'\n\nTHE BELL SYSTEM TECHNICAL JOURNAL, JULY-AUGUST 1977\n\nl-P O,l\n\n(a)\nOPTIMAL STATISTIC\n\n(b)\nAD HOC STATISTIC\n\nFig. 15-State diagram for the ad hoc and optimal 5XB group statistics. (a) Optimal\nstatistic. (b) Ad hoc statistic.\n\nwhere 7ri,j = P(zn = j/Zn-l = i). Of course, the stationary distribution\nP satisfying P7r = Pis\nP = [(1 - p)(1 - Po,r), (1 - P)PO,b pPI,o, p(1 - PI,o)].\n\nThe state diagram corresponding to the Markov chain \\zd is shown in\nFig. 15a. If 6 = {3 = 0, we obtain the ad hoc algorithm, for which the sequence \\zd is a three-state Markov chain, with natural states 0, a - a\nand -a. The state diagram for this chain is shown in Fig. 15b.\nFigures 16 and 17 are plots of the mean statistic update vs group occupancy for the implementable version of the 5XB group algorithms.\n(Log base 10 is used in this paper.) These figures are drawn for a killer\ntrunk with parameter r = 10. Also shown is the corresponding plot for\na normal trunk (r = 1).\nWe close this section by indicating an approximate analysis of E(z)\nwhich doesn't assume that \u00a2 is known. Thus, in practice, \u00a2 is unknown\nTRUNK-DETECTION ALGORITHMS\n\n959\n\nand is estimated by \u00a2. Hence eq. (46) should read:\nZn\n\n= (,6(<1>0)\n\nif\n\n(xn-J,x n )\n\n= (0,0)\n\nand\n\n\u00a2 = \u00a2o.\n\nConditioning on \u00a2, we have\nE(z) = E1E(z/\u00a2)1,\n\nwhere\nE(z/\u00a2) = b(\u00a2)P(Xn-I = O,xn = O/\u00a2) +\"\"\".\n\nNow by assuming that (Xn-I,X n ) and \u00a2 are independent,* we get eq.\n(50) with the constant weights a(\u00a2),. \" \" replaced by the mean values\nEla(\u00a2)l,\"\"\". The mean values can be approximated in either one of two\nways:\n(i) Ela(\u00a2)l == a[E(\u00a2)] = a(\u00a2), which obviously amounts to assuming\n\u00a2 is known.\n\nvar(\u00a2) d 2a t\n\n(u) Ela(\u00a2)l == a(\u00a2) + - , - d A2\n2.\n\u00a2\n\u2022\u2022\n\nA\n\nl\nA_\n\nrj>-rj>,\n\nwhich factors the available variance of \u00a2 into the picture.\n6.2 Mean time to detection\n\nThe basic structure of all the detection algorithms in this paper are\nthe same: a statistic Si is evaluated at the end of the ith accumulation\nperiod, i = 1,2,. \"\" and a decision is made the first time that the sum SI\n+ S2 +\"\"\" falls outside an interval (To,TI). Presumably, the random walk\ntype statistic Si has a negative drift under Ho (trunk normal) and a\npositive drift under HI (trunk killer). Wald's SPRT always has the appropriate drift: if H 0 and HI correspond to the probability distributions\nPo(w) and PI (w), respectively, and if f(w) is defined by\nPI(w)\nf(W) = log-Po(w) ,\nA\n\nthen Eli(w)l < 0 under Ho and Eli(w)l > 0 under HI. The proof is immediate by using the inequaiityI2\n- LPi log Pi < - L Pi log qi,\ni\n\ni\n\n* For reasonable-size trunk groups, we expect very little dependence b.etween the\nsampled state process of an individual trunk (Xl,\u00b7 \u2022\u2022 ) and the group process \u00a2.\nt This is a Taylor expansion to second order.\nTRUNK-DETECTION ALGORITHMS\n\n961\n\nwhere Ipd and Iqi\\ are distinct probability distributions. In Appendix\nE, we show that both the ad hoc (6 = ~ = 0) and the additional (a = a\n= 0) parts of E(z) (eq. 50) have the appropriate drift. This in turn shows\nthat both the ad hoc and additional parts of the 5XB group statistic (eq.\n(51a)) have the appropriate drift.\nSuppose Y bY2, .. are i.i.d. random variables with common mean J.\u00a3\nand consider a random walk\nn\n\nSn =\n\n2: Yi\n\nn = 1,2,\u00b7 ..\n\ni=I\n\nwith absorbing barriers at To and T I . If J.\u00a3 is small compared to To and\nT I , then the mean stopping time (mean number of steps to absorption)\nE(n) is approximately given by\nPoTo + PIT I\nJ.\u00a3\n\nwhere Po and PI are the probabilities of absorption at To and Tb respectively. This follows from Wald's identityll\nE(Sn) = J.\u00a3E(n)\n\nif we approximate the mean value of the random walk at absorption by\nPoTo + PIT I .\n\nIn our detection theory context, Po and PI correspond to {3 and 1 {3, respectively, if the trunk is a killer ({3 = probability of miss) and 1 a and a, respectively, if the trunk is normal (a = probability of false\nalarm). If we denote the mean number of accumulation periods needed\nto reach a decision under H 0 and HI by E ( TN) and E (Tk ), respectively,\nand assume (i) successive statistic updates are independent and (ii) the\nmean statistic update is small compared to To and T I , we obtain\nE(TN) == (1 - a)To + aT I\nEISm (c/>,ro))\n\n(52a)\n\nE(T ) == {3To + (1 - (3)T I\nk\nEISm (c/>,ro) I '\n\n(52b)\n\nand\n\nwhere the mean statistic update EISm (c/>,ro) I is evaluated for r = 1 in (52a)\nand for r ~ ro in (52b).\nThe assumption that successive statistic updates are independent is\nnot strictly true if the successive statistic updates are contiguous.\nHowever, one expects that the slight (end-effect) dependence will not\ngive rise to very much error.\nLet Tko be the time required to decide (incorrectly) that a killer trunk\nis normal. Similarly, let Tkl be the time required to decide (correctly)\n962\n\nTHE BELL SYSTEM TECHNICAL JOURNAL, JULY-AUGUST 1977\n\nthat a killer trunk is a killer. Then we have\nE(T,J = (3E(Tho ) + (1 - (3)E(Th I)'\n\nwhich suggests that\n(53)\nThe moments of the conditional stopping times Tho and Thl can be obtained by using a well known technique of Wald's,* and one finds that\napproximation (53) is reasonable if Tl and (-To) are sufficiently\nlarge.\nIn our faulty-trunk detection context, a type 1 error (\"false alarm\")\nmay result in the misuse of craft resources (e.g., testing a perfectly good\ntrunk). A type 2 error (\"miss\") on the other hand, will result in an increased time to detection. Assuming type 1 and 2 errors of 10-6 and 10- 2,\nrespectively (realistic implementation values), implies approximate\nthresholds To = -2 and Tl = 6 (formulae 4.5c and d, log base 10). With\nthese parameter values, the mean detection time E(Th I) can be approximated by\nE(T ) --'-hI\n\n-\n\nTl\n\nE1S m (\u00a2,ro)l\n\n(54)\n\nFor a normal trunk, the mean statistic update is comparable to To and\nhence expression (52a) isn't applicable, nor is it needed since the 5XB\ngroup algorithm reaches a decision on a normal trunk after one or two\nupdates.\nFigures 18 and 19 are plots of the mean-detection time vs group occupancy for the implementable versions of the 5XB group algorithms.\n[The dashed line portion of Figs. 18 and 19 indicates where approximation (54) involves considerable error (e.g., the region in which\nE1S m (\u00a2,ro)l is a significant fraction of Tl)'] It is apparent from these\nfigures that\n(i) The mean detection time for both the ad hoc and optimal algorithms is enhanced by using the 100-second sampling option. This enhancement is far more pronounced for the ad hoc algorithm.\n(ii) The optimal algorithm is \"faster\" than the ad hoc algorithm. This\ncontrast is greater for the 200-second sampling option.\n6.3 False alarm probability of the 5XB group algorithms\n\nIf B(a,(3) and A (a,(3) are the test thresholds that result in type 1 and\n2 errors a and (3, respectively, for a SPRT, Wald showed l l that using\n* See eq. 158 and 159 in Appendix A.5.2 of Ref. 11. The method ignores (as usual) the\n\"excess over the boundaries\" and hence yields approximate results.\nTRUNK-DETECTION ALGORITHMS\n\n963\n\n50r------------.~----------------------_.\n\nKILLER TRUNK PARAMETER, r = 10\nSINGLE-HOUR ACCUMULATION,\nm = 18\nUPPE R TEST TH R ESHO LD, T 1 = 6.0\n\n40\n\nFALSE-ALARM PROBABILITY ~ 10- 6\nDESIGN, ro = 5\nT = 200 SECONDS\n\nfL -1 = 180 SECONDS\n 0 ~ ho < 0 and E(x) < 0 ~ ho > o. Assuming that the excess of Sn over the boundaries is small, eq. (56) yields\nthe standard approximation 11, 17\n\nPT\n\ne hoTl - 1\n-'------\n\no - ehoTl _ e hoTo\n\n(57a)\n\nand\n1-\n\ne hoTo\n\nPT = - - - - 1\n\nehoTl _ e hoTo\n\n(57b)\n\nNote that the probability of false alarm (type 1 error) corresponds to P T1\nif the random walk increment is that of a normal trunk [8 m (cp,ro), r =\n1]. Similarly, the probability of miss (type 2 error) corresponds to PTo\nif the random walk increment is that of a killer trunk [8 m (cp,ro), r ~\nro].\n\nTo use these approximations, we must compute the moment generating function\n(58)\n\nby using the joint distribution p(t,n) derived in Appendix B. [Note that\nour discussion applies equally well to the additional_and optimal statistics. In general, we need E!exp [8 m (cp,ro),.L]J, where 8 m (cp,ro) is given\nby eq. (48).] Choosing the test thresholds To and Tl for the ad hoc algorithm according to the Wald SPRT formulae [eqs. (10c) and (10d)]\ntypically results in PTo < {3 and P T1 < [Y.\nVII. SUMMARY\n\nA class of killer-trunk detection algorithms has been developed that\nuse the individual trunk usage and transition accumulations available\nin EADAS/ICUR. Because this data is essentially a sufficient statistic for\nthe Markov chain used to model the (unobservable) sampled data, one\nof the algorithms developed is Wald's celebrated SPRT.\nThe detection algorithms developed can be partitioned in two natural\nways:\n(i) By sampling rate (100 or 200 seconds).\n(ii) According to whether grouping information is used.\n\nThe algorithms which do not use grouping information are applicable\nto all trunks (one way or two way) independent of the type of switching\nmachine used. A version of one of these individual trunk algorithms is\ncurrently in use in leAN, testing trunks on 1XB, XBT and step-by-step\n* See Appendix A.2.1 of Wald's original treatise (Ref. 11).\n966\n\nTHE BELL SYSTEM TECHNICAL JOURNAL, JULY-AUGUST 1977\n\nswitching machines. The algorithms that exploit grouping information\ndetect killers more quickly but are tailored to a specific switching machine. A \"group\" algorithm of this type is currently being used to test\ntrunks associated with 5XB switching machines.\nIn the course of this study several problems of independent interest\nwere studied. These include:\n(i) The server covariance in a M/G/l-10ss and GI/M/l-10ss system.\n(ii) The structure of the likelihood statistic that arises in testing\n\nsimple hypotheses characterized by a binary valued Markov chain.\n(iii) The occupancy of nonidentical trunks in a random-selection\n(Markovian) loss system.\nThe major conclusion in this study is, of course, that accumulated\nswitch-count and state-transition data on individual trunks (based on\nsampling intervals on the order of a normal holding time) can be used\nto reliably detect abnormally short holding time trunks. Moreover the\n(near) optimal sequential detection algorithms using this accumulated\ndata are easily exhibited, simple in structure, and intuitively appealing.\nVIII. ACKNOWLEDGMENTS\n\nVarious stages of this study benefited from discussions with A. E.\nEckberg, R. L. Franks, S. Horing, E. J. Messerli, and T. E. Rutt.\nAPPENDIX A\nSensitivity of the Transition Probabilities to Modeling Assumptions\n\nTo get an idea about the sensitivity of the algorithms to some of the\nmodeling assumptions, the transition probability P1,o = P(Xt+T = O/Xt\n= 1) was studied for the following two cases:\n(i) M/G/l-10ss, where the service distribution function F(\u00b7) is the\nmixed exponential given by\n\nF(t) = 1 - d1e- x1t - d 2e- x2t\n\nt ~0\n\n(ii) GI/M/l-10ss, where the arrival process is the switched-Poisson\nprocess 8 commonly used to model overflow traffic.\n\nBecause the methods used to obtain P1,o for these two models differ,\nwe discuss these models separately.\nA.1 The M/G/1-loss model\n\nAn observer viewing the server in an M/G/l-10ss system sees an alternating sequence of busy and idle intervals. The busy intervals are\ndistributed according to some distribution F(.) and are independent.\nTRUNK-DETECTION ALGORITHMS\n\n967\n\nThe idle intervals are exponentially distributed with mean A-1 (A = mean\narrival rate) and are independent. Thus, the sequence of alternating busy\nand idle intervals constitutes an alternating renewal process. In this\ncontext, the conditional probability\nP 1,o = P(Xt+T = O/Xt = 1),\n\n(59)\n\nwhere\nI\nx - {\nt 0\n\nif server is busy at epoch t\nif server is idle at epoch t\n\nhas already been studied,18 and we have the following result:\n\nTheorem 4: Consider an M/G /1-10ss system in equilibrium with a service time distribution F(t) having Laplace transform f* (s). If P~,o(s)\ndenotes the Laplace transform of P 1,o( T), then we have\nP* (s) 1,0\n\n-\n\nJl[I - f*(s)]\nsis + A[I - f*(s)]l\n\n(60)\n\nwhere A and Jl are the mean arrival and service rates, respectively.\nProof: See Section 7.4 of Ref. 18 [t;(s) = A/S + A andf~(s) = f*(s)].\nFor the mixed exponential service time distribution mentioned above\nlet\nand\nX2 =\n\n2Jl(I - d),\n\n0 ~ d ~ 1.\n\nIf T is distributed according to this two-parameter (Jl,d) family of distributions, then\n(i) E(T) = Jl- 1\u2022\n\n(ii) var(T) = Jl- 2\n\n(2 ~ 0), where 0= 4 d (1 - d).\n\n(iii) c(T) = (J(T) =\nE(T)\n\n(2 -0 0) 1/2.\n\nThus, the mean is fixed at Jl- 1 and the coefficient of variation satisfies\nc ~ 1, with equality occurring when 0 = 1, which corresponds to the\nM/M/I-Ioss system.\nEquation (60) is easily inverted for this family of mixed exponential\ndistributions, obtaining the following result:\nP 1,o(p, T) = (1 - p) +\n\nrl + 0\nr2 + 0\ne rrllT +\ne r2llT ,\nr1 (rl - r2)\nr2(r2 - r1)\n\n(61)\n\nwhere\n968\n\nTHE BELL SYSTEM TECHNICAL JOURNAL, JULY-AUGUST 1977\n\nrl = -\n\na+2) + [ (I - 0)(1 + a) + (a)2]112\n\"2\n(-2-\n\nr2 = -\n\n(a ; 2) - [ (1 - 0)(1 + a) + (~rr\no= 4d (1 - d),\n\na = -pI-p\n\nand p = >../(>.. + 11) is the mean occupancy of the server.\nIn Fig. 5, P 1,O(p,T) [eq. (61)] is plotted vs p for several different values\nof c (c = 1, 1.5, and 2) assuming\n(i) 11- 1 = 180 seconds\n(ii) T = 200 seconds.\n\nAlso shown is a plot of P 1,o vs p for a killer trunk with r = 10 [11 in (61)\nis replaced by rll]. The normal trunk PI 0 characteristic with c = 1 corresponds to the M/M/l-loss system.\n\nA.2 The GIIMI1-loss model\n\nThe covariance function R(\u00b7) for the GI/M/l-loss model with a\nswitched Poisson arrival process has the form:\n(62)\nwhere the coefficients Ci and the exponents Wi are messy expressions\ninvolving the three switch parameters w, 'Y, and>\" (Ref. 8) and the mean\nservice rate 11. The derivation of this covariance function is straightforward but tedious and is therefore omitted. (For the switched Poisson\narrival prccess, the Markovian state equations can be solved for\nP(Xt,Xt+T)' where Xt = state of server at epoch t.) Our purpose here is\nto explain how eq. (62) was used in generating Fig. 4.\nIf p is the mean occupancy of the server (p = E(xd) and a is the offered\nload in a GI/M/l-loss system, then it is easy to show that the peakedness6\nz satisfies\n\nP)\n\n1z=a ( p-.\n\n(63)\n\nFor GI/M/l-loss system the call congestion is \u00a2(Il) and is related to the\ntime congestion (p) by a(1 - \u00a2(Il)) = p. So using z(J1) = 1/[1 - \u00a2(J1)] a yields the result. 2 (\u00a2(.) is the L.S. transform of the interarrival time\ndistribution.) Therefore, specifying p and z uniquely determines a.\nHence, with a and z known, we obtain the equivalent random parameters\nand use the three-moment match to obtain the switch parameters (see\nTRUNK-DETECTION ALGORITHMS\n\n969\n\nRef. 8). Using this procedure, we obtain R(r) vs p paramete'rized by z.\nEquation (1) then yields Pl,o.\nAPPENDIX B\nThe Likelihood Statistic Based on the Observable Data\n\nFor ease of derivation, the likelihood statistic derived in Section 4.2\nwas based on the raw data Xm = (XI,\"\u00b7 \u00b7,x m) rather than on the observable\ndata [t(m),n(m)]; t(m) and n(m) are defined in Section 2.1. We will now\nstudy i m (t,n) and verify that the two statistics differ only in their endeffect terms. We will also examine the end-effect term based on t(m) and\nn(m) and show how it \"tracks\" the end-effect term based on Xl and\nXm\u00b7\n\nWe begin by expressing the probability of Xm = (Xl,\u00b7 \u00b7,x m ) in terms\nof t(m), n(m), Xl, and Xm:\nLemma 3: If IXi} is a binary state stationary Markov chain with transition probabilities Po, 1 and Pl,o and if Xm = (Xl,\u00b7 \u00b7,x m ), then\nP(xm ) = P(Xl) X Q(Xl,X m ) X Pt;J(l - P l ,0)n-(t/2)\nX Pt/2(1\n- P 0,1 )m-n-(t/2) ,\n0,1\n\n(64)\n\nwhere\n1-x m )/2 p-(x 1+x m )/2 p-(x 1-x m )/2 p(xJ+x m )/2+1\nQ( X b Xm ) = p(x\n1,0\n1,1\n0,1\n0,0\n\n(65)\n\nand\nP (X 1) =\n\n{p\n\n1- p\n\n~f Xl = 1 .\nIf Xl = 0\n\nProof: This result is obtained from lemma 2 using eqs. (12a) and\n\n(12b).\nFor convenience, we introduce the following notation\n\n(ii) g (~;m - n,Po,l) =\n\npUr(1 - P O,1)m-n-t/2.\n\n(iii) Px,y(t,n) = P(t(m) = t,n(m) = n,Xl = X,Xm = y).\n970\n\nTHE BELL SYSTEM TECHNICAL JOURNAL, JULY -AUGUST 1977\n\n(iu) SX,y(t,n) = number of binary m-tuples satisfying t(m) = t, n(m)\n= n, x I = x, and Xm = y.\n\nThus, we can write\nI\n\nI\n\nP(t(m) = t,n(m) = n) = L 2: PX,y(t,n)\nx=o y=o\n\n(66)\n\nand\nPx,y(t,n) = f (~;n'PI'o) g (~;m - n,Po,I) P(x)Sx,y(t,n)Q(x,y).\n\n(67)\n\nEquations (66) and (67) imply that\nP(t, n(m) = t, n(m) = n}\n\n{t\nt P(x)SX,y(t,n)Q(x,y)} (68)\nx=Oy=O\n\n= f (!;n,PI,o) g (!;m - n,Po,I)\n\n2\n\n2\n\nand therefore it is easily seen that:\n... (\n\n)_ I\n\nP*(t(m) = t,n(m) = n)\n\nem t,n - og P(t(m) = t,n (m) = n )'\n=\n\n[a~-an] + [(J~-b(n-m)] +E(t,n),\n\n(69)\n\nwhere\n\nE(t,n) = log\n\n{\n\nI\n\nI\n\nx~Oy~o p*(x)sx,y(t,n)Q*(X,y)}\n.\nI\n\n(70)\n\nI\n\n2: 2: P(x)Sx,y(t,n)Q(x, Y)\n\nx=o y=o\n\nComparing eqs. (70) and (22), we see that im(t,n) and i(xm) differ\nonly in their respective end-effect terms. The following result is perhaps\na bit surprising:\nLemma 4: e(t,n) = f(x m) if t is odd.\nProof: todd ==> Xl :;6: Xm ==> e(O,l) = e(l,O) = a + b/2 (see eq. (22b)). todd\n==> So,o(t,n) = SI,I(t,n) = so E(t,n) for t odd may be written:\n\n\u00b0\n\n(1 - p)So IQ*(O,l) + pSI oQ*(l,O)\n,\nE( t n ) = I o g '\n,\n(1 - p)So,IQ(O,l) + pSI,oQ(l,O) .\n\nNow using (4) E(t,n) for t odd can be manipulated into the following\nform\nE(t,n) = log (1 - p)So,IQ*(O,l) + pSI,oQ*(l,O) .\n(1 - p)So,IQ(O,l) + pSI,oQ(l,O)\nTRUNK-DETECTION ALGORITHMS\n\n971\n\nbut PO,t/P 1,0 = P~,IIP~,o = p/1 - p which completes the proof.\nIf t is even then Xl = X m ,\ne(O,O) = b\n\nand\ne(l,l) = a.\n\nFor even t, eq. (70) can be written as\n\nE( t,n ) -- I og {\n\n8 0 ,0 + 8 1,1\n\n)8 +( 1 - P )8\n(11- POI\nP\n\np\n\n0,0\n\n10\n\n}.\n1,1\n\nThus, for even t, E(t,n) is a complicated function* of t and n. Note\nhowever that E(t,n) ~ 0 and\na\nE(t,n) = { b\n\nif 8 0 ,o(t,n) = 0\nl'f 8 1,1 (t,n ) = 0\n\nIt can be shown that\n\nt\nn--\n\n81,l(t,n) = _ _ _2_\nSO,o(t,n)\n\nt\n\nm -n--\n\n2\n\nif (t,n) is such that 81,1 and 8 0 ,0 are nonzero.\n\nAPPENDIX C\nThe End Effect EI/(xim;xim+1)1\n\nThe end effect\nEII(xim;xim+dl = H(Xim+l) - H(Xim+t/Xim),\n\nwhere\n\nand\nH(Xim+1), H(Xim+t/O) and H(Xim+t/1)\n\nare the binary entropy function ,71 (x) evaluated at p, P O,1 and P 1,o, respectively (7I(x) = -x log x - (1 - x) log (1 - x), 0 ~ x ~ 1).\nTable I exhibits EII(xim;xim+1)1 and Eli(xm)l as a function of the\ntrunks occupancy p-for a normal trunk, with a single-hour accumula972\n\nTHE BELL SYSTEM TECHNICAL JOURNAL, JULY-AUGUST 1977\n\nTable I -\n\nEnd effect as a function of occupancy\n\n(T = 100 seconds)\n\n(T = 200 seconds)\n\np\n\nEIl(xim+ l;Xim)\\\n\nElf(xm}l\n\nEII(xim+l;xim}1\n\nElf(xm}l\n\n0.10\n0.20\n0.30\n0.40\n0.50\n0.60\n\n0.04\n0.05\n0.04\n0.03\n0.02\n0.01\n\n-1.36\n-1.60\n-1.50\n-1.21\n-0.84\n-0.47\n\n0.01\n0.01\n0.01\n0.01\n0.00\n0.00\n\n-0.22\n-0.20\n-0.15\n-0.09\n-0.04\n-0.01\n\ntion period (m = 36 and 18 for the 100- and 200-second sampling options,\nrespectively). The M/M/l-loss model is used with I/J.l = 180 seconds. It\nis clear that the mean end effect is negligible compared to the mean\nstatistic update.\n-\n\nAPPENDIX D\nOccupancy Formulae for a Random-Selection Loss System\n\nTheorem: Consider an N server Markovian loss system with random\nselection of idle servers and\n(i) N - 1 servers with mean service rate J.l.\n(ii) 1 server with mean service rate rJ.l (r > 0).\n(iii) Mean arrival rate A.\nLet Pr and P; denote the mean occupancy of the servers with mean\nservice rates J.l and rJ.l, respectively, and let B denote the blocking (call\ncongestion). Also let _\n\n~-\n\nBe\n\n~\n\n\\\n\n, ;!:5-~'e\\--------'-----.yp\n\nY'\n\nIY,\n\n_ _ __\n\nz'\n\n'\n\n-~\n\n~\n\n\\\n\"\n\nREF LECTOR AXIS\n\nI\n\n~---------~----------J\nFig. I-Geometry of offset reflector.\n\ndeduced. In Section III numerical calculations of practical examples are\ngiven.\nIn the appendix the previously unexplained measured polarization\nrotation* of a parabolic grid 5 is calculated. This example is given here\nas experimental evidence of agreement with the predicted rotation of\nradiation from a polarization grid.\nII. CANCELLATION OF POLARIZATION ROTATION\n\nLet us first briefly review the salient properties of the cross-polarized\nfield in the aperture of an offset paraboloid as shown in Fig. 1. For a\nbalanced feed radiation,\nCOS \u00a2'\n\nEf = F(8', \u00a2')\n\n()' 1=\n[\n\nsin \u00a2'\n\nsin ~'] exp(-jp)\n\u00a2'\n\np\n\n,\n\n(1)\n\ncos \u00a2'\n\nwhere (p, 8', \u00a2') are spherical coordinates with respect to the z' axis and\n(1)', \u00a2') are the corresponding unit vectors. Since the reflected field from\nthe paraboloid is\n\n* The design was initially proposed by Comsat for the Comstar satellite.\n978\n\nTHE BELL SYSTEM TECHNICAL JOURNAL, JULY-AUGUST 1977\n\nwhere n is a unit vector normal to the reflector surface. The principal\nand cross-polarized field components in the reflector aperture can be\nwritten respectively:1\n\nxp\n\nM = E r .\" =\n\nYP\n\nF(()', \u00a2') [. 0' . 0\n,. 2\nsm sm 0 cos 1> - sm \u00a2'\ntp\n\n. (cos ()o + cos ()') - cos 2 \u00a2'(1 + cos ()o cos ()')]\n\n(2)\n\nYP\nF(()',\u00a2') [. 0' . () . ,\nN = E r .\" = =t=\nsm sm 0 SIn \u00a2\nXp\ntp\n\n- sin \u00a2' cos \u00a2'(1 - cos 0')(1 - cos ()o)],\n\n(3)\n\nwhere t = 1 + cos 0' cos 00 - sin 0' sin ()o cos \u00a2', M2 + N2 = F2j p2, and N\nvanishes when 00 = o. The offset angle ()o is between the feed axis and the\nreflector axis. The sign combination in eqs. (2) and (3) indicates that the\nrotation of the polarization vector due to offset in a paraboloidal aperture\nhas the same magnitude and is in the same direction as illustrated in Fig.\n1 for any orientation of the incident linear polarization. The projection\nof the intersection of a circular cone (with vertex at the focus) and the\noffset paraboloid onto the xpYp plane is a circular aperture with center\nXc = ---'----.::....--\n\n2{ sin ()o\ncos ()o + cos ()c\n\n(4)\n\n2{ sin Oc\ncos ()o + cos ()c '\n\n(5)\n\nand radius\na=----=-----=------\n\nwhere Oc is the half angle of the cone. Equations (4) and (5) will be used\nlater to obtain the relations in eqs. (12) and (13).\nRadiation from transmitting and reflecting wire grids can be obtained\nby magnetic and electric current sheet models, respectively. The principal and cross-polarized components are 4\np = -C [1 - cos 2 \u00a2' (1 - cos 0') - sin ()' cos \u00a2' tan 0]\n\n(6)\n\nX = \u00b1C[sin \u00a2' cos \u00a2'(1 - cos 0') + sin ()' sin \u00a2' tan 0],\n\n(7)\n\nwhere C is a proportionality constant, 0' and \u00a2' are the spherical coordinates of the feed (z') axis, and 0 is the angle between the conducting\nwires and the x'y' plane as shown in Fig. 2; the expressions inside the\nbrackets are identical to those of eqs. (9) and (10) in Ref. 4, provided one\nmakes the following substitutions: \u00a2' = \u00a2 - 90\u00b0 and 0 = 90\u00b0 - 'Y. The\nchanges of notation are made for the purpose of comparison with eqs.\n(2) and (3). The upper and lower signs in eq. (7) correspond to the\ntransmitting and reflecting cases. The orientations for the transmitting\nPARABOLOID ANTENNA\n\n979\n\nXI'\n\n\\\n\nX'\n\n\\\n\\\n\\\n\n\\\n\nTRANSMITTING---- y,-7'&--r---I,,----------l~Zp _ _ _ _ ~\nPOLARIZATION\n\"\nVERTEX OF\n\",- REFLECTING\n\nPARABOLOID\n\nPOLARIZATION\n\nPOLARIZATION GRID WITH\nCONDUCTING WIRES\nPARALLEL TO THE x' z' PLANE\n\nFig. 2-Configuration for cancellation between polarization rotations of an offset paraboloid and a polarization grid.\n\nand reflecting polarizations together with a given grid geometry are\nshown in Fig. 2 where the conducting wires are parallel to the plane of\nthe figure.\nOne notes that the leading terms, which contain first power of ()', in\neqs. (3) and (7) have the same sinusoidal dependence on ()' and \u00a2'. Furthermore, the sign combination in eqs. (6) and (7) indicates that the\ntransmitting and reflecting orthogonal polarizations rotate in the same\ndirection, opposite to the rotation in the aperture of an offset paraboloid.\nLet us take the first-order approximation-i.e., cos ()' ~ i-in eqs. (2),\n(3), (6) and (7), but sin ()' is retained. Then the cross polarization in eq.\n(3) normalized with respect to eq. (2) cancels that in eq. (7) normalized\nwith respect to eq. (6):\n)(]V\nP M\n\n.\n\n()o\n\n- + - = 0 If 0 = - .\n2\n\n(8)\n\nPolarization rotation of the radiation from a wire grid, as predicted\nby eqs. (6) and (7), also explains data measured using a cylindrical re980\n\nTHE BELL SYSTEM TECHNICAL JOURNAL, JULY-AUGUST 1977\n\nflector made of a curved wire grid. The report on this experiment5 misinterpreted the polarization rotation as a consequence of diffraction and\nthe offset geometry. A comparison between the calculated and measured\npolarization rotations of this case is given in the Appendi~.\nIII. NUMERICAL EXAMPLES\n\nSince the cancellation of polarization rotation discussed in the preceding section only eliminates the leading terms, it is of interest to determine the residual cross polarization. Assuming that the offset reflector\nis located in the far zone of the radiation from a wire grid, as'shown in\nFig. 2, the principal and cross-polarized components in the reflector\naperture can be written\nP = F(t9')[l - cos 2 \u00a2p (l - cos 8p ) + sin 8p cos \u00a2p tan (0]\n\n(9)\n\nX = =rF(8') [sin \u00a2p cos \u00a2p (1 - cos 8p ) - sin 8p sin \u00a2p tan (0], (10)\n\nwhere F(8') is the feed-radiation pattern and\n8' = COS-I [cos 8p cos 80 + sin 8p sin 80 cos \u00a2p].\n\n(11)\n\nThe above equations are simply a decomposition of the grid radiation\ninto the two orthogonal components of a balanced feed whose axis\ncoincides with the paraboloidal axis. The expressions inside the brackets\nof eqs. (9) and (10) are of the same form as those of eqs. (6) and (7); but\n8p and \u00a2p are the spherical coordinates with respect to the paraboloidal\n(zp) axis instead of the feed axis, and (0 = (80 - 0) is the angle between\nthe conducting wires and the xPyp plane, as shown in Fig. 2.\nTo relate eqs. (9) and (10) to the normalized aperture coordinates r\n= (Pala) and \u00a2a, the following expressions can be obtained with the aid\nof eqs. (4) and (5):\n8 = 2 tan-I\n\n[v(r sin 8e sin \u00a2a)2 + (sin 8 + rsin 8e cos \u00a2a)2 ]\n0\n\ncos 8e + cos 80\n\np\n\n(12)\n\u00a2p = tan\n\n-I [\n\nr sin 8e sin \u00a2a\n]\n.\nsin 80 + r sin 8e cos \u00a2a\n\n(13)\n\nNumerical examples of several combinations of parameters (80 , 8e and\n(0) have been calculated for the principal and residual cross-polarization\ncomponents from eqs. (9) and (10). The feed pattern has a gaussian shape\nwith 10-dB taper at the edge of the reflector. The principal polarization\nis close to unity (0 dB) around the center of the reflector aperture. The\nmaximum, calculated, residual cross polarization is given in Table I for\na number of examples. Fig. 3 shows a plot of both principal and cross\npolarizations for the case 80 = 50\u00b0, 8e = 20\u00b0, and (0 = 25\u00b0. Only half of the\nPARABOLOID ANTENNA\n\n981\n\nTable I 00\n\nCross Polarization in the aperture of an offset reflector\n\n(Deg)\n\nMax. Residual Cross\nPol. With Grid\n(dB)\n\nMax. Cross Po1.6\nBalanced Feed\nWithout Grid (dB)\n\n25\n23\n27\n30\n30\n45\n45\n\n-38.6\n-36.4\n-36.1\n-38.0\n-30.9\n-34.3\n-40.5\n\n-24.0\n-24.0\n-24.0\n-22.5\n-18.0\n-17.5\n-20.0\n\n0('\n\nf\n\n(Deg)\n\n(Deg)\n\n50\n50\n50\n\n20\n20\n20\n20\n30\n20\n14\n\n60\n60\n90\n90\n\naperture needs to be shown for each polarization because of the symmetry. The maximum residual cross polarization in this case is -38.6\ndB, reduced from -24 dB for the same reflector aperture illuminated\nby a balanced feed without a polarizer. Keeping the same set of parameters, 00 = 50\u00b0 and Oc = 20\u00b0, the calculated residual cross polarization\nPRINCIPAL POLARIZATION ( d B ) - \\ -\n\nCROSS POLARIZATION (dB)\n\nFig. 3-Relative amplitude levels in the aperture of an offset paraboloid. 00 = 50\u00b0, Oc\n\n= 20\u00b0, f = 25\u00b0.\n982\n\nTHE BELL SYSTEM TECHNICAL JOURNAL, JULY-AUGUST 1977\n\nbecomes -36.4 dB for E = 23\u00b0 and -36.1 dB for E = 27\u00b0. These results\nindicate that the residual cross polarization is not overly sensitive to a\nslight departure from the optimum orientation of E = 00 /2.\nThe examples for 00 = 60\u00b0 and E = 30\u00b0 show residual cross polarizations of -38.0 dB and -30.9 dB for De = 20\u00b0 and 30\u00b0, respectively. The\nsecond-order terms are not quite negligible at Oe = 30\u00b0; however, the\ncancellation of cross polarization appears to be significant.\nIV. DISCUSSION\n\nIn view of the residual second-order (1 - cos 0') terms, the half-cone\nangle of the reflector subtended at the focus should not exceed about\n20\u00b0 in order to take full advantage of the cancellation. If the reflectors,\nsuch as in an offset cassegrain configuration, do not cause significant\ncross polarization, the conducting direction of a polarization diplexing\ngrid should be oriented to avoid introducing any polarization rotation,\nas discussed in Ref. 4.\nWhen 00 - Oe is less than about 30\u00b0 and E = 0 = 00/2, the feed horn\nassociated with the polarization reflected from the grid will introduce\nsome blockage, as shown in Fig. 2. The blocking problem can be eased\nby using a smaller value of E. This practical difficulty may prevent optimum orientation of the grid wires for reflectors of small offset angle,\nand hence reduce the effectiveness of the cancellation. The practical\napplication of this scheme should indeed lie in reflectors with large offset\nangle.\nThe expression E = 00/2 implies that the grid wires are approximately\n. parallel to the tangent plane at the center of the offset reflector. One\nnotes the similarity between this case and a symmetrical small-coneangle paraboloid illuminated by a grid-covered feed.\nACKNOWLEDGMENT\n\nThe author is indebted to M. J. Gans and D. C. Hogg for valuable\ndiscussions, and to Mrs. Diane Vitello for assistance with the computation.\nAppendix\nPolarization Rotation of an Offset Parabolic Grid\n\nAn offset cylindrical-reflector system fed by two line sources of pillbox\ntype (as shown in Fig. 4) was proposed 5 as a dual-polarized antenna with\nan elliptically shaped coverage pattern. The reflecting system consists\nof a vertically polarized grid attached to the surface of a parabolic cylinder, the front surface of the grid having the same curvature as the cylindrical reflector. The measured data 5 showed excellent orthogonality\n(within 1\u00b0) between vertical and horizontal polarizations over the whole\nPARABOLOID ANTENNA\n\n983\n\nBEAM DIRECTION\n\n... -\n\n_ - OFFSET\nPARABOLIC\nCYLINDER\n\nPOLARIZED GRID\n\nGRID-- __\nFOCAL LINE\n\nt,\n\nx\n\n'/\n\nVERTICALLY - - POLARIZED\nLINE SOURCE\n\n---\n\nz\n/\n\n~~//j\\\n\nI,\",\n\\\n\\\n\n--PARABOLIC\nCYLINDER\nFOCAL LINE\n\n.__--GRID\nVERTEX\n\n+\"\"'-- PARABOLIC\nCYLINDER\nVERTEX\n\nI\nHORIZONTALL Y\nPOLARIZED\nLINE SOURCE\n\nFig. 4-Configuration of a dual-polarized cylindrical reflector antenna (Ref. 5).\n\n6.8\u00b0 X 3.4\u00b0 (3 dB) elliptical beam. However, significant polarization\nrotations, in the same direction for both polarizations, were observed.\nMaximum rotations of about 2\u00b0 occur on the major axis (xz plane) of the\nhalf-power ellipse of the beam. No adequate explanation was given for\nthis measured polarization rotation. Here we explain the rotation using\nelectric and magnetic current sheet models for the grid.