In this paper are discussed several types of crystal band-pass
filters which can be used in unbalanced circuits. These types of
filters are all resistance compensated, i.e., the resistances associated
with the filter elements are in such a position in the filter that they
can be effectively brought to the ends of the filter and combined
with the terminal resistances with the result that the dissipation
produces an additive loss for the filter characteristic and does not
affect the sharpness of cut-off attainable. It is shown that all these
types of networks can be reduced to three lattice types of crystal
filters, and the formulae for these three networks are given. A
comparison is given between the characteristics obtainable with
resistance compensated crystal and electrical filters and a conclu-
sion regarding their comparison given by V. D. Landon ‘ is shown
to be incomplete.

employing quartz crystals as elements. Most of these filters were
of the lattice type and hence were inherently balanced. For some
purposes, however, such as connecting together unbalanced tubes, it is
desirable to obtain a filter in an unbalanced form and it is the purpose
of this paper to show several forms for constructing resistance com-
pensated band-pass crystal filters which will give results similar to
those described previously. Another purpose is to give a numerical
comparison between the characteristics obtainable with resistance
compensated crystal and electrical filters.

II. A COMPARISON OF THE PERFORMANCE CHARACTERISTICS OF
CRYSTAL vs. CoIL AND CONDENSER FILTERS

filters it is instructive to give a comparison between the types of
characteristics which can be obtained by using crystal and coil and

1“Electrical Wave Filters Employing Quartz,Crystals as Elements,” W. P. Mason,
B.S. T. J., July, 1934, p. 405. a

condenser filters. The quartz crystal filter considered here is shown
on Fig. 1. :

By using the balancing resistance R, of Fig. 1 the crystal filter can be
made entirely compensated for coil resistance ; i.e. the resistance associ-
ated with the coils of the network is in such a place in the network that

it can be effectively brought to the ends of the filter and combined with
the terminal impedances with the result that the effect of the dissipa-
tion in the coils is only to produce an additive loss for the filter charac-

teristic and does not affect the sharpness of cut-off attainable. In fact

if the filter works into a vacuum tube the dissipation in the coil can be
used to terminate the filter completely, and introduces no loss.

For the electrical filter, however, the dissipation introduced by the
electrical elements which replace the crystal is not compensated and
causes a considerable distortion of the pass band which becomes more
prominent as the band width is narrowed. To show this let us consider

the network of Fig. 2. In analyzing such networks it is usually more
convenient to reduce them to their equivalent lattice form and apply
network equivalences holding for lattice type networks. This can be
done by applying Bartlett’s Theorem? which states that any network
which can be divided into two mirror image halves can be reduced to an
equivalent lattice network by placing in the series arms of the lattice a
two-terminal impedance formed by connecting the two input terminals
of one half of the network in this arm and short-circuiting all of the cut
wires of the network, and in the lattice arm placing the same network
with all its cut wires open-circuited. Applying this process to Fig. 1,
a lattice network equivalent to the network of Fig. 1 is that shown on
Fig. 3. In this network the capacitances can be considered as sub-

stantially dissipationless and if the network representing the crystal can
also be considered dissipationless, the resistance introduced by the
coils can be effectively brought outside the lattice and incorporated
with the terminal resistances. This follows from the fact that an
inductance with an associated series resistance can just as well be
represented over the narrow-frequency range of the filter by an in-
ductance paralleled by a much higher resistance. The impedance of an
inductance and resistance in series and the impedance of an inductance
and resistance in parallel are given by the expressions

This relation holds strictly only for a single frequency, but over a
narrow-band filter the relation holds quite accurately.

Employing this conception, the lattice network can be reduced to
that of Fig. 4 in which a resistance R parallels each arm of the lattice.

This is made possible by the adjustable resistance R, which is fixed at
such a value that the parallel resistance associated with the inductance
L; + 2Lz is equal to that associated with L;. Then by employing the
two lattice equivalents shown on Fig. 5, first proved by the writer,? it is

possible to take these resistances outside the lattice and combine them
with the terminating impedance, leaving all the elements inside the
lattice dissipationless. The two remaining arms of the lattice have the
impedance characteristic shown on Fig. 6A. A lattice filter has a pass
band when the two impedance arms have opposite signs and an at-
tenuation band when they have the same sign. When the impedance
of two arms cross, an infinite attenuation exists. Hence the character-
istic obtainable with this network is that shown on Fig. 6B.

Next let us consider an electrical filter in which coils and condensers
take the place of the essentially dissipationless crystal. In this case the
dissipation due to L; and Lz can be balanced as before and the only
question to consider is the effect of the dissipation associated with L;
and C;. Ina similar manner to that employed for the coil we can show

that a series tuned circuit with a series resistance R, is equivalent to a
second series tuned circuit having the same resonant frequency as the
first shunted by a resistance R,’ where
Al
C,\

At two frequencies for which the absolute values of the reactances are
the same and therefore the value of Q equal, it is possible to replace the
series resistance by a shunt resistance and hence compensate it by
varying the resistance R,. Since, however, the reactance of the tuned
circuit varies from a negative value through zero to a positive value
over the pass band of the filter, the value of this shunt resistance is not

even approximately constant and hence the filter cannot be resistance
compensated throughout the band of the filter. It cari, however, be
compensated at the frequencies of infinite attenuation and high losses
can be obtained at these frequencies.

The effect of the lack of resistance compensation throughout the
band can best be shown by a numerical computation of the loss of an
electrical filter as compared to that for a crystal filter. A practical
example has been taken of a filter whose band width is 12 kilocycles
wide with the mean frequency at 465 kilocycles. In order to obtain the
best Q’s with reasonably sized coils an arrangement suggested by R. A.
Sykes is used. The coils L; are obtained by using the two equal wind-
ings of a coupled coil series aiding so that ZL; equals the primary induct-
ance plus the mutual inductance. Since in an air core coil all of the
dissipation is associated with the primary inductance and none with the
mutual this gives a high Q for L;. The inductance L» neutralizes the
negative mutual inductance —M and supplies in addition a small
positive inductance. The Q of this combination is poor but it makes
unnecessary the use of a high resistance R, for balancing purposes. By
this method a much higher effective Q is obtained than can be obtained
by a single coupled coil or by three separate coils.

The calculated curve for the electrical filter assuming Q’s of 150 for all
the coils is shown on Fig. 7 by the dotted lines. A similar curve for a
crystal filter is shown on Fig. 7 by the full lines. As is evident the
effect of the coil dissipation is to round off the edges of the pass band
and to limit the effective discrimination between the passed and
attenuated bands.

This result does not agree with that given by Landon,‘ who in a
recent paper makes a comparison between the results obtained with
crystal and elec rical filters which appears to be somewhat misleading.
It is stated in this paper that the electrical filter circuits given are com-
pletely resistance compensated and “‘in crystal filters in which the
crystal is confined to the rejector meshes of the network, the limitation
is about the same as for electrical filters.” By referring to the curves
of Fig. 7 it is readily seen that high losses can be obtained outside the
pass band with resistance compensated electrical filters,® but that the

4“ *VW Derived’ Band-Pass Filters with Resistance Cancellation,” Vernon D.
Landon, R. C. A. Review, Oct. 1936, Vol. 1, No. 2, Page 93.

5 The use of resistance for compensating and balancing the attenuation in electrical
filters has been worked out by H. W. Bode and S. Darlington (see U. S. patents
2,002,216, 1,955,788, 2,029,014, 2,035,258). The first work was done for low- and high-
pass filters but it was later extended also to band-pass filters. Some of these results
are analogous to those of Landon, while others give a better compensation within the

transmitted band. The use of the resistance in the crystal filter of Fig. 1 was sug-
gested by Mr. Darlington.

Fig. 7—Numerical comparison_between the loss characteristics of a crystal filter and

pass band of the filter is seriously distorted unless elements, such as
crystals, are used which have negligible dissipation.

All of the wide-band resistance compensated crystal filters proposed
so far can be shown to be equivalent to the two general types of lattice
crystal filters shown on Fig. 8. For example the crystal filter of Fig. 1
was shown to be equivalent to the lattice type filter of Fig. 8 (b) in which
the crystals in the lattice arms are left out.

In the lattice filters of Fig. 8 the number of crystals employed can be
cut in half by employing in two similar arms a crystal with two pair of
equal plates. It can be shown that such a crystal used in similar arms
is equivalent to two identical crystals of twice the impedance of the
crystal used as a single plate and having the same resonance frequency.
Hence the lattice filters of Fig. 8 are as economical of elements—except
for two condensers—as an unbalanced type filter. For some purposes,
however, such as connecting together unbalanced tubes, it is desirable
to obtain a filter in an unbalanced form. Also, at high frequencies the
crystals become quite small and hence it becomes difficult to divide the

aS plating on such crystals. It is the purpose of this section to list a
number of filters of the unbalanced type which are equivalent to the
lattice filters of Fig. 8. They do not have as general filter character-

spectively to the lattice crystal filters of Fig. 8. The equivalent lattice
configurations are shown on Fig. 9. The first two filters have series
coils which inherently give low-impedance filters. The second of these
is equivalent to the filter of Fig. 8 (a) with one pair of the crystals
eliminated. If the inductance L2 were eliminated from Fig. 9 (a) or (b)
the filters will be resistance compensated, for all of the resistance will
be on the ends of the filter. Furthermore if a small amount of coupling
is allowed between the two end coils, the effect of this will be to intro-
duce the small coil L2/2 in the desired place as can be seen from the 7
network equivalent of a coupled coil as shown on Fig. 10. Further-
more if the coils are air core, no dissipation is associated with the mutual
inductance and hence if coupled coils are used the networks still have a
resistance balance. Similarly the filters shown on Figs. 9 (c) and (d) are
equivalent to the high-impedance type filter shown on Fig. 8 (b) with all
crystals present or with crystals missing from the lattice arms. By

employing coils with a small amount of mutual inductance these types
can also be made with a resistance balance. They can also be made to
balance for physical coils by employing the resistances shown. It is
obvious from the equivalent lattice structures that these networks have
limitations on band widths and allowable attenuation which are not
present for the original lattice structures of Fig. 8. However, for filters
whose pass bands are less than the maximum pass bands, useful results
can be obtained.

Another method for obtaining results similar to that obtainable in a
lattice network is to use a hybrid coil with series aiding secondaries
which are connected to a crystal and a condenser as shown on Fig. 11,
This circuit, which has been used extensively to provide a narrow band
crystal filter in telegraph work, was invented first by W. A. Marrison °
of the Bell Telephone Laboratories. Under certain circumstances this
configuration can be shown to give results similar to the narrow-band

lattice filter of Fig. 12. A hybrid coil with series aiding windings con-
nected to two impedances 2Z; and 2Z2 as shown by Fig. 13A can be
shown to be equivalent to the circuit of Fig. 13B in which a lattice

network with the branches Z; and Z; is placed in series with the trans-
forming network and the series terminating inductances. Hence if the
hybrid coil has nearly a unity coupling between its secondary coils and

the remainder of the transformer is designed to work into the impedance
of the filter, the network of Fig. 11 is equivalent to the narrow-band
lattice filter of Fig. 12 with crystals removed from the lattice arms, plus

a transformer. As usually used, however, the impedance of the trans-
former is much lower than that of the filter and as a consequence the
band-pass characteristic of the filter is lost. As a result the network
passes only a single frequency and gives results similar to those obtain-
able with a very sharply tuned circuit. By placing a crystal in the
other arm of the network as shown by Fig. 14,’ this configuration can
be made equivalent to the filter shown in Fig. 12.

It is obvious from the equivalence of Fig. 13 that the configurations of
Fig. 11 and Fig. 14canalsobe used togivea wide-band filter. This follows
since the series inductances can be taken inside the lattice and the low-
impedance crystal filter of Fig. 8 (a) results. The Q of the coils included
in the filter will ordinarily not be high since the inductance is obtained
by a difference of primary and mutual inductances, and a better result
will be obtained by making the secondary coupling high and including
physical coils in series with the crystals.

We see then that all of the resistance compensated wide-band filters
are equivalent to the lattice filters of Figs. 8 and 12, and all their design
equations are known when the design equations of the equivalent
lattices are calculated. This requires two steps, first the calculation of
the spacing of the resonant frequencies of the network to give the
required attenuation and secondly the calculation of the element values
from the known resonances by means of Foster’s theorem. Such
calculations are familiar in filter theory and hence only the results are
given here. The results are given in Tables I, II, and III for the
network of Figs. 8 (a), 8(b) and 12 respectively. These values are given
in terms of the characteristic impedance Zp of the filter at the mean
frequency, the lower and upper cut-off frequencies f; and fz respectively
and the b’s of the network. These last, are parameters which specify

TABLE III
Element Formula Element Formula
C + be) C biba(f2? —
+ firbibe L Zo( + fi2bibe)*
2aZof i + b2) + b2)(fs? — fi?)
C (by + be) (fe? — fi?) L Zof + bs)
2aZofi(1 + bibs) (fo? + 2afibiba( — fi*)

the location of the attenuation peaks of the network with relation to the
cut-off frequencies and are given by the expression :

These tables give the design formulae for the networks of Figs. 8 and
12. To obtain the equations for a network having crystals in the
series arms alone, it is only necessary to let b; = 0. If one of the
peaks of the filter of Fig. 8 (a) is placed at infinity-——-which results when

= fe/f:—the two coils will have equal values and by the theorem
illustrated by Fig. 5 can be brought out to the ends of the filter,
simplifying the construction. In a similar manner if one of the peaks
of the filter of Fig. 8 (b) is placed at zero frequency, i.e. b2 = 1, the two
shunt inductances are equal and can be brought out to the ends of
the filter. The design equation of the narrow band filter of Fig. 12
with the lattice crystals replaced by condensers can be obtained from
Table III by letting b. =

Magnetic Generation of a Group of Harmonics*
By E. PETERSON, J. M. MANLEY and L. R. WRATHALL

A simple physical picture of the action of the circu t has been
derived from an approximate mathematical analysis. The prin-
cipal roles of the non-linear coil may be regarded as fixing the
amount of charge, and timing the charge and discharge of a con-
denser in series with the resistance load. By suitably propor-
tioning the capacity, the load resistance, and the saturation in-
ductance of the non-linear coil, the amplitudes of the harmonics
may be made to approximate uniformity over a wide frequency
range. The sharply peaked current pulse developed by condenser
discharge passes through the non-linear coil in its saturated state
and so contributes nothing to the eddy current loss in the core.
In this way the efficiency of frequency transformation is main-
tained at a comparatively high value for the harmonics in a wide
frequency band, even with small core structures. The theory has
also been adequate in establishing a basis for design, and in evalu-
ating the effects of extraneous input components.

HE use of non-linear ferromagnetic core coils to generate har-
monics started with a simple type of circuit due to Epstein !
which appeared in 1902. Application of the idea was not made to any
great extent until it was elaborated by Joly ? and by Vallauri * in 1911.
The frequency multipliers thus developed were limited to doublers and
to triplers, polarization being required for the doubler. In these, as
well as in subsequent developments, single and polyphase circuits were
used, and various arrangements were adopted for the structure of the
magnetic core and for the circuit, by which unwanted components were
balanced out of the harmonic output path. Later developments had
to do with improvements in detail, and with the generation of higher
harmonics in a single stage and in a series of stages. The applications

* Presented at the Pacific Coast Convention of A. I. E. E., Spokane, Washington,
September 2, 1937. Published in Elec. Engg. August 1937.

of perhaps greatest importance were to high power, long-wave radio-
telegraph transmitters, where the fundamental input was obtained
from an alternator. Other applications of the idea of harmonic pro-
duction by magnetic means have been made in the power and com-
munication fields.‘

It appears that these circuits were all developed primarily to generate
a single harmonic. Comparatively good efficiencies were obtained,
values from 60 to 90 per cent being reported for the lower harmonics.
The theory of frequency multiplication was investigated by a number
of workers, among whom may be mentioned Zenneck ° and Guillemin.°
The latter, after analysis which determined the optimum conditions for
the generation of any single harmonic, found experimentally that the
efficiency of harmonic production decreased as the order of the har-
monic increased. He obtained efficiencies of 10 per cent for the 9th
harmonic, and 3 per cent for the 13th harmonic of 60 cycles.

Where the circuits are properly tuned and the losses low, free oscilla-
tions may be developed. The frequencies of these free oscillations may
be harmonic, or subharmonic as in the circuit described by Fallou; 7?
they may be rational fractional multiples of the fundamental, or in-
commensurable with the fundamental, as in Heegner’s circuit. The
amplitudes of these free oscillations are usually critical functions of the
circuit parameters and input amplitudes, and where the developed
frequencies are not harmonic, they are characterized by the fact that
the generated potentials are zero on open circuit. The theory of the
effect has been worked out by Hartley.® It is presumably this effect
which is involved in the generation of even harmonics by means of an
initially unpolarized ferromagnetic core, an observation which has been
attributed to Osnos.'°

The harmonic producer circuit which forms the subject of the
present paper differs from those mentioned in that it is designed to
generate simultaneously a number of harmonics at approximately the
same amplitude.

Harmonics developed in circuits of this type have been used for the
supply of carrier currents to various multi-channel carrier telephone
systems, for synchronizing carriers used in radio transmitters, and for
frequency comparison and standardization. Only odd harmonics are
generated by the harmonic producer when the core of the non-linear
coil is unpolarized, as is the case here. To generate the required even
harmonics, rectification is employed. This is accomplished by means
of a well balanced copper oxide bridge, which provides the even har-
monics in a path conjugate to the path followed by the odd harmonics.

A typical circuit used for the simultaneous generation of a number of
odd and even harmonics at approximately equal amplitudes is shown
schematically in Fig. 1. Starting with the fundamental frequency

input, a sharply selective circuit (F) is used to remove interfering com-
ponents, and an amplifier (A) provides the input to the harmonic
generator. The shunt resonant circuit (ZoCo) tuned to the funda-
mental serves primarily to remove the second harmonic generated in
the amplifier. The elements C,Z; are inserted to maintain a sinusoidal
current into the harmonic producer proper, as well as to tune out the
circuit reactance.

Fig. 2—Cathode ray oscillogram of output current wave form with fundamental input
current as abscissa,

L2 is a small permalloy core coil which is operated at high magnetiz-
ing forces well into the saturated region. The circuit including Le, C2,
and the load impedance, which is practically resistive to the desired
harmonics, is so proportioned that highly peaked current pulses rich in
harmonics flow through it. Two such pulses, oppositely directed, are
produced during each cycle of the fundamental wave, the duration of
each being a small fraction of the fundamental period. The typical
output wave shown in Fig. 2 was obtained by means of a cathode ray
oscillograph, the ordinate representing the current in the load re-
sistance, and the abscissa representing the fundamental current into the
coil. The desired odd harmonics are selected by filters connected
across the input terminals of the copper oxide bridge. The even har-
monics are obtained by full-wave rectification in the copper-oxide
bridge. They appear at the conjugate points of the bridge, and are
connected through an isolating transformer to the appropriate filters.
Thus the harmonics are produced in two groups, with the even harmon-
ics separated from the odds to a degree depending largely upon the
balance of the copper-oxide bridge, as well as upon the amount of
second harmonic passed on from the amplifier. In this way the re-
quired discrimination properties of any filter against adjacent harmonics
are reduced to the extent of the balance.

A particular application of the circuit described above to the genera-
tion of carriers for multi-channel carrier telephone systems uses a
fundamental frequency of 4 kc., from which a number of harmonics
are developed. Of these the 16th to the 27th are used as carriers.
A photograph of an experimental model of this carrier supply system *
is shown in Fig. 3. The top panel includes an electromagnetically driven
tuning fork serving as the highly selective circuit (F), the amplifier (A),
the output stage of which consists of a pair of pentodes in push-pull, and
the tuned circuit LoCo. The next panel includes the elements L,C), Ls,
C2, B, and T, together with a thermocouple and meter terminating in a
cord and plug for test and maintenance purposes. The last two panels
include the twelve harmonic filters, with test jacks and potentiometers
for close adjustment of the output of each harmonic.

A few of the more interesting performance features are given in
Fig. 4. The harmonic power outputs shown in Fig. 4a represent
measurements at the input terminals of the filters. The variation
observed is produced by the non-uniform impedances of the filters.
When these are corrected, the variations due to the harmonic generator
proper are less than + 0.2 db from the 16th to the 27th harmonic.
Outside this region the amplitudes gradually decrease to the extent

Fig. 3—Carrier supply unit, furnishing twelve harmonics of 4 kc.
(experimental model).

of 4 db at the 3d and 35th harmonics, and 11 db at the fundamental
and the 61st harmonic. The variation of harmonic output with
change of amplifier plate potential is given for the two harmonics
indicated in Fig. 4b. Figure 4c shows the 104 kc. output as a function
of the 4 kc. input. Arrows are used to indicate normal operating
points. The input amplifier is operated in an overloaded state so that
beyond a critical input, the fundamental output of the amplifier and

Fig. 4—Performance curves of channel harmonic generator. (A) Harmonic
outputs; (B) Variation of 16th and 26th harmonics with amplifier plate potential;
(C) Variation of 26th harmonic with fundamental input.

Fig. 5—Construction of experimental non-linear coils used for harmonic generation,
showing core forms, magnetic tape, wound coils, and assembled units.

the harmonic output corresponding are but little affected by change of
input amplitude. With a linear amplifier the harmonic output current
would vary roughly as the four-tenths power of the input current.

Another application involving higher frequencies has been made to
the generation of the so-called ‘‘group”’ carriers used in conjunction
with a coaxial conductor." There odd harmonics of 24 kc. from the
9th to the 45th are used. The circuit differs from Fig. 1 in that the
copper oxide bridge is omitted, and the non-linear coil is provided with
two windings to facilitate impedance matching. The performance of
an experimental model is similar to that of the generator described
above. A notion of the physical size and construction of the non-
linear coils used may be had from the photographs of Fig. 5.

In both applications the required harmonics are generated at ampli-
tudes high enough to avoid the necessity for amplification.

To avoid these difficulties, an expedient is adopted by which the
hysteresis loop is replaced by a single-valued characteristic made up of
connected linear segments ° as shown in Fig. 6b. It is then possible to
formulate a set of linear differential equations with constant coefficients,
one for each linear segment. The solutions are readily arrived at and
may be pieced together by imposing appropriate conditions at the
junctions, so that a solution for the whole characteristic is thereby
obtained. From this solution the wave form of current or voltage
associated with any circuit element may be calculated. Resolution of
the wave form into components may then be accomplished by an
independent Fourier analysis.

The assumed B-H characteristic of Fig. 6b is made up of but three
segments. While it is manifestly a naive representation of a hysteresis
loop, it will be shown by comparison with experiment that the main
performance features of harmonic generators may be reproduced by
this crude model.

It will be noted on Fig. 6b that the differential permeability of the
assumed non-linear core, a quantity proportional to dB/dH, takes on
one of two values, determined by the absolute value of the magnetizing
force. These are designated by u in the permeable region and y, in the
saturated region. The corresponding inductances are Loo and Lo, Loo
being many times greater than L2,. The values of current through the
coil at which the differential inductance changes are designated + [o,

Fig. 6—Diagrams illustrating operation of the harmonic generator. (A) Harmonic
generator circuit; (B) Differential inductance and flux density of assumed non-linear
coil as functions of magnetizing force; (C) Variation with time of currents in primary
and secondary meshes, and in non-linear coil; (D) (EZ) (F) Equivalent circuits of the
harmonic generator for the three time intervals indicated.

