diff --git "a/derived/Source/work/cache/REF.txt" "b/derived/Source/work/cache/REF.txt" new file mode 100644--- /dev/null +++ "b/derived/Source/work/cache/REF.txt" @@ -0,0 +1,6701 @@ +Fourth Edition, last update November 06, 2021 + 2 + Lessons In Electric Circuits, Volume V – Reference + + By Tony R. Kuphaldt + + Fourth Edition, last update November 06, 2021 + i + + ©2000-2023, Tony R. Kuphaldt + This book is published under the terms and conditions of the Creative Commons License. +These terms and conditions allow for free copying, distribution, and/or modification of this +document by the general public. The full Creative Commons License text is included in the +last chapter. + As an open and collaboratively developed text, this book is distributed in the hope that it +will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MER- +CHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the Creative Commons +License for more details. + Available in its entirety as part of the Open Book Project collection at: + +https://www.ibiblio.org/kuphaldt/electricCircuits + + + + + PRINTING HISTORY + + • First Edition: Printed in June of 2000. Plain-ASCII illustrations for universal computer + readability. + + • Second Edition: Printed in September of 2000. Illustrations reworked in standard graphic + (eps and jpeg) format. Source files translated to Texinfo format for easy online and printed + publication. + + • Third Edition: Equations and tables reworked as graphic images rather than plain-ASCII + text. + • Fourth Edition: Printed in XXX 2001. Source files translated to SubML format. SubML is + a simple markup language designed to easily convert to other markups like LATEX, HTML, + or DocBook using nothing but search-and-replace substitutions. + ii + Contents + +1 USEFUL EQUATIONS AND CONVERSION FACTORS 1 + 1.1 DC circuit equations and laws . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 + 1.2 Series circuit rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 + 1.3 Parallel circuit rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 + 1.4 Series and parallel component equivalent values . . . . . . . . . . . . . . . . . . 3 + 1.5 Capacitor sizing equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 + 1.6 Inductor sizing equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 + 1.7 Time constant equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 + 1.8 AC circuit equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 + 1.9 Decibels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 + 1.10 Metric prefixes and unit conversions . . . . . . . . . . . . . . . . . . . . . . . . . . 12 + 1.11 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 + 1.12 Contributors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 + +2 COLOR CODES 17 + 2.1 Resistor Color Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 + 2.2 Wiring Color Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 + Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 + +3 CONDUCTOR AND INSULATOR TABLES 23 + 3.1 Copper wire gage table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 + 3.2 Copper wire ampacity table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 + 3.3 Coefficients of specific resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 + 3.4 Temperature coefficients of resistance . . . . . . . . . . . . . . . . . . . . . . . . . 26 + 3.5 Critical temperatures for superconductors . . . . . . . . . . . . . . . . . . . . . . 26 + 3.6 Dielectric strengths for insulators . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 + 3.7 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 + +4 ALGEBRA REFERENCE 29 + 4.1 Basic identities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 + 4.2 Arithmetic properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 + 4.3 Properties of exponents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 + 4.4 Radicals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 + 4.5 Important constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 + + iii + iv CONTENTS + + 4.6 Logarithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 + 4.7 Factoring equivalencies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 + 4.8 The quadratic