\nThe first-order approximation of polarization rotation by a wire grid\nis simply sin () cos \u00a2 cot 'Y (eq. 7 in Section II or eq. (10) in Ref. 4), where\nois the angle off the beam axis, cos \u00a2 is unity in the xz plane of maximum\nrotation, and 'Y the angle between the conducting wires and the beam\naxis. Since the wires of the curved grid have a variable direction, the\nrotation ~ in the plane of maximum rotation can be obtained by averaging cot 'Y over the parabolic curve, y2 = 4{z.\n.\nsin () f E dz V (dy)2 + (dz)2\nsm()\ndy\n~ = - - f E cot 'Y ds = ---;:-=-~=:::::::::======:;--fEds\nfEv(dy)2+(dz)2.\n\n(14)\n\nwhere E is the aperture field distribution. Let u = y/2{, eq. (14) be\ntransformed into\n984\n\nTHE BELL SYSTEM TECHNICAL JOURNAL, JULY -AUGUST 1977\n\nFig. 5-Measured angles of nominal vertical and horizontal polarizations around -3-dB\npattern contours of 6.8 0 X 3.4 0 for a dual-polarized cylindrical antenna with a parabolic\ngrid; + indicates locations of measurement.\n\nr\n\nsin ()\n\n1\n\nE Vf+U2 u du\n\nJO.1763\n\n(15)\n\n~=-----------1\n\nr\n\nE Vf+U2du\n\nJO.1763\n\nwhere the upper and lower limits of integration are obtained from y =\n2f tan 1/;/2 with 1/; = 90\u00b0 and 20\u00b0, respectively. ~ is not sensitive to the\naperture distribution. Numerical calculation gives ~ = 0.61 sin () for both\ncases when E is assumed to be uniform and when E has a 10-dB edge\ntaper-i.e., when\nE = -0.396 + 4.746\n\n(;f) - 4.034 (;f)\n\n2.\n\n(16)\n\nThe quadratic form has been chosen to perform the integration in closed\nform. When () = 3.4\u00b0, ~ = 0.0362 rad = 2.07\u00b0; agreement between this\ncalculated value and Wilkinson's measured rotation shown in Fig. 5 is\nindeed very good.\nFurthermore, eqs. (6) and (7) in Section II indicate that the transmitted and reflected orthogonally polarized fields from the grid rotate\nin the same direction, just as in the measured rotations. The planes of\nmeasured maximum and null rotation also agree with the predictions.\nSince the two polarizations have the same sense of rotation, orthogonality\nis preserved. However, if this rotation occurs in the feed radiation,\nnonorthogonal elli ptically polarized radiations from the reflector will\nresult.\nREFERENCES\n1. T. S. Chu and R. H. Turrin, \"Depolarization Properties of Offset Reflector Antennas,\"\nIEEE Trans. Ant. Propag., AP-21 (May 1973), pp. 339-345.\n\nPARABOLOID ANTENNA\n\n985\n\nCopyright \u00a9 1977 American Telephone and Telegraph Company\nTHE BELL SYSTEM TECHNICAL JOURNAL\n\nVol. 56, No.6, July-August 1977\n\nPrinted in U.S.A.\n\nTen Years of Power Aging of the Same Group\nof Submarine Cable Semiconductor Devices\nBy A. J. WAHL\n(Manuscript received January 18, 1977)\n\nThe active devices in the first Bell System transistorized submarine\n.cable system (SF) are unpassivated, diffused-base, germanium transistors and oxide-passivated, silicon diodes. At the date of this writing\nthese devices have accumulated over 550 million device hours of powered operation in service and on the aging rack without failure or impaired device performance for a demonstrated failure rate of less than\n0.00045 percent per thousand hours (4.5 FITS) with 90-percent confidence. This paper reports details of the behavior of 500 of these devices\nthat have reached ten years of controlled power aging. The overall results indicate that initial reliability objectives are being achieved and\nthat the semiconductor devices should not be expected to limit the\ndesired life span of SF submarine cables.\nI. INTRODUCTION\n\nIn the initial stages of the project, the decision to use germanium\ntransistors in the first Bell System transistorized submarine cable was\na rather bold gamble to take advantage of their then superior frequency\ncapability while also attempting to mitigate any reliability inferiority\nto silicon transistors. When the decision was made, in the time period\nof 1960-61, silicon transistors were clearly the wave of the future and,\nalthough still inferior to germanium transistors in frequency capability,\nhad already indicated their reliability superiority. Nevertheless, the\nresults reported here, together with the results of regular aging and actual\nservice experience thus far, offer rather convincing evidence that the\ndesired reliability objectives are being achieved. The first submarine\ncable using these transistors, a relatively short cable with 136 repeaters,\nhas been in service over eight years. A transatlantic cable with 363 repeaters has been in service nearly seven years. No semiconductor device\nfailure nor degradation toward failure has yet been observed in any of\nthe systems that have no redundancy and in which the failure of even\n987\n\n42r-----------------------------------------~----~\n\n~r\n\n40\n\nl?\n\nZ\n\nl?\n\nr'\n\n__~l___~L__I~~I__~I___~I~I__~I___~I__~I~\n6\n12\n18\n24\n30\n36\n\nO~~~\n\no\n\nBEFORE AGING\n\nFig. 20-Reverse leakage current in nA at 8 V for L2320 diodes-before and after 10\nyears of aging at 2 rnA in breakdown region.\n\ncurrent levels in each direction during long-term power aging.\nFigure 18 shows the behavior of the forward voltage of one hundred\nL2318 diodes in one direction and at one current level across ten years\nof power aging. No discernible aging can be seen. The behavior of the\nother forward voltages is not shown because they look no different.\n4.6 L2320 diodes\n\nThe L2320 diodes, coded as 467B, are silicon pn junction limiter devices used in the third stage of the amplifier of the SF repeater. Operation\nis at 2.0 rnA in the breakdown region, and the devices are aged under\nthese power conditions.\nFigure 19 shows the behavior of the breakdown voltage of one hundred\nL2320 diodes across ten years of power aging. No discernible shift in this\nparameter is evident.\nIn Fig. 20, a definite upward shift in the reverse-leakage currents can\nbe seen. This is the one case where a significant amount of scatter is\nencountered in the magnitudes of the parameter shifts among the\nhundred devices. The data suggests that percent change rather than\nPOWER AGING\n\n1003\n\n0.915 r - - - - - - - - - - - - - - - - - - - - - - - - - - - - ,\n\n0.905\n\n0.860\n\nLINE OF NO CHANGE---_Y.\n\n/\n\n/.\n\n/-\n\nCJ\n\n(Je/-'\n\nz\nG 0.850\n _/) is con- \nstrained, serves as a proving ground for theoretical explorations of the \nrelative efficacy of proposed techniques. Specific methods have been \ndiscussed as candidates for improving efficiency. Three candidates are \nHigher-Dimensional Constellations (HDCs),\u2019 Ungerbock\u2019s Trellis \nCoding (UTC),? and Faster Binary Signaling (FBS).? Both HDC and \nUTC have lent themselves to analysis and their significant value over \nthe QAM method has been established. Moreover, we are beginning \nto understand the relative value of UTC over HDC.* On the other \nhand, the effectiveness of FBS has hitherto remained a mystery. In \nRef. 5* some theoretical results on FBS for some special pulses are \npresented but the relative effectiveness issue is not settled.\n\nTo understand the FBS method, consider the elementary QAM \nmethod, 4-PSK (phase-shift keying), in a situation comfortably meet- \ning a stringent probability of error (P.) constraint. If the bit rate \nrequirement increases it can be met without expanding bandwidth by \nincreasing the number of points in the QAM constellation. FBS is a \nnatural alternative means of transmitting at higher bit rates. In FBS, \none fixes the constellation at four points and increases the symbol \nrate as much as necessary. Maximum Likelihood Sequence Detection \n(MLSD) is employed to overcome the consequent Intersymbol Inter- \nference (ISI) in the best way possible (see Refs. 6 through 8 for \ntreatments of MLSD). The minimum separation between distinct \npoints in the planar FBS constellation is greater than for the QAM \nconstellation. One might say FBS trades freedom from ISI for added \nnoise immunity and then MLSD is used to mitigate the ISI.\n\nWith the efficacy of FBS unknown, it looms as a possibly competi- \ntive technique. Here we help the process of evaluating the field of \ncandidate methods for moving beyond the capabilities of QAM by \nshowing how to analyze FBS. We show by examples that FBS is, at \nbest, of marginal value relative to QAM, even if one allows for \nimplementation capabilities far beyond those of forthcoming proces- \nsors. Specifically, we allow for complexity of up to 10\u00b0 states. Given \nthe strides in processor technology in the last few decades and the \nimminent hardware advances, a number like 10\u00b0 is chosen to avoid \noutdating of this paper for a long time. Such prudence is needed. \nIndeed, the analysis that follows leaves open the possibility that FBS\n\n* The terminology \u201cfaster binary signaling\u201d is not used in [A] and [M]. In [M] the \nterm \u201cfaster than Nyquist signaling\u201d is used.\n\nwould offer substantial improvement over QAM if complexity were \nnot a consideration. Moreover, one must also consider that fast detec- \ntors could go far beyond conventional MLSD in processing efficiency.?\n\nThe data transmission medium is represented here in the simplest \nidealized form as a lossless characteristic with additive white Gaussian \nnoise. The channelization is shown in Fig. 1. On each channel the \ntransmitted signal is subject to an average power constraint and it is \nassumed that, for all the systems that we discuss, the average trans- \nmitted power is much greater than the noise power. [The ramification \nof this high signal-to-noise ratio (s/n) assumption is discussed in \nSection III.] In the analysis that follows, we assume that the channels \nare isolated from each other in that it is not permitted to mitigate \nAdjacent Channel Interference (ACI) through some elaborate scheme \nrequiring coordination among channels. It is required that R bits per \nsecond be transmitted over the channel. Whatever the form of modu- \nlation used, soft maximum likelihood sequence detection is employed \nat the receiver.\u2019\u00b0\n\nIt is because of the current prominence of QAM in applications that \nthe work here is presented with QAM as the benchmark method. Since \na flat channel transfer characteristic is assumed, it is trivial to relate \nresults to the equivalent baseband channel representing a QAM rail. \nWe use M = m? to denote the number of points in the QAM constel- \nlation. So, constellations with 16, 64, 256, and 1024 points correspond \nto FBS operating at 2, 3, 4, and 5 times the conventional rate. We \nelected to work with square QAM constellations even though certain \ndepartures from such constellations yield superior performance.\u2019 The \nreason for our choice is that we want to analyze FBS in isolation and \nthe aforementioned departures can be viewed as the first step in using \nthe HDC method. Finally, we employ the harmless expediency of \ndealing with M as if it is a continuous variable in our calculations and \nin some of our graphs. When M is a positive integer that is not a\n\nperfect square, one can find a two-dimensional constellation that \nrealizes the situation covered by the analysis.\n\nThroughout we will assume that the standard QAM method is \nmeeting a P, requirement (107\u00b0 or less). When we compare alternatives \nto the QAM method, we will associate primed variables with parame- \nters of the non-QAM system where needed to avoid ambiguity.\n\nThe generic system structure depicted in Fig. 2 is interpreted here \nfor the special case of FBS. For FBS the binary data are blocked into \nsuccessive 2-bit words. A pair of independent, synchronous, delta \nfunction streams are formed using the two bits to randomly sign the \npair of delta functions that are input to the pair of baseband filters. \nThe baseband filters nominally cut off at W cycles/second. On each \nrail the pulse rate is r = R/2. For convenience we use JT\u2019 = 1/r to \ndenote the time interval between impulses. The filter outputs combine \nto form the in-phase and quadrature rails of a passband signal. Thus, \nit may seem that what we have is 4 PSK; but FBS is unusual in that \nits symbol rate, 1/T\u2019, is higher than the conventional 1/T = 2 W.\n\nThe higher rate does not increase bandwidth but it does cause ISI, \nwhich will be combatted with MLSD. The ISI is assumed to involve a\n\nFig. 2\u2014Generic system structure. For QAM the transmit and receive filters are low- \npass filters. For the FBS case they are a matched pair with finite memory in the sampled \ndata domain. The nominal cutoff frequency of the low-pass filters is W= 4/2.\n\nmemory of \u00bb, i.e., the bandlimited baseband filters are such that the \nimpulse response sampled at times {n/T\u2019}?_-.. have the form h = 0, \nho, hi, --- h,, 0. Thus MLSD requires 2\u2019*! states (2\u201d per rail).*\n\nWe would like to, if we could, make the following idealizations \nconcerning H(f), the Fourier transform of the impulse response of the \nbaseband filter.\n\nA. Each member of a bank of FBS passband systems is spectrally \ndisjoint [in baseband, H(f) vanishes outside (~W, W)].\n\nW\u2019 [W\u2019 = 1/(2T\u2019) > W). \nThe first of the above is needed for spectral efficiency. Statement B \nis needed to be consistent with the assumption that MLSD involves a \nmemory of vy. Mathematically it would seem impossible to meet A and \nB. After all, if H(f) is a trigonometric polynomial vanishing on \n[W, W\u2019], it vanishes everywhere. There is no real difficulty here. We \nwill adhere to B with v the degree of H(f). While A will not strictly \nhold, one can get as close to ideal as desired as long as v is large enough \nto meet out-of-band energy constraints. In MLSD a matched filter is \nused to initiate the detection process. The matched filter receiver \nserves to select the desired band [-W, W]. We have a dual view of \nwhat the frequency band is. From the point of view of where the signal \npower is concentrated, [\u2014W, W] is the band. From the point of view \nof MLSD, we are dealing with a sampled temporal response, which \ncan only correspond to a transform that is a polynomial on [\u2014W\u2019, \nW\u2019]. So long as the degree of the polynomial is large enough the two \nviews of bandwidth can be reconciled.\n\nThere are several questions before us. Can we make the energy \noutside the [-W, W] band so small that the interference between \nneighboring systems is negligible, yet the number of states involved in \nMLSD is reasonable? If we can accomplish this, does the FBS system \nperform better than the comparable QAM system? How much better \ndoes it perform and at what complexity?\n\nWe investigate these questions in the context of three kinds of \ndiscrete impulse responses. The first of these is the Nyquist responses \n(\u201cbrickwall spectra\u201d on [\u2014W, W]) truncated to memory \u00bbv. For these \nwe shall see that the interference from neighboring systems is prohib- \nitive for reasonable v. The second set of impulse responses are the \ndiscrete prolate spheroidal wave functions, which, for fixed total energy \nand fixed v, have the least interference from neighboring systems. We \ndemonstrate that their performance is not good. Finally we explore \noptimally designed responses and find that for reasonable v, even for \nthe most favorable cases, the advantage over QAM is very modest.\n\n*Notice that if the constellation were not the product of two one-dimensional \nconstellations, as we have assumed, the complexity would grow as 4\u2019 instead of 2\u2019\u201d*?.\n\nThe probability of bit error, P., is an important performance mea- \nsure for data communication systems. For QAM as well as the systems \nemploying HDC, UTC, or FBS, if MLSD is used the probability of bit \nerror decays exponentially as the noise spectral density is decreased \n(except for an algebraic multiplier). That is, an exponentially tight \nbound on P, has the form\n\nwhere x and & are independent of o\u201d, the noise power spectral density \non a single dimension. For FBS viewed in the MLSD context, the \nexponentially tight bound has the form\n\nwhere * denotes convolution and the minimum is over all doubly \ninfinite sequences e of the form\n\nOlen 2+ ex0, \nwhere e, belongs to {0, 1, -1} and K can be any nonnegative integer. \nClearly, din < |] h||*. In cases where d2in = || h||? it is common\n\nto say that the matched filter bound is attained. What is meant is that \nthe exponent of P, is the same as if there were only a single data pulse \nto be detected (no ISI). The terminology stems from the fact that, \nwhen there is no ISI, MLSD employs simply a matched filter (along \nwith a threshold comparator).\u2019\u201d\n\nWe take the quantity & as a convenient indicator of performance in \nthe high s/n realm. (We stress that, for models of specific systems, \nmore refined computations estimating the actual error probability are \noften needed.) The \u201cgain\u201d of one system over another is expressed as\n\nWe shall be concerned in this paper with estimating the gain that FBS \nexhibits over QAM. Both UTC and HDC exhibit substantial gain over \nQAM. For UTC, gains in the range of 3 to 6 dB have been reported \nand, for a 3-dB gain, the required complexity is extremely reasonable.\u201d\n\nFor the conventional QAM system, ||h||*? denotes the energy per \npulse prior to multiplication by a; belonging to [+1, +3, --- +\n\n(L \u2014 1)], so the modulated pulse has average energy (L? \u2014 1)/3 || h||?. \nIf there is one symbol every 7\u2019 seconds, the average signal power is \n[(L? \u2014 1)/3] [|| h||7/T]. Since the information rate per rail is \n(log.L.)/T b/s, FBS must operate at a rate of (logeL)/T pulses/s. Let \nh\u2019 be the impulse response for FBS. For the two systems to have \nidentical signal power we must have\n\nFor FBS, accounting for the wider bandwidth, the noise variance per \nsample is o\u201d (log.L.)/T. Not necessarily all of || h\u2019 ||? is realized in the \nerror exponent.\n\nG = 10 logy (2) \nwhere p = log,.L = W\u2019/W = T/T\u2019. One could interpret 10 logio[(4\u2019 \u2014 \n1)/3p] as a noise immunity gain and 10 logjo(d2in/||h||7) as the \npenalty for ISI.\n\nShortly it will prove useful to allow for replacing the noise power \nspectral density on the FBS system by a level greater than that on the \nslower system, say (1 + 8)o? with 6 > 0 in place of o\u201d. This will enable \nus to compensate for interference from adjacent channels. When, and \nif, the matched filter bound is attained the gain is expressed by 10 \nlogio(4\u00b0 \u2014 1)/[3o(1 + 8)]. Figure 3 depicts this function with 8 as a \nparameter. It is evident from the 6 = 0 curve that, depending on p, if \nthe matched filter bound is attained, the gain can be considerable.\n\nWe consider now the interference in the band (\u2014W\u2019, W\u2019) that stems \nfrom those channels (other than the primary channel centered at zero) \nwhose power spectral density is nonzero in (-W\u2019, W\u2019). The determi- \nnation of the additional power due to these interfering channels is \nstraightforward. When measured for a single rail, at the output of the \nmatched filter, H*(w), the power is the same as if o\u201d were replaced by\n\nThe sum is over all neighboring systems overlapping the (-W\u2019, W\u2019) \nband. Because of its genesis, the term that adds to o\u201d in (3) is called \nthe Adjacent-Channel Interference term or ACI. For H\u2019(f) with nearly \nall the energy in the (\u2014W, W) band, | H\u2019(f) |?/fw | H\u2019(g) |?dg has a \nmean value of approximately T on (\u2014W, W). Since each channel is \nsymmetrically disposed relative to its neighbors, the integral in the\n\n1 2 3 4 \nSPEED FACTOR, p \nFig. 3\u2014Adjusted gain versus speed factor when matched filter bound is attained. \nee\n\nnumerator of (3) can be replaced by f W,. It follows that the strength \nof the ACI term in (3) is roughly indicated by that energy in a pulse \nwith transform H\u2019(f) that is out of the band (\u2014W, W). (We use OBE \nto denote out-of-band energy.) This approximation becomes more \nprecise if H\u2019(f) is approximately flat in (-\u2014W, W) (as is the case in \nSection IV).\n\nIf ACI is not negligible, it is reasonable to modify the gain by \nsubtracting 10 logio(1 + OBE/o\u201d) or, the more precise but more \ncomplex, 10 log,o(1 + ACI/c\u201d). No matter which gain expression is \nmost appropriate, if we insist on some degree of spectral isolation it is \nunclear how much gain can be attained at specific levels of complexity\n\n(2\u2019*! with v < 26). In the sequel we will find that the answer is not \nmuch gain. For the analysis in Sections IV and V we consider OBE in \nthe range [0, o\u201d]. As we note in Section VI there is no point in \nconsidering OBE outside this range.\n\nWe can see from the formula for minimum distance (1) that, if we \nslide a window of size v along an error sequence e, a repeated state is \nforced to occur by 3\u201d shifts. It follows that, to attain the minimum, \none need not search over more than 3\u00b0 events. Since {3\u00b0 |\u00bb = \n1, 2, 3, 4, ---} = {27, 19683, 7.63 x 101\u201d, 4.4 x 10\u00b08, ..-}. We see that, \neven for v = 3, a brute force search is extremely ambitious and for py = \n4 it is completely out of the question. (Reference 13 discusses three \nother state symmetries as well as a repeat.)\n\nFor future reference, we borrow from Ref. 13 and list four useful \nrepresentations and notations for error events in Appendix A.\n\nFor each \u00bb, it is useful to view a set of error events, one of which is \nguaranteed to achieve d2,in as a tree. Construct a tree of sequences \nwith three branches emanating out of each node and with the labeling \nillustrated in Fig. 4. The labels along each upward path represent the \nbeginning string for the nonzero portion of an error event. Once a \nstring of v consecutive zeros is encountered, the growth out of such a \nnode is pruned from the tree, since continuing the event with nonzero \nelements will correspond to creating labelings for beginnings of events \nwith a greater || h+*e||? than the all-zero continuation.\n\nTo envision a computer search for d2i, for a specific h, one can \nthink of climbing up the tree and to the left and at each node \ncomputing the accumulated\n\non the upward path to the node. There is one summand for each node \nin the upward path. Climb higher if the record low for a completed\n\nerror event (a number < ||/]||\u201d) has not been exceeded. Otherwise, \nclimb down to the first node that offers an unclimbed branch and then \nclimb that branch. Whenever a node with y consecutive zeros is \nreached, and the old record has not been reached, record the new \ncandidate event for achieving d2,;, and the new record before climbing \ndown.\n\nSome additional special search tools prove useful. Specifically, one \ncan terminate an upward climb whenever any of the four symmetries \nA; = +A;(i 1 and, as we have already mentioned, the signal \nbandwidth is invariant to p but ISI arises. A hypothetical FBS system \nbased on such a pulse incorporates a level of idealization beyond the \nstandard one associated with the abrupt cutoff. Namely, the system \nrepresents the limits of infinite decoding complexity as well as zero \nenergy in the bands, W < |/| < W\u2019.\n\nFor each system, assuming the pulse energy is normalized to 1 and \nW\u2019 is normalized to 1/2, we have \n2\n\nThe infimum is over all error events with \u00ab, belonging to {0, 1, \u20141} \nand K ranging over the positive integers. Expression (4) is considered \nin Ref. 5 where it is demonstrated that d2;, > 0 for all p => 1. The \nintriguing question of whether, for such systems, a positive \u201cgain\u201d is \navailable remains open. \nLet\n\ndenote the FBS pulse transform normalized to unit energy. While \nexpression (4) allows for infinite complexity, for any implementation, \napproximations of H\u2019\u201d must be considered. The optimum least-mean-\n\nsquare approximations, the Fourier series {HN\u00a5(w)A 6 qne\u2019\u201d\u201d}, are \nnatural responses to use to inquire whether, as v increases, FBS \nperforms better than QAM. Of course, if \u00bb becomes too large the \nrequired detector becomes forbiddingly complex.\n\nThe tree search discussed in Section 3.3 was used to determine the \n\u201cgain\u201d for the least-mean-square approximations. The symmetry of \nthe impulse responses allowed the addition of the test of Appendix B \nto significantly reduce the running time of the algorithm.\n\nThe results are shown in Fig. 5. The \u201capparent gains\u201d are only \nmeaningful if the Out-of-Band Energies (OBEs) are sufficiently small. \nIndeed, they are not sufficiently small as we now discuss. Figure 6 \nshows the out-of-band energy for a unit energy response for v = 26. \nAlso shown are the noise levels for the benchmark QAM system \nproviding the same information rate at a P, of 10-* and 10\u00b0\u00b0. Of the \nfour points p = 2, 3, 4, and 5, only p = 2 shows the out-of-band energy \nbelow the noise level. The margin for P, = 107\u00b0 is slight (=4 dB) but, \nfrom Fig. 5, we see that for y = 26 the \u201cgain\u201d is negligible (~0.1 dB). \nFor p = 2, if we reduce v to increase the \u201cgain\u201d, the attempt is \nundermined by the increase in out-of-band energy. The out-of-band \nenergies for vy = 20 and py = 14 are also shown in Fig. 6, for p = 2.\n\nWe conclude that, for the least-mean-square approximation of a \nNyquist pulse, FBS signaling under the mild requirement P, = 107\u00b0 \ndoes not offer any significant gain over QAM. In making the compar- \nison, we have allowed FBS the extraordinary complexity of 27\u00b0 = 6 x \n10\u2019 states per rail (>10\u00ae states total). If P. were decreased, FBS would \nfare even worse.\n\nFigure 7 illustrates approximate Nyquist spectra for v = 26 and \nminimizing error events. We note that for \u00bby = 26 the number of \ncandidate error events exceed 10%\u201d < 3\u00b0,\n\nAllowing for complexity not exceeding 10\u00b0 states, FBS is not attrac- \ntive relative to QAM for the examples considered thus far. As we \nmentioned in the last section, for the asymptote of infinite complexity \n(vy \u2014 o) and stringent out-of-band energy constraint, the limiting \nsquared distance is expressed in (4). Although we cannot compute the \ngain G,, we can find an upper bound using candidate error events. We \nused events revealed to be useful in the tree search for v < 26. The list \nof trigonometric polynomials below {E,(w)}\u00b0-2 was used to bound d3in:\n\nFig. 5\u2014Apparent gain of FBS over QAM (gains unachievable because of interference from adjacent bands).\n\nThey yield Ge < 0.107 dB, G3 < 1.4 dB, G4 < 0.477 dB, and Gs <1.1 \ndB. This shows that, even allowing for an arbitrarily large number of \nstates, in the limit of stringent out-of-band energy requirements, the \ngains available using a Nyquist pulse are at best very modest. The \nE,(w) characteristics are illustrated in Fig. 8.\n\nIn Section IV we investigated whether the approximations HY\u201d have \ngood distance properties for FBS with p = 2, 3, 4, and 5. We found \nthat, for reasonable complexity and out-of-band energy constraints,\n\nMe . - re ae of | HXY |? and extremal error event (+ and \u2014 mean +1 and \u20141). Vertical dotted line marks transition from in-band to \n- - n \u20185\n\nthey do not. The H,\" minimize J, | Hi\u2019 \u2014 \u00a5% qne\u2019\u201d* |?w(w)dw in \nthe special case when the weight function w(w) = 1. In light of the \nresults of Section IV, we can reformulate the least-mean-square ap- \nproximation using a w(w) that is 0 on (\u2014z/p, z/p) and 1 otherwise. \nThe weighting reflects the fact that it is essential to keep the out-of- \nband energy small but, having seen that the flat transform has no \nspecial distance properties, we have no motivation for keeping the \ntransfer characteristic flat within (\u20147/p, z/p).\n\nThe extremal responses so obtained are called the Discrete Prolate \nSpheroidal Wave Functions (DPSWF).\u201d* Their theory has been devel- \noped by Slepian.\u2019\u00b0 Wyner has suggested their consideration for use in \ndata communication systems for reasons other than those we are \nconsidering here.\u2019 Let H?% denote the transform of the discrete \nspheroidal wave function of memory v corresponding to an FBS system\n\nwith parameter p. Since minimizing the out-of-band energy corre- \nsponds to maximizing the in-band energy, the coefficients of H?* are \nthen components (q,, qi, --: g,) of the eigenvector of the matrix of the \nsymmetric quadratic form\n\ncorresponding to the largest eigenvalue, i,,,. Since we normalize by \nconstraining HfS to have unit energy, the quantity 1 \u2014 ),,, is the out- \nof-band energy.\n\nIn Fig. 6, 10 logio(1 \u2014 X,,,) is plotted against p for various vy (see \ndashed curves). Unlike HNY we see that a significant portion of the \nloci for H\u00ae> are disposed well above curves for the noise levels for \nP, = 107\u00b0 and P, = 10~*. Thus, there are spaces of systems of moderate \ncomplexity with small out-of-band energy, whose distance properties \nare of interest. What are the distance properties of H?\u2019S in the range \np = 2, 3, 4, 5? They are not good. Use of the search algorithm of \nSection 3.2 demonstrated no gain for any HS whose (\u00bb, p) coordinate \ncorresponded to an out-of-band energy below the level of the Gaussian \nnoise for P, of 10~*. For example, for p = 2 at v = 4, the out-of-band \nenergy is \u201426.3 dB, which is below the level of the additive noise. \nHowever, the minimum distance of H\u00a53 is poor, specifically G = \u20141.33 \ndB. For larger v, the out-of-band energy drops precipitously but \ndistance decreases as well. As p increases in the range 3, 4, and 5, the \nsituation worsens: G values significantly below 0 dB occur with out- \nof-band energy prohibitively above the noise level. As y is increased, \nthe distance drops markedly.\n\nAt this point we have an interesting situation. The least-mean- \nsquare approximations to the Nyquist pulse are shown to have attrac- \ntive \u201capparent gains\u201d relative to QAM but the gains cannot be realized \nbecause the signal spectrum is not adequately confined. On the other \nhand, the results for DPSWF\u2019s show that great spectral confinement \nis possible, but these pulse shapes do not exhibit any gain over QAM. \nThe question remains as to how much gain we can achieve under a \nspectral confinement constraint for a specific complexity. This is \naddressed in Section VI.\n\noptimal h. (Since H can have 2p zeros disposed in inverse conjugate \npairs there can be as many as 2\u2019 possible factors of H that have real \ncoefficients.) The problem of finding optimal h is essentially a linear \nprogramming (LP) problem. The suggestion of viewing optimum \nMLSE system design as an LP problem appears in my paper with R. \nR. Anderson.?? It turns out that, in most cases of interest, the number \nof constraints corresponding to the various error events is too large \nfor the LP to be useful by itself. The LP is combined with the tree \nsearch algorithm that serves to eliminate most error events from \nconsideration. The LP-tree search algorithm solves the design prob- \nlem. We proceed now to describe the LP and show how it is integrated \nwith a tree search algorithm. Then we present the performance results \nfor optimally designed pulses.\n\nRecall that an LP problem is one of the following type: Given a \nvector \u00a2, find a vector y that maximizes (y, c) subject to a set of linear \nconstraints of the form (y, a;) = b;, i belonging to Z a finite index set. \nThe a; and b; are given vectors and scalars, respectively. It is very \nuseful that < constraints can be converted into = constraints by \nchanging sign and so equality constraints can be represented by a pair \nof = constraints.\n\nIn our application, 7 is infinite. Since we shall see that the feasible \ny exists in a bounded set we can, in principle, obtain a solution as \nclose to optimum as desired by solving an LP with sufficiently many \nconstraints.