The current flowing in the input mesh is made practically sinusoidal
by tuning Z;, C;. If now we start at the negative peak of the sinus-
oidal input current of amplitude 7, and frequency p/27, the non-linear

Bm
LINEAR
-Io| Io H
(a)
I
lp}
fe)
(c)
te tg
t ta<t <P
o<tStc te< stg d< <p
Las L2o0 Los
Lao—t ‘2 Logs—— ‘2
dt dt
(F)

coil is worked in the saturated state where its inductance L», is low.
Since the resistance of the winding is small, the potential drop across

Los; 12 reverses its direction, maintaining the coil in the saturated region.

teristic of this type of harmonic generator are determined by the values
of the elements just mentioned. The resistance, capacity, and satura-
tion inductance effectively in circuit are adjusted to permit the current
to rise to a high maximum, to damp the pulse, and to shorten the pulse
duration to the point at which the highest harmonic required reaches
the desired amplitude. Under the working conditions which will be
assumed in the following, this insures that the pulse dies away before
the end of the half-cycle as shown in Fig. 6c. At that time the currents
and potentials are the same, except for reversals of sign, as those at the
start, so that the current wave consists of an alternating succession of
these pulses. Equivalent circuits for the three respective time inter-
vals of a half-cycle are shown in Figs. 6d, 6e, 6f. The similarity of the
load current wave form derived above to that experimentally observed
and shown in Fig. 2, is to be noted.

During this interval the secondary circuit is practically isolated from
the primary. The switching process is sustained by the alternations of
the sinusoidal primary current and is periodic, as we have seen, since
similar conditions exist at the start of each pulse. The times at which
switching occurs are those at which the current through the coil passes
through the critical values (+ Jo) where the inductance changes.

Since the narrow discharge pulse provides the principal contribution
to the higher harmonics in which we are interested, and since this
discharge takes place in the secondary independently of the primary, the
elements of the secondary mesh during discharge determine the form of
the output spectrum. From this viewpoint we may regard the con-
denser as the source of energy for these harmonics and hence as a
possible location for equivalent harmonic generator e.m.f.’s. In this
light, the discharge circuit becomes a half-section of low-pass filter
terminated in resistance Re, with Le, as the series element and C; as the
shunt element.

To connect the three solutions which hold for the three linear regions
of the B-H characteristic, conditions at the junctions are introduced
which lead to transcendental equations. These may be solved graph-
ically when definite values are assigned to the circuit parameters.
From these may be obtained the maximum value Q,, of charge on C2
which is reached at the end of the charging stage.

By plotting a representative group of these final charges over a range
of parameters ordinarily encountered, an empirical equation has been
deduced for Q,, as follows:

For the usual operating conditions the narrow peaked discharge part
of the current pulse is most important in the determination of the
higher harmonics (say beyond the 9th) with which we are concerned
here. The charging interval then may be neglected in calculating the
higher harmonics. The form of the discharge pulses is determined by
the parameters pC2R, and k, where

The familiar criterion for oscillation in a series circuit containing
inductance, capacity and resistance may be expressed in terms of k.
If k > 3, the discharge is an exponentially decaying oscillation; if

k = }, the discharge is an exponentially decaying pulse. This last
condition is the one assumed in the description of operation given
above.

If the discharge is oscillatory, and if further the second peak is large
enough, the current through the coil may become less than J» during
the discharge interval. Thus Lz will return to its larger value, and
recharging of the condenser will result. This process may lead to large
and undesired variations in the amplitudes of the harmonics. To
maintain the frequency distribution as uniform as possible over the
frequency range of interest, the circuit parameters are usually adjusted
so that recharging does not occur.

Harmonic analysis shows that the nth harmonic amplitude under the
above assumptions is given by

where n is odd. This expression neglects the contributions due to the
charging stage, which are usually small for harmonics higher than
the ninth.

where W, is a convenient parameter which does not vary with nm and
hence serves as an indication of the power of the output spectrum. It
is related to W, the total power delivered to the load resistance, by
the equation,

and NV is the number of turns wound on the toroidal! core of diameter d
cm. and cross-sectional area A cm.?

In Fig. 7 the power spectrum is shown by plotting W, in db above or
below Ws as a function of npC2R, for several values of k. These
curves illustrate the degree of uniformity obtainable in harmonic am-

Fig. 7—Harmonic power spectrum plotted from eq. (2) as function of npC2R2 with k
as parameter.

plitudes under different conditions. It may be shown from (3) that
W,, has a maximum with respect to n when k is greater than }, if

A number of relations may be derived from these equations which
are useful for design purposes. Thus the form of harmonic distribution
is fixed by k and pC:R2. The output power for a given magnetic ma-
terial worked at a given fundamental magnetizing force then depends
solely upon the volume of core material. Finally, the impedance is fixed
by the number of turns per unit length of core. If the impedances
desired for primary and secondary circuits differ, separate windings
may be used for each circuit.

In order to make practical use of the results given above, we need
some basis for deriving the assumed parameters of the non-linear coil
from the physical properties of the magnetic materials used in harmonic
producers.

The fact that the actual magnetization curve is a loop instead of a
single-valued curve as assumed requires increased power input to the
circuit to provide for the hysteresis and eddy losses in the core. Other
than this, the principal remaining effect of the existence of a loop is a
lag in the time at which the pulses occur, an effect which is of no great
moment in determining the form or magnitude of the resulting pulses.

The next point requiring consideration is the effect introduced by the
assumed abrupt change of slope contrasted to the smooth approach to
saturation actually observed. While no rigorous comparisons can be
drawn, the effect of the more gradual approach to saturation was ap-
proximated analytically by introducing an additional linear segment
between the permeable region and each saturated region of the B-H
characteristic, at a slope intermediate between the two, so as to form a
B-H characteristic of five segments in place of the original three. The
solutions for these two characteristics were found to yield negligibly
small differences in the amplitudes of the higher harmonics. It was
inferred from this result that no substantial change would be introduced
by a smooth approach to saturation.

- saturated region, while the analysis considered a small linear variation.

A rough approximation for the effect of this curvature, which leads to
fair agreement with experiment, consists in taking for Ls, the average
of the actual slope, from its minimum value reached during the dis-
charge peak down to the point at which the slope is one-tenth maxi-
mum. To this is added the linear inductance contributed by the
dielectric included within the winding.

To summarize then, the harmonic outputs obtained from the
analysis with the assumed B-H characteristic may be brought into line
with experimental observations by the introduction of quantities ob-
tained from actual B-H loops at appropriate frequencies and magnetiz-
ing forces. In these the maximum slope found on the loop is taken for
Lo, the average slope over the saturated region is taken for L2,, and the
energy corresponding to the area of the real B-H loop must be added to
that originally supplied the harmonic generator input.

A comparison between measured and calculated harmonic distri-
butions obtained with a 4-kc. fundamental input is shown in Fig. 8. In
this case the harmonic distributions were measured for four different

values of the secondary condenser C; as shown by the plotted points.
The power output of each harmonic is plotted in terms of the quantity
npC2R:z. Calculated values are indicated by dashed lines. It is
observed that while the agreement between calculation and experiment

30
THEORETICAL
OBSERVED
FUNDAMENTAL (4 KILOCYCLES)
MAGNETIZING FORCE =8.1 OERSTEDS

Fig. 8—Comparisons of calculated and measured harmonic distributions, plotted as
functions of npC;R:, with C; as parameter.

is perhaps as good as could be expected for the two highest curves, a
substantial divergence is noticed in the two lowest sets; the forms of the
two sets are significantly different, and it seems that the divergence
might become even greater at larger values of mpC2,R2 than those
shown. Upon examination of the equations, however, it turns out that
the conditions existing for the lowest pair of curves are just those for
which recharging occurs, so that the conditions for which the equations
were framed hold no longer. The calculated distributions might be
expected to be too low for the higher harmonics, since we have taken an
average value for the saturation inductance. This means that the peak
of the discharge pulse will be sharper than that calculated, with a
corresponding effect upon the higher harmonics.

Another comparison between calculated and observed values is
shown in Fig. 9 for a fundamental input of 120 kc. with two values of
resistance load. Fair agreement is observed over the greater part of
the frequency range which extended to5 MC. The distribution curve
for the smaller resistance load undulates as the load resistance is re-
duced, since multiple oscillations and recharging are then promoted, in
consequence of which the output power tends to become concentrated
in definite bands of harmonics. In general, agreement within a few db
is found over a wide range of circuit parameters when working into a
resistance load, provided that recharging does not occur.

Fig. 9—Comparisons of calculated and measured harmonic distributions plotted as
functions of npC:R2, with R; as parameter.

When the resistance termination is replaced by a bank of filters as it
is in practice, the resistance termination is approximated over the
frequency band covered by the filters. Where the band is wide the
results obtained do not differ greatly from those with the pure resist-
ance load, but when only a few harmonics are taken off by filters and
the impedances to the other harmonics of large amplitude vary widely
over the frequency range, then the wave form of the current pulse is
substantially altered, with corresponding effect upon the frequency
distribution, and the calculations for a pure resistance termination do
not apply.

fundamental input and harmonic output may vary widely with small
changes in supply potentials and circuit parameters. This troublesome
source of variation may be avoided in a number of different ways, of
which the simplest is to increase the resistance of the resonant mesh.
In the present case this is effectively accomplished without sacrificing
efficiency by using pentodes, which have high internal resistances, in
the amplifier stage connected to the resonant mesh.

The efficiency of power conversion from fundamental to harmonics
may be found from the fundamental power input to the circuit, as
derived from measurements on a cathode ray oscillograph, and from the
total harmonic output measured by means of a thermocouple. The
maximum efficiency obtainable with the low-power circuits described in
the second section is in the neighborhood of 75 per cent, and decreases
with increasing fundamental frequency because of the increased dissi-
pation due to eddy currents. It should be noted that this figure does
not include losses in the primary inductance Z;. When only a few
harmonics are used, the efficiency of obtaining this useful power
naturally drops to a much lower value, which for the particular
cases mentioned in the second section, is between 15 and 25 per cent.

In any practical case the fundamental input to the harmonic pro-
ducer is accompanied by extraneous components introduced by cross-
talk, by modulation, or by an impure source. Thus if the fundamental
is derived as a harmonic of a base frequency, small amounts of adjacent
harmonics will be present. Or if the amplifiers are a.-c. operated, side-
frequencies are produced differing from the fundamental by 60 cycles
and its multiples. Extraneous components of this sort in the input
modulate the fundamental and produce side-frequencies about the
harmonics in the output. When the harmonics are used as carriers,
the accompanying products must be reduced to a definite level below
the fundamental if the quality of the transmitted signal is to be un-
impaired. The requirements imposed by this condition can be calcu-
lated by simple analysis, the results of which agree rather well with
experimental values.

The method of analysis used is to consider the extraneous component
at any instant as introducing a bias" to the non-linear coil. The
primary effect of a small bias (0) is to shift the phase of the discharge
pulse by + }/H, radians, H, being the amplitude of the fundamental
magnetizing force. The sign of the shift. alternates so that intervals
between pulses are alternately narrowed and widened.

The effect of this shift on the harmonics produced may be found by
straightforward means in which the amplitude of any harmonic is
expressed in terms of the bias. Hence when the extraneous component
or components vary with time, the sidebands produced may be evalu-
ated when the bias is expressed by the appropriate time function.

If the bias is held constant, the wave is found to include both odd and
even harmonics, the amplitudes of which are given by

I(n) being the harmonic distribution in the absence of bias as given
by eq. (2).
If the extraneous input component is sinusoidal, we have

Substituting this expression for } in the equation for the harmonic com-
ponents yields odd harmonics of the fundamental, and modulation
products with the angular frequencies mp + /g, which may be grouped
as side-frequencies about the odd harmonics. The amplitude of the
nth (odd) harmonic is

Considering the side-frequencies about the mth harmonic, the largest
and nearest of these are (n + 1)p — q and (m — 1)p +, m being
odd. The ratio of the amplitudes of either side-frequency to the mth
harmonic is

on the assumption that the harmonic distribution in the neighborhood
of is uniform so that J(n +1) = J(m). If the arguments of the
Bessel functions are less than four-tenths, a good approximation to the
right member of eq. (9) is (m + 1)Q/2H;. Hence with sufficiently
small values of interference, the sidebands produced are proportional

to the amplitude of the interference, and increase linearly with the
order of the harmonic. These relations apply to harmonic generators
which produce sharply peaked waves in general, and are not peculiar
to the magnetic type.

Neighboring modulation products involving the interfering com-
ponent g more than once have much smaller amplitudes in normal
circumstances than the product considered above. Because of the
tuning in the input mesh, interfering components far removed in fre-
quency from the fundamental are greatly reduced and the most
troublesome interference is likely to be close in frequency to the
fundamental.

It may be noted that where the interference is produced by amplitude
modulation of the fundamental, so that two interfering components
enter the input, the distortion produced may be approximated by
doubling the amplitudes of the side-frequencies produced by one of the
interfering components. If the disturbance is the second harmonic of
the fundamental, the effect is nearly the same as that for constant bias,
and the relations (5) may be used if } is taken as the amplitude of the
second harmonic magnetizing force. '

Fig. 10—73rd and 74th harmonic amplitudes as functions of direct current flowing
through non-linear coil. Ordinate is ratio of harmonic amplitude with bias indicated,
to that of 73rd harmonic with zero bias. Abscissa is harmonic number multiplied by
the — of bias to fundamental. Dashed lines calculated from eq. (5), full lines
measured.

To illustrate the effects of d.-c. bias, Fig. 10 shows the amplitudes of
the 73d and 74th harmonics of 4 kc. as functions of the parameter
nQ/H;. The agreement between measured and calculated values
indicates that the most important effects of bias have been included in
the simple analysis.

Since the first transatlantic radio telephone circuit was opened
for service over ten years ago, an increasing number of voice-
operated switching devices has been added to the international
telephone network. All of these have the common purpose of
preventing echo and singing effects due to arranging the facilities
to give the best possible transmission, even under difficult radio
conditions. Differences in the design and performance of the
several types of devices suggest that the advantages and dis-
advantages of each be made available.

HE interconnection of ordinary telephone systems by means of
long radio-telephone links presents some unique and interesting
technical problems. Since radio noise is often severe as compared

with that in wire lines, radio transmitter power capacity is relatively
large and expensive, and it is in general economical to control the
speech volumes so that the radio transmitter will be fully loaded and
thus the effect of noise minimized for a given transmitter power rating.
This volume control, to be fully effective, calls for voice-operated
switching devices to suppress echoes and singing.

The general principles and applications of the vodas have been
discussed from time to time in various papers listed at the end of this
text. The present paper goes somewhat more into detail regarding the
transmission performance of the vodas, including a description of an
improved form of circuit which discriminates between line noise and the
syllabic characteristics of speech.

* Presented at the Pacific Coast Convention of A.I.E.E., Spokane, Washington,
September 2, 1937. Published in Elec. Engg., August, 1937.

The two-way problem in telephony began with the invention of the
telephone itself, and was the subject of considerable pioneering activity
during the latter part of the nineteenth century. The invention of the
amplifier brought about new problems when applied in a repeater for
two-way op®ration. Even before a practical repeater had been devised,
inventors visualized controlling the direction of transmission through
amplifiers in a line by relays controlled from switches associated with
the subscribers’ instruments, an idea which is in use today on airplanes
and small boats and in special circuits where this type of two-way
operation is practicable. It is also used by amateur radio telephone
operators. But for public telephone service more rapid and automatic
control of two-way conversation is preferable.

To control the direction of transmission in a manner that would meet
public convenience, invention progressed through the early part of the
twentieth century toward devices for switching the speech paths
automatically by voice waves. During this period, long distance radio
telephony was first demonstrated to be practical on a one-way basis.

From that time until the first transatlantic radio telephone circuit
was placed in service on January 7, 1927, anti-singing voice-operated
devices underwent a process of development aimed at meeting the
requirements of two-way radio telephone service. The vodas was one
result. Since 1927, improvements have been made in cheapening and
simplifying the equipment and in making a vodas that will operate
better on speech and not so frequently on noise. It has also been
possible to arrange a vodas so as to permit using the same privacy
apparatus for both directions of transmission, thereby saving the cost
of duplicate apparatus.

The conditions encountered when joining two-wire two-way circuits
by radio links are illustrated in Fig. 1 in which (a) shows a connection
between two subscribers, W and E, while (b) shows the paths of direct
transmission and echo when E talks. In addition to the talker and
listener echoes which arise in such a connection, singing can occur
around the closed circuit CAFGDBC if the amplification is great
enough. Also, when the same frequency band is used to transmit in
both directions, two cross-transmission paths AB and DF are set up,
and echoes and singing can take place around the end paths ABC and
DFG. Any echoes or singing are of course primarily due to reflections
of energy at points of impedance irregularities in the two-wire plant,
including the subscribers’ telephones themselves.

In wire circuits, simple hybrid coils and echo suppressors? are
usually adequate to prevent such effects because the gains are not
increased to provide for loading the circuit with energy when speech is
weak, and also because the cross-transmission paths are absent. In
long radio circuits, however, singing may result from the adjustments
of amplification made to load the radio transmitter in case of weak
speech and thus override noise, even though separate frequency bands
are used in the two directions. Moreover, it is desired that the users of
the service have as good transmission over the entire connection,
including these radio links, as that to which they are accustomed in
their own wire telephone systems, and even better transmission may
be desired owing to differences in the language habits of the sub-
scribers. Consequently, the overall transmission efficiencies of inter-
continental radio circuits are sometimes better than those of the best
land lines in the areas to be interconnected.

A voice-operated device to suppress singing effects can be designed
to have three possible arrangements:

1. The terminal can normally be blocked in one direction and con-
nected through in the other.

2. Both directions of transmission can normally be blocked and
activated in either direction but not both directions by the voice
waves.

3. The circuit can remain activated in the last direction of speech
and blocked in the other direction.

Where there is no noise on the transmission system under con-
sideration any of these three arrangements will give satisfactory opera-
tion as there is then nothing to prevent making the voice-operated
devices as sensitive as may be necessary to obtain full operation on
weak as well as on strong voice waves. If there is any noise on the
system which tends to operate the device it is necessary to make it less
sensitive to avoid false operation. A point may be reached where the
sensitivity is so low that the weakest parts of speech will not cause
operation, and the weak consonants will be lost. The reduction in
articulation has been found to be proportional to the time occupied by
these lost or ‘‘clipped”’ sounds.*®

If the device is located at a point in the circuit where the signal-to-
noise ratio coming from one direction is poorer than that coming from
the opposite direction it is obvious that a considerable advantage will
be gained by using arrangement 1, since the device may be pointed in

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the direction in which the normally blocked path is exposed to the
better signal-to-noise ratio and the normally activated path is exposed
to the poorer signal-to-noise ratio. The vodas is, of course, arranged so
that the normally blocked (transmitting) side is exposed to the land
lines, which are usually quieter than the radio links. In the receiving
side, the device can be less sensitive because there is no need for having
it completely operated under control of the voice waves. All that is
necessary is to have this side sensitive enough to operate in response to
comparatively large voice or noise waves which might otherwise, after
reflection and passage into the outbound path, result in false operation
of the more sensitive side associated with this path.

In the vodas the principle of balance is used to keep the reflected
currents small and thus allow the sensitivity of the normally activated
device to be further reduced if necessary. Where a high degree of
balance is not obtained and when noise from the radio limits the
sensitivity of the receiving device it is sometimes necessary, particularly
for weak outgoing volumes, to reduce the incoming volume so as to
prevent echoes from operating the normally blocked transmitting side.

This echo limitation is primarily due to noise in the radio link,
reflections from the two-wire plant and weak volumes from the
subscribers. It is difficult to produce any large improvement in talker
volumes and balance; so it would appear that the solution of the
difficulty would probably come from the direction of improving radio
transmission. Some benefit has also been obtained by reducing the
effect of radio noise on the vodas with special devices of which the
“Compandor”’ 18 and the ‘“‘Codan”’ 2° are examples. More re-
cently, use has been made of a new voice-controlled device called a
“Noise Reducer”’ *!: 2 which reduces the received noise between speech
sounds.

The diagram of the relay circuit in Fig. 3 shows how various time
actions are obtained. Relays 1, 2, 4 and 5 are operated from battery
B, when the ground contact of relay TM is opened. Thus the travel
time of any relay armature is not a factor in securing fast initial

* The vodas apparatus, together with the volume control devices and technical
operator’s circuits, go to make up what is called a Type A Control Terminal.

operation. When the armature of relay 7M reaches its left-hand
contact, relay H; operates and delays release of the relay train even if
TM is at once restored to normal. J/; is delayed in releasing by the
time required to charge condenser C;. The final release of relays 1
and 4 is then controlled by the time constant of an auxiliary circuit
involving relay H2 and condenser C2, while that of relays 2 and 5,
which is made later so as to suppress delayed echoes, is controlled by
the circuit charging C;. On the receiving side, condenser C, is ad-
justable so as to permit the technical operator to select the shortest
release time for suppressing the delayed echoes in a given land line
extension.

The vodas control terminal of the A type * used at New York con-
sists of a line of technical operating positions with cross-connections to
other lines of equipment containing the delay units, repeaters, vodas
amplifier-detectors and privacy apparatus. Figure 4 shows an
arrangement of a single terminal at San Francisco. The control bay
is placed between two line testing bays on the left and two trans-
mission testing bays on the right of the operating lineup. The dis-
tributing frame is in the center of the picture; and repeaters, ringers
and privacy apparatus are shown at its left. At the extreme left is
the vodas bay.

The desire for a cheaper control terminal than the Type A led to
the development of a second type, known as Type B, in which the
vodas employs the same fundamental principles. In this vodas added
protection against false operation from line noise is secured by the use
of a new principle in voice-operated devices, called ‘‘syllabic’’
operation.

It is observed that in many types of noise a large component of the
long-time average power is steady. Speech, however, comes as a
series of wave combinations of relatively short duration. These
facts suggested a device which distinguishes between the rates of
variation of the envelopes of the impressed waves. This is accom-
plished by a filter in the detector circuit which passes the intermodu-
lated components of speech in the syllabic range, but suppresses those
of line noise which are above or below this range.

Figure 5 shows a schematic diagram of the application of this device
to a Type B control terminal. The privacy switching circuits are
omitted from this drawing, as are also the circuits for delaying the
release of the relays. In comparing this drawing with Fig. 2, it will
be seen that relays 1, 2 and 3 perform the same functions, but the
transmitting branch of the vodas consists of two portions, one a
sensitive detector with a syllabic frequency filter, which on operation
increases the sensitivity of the second portion.

Considering the action of Fig. 5 on transmitted speech, the output
of the sensitive detector of the syllabic device is a complex function
of the applied wave having intermodulated components in the range
passed by the tuned input circuit, together with a d-c. component and
various low frequency components set up by the syllabic nature of
the speech. There are also various components of any noise waves
which may be present including a d-c. component. The first step in
getting rid of the noise is to pass the detector output through a re-
peating coil which blocks the d-c. component of both the speech and
noise, but passes frequencies above about 14 cycle per second. The
resulting waves enter the low-pass filter, the output of which contains
frequencies between 144 and 25 cycles per second, which “syllabic
range” is between the d-c. component of zero frequency and the
fundamental frequency of the line noise. These syllabic frequency
currents cause momentary operations of relays (J) and (F). Relay (J)
operates when a speech wave is commencing and relay (F), which is
poled oppositely, operates while the impulse is dying out, thus sending
current out of the filter in the opposite direction. Operation of either
(J) or (F) effectively inserts gain ahead of the upper detector, thereby

Fig. 6—Technical operator at Forked River, N. J., using a type B control terminal to
establish a circuit between a steamship and a shore telephone operator.

increasing the sensitivity of relay (K), when speech is present. Even
if the noise is strong enough to operate relay (K) over the upper
branch when the gain is inserted, the release of relay (F) at the end
of a speech sound will remove the gain and permit (K) to fall back.
Thus, it is possible to work relay (K) more sensitively on weak speech
than would be possible without the syllabic device.