formula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 + 4.9 Sequences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 + 4.10 Factorials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 + 4.11 Solving simultaneous equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 + 4.12 Contributors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 + +5 TRIGONOMETRY REFERENCE 47 + 5.1 Right triangle trigonometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 + 5.2 Non-right triangle trigonometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 + 5.3 Trigonometric equivalencies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 + 5.4 Hyperbolic functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 + 5.5 Contributors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 + +6 CALCULUS REFERENCE 51 + 6.1 Rules for limits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 + 6.2 Derivative of a constant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 + 6.3 Common derivatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 + 6.4 Derivatives of power functions of e . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 + 6.5 Trigonometric derivatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 + 6.6 Rules for derivatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 + 6.7 The antiderivative (Indefinite integral) . . . . . . . . . . . . . . . . . . . . . . . . 55 + 6.8 Common antiderivatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 + 6.9 Antiderivatives of power functions of e . . . . . . . . . . . . . . . . . . . . . . . . 56 + 6.10 Rules for antiderivatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 + 6.11 Definite integrals and the fundamental theorem of calculus . . . . . . . . . . . . 56 + 6.12 Differential equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 + +7 USING THE SPICE CIRCUIT SIMULATION PROGRAM 59 + 7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 + 7.2 History of SPICE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 + 7.3 Fundamentals of SPICE programming . . . . . . . . . . . . . . . . . . . . . . . . 61 + 7.4 The command-line interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 + 7.5 Circuit components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 + 7.6 Analysis options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 + 7.7 Quirks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 + 7.8 Example circuits and netlists . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 + +8 TROUBLESHOOTING – THEORY AND PRACTICE 113 + 8.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 + 8.2 Questions to ask before proceeding . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 + 8.3 General troubleshooting tips . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 + 8.4 Specific troubleshooting techniques . . . . . . . . . . . . . . . . . . . . . . . . . . 117 + 8.5 Likely failures in proven systems . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 + 8.6 Likely failures in unproven systems . . . . . . . . . . . . . . . . . . . . . . . . . . 123 + CONTENTS v + + 8.7 Potential pitfalls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 + 8.8 Contributors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 + +9 CIRCUIT SCHEMATIC SYMBOLS 129 + 9.1 Wires and connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 + 9.2 Power sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 + 9.3 Resistors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 + 9.4 Capacitors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 + 9.5 Inductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 + 9.6 Mutual inductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 + 9.7 Switches, hand actuated . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 + 9.8 Switches, process actuated . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 + 9.9 Switches, electrically actuated (relays) . . . . . . . . . . . . . . . . . . . . . . . . 136 + 9.10 Connectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 + 9.11 Diodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 + 9.12 Transistors, bipolar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138 + 9.13 Transistors, junction field-effect (JFET) . . . . . . . . . . . . . . . . . . . . . . . . 