\n\nNow h=0h.,,--- ,h,, ---, h, 0. We will represent h in a 2v + 2 \ndimensional space where the first 2v + 1 coordinates are (h_,, --- , \nh,). An additional coordinate augments the projection of h so that we \nhave (h_,, --- , h,, s). The augmented vector of 2v + 2 components is \ndenoted y. The additional coordinate, s, is a mathematical convenience \nthat will facilitate maximization of the minimum squared distance, as \nwe shall see.\n\n1. As a convenient normalization, we assume that the energy in h \ncannot exceed 1, so h, < 1; therefore,\n\n3. H(w) is nonnegative. H(w) is the function that has h for Fourier \ncoefficients and the operation of Fourier series is a linear one. So the \nconstraints H(w) = 0, 0 < w < a, can be put in the form (y, a.) = 0 \nby defining a,, appropriately. There is one constraint for each w on \n0 < w < x. In our application we can use a discrete set of the form \n{wn = (nr)/N}%-, with N sufficiently large to give adequate accuracy.\n\n5. The 2v + 2 component, seemingly extraneous so far, now comes \ninto play. Let {E;(w)};.- be the error polynomials. Project them into a \n2v + 2 dimensional space using the successive Fourier coefficients with \nindex of absolute value < pr to get the first 2v + 1 components and use \n\u20141 for the last component. Call the resulting vectors {e;};._\u00a2. It will \nnot bother us if some E;(w) have nonzero Fourier coefficients with \nindex exceeding v. Taken together, the constraints {(y, e;) = 0}j-\u00a2 \namount to a statement that, for each admissible h, the squared \nminimum distance is never larger than a candidate distance.\n\nThe optimal h is the one maximizing the minimum distance. So the \nconstrained y attaining max (y, 1,42) has the optimum design for its \nfirst 2v + 1 coordinates and the optimal exponent for the last coordi- \nnate.\n\nIn 2v + 2 space, the set of all y meeting constraints is denoted Y. \nY is not empty. For example, it contains 61,41, where 6 is a number \nsmall enough that energy constraints are met. The optimization will \nnot degenerate as Y is closed and bounded. Y is closed since it is \nexpressible as the intersection of closed half-spaces. Y is bounded \nsince each component of y is bounded by the pulse energy constraint. \nTo see why, note that e = 1,4; shows y2,42 < 1. For the remaining \nbounds on the components of y we note H(w) = \u00a5\u201d, xm4i1+,e7\" = 0 \nand so factorization is possible, H(w) = H(w) H*(w). Fourier coeffi- \ncients (x1, x2, --- , Xey+1) are sums of products and so, by the Schwarz \ninequality, y,+1 = x,4; bounds all the components of each y vector.\n\nples of interest, there are too many error events. For example, for v as \nsmall as 4, the estimate in Section 3.1 indicated that there are over \n10*\u00b0 error events about which we should be concerned. The difficulty \nof too many constraints may sometimes be handled by solving a \nproblem with a manageable number of the constraints. If it can be \nverified that the optimum meets all constraints (not just the manage- \nable ones), then the solution to the simplified problem is the same as \nthe solution to the difficult problem. We design, via an LP, a response \nmaximizing the minimum distance over some error events and then \nseek to verify, using a tree search, that the minimum distance is not \nreduced if one minimizes over all error events.\n\nIf the above procedure is unsuccessful, one can repeat it, enlarging \n~ to include the minimizing error event revealed by the tree search. \nEventually, the iteration process will converge. Prior to convergence, \nLP gives an upper bound while the tree search gives a lower bound to \nthe d2.in achievable by the optimum design.\n\nThe LP provides an h, while the tree search requires an h. The \nminimum-phase deconvolution, fh, is suggested, since, among all h \nsatisfying h\u2019\u00abh = h, h has the greatest Y., h? for each k.!7\"8 This \nmaximal frontal energy concentration expedites the tree search, which \noperates first on the leading coordinates of h. (Orders of magnitude \nof difference in running time have been observed between minimum- \nand maximum-phase deconvolutions in the tree search algorithm.)\n\nIn estimating the performance of the optimum system employing \nan h of memory \u00bb, power levels were set as follows: For the FBS \nsystem, as we mentioned in Section 6.2, the pulse energy was bounded \nabove by one. The noise level was set to meet the required P, in the \nbenchmark system operating at maximum power. Finally, the out-of- \nband energy constraint was set to a fraction of the noise power.\n\nThe resulting gain versus v curves are shown in Fig. 9 with v as a \nparameter. The OBE is constrained to 07/10 so a penalty of 0.414 = \n10 log 11/10 is included in the gain calculation. It is apparent from \nthe curves that, even at extraordinary complexity (exceeding 10\u00b0 \nstates) and a P, requirement of 107\u00b0, the resulting gains are very \nmodest. This conclusion is not sensitive to the exact premises under- \nlying the computation. Calculation shows that, for v = 26, if we allow \n6 to be larger than 1/10, the gains generally decrease because of the \nOBE penalty. There is little to achieve by making OBE smaller than \no\u201d/10 since the design is merely more constrained, and omitting the \nOBE penalty cannot add more to the gain than 0.414 dB. When the \ngain is positive, the ACI levels are generally within 0.25 dB of the \nOBE level so the gains based on ACI are not different in any important\n\nFig. 9\u2014Gain limit versus memory under spectral confinement constraint for P. =\n\nway from those based on OBE. There is no point in showing curves \nfor P. < 107\u00b0 in the benchmark system, as the gains can only decrease \nif the design is further constrained.\n\nFigure 9 has enabled us to determine the relative merit of FBS for \nreasonable complexity. The possibility remains that, for extremely \nlarge v, FBS could exhibit substantial gains and that these asymptotic \ngains could improve as p increases.\n\nFigure 9 was derived using a list of 50 error events obtained by \nrunning the LP-tree search iteration for successive v values. To con- \nclude that FBS offers at best a very modest improvement over QAM, \nit is only necessary to present upper bounds in Fig. 9 rather than exact \nmaximum gains. However, in preparing Fig. 9, we established that it \nis reasonable to exercise the LP-tree search algorithm to guarantee \nthe precise optimum gain that can be attained for up to 10\u00b0 states. It\n\nFig. 10a\u2014Example of an optimally designed transmitter characteristic and an error \nevent characteristic. Vertical dotted line delineates the band edge.\n\nis interesting to note that optimum system design can be accomplished \nfor systems with such an enormous number of states.\n\nFigure 10a illustrates an optimally designed spectrum and a corre- \nsponding minimizing error event. Figure 10b illustrates an interesting \nconstrast between a pulse spectrum and an extremal error event.\n\nFor p = 5/4, the gain is only about 0.5 dB but a very interesting \nbehavior is observed. Namely, with little complexity, the maximum \ndistance possible is attained in the sense that the matched filter bound \nis obtained. From Section III, eq. (2), we can write the following \nexpression for the gain (neglecting the OBE penalty):\n\nwhere the function c(p, v) gives the fraction of the matched filter \nenergy attained. For fixed p, c(p, v) is a nondecreasing function of vp.\n\nFig. 10b\u2014The in-band transmitter spectrum is optimized for a limited set of error \nevents, one of which is shown. The extraordinary flexibility afforded by over one million \nstates allows the optimum spectrum to have some peaks and valleys in opposition to \nthose of the minimizing error event.\n\nthat the answer is yes. For p > 3 consideration of the error transform \n|1 \u2014 e|? shows that the answer is no, as\n\nin the limit of stringent out-of-band energy constraints. In light of the \nlimited gains available with optimal FBS, it would be of only academic \ninterest to pinpoint the largest \u00bb value for which the matched filter \nbound is attained as complexity is increased. Consequently, we shall \nnot pursue this question further.\n\nAt this point it is natural to question whether it is worthwhile to \ngeneralize and consider Faster Multilevel Signaling (FMS). Motiva-\n\ntion for considering FBS comes from Ref. 5, where the first theoretical \nresults on FBS were reported; from Ref. 3, where highly significant \nbenefits of FBS were suggested but not established; and from discus- \nsions with J. Salz, who related that the idea of FBS has been around \nfor many years and that it is important to settle the question of its \n\u2018merit. Since FBS proves to be unattractive, why should one consider \nFMS, especially when we know that increasing the number of levels \ntoward that of the competing QAM system would seem to blur the \ndistinction? Can one generally discount the competitiveness of FMS? \nWe discuss why we cannot dismiss FMS and why, despite the findings \non FBS, FMS systems may have some value.\n\nFBS fared poorly. If we look back on our analysis of FBS it is \nobvious that it was the OBE constraint that drove the performance \nlevel of FBS. We noticed in Section IV suboptimal pulses exhibiting \nsubstantial gains that could not be realized because of prohibitive \nOBE. The stringency of the OBE constraint was necessitated by the \nsubstantial overlap of spectra between neighboring systems. As we \nmove away from binary toward more levels, in the class of FMS \nsystems, to compete with a fixed QAM system, the ratio p = W\u2019/W> \n1 decreases. The OBE constraint we need to impose is seen to be more \nrelaxed.\n\nMoreover, as we decrease p, systems are represented for which the \nACI constraint is not of any direct importance. There is the interesting \nclass of questions pertaining to transmitter filter smoothness consid- \nerations. For example, which performs better\u2014a QAM system em- \nploying a square root raised cosine pulse with roll-off a = p \u2014 1, or an \noptimized FMS system with band-edge nulls of specified order and \nwith system memory v? The two systems are required to have the \nsame power and information rate. The answer, of course, depends on \nM, a, v, and the degree of the band-edge null. The band-edge null is \nuseful for spectral confinement as well as for easing synthesizability. \nThe imposition of nulls of specific order at specific frequencies lead to \nadditional linear constraints and is easily handled by the LP-tree \nsearch program.\n\nThe simple partial response 0, 1, 1, 0 can be used to illustrate that \nthere are situations where FMS can be very beneficial relative to \nQAM. Among all systems required to have a band-edge null, the system \n0, 1, 1, 0 requires the least number of states, m per rail. It is easily \nshown that the response attains the matched filter bound independent \nof m. Figure 11 shows a gain versus roll-off plot, which speaks for \nitself concerning the substantial gains that are available in certain \ncases.\n\nFig. 11\u2014Gain versus rolloff characteristics for partial response 2~\u201d? (0, 1, 1, 0), \nwhere the approximate number of constellation ee are shown for competing QAM \nsystem, and the number of levels equals the number of states per rail.\n\nA class of examples where ACI is not of direct concern occurs with \nthe voiceband channel, which has severe band-edge attenuation. The \nchannel shapes are irregular mounds and there is no obvious spectral \nsupport to assume. For a specific information rate, what is the best \nbaud to use if the transmitter spectrum has a null of given order and \nzero rolloff? This is paraphrasal of the FMS issue coupled with a \nsimpler question of where to center the signal spectrum. (The trans- \nmitter design must also account for the effect of nonlinearities and \nthe fact that the exact modulus of the channel transfer characteristic \nis not known at the transmitter.)\n\nAside from the new information on FBS, a major finding of this \nreport is that, for the class of MLSD systems considered, optimum \ndesigns can be accomplished involving numbers of states correspond- \ning to the capabilities of forthcoming MLSD implementation technol- \nogy (and far beyond). We have concentrated here on binary systems \nand a very special channel. However, the algorithm extends to apply \nto designing optimum m-ary systems of prescribed complexity oper- \nating over arbitrary linear dispersive channels. The astronomical \nnumber of error events is not an obstacle.\n\nThe extended algorithm, now being programmed in the course of \njoint work with G. Vannucci, will provide a basic tool for probing the \nfundamental relationship between attainable rates and system com- \nplexity for very general systems. Suppose one wants to achieve a \ncertain information rate, under spectral confinement requirements \nand with a specific level of complexity. By exercising the LP-tree \nsearch algorithm for a sufficient number of p values, one can locate \nPopt, the optimum p 2 1, and the associated optimum gain over a \ncorresponding QAM system with cosine rolloff spectral shaping.\n\nIt is a pleasure to acknowledge numerous valuable, stimulating \ndiscussions with G. Vannucci. These discussions involved both the \ntheoretical and software aspects of this work. L. J. Domenico\u2019s assist- \nance with the programming is greatly appreciated.\n\n1. A. Gersho and V. B. Lawrence, \u201cMultidimensional Signal Design for Digital Trans- \nsein hts Bandlimited Channels,\u201d Proc. IEEE ICC, 1, Amsterdam, May 1984, \npp. 377-80.\n\n2. G. Ungerboeck, \u201cChannel Coding with Multilevel/Phase Signals,\u201d IEEE Trans. \nInform. Theory, /T-23, No. 1 (January 1982), pp. 55-67.\n\n3. A. S. Acampora, \u201cAnalysis of Maximum Likelihood Sequence Estimation Perform- \nance for Quadrature Amplitude Modulation,\u201d B.S.T.J., 60, No. 6 (July-August \n1981), pp. 865-85.\n\n. G. D. Forney, Jr., \u201cLower Bounds on Error Probability in the Presence of Large \nIntersymbol Interference,\u201d IEEE Trans. Commun., COM-20, No. 1 (February \n1972), pp. 76-7.\n\n7. G. D. Forney, Jr., \u201cMaximum-Likelihood Sequence Estimation of Digital Sequences \nin the Presence of Intersymbol Interference,\u201d IEEE Trans. Inform. Theory, /T- \n18 (May 1972), pp. 363-78.\n\n8. G. J. Foschini, \u201cPerformance Bound for Maximum Likelihood Reception of Digital \nData,\u201d IEEE Trans. Inform. Theory, [T-21 (January 1975), pp. 47-50.\n\n9. G. J. Foschini, \u201cA Reduced State Variant of MLSD Attaining Optimum Perform- \nance for High SNR,\u201d IEEE Trans. Inform. Theory, /T-23, No. 5 (September \n1977), pp. 605-9.\n\n10. A. J. Viterbi and J. K. Omura, Principles of Digital Communication and Coding, \nNew York: McGraw Hill, 1979.\n\n11. G.J. Foschini, R. D. Gitlin, and S. B. Weinstein, \u201cOptimization of Two Dimensional \nSignal Constellations in the Presence of Gaussian Noise,\u201d IEEE Trans. Commun., \nCOM-22, No. 1 (January 1974), pp. 28-38.\n\n12. R. W. Lucky, J. Salz, and N. Weldon, Principles of Data Communication, New York: \nMcGraw Hill, 1968.\n\n13. R. R. Anderson and G. J. Foschini, \u201cThe Minimum Distance for MLSE Digital \nData Systems of Limited Complexity,\u201d IEEE Trans. Inform. Theory, IT-21, No. \n5 (September 1975), pp. 544-51.\n\n15. D. Slepian, \u201cProlate Spheroidal Wave Functions, Fourier Analysis, and Uncer- \noe ae The Discrete Case,\u201d B.S.T.J., 57, No. 5 (May-June 1978), pp. 1371- \n430.\n\n16. A. D. Wyner, \u201cSignal Design for PAM Data Transmission to Minimize Excess \nBandwidth,\u201d B.S.T.J., 57, No. 9 (November 1978), pp. 3277-307.\n\n18. H. P. McKean and H. Dym, Fourier Series and Integrals, New York: Academic \nPress, 1972, pp. 175-6.\n\nAi, As, As, --+, Ax++1, Where the states A; are defined as the \nsuccessive v-tuples of the sequence representation, where the all-zero \ny-tuples are omitted, except for the v-tuple abutting ex. \n(0, 0, ee 0, \u20ac0), (0, 0, sry \u20ac0, \u00e91);\n\nA.3 Augmented state representation \nAj, Ag, Ag, --- Ak+41, where the augmented states Aj are defined \nas the successive (v + 1)-tuples of the sequence representation\n\nwhere h\u00ae 4 (h,, h,-1, --- , ho) and the inner product is defined in the \nusual way. The b superscript is read \u201cbackward\u201d and the b operation \nis also applied to error events in the memorandum.\n\nThe error sequence maps to the nonnegative cosine polynomial \nE(w) = |e + ae + --- + exeR |?\n\nWe shall refer to each e as an error sequence, error event, or error \npattern. Let H(w) 4 | ho + hie + --- + h,e\u2019\u201d\u201d\u2019|? and define (E, H) \n1/(27) f2, E(w)H(w) dw. Then by Parseval\u2019s theorem, (E, H) \n||e+h||?, so we have\n\nWe present some observations other than the four symmetry con- \nditions that are useful for efficient calculation of d?,;, and a minimizing \nerror event e for a symmetric transmitter impulse response.\n\nLet {S;}2. denote the resulting sequence of scalar products in hee. \nLet K be the smallest integer satisfying sjsx ~ 0 with s, = 0 fork \u00a2 \n{1, 2, --- K}. If, in the course of searching the tree, an error event \nbreaking the current record, A, is encountered, then, for it to be a \nminimizing event, we must have\n\nLet [K/2] denote the largest integer less than or equal to K/2. For a \nrecord breaking error event or that error event in reverse (or both) we \nmust have\n\nSince || h*e||? = || h*(+e\u00b0) ||? error events for which it is established \nthat the inequality (5) is reversed need not be explored further in the \ntree search for d2,;,.\n\nTo expedite the process of seeking d?,;, among error sequences for \nwhich (5) holds, we discuss the calculation of the height at which the \nexploration of the growth of nodes terminates. Let L be the first \ninteger for which the accumulated sum of s? + s\u00a7 + +--+ Si4,; > A/2 \nso that s? + so + --- si < A/2. Clearly, L = [K/2] so2L+1>K. \nOnce L is detected there is no need to explore any events involving \n2L + 2 scalar products. To put it another way, if L\u2019 = L + 1 is the \nfirst index for which A/2 is exceeded, then s2z, = 0 and 2L\u2019 > K.\n\nIt is not always necessary to search to height 2L\u2019 to terminate \ngrowth exploration. To see this note that from the height, 7\u2019, of \noccurrence of the last nonzero element in the event under exploration \nwe have that K > \u201d + v. So once L\u2019 is determined exploration of \ngrowth is terminated if 7 + vy > 2L\u2019.\n\nGerard J. Foschini, B.S.E.E., 1961, Newark College of Engineering, Newark, \nNJ; M.E.E., 1963, New York University, New York; Ph.D., 1967 (Mathemat- \nics), Steven Institute of Technology, Hoboken, NJ; AT&T Bell Laboratories, \n1961\u2014. At AT&T Bell Laboratories Mr. Foschini initially worked on real- \ntime program design. For many years he worked in the area of communication \ntheory. In the spring of 1979 he taught at Princeton University. Mr. Foschini \nhas supervised planning the architecture of data communications networks. \nCurrently, he is involved with digital radio research. Member, Sigma Xi, \nMathematical Association of America, IEEE, New York Academy of Sciences.\n\nAdaptive Transversal Equalization of Muliipatn \nPropagation for 16-QAM, 90-Mb/s Digital Radio\n\nAdaptive transversal equalization is an effective and relatively new coun- \ntermeasure for dispersive multipath propagation in terrestrial digital radio \nnetworks. In this paper we describe the design and performance of a five-tap \nbaseband analog equalizer developed for a family of 16-QAM, 90-Mb/s radio \nsystems. Laboratory measurements and field evaluation during a five-month \nfading season in Palmetto, Georgia, indicate that the use of this adaptive \ntransversal equalizer can significantly reduce the need for costly space-diver- \nsity equipment.\n\nThe impairment of terrestrial digital microwave reliability due to \nmultipath propagation is widely recognized.' Unlike FM radio systems, \nwhere system outage is predominantly determined by the thermal \nnoise aspect of fading, digital radio is also affected by the dispersive \ncharacter of multipath fading. This dispersion, engendered by signifi- \ncant amplitude and delay distortion across the channel bandwidth, \ncauses considerable Intersymbol Interference (ISI) that degrades dig- \nital radio reliability well beyond that expected from the flat fade \nmargin alone.\u201d Multipath-induced distortion thus is considered the \npredominant cause of digital radio outage for frequencies under 12 \nGHz.\n\ntipath fading. These include frequency diversity,\u00ae space diversity,* and \nadaptive Intermediate Frequency (IF) equalization. Examples of the \nlatter include slope equalizers\u00ae and notch or resonance equalizers.\u00ae \nHowever, frequency-selective fading corrupts both the amplitude and \nphase of a transmitted signal. While IF equalizers can be designed to \ncondition a channel properly for minimum phase fading, they double \nthe delay distortion during periods of nonminimum phase fading. \n(Minimum phase and nonminimum phase fading is clearly defined by \nGiger and Barnett\u2019 for a two-path statistical model of multipath \npropagation.) This effect naturally impacts the outage of those digital \nradio systems that rely solely on amplitude correction.\u2019\n\nAlthough adaptive transversal equalizers are a relatively new coun- \ntermeasure to multipath fading in digital radio systems,\u00b0\u00ae their prior \napplication in mitigating the effects of linear distortion in other, lower- \nspeed, digital communication networks is firmly established. Current \npractice is to use transversal equalizers in conjunction with IF equal- \nizers. In a recent study, Foschini and Salz\u00ae considered the application \nof equalization techniques to digital data transmission over radio \nchannels subject to frequency-selective fading. Their theoretical study \nof ideal transversal equalizers with an infinite number of taps clearly \nestablished the utility of linear equalization during multipath propa- \ngation. These equalizers are especially noteworthy in that they are \ncapable of providing amplitude and delay equalization for minimum \nand nonminimum phase fades.\n\nThe baseband synchronous transversal equalizer briefly described \nhere was designed for a family of 16-QAM (Quadrature Amplitude \nModulation), 90-Mb/s radio systems. Designated DR 6-30 and DR 11- \n40, these digital systems provide 3-bit/Hz operation in the 6- and 11- \nGHz common carrier bands, respectively.\u2019\u00b0 In this paper, we focus on \nthe design and performance features of a high-speed (approximately \n22.5-MHz) synchronous transversal equalizer. A theoretical develop- \nment of equalization principles is specifically omitted since those \npoints are amply discussed in the technical literature (for example, \nsee Chapter 6 of Ref. 11).\n\nFigure 1 functionally depicts the DR 6/DR 11 digital radio system. \nTwo independent, 45-Mb/s random data streams are differentially \nencoded to form two rails, each with four-level amplitude states, and \nthen modulated in quadrature to form a 16-QAM, 90-Mb/s IF signal \nat 70 MHz. The Radio-Frequency (RF) transmitter modulates the IF \nsignal up to 6 or 11 GHz for transmission over a line-of-sight terrestrial \npath to the digital receiver. At the receiver the signal is down-converted\n\nto IF, where it is processed by an Automatic Gain Control (AGC) \namplifier and adaptive slope equalizer. The baseband receiver de- \nmodulates the IF signal into in-phase (I) and quadrature (Q) rails, \nwhere the baseband data states are detected and estimates of the \noriginal transmitted data are made. An error detector provides for \nsystem performance monitoring.\n\nbaseband equalization, the transmitted symbol states are estimated at \nthe decision point, and the decoded binary signals are used in subse- \nquent digital processing.\n\nTo remove in-rail and cross-rail intersymbol distortion, two adaptive \ntransversal filters (each with five complex-valued tap weights) are \nconfigured for baseband equalization of QAM signals. The selection \nof five taps is based on theoretical studies of equalizer performance as \na function of equalizer length. For example, Amitay and Greenstein\u2019? \nhave investigated the multipath outage performance of digital radio \nreceivers using finite-length adaptive equalizers. Using Rummler\u2019s \nstatistical description of multipath channels,\u2019\u00ae equalizer performance \nfor a broad ensemble of fading scenarios was simulated. Their study \nindicated that five synchronous taps considerably reduce ISI relative \nto performance attained with three taps and that equalizers with seven \nor more taps, while obviously further reducing ISI, exhibit a rapidly \ndiminishing relative reduction in linear distortion. (Independently, \nMurase et al.,/4 and Takenaka et al.!\u00b0 have also selected five-tap filters \nfor their transversal equalizer designs.)\n\nThe equalizer tapped-delay lines are fabricated using lumped-delay \nelements isolated with buffer amplifiers. The buffer amplifiers are \nHybrid Integrated Circuits (HICs) and provide high isolation between \nthe delay line and coefficient-weighting taps. Tap weighting is accom- \nplished with variable gain amplifiers. These, too, are hybrid integrated \ncircuits fabricated in single in-line packages, thereby permitting high- \ndensity electronics on each circuit board. Summing amplifiers (also \nHICs) then add the individual tap-weighted signals to form the filter \noutput.\n\nThe coefficient control portion of the equalizer uses zero-forcing \nadaptation and is implemented with high-speed Emitter-Coupled \nLogic (ECL). The control circuit accepts error polarity and estimated- \nsymbol polarity from the in-phase and quadrature decision circuits. \nAppropriately delayed versions of these bits are then correlated during \neach symbol period using exclusive OR gates. The time-averaged \nvalues of these correlations determine the weight of each tap in the \ntwo transversal filters. Time averaging is achieved using operational \namplifier filters optimized for the trade-off between coefficient noise \nand dynamic multipath tracking ability.\n\nThe entire equalizer consists of three 1-inch plug-in circuit packs in \na format compatible with the DR 6/DR 11 terminal or regenerative \nequipment. A photograph of these circuit packs appears in Fig. 3. Two \nof these packs are identical analog transversal equalizers, one for in- \nphase and cross-rail equalization of the I rail, the other for similar\n\nFig. 3\u2014Adaptive transversal equalizer consisting of two transversal filter circuit \npacks and one zero-forcing control circuit pack.\n\nequalization of the Q rail. Equalizer coefficient control is generated in \nthe third circuit package.\n\nIl. EQUALIZER PERFORMANCE \n3.1 Theoretical performance \n3.1.1 Reduction of peak distortion\n\nAs we noted above, five-tap synchronous transversal equalizers are \ntheoretically capable of substantially reducing intersymbol interfer-\n\nence caused by frequency-selective fading. For zero-forcing coefficient \nadaptation, the peak distortion, D,, of the corrupted digital signal is \nminimized.\"\u2019 (As used here, D, is equivalent to Peak Eye Closure \n(PEC) for binary transmission.) Representative theoretical perform- \nance is illustrated in Fig. 4. In Fig. 4 we consider one digital rail (I or \nQ) and show the variation of peak distortion\u2014with and without \nequalization\u2014of a digital signal for a 20-dB fade notch depth as a \nfunction of notch position in a +18-MHz channel. (Ideally, distortion \nin the other rail would be identical.) The ordinate on the right side of \nthis figure provides the corresponding peak eye closure for a four-level \nsignal, given by PEC = D,(L \u2014 1), where L is the number of discrete \ntransmitted symbol states on each rail. This illustrative fade grossly \ncloses the digital eye with D, > 1 over at least a portion of the channel\n\nFREQUENCY FROM CARRIER IN MEGAHERTZ \nFig. 4\u2014Theoretical reduction in peak distortion, D,, with a five-tap QAM transversal\n\nequalizer arrangement. Peak eye closure is noted for four-level transmission, that is, \none rail of a 16-QAM system.\n\nbandwidth. This latter condition highlights an analytic limitation of \nzero-forcing equalization: if D, > 1, the coefficient set may be subop- \ntimal.!\u2019 In spite of this, other analysis (to be discussed shortly) and \nour own measured data show that adaptive transversal equalizers do, \nin fact, notably reduce intersymbol interference in just such an envi- \nronment. Moreover, zero-forcing is known to assure a global minimum \nif D, < 1, affords comparative ease of circuit realization, and minimizes \nBit Error Rate (BER) in the high signal-to-noise ratio that typifies \nquiescent digital radio operation. The other dominant adaptation \napproach for automatic equalizers, Least-Mean-Square (LMS) algo- \nrithmic control, is more difficult to realize in high-speed circuits and \nhas a proclivity for unsatisfactory local minima when used in the \ndecision-directed mode.*\u00ae\n\nof equalization capability since they can be directly related to outage \npredictions for digital radio systems. The signatures are 10\u00b0? BER \ncontours: at each point on the contour, the fade notch depth corre- \nsponding to a 10-\u00b0 BER (defined as a digital radio outage) is specified \nas a function of notch position for a fixed-delay statistical model of \nmultipath propagation. Figure 5 presents theoretical signatures com- \nputed by M. H. Meyers\u2019? for no equalization, slope equalization, and \ntransversal equalization. Figures 4 and 5 confirm that five-tap trans- \nversal equalizers theoretically provide a significant reduction in linear \ndistortion. Indeed, even the use of zero-forcing control for fades with \nD, > 1 yields a degree of equalization that mitigates digital radio \noutage. The data of Fig. 5 indicate that a fade notch depth as shallow \nas 7 dB can cause an outage in the absence of countermeasures. When \nthe radio receiver is equipped with a transversal equalizer, outages are \nnot experienced until the notch depth reaches approximately 23 dB, \nwhich can occur for an unequalized D, > 1, as shown in Fig. 4. Also \nobserve from Fig. 5 that slope equalizer performance is influenced by \nthe minimum or nonminimum phase character of the fade, as we \nmentioned earlier. This is not a limitation of transversal equalization.\n\nThe definition and significance of equipment signatures were pre- \nviously mentioned. The laboratory measurement of these signatures \nis facilitated through the use of a new computer-controlled multipath \nfade simulator that continuously varies notch depth and notch fre- \nquency to achieve a 10\u00b0? BER. The simulator is inserted in the IF \npath of the receiver just before the AGC amplifier (see Fig. 1).\n\nFig. 5\u2014DR 6 theoretical equipment signatures for 16-QAM digital radio. Performance \nfor radio without equalization, with an adaptive slope equalizer, and with a five-tap \nsynchronous transversal equalizer using zero-forcing control.\n\nSignatures were measured using two DR 6 receivers, the first \nequipped with an adaptive slope equalizer (the standard arrangement) \nand the second equipped with both the adaptive slope equalizer and a \nfive-tap adaptive transversal equalizer. The 10? BER minimum phase \nand nonminimum phase equipment signatures appear in Fig. 6. As the \ndata reveal, the adaptive slope equalizer performs best when used for \nminimum phase fades, with a performance deterioration experienced \nfor nonminimum phase fades. We commented earlier that IF equalizers \ntypically double delay distortion during nonminimum phase fading, \nand this effect can degrade equipment signature performance. The \nsame effect naturally occurs when the adaptive slope and synchronous \ntransversal equalizers are used together. Comparing both sets of \ncurves, however, we also observe the significant improvement in \nequipment signature performance that can be ascribed to the trans- \nversal equalizer alone.