Figure 6 shows a photograph of a B-type terminal in ship-to-shore
service at Forked River, New Jersey. The vodas and volume control
apparatus are in the left-hand cabinet. The right-hand cabinet
contains privacy apparatus, a signaling oscillator and a vodas relay
test panel.

In any system employing voice-operated devices it is necessary for
the time actions to provide for to-and-fro conversation with a minimum
of difficulty, when the subscribers desire to reverse the direction.
The electromagnetic relays used in the vodas have advantages over
other types of switching arrangements which have been proposed in
that they (1) operate and release at definite current values, (2) have
fast operating and constant releasing times, (3) have their windings
and their contacts electrically separated, thus simplifying the circuits,
and (4) operate in circuits having low impedances.

The operating times of the two types of vodas are shown in Fig. 7
as a function of the strength of suddenly-applied single-frequency sine
waves in the voice range. These measurements were made with a
capacitance bridge.’ The sensitivities of the two types were adjusted
so that observers noted an equivalent amount of clipping. The Type
A vodas was provided with a 20-millisecond delay circuit; the Type B
had no delay. For the Type A vodas, the operating time is quite
small and constant just above the threshold of operation.

For weak inputs the operating time of the syllabic device is de-
termined by relay (J) and the filter, as shown in Fig. 7. As the
suddenly-applied input is increased, a point is reached where the less
sensitive detector operates relay (K), reducing the operating time
from around 20 milliseconds to values comparable to those of the
Type A.

The operation was also tested on waves formed by applying simul-
taneously two sine waves of equal amplitude but slightly different
frequencies. These waves were recorded on an oscillograph, together
with a d-c. indication of the operation of each of the vodas relays, with
the sensitivities adjusted the same as for Fig. 7. The time from the
beginning of a beat wave (null point) to the time of operation was
measured from these oscillograms and plotted against various values of

total applied voltages. Figure 8 shows the results for a 5-cycle-per-
second difference between the two frequencies. Negative values of
time indicate that the path was cleared before the beginning of the
wave, and these occur only with the Type A vodas due to the delay
circuit. The curves for frequency differences of less than 5 cycles
per second show more clipping and greater differences between the
devices, while those for greater frequency differences show less time
clipped and less difference between the two types of vodas. In the
case of weak waves it is evident that the syllabic will give less clipping

because the energy of the wave does not rise to the value required to
operate the Type A device until after the syllabic device has operated ;
and for very weak waves the Type A does not operate at all. In the
case of strong waves, the Type A vedas is better due to its delay
circuit. However, since the clipped time is greater on weak sounds
than on strong ones, the two types give performances on speech which
are judged to be equivalent.

A comparison of operation of the two types of vodas on a speech
wave is shown in Fig. 9. Reading from left to right, the middle trace
of this oscillogram shows the wave recorded by saying the word

‘six’? over a telephone circuit transmitting a band of frequencies
from about 800 to 2000 cycles per second, which is the range normally
effective in operating the vodas. The upper trace shows the point at

which the syllabic Type B device operated and the lower trace shows
the point at which the Type A device operated. Since the speech
wave shown was used to operate both devices, the reduction of clipping

by the delay circuit in the Type A vodas was not recorded. However,
the effect of a transmission delay of 20 milliseconds is shown by sub-
tracting 20 milliseconds from the point at which operation occurred.
This is indicated on the oscillogram for both devices. It is concluded
that on this wave the syllabic device without a delay circuit would
give about the same clipping as the Type A vodas with its delay circuit.
Figure 8 indicates that the Type A would be better for stronger speech
and the Type B would be better for weaker speech. The advantage of
a delay circuit in either case is evident.

It is evident from this analysis that the reason for using delay
circuits is not primarily because the relays are slow in operating.
When the sensitivity is limited by noise, clipping of initial consonants
can occur with infinitesimal operating times. One way of reducing
the clipping is to use long releasing times so that the relays remain

Fig. 9—Oscillogram of the word ‘‘SIX,”’ illustrating clipping and its reduction by a
delay circuit in the transmission path.

operated between syllables. This has the disadvantage of making it
harder for the opposite talker to break in. To avoid this difficulty,
the relays in the vodas are given releasing times that permit the
distant speech to break in about one sixth of a second after a United
States talker ceases to speak.

One advantage of delay circuits is to reduce the clipping of initial
consonants and thus permit using short releasing times, thereby
making it possible to reverse the circuit more readily. In addition,
delay circuits permit using a lower relay sensitivity which has two
advantages. First, more noise can be tolerated without causing false
operation. Second, more received volume can be delivered without
the echoes causing false operation of the normally blocked trans-
mitting side.

The advantage of artificial delay of various amounts has been
determined by using different types of normally blocked arrangements

to find the relation between the delay and the sensitivity required to
produce given amounts of clipping of initial sounds. The results are
shown for a Type A vodas in Fig. 10. The curves for the syllabic
device are similar. The set-up was arranged so that various delays
could be inserted in either the transmission circuit (Delay X) or the
relay circuit (Delay Y). The left ends of the curves indicate that
when delay Y is used, that is, when the net operating time of the
relay is great, a point will be reached where no reasonable increase in

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sensitivity is sufficient to prevent intolerable clipping. The value of
20 milliseconds of delay X as compared to zero is equivalent to an
increase of about 5 db in sensitivity for a given amount of noticeable
clipping.

A reasonable release time is of value in preventing clipping, as it
causes the relays to remain operated not only for trailing weak endings
of sounds, but also when the energy is temporarily reduced by inter-
mediate consonants which may be comparable with noise. Delayed
release is also important when it is required to maintain the blocked
condition while delayed echoes are being dissipated. For these

echoes, the hangover or release times should be constant for various
applied voltages. In the vodas, the change in release time over a
wide range of inputs is less than 1 per cent. Adjustments are made by
varying the condensers and resistances of the auxiliary circuits shown
in Fig. 3. Typical values obtained by this method are indicated in
“ig. 11.

The vodas amplifier-detectors have broadly tuned input circuits to
exclude by frequency discrimination many of the frequencies induced
by power sources and those which are unnecessary for speech opera-
tion. The sensitivity-frequency characteristic is shown on Fig. 12.

This figure also shows the relatively narrow frequency range passed
by the repeating coil and syllabic frequency filter of the Type B vodas.

To insure proper operation of a vodas a technical operator ® is in
attendance. He is provided with circuits which enable him to talk
and monitor on the circuit as indicated in Figs. 2 and 5. His duties
include adjusting the sensitivity of the receiving relays for the par-
ticular value of radio noise existing and adjusting the transmitting and
receiving speech volumes by the aid of potentiometers and volume
indicators. He selects the proper hangover time and coordinates the
operation of the circuit as a whole with the distant end. At times,
he may be required to increase the sensitivity of the transmitting side
of the vodas in the case of talkers with poor ability to operate relays
or to decrease the sensitivity when weak volumes are supplied from
land lines with more than the usual amount of noise.

The vodas is used in radio telephony to switch the voice paths
rapidly to and fro, and thus prevent echoes and singing that would
otherwise occur at unpredictable times. It is also used to save privacy
apparatus by permitting the use of the same apparatus for both
directions of transmission. The performance characteristics of the
electromagnetic relays used in the vodas are very suitable in that
they have small operating and constant releasing times.

Improved performance of the voice-operated relays in the presence
of line noise can be secured by the use of a syllabic type of vodas
which discriminates between the characteristic voltage-time envelopes
of the noise and speech waves. Laboratory and field tests indicate
that this device, even without delay circuits, gives slightly better
performance on most conditions than the original vodas with delay.
When provided with a transmitting delay circuit, the syllabic device is
decidedly better than the older vodas.

The International Bibliography on the Coordination of Radio
Telephony and Wire Telephony is given in the C.C.I.F. Green Book
Volume I of the Proceedings of the Xth Plenary Meeting, held at
Budapest, September 1934. Below is a chronological list of Bell
System papers relating to the vodas.

1. ‘‘The Limitation of the Gain of Two-Way Telephone Repeaters by Impedance
Irregularities,’ George Crisson, Bell Sys. Tech. Jour., Vol. 4, No. 1, January,
1925, pp. 15-25.

‘Echo Suppressors for Long Telephone Circuits,” A. B. Clark and R.C. Mathes,
A.1.E.E., Jour., Vol. 44, No. 6, June, 1925, pp. 618-626; Elec. Commun..
bone a 1, July, 1925, pp. 40-50; A.J.E.E., Trans., Vol. 44, 1925, pp.
481-490.

. ‘Echo Elimination in Transatlantic Service,” G. C. Crawford, Bell Lab. Record,

. ‘Effects of Phase Distortion on Telephone Quality,” J. C. Steinberg, Bell Sys.

. “Certain Factors Limiting the Volume Efficiency of Repeatered Telephone

Broadcast Engg., Vol. 2, No. 10, October, 1935, pp. 9-11, 15. Tech. Digest in
Bell Sys. Tech. Jour., Vol. 14, No. 4, October, 1935, pp. 702-707.

‘“A Noise Reducer for Radio Telephone Circuits,” N. C. Norman, Bell Lab.
Record, Vol. 15, No. 9, May, 1937, pp. 281-285.

In listening to speech transmitted over radio circuits, the noise
arriving in the intervals between the signals may be annoying.
There is also evidence that the intelligibility is reduced due to this
noise shifting the sensitivity of the ear. Reducing the noise
occurring in the intervals of no speech should therefore improve
reception.

number of conventional methods of increasing the signal with
respect to the noise. Examples of such methods are the use of higher
power, directive antennas, diversity reception and filters to narrow the
received frequency band. In addition, there are other methods of a
special character which reduce the effect of the noise interference with
the speech transmission. One example of such a device limits the
noise interference by eliminating the high peaks of noise of very short
duration and depending upon the persistence of sensation of speech in
the ear to bridge the gaps. Another method diminishes the noise in
intervals of no speech. This is the method which will be discussed
here.

Speech signals may be represented »y a group or band of frequencies
occupying a certain interval of time. In using the conventional
method of narrowing the received frequency band, filters eliminate all
noise outside the band actually required. In fact we sometimes go
beyond this and remove some of the outer frequency components of

* Presented at the Pacific Coast Convention of A. I. E. E., Spokane, Washington,
September 2, 1937. Published in Elec. Engg., August, 1937.

speech which are weak and submerged in the noise and therefore
contribute little or nothing to the intelligibility. Experiments have
shown the effect on voice transmission of removing portions of the
frequency range.'! Articulation tests were used to afford a quantitative
measure of the recognizability of received speech sounds. These show
that the upper frequencies may be cut off down to about 3000 cycles
without serious reduction in articulation. After such treatment, as the
noise level increases, the weaker and less articulate sounds become more
and more submerged in the noise and additional reduction in the
detrimental effect of the noise is required.

In addition to the speech waves covering a frequency band they
occupy intervals of time. The unoccupied intervals between the
speech sounds contain noise. Reduction of the noise reaching the ear
in these intervals has been found to result, under certain conditions, in
an improvement in speech reception. This may possibly be explained
by considering the characteristics of the ear.!. It has been shown that
noise present at the ear has the effect of shifting the threshold for
hearing other sounds or has a deafening effect. That is, there is a
reduction of the capacity of the ear to sense sounds in the presence of
noise. For example, if a person has been listening to a noise for a
certain period, his ear is made insensitive so that speech signals
following are not so easily distinguished. The ear has a sensory build-
up time, that is, a time needed for the noise to build up to a steady
loudness. By reducing the noise in the intervals of no speech the
average threshold shift seems to be diminished. Aside from this the
presence of the noise tends to distract the attention from the perception
of the speech. Removal of noise during the intervals of no speech
tends to reduce this effect.

In considering the elimination of the noise during these intervals it is
necessary to bear in mind certain characteristics of speech.? Speech
waves may be regarded as nonperiodic in that they start at some time,
take on some finite values and then approximate zero again. In
connected speech it is usually possible to approximately distinguish
between sounds and to ascribe to each an initial period of growth, an
intermediate period which in some cases approximates a steady state
and then a final period of decay. The duration intervals of various
syllabic sounds vary from about .03 to as much as .3 or .35 second.
When noise is high the weaker initial and final sounds become obscured
so that they contribute little to the intelligibility.

In connected speech, silent intervals occupy about one-fifth to one-
third of the total time. Also there are frequent intervals when the

condition for sufficient periods to override weaker intervals so that

To reduce the noise in the intervals between speech it is necessary to
depend for control upon either the speech itself or upon some auxiliary
signal usually under the control of the speech at some point in the
circuit where the signal-to-noise ratio is better. This latter condition
is illustrated on a circuit where the carrier is transmitted only during
speech intervals. The carrier then acts as an auxiliary signal which
operates a device at the receiver to remove loss.*:*+ The device to be
discussed below utilizes the speech itself at the receiver to perform this
function.

In using the speech in this way it is obvious that control can be
accomplished only when the speech energy sufficiently exceeds the
noise energy so that the presence of the speech is distinguishable. The
device could operate abruptly as, for example, a relay which removes a
fixed loss in the operated position and restores it when non-operated.
Experience indicates that the use of such a device makes the suppression
too obvious if it is to follow the speech sounds closely. It is desirable,
then, to perform this reduction by more or less gradually removing loss
as the speech increases to accentuate the difference between levels of
speech sounds and levels of noise which occur in the gaps between
speech.

This kind of performance has been secured in a device known as a
noise reducer. A comparison of the action of the noise reducer and a
relay having similar maximum loss is shown in Fig. 1. This figure
shows the input-output characteristics of these devices over the voice
amplitude range to which they are subjected on a radio circuit. The
noise reducer may be likened to a relay with a variable loss, the loss not
varying instantaneously but over a short period of time. The loss, for
any short period, may be any value within the loss range and the device
has, therefore, been likened to an elastic or shock absorbing relay.

The noise reducer has no loss for strong inputs, considerable loss for
weak inputs and changes this loss gradually over a short interval of

time. It introduces loss in the absence of speech but reduces this loss
in proportion to the amplitude and duration of waves impressed upon
it. The time required for the loss change is such that abruptness of
noise change is absent and very short impulses of static do not effec-

tively control the loss. This contrasts with a very fast limiter acting on
high-peak crashes only.

The noise may control the loss if its average amplitude is strong
enough. Therefore, the control is made adjustable so that the noise

waves are not permitted to control for any noise condition within the
range of usefulness of this device. Thus the noise in the absence of
speech is always reduced and the portions of the initial and decay
periods of the speech sounds which are also reduced vary with this
adjustment for noise intensity. Of course, if the speech-to-noise ratio
becomes too small or if other transmission conditions interfere, an
improvement becomes impossible.

Figure 2 shows the circuit of the noise reducer in simplified schematic
form.® Incoming waves pass from left to right through the fixed pad,

VARIO-
FIXED LOSSER -STAGE
INPUT PAD AMPLI- | OUTPUT
FIER
REDUCTION CONTROL
CIRCUIT
MW
RECTIFIER
'
iL
IL
REDUCTION "
IN
MAX. MIN.
OUT

the vario-losser and the amplifier to the output. At the input, part of
these waves pass through the reduction control branch circuit which
includes a variable resistor, an amplifier and a rectifier. The direct
current produced by the rectifier is applied through the condenser and
resistance filter to the copper-oxide losser circuit. For current below a
threshold value, no appreciable change occurs in the losser and the loss
introduced is about 20db. As input increases, rectified current reaches
a value where the loss begins to change rapidly. It becomes 0 db at an
input about 20 db above the point at which the loss starts to change.
The design is such that the loss remains substantially constant for
higher inputs.

The vario-losser makes use of the resistance variation with current of
copper-oxide rectifier disks. This variable resistance shunts a fixed
resistance in series with the windings of a repeating coil as shown in
Fig. 2. The maximum loss is determined by the fixed resistance when
small current is flowing through the disks while the varying loss is
determined by the shunting copper-oxide resistance which decreases
rapidly with increasing current above a threshold value until a low
value is reached. The minimum loss is limited by the output of the
control tube approaching a maximum and the shunting resistance
becoming so small that additional decrease affects the loss inappreciably.

The variable resistor setting in the reduction control circuit de-
termines the input amplitude at which reduction begins and therefore
the point above which the loss remains substantially constant. If there
is a difference in amplitude between speech and noise, the reduction

control may be so adjusted that the noise on the circuit, when no speech
is present, is appreciably reduced. The action then is as follows: In the
absence of speech, noise is reduced usually the maximum value of
20 db; during intervals of lower speech amplitudes the loss decreases in
proportion to the increase in amplitude, and during speech of high
amplitude both noise and speech are transmitted without loss. As the
noise encroaches upon the range of speech amplitude, it becomes
necessary to reduce greater amplitudes, thereby also further reducing
the weaker parts of speech.

The noise reducer is contained on a 7} inch panel for relay rack
mounting. Figure 3 gives a front view. The panel contains the
reduction control resistor and an IN-Out key which, in the Out
position, gives the device a fixed loss. Both resistor and key may be
duplicated external to the panel with the wiring arranged to give
remote control.

Figure 4 gives the 1000-cycle input-loss characteristic for three
settings of the reduction control. For any setting, there is an input
volume above which the loss remains constant, while for volumes below
this the loss increases with decreasing input until the maximum loss is
reached. The volume regulated speech range encountered on radio
circuits at some point in the circuit which is 5 db above reference
volume as measured on a volume indicator is indicated as extending
from + 13 db to — 17 db referred to 1 milliwatt for the purpose of
showing approximate corresponding speech amplitudes.

Figure 5 shows oscillograms giving the input and output charac-
teristics of noise for maximum reduction and of speech for maximum,
medium and minimum reduction. The upper trace is the input and
the lower trace the output. The middle trace is not used. It will be
noted by inspecting the IN and Out traces at the beginning and ending
of the word “bark” that there is some distortion in speech for the
maximum reduction condition, but very little distortion for minimum
reduction. Maximum reduction would be used only in case of high
noise where this distortion is less objectionable than the noise.

paom ay) jo Surpua pur Suruurseq ym astou ysry (Z) uinwixeur yWM asiou :40J jndjyno pue ynduj—g “314

Laboratory tests have been made in an attempt to evaluate the
advantages to be gained by the use of the noise reducer. It was shown
that, for the rather limited and controlled conditions which were
tested, definite advantage can be observed in judgment tests of the
effectiveness of speech transmission through noise with and without
the noise reducer. This advantage is of the order of magnitude of
3 to 5 db at the border line between commercial and uncommercial
conditions on the noisy circuit.

This figure is in approximate agreement with results obtained from
records of performance on commercial connections. A curve is
available which shows the approximate relation between percentage
lost circuit time and transmission improvement for a long-range short-
wave radio telephone circuit. From the records of lost circuit time as
affected by the noise reducer use, an improvement of 4 db is obtained
from this curve.

Observations were made and records kept for twelve months of the
use of the device at the land terminal of the high seas ship-to-shore
circuit and for shorter periods on New York-London circuits. These
observations indicate that the noise reducer most satisfactorily reduces
objectionable effects where the interference consists of noise of a fairly
steady character. As might be expected it is somewhat less effective
on crashy static. If the noise is very low there is no improvement; as

the noise increases the benefit increases up to a certain point; when the
noise amplitudes begin to approach too closely the peak amplitudes of
the voice waves it becomes impossible to distinguish between them
without producing objectionable speech distortion and there is again no
advantage. Where volume fading is present there is a tendency to
accentuate the volume changes and it becomes necessary to adjust the
reduction control to limit this. Otherwise this effect may offset the
possible noise improvement. The operating practice is to adjust the
reducer control circuit for each noise or transmission condition so that
optimum reception as judged by the technical operator is obtained.
The general rule is to use the minimum reduction possible.

On radio telephone circuits for connection to the land telephone
system, control terminal equipment is used at the junction of the land
lines and the two one-way radio channels (one transmitting the other
receiving) necessary for two-way communication. In making this
connection a widely used method is one in which the two-wire land
circuit is normally connected to the receiving radio channel and is

Figure 6 shows the application of the noise reducer to such a control
terminal. Speech entering the terminal from the left goes through the
upper branch of the circuit, with volume regulating means and privacy
apparatus, to the radio transmitter. Speech received from the distant
terminal enters at the lower right from the radio receiver and proceeds
through the privacy apparatus, the noise reducer, receiving regulating
network and amplifier to the two-wire line. Outgoing speech operates
the transmitting path and disables the receiving path. Incoming
speech operates the receiving amplifier detector, which disables the
transmitting amplifier detector, thus preventing singing and reradia-
tion of received waves.

Without the noise reducer the receiving relay may be operated by
noise in the receiving path and such operation to an excessive extent
will interfere with outgoing speech. To avoid this effect, it is custom-
ary to reduce its sensitivity so that noise may not operate it. This
results in the weaker speech parts also failing to operate the receiving
relay. This weak speech and noise returned to the transmitting path
through the land line connection may be strong enough to operate the
transmitting relays and thus cut off incoming speech. This is avoided
by reducing the volume to the land line. Therefore, any device which
reduces noise in the receiving path in the absence of speech effects an
improvement not only in the switching operation but also in the
received volume. By placing the noise reducer in the receiving path
false operation is diminished and volume increases of 5 to 15 db are
realized. The noise reducer is applied to the receiving side of the
terminal beyond the privacy apparatus so that it does not introduce
any distortion in the privacy portion of the circuit. It is placed
ahead of the receiving amplifier detector, thereby reducing noise
between words which might affect the operation of this relay apparatus.

The noise redicer, which is a voice controlled variolosser with
limited and controllable action, has been provided for use on short-
wave radio telephone circuits and has proved to be a valuable and
relatively inexpensive means of securing noise reduction. Improved
reception is obtained for many of the transmission conditions experi-
enced on such circuits. This results in better intelligibility to the

. “Effects of Phase Distortion on Telephone Quality,” J. C. Steinberg, Bell Sys.
Tech. Jour., July, 1930.

. ‘A Telephone System for Harbor Craft,” W. K. St. Clair, Bell Laboratories
Record, November, 1932.

. ‘A Noise Reducer for Radio Telephone Circuits,” N.C. Norman, Bell Labora-
tories Record, May, 1937.

. ‘The Reliability of Short-Wave Radio Telephone Circuits,” R. K. Potter and A.
C. Peterson, Jr., Bell Sys. Tech. Jour., July, 1934.

. ‘‘Two-Way Radio Telephone Circuit,” S. B. Wright and D. Mitchell, Bell Sys.
Tech. Jour., July, 1932.

N utilizing the broad frequency ranges which the newer carrier
systems can transmit the telephone engineer has a problem of
choice in band width per channel to be allotted to speech currents.
A sufficient width is vital to faithful speech reproduction ; and desire
for better telephone service always recommends an increase in band
width over past practice. A reasonable balance, however, must ob-
tain between various economic factors; and there must always be
considered the relation between a proposed system and the other parts
of the telephone plant, and also the trend of the art.

The message band widths and the channel spacing which have been
chosen by the Bell System for various new systems are summarized
and discussed in this paper. These systems are expected to play a
large part in the future growth of its long distance plant; and the
reasons underlying this choice may therefore be of general interest.

Different broad band systems are under development: A 12-channel
system for use on open-wire lines employing frequencies up to 140,000
cycles, a 12-channel system for use on 19-gauge pairs in existing toll
cables using frequencies up to 60,000 cycles, and a coaxial system
capable of transmitting frequencies up to a million cycles or more,
from which it is proposed to obtain 240 or more channels.