138 + 9.14 Transistors, insulated-gate field-effect (IGFET or MOSFET) . . . . . . . . . . . . 139 + 9.15 Transistors, hybrid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 + 9.16 Thyristors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 + 9.17 Integrated circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 + 9.18 Electron tubes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144 + +10 PERIODIC TABLE OF THE ELEMENTS 145 + 10.1 Table (landscape view) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 + 10.2 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 + +A-1 ABOUT THIS BOOK 147 + +A-2 CONTRIBUTOR LIST 151 + +A-3 CC BY License 159 + +INDEX 162 + Chapter 1 + +USEFUL EQUATIONS AND +CONVERSION FACTORS + +Contents + 1.1 DC circuit equations and laws . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 + 1.1.1 Ohm’s and Joule’s Laws . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 + 1.1.2 Kirchhoff ’s Laws . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 + 1.2 Series circuit rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 + 1.3 Parallel circuit rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 + 1.4 Series and parallel component equivalent values . . . . . . . . . . . . . . 3 + 1.4.1 Series and parallel resistances . . . . . . . . . . . . . . . . . . . . . . . . 3 + 1.4.2 Series and parallel inductances . . . . . . . . . . . . . . . . . . . . . . . . 3 + 1.4.3 Series and Parallel Capacitances . . . . . . . . . . . . . . . . . . . . . . . 4 + 1.5 Capacitor sizing equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 + 1.6 Inductor sizing equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 + 1.7 Time constant equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 + 1.7.1 Value of time constant in series RC and RL circuits . . . . . . . . . . . . 7 + 1.7.2 Calculating voltage or current at specified time . . . . . . . . . . . . . . . 8 + 1.7.3 Calculating time at specified voltage or current . . . . . . . . . . . . . . . 8 + 1.8 AC circuit equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 + 1.8.1 Inductive reactance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 + 1.8.2 Capacitive reactance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 + 1.8.3 Impedance in relation to R and X . . . . . . . . . . . . . . . . . . . . . . . 9 + 1.8.4 Ohm’s Law for AC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 + 1.8.5 Series and Parallel Impedances . . . . . . . . . . . . . . . . . . . . . . . . 9 + 1.8.6 Resonance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 + 1.8.7 AC power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 + 1.9 Decibels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 + 1.10 Metric prefixes and unit conversions . . . . . . . . . . . . . . . . . . . . . . 12 + + 1 + 2 CHAPTER 1. USEFUL EQUATIONS AND CONVERSION FACTORS + + 1.11 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 + 1.12 Contributors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 + + + + +1.1 DC circuit equations and laws +1.1.1 Ohm’s and Joule’s Laws + Ohm’s Law + +E = IR I= E R= E + R I + + Joule’s Law + 2 +P = IE P= E P = I2R + R + + Where, + E = Voltage in volts + I = Current in amperes (amps) + R = Resistance in ohms + P = Power in watts + NOTE: the symbol ”V” (”U” in Europe) is sometimes used to represent voltage instead of +”E”. In some cases, an author or circuit designer may choose to exclusively use ”V” for voltage, +never using the symbol ”E.” Other times the two symbols are used interchangeably, or ”E” is +used to represent voltage from a power source while ”V” is used to represent voltage across a +load (voltage ”drop”). + + + +1.1.2 Kirchhoff’s Laws + ”The algebraic sum of all voltages in a loop must equal zero.” + Kirchhoff’s Voltage Law (KVL) + + + + ”The algebraic sum of all currents entering and exiting a node must equal zero.” + Kirchhoff’s Current Law (KCL) + + +1.2 Series circuit rules + • Components in a series circuit share the same current. Itotal = I1 = I2 = . . . In + 1.3. PARALLEL CIRCUIT RULES 3 + + • Total resistance in a series circuit is equal to the sum of the individual resistances, mak- + ing it greater than any of the individual resistances. Rtotal = R1 + R2 + . . . Rn + + • Total voltage in a series circuit is equal to the sum of the individual voltage drops. Etotal + = E1 + E2 + . . . En + + +1.3 Parallel circuit rules + • Components in a parallel circuit share the same voltage. Etotal = E1 = E2 = . . . En + + • Total resistance in a parallel circuit is less than any of the individual resistances. Rtotal + = 1 / (1/R1 + 1/R2 + . . . 