\n\nFig. 6\u2014DR 6 measured equipment signatures for 16-QAM digital radio. Performance \nfor radio with adaptive slope equalization and adaptive slope and transversal equaliza- \ntion for 6.3-ns path delay. (Adapted from Ref. 20.)\n\nare compared. The predicted relative outage reduction factor, derived \nfrom theoretical equipment signatures for combined ideal slope and \ntransversal equalization (see Fig. 5) is 5. This assumes equally probable \nminimum and nonminimum phase fading. The predicted relative \noutage reduction factor for the measured equipment signatures (see \nFig. 6) is 4.5, again assuming equally probable minimum and non- \nminimum phase fading. The relative reduction factors for other ratios \nof minimum to nonminimum phase fading range from 4 to 5. The \nmeasurements in Fig. 6 attest to the quality of the transversal equalizer \ncircuit design itself. Regarding this point, baseband implementation \nof the equalizer permits integration of substantial portions of the \ncircuitry, thus simplifying design and manufacture. The development \nof new carrier and timing recovery circuits also helps place laboratory \nperformance close to the theoretical limit shown in Fig. 5.\n\nAn important aspect of multipath propagation is its rapid temporal \nvariation. To assure optimal equipment performance in the field, \ndynamic (time-varying) tests were performed during the development \nphase. Dynamic multipath fading is produced in the laboratory by\n\ncontrolling the continuously variable fade simulator with a microcom- \nputer. Realistic time sequences of multipath behavior were pro- \ngrammed into the simulator. Equalizer performance was monitored \nduring the simulation of these dynamic fades, thereby permitting \noptimization of the equalizer timing-recovery, carrier-recovery, and \ncoefficient-updating loop parameters.\n\nSeveral aspects of an equalizer\u2019s response to dynamic multipath \npropagation are exercised with the following test sequence (schemat- \nically depicted in Fig. 7): starting with a shallow fade notch depth d, \nat a particular notch frequency f,, the notch depth increases at a rate \n$; until a notch depth d, is reached. The notch then sweeps across a \nband of frequencies from f; to f. at a rate so. At the notch frequency \nfe, the notch depth decreases from dz back to d,; at a rate s3. This \nfading trajectory retraces itself and is repeated several times for \nstatistical averaging of the receiver\u2019s error performance. A test se- \nquence like this tests the receiver\u2019s ability to track notch depth and \nnotch frequency dynamics. For trajectory parameters of d; = 6 db, de \n= 15 dB, s; = s3 = 9 dB/s, f, = \u201412 MHz (12 MHz below the IF \nfrequency), fe = +12 MHz, and s, = 24 MHz/s, the transversal equalizer \nconsistently operates error free. Those test velocities are also faster \nthan 90 percent of all observed notch depth and notch position rates \nof change reported by Sakagami et al.\u201d\u201d\n\nThe adaptive transversal equalizer was installed in a DR 6-30 field \ntest facility at Palmetto, Georgia, on June 4, 1982. This modified\n\nbaseband receiver was compared with a standard DR 6 receiver \n(equipped with an adaptive slope equalizer) during a multipath season \nfrom June 6 to November 6, 1982. Propagation data collected during \nthe field evaluation period are shown in Fig. 8.\u201d\u00b0 The abscissa of this \nfigure reports fade notch depth; the ordinate indicates time faded \nbelow the respective abscissa value. A considerable amount of fading \nexhibits notch depths in excess of 10 dB, which, from Fig. 5, could \ncorrespond to an outage in the absence of suitable countermeasures. \nThe two baseband receivers shared the same RF and IF front ends. \nField measurements, monitored by AT&T Bell Laboratories personnel\n\nfrom Merrimack Valley, were grouped into 11 two-week intervals. In \nFig. 9, the number of seconds for which BER > 10\u00b0 is presented for \nboth receivers for each of the two-week intervals. Also presented is \nthe ratio of these two time measurements, representing a composite \nimprovement factor attributable to the transversal equalizer, alone. \nFigure 10 presents similar data for a BER > 10~*. In Fig. 11 we show \nthe incidence of frame loss with and without the equalizer, as well as \nthe corresponding reduction in loss of frame.\n\ntransversal equalizer provided composite improvement factors of 3.6 \nfor BER > 10~\u00b0, 3.7 for BER > 10~+, and 2.9 for frame loss. The 107* \nBER improvement factor of 3.7 is only 20 percent below the predicted \nimprovement factor of 4.5, based on laboratory-measured equipment \nsignatures.\n\nBecause of their ability to adaptively equalize multipath-induced \namplitude and delay distortion for minimum and nonminimum phase\n\nfading, synchronous transversal equalizers promise to play an impor- \ntant role as a multipath countermeasure for terrestrial digital micro- \nwave networks.\n\nIn this paper we summarize the major design and performance \nfeatures of a five-tap analog transversal equalizer for the baseband \nreceivers of two 16-QAM, 90-Mb/s digital radio systems. The equal- \nizers heavily rely on HIC technology for their tapped-delay line buffer \namplifiers, tap-weighting coefficients, and summing circuitry. The\n\nzero-forcing adaptation portion of the equalizer is realized with high- \nspeed ECL logic. The entire equalizer is packaged in three 1-inch plug- \nin circuit packs.\n\nDuring design, the equalizer was tested for its static equipment \nsignature performance and dynamic tracking capability. The latter \nevaluation was facilitated with a special-purpose, computer-controlled \nmultipath fade simulator. During a 22-week field trial evaluation in \nPalmetto, Georgia, the equalizer reduced the overall incidence of DR \n6-30 radio outage by more than a factor of 3. System estimates indicate \nthat this improvement factor could eliminate the need for space- \ndiversity reception on more than 50 percent of the short-haul digital \nradio hops that currently use it. Use of the baseband adaptive trans- \nversal equalizer thus can provide considerable cost savings.\n\nCompletion of this project required the synergistic efforts of many \nindividuals. The authors are pleased to acknowledge the following \ncontributors: J. S. Bitler, for designing many of the analog integrated \ncircuits; G. L. Frazer, for special insights into carrier and timing \nrecovery; M. H. Meyers, for theoretical BER and equipment signature \ncalculations; K. L. Seastrand, for initially proposing transversal equal- \nization in our digital radio systems; M. A. Skinner, for overseeing the \nproject during its development phase; and R. B. Ward, for contribu- \ntions to the carrier recovery design.\n\n12. N. Amitay and L. J. Greenstein, \u201cMultipath Outage Performance of Digital Radio \nReceivers Using Finite-Tap Adaptive Equalizers,\u201d NATO/AGARD 33rd Sympo-\n\nsium itd Electromagnetic Wave Propagation Panel, Spatind, Norway, October \n4-7, 1983.\n\n13. W. D. Rummler, \u201cA New Selective Fading Model: Application to Propagation Data,\u201d \nB.S.T.J., 59, No. 5 (May-June 1979), pp. 1037-71.\n\n14. T. Murase et al., \u201c200 Mb/s 16-QAM Digital Radio System With New Countermea- \nsure Techniques for Multipath Fading,\u201d ICC \u201981 (June 1981), pp. 46.1.1-5.\n\n15. S. Takenaka et al., \u201cA Transversal Fading Equalizer for a 16-QAM Microwave \nDigital Radio,\u201d ICC \u201981 (June 1981), pp. 46.2.1-5.\n\n16. J. E. Mazo, \u201cAnalysis of Decision-Directed Equalizer Convergence,\u201d B.S.T.J., 59, \nNo. 10 (December 1980), pp. 1857-76.\n\n17. M. Emshwiller, \u201cCharacterization of the Performance of PSK Digital Radio Trans- \nmission in the Presence of Multipath Fading,\u201d ICC\u201978 (June 1978), pp. 47.3.2-6.\n\n18. C. W. Lundgren and W. D. Rummler, \u201cDigital Radio Outage Due to Selective \nFading\u2014Observation vs. Prediction From Laboratory Simulation,\u201d B.S.TWJ., 58, \nNo. 5 (May-June 1979), pp. 1073-100.\n\n20. C. P. Bates and M. A. Skinner, \u201cImpact of Technology on High-Capacity Digital \nRadio Systems,\u201d ICC\u201983 (June 1983), pp. F2.3.1-5.\n\n22. S. Sakagami et al., \u201cInband Amplitude Dispersion Characteristics During Multipath \nFading on Microwave Links,\u201d Rev. Elec. Commun. Lab., 29 (November-December \n1981), pp. 1295-303.\n\nGerald L. Fenderson, B.S.E.E., 1960, University of Maine; M.S.E.E., 1963, \nNortheastern University; AT&T Bell Laboratories, 1960\u2014. Since joining \nAT&T Bell Laboratories, Mr. Fenderson has participated in the development \nof FM and digital microwave radio systems. His most recent responsibility \nhas been in the design of digital modems, including adaptive transversal \nequalization. Mr. Fenderson received an AT&T Bell Laboratories Distin- \nguished Technical Staff Award in December 1982. Member, Tau Beta Pi, Eta \nKappa Nu.\n\nJames W. Parker, A.S.M.E.T., 1978, Vermont Technical College; AT&T \nBell Laboratories, 1978\u2014. Mr. Parker has worked on a variety of physical \ndesign projects for digital radio systems and is currently involved in the design\n\nand development of advanced and international radio bays. Member, Tau \nAlpha Pi.\n\nPatrick D. Quigley, A.S.E.E.T., 1978, S.U.N.Y. at Alfred; B.S.E.E.T. 1983, \nUniversity of Lowell, Lowell, MA; AT&T Bell Laboratories, 1978\u2014. Mr. \nQuigley has worked on analog, digital, and firmware development projects for \nthe AR6 and DR6 radio systems. He is presently a Member of Technical Staff \nin the Microwave Radio Systems department, working on the development of \na digital monitoring receiver for advanced digital radio systems.\n\nScott R. Shepard, B.S. (Electrical Engineering) and B.S. (Physics), 1979, \nKansas State University; M.S. (Electrical Engineering), 1981, The Massachu- \nsetts Institute of Technology; AT&T Bell Laboratories, 1979\u2014. While at \nK.S.U., Mr. Shepard was employed as a research assistant for various problems \nin electromagnetic theory, including the design and construction of optical \nlogic devices and the focusing of charged particles in a linear accelerator. His \nmaster\u2019s research involved the analysis of a nonlinear optical pulse-shaping \ndevice by means of symbolic manipulation software at M.I.T.\u2019s artificial\n\nintelligence laboratory. Mr. Shepard\u2019s major responsibilities at AT&T Bell \nLaboratories have been the design of the adaptive transversal equalizer and \nthe design of the dynamic multipath fade simulator. Currently, in addition to \nchannel modeling and channel conditioning, he is involved in high-speed, \nhigh-accuracy, analog-to-digital and digital-to-analog signal conversion. Mem- \nber, IEEE, Eta Kappa Nu, Sigma Pi Sigma, Tau Beta Pi, Phi Kappa Phi, and \nSigma Xi.\n\nCurtis A. Siller, Jr., B.S.E.E., 1966, M.S. (Plasma Physics), 1967, Ph.D. \n(Electrical Engineering), 1969, The University of Tennessee, at Knoxville; \nAT&T Bell Laboratories, 1969-1978, 1979\u2014. Mr. Siller\u2019s earliest experience \nat AT&T Bell Laboratories was in the analysis and design of reflector antennas \nfor terrestrial microwave communications. He subsequently initiated an ex- \nploratory investigation of adaptive transversal equalization for advanced dig- \nital radio systems. His more recent research interests were in digital signal \nprocessing, particularly equalizer control algorithms and new techniques for \ndigital filtering. Mr. Siller is presently involved in system engineering of future \ndigital transmission systems. Mr. Siller is the recipient of an AT&T Bell \nLaboratories Distinguished Technical Staff Award. Member, Phi Eta Sigma, \nEta Kappa Nu, Tau Beta Pi, Phi Kappa Phi, Sigma Xi, American Association \nfor the Advancement of Science, and the IEEE, where he is a Senior Member \nand serves on the Signal Processing and Communication Electronics Technical \nCommittee.\n\nAdaptive Differential Pulse Code Modulation (ADPCM) systems can pro- \nvide high-quality digitizations of telephone-bandwidth speech at a bit rate of \n32 kb/s. At a lower bit rate such as 24 kb/s, the quality of the speech is limited \nby an easily perceptible level of quantization noise. This paper proposes an \nadaptive postfiltering procedure that can significantly enhance the quality of \nlower bit rate ADPCM. The coefficients of the postfilter are easily derivable \nfrom the predictor coefficients in the ADPCM decoder. In a subjective test \ninvolving 18 listeners and two sentence-length test inputs, the enhanced \n24-kb/s speech with an optimized postfilter design ranks very close to conven- \ntional 32-kb/s speech. A suggested application of the postfiltering procedure \nis in packet voice or mobile radio systems where substandard bit rates such as \n24 kb/s or 16 kb/s are sometimes necessary. The postfiltering algorithm has \nalso been successfully tested in non-DPCM situations, such as in the enhance- \nment of speech degraded by additive white Gaussian noise.\n\nRecent algorithms for adaptive prediction\u2019 and adaptive \nquantization? have led to the realization of high-quality ADPCM \nsystems at 32 kb/s. This bit rate is the result of 8-kHz sampling and \nquantization using 4 bits/sample. The quality of 24-kb/s speech using \nthe same prediction algorithm and 3-bits/sample coding is limited by \na clearly perceptible level of quantization noise. This paper proposes \na very simply implemented postfiltering algorithm, which provides a \nsignificant enhancement of 24-kb/s quality. In a subjective test to be\n\nA natural application of the postfiltering procedure would be in \nvariable bit rate ADPCM systems such as packet networks or mobile \nradio where substandard bit rates such as 3 or 2 bits/sample are \noccasionally encountered. The postfiltering technique described in this \npaper is particularly effective at the bit rate of 3 bits/sample. It is also \neffective in non-DPCM situations such as in the enhancement of \nspeech degraded by additive white Gaussian noise. When the signal- \nto-noise ratio (s/n) at the input to the postfilter is too low (as in 2-bit \nADPCM or with white Gaussian noise at a relative noise level exceed- \ning approximately \u20143 dB), noise suppression can only be achieved at \nthe expense of severe distortion of the speech signal itself. When the \n24-kb/s ADPCM is enhanced, the introduction of speech distortion is \nperceptible, but the effect of noise reduction is by far the more \ndominant phenomenon.\n\nThe philosophy of the postfiltering technique is represented in Fig. \n1. Part (a) of the figure shows a signal spectrum with two narrowband \ncomponents in the frequency regions W, and Ws, and a flat noise \nspectrum that is 15 dB below the first signal component but 5 dB \nabove the second signal component. An ideal postfilter for this situa- \ntion would have a gain of unity (0 dB) in the regions W; and W2 and \na gain of zero (\u2014 \u00a9 dB) in the rest of the frequency range. In real \nspeech applications, implementation of such all-or-none responses is \nimpractical except in the special cases where the stopband regions of \nthe postfilter are merged into a single contiguous frequency region as \nin a low-pass or high-pass postfilter.**\n\nA more practical approach, proposed in this paper, is the use of a \npostfilter frequency response that peaks in the regions W; and Wo, \nbut is significantly lower in the rest of the frequency range. Figure 1b \nillustrates an extreme example of this approach. Here, the transfer \nfunction of the postfilter is chosen to be identical to the input signal \nspectrum in Fig. la. The resulting spectra of postfiltered signal and \npostfiltered noise preserve the original signal-to-noise ratios of 15 dB \nand \u20145 dB in the regions W, and W2, respectively. However, the noise \nin the rest of the illustrated frequency range is now much lower, \nrelative to the signal levels, than in part (a) of the figure. Specifically, \nthe signal-to-background-noise ratios for regions W, and W2 are now \n45 dB and 10 dB, in place of 15 dB and \u20145 dB in the absence of \npostfiltering. This suppression of background noise also implies that\n\nFig. 1\u2014An idealized explanation of the effects of postfiltering, assuming a signal \nwith two narrowband components and a noise spectrum that is white. (a) Signal and \nnoise spectra at the input to the postfilter, showing signal-to-noise ratios of 15 dB and \n\u20145 dB in signal frequency bands W, and W.. (b) Spectra of postfiltered signal and \npostfiltered noise, assuming a postfilter transfer function identical to the signal spectrum \nin (a). Regions W; and W, continue to have local signal-to-noise ratios of 15 dB and \u20145 \ndB as in (a), but the signals are now 45 dB and 10 dB above the out-of-band noise level. \nIn (a) the corresponding numbers are only 15 dB and \u20145 dB. The overall effect is a \nreduction of perceived noise, but the price paid is a change in the relative strengths of \nthe signal components in W, and W2.\n\nthe residual noise spectrum after postfiltering is very similar to the \ninput signal spectrum itself. In speech applications, noise that is \nshaped in this manner tends to be perceived as speech.\n\nIn the applications discussed, the technique realizes a broad range of \npostfilter design over which the phenomenon of noise suppression \ndominates the phenomenon of signal distortion.\n\nAlthough speech enhancement\u2019 is an \u201cancient\u201d art, we believe that \nthe adaptive postfiltering technique discussed in the next section is \nnovel. It can be used as a very general technique for speech enhance- \nment. It can also be used very effectively in the specific context of \nADPCM noise. The coefficients of the proposed postfilter are inspired \nby the coefficients of the adaptive predictor in ADPCM coding, and \nare in fact very closely related to these coefficients.\n\nFigures 2 and 3 provide block diagram descriptions of ADPCM with \nadaptive postfiltering.\n\nFigure 2 shows the decoder part of the system. Broken lines in the \nfigure refer to parts of the system that compute the coefficients of the \nadaptive predictor and the adaptive postfilter. The coefficients used \nin the postfilter are differently scaled versions of the coefficients used \nin the adaptive predictor. These coefficients are already available in \nconventional ADPCM. In the case of a system with Backward-Adap- \ntive Prediction (APB), the predictor coefficients are updated in gra- \ndient-search algorithms driven by a recent history of the input and \noutput of the ADPCM decoder.\n\nA more complete block diagram of the ADPCM system appears in \nFig. 3. The quantizer and predictor assumed in this paper are both\n\nINPUT TO CONVENTIONAL ENHANCED \nADPCM ADPCM ADPCM \nDECODER OUTPUT OUTPUT \n/ \\ N \n/ \\ \\\n\nFig. 2\u2014Adaptive postfiltering of the output of an ADPCM decoder. The coefficients \nof the postfilter are scaled versions of the coefficients of the adaptive predictor in \nDPCM. In DPCM-APB, the predictor coefficients are obtained on the basis of obser- \nvations of a recent history of decoder input and decoder output. The parts of the circuit \nthat determine coefficient values are shown by broken lines.\n\nbackward-adaptive devices, implying that no special side information \nneeds to be explicitly transmitted to the ADPCM decoder to enable \nadaptations of quantizer step size and predictor coefficients.\n\nThis adaptive predictor we assumed is a pole-zero predictor, similar \nto that in Ref. 1. As Fig. (8) shows, the predicted value x(n) of input \nx(n) is a combination of two components, the outputs \u00a3,(n) and x,(n) \nof an all-zero predictor B(z) and an all-pole predictor A(z). Formally,\n\nFig. 3\u2014Complete block diagram of an ADPCM system with a pole-zero predictor \n[defined by all-zero and all-pole components A(z) and B(z)] and a pole-zero postfilter \n[defined by components A\u2019(z) and B\u2019(z) that are derived from A(z) and B(z)]. The \nextreme case of A\u2019(z) = B\u2019(z) = 0 results in conventional ADPCM without postfiltering. \nThe case of A\u2019(z) = A(z) and B\u2019(z) = B(z) results in a postfilter transfer function that \nis identical to the input signal spectrum, as in Fig. 1b.\n\nwhere u(n) is the quantized version Q[-] of the prediction error and \ny(n) is the reconstructed output:\n\nAdaptation of the predictor coefficients a; and 6; follow the updating \nalgorithms\u2019\n\nThe coefficients of the all-pole predictor are further controlled, for \nstability reasons, by the following constraints:\n\nA good starting point for designing the postfilter is the frequency \nresponse of the inverse predictor. This is the system whose input and \noutput are the innovations u(n) and the reconstruction y(n). Its \ntransfer function, derivable from linear equations that relate u(n), \nx(n), and y(n), is\n\n2 6 \nA(z) = Yaz?; Biz) = Y Bz\u201d. \nj=l j=l \nThe speech-like transfer function of Fig. 1b is approximated if the \npostfilter response is identical to the function [Y(z)]/[U(z)]. This is \nbecause the spectrum of the quantized innovations u(n) is approxi- \nmately white and that of the reconstruction y(n) is hopefully an \napproximation to that of the input x(n). More generally, as in Fig. 3, \nwe propose a postfilter transfer function\n\nThe extreme situation of Fig. 1b is approximated when a = 6 = 1. \nIn practice, this approximation can be quite poor because of the effects \nof nonideal predictor adaptation, usually resulting in an inverse pre- \ndictor transfer function that is a flattened version of the input speech \nspectrum, with poles and zeros that may also be significantly shifted \nfrom their original locations. The case of a = 6 = 0 corresponds to \nconventional ADPCM without any postfiltering. As we discuss in the \nnext section, intermediate designs provide different mixes of noise \nsuppression and speech distortion.\n\nFigure 4 shows an illustrative spectrum of input speech and com- \npares it with the transfer functions F(z) for (a = 0.2; 8 = 1.0) and \n(a = 1.0; 8 = 1.0). The latter condition simply corresponds to the \ntransfer function of the inverse predictor.\n\nIV. EXPERIMENTAL RESULTS WITH ADPCM SPEECH \nThe speech inputs used in the experiment were the sentence-length\n\nFig. 4\u2014(a) Input speech spectrum; and power transfer functions of postfilter with \nscaling coefficients for (b) a = 0.2, 8 = 1.0, and for (c) a = 1.0, 6 = 1.0. The plot (c) is \nmerely the transfer function of the inverse predictor in the DPCM-APB system. [The \n0-dB line is the same for (b) and (c) but different for (a)].\n\nutterances \u201cThe Lathe is a big tool\u201d and \u201cThe chairman cast three \nvotes,\u201d bandlimited to 3.2 kHz in each case and sampled at 8 kHz. \nThese inputs will be referred to as L8 and C8, respectively.\n\nFigures la and 1b indicate that postfiltering can result in significant \nimprovements in s/n. Table I further demonstrates this for the ex- \namples of 3-bit and 2-bit DPCM. The results tabulated are the values \nof the s/n at the input of the postfilter and the s/n after postfiltering. \n(See Fig. 3.) Table I also shows corresponding values of the segmental \ns/n. In the ranges 0 < a <1 and 0 <8 <1 for the coefficient scaling \nfactors, the greatest gains in the s/n are obtained when a = 6 = 1. \nThese gains are seen to be as high as 8.9 dB for both L8 and C8. The \ngains of the s/n at the input of the postfilter are always lower for the \ndesign a = 0.2 and 6 = 1.0. But we presently note that these settings \nof a and @ provide a subjectively desirable design.\n\nTables II and III provide the results of a subjective test involving \n14 listeners, including 9 from the AT&T Bell Laboratories Acoustics \nResearch department and 5 listeners who had no prior exposure to \nspeech coding experimentation or testing. A total of eight stimuli were \nincluded in the test. These included 4-bit ADPCM without postfilter- \ning, 38-bit ADPCM with six postfiltering conditions (including the no- \npostfiltering case of a = 6 = 0), and 4-bit ADPCM with 6-kHz sampling \nand a substandard speech bandwith of W = 2.6 kHz. This last condi- \ntion was included to provide a 4-bit, 24-kb/s alternative to the 3-bit \nADPCM stimuli, all of which also had a bit rate of 24 kb/s. The values \nof a and B used in the test were selected on the basis of a pilot test\n\nTable |\u2014Values of s/n at input of postfilter and after postfiltering \n(see Fig. 3). Numbers in parentheses are corresponding values of \nsegmental s/n ratio\n\nTable II\u2014Number of wins in a round-robin tournament involving \neight coding conditions and four listeners, where the maximum \npossible score is 196 for any given coding condition\n\nTable !/I\u2014Rank ordering of coding conditions by the group of 14 \nlisteners and by a subgroup of 9 listeners from the Acoustics \nResearch Department\n\nthat identified the interesting ranges of these parameters from the \npoint of view of perceived mixes of noise suppression and speech \ndistortion.\n\nIn general, use of postfiltering results in an amplification of the \nspeech signal as suggested in Fig. 1b. The postfiltered speech stimuli \nwere therefore appropriately scaled down to mitigate differences in \nstimulus loudness.\n\nThe subjective test involved an exhaustive pairwise comparison of \nall possible stimulus pairs, with each pair appearing at random places \nin the test once in each possible order of presentation. The total \nnumber of AB comparisons was therefore 768 (8 X 7 = 56 possible \nstimulus pairs for each of 14 listeners).\n\nTable II shows, separately for inputs L8 and C8, the total number \nof wins of each stimulus, with a maximum possible score of 196 for \neach stimulus [a maximum score of 2-(8 \u2014 1) for each of 14 listen- \ners]. It is seen that the worst two coding conditions stand apart from \nthe rest. These conditions are 3-bit ADPCM with no prefiltering and \n4-bit ADPCM with 2.6-kHz bandwidth speech input (and output). \nThis latter condition gets a particularly low total score. Table II also \nshows that the above results are not very different for the inputs L8 \nand C8.\n\nof the eight coding conditions in the subjective test. Results are shown \nseparately for the total group of 14 listeners and the group of 9 listeners \nfrom the Acoustics Research department. It is seen that the rankings \nare not significantly different for the two populations. The best setting \nof the coefficient scaling parameters is defined by\n\nin each case, and for both L8 and C8. With input L8, 3-bit ADPCM \npostfiltered as above is ranked a close second to 4-bit ADPCM speech \nof equal bandwidth. In fact, the 4-bit ADPCM coder is ranked only \nfourth when the results of all 14 listeners are pooled together. The \nsecond and third ranks in this category belong to postfilters with the \ndesign (a = 0.4; 8 = 0.8) and (a = 0.6; 6 = 0.6). The preference for the \ndesign (a = 0.2; 8 = 1.0) has a simple interpretation. It suggests a \npostfilter transfer function that mimics the approximate speech spec- \ntrum (the inverse predictor function) very closely at the zeros of that \nspectrum (8 = 1.0), but very loosely at the poles (a = 0.2). This \nsuggests a condition that seeks to maximize background noise sup- \npression and minimized perceived speech distortion. In the case of \nvoiced speech segments, the poles tend to correspond to formant \nfrequencies and the value of a = 0.2 prevents an undue emphasis of \nthe higher-amplitude spectral peaks, a situation that was indeed \nencountered in the example of Fig. 1b.\n\nAs we see in Table I, the s/n gains due to postfiltering are equally \nsignificant for both 3-bit ADPCM and 2-bit ADPCM. Perceptually, \nhowever, the general noise level in 2-bit ADPCM speech is such that \na useful degree of noise suppression requires the design of (a = 1.0; 8 \n= 1.0). With this design, the speech distortion introduced by the \npostfilter is also substantial. For this reason, the case of 2-bit ADPCM \nis not considered to be of sufficient practical importance to pursue \nformal subjective testing. Informal testing shows, however, that the \ndesign of (a = 1.0; 8 = 1.0) is again preferable to conventional 2-bit \nADPCM (a = 0; 6 = 0).\n\nThe specific postfiltering algorithm of Fig. 1b (a = 1.0; 6 = 1.0) was \nalso applied to speech degraded by additive white Gaussian noise. The \ninput speech was L8, the speech-to-noise ratios ranged from \u20143 dB to \n17 dB, and all coefficients were obtained simply by simulating the \neasily available case of 5-bit ADPCM, a bit rate high enough to \nintroduce very little quantization noise in comparison with the levels\n\nof Gaussian noise being studied. We find the postfiltering algorithm \nprovides a very useful enhancement of noisy speech if the input to the \npostfilter had a s/n of at least +3 dB. For lower values of s/n, \npostfiltering provides noise suppression, but at the cost of substantial \ndistortion of the speech itself.\n\n1. T. Nishitani et al., \u201cA 32 kb/s Toll Quality ADPCM Codec Using a Single Chip \nSignal Processor,\u201d Proc. ICASSP (April 1982), pp. 960-3.\n\n2. D. W. Petr, \u201c82 kb/s ADPCM-DLQ Coding for Network Applications,\u201d Proc. IEEE \nGlobecom Conf., December 1982. pp. A8.3.1-A8.3.5.\n\n4. J. O. Smith and J. B. Allen, \u201cVariable Bandwidth Adaptive Delta Modulation,\u201d \nB.S.T.J., 60, No. 5 (May-June 1981), pp. 719-37.\n\n6. P. Cummiskey, N. S. Jayant, and J. L. Flanagan, \u201cAdaptive Quantization in \nDifferential PCM Coding of Speech,\u201d B.S.T.J., 52, No. 7 (September 1973), pp. \n1105-18.\n\nNuggehally S. Jayant, B.Sc. (Physics and Mathematics), Mysore Univer- \nsity, 1962, B.E., 1965, and Ph.D. (Electrical Communication Engineering), \n1970, Indian Institute of Science, Bangalore; Research Associate, Stanford \nUniversity, 1967-1978; AT&T Bell Laboratories, 1968\u2014. Mr. Jayant was a \nvisiting scientist at the Indian Institute of Science in 1972 and 1975 and a \nVisiting Professor at the University of California, Santa Barbara, in 1983. Mr. \nJayant has worked in the field of digital coding and transmission of waveforms, \nwith special reference to robust speech communications. Editor, IEEE Reprint \nBook, Waveform Quantization and Coding and co-author of Digital Coding of \nWaveforms: Principles and Applications to Speech and Video (Prentice Hall, \n1984).\n\nVenkatasubbarao Ramamoorthy, B.E. (Electrical Engineering), 1970, The \nRegional Engineering College at Tiruchirappalli, India; M.Tech., 1972, The \nIndian Institute of Technology, Madras, India; Tekn.Dr., 1981, University of \nLink6ping, Link\u00e9ping, Sweden. Mr. Ramamoorthy was with the Indian Space \nResearch Organisation at Bangalore, India, prior to his joining as a staff \nmember at the department of Electrical Engineering, the University of Lin- \nkoping, Sweden, in 1974. He visited AT&T Bell Laboratories during the \nsummer of 1983. His current research interests include speech processing in \nmobile and packet radio environments, channel and source coding, digital \nmodulation techniques, and development of handicap aids for children with \nspeech problems.\n\nOn Using ine iiakura-Saiio ivieasures for Speecn \nCoder Performance Evaluation\n\nThe purpose of this paper is to discuss theoretical, as well as psychophysical, \naspects of using the Itakura-Saito type of measures for evaluating the quality \nof coded speech. We present psychoacoustic interpretations of the measures \nand identify their effectiveness as well as limitations within the theoretical \nframework of a generalized waveform coder distortion model. The discussions \nthen point out some specific issues to be resolved through psychoacoustic \nresearch effort.