In the different systems noted above, terminal apparatus is em-
ployed which has many common features: The different channels are
uniformly spaced at 4000-cycle intervals; the same band filters are
used in the ultimate channel selecting circuits; and the derived voice
circuit band widths are substantially identical for all channels of all
systems. The transmission frequency characteristic of a single link
of such systems, in accordance with present designs, is shown on Fig. 1.
A curve for five similar links connected in tandem is also indicated.
Based on a 10 db cutoff as compared with 1000-cycle transmission,
a single-link band extends from approximately 150 to 3600 cycles, and
a five-link band extends from about 200 to 3300 cycles.

There is, of course, no fixed relationship between the channel spacing
and the frequency range of the derived voice-frequency circuit. This
is largely a matter of economics in the design of a particular system.
487

The 4000-cycle channel spacing would permit obtaining a narrower
band width with some simplification in the selecting circuits. With
further development in selecting circuits, it is believed that it would
permit obtaining a somewhat wider band or, if desired, a reduction
in the cost of apparatus, maintaining the same band.

The band chosen initially for the new systems is believed to be a
desirable and forward-looking step in the direction of improving the
quality of speech transmission, a continuing trend which is as old as

telephony itself. Figure 2 shows typical band characteristics which
mark the progress of transcontinental telephony since 1915. For
shorter distances, the band widths have, of course, generally been
wider than indicated on this series of curves. In the case of carrier
systems the band depends on the number of links. The curve shown
for 1937 is for the broad-band systems, estimated on the basis of a
three-link connection.

The increase in band width is achieved without material increase in
cost, since in situations which favor their use, broad-band systems
provide circuits which are substantially more economical than other
alternatives, and the improvement can therefore be obtained by giving
up only a small portion of the savings which the systems themselves
make possible. If, as in some older types of systems, it had been
chosen to maintain a standard of 250 to 2750 cycles for a single-link
connection in the broad band systems, this could have been accom-
plished by the use of a channel frequency spacing of about 3000 cycles.
The wider transmission band is therefore obtained by a sacrifice in

the ratio of approximately 3:4 in the number of channels obtained
within a given frequency range. However, this does not mean a
4:3 increase in the cost per circuit. The amount is considerably less
than this—depending somewhat on the type of system. In the pro-
posed coaxial system, which appears to be a favorable example, where
the attenuation increases roughly as the square root of the frequency,
a frequency band increased by one-third means that for repeaters of
a given type and amplification the number of repeaters is multiplied
by approximately ¥#; that is to say, approximately 15 per cent more
repeaters are required. Furthermore, the line and terminal apparatus
costs are not changed in a case of this kind, and since they constitute
a major part of the total cost, the net increase in cost for the wider

Fig. 2—Representative transmission frequency characteristics of 3000-mile toll
circuits.

per cent in the case of the longer systems where the terminal apparatus
costs are a small factor, and only a per cent or two in the case of the
very short systems where the terminal apparatus costs predominate.

In the ideal case, using substantially perfect transmitters and re-
ceivers, articulation is improved as the upper limit in frequency
transmission is raised, as shown in Fig. 3. The increase in transmission
performance, which a step from 2750 to 3300 cycles, or 3600 cycles
for a single link, makes possible, is evidently still on the part of the
band width-articulation relationship where a measurable increase in
articulation may be expected. An improvement in band width accord-
ingly reduces the effort needed to interchange ideas, since fewer repe-

titions occur and attention can be somewhat relaxed. It also enhances
the naturalness of the received speech, and so makes the conversation
more pleasing as well as easier. It should be noted also that the pro-
posed broad-band systems will transmit frequencies approximately 50
to 100 cycles lower than earlier systems, which, while not contributing
appreciably to articulation, has the effect of increasing naturalness.
When applied in the telephone plant, the resultant effect of a given
increase in band width will of course depend on the other parts of the
circuit, and the transmission characteristics of the transmitters and
receivers. Improved transmitters and receivers are now being applied

rapidly in the Bell System. They have much better transmission
characteristics than earlier types and an effective upper frequency of
transmission for the new station set which is well above 3000 cycles,
as shown on Fig. 4.

The toll connecting trunks are important links in a typical overall
connection, and here also there has been a continued trend to provide
wider band circuits. Figure 5 shows the transmission frequency char-
acteristics of representative types of toll connecting trunks which are
being commonly installed at present. Both non-loaded and loaded
trunks are shown on the figure. Of course, in the non-loaded case,
there is no definite cutoff frequency. The curve for the loaded trunk

shows a reasonably long trunk having a 5 db loss at 1000 cycles (6.4
miles). In practice, of course, the trunk length may vary from a

Fig. 4—New station-set characteristics (inckiding two one-mile 24-gauge loops con-
nected by distortionless trunk).

FREQUENCY-CYCLES PER SECOND
Fig. 5—Toll connecting trunk characteristics.

fraction of a mile to 10 miles or more, with a corresponding effect on
the transmission characteristic. It will be noted that the effective

cutoff of the loaded trunk shown is about 3500 cycles based on a
10 db cutoff point. Other types of loading, which will also be em-
ployed, will have still higher cutoff points. Evidently the band widths
of the broad-band circuits, toll connecting trunks, and new station sets
are well matched.

Laboratory and field tests have been made with circuits simulating
the cutoff of the new broad-band systems and using various types of
station sets, including the new standard. These indicate that raising
the cutoff from 2750 cycles to 3600 cycles is equivalent to making a
reduction of 3 to 4 db in the net overall loss of the circuit. Raising
the cutoff from 2750 cycles to 3300 cycles is equivalent to a lesser
reduction. With older types of instruments which reproduce speech
less faithfully, this difference is also less, and of course, with instru-
ments providing transmission up to considerably higher frequencies,
the difference is greater.

It will be appreciated, of course, that the wider speech band which
will be made available in the new broad-band systems will not be fully
effective in all telephone connections unless other toll circuits and toll
connecting trunks and station sets are provided with improved trans-
mission frequency characteristics. From a practical standpoint it is
obvious that in a large telephone plant improvements cannot be made
in all parts at one time. They must be introduced gradually as new
systems and apparatus are applied, and with a far-sighted concern for
future trends.

The Dielectric Properties of Insulating Materials
By E. J. MURPHY and S. 0. MORGAN

This paper gives a qualitative account of the way in which
dielectric constant and absorption data have been interpreted in
terms of the physical and chemical structure of materials. The
dielectric behavior of materials is determined by the nature of the
polarizations which an impressed field induces in them. The
various types of polarization which have been demonstrated to exist
are listed, together with an outline of their characteristics.

I. OUTLINE OF THE PHyYsICO-CHEMICAL INTERPRETATION
OF THE DIELECTRIC CONSTANT

along such specialized lines that there is need of some correlation
between the newer and the older theories of dielectric behavior to
keep clear what is common to both, though sometimes expressed in
different terms. The purpose of the present paper is to outline in
qualitative terms the way in which the dielectric constant varies with
frequency and temperature and to indicate the type of information
regarding the structure of materials which can be obtained from the
study of the dielectric constant.

The important dielectric properties include dielectric constant (or
specific inductive capacity), dielectric loss, loss factor, power factor,
a.c. conductivity, d.c. conductivity, electrical breakdown strength and
other equivalent or similar properties. The term dielectric behavior
usually refers to the variation of these properties with frequency,
temperature, voltage, and composition.

In discussing the dielectric properties and behavior of insulating
materials it will be necessary to use some kind of model to represent
the dielectric. The success of wave-mechanics in explaining why
some materials are conductors and others dielectrics suggests that it
might be desirable to use a quantum-mechanical model even in a
general outline of the characteristics of dielectrics, but for the aspects
of the theory of dielectric behavior with which we are immediately
concerned here the behavior predicted is essentially the same as that
derived on the basis of classical mechanics. However, in the course
of the description of the frequency-dependence of dielectric constant
we shall have occasion to make a comparison between the dispersion

and absorption curves for light and those for electromagnetic dis-
turbances in the electrical (i.e., radio and power) range of frequencies.
The difficulty is then met that the quantum-mechanical model is
the customary medium of description of the absorption of light.
But, since the references to optical properties will be only incidental
and for comparative purposes, there is little to be lost, even in this
domain in which quantum-mechanical concepts are the familiar
medium of description, in using the pre-quantum theory concepts of
dispersion and absorption processes. Thus a model operating on the
basis of classical mechanics and the older conceptions of atomic struc-
ture will be sufficient for our present purposes.

On the wave-mechanical theory of the structure of matter a di-
electric is a material which is so constructed that the lower bands of
allowed energy levels are completely full at the absolute zero of temper-
ature (on the Exclusion Principle) and at the same time isolated from
higher unoccupied bands by a large zone of forbidden energy levels.'
Thus conduction in the lower, fully occupied bands is impossible
because there are no unoccupied energy levels to take care of the
additional energy which would be acquired by the electrons from the
applied field, while the zone of forbidden energy levels is so wide that
there is only a negligible probability that an electron in the lower band
of allowed levels will acquire enough energy to make the transition to
the unoccupied upper band where it could take part in conduction.
The bound electrons in a completely filled and isolated band of allowed
levels can, however, interact with the applied electric field by means of
the slight modifications which the applied field makes in the potential
structure of the material and hence in the allowed levels.

On the other hand in the older theory of the structure of matter the
essential condition which makes a material a dielectric is that the
electrons and other charged particles of which it is composed are held
in equilibrium positions by constitutive forces characteristic of the
structure of the material. When an electric field is applied these
charges are displaced, but revert to their original equilibrium positions
when the field is removed. In this account of the behavior of di-
electrics this model will be sufficient, but no essential change in the
relationships which will be discussed here would result if a translation
were made to a model based upon quantum-mechanics.

When an electric field is impressed upon a dielectric the positive
and negative charges in its atoms and molecules are displaced in
opposite directions. The dielectric is then said to be in a polarized

1Cf., for example, Gurney, ‘‘Elementary Quantum Mechanics,’ Cambridge
(1934); Herzfeld, ‘‘The Present Theory of Electrical Conduction,” Electrical Engt-
neering, April 1934.

condition, and since the motion of charges of opposite sign in opposite
directions constitutes an electric current there is what is called a
polarization current or charging current flowing while the polarized
condition is being formed.

For the case of a static impressed field a charging current flows in
the dielectric only for a certain time after application of the field, the
time required for the dielectric to reach a fully polarized condition.
If the material is not an ideal dielectric, but contains some free ions,
the current due to a static impressed field does not fall to zero but to
a constant value determined by the conductivity due to free ions.
More important than the static is the alternating current case, where
the potential is continually varying and where, consequently, there
must be a continuously varying current.

The dielectric behavior of different materials under different con-
ditions is reflected in the characteristics of the charging or polariza-
tion currents, but since polarization currents depend upon the applied
voltage and the dimensions of condensers it is inconvenient to use
them directly for the specification of the properties of materials.
Eliminating the dependence upon voltage by dividing the charge by
the voltage, we have the capacity (C = Q/V); and the dependence
upon dimensions may be eliminated by using the dielectric constant,
defined as « = C/Co, where C is the capacity of the condenser when the
dielectric material is between its plates and Cy is the capacity of the
same arrangement of plates in a vacuum. The dielectric constant
is then a property of the dielectric material itself.

The term ‘‘dielectric polarization” is used to refer to the polarized
condition created in a dielectric by an applied field of either constant
or varying intensity. The polarizability is one of the quantitative
measures of the dielectric polarization; it is defined as the electric
moment per unit volume induced by an applied field of unit effective
intensity. Another quantitative measure of the dielectric polarization
is the molar polarization; this is a quantity which is a measure of the
polarizability of the individual molecule, whatever the state of ag-
gregation of the material.

The concept of polarizability is as fundamental to, and plays about
the same role in, the theory of dielectric behavior as does the concept
of free ions in the theory of electrolytic conduction. Just as the con-
ductivity of a material is a measure of the product of the number of
ions per unit cube and their average velocity in the direction of a unit
applied field, so the polarizability is a measure of the number of bound
charged particles per unit cube and their average displacement in the
direction of the applied field.

In the early investigations of dielectrics two distinct types of charg-
ing current were recognized, the one in which the charging or dis-
charging of a condenser occurred practically instantaneously and the
other in which a definite and easily observable time was required. A
charge accumulating in a condenser in an unmeasurably short time
was variously referred to as the instantaneous charge or geometric
charge or the elastic displacement. The current by which this charge
is formed was called the instantaneous or geometric charging current,
and similarly the terms instantaneous dielectric constant or geometric
dielectric constant were used to describe the property of the medium
giving rise to the effect between the condenser plates. An even wider
variety of names has been used for the part of the charge which formed
or disappeared more slowly. Among these are residual charge,
reversible absorption, inelastic displacement, viscous displacement
and anomalous displacement. The modern theory still recognizes
these two distinct types of condenser charges and charging currents
but the simple descriptive designations rapidly-forming or instantaneous
polarizations and slowly-forming or absorptive polarizations will be
adopted here, as they seem sufficient and to be preferred to terms
which have more specialized connotations as to the mechanism upon
which the behavior depends. The properties of these two types of
charging currents and the dielectric polarizations corresponding to
them appear prominently in the theories of dielectric behavior.

The total polarizability of the dielectric is the sum of contributions
due to all of the different types of displacement of charge produced in
the material by the applied field. Constitutive forces characteristic
of the material determine both the magnitude of the polarizability and
the time required for it to form or disappear. The quantitative
measure of the time required for a polarization to form or disappear is
called the relaxation-time. In the following a description will be given
of the physical processes involved in the formation of dielectric polari-
zations, indicating the effect of chemical and physical structure upon
the two quantities, magnitude and relaxation-time, which determine
many of the properties of dielectric polarizations of the slowly-forming
or absorptive type.

The magnitude of the polarizability k of a dielectric can be expressed
in terms of a directly measurable quantity, the dielectric constant e,
by the relation

It is sometimes convenient to use the polarizability and the dielectric

constant interchangeably in the qualitative discussion of the magnitude
of the dielectric polarization. In dealing with alternating currents
the fact that polarizations of the absorptive type require a time to
form which is often of the same order of magnitude as, or greater than,
the period of the alternations, results in the polarization not
being able to form completely before the direction of the field is
reversed. This causes the magnitude of the dielectric polarization

Fig. 1—Schematic diagram of variation of dielectric constant and dielectric
absorption with frequency for a material having electronic, atomic, dipole and
interfacial polarizations.

and dielectric constant to decrease as the frequency of the applied
field increases. An example of this variation of the dielectric constant
with frequency is shown in the radio and power frequency section of
the curve plotted in Fig. 1. It is often convenient to refer to the mid-
point of the decreasing dielectric constant-frequency curve as the
relaxation-frequency; this frequency f, is very simply related to the
relaxation-time 7, for the theory of these effects shows that f, = 1/27r.

Various types of polarization can be induced in dielectrics: There
should be an electronic polarization due to the displacement of electrons
with respect to the positive nuclei within the atom; an atomic polari-
zation due to the displacement of atoms with respect to each other in
the molecule and in certain ionic crystals, such as rock salt, to the
displacement of the lattice ions of one sign with respect to those of the
opposite sign; dipole polarizations due to the effect of the applied
field on the orientations of molecules with permanent dipole moments;
and finally interfacial (or ionic) polarizations caused by the accumula-
tion of free ions at the interfaces between materials having different
conductivities and dielectric constants.

A classification of dielectric polarizations into rapidly-forming or
instantaneous polarizations and slowly-forming or absorptive polariza-
tions has been made. Instantaneous polarizations may be thought of
as polarizations which can form completely in times less than say 10~"°
seconds, that is, at frequencies greater than 10! cycles per second or
wave-lengths of less than 1 centimeter, and so beyond the range of
conventional dielectric constant measurements. The electronic polari-
zations are due to the displacement of charges within the atoms, and
are the most important of the instantaneous polarizations. The
polarizability per unit volume due to electronic polarizations may be
considered to be’a quantity which is proportional to the number of
bound electrons in a unit volume and inversely proportional to the
forces binding them to the nuclei of the atoms.

The effect of number of electrons and binding force is illustrated by
a comparison of the values for the polarizability per unit volume of
different gases; for the number of molecules per unit volume is inde-
pendent of the composition of the gas. Thus, although a c.c. of
hydrogen with two electrons per molecule has the same number of
electrons as a c.c. of helium, which is an atomic gas with two electrons
per atom, the quantity «€—- 1, that is the amount by which the di-
electric constant is greater than that of a vacuum, is nearly four times
as large for hydrogen as for helium. This shows that in hydrogen the
electrons are in effect less tightly bound to the nucleus than in helium,
resulting in a larger induced polarization. Nitrogen has a larger
dielectric constant than either hydrogen or helium because it has 14
electrons per molecule. Some of these are tightly bound as in helium
and some are more loosely bound as in hydrogen.

The dielectric constant of liquid nitrogen is 1.43, which is much
higher than the value 1.000600 for the gas. This is due to the fact

that the number of molecules, and consequently of bound charges,
per unit volume is much greater in the liquid than in the gas. How-
ever, the molar polarization, a quantity which is corrected for varia-
tions in density, is the same for liquid as for gaseous nitrogen.

The time required for the applied field to displace the electrons
within an atom to new positions with respect to their nuclei is so short
that there is no observable effect of time or frequency upon the value
of the dielectric constant until frequencies corresponding to absorption
lines in the visible or ultra-violet spectrum are reached. For con-
venience in this discussion the frequency range which includes the
infra-red, visible and ultra-violet spectrum will be called the optical
frequency range while that which includes radio, audio and power
frequencies will be called the electrical frequency range. For all fre-
quencies in the electrical range the electronic polarization is indepen-
dent of frequency and for a given material contributes a fixed amount
to the dielectric constant, but at the frequencies in the optical range
corresponding to the absorption lines in the spectrum of the material,
the dielectric constant, or better the refractive index, changes rapidly
with frequency, and absorption appears. (The justification for using
refractive index m and dielectric constant ¢« interchangeably for the
qualitative discussion of the properties of dielectric polarizations fol-
lows from the relation, « = n?, which is known as Maxwell's rule.
This is a general relationship based upon electromagnetic theory and
is applicable whenever « and m are measured at the same frequency
no matter how high or low it may be.)

The electronic polarization of a molecule may be regarded as an
additive property of the atoms or of the atomic bonds in the molecule,
and may be calculated for any dielectric of known composition with
sufficient accuracy for most purposes. Within any one chemical class of
compounds such as, for example, the saturated hydrocarbons or their
simple derivatives, in which all of the bonds are C—H, C—C or C—X,
the calculated values agree with the measured to within a few per
cent. For other classes of compounds—for example, benzene, in
which there are both single and double bonds such calculations must be
corrected for the fact that some of the valence electrons have their
binding forces and hence their polarizabilities altered in the double
bond as compared to the single bond. Such values of electronic
polarization, usually called atomic refractions, have been determined
for all of the different types of bonds from the vast amount of experi-
mental study of refractive indices of organic and inorganic compounds.

In some materials the electronic polarization is the only one of
importance. For example, in benzene the dielectric constant is the

same at all frequencies in the electrical range and is equal to the square
of the optical refractive index. This must mean that the only polari-
zable elements of consequence in CsHe are electrons which are capable
of polarizing as readily in the visible spectrum, where the refractive
index is measured, as at lower frequencies where dielectric constant is
measured. The refractive index in the visible spectrum provides the
means of determining the magnitude of electronic polarizations, for
other types of polarization are usually of negligible magnitude when
the frequency of the impressed field lies in the visible spectrum. For
materials having only electronic polarizations the dielectric properties
are very simply dependent upon the chemical composition and the
temperature, and are independent of frequency in the electrical
frequency range. In many materials, however, there are also other
polarizations which can form at low frequencies but not at high; these
are characterized by more complex dielectric behavior.

Included among the polarizations which may be described as in-
stantaneous by comparison with the order of magnitude of the periods
of alternation of the applied field in the electrical frequency range are
those arising from the displacement of the ions in an ionic crystal
lattice (such as rock salt) or of atoms in a molecule or molecular lattice.
In some few materials, for example the alkali halides, sufficient study
has been made of the infra-red refractive index to provide data on the
atomic polarizations, but for most substances little is known about
them. What is known has in part been inferred from infra-red absorp-
tion spectra and in part from the infra-red vibrations revealed by
studies of the Raman effect.

Atomic polarizations are distinguished from electronic polarizations
by being the part of the polarization of a molecule which can be at-
tributed to the relative motion of the atoms of which it is composed.
The atomic polarizations may be attributed to the perturbation by the
applied field of the vibrations of atoms and ions having their character-
istic or resonance frequencies in the infra-red. Atomic polarizations
may be large for substances such as the alkali halides and other in-
organic materials, but are usually negligible for organic materials.
The exact value of the time required for the formation of atomic
polarizations is unimportant in the electric range of frequencies with
which we are primarily concerned. The essential thing is that atomic
polarizations begin to contribute to e(or m*) at frequencies below
approximately 10' seconds—that is, in the near infra-red and that
below about 10” cycles per second, where the optical and electrical

frequency ranges merge, atomic polarizations contribute a constant
amount to e(or m?) for a given material. The atomic polarization is
determined as the difference between the polarization which is meas-
ured at some low infra-red or high electric frequency and the electronic
polarization as determined from refractive index measurements in the
visible spectrum.

The electronic and atomic polarizations are considered to comprise
all of the so-called instantaneous polarizations; that is, the polariza-
tions which form completely in a time which is very short as compared
with the order of magnitude of the periods of applied fields in the
electrical range of frequencies.

The remaining types of polarization are of the “‘absorptive”’ kind,
characterized by relaxation-times corresponding to ‘‘relaxation-
frequencies” in the electrical range of frequencies. These polariza-
tions include the important type which is due to the effect of the applied
field on the orientation of molecules with permanent electric moments,
the theory of which was developed by Debye. Among the other
possible polarizations of the absorptive type are those due to inter-
facial effects or to ions which are bound in various ways.

Debye,’ in 1912, suggested that the high dielectric constant of water,
alcohol and similar liquids was due to the existence of permanent
dipoles in the molecules of these substances. The theory which Debye
based upon this postulate opened up a new field for experimental
investigation by providing a molecular mechanism to explain dielectric
behavior which fitted into and served to confirm the widely held
views of chemical structure. Debye postulated that the molecules
of all substances except those in which the charges are symmetrically
located possess a permanent electric moment which is characteristic
of the molecule. In a liquid or gas these molecular dipoles are oriented
at random and therefore the magnitude of the polarization vector is
zero. When an electric field is applied, however, there is a tendency
for the molecules to align themselves with their dipole axes in the
direction of the applied field, or, put in another way, to spend more
of their time with their dipole axes in the direction of the field than
in the opposite direction. This dipole polarization is superimposed
upon the electronic and atomic polarizations which are also induced by
the field. The theory as developed by Debye accounts for the ob-
served difference between the temperature and frequency dependence
of the dipole polarizations and the instantaneous polarizations. While
the latter are present in all dielectrics, the dipole polarizations can
2 P. Debye, Phys. Zeit., 13,97, (1912); Verh. d. D. phys. Ges., 15, 777 (1913).

occur only in those made up of molecules which are electrically,
asymmetrical.

Polar molecules (that is molecules with permanent electric moments
are, by definition, those in which the centroid of the negative charges
does not coincide with the centroid of the positive charges, but falls
at some distance from it. All materials must be classed either as
polar or non-polar, the latter class including those which are elec-
trically symmetrical. Some simple examples of non-polar molecules

Fig. 2—-Methane and carbon tetrachloride are non-polar molecules each having
four equal vector moments whose sum is zero. Methyl chloride is polar because the
sum of the vector moments is not zero.

are He, Ne, Oz, CCl, and CeH¢. In these molecules each C — H,
C — Cl or other bond may be regarded as having a vector dipole mo-
ment of characteristic magnitude located in the bond. Where the
sum of these vector moments is zero the molecule will be non-polar.
Both CH, and CCl, meet this requirement but CH;Cl is polar because
the C — Cl vector moment is considerably greater than the resultant of
the three C — H vectors. (See Fig. 2.) Polar molecules are the rule
and non-polar the exception.