1/Rn ) + + • Total current in a parallel circuit is equal to the sum of the individual branch currents. + Itotal = I1 + I2 + . . . In + + +1.4 Series and parallel component equivalent values +1.4.1 Series and parallel resistances + Resistances + +Rseries = R1 + R2 + . . . Rn + + 1 +Rparallel = + 1 1 1 + R1 + R2 + . . . Rn + + + +1.4.2 Series and parallel inductances + Inductances + +Lseries = L1 + L2 + . . . Ln + + 1 +Lparallel = + 1 1 1 + L1 + L2 + . . . Ln + + Where, + L = Inductance in henrys + 4 CHAPTER 1. USEFUL EQUATIONS AND CONVERSION FACTORS + +1.4.3 Series and Parallel Capacitances + + + Capacitances + 1 +Cseries = + 1 1 1 + C1 + C2 + . . . Cn + +Cparallel = C1 + C2 + . . . Cn + + Where, + C = Capacitance in farads + + + + +1.5 Capacitor sizing equation + + + εA +C= + d + Where, + + C = Capacitance in Farads + ε = Permittivity of dielectric (absolute, not + relative) + A = Area of plate overlap in square meters + d = Distance between plates in meters + + ε = ε0 K + + Where, + ε0 = Permittivity of free space + ε0 = 8.8562 x 10-12 F/m + K= Dielectric constant of material + between plates (see table) + 1.5. CAPACITOR SIZING EQUATION 5 + + + Dielectric constants + Dielectric K Dielectric K + Vacuum 1.0000 Quartz, fused 3.8 + Air 1.0006 Wood, maple 4.4 + PTFE, Teflon 2.0 Glass 4.9-7.5 + Mineral oil 2.0 Castor oil 5.0 + Polypropylene 2.20-2.28 Wood, birch 5.2 + ABS resin 2.4 - 3.2 Mica, muscovite 5.0-8.7 + Polystyrene 2.45-4.0 Glass-bonded mica 6.3-9.3 + Waxed paper 2.5 Poreclain, steatite 6.5 + Transformer oil 2.5-4 Alumina Al2O3 8-10.0 + Wood, oak 3.3 Water, distilled 80 + Hard Rubber 2.5-4.8 Ta2O5 27.6 + Silicones 3.4-4.3 Ba2TiO3 1200-1500 + Bakelite 3.5-6.0 BaSrTiO3 7500 + + + + + A formula for capacitance in picofarads using practical dimensions: + + + + + 0.0885K(n-1) A 0.225K(n-1)A’ + C= = + d d’ + A + Where, d + C = Capacitance in picofarads + K = Dielectric constant + A = Area of one plate in square centimeters + A’ = Area of one plate in square inches + d= Thickness in centimeters + d’ = Thickness in inches + n= Number of plates + 6 CHAPTER 1. USEFUL EQUATIONS AND CONVERSION FACTORS + +1.6 Inductor sizing equation + + N2µA +L= + l +µ = µr µ0 + r + + Where, l + L = Inductance of coil in Henrys + N = Number of turns in wire coil (straight wire = 1) + µ = Permeability of core material (absolute, not relative) + µr = Relative permeability, dimensionless ( µ0=1 for air) + -6 + µ0 = 1.26 x 10 T-m/At permeability of free space + A = Area of coil in square meters = πr2 + l = Average length of coil in meters + Wheeler’s formulas for inductance of air core coils which follow are useful for radio fre- +quency inductors. The following formula for the inductance of a single layer air core solenoid +coil is accurate to approximately 1% for 2r/l < 3. The thick coil formula is 1% accurate when +the denominator terms are approximately equal. Wheeler’s spiral formula is 1% accurate for +c>0.2r. While this is a ”round wire” formula, it may still be applicable to printed circuit spiral +inductors at reduced accuracy. + + + r c c + r r + + l + 2 2 + Nr + L= + 9r + 10⋅l l + 0.8N2r2 N2r2 + L= L= + 6r + 9⋅l + 10c 8r + 11c + Where, + L = Inductance of coil in microhenrys + N = Number of turns of wire + r = Mean radius of coil in inches + l = Length of coil in inches + c = Thickness of coil in inches + 1.7. TIME CONSTANT EQUATIONS 7 + + The inductance in henries of a square printed circuit inductor is given by two formulas +where p=q, and p6=q. + + L = 85⋅10-10DN5/3 L = 27⋅10-10(D8/3/p5/3)(1+R-1)5/3 + p + Where, Where, + D + D = dimension, cm D = coil dimension in cm + N = number turns q N = number of turns + p=q R= p/q + + + + +Wire sizing for inductors + +The wire table provides ”turns per inch” for enamel magnet wire for use with the inductance +formulas for coils. The circular-mil cross-section area determines current carrying capacity