\n\nA \u201cgood\u201d speech quality measure is central to progress in the \nresearch and development of speech processing systems. In speech \ncoding, for example, we need a quality measure to provide insight into \ndifferent distortions that are present in a coder output. If such a \nmeasure existed, it would help speech researchers identify how various \nkinds of distortions could be traded in order to improve the perceptual \nperformance of the speech coder. In an engineering context, a measure \nthat indicates the perceptual quality is a criterion to be optimized in \nspeech coder design. Without such a measure, tuning coding schemes \nto achieve optimal quality is not a trivial task and the performance \ncannot be conveniently evaluated.\n\nSpeech quality assessment, however, involves subjective, psycholog- \nical attributes of human perception, an area in which mathematicians\n\nand engineers are usually not well versed. Thus, speech quality eval- \nuation has never been established satisfactorily in mathematical terms. \nThe conventional signal-to-noise ratio (s/n), widely used in character- \nizing signal transmission/reception environments, is an ineffective \nmeasure of speech quality. Several other measurement methods and \nparameters, such as the isopreference method! and the subjective \ns/n,\u201d have been proposed during the last two decades. General surveys \nof classical approaches can be found in Refs. 1 and 3. Reference 2 and \nits references also provide a summary of past efforts. Among these \napproaches, one particular class of measures based upon the Itakura- \nSaito measure has attracted engineers and scientists taking an analyt- \nical approach toward the problem. The Itakura-Saito measure and its \nvariations, such as the Itakura or log likelihood ratio measure* and \nthe likelihood ratio measure,\u2019 have been employed in noise studies by \nSambur and Jayant;\u00ae in vocoder designs by Juang et al.\u2019 and Wong et \nal.;3 in automatic speech recognition by Itakura\u00ae and Rabiner;\u00b0 and \nas quality measures by Goodman et al.,!' Crochiere et al.,!? and \nBarnwell et al.!\u00b0\n\nAlthough successful applications of this class of measure are wide- \nspread in speech processing, none of them comes close to being justified \nas the speech quality measure. This paper attempts to identify the \neffectiveness as well as limitations of using this class of measure for \nspeech quality within the theoretical framework of a generalized \nwaveform coder distortion model.\u201c We will further point out that \nsuch limitations also exist in current automatic speech recognizers \nthat rely upon spectral matching. We then present some considera- \ntions relating to psychoacoustic studies, aiming at a better understand- \ning of the fundamental concepts of speech quality in the presence of \nspectral distortion. These considerations will help direct future rele- \nvant psychoacoustic experiments for studying the dynamics of speech \nperception.\n\nLet s(i) and s\u2019(i) be two sampled speech signals, and let x,(i) and \nx/,(i) be two windowed segments, or frames, of s(i) and s\u2019(i), respec- \ntively. Segments x,(i) and x;,(i) are obtained by applying a window \nfunction w(t), with w(t) = 0 fori <0 andi 2 N, to the speech signals \nat instance n; in particular,\n\nThe windowing operation greatly facilitates using spectral represen-\n\ntations for speech analysis because speech is considered as a quasi- \nstationary signal. We denote the z-transform of x,(i) and x,(i) by \nX,(z) and X;(z), respectively. The Fourier transform is obtained by \nevaluating the z-transform on the unit circle, i.e., z = e\u2019\u201d, and thus the \nnotations X,,(e\u201d) and X/(e/\u201d) are used to designate the Fourier trans- \n-form of two windowed signals, respectively. For every such pair of \nspectral representations, X,(e/\u201d) and X/(e/\u201d), a spectral distortion \np[Xn, X/] can be defined to measure the dissimilarity between X,,(e\u2019\u201d) \nand X/(e?*). In speech analysis, one particularly interesting distortion \nmeasure is the Itakura-Saito measure, which is defined as\n\nThis mathematically tractable distortion measure has been success- \nfully employed in vocoder designs.\u2019 Detailed analytical properties of \nthe measure can be found in Refs. 4 and 5.\n\nIt has been shown in short-time Fourier analysis that a signal can \nbe reconstructed from a properly time-sampled sequence of short-time \nFourier transforms.\u2019\u00ae We can, thus, further represent the two signal \nsequences, s(i) and s\u2019(1), by their corresponding short-time spectral \nsequences. Using \u00a9 to denote the reconstruction process,\n\nIn the above / is the underlying interval for short-time Fourier analysis \nand has been dropped in the final expressions without ambiguity. Such \na representation allows us to characterize the dissimilarity between \ns(i) and s\u2019(i) in terms of distortion measures obtained from short- \ntime spectral representations. A distortion sequence between two \nspeech signals is then defined as\n\nExtending the definition (3) to (7), then, we have a sequence of \nItakura-Saito distortions.\n\nThe Itakura-Saito distortion measure defined by (3) and (4) is in \nfact the distortion measure for all-pole signal modeling; it was origi- \nnally introduced as an error-matching function in maximum likelihood \nestimation of autoregressive spectral models.!\u2019 Therefore, we shall \nconfine ourselves to the analysis of Mth-order all-pole signal models \ndespite the fact that a distortion measure could be more general. \nSeveral important results of the measure related to all-pole signal \nmodeling are:\n\nwhen the gain terms are identical. A;,(z) takes the same form as A,(z) \nin (11). In the above expressions, we have assumed that A,(z) and \nA(z) have all their roots within the unit circle. Therefore,\u2019\u00ae\n\nFor clarity, we further define the likelihood ratio measure and the \nlog likelihood ratio (or Itakura) measure as follows:\n\nIn defining the above two measures, A,(z) and A,(z) are the optimal \nMth-order inverse filters of X,(z) and X/(z), respectively.'\u00ae Further- \nmore,\n\nNote that a, is the minimum Mth-order prediction residual energy \npertaining to signal X,,(z).\n\nThe Itakura-Saito distortion between the input and output signals \nof a linear system H(e\u2019\u201c) can be easily calculated. Denoting the input \npower spectrum as | X,(e\u2019\u201d)|?, we have the output power spectrum \n| X7,(e%*) |? = | X(e*)H(e**) |?. Therefore,\n\nwhere A,,(z), as defined above, is the optimal Mth-order inverse filter \nof X,(z) and B,(z) is another Mth-order Finite Impulse Response \n(FIR) filter, taking the same form as (11). We also assume that A,(z) \nand B,,(z) both have all their roots within the unit circle. The input/ \noutput relationship of the system is illustrated in Fig. 1. Since A,(z) \nis the optimal Mth-order inverse filter of X,(z), E,(z) is then the \nresidual signal. X;,(z) is obtained by driving another all-pole filter 1/ \nB,(z) with such a residual signal. The distortion between X,(z) and\n\nFig. 1\u2014A particular class of linear system in which A,(z) is the optimal Mth-order \ninverse filter of X,(z).\n\n= pis A,\u201d B, ; (21) \nwhich is determined by the two all-pole filters, and has the same \nexpression as the likelihood ratio measure of (14). This result gives us \na convenient means of modifying a signal in order to achieve a \nprescribed distortion level from the original signal. Detailed discus- \nsions in Section IV are based upon this concept. It is, however, \nimportant to note that in eq. (21), B,(z) is not unique, and is not \nnecessarily the optimal Mth-order inverse filter of the output signal \nX/(z). It is simply stated that within the Mth-order autoregressive \nmodel framework, a prescribed Itakura-Saito spectral distortion can \nbe obtained from a given signal through proper filtering operations, \nwhich will be convenient to realize.\n\nFigure 2 shows a block diagram of the waveform coder distortion \nmodel used by Crochiere et al. for an interpretation of the log likelihood \nratio measure.\u201d This coder distortion model is composed of a time- \nvarying linear filter h(i), to model the \u201clinearly correlated\u201d distortions, \nand an additive noise source q(i), to account for the nonlinear, uncor- \nrelated distortions in the coder. Since the model attempts to split the \ncomponents of distortion, it was expected that distinctively different\n\nFig. 3\u2014Measuring coder performance with the likelihood ratio in a forward manner.\n\nperceptual effects could be meaningfully studied separately with such \na model.\n\nMeasurement of the coder performance with the likelihood ratio \nmeasure is shown in Fig. 3, which introduces the notion of inverse \nfiltering. We use the likelihood ratio measure, rather than the Itakura- \nSaito measure, because we try to avoid, in the following discussions, \nextra complications in speech quality measurement due to amplifica- \ntion or attenuation. We follow the notation of Section II, except that \nthe subscript indicating the frame index has been dropped, since, for \nmost of the subsequent expressions, signal stationarity is assumed. \nWe shall reinstate the frame index wherever necessary. The two \nparameters, a and a\u2019, are defined as in (17) by\n\nwhere A(z) and A\u2019(z) are the optimal Mth-order inverse filters of X(z) \nand X\u2019(z), respectively. In other words, a and a\u2019 are the minimum \nMth-order prediction residual energies corresponding to x(i) and x\u2019 (i) \nsequences, respectively. The energy of v\u2019(i), denoted by 8\u2019, is then\n\nThe energy of w\u2019(i), on the other hand, is unity due to the normali- \nzation factor 1/ Va\u2019 and eq. (23). The energy ratio of the two filtered\n\ncan be reduced to \n= T | A\u2019(e%*) |? dw \nes \u2018x |A(e*) |? 2m 2) \nsince both A(z) and A\u2019(z) are Mth-order FIR filters, and the first \nM + 1 autocorrelation coefficients of the {[x(i)]/Va } sequence are \nequal to those of the impulse response of 1/A(z). Therefore, the\n\nlikelihood ratio measure of (14) can be expressed in terms of the energy \nratio of the two filtered outputs, v\u2019(i) and u\u2019(i), and\n\nAlternatively, we may replace the filter A\u2019(z) by A(z), the inverse \nfilter of the x(i) sequence, as shown in Fig. 4. In such a case, the \nenergy of u(i), denoted by y, is the likelihood ratio, and the distortion\n\nFig. 4\u2014Measuring coder performance with the likelihood ratio in a backward manner.\n\nThe interpretation of the log likelihood ratio as a coder performance \nmeasure by Crochiere et al. follows the comparison order of eq. (28).2\u201d \nMore specifically, the measure they discussed was log vy, instead of \n+ \u2014 1. The difference between the log likelihood ratio measure and \nthe likelihood ratio measure may be insignificant in terms of measure- \nment. However, the likelihood ratio measure of eq. (14) appears to \ncorrespond more closely to the Itakura-Saito measure in representing \nthe distortion relationship between the input and output signals of a \nparticular class of linear systems. This was shown in eq. (21).\n\nWe now express the measures within the coder model. Referring to \nFig. 2 and denoting the Fourier transforms of h(i) and q(i) by H(e?\u201c) \nand Q(e\u2019*), respectively, we have\n\nFor simplicity we assume that H(z) does not have poles and zeros on \nthe unit circle. From (24), the likelihood ratio distortion measured \nfrom {x(i)} to {x\u2019(z)} is thus\n\nthe following way: \n1. Additive noise distortion, p,, is defined when there is no corre-\n\nIn the above, the superscripts, f and b, denote the forward and \nbackward measurements, respectively.\n\n2. Correlated spectral distortion, p,, is defined when the additive \nnoise component vanishes, i.e.,\n\nThe above decomposition of the measure into additive noise and \ncorrelated spectral distortions provides a helpful means in cross- \nverification between the measure and many known perceptual attri- \nbutes. In the following we shall discuss the merits as well as limitations \nof the above measure in measuring the perceptual quality of waveform- \ncoded speech signals. Such discussions point to some necessary psy- \nchophysical experiments for a closer link between objective and sub- \njective measures.\n\nThe key contribution of the uncorrelated additive noise, q(t), ap- \npears in the integral terms in (33) and (34). Let us consider (34), where \nthe integrand involves the inverse filter A(z) for the input speech \nsignal.\n\nwhere P, is a constant, when A(z) is the optimal (Mth-order) inverse \nfilter of the g(i) sequence. In other words, for a given noise power, the \nintegral is minimized if the noise has the same spectral shape as the \ninput speech, within the Mth-order autoregressive signal modeling \nframework. This appears to be in very good agreement with the results \nof auditory masking that has been proposed as a method for improving \nthe perceived quality of digitally encoded speech.\u2019\u00ae\u201d\u00b0 The same obser- \nvation can also be made on (33), where the integrand involves A\u2019 (z) \ninstead of A(z). A\u2019(z) is the optimal Mth-order inverse filter of the \nencoded output sequence x\u2019(t). If q(t) is truly uncorrelated with x(i) \n(recall that | H(e/\u201d) | = 1 here) and has the same spectral shape as \nx(i), then A\u2019(z) is, in fact, identical to A(z). However, when exact \nshaping of noise spectra is not achievable (as in most practical coder \nsystems), (83) and (34) lead to significantly different distortion mea- \nsurements since a\u2019 involves A\u2019(e/\u201d), which demonstrates attributes of \nQ(e\u2019\u201d). The following example illustrates the difference between the \nforward and the backward measurements.\n\nConsider two signals, one being tonelike and the other being white \nnoise. These two signals are represented in terms of second-order all- \npole models as 1/A,(z) and 1/A,,(z), where\n\nThe two roots of A;,(z) are 0.9 e*/*, which indicate a resonance at \na/4 normalized frequency or at 1000 Hz when the sampling frequency \nis 8000 Hz. These two all-pole models have corresponding reflection \ncoefficient vectors k, and k,,:'\u00b0\n\nClearly, if measured in the forward direction, when an input tonelike \nsignal is being distorted into white noise, the distortion is higher than \nvice versa. The result is reversed if the distortion is measured in the \nbackward direction; that is, distorting an input noise signal into a \ntonelike signal will result in a more serious objective distortion mea- \nsurement than distorting a tone-like signal into white noise. Previous \nstudies in auditory masking demonstrated a similar asymmetry of \nmasking between tone and noise.\u201d\"~\u201d In particular, it has been reported \nthat noise masks a tone more effectively than a tone masks noise. A \n1-kHz tone masked by noise that is one critical band wide typically is \ninaudible at a signal-to-masker ratio of \u20144 dB, while the corresponding \nratio for noise signal masked by tone is approximately \u201424 dB. In \nother words, it is easier to perceive noise in a tone than it is to perceive \na tone in noise. For an objective measure to consistently predict the \nperceived quality, we thus would require that such a measure show \nhigher distortion when the input tone is corrupted by noise and that \nit show lower distortion when input noise is distorted by an additive \ntone signal. Despite the slight difference between masking and distor- \ntion, forward measurements of (33) thus appear to be more justifiable. \nMore rigorous psychoacoustic studies are obviously very important in \ncarefully resolving this measurement direction issue.\n\nCompared to additive noise, correlated spectral distortion has not \nbeen as well studied in the past, but it is a key factor affecting the\n\nperceived quality. One well-known example is that \u201ctelephone speech\u201d, \nwhich is essentially bandlimited to the range of 200 to 3200 Hz, is \nconsidered to be of poorer quality and of lower intelligibility than the \nunfiltered original speech. Since correlated spectral distortion can be \na result of the filtering operation, we shall discuss it using linear \nfiltering concepts.\n\nLinear systems can be categorized into time-invariant and time- \nvariant systems. Accordingly, correlated spectral distortion can be \ntime-invariant or time-variant as demonstrated in eq. (19), where the \ncorrespondence between the filtering operation and the distortion \nmeasure was established. The above-mentioned bandpass filtered \nspeech signals, such as telephone speech, have essentially a time- \ninvariant spectral distortion (here we are not considering tone noise, \nclicks, or channel variations, etc.), while Linear Predictive Coding \n(LPC) vocoders involve many time-variant spectral distortions, as will \nbe discussed shortly.\n\nThe use of the Itakura-Saito type of measure for time-invariant \nspectral distortions, such as (3), (14) and (15), appears to be justifiable, \nat least within the short-time frame boundary where stationarity is \nreasonably assumed. This can be seen from the application of the \nlikelihood ratio measure in vector quantization for voice coding.\u201d* In \nfact, the code words designed for vector quantization using (14) are \nsubstantially consistent with the vowel triangle of Peterson and Bar- \nney from an acoustic-phonetic point of view.\u00ae It also has been shown \nthat the log likelihood ratio measure usually leads to a better recog- \nnition rate in speech recognition schemes.\u2019\u00b0\u201d> (Note that the log \nlikelihood ratio and the likelihood ratio measure make no significant \ndifference in most speech recognition applications. The only theoret- \nical difference is in template generation where minimization of some \ncriterion, such as the average distortion or maximum distortion, is \nrequired.) For interests in psychoacoustic studies, however, it may be \ndesirable to further translate the measurement into a perceptual scale \nthat better interprets the relative perceived quality. (The complication \nhere is the possible sound dependence on a perceptual scale. Consider \nthe following example. Suppose X has been distorted, resulting in Y \nand Z. We can confidently say Y sound is closer to X sound than Z \nsound is, if p[X, Y] < pLX, Z]. However, we are not sure that Y is \nperceptually closer to X than Z is to W, even if p[X, Y] < p[Z, W].)\n\nBeyond the short-time stationary segment level, the time-variant \ndistortion is a more important and complicated factor to consider in \nspeech processing. Spectral distortion measures are defined for every \npair of spectral representations. A natural extension of the distortion \nmeasure for measuring dissimilarity between time-varying signals is \nthus the distortion sequence is expressed by (7). Previous experiments\n\nand several reported results that help illustrate the effect of time- \nvariant spectral distortions upon speech quality are in order.\n\nVoice coding results in time-variant spectral distortion. The key \ncontribution to the time variation of distortion in voice coding such \nas LPC is a result of parameter quantization, although the parameter \nanalysis procedure itself may also introduce some time-variant distor- \ntion because of frame alignment, change in excitation, etc. The effect \nof such distortion thus can be best explained in performance compar- \nison of different parameter quantization schemes.\n\nThe experiment in Ref. 7 that compared the distortion performance \nof vector and scalar quantization for LPC voice coding provides \nimportant insights in this regard. In order to conduct the so-called \nequal average distortion comparison in the experiment, speech signals \nwere vocoded at a lower bit rate with vector quantization and at a \nhigher bit rate with scalar quantization. Subjective comparison of \nthese two sets of synthesized signals of equal average distortion showed \nthat the vector quantization synthesis samples sounded smoother and \nmore pleasant, and were considered of better quality. Substantial \nbackground warble was perceived in the scalar quantization samples. \nDifferences in spectral continuity, distortion contour, and some sta- \ntistics of the distortion process {p,} between the two sets of synthesis \nsamples were then reported to explain the difference in the perceived \nsynthesis quality. It was concluded that a coder that preserves more \nspectral continuity, achieves smoother distortion contour, and pro- \nduces less divergent distortion statistics is better than a coder with \notherwise different distortion performance, even though they yield the \nsame average distortion. Vector quantizers appear to produce \u201cbetter\u201d \ndistortion sequences than do scalar quantizers in LPC voice coding. \nThe importance of considering the distortion as a process or sequence \n(instead of just an average distortion) and of looking into the spectral \ncontinuity (a mathematical definition of which has yet to be obtained) \nwas thus highlighted.\n\nThe concepts of time-variant distortions and spectral continuity \nalso raise a possible explanation for the experimental results of Tri- \nbolet et al.?\u00b0 Here, performances of four different types of waveform \ncoders at three different bit rates were compared. An average noise- \nto-signal measure [eq. (2) of Ref. 26], 4,, which was derived through \nthe concepts of log likelihood ratios, was used as an objective measure \nto predict the subject performance. As seen from Figs. 5 and 6 (dupli- \ncated from Figs. 7 and 9a of Ref. 26), the main failures of the likelihood- \nratio-derived measure are in predicting the performance of all coders, \nat 9.6 kb/s [in particular, Sub-band Coder (SBC) at 9.6 kb/s] and \nAdaptive Differential PCM (ADPCM) coder with a fixed predictor at \n24 kb/s. At 9.6 kb/s all coders perform subjectively worse than objec-\n\nFig. 6-\u2014Objective noise-to-signal measure, 4,, averaged over 16 articulation bands for \nthe 12 coders in Fig. 6.\n\ntively predicted. At 9.6 kb/s, SBC is objectively very close to the \nAdaptive Transform Coder (ATC) but turns out to be subjectively \neven worse than the ADPCM with a variable predictor. At 24 kb/s, \nADPCM with fixed predictor is objectively much worse than ADPCM \nwith variable predictor, but they in fact are subjectively very close. \nThese failures can be attributed to the fact that 4, does not correctly \nconsider the correlated spectral distortion, and more importantly, it is \nonly an average over the entire speech sample, revealing no informa- \ntion on possible perceptual degradation due to time-variant spectral \ndistortions. The outcome that all coders perform subjectively worse \nthan objectively predicted at lower bit rates is probably a result of \nincreased sporadic spectral distortions and reduced spectral continuity \nalong the time axis. Sub-band coding schemes inherently preserve less \nspectral continuity at lower bit rate, and thus it is possible that \nrelatively more quality degradation is perceived at 9.6 kb/s with SBC. \nFinally, the ADPCM coder with adaptive, variable predictor poten- \ntially introduces more spectral discontinuity, due to quantization of \nthe predictor parameters, than does the ADPCM with a fixed, un- \nquantized predictor.\n\nTo illustrate this, plots of the log spectral (eighth-order all-pole) \ndifference between the original and the reconstructed speech signals \nare shown in Fig. 7. Coders used in Fig. 7 are ADPCM with fixed \npredictors and adaptive predictors, respectively. More spectral discon- \ntinuity is observed in the adaptive predictor case, particularly in the \nlow frequency region. Therefore, even though adaptive predictors yield \nhigher prediction gain than fixed predictors,\u201d\u2019 this objective advantage \nhas been subjectively offset by the perceptual sensitivity to time- \nvariant distortions, particularly at higher bit rates, where the effect of \nadditive noise becomes relatively less significant. As a result, the \nsubjective performance gap between the two coders is substantially \nreduced.\n\nSimilar limitations apply to automatic speech recognition schemes \nthat use one single average or accumulative figure to represent the \ndissimilarity between the spectral sequences of the input speech and \nthe stored reference template. In parallel with the concept of meas- \nuring speech quality with the segmental s/n, recognition schemes \nusually resort to segmentation and time warping in order to obtain \nbetter distortion or distance measurements for more accurate recog- \nnition decisions. Nevertheless, segmentation schemes produce hard \nsegmental boundaries, instead of natural, soft transitions, and are \nnever completely reliable. The original problem of measuring the \ndissimilarity between time-varying signals thus has never been entirely \nsolved.\n\nFig. 7\u2014Log spectral difference between the original and reconstructed signals: (a) \nwith a fixed, unquantized predictor; (b) with an adaptive, quantized predictor.\n\nThe above considerations clearly point out the necessity of psycho- \nphysical experiments for developing a better speech quality measure. \nSpecifically, with regard to using the Itakura-Saito type of measures, \nissues to be further studied are: the measurement direction, the feasi- \nbility of characterizing subjective quality by distortion sequences, and \nthe incorporation of some transitive functions into the distortion \nmeasure to account for spectral continuity. In light of the analytical \nfeatures of the Itakura-Saito type of measures, research on these issues \nappears to be vitally important to an analytical speech perception \nmodel.\n\nIt is beyond the scope of this paper to propose and discuss in detail \nthe psychophysical experiment procedures necessary to answer al] the \nquestions above. It is, however, appropriate to address one of the \ndifficulties in psychoacoustic experiment designs here. In addition, we \nshall propose to consider a class of transitive functions to be used in \ndefining the spectral continuity measure.\n\nFigure 8 illustrates the modification procedure. The speech signal is \nfirst inverse filtered by A,(z) to obtain the residual E,,(z), which then \ndrives the chosen filter 1/B,(z) to form the desired signal.\n\na prescribed value can be made simple if we have a good-sized vector \ncode book, as designed in vector quantization.\u2019 The search for 1/B,,(z) \nis then quantum-selectively finite, although there are theoretically \ninfinite number of all-pole filters. Also, the test stimuli designed \naccording to (45) are free from excitation variations, such as funda- \nmental frequency changes, that are better considered separately. \n4.2 Spectral continuity \nAs discussed above, spectral continuity is an important factor af- \nfecting the perceived quality of speech signals. Speech signals carry \ndistinctive time-frequency or spectral transition patterns. Phonetic \nmanifestation in articulated speech signals could be very fast, like \n/str/ in \u201cstrange\u201d, or sustainingly slow, like /i/ in \u201ceat\u201d. To avoid \ncomplications due to such an inherent nonuniform spectral change, \nRef. 7 used the model error spectral sequence {A,(w)}, defined by \nAn(w) = log\n\n| An(e\u2019*) |? | A,(e?*) |?\u2019 \nwhere A,,(z) is a quantized version of A,,(z), to illustrate the difference \nof the ability of various quantization schemes in preserving spectral \ncontinuity. The rationale was based upon the fact that the ultimate \nspectral continuity to be retained is the inherent spectral transition \npattern, and that if a coder produces spectral distortion that is inde- \npendent of time, that is,\n\nthen the time-variant spectral distortion is completely eliminated. \nWhile {A,,(w)} adequately explained the spectral continuity differences,\n\nmore rigorous alternatives are necessary for, at least, the following \nreasons: (1) the variation in A,(w) along the frequency axis, w, as well \nas the time axis, n, is often so substantial that it is difficult to use \nonly (47) to define a spectral continuity measure; (2) it was never \nconcluded that the change in A,,(w) along the time axis, if regarded as \nan indication of spectral smoothness, is indeed perceptually independ- \nent of the spectral transition pattern of the speech signal.\n\nBefore we can completely characterize the spectral continuity along \nboth the frequency and time axis, we would like to propose to tenta- \ntively consider two transitive functions that indicate the spectral \nchanges in a speech signal as a function of time. The notion of eq. \n(21), measuring the distortion between two all-pole spectra, is empha- \nsized in defining such transitive functions. Denoted by \u00a2,(k), the \nforward transitive function is defined by\n\nwhere ); is a time constant and, A,(z) and Az-,(z) are the optimal \nMth-order inverse filters of X;,(z) and X;-,(z), respectively. \u00a2,(k) \nmeasures the all-pole spectral change in the speech signal in a forward \nmanner, i.e., it measures the distortion resulting from replacing the \ncurrent spectral envelope with previous spectral envelops. Character- \nistic changes in excitation, such as the pitch inflection, are not actively \nconsidered in \u00a2;(k), although they may affect the estimation of all- \npole spectral models. One interpretation of measuring the transition \nin speech by the distortion between all-pole models instead of speech \nspectra is that we try to keep the current excitation signal unchanged, \nas if it were present in the previous segments as implied by eq. (21). \nWe also assume that the time constant );, accounting for short-time \nauditory memory,\u201d is independent of the particular sound that is \narticulated and perceived. \nSimilarly, we define the backward transitive function \u00a2,(k) as\n\nNote that if the distortion measure were symmetrical and if dy = As, \nthe two transitive functions would be identical. The appropriateness \nof these functions remains to be studied.\n\nThe transitive functions are to be regarded as part of the speech \nsignal. When a speech signal is distorted because of processing or \nencoding, the corresponding transitive functions are distorted also. \nThe distortion, or noise, in the transitive functions thus provides a \nmeasure of the time-variant spectral distortion that affects the spectral \ncontinuity in the original signal. Further research effort, of course, is\n\nnecessary to verify the suitability of these functions or to develop a \nbetter spectral continuity measure. We feel that the concept in (49) \nand (50) provides a good starting point.\n\nWhile the Itakura-Saito distortion measure and its variations have \nbeen widely employed and are considered promising in characterizing \nspeech quality,\u2019 limitations in such measures still exist and have been \nidentified within the theoretical framework of a generalized waveform \ncoder distortion model in the above discussion. This type of measure \nis inherently nonsymmetric and therefore, in measuring distortions, a \nproper measurement direction needs to be determined. Subjective \nquality evaluation involves perceptual response to various degrees of \ndistortion that has to be considered as a time function or a stochastic \nprocess. The feasibility of describing the subjective quality by finite- \norder statistics of the distortion process is to be studied. Furthermore, \nevidence shows that speech spectral continuity is also a key, if not the \nmost important, factor affecting the subjective quality and thus, the \nspeech spectral transition pattern should be regarded as a vital part \nof the speech signal. An even more fundamental and difficult task is, \nthen, the incorporation of the spectral transition patterns into the \nrather static measurements of the Itakura-Saito distortion. Psychoa- \ncoustic studies are necessary to resolve these issues.