In the discussion of dipole polarizations it has frequently been
pointed out that non-polar materials usually obey the general relation-

the dielectric constant as measured in the electric range of frequencies.

dielectric constant only in the electrical frequency range; this is the
most frequent source of the above mentioned discrepancy. The
general relationship « = n? should apply for any material at any fre-
quency provided ¢ and » are measured at the same frequency. The
refractive index of water when measured with electric waves,’ for
example, at a million cycles, is found to be slightly less than 9, the
square of which agrees very well with the observed value ¢ = 78.
However, it does not always follow that when e > mn? the molecules of
which the material is composed have permanent dipole moments, for
this condition can also result from the presence of any slowly-forming
or absorptive polarization or of a large atomic polarization. Experi-
mental investigations based upon the Debye theory have shown,
however, that in the case of water and many other familiar compounds
the orientation of dipole molecules actually accounts for the high
dielectric constant.

The Debye theory shows that the magnitude of the dipole polariza-
tion of a material is proportional to the square of the electric moment
of the molecule, which, as has been pointed out, may be regarded as
the vector sum of a number of constituent moments characteristic of
the individual atoms or radicals of which the molecule is composed,
or alternatively, of the bonds which bind these atoms into molecules
or more complex aggregates. The very great amount of experimental
study of the Debye theory has shown that the NO, and CN groups
have the largest group moments while CO, OH, NHz, Cl, Br, I and
CH; have progressively smaller group moments. The value 34 for the
dielectric constant of nitrobenzene (CsH;NO2), as against 5.5 for
chlorobenzene (C,H;Cl), 2.8 for methyl benzene (CsH;CHs) and 2.28
for benzene (CsH,), which is non-polar, are evidence of the large
differences in the magnitudes of these group moments and the large
part that dipole moments can play in determining the dielectric
constant.

Another point regarding molecular structure shown by stich studies
is that it is not only the presence of polar groups in the molecule bu:
also their position which determines the electric moment of the mole-
cule. This is nicely illustrated by the dichlorobenzenes, of which
there are three isomers. As is shown in Fig. 3, ortho-dichlorobenzene,
having the two substituent groups in adjacent positions, is the most
asymmetrical of the three compounds, and consequently has the high-

Fig. 3—Ortho dichlorobenzene being the more asymmetrical has a higher electric
moment than the meta isomer; the para isomer which is symmetrical has zero electric
moment.

est electric moment, « = 2.3. The meta compound has about the
same moment as monochlorobenzene, w = 1.55. The para compound,
however, is symmetrical and has zero electric moment because the
Cl atoms are substituted on opposite sides of the benzene ring so that
their vector moments cancel. These values of electric moment are
reflected in the values of dielectric constant which are respectively
10, 5.5 and 2.8 for the three isomeric dichlorobenzenes.

DIELECTRIC PROPERTIES OF INSULATING MATERIALS — 505
Dielectric studies of this kind have also shown, for example, that
H,0 is not a symmetrical linear molecule, H — O — H, but rather a

is determined to be a linear molecule O = C = O. Thus, dielectric
measurements interpreted by the Debye theory have become estab-
lished as one of the standard means of studying molecular structure.
Since dipole polarizations depend upon the relative orientations of
molecules, rather than upon the displacement of charges within the
atom or molecule, the time required for a polarization of this type to
form depends upon the internal friction of the material. Debye
expressed the time of relaxation of dipole polarizations in terms of the
internal frictional force by the equation:

2kT =
where ¢ is the internal friction coefficient, n is the coefficient of viscosity,
a the radius of the molecule and T the absolute temperature.t| This
latter expression, because it depends on Stokes’ law for a freely falling
body, is rigidly applicable only to gases or possibly to dilute solutions
of polar molecules in non-polar solvents in which the polar molecules
are far enough apart that they exert no appreciable influence on each
other.

Applying this equation to the calculation of the relaxation-time of
the orientational polarizations in water at room temperature we obtain
t = 10°-!° seconds, assuming a molecular radius of 2 & 10~-* cm. and
taking the viscosity as 0.01 poises.2 The relaxation-frequency corre-
sponding to this relaxation-time is about 1.6 & 10° cycles/sec., agreeing
with the results of experimental studies on water which show that
in the range of frequencies extending from 10° to 10" cycles the
dielectric constant decreases from its high value to a value approxi-
mately equal to the square of the refractive index. Thus the drop in
dielectric constant occurs in the frequency range which corresponds to
the calculated value of the re!axation-time.

Similar experiments on dilute solutions of aicohols*® in non-polar
solvents yield values of r of about 10~* seconds. The shortest relax-
ation-times which dipole polarizations can have are probably not

5 The viscosity of a liquid in poises is given by the force in dynes required to
maintain a relative tangential velocity of 1 cm./sec. between two parallel planes in the
liquid each 1 cm.? in area and 1 cm. apart, the distance being measured normal to their

much less than the order of 10~-!! seconds, since in general either the
internal friction or the molecular radius of materials having polar
molecules will be greater than those of water, resulting in longer
relaxation-times. No long-time limit can be placed on the relaxation-
times which dipole polarizations may have, for they are limited only
by the values which the internal friction can assume. For materials,
such as glycerine, which tend to become very viscous at low tempera-
tures the time of relaxation of the dipoles may be a matter of minutes.
Studies of the dielectric constant of crystalline solids, to be discussed
in a later paper, show also that in some cases polar molecules are able
to rotate even in the crystalline state, where the ordinary coefficient
of viscosity has no meaning because the materials do not flow. In
connection with the dielectric properties we are concerned only with
the ability of the polar molecules to undergo rotational motion and
it is likely that in these solids, which constitute a special class, the
internal frictional force opposing rotation of the molecules is small
even though the forces opposing translational motion may be very
large. The particular equation for the calculation of the time of
relaxation given above obviously does not apply to solids.

In discussing the three types of polarizations which have been
considered thus far, it has been pointed out that the magnitude of
the dielectric constant depends upon the polarizability of the material.
Each type of polarization makes a contribution to the dielectric
constant if the measuring frequency is considerably below its relax-
ation-frequency. However, if the frequency of the applied field used
for measuring the dielectric constant is too high the presence of
polarizations with low relaxation-frequencies will not be detected.
Thus the refractive index of water in the visible spectrum is 1.3 and
therefore gives no evidence whatever of the presence of permanent
dipoles. This is due to the fact that the H,O molecules do not change
their orientations rapidly enough to allow fields which alternate in
direction as rapidly as those of light to cause an appreciable deviation
from the original random orientation which prevails in the absence of
an applied field.

The band of frequencies in which the dielectric constant decreases
with increasing frequency because of inability of the polarization to
form completely in the time available during a cycle, is called a region
of absorption or of anomalous dispersion. The discussion of this
characteristic of dielectric matetials forms an important part of
dielectric theory. The term anomalous dispersion is no doubt usually
thought of in connection with the anomalous dispersion of light: when
the refractive index of light decreases with increasing frequency the

DIELECTRIC PROPERTIES OF INSULATING MATERIALS 507
material is said to display anomalous dispersion in the range of fre-
quencies concerned. However, in a paper published in 1898 Drude ?
applied this term to the decrease of dielectric constant with increasing
frequency in the electrical range of frequencies. The justification
for this extension of the original application of the term is very direct
for electromagnetic theory shows that the dielectric constant and the
refractive index of a material are connected by the general relationship
« = n* whatever the frequency of the electromagnetic disturbance.
As the dispersion of light by a prism is due to the variation of its re-
fractive index with frequency, the use of the expression anomalous
dispersion to refer to the decrease of dielectric constant with increasing
frequency is consistent and has become generally accepted.

The polarizations thus far considered are the main types to be
expected in a homogeneous material. They depend upon the effect
of the applied field in slightly displacing electrons in atoms, in slightly
distorting the atomic arrangement in molecules and in causing a slight
deviation from randomness in the orientation of polar molecules.
The remaining types of polarization are those resulting from the
heterogeneous nature of the material and are called interfacial polariza-
tions. Interfacial polarizations must exist in any dielectric made up
of two or more components having different dielectric constants and
conductivities except for the particular case where eyy2 = eyi, y being
the conductivity * and the subscripts referring to the two components.
Heterogeneity in a dielectric may be due to a number of causes, and
in the case of practical insulating materials is probably the rule rather
than the exception. Impregnated paper condensers and laminated
plastics are obvious examples of heterogeneous dielectrics. Paper
is itself a heterogeneous dielectric, consisting of water and cellulose.
In all probability the plastic resins are also heterogeneous, and cer-
tainly so if they contain fillers. Ceramics, being mixtures of crystalline
and glassy phases, are also heterogeneous.

The simplest case of interfacial polarization is that of the two-layer
dielectric, that is, a cornposite dielectric made up of two layers, the
dielectric constants and conductivities of which are different. Max-
well showed that in such a system the capacity was dependent upon
the charging time. This is due to the accumulation of charge at the
interface between the two layers, for this charge must flow through a

7 P. Drude, Ann. d. Phystk, 64, 131 (1898), ‘Zur Theorie der anomalien elektrischen
Dispersion.”

In this expression y represents the total a.c. conductivity, a quantity which
depends on the frequency.

layer of dielectric whose resistance may be high enough that the inter-
face does not become completely charged during the time allowed for
charging. For the alternating current case this implies a decrease of
capacity with increasing frequency, which is equivalent to the anoma-
lous dispersion which has been described for the case of dipole polariza-
tions. It should be particularly emphasized that the term anomalous
dispersion describes a type of variation of dielectric constant with
frequency which can be produced by a number of different physical
mechanisms.

The two-layer dielectric is of less interest than a generalization of
this type of polarization which includes heterogeneous systems com-

of heterogeneous dielectric is of considerable importance since such
systems represent the actual structure of many practical dielectrics.
Such a generalization of the two-layer dielectric has been made by
K. W. Wagner * who developed the theory for the case of spheres of
relatively high conductivity dispersed in a continuous medium of low
conductivity. The conditions for the existence of an interfacial
polarization are, as in the two-layer case, that ey2 + ei, where the
symbols have the significance just given. This type of polarization,
which is variously referred to as an interfacial polarization, an ionic
polarization and a Maxwell-Wagner polarization, shows anomalous
dispersion like other absorptive polarizations. When the particle
size is small as compared with the electrode separation it may be
treated as a uniformly distributed polarization.

The magnitude and time of relaxation of interfacial polarizations
are determined by the differences in « and y of the two components.
There is a widely prevalent opinion that this type of polarization
always has such long relaxation-times as to be observed only at very
low frequencies. While this is true for mixtures of very low-con-
ductivity components, the general equations show that for the case
where one component has a high conductivity—for example equal to
that of a salt solution—the dispersion may occur in the radio frequency
range.

Several special types of interfacial polarization have been proposed
to explain the dielectric properties of various non-homogeneous di-
electrics where something regarding the nature of the inhomogeneity
is known. The dielectric constant of cellulose, for example, receives
a contribution from an interfacial polarization due to the water and
dissolved salt which it contains. Experimental evidence indicates
that an aqueous solution of various salts is distributed through the

cellulose in such a way as to form a reticulated pattern which may
correspond to the pattern formed by the micelles or to some feature
of it. An interesting feature of this structure is that the conductance
of the aqueous constituent can be changed by varying the moisture
content or the salt content of the material and the effect on the di-
electric constant observed."

As has been pointed out, each of the different types of polarization
may contribute to the dielectric constant an amount depending upon
the polarizability and its time of relaxation. The upper curve in Fig.
1 shows schematically the variation of the dielectric constant (or of the
square of the refractive index) for a hypothetical material possessing
an interfacial polarization with relaxation-frequency in the power
range, a dipole polarization with relaxation frequency in the high
radio frequency range and atomic and electronic polarizations with
dispersion regions in the infra-red and visible respectively. If polariza-
bility were plotted, instead of € (or n?), the curves would be of the same
general form but of different magnitudes, because of a relationship
between the two given earlier.

At the low-frequency side of Fig. 1, the dielectric constant curve
has its highest value, usually called the static or zero-frequency
dielectric constant. Here all of the polarizations have time to form
and to contribute their full amount to the dielectric constant. With
increasing frequency ¢ begins to decrease as the relaxation-frequency
of the interfacial polarization is approached and reaches a constant
lower value (called the’ infinite-frequency dielectric constant) when
the applied frequency is sufficiently above the relaxation-frequency of
the polarization that it has not time to form appreciably. It is this
decrease of ¢ with frequency which is called anomalous dispersion. The
horizontal arrows across the top of Fig. 1 indicate the frequency region
in which the various types of polarizations indicated are able to form
and contribute to the dielectric constant.

At still higher frequencies we see that e€ again decreases as the
relaxation-frequency of the dipole polarization is approached, and
again reaches a constant lower value as the frequency becomes too
high for the field to affect appreciably the orientation of dipoles.
This second region of anomalous dispersion is similar to the first,
which was due to interfacial polarizations. It has been shown as
occurring at a higher frequency, but it should be emphasized that the
frequency ranges chosen to illustrate anomalous dispersion in Fig. 1

are purely arbitrary. Anomalous dispersion due to dipole polariza-
tions has been observed at power frequencies while that due to inter-
facial polarizations has been observed at radio frequencies. The two
types of polarizations may in fact give rise to anomalous dispersion
in the same frequency range in a given dielectric.

Proceeding to still higher frequencies in Fig. 1 other regions of
dispersion appear in the infra-red and visible spectrum. These
regions show a combination of normal optical dispersion, in which the
dielectric constant, or better now the refractive index, increases with
frequency, and anomalous dispersion in which it decreases. The
dispersion in the visible range of frequencies is predominantly normal
(anomalous dispersion being confined to relatively narrow frequency
bands) whereas in the electrical range the reverse is true, normal
dispersion not being observed; the infra-red represents an intermediate
region. Dipole and interfacial polarizations are not represented in
the dispersion in the optieal range, the dielectric constant (or refractive
index) in the visible being due to electronic polarizations and in the
infra-red to electronic and atomic polarizations.

The curves plotted in Fig. 1 are merely schematic and the relative
magnitudes of the different contributions to the dielectric constant
are therefore arbitrary. However, experimental results indicate that
the contribution eg of the electronic polarization to the dielectric
constant is limited to values between 2 and 4 except for certain in-
organic materials, since very few organic solids or liquids are known
which have refractive indices in the visible spectrum which are greater
than 2 or less than 1.4. The contribution e4 of atomic polarizations
to the dielectric constant is in general small and is usually negligible,
as has been indicated on the curve, although the possibility exists of
special cases occurring in which the infra-red refractive indices are
very high. The contributions ep and ¢« of dipole and interfacial
polarizations to the dielectric constant may vary greatly from one
material to another, depending upon the symmetry of the molecule
and the physical structure of the dielectric. From the above men-
tioned limitations on the contribution to the dielectric constant which
can be expected from electronic and atomic polarizations, it is apparent
that the explanation of values of « higher than 3 to 4, at least in organic
materials, requires the existence of some absorptive polarization such
as arises from dipoles or interfacial effects. Thus all of the liquids
which have high dielectric constants such as H,O (78), alcohol (24),
nitrobenzene (34) have been shown to contain polar molecules.

The lower part of Fig. 1 shows a maximum in the absorption for
each type of dielectric polarization. The absorption, at least in the

electrical frequency range, is due to the dissipation of the energy of the
field as heat because of the friction experienced by the bound charges
or dipoles in their motion in the applied field in forming the polariza-
tions. The theory of dispersion shows that the dielectric constant and
absorption are not independent quantities but that the absorption
curve can be calculated from the dielectric constant vs. frequency
curve and vice versa. The absorption maximum is greatest for those
materials showing the greatest change in dielectric constant in passing
through the dispersion region. Thus a material having a high di-
electric constant must have a large dielectric loss at the frequency at
which ¢ has a value half way between its low and high-frequency values.

Though the quantum theory is necessary for the explanation of many
optical and electrical phenomena a simple explanation, sufficient for
our purposes, of the general form of the curves of dielectric constant vs.
frequency in the infra-red and visible spectrum may be given in terms
of the Lorentz theory of optical dispersion. In this theory the form
of the dispersion curves depends upon the variation with frequency of
the relative importance of the inertia of the typical electron and of the
frictional forces and restoring forces acting upon it. For electronic
polarizations the frictional or dissipative force is negligible, except
in the narrow frequency interval included in the absorption band, and
the inertia and restoring force terms predominate. For the atomic
polarizations the frictional force is larger and the absorption region
extends over a wider interval of frequencies. For dipole and inter-
facial polarizations the influence of inertia is entirely negligible as
compared with the frictional or dissipative forces so that in effect these
polarizations may be thought of as aperiodically damped.

The dielectric constant of a material is a constant only in the ex-
ceptional case. Besides the variation with frequency which has been
considered the dielectric constant varies with temperature. Elec-
tronic polarizations may be considered to be unaffected by the tempera-
ture. The refractive index does indeed change with temperature
but this is completely accounted for by the change of density, and the
molar refraction is independent of temperature. The atomic and
ionic vibrations are, however, affected by temperature, the binding
force between ions or atoms being weakened by increased temperature.
This factor of itself would yield a positive temperature coefficient for
the atomic polarizations but the decrease in density with the increase
in temperature acts in the opposite direction. The result is that
calculation of the temperature coefficient of atomic polarizations

usually yields zero or slightly positive values. What experimental
data there are indicate small positive temperature coefficients for
atomic polarizations.

One of the principal achievements of the Debye theory of dipole
polarizations has been the manner in which it explains the large
negative temperature coefficients of polarization of many liquids.
Debye showed that the variation of polarization with temperature
could be expressed by the relation P = A + (B/T), in which the
constant A is a measure of the instantaneous polarizations which are
independent of temperature and B is a measure of the dipole polariza-
tions. In a liquid or gas the molecules are continuously undergoing
both translational and rotational motion, and the result of this thermal
motion is to maintain a random orientation of molecules. The action
of the electric field in aligning the dipoles is opposed by the thermal
motion which acts as an influence tending to keep them oriented at
random. As the temperature decreases, the thermal energy becomes
smaller and the dipole polarization becomes larger, resulting in a
negative temperature coefficient of dielectric constant.

The effect of temperature upon interfacial polarizations has not
been experimentally investigated to an extent at all comparable with
that of dipole polarizations. However, interest in the interfacial or
ionic type of polarization has increased considerably in the past few
years, and it has applications of some importance. Among these is
diathermy which is becoming of considerable importance as a thera-
peutic agency.

The foregoing qualitative description of the behavior of the di-
electric constant and the type of information regarding molecular
structure which has been derived from it will be followed in the next
section by the derivation of some of the quantitative relationships
which are common to all polarizations of the absorptive type.

Variable Frequency Electric Circuit Theory with Application
to the Theory of Frequency-Modulation

In this paper the fundamental formulas of variable frequency
electric circuit theory are first developed. These are then applied
to a study of the transmission, reception and detection of frequency
modulated waves. A comparison with amplitude modulation is
made and quantitative formulas are developed for comparing the
noise-to-signal power ratio in the two modes of modulation.

REQUENCY modulation was a much talked of subject twenty
or more years ago. Most of the interest in it then centered
around the idea that it might afford a means of compressing a signal
into a narrower frequency band than is required for amplitude modu-
lation. When it was shown that not only could this hope not be
realized,* but that much wider bands might be required for frequency
modulation, interest in the subject naturally waned. It was revived
again when engineers began to explore the possibilities of radio trans-
mission at very short wave lengths where there is little restriction on
the width of the frequency band that may be utilized.

During the past eight years a number of papers have been published
on frequency modulation, as reference to the attached bibliography
will show. That by Professor E. H. Armstrong ¢ deals with this
subject in comprehensive fashion. In his paper the problem of
discrimination against extraneous noise is discussed, and it is pointed
out that important advantages result from a combination of wide
frequency bands together with severe amplitude limitation of the
received signal waves. His treatment is, however, essentially non-
mathematical in character, and it is therefore believed that a mathe-
matical study of this phase of the problem will not be unwelcome.
This the present paper aims to supply by developing the basic mathe-
matics of frequency modulation and applying it to the question of
noise discrimination with or without amplitude limitation.

The outstanding conclusions reached in the present paper, as
regards discrimination against noise by frequency modulation, may
be briefly summarized as follows:

(1) To secure any advantage by frequency modulation as distin-
guished from amplitude modulation, the frequency band width must
be much greater in the former than in the latter system.

(2) Frequency modulation in combination with severe amplitude
limitation for the received wave results in substantial reduction of the
noise-to-signal power ratio. Formulas are developed which make
possible a quantitative estimate of the noise-to-signal power ratio in
frequency modulation, with and without amplitude limitation, as
compared with amplitude modulation.

It is a pleasure to express our thanks to several colleagues who have
been helpful in various ways: to Dr. Ralph Bown who in a brief but
very incisive memorandum, which was not intended to be a mathe-
matical study, disclosed all the essential ideas of the quasi-stationary
method of attack; to Mr. J. G. Chaffee,* who has been conducting
experimental work on frequency modulation in these Laboratories for
some years past, by means of which quantitative checks on the
accuracy of some of the principal results have been possible; and to
various associates, especially Mr. W. R. Bennett and Mrs. S. P.
Mead, for detailed criticism of certain portions of the work.

In the well-known steady-state theory of alternating currents, the
e.m.f. and the currents in all the branches of a network in which
the e.m.f. is impressed involve the time ¢ only through the common
factor e' where i = ¥— 1 and w is the constant frequency. To this
fact is attributable the remarkable simplicity of alternating current
theory and calculation, and also the fact that the network is completely
specified by its complex admittance Y(iw). Thus, if the e.m.f. is
Ee‘, the steady-state current is

In the present paper we shall deal with the case where the frequency
is variable, and write the impressed e.m.f. as

Q(t) will be termed the instantaneous frequency. This agrees with
the usual definition of frequency when & is a constant; it is the rate of
change of the phase angle at time ¢; and in addition the interval T
between adjacent zeros of sin fQ(t)dt or cos fQ(t)dt is approximately
7/Q(t) in cases of practical importance.

Instead of dealing with an arbitrary instantaneous frequency {(f)
we shall suppose that

Q(t) = w + u(t), (3)
where w is a constant and u(t) is the variable part of the instantaneous os
frequency. In practical applications u(t) will be written as As(¢) where os
\ is a real parameter and the mean square value s* of s(t) is taken as oo

equal to 1/2. Other restrictions on y(t) will be imposed in the course
of the theory to be developed in this paper. Fortunately these
restrictions do not interfere with the application of the theory to
important problems.

The steady-state current as given by (1) varies with time in precisely
the same way as the impressed e.m.f. When the frequency is variable
this is no longer true. On the other hand, formula (1) suggests a
‘‘quasi-stationary”’ or ‘‘quasi-steady-state current’? component, J ,,.,
defined by the formula

which corresponds exactly to (1) with the distinction that the ad-
mittance is now an explicit function of time. We are thus led to
examine the significance of /,,, as defined above and the conditions
under which it is a valid approximate representation of the actual
response of the network to a variable frequency electromotive force,
as given by (2).