of +wires. + + AWG turns/ AWG turns/ AWG turns/ AWG turns/ + gauge inch gauge inch gauge inch gauge inch + 10 9.6 20 29.4 30 90.5 40 282 + 11 10.7 21 33.1 31 101 41 327 + 12 12.0 22 37.0 32 113 42 378 + 13 13.5 23 41.3 33 127 43 421 + 14 15.0 24 46.3 34 143 44 471 + 15 16.8 25 51.7 35 158 45 523 + 16 18.9 26 58.0 36 175 46 581 + 17 21.2 27 64.9 37 198 + 18 23.6 28 72.7 38 224 + 19 26.4 29 81.6 39 248 + + + + +1.7 Time constant equations + +1.7.1 Value of time constant in series RC and RL circuits + +Time constant in seconds = RC + Time constant in seconds = L/R + 8 CHAPTER 1. USEFUL EQUATIONS AND CONVERSION FACTORS + +1.7.2 Calculating voltage or current at specified time + +Universal Time Constant Formula + + 1 +Change = (Final-Start) 1 - + et/τ + Where, + Final = Value of calculated variable after infinite time + (its ultimate value) + Start = Initial value of calculated variable + e = Euler’s number ( 2.7182818) + t = Time in seconds + τ = Time constant for circuit in seconds + + + + +1.7.3 Calculating time at specified voltage or current + + Change +t = −τ ln 1 - + Final - Start + + + + +1.8 AC circuit equations + +1.8.1 Inductive reactance + + XL = 2πfL + +Where, + XL = Inductive reactance in ohms + f = Frequency in hertz + L = Inductance in henrys + 1.8. AC CIRCUIT EQUATIONS 9 + +1.8.2 Capacitive reactance + + XC = 1 + 2πfC + +Where, + XC = Inductive reactance in ohms + f = Frequency in hertz + C = Capacitance in farads + + + +1.8.3 Impedance in relation to R and X + ZL = R + jXL + + ZC = R - jXC + + + + +1.8.4 Ohm’s Law for AC + +E = IZ I= E Z= E + Z I + + Where, + E = Voltage in volts + I = Current in amperes (amps) + Z = Impedance in ohms + + + +1.8.5 Series and Parallel Impedances +Zseries = Z1 + Z2 + . . . Zn + + 1 +Zparallel = + 1 1 1 + Z1 + Z2 + . . . Zn + NOTE: All impedances must be calculated in complex number form for these equations to +work. + 10 CHAPTER 1. USEFUL EQUATIONS AND CONVERSION FACTORS + +1.8.6 Resonance + + 1 +fresonant = + 2π LC + + NOTE: This equation applies to a non-resistive LC circuit. In circuits containing resistance +as well as inductance and capacitance, this equation applies only to series configurations and +to parallel configurations where R is very small. + + + + +1.8.7 AC power + + E2 + P = true power P = I2R P= + R + Measured in units of Watts + + + + E2 + Q = reactive power Q = I2X Q= + X +Measured in units of Volt-Amps-Reactive (VAR) + + + + E2 + S = apparent power S = I2Z S= S = IE + Z + Measured in units of Volt-Amps + + + + + P = (IE)(power factor) + + S= P2 + Q2 + + Power factor = cos (Z phase angle) + 1.9. DECIBELS 11 + +1.9 Decibels + AV(dB) + +AV(dB) = 20 log AV(ratio) AV(ratio) = 10 20 + AI(dB) + +AI(dB) = 20 log AI(ratio) AI(ratio) = 10 20 + AP(dB) + +AP(dB) = 10 log AP(ratio) AP(ratio) = 10 10 + 12 CHAPTER 1. USEFUL EQUATIONS AND CONVERSION FACTORS + +1.10 Metric prefixes and unit conversions + • Metric prefixes + • Yotta = 1024 Symbol: Y + • Zetta = 1021 Symbol: Z + • Exa = 1018 Symbol: E + • Peta = 1015 Symbol: P + • Tera = 1012 Symbol: T + • Giga = 109 Symbol: G + • Mega = 106 Symbol: M + • Kilo = 103 Symbol: k + • Hecto = 102 Symbol: h + • Deca = 101 Symbol: da + • Deci = 10−1 Symbol: d + • Centi = 10−2 Symbol: c + • Milli = 10−3 Symbol: m + • Micro = 10−6 Symbol: µ + • Nano = 10−9 Symbol: n + • Pico = 10−12 Symbol: p + • Femto = 10−15 Symbol: f + • Atto = 10−18 Symbol: a + • Zepto = 10−21 Symbol: z + • Yocto = 10−24 Symbol: y + + METRIC PREFIX SCALE + T G M k m µ n p + tera giga mega kilo (none) milli micro nano pico + 1012 109 106 103 100 10-3 10-6 10-9 10-12 + + + + + 102 101 10-1 10-2 + hecto deca deci centi + h da d c + 1.10. METRIC PREFIXES AND UNIT CONVERSIONS 13 + + • Conversion factors for temperature + • o F = (o C)(9/5) + 32 + • o C = (o F - 32)(5/9) + • o R = o F + 459.67 + • o K = o C + 273.15 + + + Conversion equivalencies for volume + + 1 US gallon (gal) = 231.0 cubic inches (in3 ) = 4 quarts (qt) = 8 pints (pt) = 128 + fluid ounces (fl. oz.) = 3.7854 liters (l) + + 1 Imperial gallon (gal) = 160 fluid ounces (fl. oz.) = 4.546 liters (l) + + + Conversion equivalencies for distance + + 1 inch (in) = 2.540000 centimeter (cm) + + + Conversion equivalencies for velocity + + 1 mile per hour (mi/h) = 88 feet per