\n\n1. W. A. Munson and J. E. Karlin, \u201cIsopreference Method for Evaluating Speech- \nTransmission Circuits,\u201d J. Acoust. Soc. Amer., 34 (1962), pp. 762-74.\n\n2. M. Nakatsui and P. Mermelstein, \u201cSubjective Speech-to-Noise Ratio as a Measure \nof Speech Quality for Digital Waveform Coders,\u201d J. Acoust. Soc. Amer., 72, No. \n4 (1982), pp. 1136-44.\n\n3. M. H. L. Hecker and N. Guttman, \u201cSurvey of Methods for Measuring Speech \nQuality,\u201d J. Aud. Eng. Soc., 15 (1976) pp. 400-3.\n\n4. A. H. Gray, Jr. and J. D. Markel, \u201cDistance Measures for Speech Processing,\u201d IEEE \na Acoustics, Speech, Signal Processing, ASSP-24 (October 1976), pp. \n380-91.\n\n5. R. M. Gray, A. Buzo, A. H. Gray, Jr., and Y. Matsuyama, \u201cDistortion Measures for \nSpeech Processing,\u201d IEEE Trans. Acoustics, Speech, Signal Processing, ASSP- \n28 (August 1980), pp. 367-376.\n\n6. M. R. Sambur and N. S. Jayant, \u201cLPC Analysis/Synthesis From Speech Inputs \nContaining Quantizing Noise or Additive White Noise,\u201d IEEE Trans. Acoustics, \nSpeech, Signal Processing, ASSP-24 (December 1976), pp. 448-94.\n\n7. B.-H. Juang, D. Y. Wong, and_A. H. Gray, Jr., \u201cDistortion Performance of Vector \nQuantization for LPC Voice Coding,\u201d IEEE Trans. Acoustics, Speech, Signal \nProcessing, ASSP-30 (April 1982), pp. 294-304.\n\n8. D. Y. Wong, B.-H. Juang, and A. H. Gray, Jr., \u201cAn 800 Bits/s Vector Quantization \nLPC Vocoder,\u201d IEEE Trans. Acoustics, Speech, Signal Processing, ASSP-30 \n(October 1982), pp. 770-80.\n\n9. F. Itakura, \u201cMinimum Predication Residual Principle Applied to Speech Recogni- \ntion,\u201d IEEE Trans. Acoustics, Speech, Signal Processing, ASSP-23 (February \n1975), pp. 67-72.\n\n10. L. R. Rabiner, \u201cOn Creating Reference Templates for Speaker Independent Rec- \nognition of Isolated Words,\u201d IEEE Acoustics, Speech, Signal Processing, ASSP- \n26 (February 1978), pp. 34-42.\n\n\u201cObjective and Subjective Performance of Tandem Connections of Waveform \nCoders With an LPC Vocoder,\u201d B.S.T.J., 58, No. 3 (March 1979), pp. 601-29.\n\n12. R. E. Crochiere, L. R. Rabiner, N. S. Jayant, and J. M. Tribolet, \u201cA Study of \nObjective Measures for Speech Waveform Coders,\u201d in Proc. 1978 Zurich Seminar \non Digital Commun., pp. H1.1-7.\n\n13. T. P. Barnwell, III, A. M. Bush, R. M. Mersereau, and R. W. Schafer, \u201cSpeech \nQuality Measurement,\u201d Georgia Inst. Technol., Atlanta, Tech. Rep. E21-655-77- \nTB-1, June 1977.\n\n14. M.R. Aaron, J.S. Fleischman, R. W. McDonald, and E. N. Protonatarios, \u201cResponse \nof Delta Modulation to Gaussian Signals,\u201d B.S.T.J., 48, No. 5 (May-June 1969), \npp. 1165-95.\n\n15. R. E. Crochiere, J. M. Tribolet, and L. R. Rabiner, \u201cAn Interpretation of the Log \nLikelihood Ratio as a Measure of Waveform Coder Performance,\u201d IEEE Trans. \nAcoustics, Speech, Signal Processing, ASSP-28 (June 1980), pp. 318-23.\n\n16. J. B. Allen, \u201cShort-Term Spectral Analysis and Synthesis and Modification by \nDiscrete Fourier Transform,\u201d IEEE Trans. Acoustics, Speech, Signal Processing, \nASSP-25 (June 1977), pp. 235-8.\n\n17. F. Itakura, \u201cSpeech Analysis and Synthesis Systems Based on Statistical Method,\u201d \nDoctor of Engineering Dissertation (Department of Engineering, Nagoya Univer- \nsity, Japan, 1972). (In Japanese).\n\n18. J. D. Markel and A. H. Gray, Jr., Linear Prediction of Speech, New York: Springer- \nVerlag, 1976.\n\n19. M. R. Schroeder, B. A. Atal, and J. L. Hall, \u201cOptimizing Digital Speech Coders by \nExploiting Masking Properties of the Human Ear,\u201d J. Acoust. Soc. Amer., 66 \n(1979), pp. 1647-52.\n\n22. J. L. Hall and M. R. Schroeder, \u201cLoudness of Noise in the Presence of Tones: \nMeasurements and Non-linear Model Results,\u201d in Psychophysical, Physiological, \nand Behavioral Studies in Hearing, G. van den Brink and F. A. Bilsen, Eds., Delft, \nThe Netherlands: Delft University Press, 1980, pp. 329-32.\n\n23. R. P. Hellman, \u201cAsymmetry of Masking Between Tones and Noise,\u201d Percept. \nPsychophys., 11 (1972), pp. 241-6.\n\n24. J. Zwislocki, \u201cAnalysis of Some Auditory Characteristics,\u201d in Handbook of Mathe- \nmatical Psychology, Vol. 3, R. D. Luce, R. R. Bush, and E. Galanter, Eds, New \nYork: Wiley, pp. 1-97.\n\n25. B. A. Dautrich, L. R. Rabiner, and T. B. Martin, \u201cOn the Effects of Varying Filter \nBank Parameters on Isolated Word Recognition,\u201d J. Acoust. Soc. Amer., Supple- \nment 1, 72 (Fall 1982), p. 531.\n\n26. J. M. Tribolet, P. Noll, B. J. McDermott, and R. E. Crochiere, \u201cA Comparison of \nthe Performance of Four Low-Bit-Rate Speech Waveform Coders,\u201d B.S.T.J., 58, \nNo. 3 (March 1979), pp. 699-712.\n\n27. P. Noll, \u201cA Comparative Study of Various Schemes for Speech Encoding,\u201d B.S.T.J., \n54, No. 9 (November 1975), pp. 1597-1614.\n\n28. G. A. Miller, \u201cThe Magical Number Seven, Plus or Minus Two: Some Limits in \nOur Capacity for Processing Information,\u201d Psychol. Rev., 63 (1956), pp. 81-97.\n\nA Packei/Circuit Switcn \nBy Z. L. BUDRIKIS* and A. N. NETRAVALI* \n(Manuscript received July 29, 1983)\n\nWe propose a switch, suitable for an integrated local communications \nnetwork, that will support packet switching and circuit switching, with a wide \nrange of bit rates. Key components are two serial memories; a multiplicity of \naccess units, each capable of writing and reading uniformly formatted, ad- \ndressed information; and a programmed controller. Circuit switching is \nachieved when the controller repeatedly allocates memory slots, following call \nsetup. Data communications can proceed concurrently without setup, compet- \ning for unused slots. We give an example of a 10,000-telephone-line switch \ncarrying a similar load of other traffic. The switch would delay voice by less \nthan 5 ms and could be interfaced to the existing telephone system. We \nindicate a method of fault detection and isolation that will limit the impact of \na failure on a serial memory to an arbitrarily small group of connected lines. \nWe define an index for measuring failure impact and use it to derive most- \nfavorable fault-isolating partitions.\n\nThe telephone system is by far the world\u2019s largest communications \nnetwork. It was primarily designed for voice, but its role widens \ncontinuously, as it adapts to new requirements. Presently it is changing \nto accommodate data communications.\n\nAlready the network extensively caters to data communications, but \nnot yet as well as it might. Although internally the telephone system\n\n* AT&T Bell Laboratories. On leave from the Department of Electrical and \nElectronic Engineering, University of Western Australia, Nedlands. \u2018AT&T \nBell Laboratories.\n\nCopyright \u00a9 1984 AT&T. Photo reproduction for noncommercial use is permitted with- \nout payment of royalty provided that each reproduction is done without alteration and \nthat the Journal reference and copyright notice are included on the first page. The title \nand abstract, but no other portions, of this paper may be copied or distributed royalty \nfree by computer-based and other information-service systems without further permis- \nsion. Permission to reproduce or republish any other portion of this paper must be \nobtained from the Editor.\n\nis rapidly becoming a vast interconnected computer system, proffered \ndata are still largely carried as analog signals externally. That will \nchange, however, as special provisions for data come on-line. As more \nof the plant, including switches, becomes digital, it will be possible to \noffer, on a selective basis, switched digital telephone channels usable \nfor 56-kb/s data throughput. Also, packet-switched data services will \nwiden in scope and access. Packet-switched data services are overlay \nnetworks that use the digital transmission facilities of the telephone \nnetwork but bypass its switches, of which many are still analog. The \npacket networks eventually may become totally interconnected, just \nas the voice network, and also may become integrated with it.\n\nIn-house, or proprietary, telephone networks can benefit from the \nchanging character of the overall network more immediately. Already \navailable are switches and other components that permit an all-digital \nnetwork that will accommodate on one facility both voice and data. \nAs good as this already is, we are proposing a switch that could make \nthe private network even better. Eventually it might even influence \nthe entire system.\n\nCurrently available switches provide only circuit-switched connec- \ntions. This gives fixed-capacity channels on a continuous basis, \nwhereas much of data comes in bursts. Thus, computer communica- \ntions are characterized by very long call durations with only low \naverage, but in many instances very high, peak rates. Given the option, \ndirect memory transfers could proceed in some instances at rates of \nmany megabits per second. This is far too high for a switched and \ncontinuously held circuit.\n\nIt is true that the needs of bursty traffic can be catered to by what \nalready is available, namely by some packet-switched networks. But \nthat introduces a separate communications network for data, with the \nconsequences of proliferating wiring plans, divided responsibilities, \nand probable long-term dyseconomies. It is better for one facility to \nserve all communications, and to do so without imposing mismatches.\n\nWe propose a switch and, more generally, a new switch architecture \nthat support within one switching fabric both circuit- and packet- \nswitched connections. This would largely avoid mismatches in respect \nto bursty data traffic, while preserving unity in communications.\n\nThe cardinal components of the switch (see Fig. 1) are a pair of \nSerial Memories (SMs), a Central Controller (CC), and Accessing \nUnits (AUs). The memories do not recirculate and both ends (head \nand tail) of each terminate on the central controller. The AUs are \nconnected to read-and-write taps along the SMs, an AU having one \nconnecting tap to each memory. The two taps of an AU form a \nsymmetrical pair: the tap to the second memory is as many places \nfrom the tail end as that to the first is from the head. Thus, each AU\n\nFig. 1\u2014Block schematic of switch. Access Units (AUs) communicate via two Serial \nMemories (SMs) on behalf of client Stations (Sts). Central Controller (CC) reserves \nslots for circuit-switched communications.\n\ncan reach every other AU by either one, or the other, memory. It can \u00a9 \nreach, and be reached by, the central controller by either memory. All \nwriting is logical OR.\n\nAn AU acts as an agent of a client station (St) (e.g., telephone, \nfacsimile terminal, computer) and mediates communications between \nit and other stations by way of corresponding AUs. Communications \nare carried on by write-and-reads in memory/time slots of uniform \nlength and format. Each slot consists of a data field and several control \nfields. Collectively, the control fields provide synchronization, \u201cSlot \nbusy\u201d indication, source and destination addressing, and slot pleading. \nA circuit-switched communication is carried on in regularly recurring \nslots, which are appropriately premarked by the central controller. \nFor a packet-switched communication an AU simply uses the next \navailable slot.\n\nThe capacity of a connected circuit can vary over a wide range, from \na small fraction of a single (64-kb/s) telephone channel up to a large \nmultiple of that capacity. It is settled by negotiation with the CC at \nthe time of circuit setup, and need not be the same on different \noccasions. The capacity available to a packet-switched communication \ndepends on the prevailing competition and can be any portion of the \ntotal switch capacity. The latter is a function of size and would be just \nseveral megabits per second for a 100-line switch and several hundred \nmegabits per second for a switch that supports 10,000 lines.\n\nA simple realization of the serial memories would be by clocked \nshift registers. The shift registers can be bit-paralleled to any degree \nneeded to keep the clock rate low. The memories and all access units \ncan be located centrally at the controller, with all connections to the \nswitch then forming a single star. But it is also possible to segment \nthe memories and form the network in clusters. The segments of \nmemory would be connected serially to each other and to the central \ncontroller by transmission lines, forming two contrary rings, and the \nclusters again would form star topologies.\n\nAll elements of our proposal are well established and tried. Central, \nor stored program, control in circuit switching is over twenty years \nold.'! The idea of switching by time slot interchanges is even older,\u201d \nfollowed shortly by its realization through read-and-writes in computer \nmemory.** Packet switching is more recent,\u00b0 but is also well estab- \nlished both in local and wide-area networks.\u00ae\u00ae\n\nIn essence, our scheme is an adaptation of seemingly diverse pro- \ncedures, so that they may coexist. Time division slots are enlarged \nfrom what is usual in circuit switching, so that they can carry the \ncontrol information essential to packet switching. Unlike normal \npacket-switched schemes, packets are of a single fixed length so that \nthey can also be circuit-switched. Instead of separate time and space \ndivision stages, common in current telephone switches, we have a \ncombined space/time fabric, abstracted from ring and bus networks, \nwith a particular debt to Fasnet.? This makes packet switching possible \nwithout controller intervention. Finally, the controller maintains cir- \ncuit connections by repetitive slot allocations, which is only marginally \ndifferent from what takes place in a time division stage of a standard \nswitch.\n\nAlso, our proposal is not first in its suggestion that voice and data \nbe integrated on a common network.\u2019 But it appears to be first in \nsuggesting a common switch for circuits and packets as the basis for \nthat integration. With few exceptions,\u201d prior suggestions have been \nto treat voice as data and to packet-switch it both in local and wide- \narea networks. However, these proposals have attendant delays that \nhave to be addressed.\n\nThe point is important since, in the global telephone system, trans- \nmission delays can limit the quality of many possible connections. In \nthe case of our switch, the delay of voice signals can be kept to less \nthan 5 ms. It depends only on the clock rate, the size of switch, and \nthe size of slots. Since delay considerations have an overriding sway \non system choices, we discuss them in Section II. In Section III we \ngive further details of our proposal.\n\nIn Section IV we address the question of reliability in our switch. \nWe do this because our proposal may be seen as being particularly\n\nvulnerable, since all its communications are to take place via two \nserial memories to which all AUs have writing privileges. We introduce \na scheme for sectional detection and isolation of faults applicable to \nour switch. We show that this would limit the impacts of faults in our \ncase to those that would prevail in switches that have much more \ndispersed and/or redundant architectures.\n\nA communication system is expected to deliver messages to the \ndestination in a timely fashion. The permitted delay is different in \ncharacter for data and for real-time signals. We review the two cases \nseparately.\n\nWithin limits, the exact times of arrival at the destination of the \ndifferent parts in a data stream generally are unimportant. It is usually \nrequired that the sequence in the stream be preserved and that the \naverage delay does not exceed some specified value. When data are \npresented for transmission at a fluctuating rate and there is not \nsufficient transmission capacity to cope with the peaks, the flow is \nsmoothed by buffering. Waiting times in buffer stores are the predom- \ninant cause of delay.\u2019\u00b0\n\nIn the transmission of real-time signals, the delay should be a \nconstant and not greater than a specified value. Given fluctuation in \ntransmission rate, there will be a time-varying delay W,(t) in a buffer \nat the sending end. A further delay W,(t) must be deliberately intro- \nduced in a buffer at the receiver,!\u00ae so that the total delay could stay \nconstant:\n\nIf, at some time, W, exceeds D, then, at the same time, the buffer \nat the receiver will become empty and there will be a break in the \nreceived signal. Hence, there is no point in storing more at the \ntransmitter than the amount of data that represents the total designed \ndelay. If the rate \\ of the real-time data is constant, as in Pulse Code \nModulation (PCM) voice, then waiting times are directly related to \namounts of stored data. The buffer-store capacities, N, and N,, that \nneed to be provided at the two ends are equal, given by\n\nIf X is not constant, then the required capacities are still equal and are \nfound by substituting the maximum value of ) in eq. (2).\n\nIt is important to note that, given fluctuations in data and/or \ntransmission rate(s) and buffer stores to smooth them, the relevant \ndelay for real-time signals is the maximum, i.e., designed, value, not \nthe statistical average. How much larger that designed delay is to be \nthan the average depends on the actual fluctuations in rate(s) and the \nrelative tolerance to lost quality by signal discontinuities and by delay.\n\nThe basic configuration of the switch was shown in Fig. 1 and \noutlined in the Introduction. The functions of the AUs and the CC \nwill be defined in more detail when we discuss protocols in the next \nsubsection. It will be seen that there are considerable differences in \nthe tasks of an AU that is mediating a circuit-switched, as compared \nto packet-switched, communication. Further differences in speed and \nbuffer requirements may be identified between, and within, those two \ncategories.\n\nClearly, there is a choice between designing a number of special- \npurpose AUs and designing a single universal AU. Further choices \nconcern sharing of, and multitasking by, access units. Should AUs be \nplaced in a common pool and shared by a larger group of stations? \nThat would entail further switching outside the main switch to mediate \nconnections between AUs and stations. Should an AU be multitasked, \nserving simultaneously different stations? That would make the AU a \nmore complex device. Figure 2 illustrates a switch that incorporates \nboth sharing and multitasking.\n\nOur inclination is towards universal AUs, one to each station, and \ntowards neither sharing nor multitasking. True, this calls for the \nlargest number of AUs, and not the least complex, at that. But it has \nthe advantage of uniformity and, in the light of technology trends, of \nlikely overall economy.\n\nThe next choice concerns the serial memories. They may be active, \nmade in semiconductor, or also, reverting to earlier technologies, \npassive, e.g., acoustic or electromagnetic delay lines. Passive compo- \nnents are attractive because they promise more reliability. However, \nour purpose would be better served by clocked shift register memories \nin an arrangement as, say, shown in Fig. 3. This makes for easier \nsynchronization and permits bit-paralleling to hold down clock rates.\n\nFig. 2\u2014Different options in AU tasking. All AUs could be of one type, each serving \na single station (right); AUs could be shared by a larger group of stations requiring \nselector switching outside the main switch (center); or an AU could be multitasked, \nserving more than one type of station (left).\n\nReliability is a matter of overall design and implementation. In Section \nIV we discuss an architecture-related aspect of reliability, namely \nisolation of faults to limited sections.\n\nFinally, we have the question of overall network topology. Three \ndifferent arrangements are shown in Fig. 4. Figure 4a shows the \ntraditional topology of a central switch and star network. In Fig. 4b a \ncompletely distributed arrangement is shown in which the serial \nmemories wend their way past every station. This would make it \nsimilar to a local area ring network and would be possible only with \npassive lines as the memories. A compromise between the above two, \nand an interesting topology for a PBX that has to serve an extended \narea, is shown in Fig. 4c. The serial memories are cut into sections, \nand each section is placed close to the group of stations that it serves.\n\nFig. 3\u2014Shift register realization of serial memories. Access points are at the inputs \nof clocked unit delays; the writing is through OR gates.\n\nThe lines connecting the individual sections and the central controller \ncould be optic fibers, which would carry the total information streams \nserially even in a large switch.\n\nIn the context of our proposal, a packet used in packet-switched \ncommunication is made up of five control fields and data, as shown in \nFig. 5. The same format could be used in circuit-switched packets. But \nfor these, at least one of the two address fields is unnecessary. Its \nspace may either be added to the data field, or it could be used as a \nseparate channel, a companion to the main channel.\n\n. RCVR\u2014address or password of AU intended to receive packet \n. DATA\u2014data field\n\nThe roles of all the fields, except RQST and SYNC, are self-evident. \nRQST is used by packet-switching AUs and we will see its function \npresently when we discuss data communications. The SYNC field is \nwritten by the central controller to ensure slot and frame synchroniz- \nation. Although both synchronizations could be achieved with just one \nbit per slot, a field of two bits will make them more secure. Altogether, \nthe following numbers would be of the right order: BUSY and RQST \none bit each, SYNC two bits, the addresses 14 bits each, and DATA \n192 bits, for a total packet of 224 bits, or 28 bytes.\n\nFig. 4\u2014Network topology options: (a) central switch, stations connected by lines; (b) \nswitch completely distributed with AUs at individual stations and connected by the \nserial memories realized as buses; (c) switch distributed in clusters, the seral memories \nwithin clusters realized by shift registers and between clusters by transmission lines.\n\npropagated memory block as consisting of the same number of bits \nand divided among respective fields. Note, however, that it is not \nnecessary that the different parts of a packet be placed into a single \nslot or block. There may be interleaving of packet parts to any extent \nthat is desirable.\n\nThus, it is conceivable that in order to alleviate the pressure of time \nfor the signaling from receiver to transmitter within the AU, the\n\nFig. 5\u2014Slot format. Typically, BUSY, RQST and SYNC would be one-bit fields, the \naddress fields could be two bytes each and the data field 24 bytes.\n\nBUSY field could refer to the state of occupancy\u2014not of the slot that \nit is riding in, but of the following slot. Similarly, other fields could be \nadvanced or retarded, and not necessarily by only one slot, nor, indeed, \njust as a complete field. Thus, the DATA field could be broken into \nsingle bytes or even bits, and the fragments made to follow the header \nas an arbitrarily dispersed tail, provided only that all packets are \nfragmented and dispersed identically.\n\nThe extreme fragmentation of packets, as just alluded to, may seem \nan attractive way of restoring smoothness to data flow for circuit- \nswitched communications. Indeed, almost complete smoothness is \npossible for any one chosen rate. But it would be at the expense of \nconsiderable complication for all other communications, particularly \nthe packet-switched and the circuit-switched that have higher rates \nthan the one singled out for favorable treatment. We will dismiss it \nfrom further consideration and turn to describing procedures.\n\nAssume that AU addresses are in numerical order along the two \nmemories, ascending in the direction of propagation along one and \ndescending along the other. We will call the memory with ascending \naddresses the forward channel, and hence the other the reverse chan- \nnel.\n\nSuppose that an AU has to communicate to another AU of higher \naddress. It must send a message, or packet(s), on the forward channel. \nTo do so, the dispatch processor of the AU will follow the data dispatch \nroutine of Fig. 6. This can be understood more easily with the help of \nthe state diagram of Fig. 7. For the sake of description, this diagram \nrelates to an exclusive forward channel dispatcher, although in practice \na single dispatcher would service both directions.\n\nWhen idle, the dispatcher is normally in the \u201cGo\u201d state and monitors \nthe sending buffer (for the forward channel), checking whether it \ncontains a packet for transmission. If it does, it reads the BUSY field \nof the next block on the forward channel and at the same time writes \na \u201cONE\u201d in that field so as to seize the slot, should it be available. If \nit is not, i.e, BUSY was already \u201cONE,\u201d then it will write \u201cONE\u201d in \nthe next RQST field on the reverse channel and wait for the next \nBUSY field on the forward channel. It will repeat reading and writing \nof BUSY on the forward channel and sending RQSTs on the reverse \nchannel until a \u201cZERO\u201d BUSY occurs. It will then write in the related \nSNDR, RCVR, and DATA fields, so dispatching a packet.\n\nHaving sent a packet, the dispatcher moves to the \u201cOne packet sent\u2019 \nstate. If the sending buffer has at that moment one or more further \npackets for dispatch, then the dispatcher will behave exactly as in the \n\u201cGo\u201d state and send off the next packet, thereby moving to the \u201cTwo\n\npackets sent\u201d state. But if there is no packet in the sending buffer on \nentry to the \u201cOne packet sent\u201d state, then the dispatcher will proceed \nto the \u201cHalt\u201d state. It will remain there until the next \u201cZERO\u201d is \nwritten in the RQST fields on the reverse channel, whereupon it will \nrevert to the \u201cGo\u201d state. Similar conditions apply on entry to the \u201cTwo \npackets sent\u201d and further states, until the dispatcher has sent in a \ncontiguous sequence M packets and entered the \u201cM packets sent\u201d \nstate. From this it must proceed unconditionally to \u201cHalt.\u201d\n\nFig. 7\u2014State diagram of data dispatcher. The dispatcher goes temporarily into HALT \nstate whenever it has no more packets to send or has already sent M packets since the \nae oe It goes from HALT to GO as soon as the RQST bit on the reverse channel \nis :\n\nM is a parameter that may vary with AU. It represents priority \nstanding: The larger its value, the less sensitive the AU is to pleadings \nfor slots by other AUs that are downstream from it. It is normally set \nin relation to the rate of the station that the AU serves.\n\nThe task of receiving is less involved but no less time consuming, \nand an AU will have a separate processor for it. A routine that it could \nfollow is given in Fig. 8. This is set out on the assumption that the \nSNDR and RCVR fields of a packet would precede the DATA field by \none slot.\n\nAn AU serving a real-time device has to act in two distinct modes, \none in setting up or tearing down a circuit and the other in transmitting \nand receiving the real-time signals when the circuit is set up. We\n\noutline the procedure, limiting our attention to telephony. Other \ndevices requiring circuit connections would be served similarly.\n\nLooked at from the telphone, the AU would appear as the line \nselector of the standard switch. When the telephone is taken off hook, \nthe AU would supply dial tone. As the number is dialed, it would be \nstored by the AU, which, on completion, would assemble a packet for \ntransmission to the CC. The DATA field of that packet would disclose \nthe fact that a telephone link is being sought, and the numbers of the \ncalling and called stations. The sending procedure for the packet could \nfollow the routine of Fig. 6, even though a simpler routine is possible \nsince no \u201cHalt\u201d state is necessary.\n\nThe CC would process received requests using a routine that could \nbe as in Fig. 9. First, the CC would check the total switch capacity \nalready committed to circuit traffic, and from this it would decide \nwhether the setting up of the further circuit is permitted. If it is not \npermitted, then the CC would inform the originating AU, and that \nwould terminate the processing. If setting up the circuit is permitted, \nthen the CC would determine which AU serves the called station and \ncheck whether it is engaged. If it is engaged, then the CC would inform \nthe originating AU accordingly. If it is not engaged, then the CC would \ntag both AUs as engaged and send messages to both AUs and inform\n\nthem of each other\u2019s addresses. The two addresses would also be \ninserted at appropriate places in ring buffers to cause the necessary \npremarking of slots by writing of BUSY and SNDR on the correct \nchannels at the right frequencies. This would complete the setting up \nof the two-way circuit. Given a setup circuit, the dispatch and reception \nof the real-time data would follow the routines of Fig. 10.\n\nFig. 10\u2014Flowchart of (a) real-time signal dispatch, and (b) real-time signal reception.\n\nmissions: The receiver is given the sender\u2019s address and recognizes it \nfor the duration of the call. Apart from saving one address field for \nother use, there is a further bonus in that more than one receiver can \nbe given the same SNDR address and simultaneously receive the same \nreal-time signal. This leads to the possibility of a simple arrangement \nfor broadcasting to designated outlets for, say, a public address system. \nIf, furthermore, the AU\u2019s receiver capability was enlarged to noting \nseveral SNDR addresses and taking in packets with those markings, \nthen a telephone conference facility, with voice signal summation at \neach receiver, would be possible.\n\nThe setting up, tearing down, and maintaining of calls to subscribers \noutside the switch\u2019s own area would have to interwork with equipment \nin other offices. But there is no particular problem about this. The \nAU serving a trunk would interface with the outside system, sending \nand responding to signals in conformity with existing specifications. \nBut, in other respects, it would not be different from an AU serving a \nlocal subscriber. Data out of, and into, the local switch area could also \nbe carried by circuit-switched trunks, with suitable interfacing to a \nwider-area data network. The role of an AU providing that interfacing \nwould then amount to that of a gateway processor.\n\nThe bit rate required along the SMs is related to the total peak load \nfor which the system is designed, multiplied by a factor that accounts \nfor efficiency. Assuming a telephone voice signal sampled at 8 kHz,\n\nrepresented by 8 bits per sample and an allowed delay due to packe- \ntization of 3 ms, a packet may contain 24 samples or 192 bits of data. \nThe overheads are mainly in the addresses: Assuming a 10,000-voice- \nline switch and a total number of AUs not exceeding 16K, the SNDR \nand RCVR fields could be 14 bits each. As we already noted, BUSY \nand RQST need be only 1 bit each, and SYNC 2 bits. The total \noverhead will then be 32 bits and the packet length will be 224 bits.\n\nAnother criterion by which the overall size of a packet can be \ndecided is efficiency. Since the allowable delay for voice is binding, \nthe best size indicated for maximum efficiency will be of interest only \nif it is smaller than that already decided.