We start with the fundamental formula of electric circuit theory.'
Let an e.m.f. F(t) be impressed at time ¢ = 0, on a network of indicial
admittance A(t); then the current /(t) in the network is given by

Here A’(t) = d/dt-A(t) and it is supposed that A(0) = 0. (This
restriction does not limit our subsequent conclusions and is introduced
merely to simplify the formulas. Furthermore A(0) is actually zero
in all physically realizable networks. )

Substituting this expression in (5) for F(t — r) and writing
Jo
we have for the current in the network
I = eS oat. M(t, (9)
Jo
We now split the integral into two parts, thus:
t
The second integral on the right represents an initial transient which
dies away for sufficiently large values of time, ¢, while the infinite

integral represents the total current, J, for sufficiently large values of ¢.
We have therefore

The foregoing formulas correspond precisely with the formulas for
a constant frequency impressed e.m.f.; these are

2 Hereafter the transient term 7 of (10) will be consistently neglected and the
symbol J will refer only to the quasi-stationary current.

We have now to evaluate Y(iw,t) as given by (11). We shall
assume tentatively, at the outset, that u = As(t) has the following
properties:

With these restrictions the instantaneous frequency lies within the
limits w + X.
Let us now replace M(t, r) by the formal series expansion

which converges in the vicinity of all values of ¢ for which s has a
complete set of derivatives. Then, if we write

Now consider the quasi-stationary admittance Y(iQ2). Writing
2 = w+ u(t) and expanding as a power series, we have (assuming
that the series is convergent)

., dp
D; = — — 20
3 Pit de” ( )
ae Consequently, the total current, after initial transients have died

We have thus succeeded in expressing the response of the network in
terms of the quasi-stationary current

and a correction series A, which depends on the derivatives of the
steady-state admittance Y(iw) with respect to frequency and the
derivatives of the variable frequency u(t) with respect to time.

If the parameter ) is sufficiently large and the derivatives of s are
small enough so that C, may be replaced by the two leading terms,
we get

The preceding formulas are so fundamental to variable frequency
theory and the theory of frequency modulation that an alternative
derivation seems worth while. We take the applied e.m.f. as

the phase angle @ being included for the sake of generality.
Now in any finite epoch 0 = ¢ = 7, it is always possible to write

thus expressing the function on the left as a Fourier integral. For
present purposes it is quite unnecessary to evaluate the Fourier
function F(iw).

We suppose as before that, in the interval 0 = ¢ = 7, u(t) and its de-
rivatives are continuous. We can then expand the admittance func-

I = E-exp (iat + 66) ¥ (ies) (27)
But by the identity (24) and repeated differentiations with respect
to t, we have

Formula (25), as it stands, includes the initial transients at time
t = 0 as well as any which occur at discontinuities in u(t). Differ-
entiation with respect to ¢ under the integral sign, however, in effect
eliminates these transients and (29) leaves only the quasi-stationary
current (plus the correction series given in (19)).

The series appearing in formula (29) may not be convergent; in any
case its computation is laborious. Furthermore, in its application to
the theory of frequency modulation, terms beyond the first two
represent distortion. For these reasons it is often preferable to
proceed as follows:

must be kept small if the finite series in (31) is to be an accurate repre-
sentation of the current 7. While it is not in general computable, we
see that, in order to keep it small, R,(w., w) must be small over the
essential range of frequencies of F(iw). In cases of practical im-
portance we shall find (see Appendix 1) this range is from w = — Xd
tow =

If the transducer introduces a large phase shift, the linear part of
which is predominant in the neighborhood of w = w,, it is preferable
to express the received current J in terms of a “‘retarded”’ time. To
do this, return to (25) and write

which corresponds precisely with (29) except that it is expressed in
terms of the retarded time ¢’.. If the transducer introduces a large
phase delay, (35) may be much more rapidly convergent than (29)
and should be employed in preference thereto.

The foregoing will now be applied to the Theory of Frequency
Modulation. A pure frequency modulated wave may be defined as a
high frequency wave of constant amplitude, the ‘‘instantaneous”’

frequency of which is varied in accordance with a low frequency signal
wave. Thus

is a pure frequency modulated wave. Here w, is the constant carrier
frequency and s(t) is the low frequency signal which it is desired to
transmit. 2 is a real parameter which will be termed the modulation
index. The ‘‘instantaneous”’ frequency is then defined as

In all cases it will be postulated that \ < «..
With the method of producing the frequency modulated wave (38)
we are not here concerned beyond stating that it may be gotten by
varying the capacity or inductance of a high frequency oscillating
circuit by and in accordance with the signal s(t).
Corresponding to (38), the pure amplitude modulated wave (carrier
suppressed) is of the form

If the maximum essential frequency in the signal s(t) is w., the wave
(39) occupies the frequency band lying between w. — wa and w, + wa,
so that the band width is 2w,. In the pure frequency modulated wave
the ‘‘instantaneous”’ frequency band width is 2d. In_ practical
applications \ >> wa. We shall now examine in more detail the concept
of ‘‘instantaneous”’ frequency and the conditions under which it has
physical significance.

The instantaneous frequency is, as stated, w. + As(t); a steady-state
analysis is of interest and importance. To this end we suppose
s(t) = cos wt so that w is the frequency of the signal. Then the wave
(38) may be written

where J, is the Bessel function of the first kind. Thus the frequency
modulated wave is made up of sinusoidal components of frequencies

If \/w >> 1 (the case in which we shall be interested in practice) the
terms in the series (40) beyond m = X\/w are negligible; this follows
from known properties of the Bessel functions. In this case the
frequencies lie in the range

which agrees with the result arrived at from the idea of instantaneous
frequency. On the other hand, suppose we make X so small that
A/w K1. Then (40) becomes to a first order

so that the frequencies w,, w, +, we — w are present in the pure
frequency modulated wave.

It is possible to generalize the foregoing and build up a formal
steady-state theory by supposing that

On this assumption, it can be shown that the frequency modulated
wave (38) is expressible as

Formulas (42) and (43) are purely formal and far too complicated
for profitable interpretation. Consequently this line of analysis will
not be carried farther.‘

If we compare the pure frequency modulated wave, as given by (38),
with the pure amplitude modulated wave, as given by (39), it will be
observed that, in the latter, the low frequency signal s(¢), which is
ultimately wanted in the receiver, is explicit and methods for its
detection and recovery are direct and simple. In the pure frequency
modulated wave, on the other hand, the low frequency signal is
implicit; indeed it may be thought of as concealed in minute phase or
frequency variations in the high frequency carrier wave.

t
exp ( ive f sit) (45)
0
is still a pure frequency modulated wave. The second term,
t
As(0)-exp ( sdt ), (46)
0

is a “‘hybrid”’ modulated wave, since it is modulated with respect to
both amplitude and frequency. The important point to observe is
that, by differentiation, we have ‘‘rendered explicit’’ the wanted low
frequency signal. We infer from this that the detection of a pure
frequency modulated wave involves in effect its differentiation. The
process of rendering explicit the low frequency signal has been termed
“frequency detection.”” Actually it converts the pure frequency
modulated wave into a hybrid modulated wave.

Every frequency distorting transducer inherently introduces fre-
quency detection or ‘‘hybridization”’ of the pure frequency-modulated
wave, as may be seen from formula (16). The transmitted current is
conveniently written in the form

In passing it is interesting to compare the distortion, as given by
(47), undergone by the pure frequency-modulated wave, with that suf-
fered by the pure amplitude-modulated wave (39), in passing through
the same transducer. The transmitted current corresponding to the

In this section we consider the recovery of the wanted low frequency
signal s(t) from the frequency-modulated wave. This involves two
distinct processes: (1) rendering explicit the low frequency signal
‘“implicit’’ in the high frequency wave; that is, ‘‘ frequency detection”’
or ‘“‘hybridization”’ of the high frequency wave; and (2) detection
proper.

suppose that the transducer proper is equalized in the neighborhood of
the carrier frequency ,; that is,

Frequency detection is then effected by a terminal network. We
therefore take as the over-all transfer admittance

y(iw) represents the terminal receiving network; it is under control and
can be designed for the most efficient performance of its function. As
we shall see, it should approximate as closely as possible a pure reactance.
Taking the over-all transfer admittance as (51), we have from (47),

Inspection of (52) shows that the terms beyond the second simply
represent distortion. The terminal network or frequency detector
should be so designed as to make the series

rapidly convergent from the start. In fact the ideal frequency de-
tector is a network whose admittance y(iw) can be represented with

Supposing that this condition is satisfied, the wave, after passing
over the transducer and through the terminal frequency detector, is
(omitting the constant y- Y)

If y is a pure reactance, w; is a pure real; due to unavoidable dissi-
pation it will actually be complex. To take this into account we
replace w; in (54) by w,e~** where now a; is real; (54) then becomes

Now let A/w; be less than unity and let the wave (55) be impressed on
a straight-line rectifier. Then the rectified or detected output is

The second term is the recovered signal and the third term is the first
order non-linear distortion.

Inspection of the foregoing formulas shows at once that, for detection
by straight rectification, the following conditions should be satisfied:

(1) /w: must be less than unity.
(2) The terminal network should be as nearly as possible a pure
reactance to make the phase angle a as nearly zero as possible.

(3) To minimize both linear and non-linear distortion it is necessary
that the sequence
\3

The first term of (58) is simply direct current and has no significance
as regards the recovered signal. When we come to consider the
problem of noise in the next section, we shall find that its elimination is
important. This can be effected by a scheme which may be termed
balanced rectification. Briefly described the scheme consists in termi-
nating the transducer in two frequency detectors y; and ye in parallel;
these are so adjusted that yi(iw.) = — ye(iwe) and dy;/dw, = dy2/dw..
w, is therefore of opposite sign in the two frequency detectors. The
rectified outputs of the two parallel circuits are then differentially
combined in a common low frequency circuit. Corresponding to (58),
the resultant detected output is

This arrangement therefore eliminates first order non-linear distortion,
as well as the constant term.

Rectification is the simplest and most direct mode of detection of
frequency-modulated waves. However, in connection with the problem
of noise reduction other methods of detection will be considered.

As a specific example of the foregoing let the terminal frequency
detector, specified by the admittance y(iw), be an oscillation circuit
consisting simply of an inductance L in series with a capacitance C.

then the combined rectified output of the two parallel circuits is
proportional to

Thus the constant term and the first order distortion are eliminated
in the low frequency circuit.

The most important advantage known at present of frequency-
modulation, as compared with amplitude-modulation, lies in the possi-
bility of substantial reduction in the low frequency noise-to-signal
power ratio in the receiver. Such reduction requires a correspondingly
large increase in the width of the high frequency transmission band.
For this reason frequency-modulation appears to be inherently
restricted to short wave transmission.

In the discussion of the theory of noise which follows, it is expressly
assumed that the high frequency noise is small compared with the high
frequency signal wave. Also ideal terminal networks, filters and
detectors are postulated.

In view of the assumption of a low noise power level, the calculation
of the low frequency noise power in the receiver proper can be made to
depend on the calculation of the noise due to the typical high fre-

Corresponding to the noise element (60), the output of the ideal
frequency detector is

occurs so frequently in the analysis which is to follow, it is convenient
to adopt the notation
Qn, = wn — As(t),

With this notation and on the assumption that A, <1 and «, real,
the amplitude of the wave (61) is

In this formula the argument of the cosine function should be
strictly
t
f + On.
0

The phase angle @, is random however and does not affect the final
formulas; it may therefore be omitted at the outset. Consequently,
if the wave (61) is passed through a straight line rectifier, the rectified
or low frequency current is proportional to

The first term is the recovered signal and the second term the low
frequency noise or interference corresponding to the high frequency
element (60).

Now the wave (63), before reaching the receiver proper, is transmitted
through a low-pass filter, which cuts off all frequencies above wa; wa is
the highest essential frequency in the signal s(t). Consequently, in
order to find the noise actually reaching the receiver proper, it is

necessary in one way or another to make a frequency analysis of the
wave (63). This is done in Appendix 2, attached hereto, where
however, instead of dealing with the special formula (63), a more
general expression

is used for the low frequency current. This will be found to include,
as special cases, several other important types of rectification, as well
as amplitude limitation, which we shall wish to discuss later.6 Then,
subject to the limitation that the noise energy is uniformly distributed
over the spectrum, it is shown in Appendix 2 that

These formulas are quite important because they make the calcula-
tion of low frequency noise-to-signal power ratio very simple for all the
modes of frequency detection and demodulation which we shall discuss.
Applying them to formula (63) we find for straight line rectification

It is known that in practice >> \’s? and >> w.2. Consequently
in the factor + w? + the largest term is Therefore
it is important, if possible, to eliminate this term. This can be
effected by the scheme briefly discussed at the close of section III;
parallel rectification and differential recombination. For this scheme
the low frequency current is found to be proportional to

Consequently, for parallel rectification and differential recombination,

6 The formula is also general enough to include detection by a product modulator,
which however is not discussed in the text as no advantage over linear rectification
was found.

Here, in the factor (4w,? + d*s), the term 42s? is predominant. The
elimination of the term w,? has resulted in a substantial reduction in
the noise power.

Returning to the general formula (66) for Py, it is clear, that, if in
addition to eliminating the term w,*, the parameter v = yw/A can be
made equal to — 1, the noise power will be reduced to its lowest
limits:

This highly desirable result can be effected by amplitude limitation,
the theory of which will now be discussed.

When amplitude limitation is employed in frequency-modulation,
the incoming high frequency signal is drastically reduced in amplitude.
If no interference is present this merely results in an equal reduction
in the low frequency recovered signal which is per se undesirable.
When, however, noise or interference is present, amplitude limitation
prevents the interference from affecting the amplitude of the resultant
high frequency wave; its effect then can appear only as variations in
the phase or instantaneous frequency of the high frequency wave. To
this fact is to be ascribed the potential superiority of frequency-
modulation as regards the reduction of noise power. This superiority
is only possible with wide band high frequency transmission; that is,
the index of frequency-modulation \ must be large compared with the
low frequency band width wa. Insofar as the present paper is con-
cerned, the potential superiority of frequency-modulation with ampli-
tude limitation is demonstrated only for the case where the high fre-
quency noise is small compared with the high frequency signal wave.

added the typical noise element A, exp (tw. + twat + 6,), the re-
sultant wave may be written as

Postulating that A, <1 and therefore neglecting terms in A,’,
the real part of (71) is

If this wave is subjected to amplitude limitation, the amplitude
variation is suppressed, leaving a pure frequency-modulated wave,
proportional to the real part of

(but drastically reduced in amplitude).
After frequency detection the wave (73) is, within a constant,

This is the amplitude of the low frequency wave after rectification; it is
obviously proportional to

which is a special case of (64) and may be used in calculating the
relative signal and noise power’with amplitude limitation. Hence we

(These are, of course, relative values and take no account of the
absolute reduction in power due to amplitude limitation.)

Comparing (78) with (68) it is seen that, for detection by straight line
rectification, the ratio of the noise power with to that without amplitude
limitation is

Since in practice w; >> w, and \ > w,, amplitude limitation results in a
very substantial reduction in low frequency noise power in the receiver
proper. Reference to formula (70) shows that, as compared with
parallel rectification and recombination, amplitude limitation reduces
the noise power by the factor
1

It should be observed that without amplitude limitation little reduc-
tion in the noise-to-signal power ratio results from increasing the
modulation index A (and consequently the high frequency transmission
band width). On the other hand, with amplitude limitation, the ratio
p of noise-to-signal power is

The ratio p is then (within limits) inversely proportional to the
square of the modulation index X, so that a large value of } is indicated.
It should be noted that, within limits (A < w,), the power transmitted
from the sending station is independent of the modulation index \.

It might be inferred from formula (82) that the noise power ratio p
can be reduced indefinitely by indefinitely increasing the modulation
index \. Actually there are practical limits to the sizeof \. First, if
is made sufiliciently large, the variable frequency oscillator generating
the frequency-modulated wave may become unstable or function
imperfectly. Secondly, the frequency spread of the frequency modu-
lated wave is 2\ (from w, — \ to w, + A) and, if this is made too large,
interference with other stations will result. Finally, the stationary
distortion of the recovered low frequené¢y signal s(t) increases rapidly
with the size of X.

To summarize the results of the foregoing analysis the potential
advantages of frequency-modulation depend on two facts. (1) By
increasing the modulation index it is possible to increase the recovered
low frequency signal power at the receiving station without increasing
the high frequency power transmitted from the sending station.
(2) It is possible to employ amplitude limitation (inherently impossible
with amplitude-modulation) whereby the effect of interference or noise
is reduced to a phase or ‘‘instantaneous frequency” variation of the
high frequency wave.

Formula (40) et sequa establish the fact that the actual frequency of
the wave (29) varies between the limits

provided s(t) is a pure sinusoid \ sin wt and A>>w. This agrees with the
concept of instantaneous frequency.

When s(t) is a complex function—say a Fourier series—the frequency
range of W can be determined qualitatively under certain restrictions, as
follows:

The Fourier formulation is supposed to be valid in the epoch 0 = ¢ = T
and T can be made as great as desired. Then

T
sdt
| Jo
becomes very large compared with 27. On this assumption, it follows
from the Principle of Stationary Phase, that, for a fixed value of w, the

important contributions to the integral (3a) occur for those values of
the integration variable ¢ for which

Consequently the important part of the spectrum F(iw) corresponds
to those values of w in the range

Therefore the frequency spread of W lies in the range from w, + ASmin
to We + MSmax or We + if Smax Smin =

- where w, is the carrier frequency and s = s(t) is the low frequency co
signal. dis areal parameter, which fixes the amplitude of the frequency
spread.
7 Correspondingly, we take the typical noise element as
Anos ((we + + On). (2b)
es For reasons stated in the text, we take the more general formula for es
he the low frequency current as proportional to
be
in

where wo, A, wu are real parameters. The term As is the recovered signal
and the second term is the low frequency noise corresponding to the
high frequency noise element (25).

We suppose that the noise is uniformly distributed over the frequency
spectrum, at least in the neighborhood of w = w,, so that, corresponding
to the noise element
A, COS (Wat + On),

and the corresponding noise power for the frequency interval w; < w, < we
is, by the Fourier integral energy theorem,

The Fourier integral energy theorem states that, if in the epoch
0 = t= T, the function f(t) is representable as the Fourier integral

Replacing (46) by (5d) to take care of the distributed noise, the
noise term of (3b) becomes

Now this noise in the low frequency circuit is passed through a low
pass filter, which cuts off all frequencies above ws. wa is the maximum
essential frequency in the signal s(¢).

It is therefore necessary to express (9b) as a frequency function
before calculating the noise power. To this end we write the Fourier
integrals

Substituting (10d), (115), (12d) and (13d) in (96) and carrying
through straightforward operations, we find that the noise is given by

7See ‘‘Transient Oscillations in Electric Wave Filters,’ Carson and Zobel,
B.S. T. J:, July, 1923.

The limits of integration of w, are determined by the fact that,
w — w, in the first integral of (146) and w + w, in the second, must
lie between + w,; all other frequencies are eliminated by the low
pass filter.

From formula (145) and the Fourier integral energy theorem, the
noise power Py is given by

+ [(wo — (1 + v)w)? + (180)
where vp =
Replacing F,? and F,,? in (18b) by their values as given by (15d)
and (16b), we get

Here, for convenience, we have replaced N?/x? of (196) by N?, so that
N? of (23) may be defined and regarded as the high frequency noise
power level.

It remains to establish formulas (200), (21) and (226). From the
defining formulas (105) and (11b) and the Fourier integral energy
theorem, we have

Adding we get (20d).
Now differentiate (10) and (11) with respect to ¢ and apply the
Fourier integral energy theorem; we get

57-64, Feb, 1922
Frequenzmodulation,” Telefunken-Zeitung, 10, pp. 48-54,
lec., 192
Heilmann, A., ‘Einige zum der Frequenzmodulation,”’
Elek. Nach. Tech., 7, pp. 217-225, June, 1930.
B., “Frequency Modulation,” Proc. I. R. E., 18, pp. 1194-1205,
uly, 1 4
. Eckersley, T. L., ‘“‘Frequency Modulation and Distortion,” Exp. Wireless and
Wireless Engg., 7, pp. 482-484, Sept., 1930.
" Runge, W., “Untersuchungen an amplituden- und frequenz-modulierten Send-
ern, ' Elek. Nach. Tech., 7, pp. 488-494, Dec., 1930.
Roder, H., “‘Amplitude, Phase and Frequency- Modulation,” Proc. I. R. E., 19,
pp. 2145- 2173, Dec., 1931.
. Andrew, V. J., “The Reception of Sey Modulated Radio Signals,” Proc.
I. R. E., 20, pp. 835-840, May, 1932.
. Barrow, W. L., ‘Frequency Modulation and the Effects of a Periodic Capacity

. Barrow, W. te “On the Oscillations of a Circuit Having a Periodically Varying
Capacitance; Contribution to the Theory of Nonlinear Circuits with -—-
Applied besa Proc. I. R. E., 22, pp. 201-212, Feb., 1934, also M. I. T.
Serial 97, Oct., 1934.

Armstrong, Kicthod of Reducing Disturbances in Signaling by
i930 of Frequency- Modulation,” Proc. I. R. E., 24, p 689-740, ay,
1

Irregularities in Broad-Band Wire Transmission Circuits
By PIERRE MERTZ and K. W. PFLEGER

The effects of inhomogeneities along the length of a wire trans-
mission circuit are considered, affecting its use as a broad-band
transmission medium. These inhomogeneities give rise to reflec-
tions of the transmitted energy which in turn cause irregularities
in the measured sending or receiving end impedance of the circuit
in its overall attenuation, and in its envelope delay. The irregu-
larities comprise departures of the characteristic from the average,
in an ensemble of lines, or departures from a smooth curve of the
characteristic of a single line when this is plotted as a function
of frequency. These irregularities are investigated quantitatively.

IRE transmission circuits in their elementary conception are
considered as perfectly uniform or homogeneous from end to
end. Actually, of course, they are manufactured in comparatively
short pieces and joined end to end, and there is a finite tolerance in the
deviation of the characteristics of one piece from those of the next and
also from one part of the same piece to another. A real transmission
circuit therefore has a large number of irregularities scattered along its
length which reflect wavelets back and forth when it is used for the
propagation of a signal wave. When a cable pair, coaxial conductor,
or similar medium is used for broad-band transmission it is important
to know how these irregularities influence the transmission character-
istics of the medium.

The transmission characteristics which will be studied are the im-
pedance, the attenuation, the sinuosity of the attenuation (to be
defined), and the delay distortion. The derivations for the first two
characteristics parallel substantially those published by Didlaukis and
Kaden (ENT, vol. 14, p. 13, Jan., 1937). They are set forth here for
completeness of presentation because the steps in them illustrate the
more complicated steps in the derivation of the last two characteristics.

When the characteristic impedance changes from point to point, its
variation from the average characteristic impedance for the whole
length of conductor forms the irregularities which produce reflections.
Assume that successive discrete elementary pieces of the circuit are
homogeneous throughout their length, that the lengths of these ele-
mentary pieces are equal throughout the length of the whole circuit,
and that there is no correlation between the deviations from average

characteristic impedance of any two elementary pieces. This repre-
sents a first approximation to the problem. It is fairly accurate for
pairs in ordinary cable in which the outstanding irregularities are devia-
tions, from the average, between whole reel lengths; and in which the
lengths of the successive: spliced pieces (reel lengths) are at least
roughly the same.

There are irregularities in some coaxial conductors in which the
impedance change is gradual rather than abrupt from one element to
the next, and in which the elements can vary in length along the line.
For these cases the approximation is a little over-simplified. However,
although this somewhat affects the echo wavelets as computed from
the impedance deviations along the line, Didlaukis and Kaden, as
referred to above, have shown that it does not affect the ratio between
the echo wavelets, suitably averaged, reaching the receiving end and
those, similarly averaged, returning to the sending end.