minute (ft/m) = 1.46667 feet per second (ft/s) + = 1.60934 kilometer per hour (km/h) = 0.44704 meter per second (m/s) = 0.868976 + knot (knot – international) + + + Conversion equivalencies for weight + + 1 pound (lb) = 16 ounces (oz) = 0.45359 kilogram (kg) + + + Conversion equivalencies for force + + 1 pound-force (lbf) = 4.44822 newton (N) + + + Acceleration of gravity (free fall), Earth standard + + 9.806650 meters per second per second (m/s2 ) = 32.1740 feet per second per sec- + ond (ft/s2 ) + + + Conversion equivalencies for area + + 1 acre = 43560 square feet (ft2 ) = 4840 square yards (yd2 ) = 4046.86 square + meters (m2 ) + 14 CHAPTER 1. USEFUL EQUATIONS AND CONVERSION FACTORS + + Conversion equivalencies for pressure + + 1 pound per square inch (psi) = 2.03603 inches of mercury (in. Hg) = 27.6807 + inches of water (in. W.C.) = 6894.757 pascals (Pa) = 0.0680460 atmospheres (Atm) = + 0.0689476 bar (bar) + + + Conversion equivalencies for energy or work + + 1 british thermal unit (BTU – ”International Table”) = 251.996 calories (cal – + ”International Table”) = 1055.06 joules (J) = 1055.06 watt-seconds (W-s) = 0.293071 + watt-hour (W-hr) = 1.05506 x 1010 ergs (erg) = 778.169 foot-pound-force (ft-lbf) + + + Conversion equivalencies for power + + 1 horsepower (hp – 550 ft-lbf/s) = 745.7 watts (W) = 2544.43 british thermal units + per hour (BTU/hr) = 0.0760181 boiler horsepower (hp – boiler) + + + Conversion equivalencies for motor torque + + Newton-meter Gram-centimeter Pound-inch Pound-foot Ounce-inch + (n-m) (g-cm) (lb-in) (lb-ft) (oz-in) + n-m 1 1020 8.85 0.738 141.6 + -6 -3 -6 + g-cm 981 x 10 1 8.68 x 10 723 x 10 0.139 + lb-in 0.113 115 1 0.0833 16 + lb-ft 1.36 1383 12 1 192 + -3 -3 + oz-in 7.062 x 10 7.20 0.0625 5.21 x 10 1 + + Locate the row corresponding to known unit of torque along the left of the table. Multiply +by the factor under the column for the desired units. For example, to convert 2 oz-in torque +to n-m, locate oz-in row at table left. Locate 7.062 x 10−3 at intersection of desired n-m units +column. Multiply 2 oz-in x (7.062 x 10−3 ) = 14.12 x 10−3 n-m. + + Converting between units is easy if you have a set of equivalencies to work with. Suppose +we wanted to convert an energy quantity of 2500 calories into watt-hours. What we would need +to do is find a set of equivalent figures for those units. In our reference here, we see that 251.996 +calories is physically equal to 0.293071 watt hour. To convert from calories into watt-hours, +we must form a ”unity fraction” with these physically equal figures (a fraction composed of +different figures and different units, the numerator and denominator being physically equal to +one another), placing the desired unit in the numerator and the initial unit in the denominator, +and then multiply our initial value of calories by that fraction. + Since both terms of the ”unity fraction” are physically equal to one another, the fraction +as a whole has a physical value of 1, and so does not change the true value of any figure +when multiplied by it. When units are canceled, however, there will be a change in units. + 1.10. METRIC PREFIXES AND UNIT CONVERSIONS 15 + +For example, 2500 calories multiplied by the unity fraction of (0.293071 w-hr / 251.996 cal) = +2.9075 watt-hours. + + + + + Original figure 2500 calories + + + 0.293071 watt-hour + "Unity fraction" + 251.996 calories + + . . . cancelling units . . . + + 2500 calories 0.293071 watt-hour + 1 251.996 calories + + + + Converted figure 2.9075 watt-hours + + + + + The ”unity fraction” approach to unit conversion may be extended beyond single steps. Sup- +pose we wanted to convert a fluid flow measurement of 175 gallons per hour into liters per day. +We have two units to convert here: gallons into liters, and hours into days. Remember that +the word ”per” in mathematics means ”divided by,” so our initial figure of 175 gallons per hour +means 175 gallons divided by hours. Expressing our original figure as such a fraction, we +multiply it by the necessary unity fractions to convert gallons to liters (3.7854 liters = 1 gal- +lon), and hours to days (1 day = 24 hours). The units must be arranged in the unity fraction +in such a way that undesired units cancel each other out