\n\nIt is a reasonable simplification to suppose that all offered traffic \ndivides into two categories: very short bursts, and prolonged streams. \nFurthermore, it is reasonable to assume that the number of packets- \nper-second from the very short burst will be independent of packet \nsize. Thus, such very short bursts would be produced by single ASCII \ncharacters from, and echoed to, computer terminals, when carried in \nindividual packets. On the other hand, circuit-switched traffic and \ndata file transfers are examples of streamed flow.\n\nConsider the total bit rate, R, that results from traffic consisting of \nb, short bursts per second, and an aggregated stream flow of S bits per \nsecond. If the packet has h bits of header and x bits of DATA, then\n\nIn a system serving a business, one might provide for a busy-hour \nvoice traffic of 10 ccs (hundred call seconds) per telephone. In the \nswitch, this will divide equally between the two memories. With 10,000 \ntelephones, the aggregate stream S, on each SM due to voice would \nthen be\n\nA reasonable assumption for the present is that all other traffic would \namount to 20 percent of the total, or in our example it would be a \nfurther 22 Mb/s.\n\nFor the sake of illustration, assume that the very short burst rate, \nb, is 20,000 packets per second. If each of these carries only one 8-bit \nbyte, then the net traffic from them is 160 kb/s, a negligible amount \nwithin the assumed 22 M/bs. But the gross traffic may be much larger, \ndepending on packet size. Hence, the decision for best size of DATA \nfield, which, with the numbers already invoked, follows from eq. (4):\n\nFor xp to be less than 192 bits, decided by delay considerations, the \nvery short burst traffic would have to be 4.8 times larger than was \nassumed. But the assumed rate is already large, and therefore it is \nunlikely that efficiency considerations would indicate a smaller packet \nthan given from delay.\n\nGiven packets of 224 bits and the numbers cited above, the rate, R, \nin each memory follows from eq. (3) as 134 Mb/s. If 8-bit bytes are \npropagated in parallel, then the required clock rate is 16.75 MHz, a \nnone too demanding frequency for present technology. The packet \nrate, which is of greater relevance to AU and CC speeds, would be 598 \nkHz.\n\nA switch would be designed for a given ultimate size and given an \nappropriate clock rate from the start. But it would not be necessary \nto give it immediately the full complement of AUs, nor, indeed, full \nlengths of memories. AUs could be added without any disruption and \nmemory sections with only a minor pause.\n\nAvailability of communications services is extremely important and \nhas prompted switch designers to adopt the very highest standards of \nreliability.*'\u00b0 Thus, it is accepted practice to have two identical central \ncontrollers, one being a \u201chot\u201d standby that can take over at any \ninstant. This and other common practices would also apply to our \nswitch. The features by which our switch is rendered most vulnerable \nin respect to reliability are its serial memories, which carry all messages \nand are accessed by all AUs. Below we consider the general question \nof disruptive impact by failures and suggest a measure for it. Then we \nintroduce a fault detection and isolation scheme that would make the \nrobustness of switching by serial memories with multiple read-and- \nwrite taps comparable to that of much more redundant architectures.\n\nIn switching equipment, including ours, failures are unequal in \nlikelihood and in disruptive consequence. We introduce the notion of \nexpected failure impact. Let 7; be the probability that component C; \nwill fail during the course of one year; let the expected repair time for \nit be 7;,; and the number of potential communication connections that \nare unavailable while C; is in the failed state be v;,. We define U;, the \nexpected per annum failure impact (EPAFI) of C;, as\n\nWe assume that failures are statistically independent and disregard \nthe probability of another component failing during the repair time of\n\nan existing failure. EPAFI values then are additive, and U, with respect \nto an assembly of N components, is\n\nU _ > U;. (6) \ni=l \nWe consider the expected failure of the SMs and all the AUs connected \nto them. Suppose that there are altogether N AUs, each with (1) a per \nannum rate 7; of failing in a way that affects only one subscriber and \ntakes time 7, to repair, and (2) a rate 72, which disrupts communica- \ntions on the memory past the failed AU and takes 7 to repair. Also, \nlet the memories have a rate 73 of failing at each of the 2N connecting \npoints, with expected repair times 73. \n- With N mutually communicating AUs in the system, the number of \npotential two-way communication links is N(N \u2014 1)/2. If an AU \nfailure of the first kind occurs, then vy; = (N \u2014 1) of these are disrupted. \nWhen the failure of the AU is of the second kind, or when a memory \nfails, then the number of disrupted links is much larger and depends \non the actual location of the failure. One can calculate an average \nnumber on the assumption that all potential failure locations are \nequally likely. It is found to be approximately (N\u201d)/3. Hence the total \nexpected impact due to failures of AUs and memory links is\n\nWe propose to divide the memories into sections and have a fault \ndetector at the end of each section. Further, each section would have \na bypass and, in case of a detected failure, a switch would be actuated \nto pass on to the next section the data stream at the output of the \nbypass (Fig. 11). Thus, effectively, the consequence of the fault is \nisolated to one section. A possible realization of the switch is shown \nin Fig. 12.\n\nA Fault Detector (FD) would compare the data streams at the \noutputs of the memory section and the bypass, and it would decide \nthat failure has occurred when the evident modification to the stream \nin passage through the memory section violates existing constraints. \nThe particular constraint of the several that exist in our case and \nwhich we use is the following: There may never be a change of any \nfield that is already nonzero. Detecting any such illegal changes will \ncatch failures both in AUs and the memories. The detection will, of \ncourse, rely on the output from the bypass being a flawless replica of \nwhat entered that section. If necessary, redundancies and error control \ncould be implemented on the bypasses to make that more sure.\n\nFig. 11\u2014Fault isolation using bypasses. Whenever the Fault Detector (FD) detects \nconstraint violations, it switches input to next section to output of the bypass from the \nprevious section.\n\nWith the memories divided into sections and with fault detection \nand isolation in place, failure impacts will be reduced. Unless the fault \nis in the fault detector itself, then if each memory is divided into m \nsections, only the N/m stations within a section will be affected by a \nfault. The disruption depends on which section and which point within \nthe section is involved. Again assuming equal likelihoods for locations, \nwe can derive the average number of potential connections that are \ndisrupted and find this, to a good approximation, amounting to 0.75 \n(N2/m).\n\nSuppose that fault detectors have their own failure rate 7,4 for \nfailures that produce an open line and z; for switching off a section \nwhen it should not be. Further, suppose that these have expected \nrepair times 74 and 75, OF ws = 7474 and ws = 7575. On average, these \nevents disrupt, respectively, N?/3 and N?/2m potential connections.\n\nThe total EPAFI value, with division into m sections and fault \ndetection and isolation, is then\n\nThe first and last terms in eq. (8) are much smaller than the others \nand may be neglected. The value of m that results in minimum U,, is\n\nFig. 12\u2014Realization of two-way switch for fault isolation. FD outputs F and F are \ncomplementary, signifying FAULT and NO FAULT.\n\nand the failure impact, with the first and last terms in eq. (8) neglected, \ncomes to\n\nThis should be compared with the expected failure impact without \nsectional detection and isolation, as found in eq. (7). The improvement \nratio is\n\nFurther improvement is possible by instituting super sections by which \na number of consecutive sections would be bypassed and again fault- \ntested and isolated, as shown in Fig. 13. Indeed, one can take the \nhierarchy of protection to any number of levels.\n\nWith just one level of protection and, say, N = 10,000, and the \ndifferent failure rates and repair times comparable to each other, the \noptimum number of sections would be around 185, or 55 AUs to one \nsection. The improvement over no protection would be by a factor of \n40. A second level of protection would increase the improvement by a \nfurther factor of around 5. Asymptotically, as the hierarchy of protec- \ntion is taken to higher levels, the functional dependence of EPAFI on \nN becomes quadratic, which is the relationship that applies when the \neffect of a failure is confined to a single AU.\n\nWe have proposed a switch architecture that supports circuit- and \npacket-switched communications. Both kinds of communications can \nproceed at widely varying rates: Circuits can be set up with different \ncapacities, selectable as a binary fraction or multiple of a basic capac- \nity, while packet-switched communications share in the pool of the \ntotal switch capacity that is not in use at any given time. Thus, the \nproposed switch could cater efficiently in mediating real-time signals\n\nand data. Specifically, it could be a PBX that, apart from voice, could \nprovide other circuit- and packet-switched services.\n\nThe possibility for the two modes is brought about by having \nenlarged time slots that can include addressing information, and then \nby making these of fixed length so that they can be made available \nregularly. Further, the switching is performed by access units that \nwrite and read on serial memories on which synchronization can be \nmaintained without interruptions and information transfers can occur \nwithout collisions.\n\nWe have proposed that data packets be fixed at 192 bits, or 24 \nsamples of pulse-code-modulated voice. This limits the delay due to \npacketization to 3 ms. The total delay, which includes propagation \nalong the memories, will then be less than 4 ms, even in a very large \nswitch.\n\nIt is recognized that a switch used in telephony should conform to \nvery high standards of reliability. We have proposed a scheme of fault \ndetection and isolation applicable to memories as in our switch. This \nwould substantially overcome any added vulnerability due to the serial \nnature of the signal paths. However, other issues (e.g., overall system \nreliability) not addressed by us remain to be resolved. In summary, \nour proposed switch offers the possibility of integrating voice and data \nin a way that would preserve the quality and reliability of voice \ncommunications and therefore, in turn, could be integrated with the \ntelephone system at large. We believe that, provided no compromises \nneed to be made, very real benefits flow from having all communica- \ntions mediated by a common facility. It is possible that our proposed \nswitch could meet such objectives.\n\nThe authors would like to thank M. G. Hluchyj for helpful discus- \nsions during early phases of this work.\n\n. H. E. Vaughan, \u201cResearch Model for Time-Separation Integrated Communication,\u201d \nB.S.T.J., 38 (July 1959), pp. 909-32.\n\n. H. Inose et al., \u201cA Time-Slot Interchange System in Time-Division Electronic \nExchanges,\u201d IEEE Trans. Commun. Syst., CS-11 (September 1963), pp. 336-45.\n\n. A. G. Fraser, \u201cDatakit\u2014A Modular Network for Synchronous and Asynchronous \nTraffic,\u201d Proc. ICC (June 1979).\n\n. R.M. Metcalfe and D. R. Boggs, \u201cEthernet: Distributed Packet Switching for Local \nComputer Networks,\u201d Comm. ACM, 19 (July 1976), pp. 395-404.\n\n. G. T. Hopkins and P. E. Wagner, \u201cMultiple Access Digital Communications \nSystems,\u201d U.S. Patent 4,210,780, issued July 1, 1980.\n\n. J. O. Limb and C. Flores, \u201cDescription of FASNET\u2014A Unidirectional Local-Area \nCommunications Network,\u201d B.S.T.J., 61 (September 1982), pp. 1413-40.\n\n10. T. W. Forgie and A. G. Nemeth, \u201cAn Efficient Packetized Voice/Data Network \nUsing Statistical Flow Control,\u201d IEEE Commun. Conf. III, 1977, pp. 38.2.44\u201448.\n\n11. N. F. Maxemchuck, \u201cA Variation on CSMA/CD That Yields Movable TDM Slots \nin Pleased Voice/Data Local Networks,\u201d B.S.T.J., 61 (September 1982), pp. \n1527-50.\n\n12. G. J. Coviello et al., \u201cSystem Design Implications of Packetized Voice,\u201d IEEE \nCommun. Conf. III, 1977, pp. 38.3.48-53.\n\n13. T. Bially et al., \u201cVoice Communication in Integrated Digital Voice and Data \nNetworks,\u201d IEEE Trans. Commun., COM-28 (September 1980), pp. 1478-90.\n\n14. D. H. Johnson and G. C. O\u2019Leary, \u201cA Local Access Network for Packetized Digital \nVoice Communication,\u201d IKEE Trans. Commun., COM-29 (May 1981), pp. 679- \n88.\n\n15. L. Kleinrock, Queuing Systems, Vol. 1: Theory, New York: Wiley-Interscience, 1975, \nVol 2: Computer Applications, New York: Wiley-Interscience, 1976.\n\n16. Z. L. Budrikis, J. L. Hullet, and D. Q. Phiet, \u201cT'ransient-Mode Buffer Stores for \nNonuniform Code TV,\u201d IEEE Trans. Commun. Technol., COM-19 (December \n1971), pp. 913-22.\n\n17. E. T. Klemmer, \u201cSubjective Evaluation of Transmission Delay in Telephone Con- \nversations,\u201d B.S.T.J., 46 (July-August 1967), pp. 1141-7.\n\n18. R. W. Downing, J. S. Nowak, and L. S. Tuomenoksa, \u201cNo. 1 ESS: Maintenance \nPlan,\u201d B.S.T.J., 43 (September 1964), pp. 1961-2019.\n\n19. W. P. Karas, \u201cReliability and Maintainability Improvements Through Distributed \nControls in Communication Systems,\u201d NTC Record 1981, pp A4.4.1-7.\n\nZigmantas L. Budrikis, B.Sc., 1955, and B.E. (Hons I, Electrical Engineer- \ning), 1957, University of Sydney; Ph.D., 1970, University of Western Australia; \nP.M.G. (now Telecom Australia) Research Laboratories, 1958-1960; Aeronau- \ntical Research Laboratories, Fishermen\u2019s Bend, 1961; Electrical Engineering \nFaculty at University of Western Australia, 1962\u2014. Mr. Budrikis has had a \nnumber of visiting appointments: University of California at Berkeley, 1968; \nAT&T Bell Laboratories, 1972, 1973, 1981, 1983, 1984; TU Munich, 1977. He \nis interested in problems in communications, man-machine interfaces, and \nfoundations of electromagnetism. Fellow, IE Australia; member, IEEE, Optical \nSociety of America, New York Academy of Science.\n\nArun N. Netravali, B. Tech. (Honors), 1967, Indian Institute of Technology, \nBombay, India; M.S., 1969, Ph.D. (Electrical Engineering), 1970, Rice Uni- \nversity; Optimal Data Corporation, 1970-1972; AT&T Bell Laboratories, \n1972\u2014. Mr. Netravali has worked on problems related to filtering, guidance, \nand control for the space shuttle. At AT&T Bell Laboratories, he has worked \non various aspects of digital processing and computing. He was a Visiting \nProfessor in the Department of Electrical Engineering at Rutgers University \nand the City College. He is presently Director of the Computer Technology \nResearch Laboratory. Mr. Netravali holds over 20 patents and has had more \nthan 60 papers published. He was the recipient of the Donald Fink Prize \nAward for the best review paper published in the Proceedings of the IEEE \nand the journal award for the best paper from the SMPTE. Editorial board, \nProceedings of the IEEE; Editor, IEKE Transactions on Communications; \nsenior member, IEEE; member, Tau Beta Pi, Sigma Xi.\n\nIn most time-shared computer systems a program is processed by the central \nprocessing unit for, at most, a fixed period of time called a time slice, or \nquantum. If the program requires more processing after it has received its \nquantum, it is placed at the end of a run queue. This procedure is repeated \nuntil the program has finished executing. To the user who submitted the \nprogram the two most important performance measures of such a system are \nthe mean and variance of the program\u2019s total elapsed time of execution. This \ntotal elapsed time is often referred to as the \u201cresponse time\u201d. In this paper we \ninvestigate the effect of the quantum size on the mean and variance of the \nresponse time.\n\nThe round-robin queue has been studied by several authors as a \nmodel of time-shared computer systems. In a time-shared system, the \narrivals of requests for service as well as the service times may be \nthought of as random variables. From the user\u2019s point of view, the two \nmost important measures of performance in such a system are the \nmean and variance of the response time. The round-robin discipline \nimplicitly favors jobs with shorter service times, in the sense that the \nmean response time is approximately a linear function of the service \ntime.\u2019 Thus far, however, the variance has proved to be intractable in\n\nthe case of a general service-time distribution. In the case of exponen- \ntial service times, Muntz has found the Laplace transform of the \nwaiting-time distribution.\u201d\n\nThe round-robin model can be described as follows: New arrivals \njoin the end of the queue, and all jobs in the queue are served on a \nfirst-come first-served basis until they have completed their service \nrequirement or have received one quantum of service. When a job has \ncompleted service, it leaves the system, and the next job in the queue \nbegins service immediately. If a job requires more service after receiv- \ning its quantum, it rejoins the queue. In this paper we assume that the \narrival process is Poisson but the service times are governed by a \ngeneral distribution. Overhead due to switching between jobs can be \nincluded by adjusting the service requirement. For simplicity of ex- \nposition we assume that the quantum is constant. Variable quantum \nsizes also yield to our method of analysis.\n\n1. What value of the quantum minimizes the mean sojourn time of \na given class of jobs?\n\n2. For a given class of jobs what is the variance of the sojourn time \nand what quantum minimizes the variance in the sojourn time?\n\nHere \u201csojourn time\u201d refers to the total amount of time that a job is \nin the queueing system, both in the queue and in service. To answer \nthe second question, we use a new light traffic-heavy traffic interpo- \nlation (which we will call the RS interpolation) developed by M. \nReiman and B. Simon, which makes use of a \u201clight traffic derivative\u201d.\n\nThe mean waiting time in a round-robin queue has been studied by \nseveral authors.*\u00b0 By \u201cwaiting\u201d time we mean the total amount of \ntime that the job spends in the queue (but not in service). In this \nsection we describe the authors\u2019 analysis and set the notation that will \nbe used throughout the paper. As mentioned above, we assume that \nthe arrival process is Poisson with rate )\\ and that the service times of \n_ newly arriving jobs are independent, identically distributed random \nvariables with distribution function F and density f. Let gq denote the \nquantum size. We say that a job in the system is type j if its service \ntime requirement as a newly arriving job is between (j \u2014 1)q and jq,\n\nThe following are additional notations: \nm is the mean service time. \np is the traffic intensity, \\m. \np; is the probability a newly arriving job is type j.\n\nm, is the mean amount of time that a type (i, 7) job in the queue \nwill occupy the server the next time it receives service.\n\nM;; is the second moment of the amount of time that a type (i, /) \njob in the queue will occupy the server the next time it receives \nservice.\n\nw; is the mean amount of time that a job must wait in the queue \nin the ith time in the queue.\n\nW is the mean amount of time that an arbitrary job must wait in \nthe queue before it completes its total service-time requirement.\n\nUsing Little\u2019s Law, which takes the form Q, = \\p;w; in this case, we \ncan eliminate Q; from (1) and (2). One can easily verify that the \nmatrix form of the equations for the a; is\n\nwhere w is the vector whose ith component is w;, and M and b are a \nmatrix and a vector, respectively, that are independent of p. Finally, \nthe mean waiting time, W, is given by\n\nUsing the above results we can compute the mean waiting time W? \nof a particular class of jobs if we are given the service-time distribution \nF, of arrivals of that class:\n\nFigure 1 suggests that, at least in some fairly typical cases, the \nquantum size that minimizes the mean waiting time of a preferred \nclass of jobs is neither very big [which is, in essence, First-In First- \nOut (FIFO)] nor very small (processor-sharing), but is just big enough \nto let all the preferred jobs complete service without having to feed \nback.\n\nIn this example, F; is uniform between one and three, F, is uniform \nbetween four and eight, and F = 0.75 F, + 0.25 F\u00bb. In addition, \\ = \n0.1, so p = 0.3. Note that gq = 3 minimizes W! over all q, and in \naddition, the mean waiting time of the complementary class decreases \nwith increasing q.\n\nSince the expression for W' is complicated, it is quite difficult to \nfind the optimal quantum qo without significant computational effort. \nThe following observation (from numerical experiments) yields a \nsimple method for finding qo.\n\nObservation: The value of g that minimizes [dW'(0)]/(dp) is close \nto the value of g that minimizes W\u2019 (for arbitrary values of p, 0 < p< \n1).\n\nFig. 1\u2014Expected sojourn times as a function of the quantum for (a) type II jobs and \n(b) type I jobs.\n\ntreatment of the method. Let W,(p), 0 < p <= 1, be the nth moment of \nthe steady-state waiting time distribution as a function of p, the traffic \nintensity. Let W,,(p) = (1 \u2014 p)\"W,(p) when 0 < p <1, and let W,,(1) \n= lim(1 \u2014 p)\"W,,(p). W,,(1) is well-defined and finite by the argument\n\nNote that W,,(0) = W,,(0) is zero and W,,(1) can be calculated as the \nheavy traffic limit using a diffusion process. One can interpolate \nbetween light and heavy traffic to get the approximation formula:\n\nThis idea is, of course, well known. The novelty of the RS interpo- \nlation is that it makes use of the derivative of W,,(p) at p = 0, which \nwe will denote by W,(0). It is clear that W/,(0) = W/(0). The RS\n\nand let F; be the service-time distribution of J;, i = 1, 2. The following \ntheorem allows us to calculate W/(0).\n\nThe proof of a more general version of this result is contained in \nRef. 3. We now present a formula for W;,(0) using the above theorem. \nA straightforward calculation yields\n\nThe queueing system under consideration in this paper is a special \ncase of the multiclass feedback queue analyzed in Ref. 6. Here we \nfollow the development in Ref. 7 for the readers\u2019 convenience.\n\nwhere V(t) = L(t) \u2014 t and L(t) is the total amount of work entering \nthe system in [0, t]. (We assume the system is empty at t = 0.) Define \na sequence of systems whose parameters, and queue-length and so- \njourn-time processes are indexed by n = 1, and consider the normalized \nprocesses\n\nover some finite interval, which we normalize to [0, 1] for convenience. \nFor a heavy traffic limit we assume \\\") \u2014 m7! as n > 0. We have the \nresult of D. C. Igelhart and W. Whitt (1971).\n\nHere s is the variance in the service times, and a is the variance in \nthe interarrival times. RBM(d, o\u201d) is one-dimensional reflected \nBrownian motion with drift d and infinitesimal variance o\u2019.\n\nin probability. \nTheorem 3: Let \nY(t) = sup | Ap-Qy(t) \u2014 Aj LPO) |, \nwhere the supremum is taken first over alll 1, so that\n\nAs an example, suppose that we assume the data message queue \nempties with probability one before k + 1 voice messages relinquish \ntheir time slots. Once the voice state becomes v = Up \u2014 k \u2014 1, the voice \nservice rate nu, = 0. Substituting these values for u, and v in (56) gives\n\nEquation (62) constitutes an initial condition for (56), which can be \niterated numerically using (59). In particular, assuming no more than \nk voice messages can relinquish their time slots after the queue begins \nto empty, D(z, vo \u2014 k \u2014 1) for z = 1/[re(vo)] and z = 1/[re(vo \u2014 kR)] is \ncalculated from (62). The value of 71,,-\u00bb is subsequently computed \nfrom (59) and is used in (56) to compute D(z, vo \u2014 k) for z = 1/[re(vo)] \nand z = 1/[re(vo \u2014 k + 1)]. Equation (59) is subsequently used to \ncompute 71,,,-r+1, Which is used to compute D(z, up \u2014 k + 1), and so \nforth until D{1/[r2(vo)], vo \u2014 1} is computed.\n\nTo compute D(z, v| vi) given by (35) at z = 1/[re(vo)], we multiply \nboth sides of (33a) by z~\u00a2 and sum from d = 1 to infinity to get\n\n, (64) \nwhere 6;; is the Kronecker delta. Using the condition (33b) gives the \nboundary condition\n\nBecause D(z, v|v;) must be analytic outside the unit circle, p(v | v;, 1) \nis selected to cancel the pole at z = 1/[r2(vo)]. This implies that\n\n++, Uo \u2014 Rk \u2014 1, where k is the maximum number of voice departures \nallowed, the boundary condition (65) is first used in (66) to get\n\nwhere j is initially one and ranges from one to k + 1. This expression \nis evaluated at z = 1/[re(vo \u2014 j)] and substituted into (66) to obtain \np(Vo ~ J | Vo \u2014j + 1, 1), which is used in (64) to compute D(z, vp \u2014 j| vo \n\u2014j+1) at the appropriate values of z. This procedure continues until \nthe value of D{1/[re(vo)], vo \u2014 j | Vo \u2014 1} is obtained, whereupon j is \nincremented and the procedure starts over again. In this way the \nvalues D{1/[re(vo)], vo \u2014 J | Vo \u2014 1} for j = 1, 2, --- ,k +1 are generated \nsystematically.\n\nXv (v ell (es 1)!y, Av m=0 \\Av (v \u2014 m)\\yy \nwhere y, is given by (39). Using the initial condition, \n= sa 1 \n=T,-T)=-\u2014\u2014, 12 \nBal 1 0 eR (72)\n\nMichael L. Honig, B.S. (Electrical Engineering), 1977, Stanford University; \nM.S. and Ph.D. (Electrical Engineering), 1978 and 1981, respectively, Univer- \nsity of California, Berkeley; Bell Laboratories, 1981-1982; AT&T Information \nSystems, 1983. Present affiliation Bell Communications Research, Inc. 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Sci An 250(4): 544+, 1984. \nJin S., Sherwood R. C., Chin G. Y., Wernick J. H., Bordelon C. M., Soft Magnetic \nProperties of a Ferritic Fe-Ni-Cr Alloy. J App] Phys 55(6): 2139-2141, 1984.\n\nJin S., Vandover R. B., Sherwood R. C., Tiefel T. H., Magnetic Sensors Using Fe- \nCr-Ni Alloys With Square Hysteresis Loops. J Appl Phys 55(6): 2620-2622, 1984. \nKammlott G. W., Franey J. P., Graedel T. E., Atmospheric Sulfidation of Copper \nAlloys. 1. Brasses and Bronzes. J Elchem So 131(3): 505-511, 1984.\n\nKammlott G. W., Franey J. P., Graedel T. E., Atmospheric Sulfidation of Copper \nAlloys. 2. Alloys With Nickel and Tin. J Elchem So 131(3): 511-515, 1984. \nKlauder J. R. et al., Quantum-Mechanical Path Integrals With Wiener Measures \nfor All Polynomial Hamiltonians. Phys Rev L 52(14): 1161-1164, 1984.\n\nLam E. et al., Spectroscopic Characterization of Nitrated Purple Membranes. \nBiochem Int 8(2): 217-224, 1984.\n\nLanger W. 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Appl Phys L 44(1): 22-24, 1984.\n\nWood T. H., Burrus C. A., Miller D. A. B., Chemla D. S., Damen T. C., Gossard A. C., \nWiegmann W., High-Speed Optical Modulation With GaAs/GaAlAs Quantum \nWells in a p-i-n Diode Structure. Appl Phys L 44(1): 16-18, 1984.\n\nYafet Y., Vier D. C., Schultz S., Conduction Electron-Spin Resonance and Relax- \nation in the Superconducting State. J Appl Phys 55(6): 2022-2024, 1984.\n\nJulesz B., A Brief Outline of the Texton Theory of Human Vision. Trends Neur \n7(2): 41-45, 1984.\n\nBuschvishniak I. J., Response of an Edge-Supported Circular Membrane Electret \nEarphone. 1. Theory. J Acoust So 75(3): 977-989, 1984.\n\nBuschvishniak I. J., Response of an Edge-Supported Circular Membrane Electret \nEarphone. 2. Experimental Results. J Acoust So 75(3): 990-995, 1984.\n\nNelson W. L., Perkell J. S., Westbury J. R., Mandible Movements During Increas- \ningly Rapid Articulations of Single Syllables\u2014Preliminary Observations. J \nAcout So 75(3): 945-951, 1984.\n\nRoberts L. A., Mathews M. V., Intonation Sensitivity for Traditional and Non- \ntraditional Chords. J Acoust So 75(3): 952-959, 1984.\n\nOn the Application of Energy Contours to the Recognition of Con- \nnected Word Sequences \nL. R. Rabiner\n\nSpatial Filtering Radio Astronomical Data: One-Dimensional Case \nH. E. Rowe\n\n1982/83 End Office Connection Study: ASPEN Data Acquisition \nSystem and Sampling Plan \nJ. D. Healy, M. Lampell, D. G. Leeper, T. C. Redman, and \nK. J. Vlacich\n\n1982/83 End Office Connection Study: Analog Voice and Voiceband \nData Transmission Performance Characterization of the Public \nSwitched Network", "title": "magazine :: Bell System Technical Journal :: BSTJ V63N08 198410 Part 1", "trim_reasons": [], "year": 1984} {"archive_ref": "bitsavers_BellSystemJV64N05198505_5373266", "canonical_url": "https://archive.org/details/bitsavers_BellSystemJV64N05198505_5373266", "char_count": 192126, "collection": "archive-org-bell-labs", "doc_id": 732, "document_type": "journal_issue", "id": "bella-qwen-pretrain-doc732", "record_count": 348, "release_policy_version": "hf_public_v1", "rights_status": "public_domain", "selected_extraction_backend": null, "selected_extraction_score": null, "source_family": "archive_org", "source_url": "https://archive.org/details/bitsavers_BellSystemJV64N05198505_5373266", "split": "validation", "text": "\"AT&T Bell Laboratories = 7AT&T Information Systems | ?Sandia National Laboratories \n4AT&T Network Systems 5AT&T Technology Systems \u00ae AT&T Technologies\n\nM. D. McILROY W. FIGHTNER B. W. KERNIGHAN \nTechnical Editor L. E. GALLAHER S. G. WASILEW\n\nOn the Use of Vector Quantization for Connected-Digit \nRecognition \nS. C. Glinski\n\nIncorporation of Temporal Structure Into a Vector- \nQuantization-Based Preprocessor for Speaker-Independent, \nIsolated-Word Recognition\n\nSojourn Time Distribution in a Multiprogrammed Computer \nSystem \nK. M. Rege and B. Sengupta\n\nApplication of Decomposition Principle in M/G/1 Vacation \nModel to Two Continuum Cyclic Queueing Models\u2014Especially \nToken-Ring LANs\n\nA trellis code is a \u201csliding window\u201d method for encoding a binary data \nstream {a\u2018}, a' = 0, 1, as a sequence of signal points drawn from R\u201d. The rule \nfor assigning signal points depends on the state of the encoder. In this paper \nn = 4, and the signal points are 4-tuples of odd integers. We describe an \ninfinite family of eight-state trellis codes. For k = 3, 4, 5, --- we construct a \ntrellis encoder with a rate of k bits/four-dimensional signal. We propose that \nthe codes with rates k = 8 and 12 be considered for use in modems designed \nto achieve data rates of 9.6 kb/s and 14.4 kb/s, respectively.\n\nA trellis code is a \u201csliding window\u201d method for encoding a binary \ndata stream {a'}, a' = 0, 1, as a sequence of signal points {x'} drawn \nfrom R\u201d. The set of possible signal points is finite, and this set is \ncalled the signal constellation. The purpose of coding is to gain noise \nimmunity beyond that provided by standard uncoded transmission at \nthe same data rate. In this paper n = 4, and the signal points are \ndrawn from (2Z + 1)*, the lattice of 4-tuples of odd integers. We shall \nregard transmission of a four-dimensional signal as one use of the \nchannel, and we measure the rate of the code in bits per channel use. \nThe four-dimensional signal space can be realized by using two space- \northogonal electric field polarizations to communicate on the same \ncarrier frequency. It is also possible to regard each four-dimensional \nsymbol as two consecutive two-dimensional symbols.