With the above assumptions there will be some correlation between
the reflections at the two ends of an elementary length. If, for
example, this length happens to be high in characteristic impedance the
reflection at one end will tend greatly to be the negative of that at the
other end. For this reason we are going to break up the reflection into
two parts, at a point between any two successive elementary lengths of
circuit—one part from one length of the circuit to an infinitesimal
length of cable of average characteristics inserted between the two
elementary lengths—and the other from this infinitesimal piece to the
next elementary length of circuit. There is then 100 per cent correla-
tion between the reflections at the two ends of a given elementary
length (one being exactly the negative of the other); but there is no
correlation between the reflections from any one elementary length to
its adjacent infinitesimal piece of average cable, and the reflections
from any other elementary length to its adjacent piece. This same
treatment is used in the calculation of certain types of “reflection”
crosstalk.

The departure in characteristic impedance in the usual transmitting
circuit in the higher frequency range, where the irregularities are most
important, results essentially from deviations in the two primary con-
stants of capacitance and inductance, each per unit length. There isa
certain correlation between these, inasmuch as the capacitance devia-
tion is contributed to both by differences in the dielectric constant of
the insulation and by differences in the geometrical size, shape, and
relative arrangement of the conductors; and the inductance deviation
is contributed to by the latter alone. If there were no deviation in
dielectric constant there would be no deviation in velocity of propaga-

tion (phase or envelope), which (at the higher frequencies) is inversely
proportional to the square root of the product of the capacitance by the
inductance. Consequently the portion of the fractional deviation in
capacitance which is due to geometrical deviations correlates with an
equal and opposite fractional deviation in inductance. Since in prac-
tice the contribution from the geometrical deviation is apt to be
dominating, that due to the variation in dielectric constant will be
neglected and the above correlation assumed as 100 per cent.

The standard deviation of the capacitance of the successive ele-
mentary lengths, as a fraction of the average capacitance, will be
designated as 6.

The secondary constant of the line most affected by these irregulari-
ties is the sending end (or similarly receiving end) impedance. If we
consider a large ensemble of lines of infinite length of similar manufac-
ture (and equal average characteristics and 6) but in which the indi-
vidual irregularities are uncorrelated, then the sending end impedances
of these lines, measured at a given frequency, also form an ensemble.
The standard deviation of the real parts in this latter is VAK2, and
that of the imaginary parts VAK?.

In general, the departure in the impedance of one individual line
from the average will vary with frequency; and perhaps over a moder-
ate frequency range a sizeable sample can be collected which is fairly
typical of the ensemble of the departures at a fixed frequency in the
interval. If this is the case, and if at the same time the average im-
pedance varies smoothly and slowly with frequency, and the standard
deviation of the ensemble of departures also varies smoothly and
slowly with frequency, then the standard deviation of the sample of
departures over the moderate frequency interval is substantially equal
to that of the ensemble of departures at a fixed frequency in this inter-
val. (It is clear that this disregards exceptional lines in the ensemble,
characterized by regularity in the array of their capacitance deviations,
for which these conditions do not hold.) Under the circumstances
where this observation is valid it makes it possible to correlate measure-
ments on a single line, provided it is not too exceptional, with theory
deduced for an ensemble.

The irregularities in the transmission line will also affect its attenua-
tion. If again we consider an ensemble of lines and measure the at-
tenuation of each at a given frequency these attenuations will also
form an ensemble.

It will be found in this case, as will be demonstrated further below,
that the average attenuation is a little higher than that of a single
completely smooth line having throughout its length a characteristic

impedance equal to the average of that for the irregular line. This
rise varies slowly with frequency. The standard deviation of the at-
tenuation will also include not only the effect of the reflections which
we have been considering but in addition one caused by the fact that
the attenuations of the successive elementary pieces are not alike, and
hence their sum, aside from any reflections, will also show a distribu-
tion. This additional contribution will vary only very slowly with
frequency. The standard deviation will be VAA? + AAg? where A
represents the losses in the total line, the subscript 1 indicates the con-
tribution due to the reflections, and the subscript 2 that due to the
distribution of the individual attenuations.

The same observation may be made about the attenuation that was
made about the terminal impedance, as regards measurements made
at one frequency on an ensemble of lines and measurements over a
range of frequencies on one line; except that the contribution to the
deviation caused by the distribution of individual attenuations varies
so slowly with frequency that on each individual line it will look like a
displacement from the average attenuation, over the whole frequency
range. For the purposes of the present paper only the contributions
from the reflections will be computed.

When this information on irregularities is being used by a designer of
equalizers he is interested in two characteristics: first, how far each
attenuation curve for a number of lines will be displaced as a whole
from the average; and second, how “wiggly”’ each individual curve is
likely to be. While the observations above give the general amplitude
of the latter they do not tell how closely together in frequency the
individual “‘wiggles’’ are likely to come. To express this, the term
“sinuosity’”’ has been defined as the standard deviation of the difference
in attenuation (for the ensemble of lines) at two frequencies separated
by a given interval Af. By the previous observations this can be
extended to the attenuation differences for successive frequencies
separated by the interval Af, for a range of frequencies in a single line.

When the transmission line is used for certain types of communica-
tion, notably for telephotography or television, it is important to
equalize it accurately for envelope delay as well as attenuation. The
envelope delay is defined as

where @ is the phase shift through the line and w is 27 times the fre-
quency. For an ensemble of lines, the envelope delay at a given
frequency will also form an ensemble, the standard deviation of which

the same standard deviation also holds for the envelope delay depar-
tures over a range of frequencies on one line.

Let Fig. 1 represent a line of the type we have been discussing.
The successive n’s represent the reflection coefficients between succes-
sive elementary pieces of line. As mentioned before, to avoid correla-
tion, each 7 is broken up as shown into two h’s, representing reflections
between the elementary pieces and infinitesimal lengths of average
line.

The main signal transmission will flow as shown by the arrow a in
Fig. 1. In addition there will be single reflections as shown by the
arrow b. Following the assumptions we have set up, this really con-
sists of two reflections from infinitesimally separated points. Further
there will be double reflections, that is reflections of reflections, as
shown byc. Here again each reflection point, according to our assump-
tions, consists of two infinitesimally separated ones. There will be a
variety of double reflections according to the number of elementary
lengths between reflection points. Finally there will be triple, quad-
ruple and higher order reflections which are not shown. The wave
amplitude after reflection is cut down by the reflection coefficient.
Consequently, even though there are more of them, the total of any
given higher order reflections can always be made smaller than that of
lower order reflections by a small enough reflection coefficient. We
will here study only small reflection coefficients and therefore neglect
all reflections of higher order than needed to give a finite result. For
effects on the impedance this means neglect of all but first-order reflec-
tions. For the other effects studied it means neglect of all but first- and
second-order reflections.

The reflection coefficient between two successive impedances (one
being K), is, approximately

Following our earlier assumptions, namely that the principal cause of
impedance departures lies in geometrical irregularities, and that these
may be expressed in terms of capacitance departures,

K Cc 2C
Consequently the reflection coefficients are real, namely, they intro-
duce no phase shifts other than 0 or z in the reflections.

The irregularities in sending-end impedance have been computed in
Appendix I from the single reflections of the type } in Fig. 1. The

where ¢ is the phase shift in radians in two elementary lengths, « is
the attenuation in nepers of two elementary lengths, and 4 is, as men-
tioned before, the standard deviation in C measured as a fraction of C.
It will be noted that as a consequence of the single reflections, the ir-
regularities in impedance vary as the first power of 6.

The irregularities in attenuation have been computed in Appendix II
from the double reflections of the type c in Fig. 1. It is found, as
mentioned before, that there is a net rise in average attenuation caused
by the reflections, equal, in nepers, to

where n is the number of elementary lengths in the total line. Con-
sidering the factor in parentheses in the expression above, although the
term ¢€ is not usually wholly negligible compared with the term ¢?/2,
nevertheless the latter is dominating and sets the order of magnitude
of the factor. If the ¢ is disregarded, the expression can easily be put
in terms of the impedance irregularities, giving

where A as before represents the loss in the total line.
The standard deviation in the loss in nepers, when finally simplified,
is, for the reflections,
252
VAA 2 = e

It will be noted that these irregularities in the attenuation vary with
the square of 5, or the square of the impedance irregularities. This is a
consequence of the double reflections, and will continue to hold for the
sinuosity and irregularities in envelope delay. It will also be noted

that in this form the equation is independent of ¢, ¢, and n. It is in
this case that Didlaukis and Kaden found that the result is independent
of whether the reflection points are sharp and equally spaced or not.

The sinuosity has been computed in Appendix III. When finally
simplified and measured in nepers, it amounts to

— = — Af. 9
1 1) 2683/2 df ( )
Expressed in terms of the impedance irregularities this amounts to
[SEY
(AA; — AA)? = —— | ——Af, 10

where T is, as mentioned before, the envelope delay of the whole line,
in seconds.

In computing the above it is only the components of the echoes which
are in phase (or 7 radians out of phase) with the main transmission
which affect the results. If the echo components at right angles to
the main transmission are considered, they will give phase shifts in
the resultant signal wave. Further, an echo component whose ratio
to the main transmission is x will, when z radians out of phase with it,
give a loss of x nepers; and when at right angles to it, a phase shift of x
radians. Now the distribution of echo components in phase (or 7
radians out of phase) with the main transmission is substantially the
same as that of components at right angles to it. Consequently the
sinuosity is also numerically equal to the standard deviation of the
difference in phase shifts at two frequencies separated by the given
interval Af. Therefore if the interval is called Aw/2m and the resulting
numerical value of the sinuosity is divided by Aw it will give the
standard deviation of the envelope delay. This is

The quantity which has been used in considering the suitability of a
line from a delay standpoint for transmitting pictorial signals is its
envelope delay distortion, or maximum departure in delay each way
from a fixed average in the frequency band studied. If we make the
usual assumption that the maximum departure ordinarily met (strictly
speaking, except in about 3 cases out of 1000) is three times the
standard deviation, then the delay distortion contributed by the ir-
regularities is + 3 times the expression given in equation (11).

Expressed in more usual units, the results given in equations (6),
(8), (10), and (11) are repeated here.
AK,? |
aL,

VAR? 2
Sinuosity (db per kilocycle) = 0.0256 | » (10’)
K Va
VAK2 12 IF
Delay distortion (microseconds) = + 4.42 | (11’)
K Va
where L = length of the line in miles,
a = attenuation of the line in db per mile,
7 = envelope delay of the line in microseconds per mile.

In order to convey a notion as to possible orders of magnitude of
these effects of irregularities, and how they vary with changes in the
parameters, a few calculations have been tabulated below for some
hypothetical lines.

In Fig. 1 the circuit is divided into » homogeneous elementary
lengths. For a current of unit value traveling down the circuit at the
junction of the kth and (k + 1)th elementary lengths, the reflected

where hi, denotes the reflection coefficient (assumed to be a real number)
between the impedance of the kth elementary length and the average
impedance.

However, if the current starts with unit value at the sending end,
then the wave has to be multiplied by the factor e~*?’? in reaching the
point of reflection, where P is the propagation constant per two ele-
mentary lengths. In returning to the sending end the reflected wave
is again multiplied by a like amount so that its value on arrival there
becomes

When 1 is large, it is permissible to use the assumption that k has «
for its upper limit in the above summation. The real part of EF, is
accordingly

Then, replacing « and neglecting higher-order terms in ¢ and «,
which are small, and putting h? = 6°/4, equations (7) and (8) become

The echo Ey affects the measured impedance. If unit voltage is
impressed in series with the line, and a network having impedance K,
the current flowing, not counting the echoes, is 1/2K. The echo cur-
rent is then (E,/1)(1/2K), and the total current

For K, the real part only is to be used as it is assumed that the
imaginary part is negligible in comparison with it. Where departures
from K are considered, however, this imaginary part may not be negli-
gible in comparison with the departures.

The following is a derivation of the standard deviation of the real
part of the echo currents (which are received in phase with the direct
transmission) over a circuit such as has been assumed in Appendix I,
Accordingly, the reflected wave at the junction of the kth and (& + 1)th
homogeneous elementary lengths, for a current of unit value traveling
down the circuit at this point, is:

This wave returns toward the sending end and in turn suffers partial
reflections. Consider this secondary reflection at the point between
the jth and (j + 1)th lengths where j = k. The wave arriving at the
point in question is

so that the wave which starts back from this point in the same direction
as the original wave is:

In traveling to the junction of the kth and (k + 1)th lengths it is
again multiplied by e~?“-»/? so that the echo which is joined to the
unit wave is therefore given by

When m = 0, a slightly different treatment is necessary. Let the
circuit be represented as in Fig. 1.

A unit current traveling down the circuit will suffer a reflection loss
at each junction so that the current passing through the junction is
(1 — n;) times the current entering. The ratio of the current received

where the double reflected echoes of the previous type (m > 0) are
omitted. The echo which is joined to the unit wave when m = 0 is

Ba = {5 (hi — cos ms, (15)
j=0
assuming h’s may be taken as real and as having a symmetrical distri-
bution curve about zero, the square of whose standard deviation may be
denoted by h?.
We will consider the distribution curve of H,, which also is real.
The average value of a function H(h) in a given distribution is equal to

the integral of the product of the function by the frequency of occur-
rence for each value of it, divided by the integrated frequency of oc-
currence alone. The frequency of occurrence of individual values of
the function is the same as that of the corresponding values of its
argument, and hence can be written as F(h)dh where F(h) is the distri-
bution function of the variable h. The average value of H, is therefore

Considering the four products j4m, jht and
it will be seen that they all integrate to zero by virtue of symmetry

The average value of E., is equal to the sum of the average values of
its terms. Applying the results for Ho, Hi, and H,, we obtain

Multiplying the factors containing the h's as indicated in (30) gives
terms containing hehsh-ha where the subscripts denote some integer
such as the value for p, p+ 1, p+ 7, etc. When

there is equality among subscripts so that the terms become h,2h,? or
hw* the integration gives (h)? or h‘, respectively. However, if such
equality does not exist, or if one of the subscripts is zero or m + 1, the
integration gives zero. By integrating term by term in the manner
above indicated, adding the results, and finally thereafter putting
r = mands = m, the following result is obtained:

If the distribution of the h’s is assumed to be a normal distribution,
then:
h* = 3(h?)?. (32)

When 1 is large, it is permissible to use the assumption that m has «
for its upper limit in the above summations. It is likewise permissible
to neglect terms in the result which do not contain the factor n.
Accordingly,

The echo current which is joined to the unit received wave affects
the final resultant and therefore the effective loss of the line. From
equation (28), neglecting higher-order terms, the attenuation of the
whole line is increased (in nepers) by

The standard deviation of the attenuation (A, in nepers), from equa-
tion (34) and neglecting higher order terms, is

Sinuosity
The following is a derivation of the sinuosity of the attenuation,
defined as the standard deviation of the difference A(f + Af) — A(f).
Here A(f) is the loss in the circuit at the frequency, f.
For practical purposes, the difference of the expression E., — E.
at two discrete frequencies is

whose standard deviation will be derived below. From values of E.,
and £,, given in Appendix II we obtain

By expanding S in powers of ¢ and ¢, and neglecting those higher
than needed to give a finite result, it is found that

ev? + D?
S = —>—.— (Af). 14
(4f) (14)
In general, D is negligible compared to Q and the sinuosity is
(aa AA)? = OG (15)

EN years have elapsed since the opening to public use on January
7, 1927, of the first long distance radio telephone circuit. This
form of intercontinental communication has now come into practical
business and social use. A network of radio circuits interconnects
nearly all the land wire telephone systems of the world. The art has
passed through the pioneering stage and is well into a period of growth.
The technical side of this development, which the present paper
reviews, divides naturally into four categories. The first covers those
factors which made possible the beginning of commercial radio tele-
phony.' In the second are the things without which its rapid growth
and wide expansion could not have occurred. In the third, are a few
incidental but interesting or valuable technical features. The fourth
considers future improvements now in view.

Radio telephony presents difficulties in addition to those existing in
radio telegraphy because: (1) The communication is two-way, and the
radio system must be linked in with the wire telephone systems and
available to any telephone instrument; (2) The subscriber cannot
deliver himself of his message until the connection is actually estab-
lished, and on this account delay due to unfavorable transmission con-
ditions is less tolerable; (3) The grade of transmission required to
satisfy the average telephone user is higher than that tolerable in aural
tone telegraph reception by an experienced operator.

These requirements emphasized the need for accurate and quantita-
tive knowledge of radio transmission performance as a basis for en-
gineering radio telephone systems. There was at the same time a
similar need for transmission data in the engineering of early radio
broadcast installations. The effort brought to bear on these twin prob-
lems resulted in the development of practical field methods of measuring

* Digest of a paper presented at the Spring Convention of the Institute of Radio
a New York, May 10, 1937, and published in full in Proc. I. R. E., September,
; 1A description of the early years of radio telephone a preceding exten-
sive commercial application, together with a discussion of the origins of the whole

art, will be found in companion paper “The Origin and Development of Radio
Telephony,” by Lloyd Espenschied, published in Proc. I. R. E., September, 1937.

radio signal strength and radio noise. The employment of long dis-
tance radio telephony in commercial use was preceded by experimental
operation and tests which gave a considerable fund of statistical in-
formation covering the cyclical changes characteristic of overseas radio
transmission.

The realization that a relatively high degree of reliability was essen-
tial to success discouraged any attempt at commercial service until
high-power transmission on a practical basis was assured by the inven-
tion of a method of making water-cooled tubes.

In searching for the most efficient way of applying the power made
available by water-cooled tubes telephone engineers were led to the
employment of a method which had already been successfully used in
- high-frequency wire telephony. This method, now well known to
radio engineers, is called single-sideband suppressed-carrier transmis-
sion. As compared with the ordinary modulated carrier transmission,
it increases the effectiveness of a radio telephone system by about 10
to 1in power. This accrues partly because none of the power capacity
of the transmitter is used up in sending the non-communication bearing
carrier frequency and partly because the narrower band width permits
greater selectivity and noise exclusion at the receiver.

A very important final element was also necessary to prevent voice-
frequency singing through residual unbalances and around the entire
radio link when wire circuits and radio channels are connected together.

Recourse was again had to a device newly worked out for wire
telephone transmission. By associating together and electrically inter-
locking several of the voice current operated switching devices which
had been developed for suppressing echoes on long wire lines, an ar-
rangement now commonly known as a “vodas’’? was developed.
When the subscriber talks, his own speech currents, acting on the
vodas, cause it to connect the radio transmitter to the wire line and at
the same time to disconnect the radio receiver. When the same sub-
scriber listens the connection automatically switches back to the re-
ceiver. No singing path ever exists. The amplification in the two
oppositely directed paths can be adjusted substantially independently
of each other, and constant full load output from the radio transmitters
is secured. With this device it became possible to connect almost any
telephone line to a radio system and to adjust amplification so that a
weak talker over a long wire line could operate the radio transmitter as
effectively as a strong local talker.

2 This word, ‘‘vodas,” is synthesized from the initial letters of the words “ voice-
operated device, anti-singing.”

The first long distance radio telephone circuit operated (and it still
operates) between the United States and England with long-wave
transmission at about 5000 meters. We did not then, and we do not
today, know how any considerable amount of intercontinental radio
telephony could have been accomplished with circuits of this kind.
The frequency space available in the long-wave range would accom-
modate comparatively few channels. The high attenuation to over-
land transmission and the high noise level at these wave-lengths pre-
clude their satisfactory use for very great distances or in or through
tropical regions. The discovery that short waves could be transmitted
to the greatest terrestrial distances and could be satisfactorily received
in the tropics came at a most opportune time.

Short-wave transmission not only released the limitations on distance
and location inherent to long waves but also opened up such a wide
range of frequency space as to give opportunity for an extensive growth
in numbers of both radio telegraph and radio telephone circuits. Short
waves further encouraged the growth of radio telephony by making it
cheaper. Thus, it became possible to make directive antenna struc-
tures of moderate size which increased the effectiveness of transmission
many times, thereby reducing the transmitter power required for a
given reliability of communication. Short waves were the indis-
pensable element without which material growth could not have oc-
curred, but there were other significant things.

An important desideratum in telephony is privacy. Commercial
radio telephony would have been severely hampered if privacy systems
had not been developed to convert speech into apparently meaningless
sounds during its radio transit.

Another item of great aid in promoting growth was the development
of methods of accurate stabilization of transmitted frequencies. The
first effect of this was to eliminate the extreme distortion which charac-
terized early short-wave telephone transmission and which was found
to be due to parasitic phase or frequency modulation effects in the
transmitters. As the number of radio communication facilities, both
telegraph and telephone, grew, accurate stabilization of frequency be-
came a necessity in order to permit effective utilization of the available
frequency space without mutual interference between stations.

The ‘rhombic’ antenna is mechanically simple and electrically
nearly aperiodic, covering a wide wave-length range efficiently. It

has radically changed the character of the physical plant and invest-
ment necessary to the employment of directivity in short-wave
transmitting and receiving.

In Hawaii and the Philippines on circuits to the United States the
“‘diversity’’ method of reception is used wherein three individual
separated antennas and receivers with interlocked automatic gain
controls are combined to produce a common output having less distor-
tion and noise than a single receiver.

The effects of distortion in short-wave circuits are avoided to some
extent by an arrangement called a “spread sideband system,” which
has been used on circuits between Europe and South America. By
raising the speech in frequency before modulation the speech sidebands
are displaced two or three kilocycles from the carrier and many of the
product frequencies resulting from intermodulation fall into the gap
rather than into the sidebands.

On the Holland-Java route a system is being used whereby more than
one sideband is associated with a single carrier or pilot frequency, each
such sideband representing a different communication.

An improved signal-to-noise ratio is given by a device called a
“‘compandor”’ * employed on the New York-London long wave circuit.
It raises the amplitude of the weaker parts of the speech previous to
transmission. In depressing these raised parts to their proper relative
amplitude, after reception, the compandor also depresses the accumu-
lated radio noise.

The foregoing makes it evident that many fundamental engineering
problems have been solved and that the pioneering stage of the service,
when its possibility of continued existence might reasonably have been
in doubt, has definitely been passed. In looking toward the future we
find that the greatest needs are for improvement in reliability and in
grade of service, accompanied by reduced costs.

Improving the reliability struggles against the fact that short wave
transmission varies through such a wide range of effectiveness, and
seems to be so much influenced by the sun. We have not only a daily
cycle in the transmission of a given frequency but also an annual cycle
and beyond this an eleven-year cycle associated with the change in
sunspot activity. Superimposed upon these are erratic and occa-
sionally large variations associated with magnetic storms.

A statistical study of the data secured from operation of transoceanic
radio telephone circuits over the past several years has given valuable
help in engineering circuits to meet a given standard of reliability.
This study has shown that the percentage of lost time suffered on a
circuit appears to follow a probability law and that its relation to the
transmission effectiveness of the circuit in decibels is given by a straight
line when plotted to an arithmetic probability scale. Such a relation
tells us, for example, that if a circuit as it stands suffers 15 per cent lost
time, the lost time can be reduced to a selected lower value, say 5 per
cent, by improving the circuit a definite amount, in the assumed case
10 decibels. It then becomes possible, by making engineering cost
studies of the various available ways of securing the necessary number
of decibels improvement in performance, to choose the most economical
one. This approach is being applied to study of the radio telephone
circuits extending outward from the United States. Some of the tech-
nical possibilities which are being considered for improving these cir-
cuits are discussed below.

The performance of a radio telephone circuit may be changed by
dynamically modifying the amplification or other characteristics of
the circuit in accordance with the speech transmitted. The compandor
already mentioned is an example of this kind of improvement on long
waves. Further developments particularly suited to the vagaries of
short-wave transmission are possible.