above and below fraction bars. For +this problem it means using a gallons-to-liters unity fraction of (3.7854 liters / 1 gallon) and a +hours-to-days unity fraction of (24 hours / 1 day): + 16 CHAPTER 1. USEFUL EQUATIONS AND CONVERSION FACTORS + + + Original figure 175 gallons/hour + + + 3.7854 liters + "Unity fraction" + 1 gallon + + + 24 hours + "Unity fraction" + 1 day + + + . . . cancelling units . . . + + 175 gallons 3.7854 liters 24 hours + 1 hour 1 gallon 1 day + + + + Converted figure 15,898.68 liters/day + Our final (converted) answer is 15898.68 liters per day. + + +1.11 Data +Conversion factors were found in the 78th edition of the CRC Handbook of Chemistry and +Physics, and the 3rd edition of Bela Liptak’s Instrument Engineers’ Handbook – Process Mea- +surement and Analysis. + + +1.12 Contributors +Contributors to this chapter are listed in chronological order of their contributions, from most +recent to first. See Appendix 2 (Contributor List) for dates and contact information. + Gerald Gardner (January 2003): Addition of Imperial gallons conversion. + Chapter 2 + +COLOR CODES + +Contents + 2.1 Resistor Color Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 + + 2.1.1 Example #1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 + + 2.1.2 Example #2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 + + 2.1.3 Example #3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 + + 2.1.4 Example #4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 + + 2.1.5 Example #5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 + + 2.1.6 Example #6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 + + 2.2 Wiring Color Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 + + Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 + + + + +2.1 Resistor Color Codes + +Components and wires are coded with colors to identify their value and function. + + 17 + 18 CHAPTER 2. COLOR CODES + + + Color Digit Multiplier Tolerance (%) + + Black 0 100 (1) + Brown 1 101 1 + 2 + Red 2 10 2 + Orange 3 103 + Yellow 4 104 + Green 5 105 0.5 + 6 + Blue 6 10 0.25 + Violet 7 107 0.1 + 8 + Grey 8 10 + White 9 109 + Gold 10-1 5 + Silver 10-2 10 + (none) 20 + + The colors brown, red, green, blue, and violet are used as tolerance codes on 5-band resistors +only. All 5-band resistors use a colored tolerance band. The blank (20%) ”band” is only used +with the ”4-band” code (3 colored bands + a blank ”band”). + + + Digit Digit Multiplier Tolerance + + + + + 4-band code + + + + Digit Digit Digit Multiplier Tolerance + + + + + 5-band code + 2.1. RESISTOR COLOR CODES 19 + +2.1.1 Example #1 + + + + A resistor colored Yellow-Violet-Orange-Gold would be 47 kΩ with a tolerance of +/- 5%. + + +2.1.2 Example #2 + + + + A resistor colored Green-Red-Gold-Silver would be 5.2 Ω with a tolerance of +/- 10%. + + +2.1.3 Example #3 + + + + A resistor colored White-Violet-Black would be 97 Ω with a tolerance of +/- 20%. When you +see only three color bands on a resistor, you know that it is actually a 4-band code with a blank +(20%) tolerance band. + + +2.1.4 Example #4 + + + + A resistor colored Orange-Orange-Black-Brown-Violet would be 3.3 kΩ with a tolerance of ++/- 0.1%. + + +2.1.5 Example #5 + + + + A resistor colored Brown-Green-Grey-Silver-Red would be 1.58 Ω with a tolerance of +/- 2%. + + +2.1.6 Example #6 + + + + A resistor colored Blue-Brown-Green-Silver-Blue would be 6.15 Ω with a tolerance of +/- +0.25%. + 20 CHAPTER 2. COLOR CODES + +2.2 Wiring Color Codes +Wiring for AC and DC power distribution branch circuits are color coded for identification of +individual wires. In some jurisdictions all wire colors are specified in legal documents. In other +jurisdictions, only a few conductor colors are so codified. In that case, local custom dictates the +“optional” wire colors. + IEC, AC: Most of Europe abides by IEC (International Electrotechnical Commission) wiring +color codes for AC branch circuits. These are listed in Table 2.1. The older color codes in the +table reflect the previous style which did not account for proper phase rotation. The protective +ground wire (listed as green-yellow) is green with yellow stripe. + + + Table 2.1: IEC (most of Europe) AC power circuit wiring color codes. + Function label Color, IEC