\n\nUngerboeck\u2019 described a technique called set partitioning, which \nassigns signal points to successive blocks of input data. The rule for \nassigning signal points depends on the state of the encoder. Unger- \nboeck constructed simple trellis codes providing the same noise im- \nmunity as is given by increasing the power of uncoded transmission \nby factors ranging from 2 to 4 (coding gains ranging from 3 to 6 dB). \nCalderbank and Mazo\u201d have given a different algebraic description of \ntrellis codes. Trellis codes with a rate of 4 bits/two-dimensional symbol \nhave recently been proposed for use in modems designed to achieve \ndata rates of 9.6 kb/s on dial-up voice telephone lines. These codes \nuse the signal constellation shown in Fig. 1, which was originally \ndescribed by Campopiano and Glazer,\u00ae and gain 4 dB over uncoded \ntransmission at the same rate. In Section III of this paper we describe \nthe first code in our infinite family. This code has a rate of 8 bits/ \nfour-dimensional symbol and promises a gain of 4.7 dB over uncoded \ntransmission. The signal constellation consists of 512 four-dimen- \nsional signal points. Transmission of two consecutive two-dimensional \nsignals using one of the proposed trellis codes with a rate of 4 bits/ \ntwo-dimensional symbol requires 1024 = 32? four-dimensional signal \npoints. Furthermore, the restriction of the 512-point constellation to \nthe first two coordinates, or to the last two coordinates, is the 32-point \nconstellation shown in Fig. 1. The 0.7-dB improvement in performance \nis derived from reducing the average transmitted power.\n\nFig. 1\u2014Signal constellation for proposed trellis codes with rate 4 bits/two-dimen- \nsional symbol.\n\ncoding gain of 4.9 dB over uncoded transmission. We propose using \nthis code in modems designed to achieve data rates of 14.4 kb/s.\n\nWe assume that binary data are being encoded at a rate of k bits/ \nsignal point and that the data enter the encoder in k parallel sequences, \nfai}, {a5}, --- , {ai}. We assume that the output x! of the trellis \nencoder at time i depends not only on the present values a}, a},\n\n- , a}, of the input sequences, but also on the previous \u00bb; > 0 bits of \nthe jth sequence. If v; = 0 for some j, then a}, a}, a}, --- is said to be \na sequence of uncoded bits. The constraint length v is given by \ny= >*, v;. The output x\u2019 of the encoder is a fixed vector-valued\n\nencoder and there are 2\u201d states. Figure 2 shows a state transition \ndiagram for a trellis code with k = 3, vy; = 0, ve = 1, vg = 2. The average \ntransmitted signal power P is given by\n\nBasic to the trellis codes constructed below is a certain rate 3/4 \nbinary convolutional code with total memory 3 and free distance 4. \nThe encoder is presented in Fig. 3, which is taken from Ref. 6 (Fig. \n10.3, p. 292). The three parallel input sequences determine the output \nsequence {v' = (vj, v5, U3, v4)} according to the following rules:\n\nThe triple a} \u2018a5a5\u00b0? is the state of the encoder. The possible transi- \ntions between states are shown in Fig. 2. The edge joining state \nasa ak? to state abasay! is labeled with the outputs v\u2019' = \n(vi, vb, vs, vi) and v' = (0), 04, 05, 04) corresponding to this transi- \ntion. Note that\n\nFig. 2\u2014A state transition diagram for a trellis code with k = 3, \u00bb; = 0, vp = 1, v3 = 2. \n(Every edge represents two possible transitions.)\n\nWe change from 0, 1 notation to +1 notation (0 @ +1 and 1< -\u20141). \nAn edge joining two states is now labeled with pairs of vectors +(w,, \nWe, W3, W4), Where w; = \u00a31, i = 1, 2, 3, 4. This defines a trellis encoder \nwith a rate of 3 bits/four-dimensional symbol. The minimum squared \ndistance of this trellis code is simply four times the free distance of \nthe original binary convolutional code, namely, 16. This is because 0 \nopposite 1 contributes 1 to the free distance, whereas 1 opposite \u20141 \ncontributes 4 to the squared minimum distance.\n\nTransmission at the higher rates of 8 and 12 bits/four-dimensional \nsymbol requires more channel symbols. Indeed, to achieve any coding \ngain, we have to use more symbols than are required by uncoded \ntransmission at the same rate.\n\nUncoded transmission at the rate 4 bits/two-dimensional symbol \nuses the rectangular signal constellation shown in Fig. 4. To achieve \nuncoded transmission of a four-dimensional symbol at a rate of 8 bits/ \nsymbol, simply take two copies of this scheme. There are 256 possible \nsignals and the average power is 4(17 + 3\u00b0)/2 = 20. Since the minimum \nsquared distance between distinct signals is 4, we have\n\nFor coded transmission we shall use 2 X 256 = 512 signal points. \nRepresentative signal points are listed in Table I. The remaining \npoints are obtained from these representatives by permuting the\n\nFig. 4\u2014The rectangular constellation for uncoded transmission at 4 bits/two-dimen- \nsional symbol.\n\nTable I\u2014The signal \nconstellation for coded \ntransmission at 8 bits/four- \ndimensional symbol. All \npermutations of coordinates \nand all sign changes are\n\ncoordinates and changing signs in all possible ways. For example, \n(3131), (1815), and (5111) are all signal points (where x denotes \n\u2014x). For every vector w = (Wj, Wo, W3, W4) With w; = +1, i = 1, 2, 3, 4, \nlet S(w) be the set of 32 signal points (x, x2, x3, x4) satisfying x; = w; \n(mod 4), for 1 = 1, 2, 3, 4. The sets S(w) partition the signal \nconstellation into 16 equal parts. The set S(1111) is shown in Table \nII and the other sets are obtained from S(1111) by changing signs. For \nexample, S(1111) is obtained from S(1111) by changing the signs of \nthe second and fourth entries. The distance d(A, B) between two sets \nof vectors A and B is given by\n\nd(A, B) = min {|x \u2014 yl}. \nxE\u20acA,yEB \nThe partition into sets S(w) satisfies the following metric properties:\n\nIn Section II we described a trellis code with a rate of 3 bits/four- \ndimensional symbol and minimum squared distance d?,i, = 16. To \nachieve the higher transmission rate of 8 bits/four-dimensional sym- \nbol, we add 5 uncoded bits. There are now eight parallel input se- \nquences {ai}, --- , {a}. The sequences {a3}, {a5} determine the state \na \u2018a as? of the encoder as in Fig. 3. An edge joining two states that \nwas originally labeled by the pair of vectors +v is now labeled by the \n64 vectors in S(v) U S(\u2014v). This is because there are 64 parallel \ntransitions between states ab \u2018ta}\u2018ay? and abaai* corresponding to \nthe 64 possible inputs aja), --- a}. We allow any fixed assignment of \nchannel symbols in S(v) U S(\u2014v) to inputs aja) --- a}.\n\nConsider the distance properties of the high-rate code. Properties \n(M1) and (M2) guarantee that the squared distance of any error event \nof length 1 is at least 16. Consider any error event in the eight-state \ntrellis of length greater than 1. If the squared distance for the low-rate \ncode is\n\nl \n\u00bby Ive - v'I?, \nthen the squared distance for the high-rate code is at least \n>\u00bb a*(S(v'), S(v')). \ni=l\n\nProperty (M2) now implies that the minimum squared distance of the \nhigh-rate code is at least 16.\n\nThe average signal power P of the 512-point signal constellation is \ngiven by\n\nP 51D 27. \nThus, \nGrn) _ 16 \nP coded 7 27 \nand the coding gain (in decibels) is \n(Ginin/P) coded 16/27 \n10 1 Ta aan ame (Goa = 4. \nee eae i lo8i0 4/20 : ut ob\n\nUncoded transmission at the rate of 6 bits/two-dimensional symbol \nuses the 64-point rectangular constellation shown in Fig. 5. To achieve \nuncoded transmission of a four-dimensional symbol at a rate of 12 \nbits/symbol, simply take two copies of this scheme. There are 64? = \n2\" possible signals, and the average signal power P is 4(17 + 3? + \n5? + 7\u00b0)/4 = 84. Thus,\n\nFig. 5\u2014A rectangular constellation for uncoded transmission at 6 bits/two-dimen- \nsional symbol.\n\nTable II[\u2014The signal constellation for coded transmission at 12 bits/ \nfour-dimensional symbol. All representatives are taken from $(1111).\n\nFor coded transmission we use 2 X 2\u201d = 2} signal points. As in \nSection III we partition the signal constellation into 16 sets S(w) \naccording to congruence of the entries modulo 4. Each set S(w) \ncontains 512 signal points. Representative signal points are listed in \nTable III, where the representatives are all taken from S(1111).\n\nTo achieve the transmission rate of 12 bits/four-dimensional sym- \nbol, we add 9 uncoded bits to the low-rate trellis code described in \nSection II. There are now 1024 parallel transitions between states \nab aias? and ajajai' in the eight-state trellis. If the edge corre- \nsponding to this transition was originally labeled +v, it is now labeled \nwith the 1024 vectors in S(v) U S(\u2014v). The metric properties (M1) \nand (M2) guarantee that the squared minimum distance of the high- \nrate code is equal to the squared minimum distance of the low-rate \ncode, which is 16. An easy calculation shows that the average signal\n\nTo achieve coded transmission at the rate of k bits/four-dimensional \nsignal, we add k \u2014 3 uncoded bits to the low-rate trellis code described \nin Section II. There are 2\" parallel transitions between states \nab tai as? and ajasai\" in the eight-state trellis. Coded transmission \nrequires 2\u201d*! signal points. The points of the lattice (2Z + 1)\u2018 lie in \nshells around the origin consisting of 16 vectors of energy 4, 64 vectors \nof energy 12, and so on (see Table III). The 2\"*' signal points are \nobtained by taking all points of energy 4, 12, 20, --- and just enough \npoints of a final shell to bring the total number up to 2**!. The signal \nconstellation is partitioned into 16 sets S(v) according to congruence \nof the entries modulo 4. Each set contains 2\u2019~\u00b0 signal points. Edges in \nthe eight-state trellis originally labelled +w are now labeled with the \n2*-2 vectors in S(v) U S(\u2014v). The metric properties (M1) and (M2) \nguarantee that the minimum squared distance of this trellis code is \n16.\n\nConsider the asymptotic performance of this family of codes. For \nsimplicity suppose that the signal constellation of each code in the \nfamily is a complete union of energy shells. If x is a vector in the \nlattice (2Z + 1)*, then ||x||? = 4 (mod 8), since ||x||* is the sum of four \nodd squares. A classical result, due to Jacobi and to Legendre, is that \nevery positive integer of the form 8n + 4 is a sum of four odd squares \nin o(2n + 1) ways, where o(m) is the sum of divisors of m. The \ngenerating function\n\nm odd \nexpresses the fact that there are 16 o(m) vectors of energy 4m in the \nlattice (2Z + 1)*. The factor of 16 arises from the 16 possible sign \nchanges.\n\n2:22 \n146 + o(m)= aD O(n log n). \nout \nFor uncoded transmission we use just half this many points. The signal \nconstellation is the set of all 4-tuples x = (x1, xo, x3, x4), where x; = \n+1, +3, --- , +(2a \u2014 1). The number of points in this constellation is\n\n1. G. Ungerboeck, \u201cChannel Coding With Multilevel/Phase Signals,\u201d IEEE Trans. \nInform. Theory, /7-28, No. 1 (January 1982), pp. 55-67.\n\n2. A. R. Calderbank and J. E. Mazo, \u201cA New Description of Trellis Codes,\u201d IEEE \nTrans. Inform. Theory, /T-30 (December 1984), pp. 784-91.\n\n4, G. D. Forney, Jr., et al., \u201cEfficient Modulation for Band-Limited Channels,\u201d IEEE \nJ. Selected Areas Commun., SAC-2 (August 1984), pp. 632-47.\n\n5. S. G. Wilson, H. A. Sleeper, and N. K. Smith, \u201cFour-Dimensional Modulation and \nCoding: An Alternative to Frequency-Reuse,\u201d in Science, Systems and Services \nfor Communications, P. Dewilde and C. A. May, eds., New York and Amsterdam: \nIEEE/Elsevier-North Holland, 1984, pp. 919-23.\n\n6. S. Lin and D. J. Costello, Jr., Error Control Coding: Fundamentals and Applications, \nEnglewood Cliffs, N.J.: Prentice-Hall, 1983.\n\n7. T.M. Apostol, Introduction to Analytic Number Theory, New York: Springer-Verlag, \n1976.\n\nnn? \n= cy + O(n log n). \nThe estimates for partial sums are obtained using Euler\u2019s summation \nformula (see Ref. 7, p. 54). To prove\n\nA. Robert Calderbank, B.Sc. (Mathematics), 1975, Warwick University, \nEngland; M.Sc. (Mathematics), 1976, Oxford University; Ph.D. (Mathe- \nmatics), 1980, California Institute of Technology; AT&T Bell Laboratories, \n1980\u2014. Mr. Calderbank is presently employed in the Mathematics and Sta- \ntistics Research Center. His research interests include applications of mathe- \nmatics to electrical engineering and to computer science, and algebraic meth- \nods in combinatorics.\n\nN. J. A. Sloane, B.E.E., 1959, and B.A. (Hons.), 1960, University of Mel- \nbourne, Australia; M.S., 1964, and Ph.D., 1967, Cornell University; AT&T \nBell Laboratories, 1969\u2014. Mr. Sloane is the author of four books. He was the \neditor in chief of the IEEE Transactions on Information Theory from 1978 to \n1980. In 1979 Mr. Sloane was awarded the Chauvenet Prize by the Mathe- \nmatical Association of America. Fellow, IEEE.\n\nAstigmatic launchers that would permit a single earth station antenna to \ncommunicate with all the satellites along the geosynchronous arc have been \nfabricated and measured at a frequency of 100 GHz. Good agreement between \nmeasured data and calculated values has been obtained for astigmatic correc- \ntions required by feeds displaced 18 and 29 degrees from the focus.\n\nFor high-capacity satellite communication systems, communication \nsatellites are placed at different locations along the geosynchronous \narc with the usual practice of using a separate earth station antenna \nto communicate with each satellite in the system. If both the satellites \nand earth stations are equipped with multiple-beam antennas, these \nhigh-capacity communication systems could be achieved by using a \nsingle earth station antenna and simultaneously communicating with \nall the satellites in the system.\u2019\n\nMeasurements and theory have indicated that the geometry of an \noffset Cassegrainian antenna results in an ideal configuration?\u201d for \nboth earth station and satellite antennas. Since the antenna aperture \nhas no blockage, this significantly reduces the sidelobe levels and, in \nturn, reduces interference. However, since only one of the multiple\n\nbeams can be aimed along the axis of the antenna reflector, the \nremaining beams must be displaced from the focus. The loss in\n\nFig. 1\u2014Astigmatic correction can be obtained by a feed with two different phase \ncenters, F and F\u2019, in the two principal planes of its beam.\n\nefficiency that these displaced beams exhibit is a function of the \namount of astigmatism introduced as a result of the displacement \nfrom the focus. By using a feed with different phase centers in the two \nprincipal planes of its beam, shown in Fig. 1, one can eliminate the \nastigmatic loss.\u00ae For efficient operation over a wide band of frequen- \ncies, both the two phase centers (F, F\u2019) and the beamwidths in the \ntwo principal planes (0, 0\u2019) must be frequency independent.\n\nEarlier work by Dragone\u2019 and Chu\u00ae shows that frequency-independ- \nent astigmatic corrections can be obtained by combining a small horn \nwith two cylindrical reflectors whose focal lengths are such that a \nmagnified image of the feed horn is produced over the main reflector \naperture.\u201d However, this feed arrangement is not very suitable for an \nearth station antenna supporting multiple beams, since the distance \nbetween the two phase centers is fixed and cannot be varied after the \nfeed is constructed. If one were to vary this distance, the beamwidths \nin the two principal planes would change, causing a reduction in \naperture efficiency. This is an important restriction, for it implies that \na given feed can only be used at certain locations in the vicinity of the \nfocus; at other locations corresponding to other beam displacements, \ndifferent feed parameters are required, necessitating the design of \ndifferent feeds for different displacements. In addition, a large feed \naperture is required, along with relatively large dimensions for one of \nthe two reflectors.\n\nwhile maintaining constant beamwidth in the two principal planes. \nUsing the principles of Ref. 6, two launchers (one long and one short) \nwere designed and fabricated for operation at 100 GHz.\n\nThe electroformed feed horn used with the launchers is shown in \nFig. 2. To permit polarization rotation in the rectangular aperture of \nthe feed horn, the horn was fabricated in two sections\u2014one section \ntapering down to a square aperture and the second section tapering \ndown to rectangular waveguide. The complete feed horn can be seen \nmounted together with the mixer on the short astigmatic launcher \nshown on the right of Fig. 3.\n\nThe long astigmatic launcher, shown without feed horn on the left \nof Fig. 3, has the top parallel plate removed to display the first reflector \nthat would be illuminated by the feed horn. Both the short and long \nlaunchers shown here have identical pairs of reflectors; the only \ndifference is the length of the parallel plates.\n\nThe cylindrical wave radiated by the feed horn positioned at the \nfocus of the first reflector is guided to the first reflector by the parallel \nplates. After being reflected, the wave is again guided by the parallel \nplates in the direction of the second reflector. After some distance the \nparallel plates are truncated and the aperture illuminated by the \nreflected cylindrical wave is defined by this truncation. The width of\n\niter aaahisimatitbain itech dacniniieiboniataNnisibuahtiinlslnaiait ites inntKitioniash ialieitbMtdahitisiitaieniscwunititarrisatsiitataunniosiiincttisilistiatasnthitifsiuaserimiiteasssitat tn nubtinititbascuiuaidiisatatncha\u2019isshuseshubivbausiiisiedniinitecs\n\nFig. 3\u2014The short astigmatic launcher (right) and the long astigmatic launcher (left).\n\nthe aperture is defined by the spacing between the two parallel plates; \nthe wave radiated by this aperture illuminates the second cylindrical \nreflector.\n\nTo produce an image of the feed horn aperture over the aperture of \nthe main reflector, the distances of the phase centers of the feed horn \nand the truncated parallel plate aperture must satisfy the optical thin \nlens equation.\u00ae\n\nUsing the newly constructed anechoic chamber at the radio range \nfacilities at Holmdel, New Jersey, measurements were made of the \nradiation characteristics of the two 100-GHz astigmatic launchers \ndepicted in Fig. 3. The measured data,* both amplitude and phase, are \npresented in Figs. 4 through 7 for both launchers and are shown by \nthe solid curves. The dashed curves are the calculated theoretical \nvalues.\n\n* These data were obtained at a distance equivalent to that of the main reflector of \nan offset Cassegrainian Antenna, i.e, the data represent the actual illumination at the \naperture of the main reflector.\n\nFig. 4\u2014(a) Measurements for an electric field parallel to the plates of the short \nlauncher, and the theoretical amplitude distribution. The phase center lies in front of \nthe aperture. (Cont.)\n\nTo avoid any difficulty in visualizing the polarization of the electric \nfield, the electric field will always be referred to the plane of the \nparallel plates. Therefore, the electric field will be either parallel to or \northogonal to the plates. Further, the insert in each of these figures \nshows the position of the launcher with respect to the plane of \nmeasurements. The location of the phase center is also shown on the \ninsert.\n\nThe amplitude measurements shown by the solid curve of Fig. 4a \nwere obtained with the electric field parallel to the plates. The agree-\n\nFig. 4\u2014(b) The electric field remains parallel to the plates, but the launcher is rotated \n90 degrees. The phase center lies behind the aperture.\n\nment with the theoretical calculations is very good. An examination \nof the phase measurements shows a maximum phase variation of the \norder 6 degrees. Over much of the aperture, the phase is essentially \nconstant.\n\nFor the amplitude data shown by the solid curve of Fig. 4b, the \nelectric field is still parallel to the plates. As shown by the insert on \nthis figure, the launcher is rotated 90 degrees. The dashed curve is \nthat for a uniformly illuminated aperture. The measured data, given \nby the solid curve, are in good agreement. From the phase data shown \nhere, one sees that the phase change over the aperture is of the order\n\nFig. 5\u2014(a) Measurements for an electric field orthogonal to the plates of the short \nlauncher, and the theoretical amplitude distribution. The phase center lies behind the \naperture. (Cont.)\n\n8 degrees. However, over most of the aperture the phase is essentially \nconstant.\n\nMeasurements made with the electric field orthogonal to the plates \nare shown in Figs. 5a and b. As shown here by the dashed curves, the \nagreement between the calculated values and the measured data is \nvery good. From the phase measurements shown on these figures, one \ncan see that the phase is essentially constant across the aperture. The \ntwo pairs of measured data shown by Figs. 4 and 5 are essentially \nidentical.\n\nFig. 5\u2014(b) The electric field remains orthogonal to the plates, but the launcher is \nrotated 90 degrees. The phase center lies in front of the aperture.\n\nThe feed horn and mixer assembly were then transferred to the long \nastigmatic launcher shown at the left of Fig. 3. The amplitude and \nphase measurements obtained with the long launcher are shown in \nFigs. 6 and 7 by the solid curves. Again, the dashed curves are the \ntheoretical calculations.\n\nThe data shown in Figs. 6a and b were obtained with the electric \nfield parallel to the plates. As shown by the inserts on these figures, \nthe launcher was rotated 90 degrees to obtain the second set of data. \nHere again, the measurements agree well with the calculated values. \nThe phase deviations across the aperture are very small.\n\nFig. 6\u2014(a) Measurements for an electric field parallel to the plates of the long \nlauncher, and the theoretical amplitude distribution. The phase center lies in front of \nthe aperture. (Cont.).\n\nThe data for the long launcher were completed with the measure- \nments shown in Figs. 7a and b. For these data the electric field is \northogonal to the plates. Again, the agreement between amplitude \nmeasurements and theoretical calculations is very good and the phase \nvariations across the aperture are small.\n\nA comparison of the data presented in Figs. 4 through 7 for both \nthe short and long launchers confirms the fact that the phase center \nseparation for this arrangement of launcher can indeed be varied and \nstill maintain constant beamwidth in the two principal planes. The\n\nFig. 6\u2014(b) The electric field remains parallel to the plates, but the launcher is rotated \n90 degrees. The phase center lies behind the aperture.\n\nFig. 7\u2014(a) Measurements for an electric field orthogonal to the plates of the long \nlauncher, and the theoretical amplitude distribution. The phase center lies behind the \naperture. (Cont.)\n\nfrequency independence of these launchers was checked over a 20- \npercent band with no discernible change in beamwidth.\n\nFig. 7\u2014(b) The electric field remains orthogonal to the plates, but the launcher is \nrotated 90 degrees. The phase center lies in front of the aperture.\n\nIt is with appreciation that I acknowledge G. F. Apgar, for the \nsuccessful results obtained are due to the attention he gave to the\n\nfabrication of the feed horn and launchers. The design discussions \nwith C. Dragone are acknowledged.\n\n1. L. C. Tillotson, \u201cA Model of a Domestic Satellite Communication System,\u201d B.S.T.J., \n47, No. 10 (December 1968), pp. 2111-37.\n\n2. C. Dragone and D. C. Hogg, \u201cThe Radiation Pattern and Impedance of Offset and \nSymmetrical Near-Field Cassegrainian and Gregorian Antennas,\u201d IEEE Trans. \nAnt. Propag., AP-22, No. 3 (May 1974), pp. 472-5.\n\n3. M. J. Gans and R. A. Semplak, \u201cSome Far-Field Studies of an Offset Launcher,\u201d \nB.S.T.J., 54, No. 7 (September 1975), pp. 1319-40.\n\n4, Ta-Shing Chu and R. H. Turrin, \u201cDepolarization Properties of Offset Reflector \nAntennas,\u201d IEEE Trans. Ant. Propag., AP-21, No. 3 (May 1973), pp. 339-45.\n\n5. R. A. Semplak, \u201c100-GHz Measurements on a Multiple-Beam Offset Antenna,\u201d \nB.S.T.J., 56, No. 3 (March 1977), pp. 385-98.\n\n6. C. Dragone and R. A. Semplak, \u201cAn Antenna Feed Arrangement for Correcting for \nAstigmatism,\u201d U.S. Patent 4482898, issued November 1984.\n\n7. C. Dragone, \u201cAn Improved Antenna for Microwave Radio Systems Consisting of \nTwo Cylindrical Reflectors and a Corrugated Horn,\u201d B.S.T.J., 53, No. 7 (Septem- \nber 1974), pp. 1351-77.\n\n9. C. Dragone and M. J. Gans, \u201cImaging Reflector Arrangements to Form a Scanning \nBeam Using a Small Array,\u201d B.S.T.J., 59, No. 3 (March 1980), pp. 449-61.\n\n10. C. Dragone, \u201cFirst Order Treatment of Aberrations in Cassegrainian and Gregorian\n\nRalph A. Semplak, B.S. (Physics), 1961, Monmouth College; AT&T Bell \nLaboratories, 1955-1985. Mr. Semplak\u2019s main research interest is in studies \nof atmospheric effects on micro- and millimeter-wave propagation. He was a \nmember of the Radio Communications Research Department when he retired \nin 1985. Member, Sigma Xi, Commission F of the International Union of \nRadio Science (URSI/USNC).\n\nRecent work at AT&T Bell Laboratories has demonstrated the efficacy of \nvector quantization in greatly reducing both the computational and memory \nrequirements of isolated-word recognition systems. This efficiency is obtained \nat the expense of a marginal decrease in performance, and thus is an attractive \napproach. The purpose of this paper is to report on the results of a series of \nexperiments in the application of vector-quantization strategies to a small- \nvocabulary, connected-word recognition task. Several strategies are investi- \ngated, including the use of speaker-trained code books versus universal code \nbooks, the use of binary and higher-order tree searches versus full searches of \nthese code books, and the quantization of both test and reference frames \nversus reference frames only. For various strategies, the effect on error rate of \nvarying the code-book size is also reported. Results indicate that the vector \nquantization approach is attractive for linear predictive coding-based con- \nnected-digit recognition.\n\nIn the area of speech coding, the technique of Vector Quantization \n(VQ) has recently been successfully applied.\u2019 In the standard ap- \nproach, a speech signal is framed and a feature vector is extracted \nfrom each frame. Each element of the feature vector is then separately \nquantized. In other words, the value of each element is replaced by its \nclosest match from a set of discrete values. The set of values is chosen \nto minimize some error criterion while reducing the number of bits\n\nrequired to identify the element value. This feature vector is typically \na set of Linear Predictive Coding (LPC) coefficients and perhaps an \nenergy term. In the VQ approach, a feature vector is extracted as \nbefore. The entire vector of features is then quantized by replacing \nthe vector with its closest match from a set or \u201ccode book\u201d of feature \nvectors. Similarly, the entries in the code book are chosen to minimize \nsome distortion measure while reducing the number of bits required \nto identify each frame of speech. In addition to reducing the number \nof bits required to represent each feature vector, by using a suitably \ncompact code book in place of a large set of reference vectors, it is \npossible to greatly reduce the number of comparisons made between \nthe unknown (test) feature vector and the stored-feature vectors. Since \nthis comparison (or distortion measure) is the current bottleneck in \nmany speech recognition systems, the VQ approach is quite effectively \nused in them. In fact, VQ has been used heavily in several different \napproaches to speech recognition, including Hidden Markov Modeling \n(HMM)?* and Dynamic Time Warping (DTW),\u00b0 among others.*>\n\nThe purpose of this paper is to report on the results of a series of \nexperiments in the application of VQ strategies to a small-vocabulary, \nconnected-word recognition task.\u2019 These strategies include the use \nof Speaker-Dependent (SD) versus Speaker-Independent (SI) code \nbooks; the use of binary and higher-order tree searches versus full \nsearches of these code books, as suggested in Ref. 2; and the quanti- \nzation of both test and reference frames versus reference frames only.\u00ae\u201d \nThe effect on error rate of varying the code-book size is also reported. \nIn all experiments, the reference and test data sets are disjoint, and \ncode books are trained with reference data. That is, speaker-dependent \nreference templates are quantized by vocabulary-dependent code books \nthat are either speaker dependent or speaker independent. All test \nstrings consist of deliberately spoken, connected words.\n\nIn Section II some useful terminology is presented. In Section HI \ntheory is developed. In Section IV experimental results are presented.\n\nd(a;, V;) distortion between reference and training frames \np(l) perturbation vector\n\n{Tu (i)} set of training vectors whose best match is code word 1 \nCy (2) number of training vectors in {T'y(i)}.\n\nThe VQ procedure consists of two main parts: code-book generation \nand the classification of test frames. In both cases, a code-book search \nprocedure must be employed to classify the training or test (unknown) \nframes, respectively. The code-book generation process will be pre- \nsented first and the search strategy second.\n\nThe basic generation procedure discussed in Refs. 1, 2, and 10 is \nemployed and is illustrated in Fig. 1. The flowchart is from Ref. 10, \nbut has been generalized to allow B-way splitting of centroids versus \nthe original two-way splitting (B is a power of 2 in this work). The \noverall goal is to find a set of code words {a}, such that the mean \ndistortion D,, produced by replacing each of the J training frames by \nits closest match from the code book {a}, is minimized. Succinctly \nstated,\n\nThe distortion d can be calculated using the likelihood-ratio-dis- \ntance metric as follows:\n\nwhere row m, column n of matrix V; contains (1/N)R;(|m \u2014 n|). N \nis the window length and R is the autocorrelation vector. Only the \nspectral-shape information is used in the quantizer.\n\nof size M = B (where B is typically 2), and then successively splitting \nits code words B ways to obtain larger and larger code books until a \ncode book of the desired size is obtained (see outer loop of Fig. 1). \nEach successive code book is corrected by iteratively classifying the \ntraining set, and adjusting each code word to be the centroid of the \nsubset of training frames which best match that code word (inner \nloop). The final iteration is determined as that for which the mean \ndistortion changes by less than a threshold \u00a2 in relation to the previous \nmean distortion. Typically, \u00ab = 0.01. \nInitialization of centroids is as follows:\n\nwhere k = LogoB and 0 <1 Ss B \u2014 1. This splits the LPC reflection \ncoefficient space on the first Log.B coordinate axes. For instance, for \nB=4,\n\naccomplishes a B-way split of each reflection coefficient vector in code \nbook k. The factor 6 is typically set to 0.01. LPC model stability is \nensured by requiring that -1