The operation of the vodas, or voice-operated switching device
linking the wire and radio circuits, is adversely affected by noise.
Methods are being investigated for using single frequencies, called
‘control tones,” transmitted alongside the speech band and under the
control of speech currents, to give more positive operation of the
switching devices and reduce the adjustment required.

The transmission improvement of about 9 decibels (about 10 : 1 in
power) offered by single-sideband suppressed-carrier transmission has
been delayed in its application to short-wave transmission partly be-
cause of the high degree of precision in frequency control and selectivity
necessary to its accomplishment. In recent years successful apparatus
has been developed and proved satisfactory in trials. The introduction
of single sideband into commercial usage is already in progress.

Turning now from the transmitting to the receiving end, one funda-
mental way to reduce noise in radio telephony is to employ sharper
directivity. It has been found by observation that there is a limit to
which directivity, as ordinarily practiced, can be carried to advantage.
It is easy to design antennas so sharp that at times very large improve-
ments in signal-to-noise ratio are secured. But it is found that at other

times these antennas are actually poorer than are much less sharply
directive systems. Such observations also indicate a wide variation in
the performance of antennas as regards selective fading, and the signal
distortion accompanying it.

The result of all this work has been the development of a system
based on an entirely new approach to the problem of sharp directivity
and of telephone receiving. This system is called a MUSA System,
the word MUSA being synthesized from the initial letters of the
descriptive words Multiple Unit Steerable Antenna. An outline of
the principles and methods is given below.

By sending short spurts or pulses of short-wave radiation from one
side of the Atlantic, and receiving on the other side, it has been observed
that each spurt may be received several times in quick succession.
But these echoes do not arrive like successive bullets from the same
gun, all following the same path. They come slanting down to the
receiver from different angles of elevation, these vertical angular
directions remaining comparatively stable. While the signal received
at each of the individual directions may be subject to fading, the fading
is somewhat slower and is not very selective as to frequency. The
signal component coming in at a low angle takes less time in its trip from
the transmitter than a high angle component. Evidently the low-
angle paths are shorter. All these facts fit in well; on the average, with
the ideal geometrical picture of waves bouncing back and forth between
the ionosphere and the ground and reaching the receiver as several
distinct components which started out at different angles, have been
reflected at different angles, and have suffered different numbers of
bounces.

The ordinary directive antenna is blunt enough in its vertical receiv-
ing characteristic to receive all or nearly all of these signal components
at once. Because of their different times of transit the various com-
ponents do not mix well but clash and interfere with one another at the
receiver. This shows up as the selective fading and distortion which
characterize short-wave reception much of the time. The MUSA
method remedies this trouble.

The MUSA provides extremely sharp directivity in the vertical plane.
By its use a vertical angular component can be selected individually.
It consists of a number of rhombic antennas stretched out in a line
toward the transmitter and connected by individual coaxial lines to the
receiving apparatus. The apparatus is adjustable so that the vertical
angle of reception can be aimed or ‘‘steered”’ to select any desired com-
ponent as a telescope is elevated to pick out a star. The antennas re-
main mechanically fixed. The steering is done electrically with phase

shifters in the receiving set. By taking several branch circuits in
parallel from the antennas to different sets of adjusting and receiving
apparatus the vertical signal components may be separated from each
other.

Nature breaks the wave into several components and jumbles them
together. The first function of the MUSA system, as just described,
is to sort the components out again. Its second function is to correct
their differences so that they may be combined smoothly into a replica
of the original signal. To do this the received wave components are
separately detected and passed through individual delay circuits to
equalize their differences in transit time. They are then combined to
give a single output. As compared with a simple receiver the MUSA
receiving system gives (1) improvement in signal-to-noise ratio, as a
result of the sharp directive selectivity of the antenna; (2) improvement
against selective fading distortion, by virtue of the equalization of the
time differences between the components before they are allowed to
mix; and (3) improvement against noise and distortion, because of the
diversity effect of combining the several components.

Fortunately, it is found that the directive selection and the delay
compensation adjustments correct for one frequency are satisfactory
for a considerable band of frequencies adjacent thereto. Thus there is
offered the possibility of receiving a number of grouped channels
through one system and the prospect appears not only of improved
transmission but also of reduced cost per channel.

The possibility of grouping channels at the transmitting station may
be conceived on the basis of either ‘‘multiple”’ or ‘‘multiplex”’ trans-
mission. In the multiple arrangement each channel has its own an-
tenna and its individual transmitter whose frequency is closely spaced
from and coordinated with the adjacent channels of the group. In
‘multiplex’ transmission, the channels are aggregated into a group at
low power and handled en bloc through a common high-power amplifier
and radiating system. Particularly in the multiplex case, there are
possibilities of important economies if the technical problems are
satisfactorily solved. Passing a multiplicity of channels simultane-
ously through a common-power amplifier involves interchannel inter-
ference due to modulation products which is not met with when only
one channel is present. Severe requirements are thereby placed on the
distortion characteristics of the power amplifier.

It seems a fair conclusion that the tendency in the engineering solu-
tion of the problems of economy and growth in radio telephone de-
velopment (and perhaps also radio telegraph development) will be
toward channel grouping methods, especially for backbone routes

between important centers where large traffic may develop. This will
be a considerable departure from past practice which has resulted in
the existing system of scattered frequency assignments. It is to be
hoped that the obvious difficulties in rearranging frequency assign-

ments will not prove so unyielding as to preclude putting new engineer-
ing developments into service.

A Negative-Grid Triode Oscillator and Amplifier for Ultra-
High Frequencies *

HE author describes three negative-grid triodes of unusual design
which operate both as oscillators and as amplifiers at ultra-high
frequencies. The power output of the smallest tube as an oscillator at
1500 megacycles is 2 watts, and is still capable of an output of 1 watt at
1700 megacycles with an oscillation limit of 1870 megacycles cor-
responding to a wave-length of 16 centimeters. This tube also offers
possibilities as an amplifier at frequencies as high as 1000 megacycles.
Such capabilities of the negative-grid triode are notable since this de-
vice has appeared to lag behind the magnetron as an oscillator at fre-

* Digest of a paper presented before International Scientific Radio Union April
30, 1937 at Washington, D.C. Published in Proc. J. R. E., October, 1937.

primarily in the lead arrangement. From the section view of one of
these tubes, shown in Fig. 2, it will be observed that the grid and plate
elements are supported by wires which in effect go straight through the

tube envelope providing two independent leads to each of these ele-
ments. The filament leads are at one end only and one of these leads
is extremely short. This unusual lead arrangement possesses a number
of unique advantages.

A typical oscillator circuit is shown in Fig. 3. Here the tube is
mounted at the center of a half-wave Lecher system. This arrange-
ment provides a higher natural frequency circuit than that of the

quarter-wave Lecher system formed by removing one set of leads.
Since only half of the total charging current to the inter-electrode
capacitances flows through each set of leads, the losses due to the lead
resistances are also reduced. In the tubes under discussion the electron
transit time limitation has been met by the use of extremely small
inter-electrode spacings so that full advantage may be taken of the
increased frequency range.

For the purpose of confirming the above conclusion, efficiency curves
have been obtained on the large size tube, as shown in Fig. 1, when
operated both single- and double-ended. The results are shown in
Fig. 4. It will be observed that the efficiencies for double-ended
operation are always higher than for the single-ended case over the
range covered by the experimental data. In fact, usable outputs are
obtained at frequencies well beyond the point where the single-ended
tube fails to operate. The ratio of the cut-off frequencies for the two
tubes happens to be 1.23 for the particular conditions under which
these data were obtained.

Output and efficiency curves for the large size tube are shown in
Fig. 5. The values of 60 watts at 300 megacycles and 40 watts at 400
megacycles compare quite favorably with outputs reported from
radiation-cooled magnetrons. When the problems of modulation and
the complications of the magnetron’s magnetic field are considered, the
advantages of the negative-grid triode become more apparent. The
improvement in power output made possible by this departure in design
is illustrated by the comparison plot shown in Fig. 6.

The double-lead arrangement is also responsible for an increase in the
upper frequency limit at which stable operation as an amplifier may
be secured.

The primary cause for instability of the triode amplifier is the inter-
action between the input and output circuits which results from the
admittance coupling. between these circuits provided by the grid-plate
capacitance. A second source of coupling is that caused by common
impedances in the two circuits in the nature of the self and mutual
inductance of the tube leads. At moderately high frequencies this
latter coupling is usually of negligible importance. Stable operation is
thus possible when suitable means are provided to compensate or
‘neutralize’ the admittance coupling. At ultra-high frequencies
lead-impedance coupling can no longer be neglected. It may, of course,
be minimized by the use of short leads. The ultimate solution is to
provide independent leads for the input, output and admittance neu-
tralizing circuits. The double-lead tube is an attempt to fulfill these
conditions. It will be observed that the only common impedance

remaining is that caused by one filament lead and that this lead is
extremely short.

In the present investigation the method of neutralizing admittance
coupling has been that disclosed by H. W. Nichols in U. S. Patent

Fig. 4—Comparison plot of output efficiency for the large tube when operated single-
ended and double-ended.

1,325,879 and involves the resonating of the offending admittances at
the desired operating frequency so that the resulting parallel admit-
tance is reduced to a very low value. This takes the form of an in-
ductance connected between the grid and plate of the tube and adjusted

to resonate with the grid-plate capacitance. For ease of adjustment a
somewhat lower fixed inductance may be used and tuned by the ad-
justment of a small variable condenser in parallel. This form of
neutralization is commonly referred to as “coil” neutralization. At
ultra-high frequencies where unavoidable inductances are already
present in the form of lead inductances, this ‘“‘coil’’ scheme possesses

Fig. 6—Comparison plot of the outputs of the double-lead tubes and of commercially
available tubes.

outstanding advantages over the more usual ‘‘capacitance” schemes.
These advantages become even more pronounced with the availability
of the double-lead tube.

Verifying this analysis, a ‘‘coil-neutralized” two-stage amplifier
using two of the largest size tubes was found to yield an output of 60
watts at 144 megacycles for Class B operation. Stability, distortion,
and band width were quite comparable to the results obtained on a

pentode of similar rating. A four-stage amplifier employing the inter-
mediate tube gave comparable results and although experimental data
are not yet available, it seems reasonable to assume that the small size
tube will permit of stable operation as an amplifier at frequencies as
high as 1000 megacycles.

The double-lead tube is therefore seen to possess a number of distinct
advantages, both as oscillator and as amplifier, in the frequency range
from 100 megacycles to 1000 megacycles. While the ultimate limit to
which such developments may be pushed is still a matter of conjure it
seems safe to predict that the triode will be able to meet the demands of
the circuit designer at least for some time to come.

N the paper of the above title in the January 1937 issue of the Bell
System Technical Journal, an approximation which was not ex-
plicitly pointed out was made in deriving equation (17). A note from
Mr. K. A. Norton* of the Federal Communications Commission points
out that equation (17) does not give a reasonable result when r = 1.
The explanation is that two terms which are unimportant except near
the transmitter when the ground is a perfect dielectric were deleted.
The complete equation is

When 7 = 1 by virtue of equation (13) W must equal 1/2 and accord-
ingly the first term on the right of equation (17) is 1/4. The second
1/4 1/2
term gives 1/4 + and the last term gives + (rid
Hence when 7 = 1 equation (17) gives the following relation for the

The terms added to equation (17) produce oscillations in the curves
of Fig. 3 as shown on the following page. For any physical dielectric
the conductivity is not zero and the oscillations disappear at the greater
distances giving curves like those of the original Fig. 3.

This increases the deviation of the second factor on the right from unity
but if the ground is not a perfect dielectric the exponential reduces the
second factor to unity at the greater distances irrespective of the

* See the note at the end of ‘‘ The Propagation of Radio Waves over the Surface
of the Earth and in the Upper Atmosphere,” Proc. J.R.E., 25, 1203-1236, September,

The situation in the immediate vicinity of the antenna is more
clearly represented in Fig. 3A in which the attenuation factor is plotted
against distance in wave-lengths. This allows inclusion of curves for
¢ = 1 (i.e. for the earth replaced by air) and e = © (which is equiva-
lent to perfectly conducting earth). Comparison of these curves with
the broken lines which are replotted from Fig. 2 shows that for dis-

Fig. 3A—Variation of attenuation factor with distance in wave-lengths for trans-
mission over a dielectric plane. For d/\ small,

tances greater than a wave-length the main effect of using the curves
of Fig. 2 is to ignore the presence of the oscillations in the curves. For
a perfect dielectric the amplitudes of these oscillations do not decrease
below + 1/e*/? even at great distances as can be seen from equation
(19). The presence of some conductivity causes these oscillations to
be damped out. For example, a Q of 5 reduces the amplitudes of these
oscillations within the first four wave-lengths to a value too small to
show on the figure.

The second paragraph of the footnote referring to equation (17)
should read:

when the value of y = (1 + 7)ATTo is substituted i in his equation (7) and the result
divided by 1 + 7°. The ¢ of this paper is equal to — ¢ in Wise’s paper. By inter-
changing k; and kz in Wise’s equation (7) and proceeding along parallel lines the
corresponding equation of DIT) = y/(1 + 7°) is found to be

D 1 T 7?
Adding these two relations gives an expression for (3 aa + q im) II, where
II = 2(A +

which when ge in the above equation for E and the result divided by 2B,
where Eo = — 240in°IEo/A, gives equation (17). Since. Eo is the inverse distance
component of the free space field, this relation for Eo follows from equation (11).

Relation between Loudness and Masking.22) HARVEY FLETCHER and
W. A. Munson. A functional relationship between the loudness of a
sound and the degree to which it masks single frequency tones, that is,
the masking audiogram of the sound, is developed. A loudness-
masking function is determined experimentally. From this loudness-
masking relationship the loudness of a sound can be computed by
simply integrating the area under the masking audiogram plotted on a
special chart. Comparisons of computed and observed loudness
levels are shown for a number of sounds and serve to illustrate the
precision to be expected from the method. Finally, the results of a
large number of masking tests are given in the form of masking con-
tours, which enable one to predict the masking audiogram of a sound
from measurements of its intensity spectrum.

Coupling between Parallel Earth-Return Circuits under D.-C. Tran-
sient Conditions*® E. Goutp. In tests conducted in connection
with several d.-c. railway electrifications, the induced voltages re-
corded in paralleling communication circuits at times of short circuit
on the railway have shown marked divergences from values computed
on the basis of uniform earth resistivity and a rate of change of earth
current determined from measurements in trolley and rail circuits.
Due to the numerous factors which might contribute to these divergen-
ces, such as non-uniform division of transient current along the tracks
and associated return conductors, the presence of shielding conductors
along or near the right-of-way, etc., it was felt that a better under-
standing of the problem of induction under d.-c. transient conditions
could be obtained by experimental studies of the transient coupling
between parallel earth-return circuits, free from the effects of shielding
conductors, and with concentrated, rather than distributed, grounds.
The study described in this paper was undertaken for this purpose.

The locations for the tests were selected to provide a reasonably
large range of earth resistivity; also, at one location it was known that
the earth structure departed substantially from uniformity. At each
of these locations d.-c. transient coupling tests were performed in
which transient currents, approximately of the form encountered
during faults on d.-c. railway electrifications, were produced in an earth-
return circuit, herein referred to as the primary, and measurements
were made of the resultant voltages in earth-return circuits, herein
called secondary circuits, parallel to and at separations from the
primary circuit of from 50 or 60 to 2,000 feet. In addition to the d.-c.
transient tests, measurements were made at each location of the steady
state a.-c. coupling, in magnitude and phase angle, over a range of
frequencies from 20 or 30 cycles to 3,200 cycles. From these a.-c.
measurements the transient voltages were computed for a number of
cases by evaluating the Fourier integral. The results of the a.-c.
coupling tests were useful also in helping to explain, in a general way,
the departures of the measured transient voltages from the voltages
computed for uniform earth resistivity.

The measured transient voltages and voltages computed (1) from
the a.-c. coupling measurements and (2) on the basis of a uniform
earth resistivity, are shown for several representative cases in figures
accompanying the paper.

The Shunt-Excited Antenna. J. F. Morrison and P. H. Situ.
The paper describes an arrangement for exciting a vertical broadcast
antenna with the base grounded. Construction economy results
through the elimination of the base insulator, the tower lighting
chokes, and the usual lightning protective devices. The coupling ap-
paratus at the antenna end of the transmission line is reduced to an
extent which may make unnecessary a separate building for its pro-
tection. Greater freedom from interruptions resulting from static
discharges is expected. The performance of the design is substan-
tially the same as that obtained from the antennas now in general use.

four feet long were used as the experimental guides. At one end of
these guides were launched waves having frequencies of roughly 150
megacycles. The lengths of the standing waves so produced gave the
velocity of propagation. Other experiments utilizing a probe made up
of short pickup wires attached to a crystal detector and meter enabled
the configuration of the lines of force in the wave front to be determined.
This was done for each of four types of waves. For certain types the
properties had already been predicted mathematically. For others
the properties were determined experimentally in advance of analysis.
In both cases analysis and experiment proved to be in good agreement.

The Dependence of Hearing Impairment on Sound Intensity... JOHN
C. STEINBERG and MARK B. GARDNER. This paper discusses the
measurement of hearing loss for levels of sound that were well above
the deafened threshold and hence were audible to the deafened person.
In the tests, observers having unilateral deafness, i.e., one impaired
and one normal ear, balanced a tone heard with the deafened ear
against the tone heard with the normal ear. For some persons, the
impaired ear heard less well than the normal ear for all sound levels.
For others, tones which were well above the deafened threshold were
heard about equally well with either ear. In other words, such deaf-
ened ears tended to hear loud sounds with normal loudness. It was
found that this type of deafness could be represented quantitatively
on the assumption that it was due to nerve atrophy. Loudness

judgments for a normal ear in the presence of noise were found to be
similar to judgments by a nerve deafened ear. Relations, based on
the loudness properties of normal ears, have been extended to represent
the loudness heard by deafened ears.

H. A. AFFEL, S. B. in Electrical Engineering, Massachusetts Insti-
tute of Technology, 1914; Research Assistant in Electrical Engineering,
1914-16. American Telephone and Telegraph Company, Engineering
Department and the Department of Development and Research,
1916-34; Bell Telephone Laboratories, 1934-. As Assistant Director
of Transmission Development, Mr. Affel is engaged in development
work connected with carrier telephone and telegraph systems.

RALPH Bown, M.E., 1913; M.M.E., 1915; Ph.D., 1917, Cornell
University. Captain, Signal Corps, U.S. Army, 1917-19. American
Telephone and Telegraph Company, Department of Development and
Research, 1919-34; Bell Telephone Laboratories, 1934-. As Radio
Research Director, Dr. Bown is concerned with radio development
problems. He is a Past President of the Institute of Radio Engineers.

CHARLES R. Burrows, B.S. in Electrical Engineering, University
of Michigan, 1924; A.M., Columbia University, 1927; E.E., Univer-
sity of Michigan, 1935. Research Assistant, University of Michigan,
1922-23. Western Electric Company, Engineering Department, 1924—
25; Bell Telephone Laboratories, Research Department, 1925-. Mr.
Burrows has been associated continuously with radio research and is

now in charge of a group investigating the propagation of ultra-short
waves.

Joun R. Carson, B.S., Princeton, 1907; E.E., 1909; M.S., 1912.
American Telephone and Telegraph Company, 1914-34; Bell Tele-
phone Laboratories, 1934-. As Transmission Theory Engineer for the
American Telephone and Telegraph Company and later for the Labora-
tories, Mr. Carson has made substantial contributions to electric
circuit and transmission theory and has published extensively on these
subjects. He is now a research mathematician.

THORNTON C. Fry, A.B., Findlay College, 1912; A.M., University of
Wisconsin, 1913; Ph.D., 1920; Instructor in mathematics, University
of Wisconsin, 1912-16. Mathematician, Western Electric Company,
1916-24; Bell Telephone Laboratories, since 1924. Lecturer electrical
engineering, M.I.T., 1927; Lecturer mathematics, Princeton, 1929-30.
Dr. Fry’s work in the Laboratories has been of a mathematical
character,

J.M. MANLEY, B:S. in Electrical Engineering, University of Missouri,
1930; Bell Telephone Laboratories, 1930-. Mr. Manley has been en-
gaged principally in theoretical studies of non-linear electrical circuits.

W. P. Mason, B.S. in Electrical Engineering, University of Kansas,
1921; M.A., Columbia University, 1924; Ph.D., 1928. Bell Telephone
Laboratories, 1921-. Dr. Mason has been engaged in investigations
on carrier transmission systems and more recently in work on wave
transmission networks, both electrical and mechanical.

PreRRE Mertz, A.B., Cornell University, 1918; Ph.D., 1926.
American Telephone and Telegraph Company, Department of De-
velopment and Research, 1919-23, 1926-34; Bell Telephone Labora-
tories, 1934-. Dr. Mertz has been engaged in special problems in toll
transmission, chiefly in telephotography and television.

S. O. MorGan, B.S. in Chemistry, Union College, 1922; M.A.,
Princeton University, 1925; Ph.D., 1928. Western Electric Company,
Engineering Department, 1922-24; Bell Telephone Laboratories,
1927—. Dr. Morgan’s work has been on the relation between dielectric
properties and chemical composition.

E. J. Murpny, B.S., University of Saskatchewan, Canada, 1918;
McGill University, Montreal, 1919-20; Harvard University, 1922-23.
Western Electric Company, Engineering Department, 1923-25; Bell
Telephone Laboratories, 1925-. Mr. Murphy’s work is largely con-
fined to the study of the electrical properties of dielectrics.

E. PETERSON, Cornell University, 1911-14; Brooklyn Polytechnic,
E.E., 1917; Columbia, A.M., 1923; Ph.D., 1926; Electrical Testing
Laboratories, 1915-17; Signal Corps, U. S. Army, 1917-19. Bell
Telephone Laboratories, 1919-. Dr. Peterson’s work has been largely
in theoretical studies of carrier current apparatus.

K. W. PFLEGER, A.B., Cornell University, 1921; E.E., 1923. Ameri-
can Telephone and Telegraph Company, Department of Development
and Research, 1923-34; Bell Telephone Laboratories, 1934-. Mr.
Pfleger has been engaged in transmission development work, chiefly
on problems pertaining to delay equalization, delay measuring, tem-
perature effects in loaded-cable circuits, and telegraph theory.

A. L. SAMUEL, A.B., College of Emporia (Kansas), 1923; S.B. and
S.M. in Electrical Engineering, Massachusetts Institute of Tech-
nology, 1926. Instructor in Electrical Engineering, Massachusetts

Institute of Technology, 1926-28. Bell Telephone Laboratories,
1928-. Mr. Samuel has been engaged in research and development
work on vacuum tubes.

C. C. Taytor, B.S. in Electrical Engineering, Colorado College,
1917. American Telephone and Telegraph Company, Long Lines
Department, 1920-28; Department of Development and Research,
1929-34. Bell Telephone Laboratories, 1934-. Mr. Taylor’s work
has been concerned with radio-wire systems.

L. R. WRATHALL, B.S., University of Utah, 1927; Graduate School,
1927-28. Bell Telephone Laboratories, 1929-. Mr. Wrathall has
been engaged in the study of non-linear reactances.

S. B. Wricut, M.E. in Electrical Engineering, Cornell University,
1919. Engineering Department and Department of Development and
Research, American Telephone and Telegraph Company, 1919-34;
Bell Telephone Laboratories, 1934-. Mr. Wright is engaged in trans-
mission development of radio systems.

The Bell System Technical Journal  1937-10: Vol 16 Iss 4