Color, old IEC + Protective earth PE green-yellow green-yellow + Neutral N blue blue + Line, single phase L brown brown or black + Line, 3-phase L1 brown brown or black + Line, 3-phase L2 black brown or black + Line, 3-phase L3 grey brown or black + + + UK, AC: The United Kingdom now follows the IEC AC wiring color codes. Table 2.2 lists +these along with the obsolete domestic color codes. For adding new colored wiring to existing +old colored wiring see Cook. [1] + + + Table 2.2: UK AC power circuit wiring color codes. + Function label Color, IEC Old UK color + Protective earth PE green-yellow green-yellow + Neutral N blue black + Line, single phase L brown red + Line, 3-phase L1 brown red + Line, 3-phase L2 black yellow + Line, 3-phase L3 grey blue + + + US, AC:The US National Electrical Code only mandates white (or grey) for the neutral +power conductor and bare copper, green, or green with yellow stripe for the protective ground. +In principle any other colors except these may be used for the power conductors. The colors +adopted as local practice are shown in Table 2.3. Black, red, and blue are used for 208 VAC +three-phase; brown, orange and yellow are used for 480 VAC. Conductors larger than #6 AWG +are only available in black and are color taped at the ends. + Canada: Canadian wiring is governed by the CEC (Canadian Electric Code). See Table 2.4. +The protective ground is green or green with yellow stripe. The neutral is white, the hot (live +or active) single phase wires are black , and red in the case of a second active. Three-phase +lines are red, black, and blue. + 2.2. WIRING COLOR CODES 21 + + + Table 2.3: US AC power circuit wiring color codes. + Function label Color, common Color, alternative + Protective ground PG bare, green, or green-yellow green + Neutral N white grey + Line, single phase L black or red (2nd hot) + Line, 3-phase L1 black brown + Line, 3-phase L2 red orange + Line, 3-phase L3 blue yellow + + + Table 2.4: Canada AC power circuit wiring color codes. + Function label Color, common + Protective ground PG green or green-yellow + Neutral N white + Line, single phase L black or red (2nd hot) + Line, 3-phase L1 red + Line, 3-phase L2 black + Line, 3-phase L3 blue + + + IEC, DC: DC power installations, for example, solar power and computer data centers, use +color coding which follows the AC standards. The IEC color standard for DC power cables is +listed in Table 2.5, adapted from Table 2, Cook. [1] + + + Table 2.5: IEC DC power circuit wiring color codes. + Function label Color + Protective earth PE green-yellow + 2-wire unearthed DC Power System + Positive L+ brown + Negative L- grey + 2-wire earthed DC Power System + Positive (of a negative earthed) circuit L+ brown + Negative (of a negative earthed) circuit M blue + Positive (of a positive earthed) circuit M blue + Negative (of a positive earthed) circuit L- grey + 3-wire earthed DC Power System + Positive L+ brown + Mid-wire M blue + Negative L- grey + + US DC power: The US National Electrical Code (for both AC and DC) mandates that +the grounded neutral conductor of a power system be white or grey. The protective ground +must be bare, green or green-yellow striped. Hot (active) wires may be any other colors except +these. However, common practice (per local electrical inspectors) is for the first hot (live or +active) wire to be black and the second hot to be red. The recommendations in Table 2.6 are + 22 CHAPTER 2. COLOR CODES + +by Wiles. [2] He makes no recommendation for ungrounded power system colors. Usage of the +ungrounded system is discouraged for safety. However, red (+) and black (-) follows the coloring +of the grounded systems in the table. + + + Table 2.6: US recommended DC power circuit wiring color codes. + Function label Color + Protective ground PG bare, green, or green-yellow + 2-wire ungrounded DC Power System + Positive L+ no recommendation (red) + Negative L- no recommendation (black) + 2-wire grounded DC Power System + Positive (of a negative grounded) circuit L+ red + Negative (of a negative grounded) circuit N white + Positive (of a positive grounded) circuit N white + Negative (of a positive grounded) circuit L- black + 3-wire grounded DC Power System + Positive L+ red + Mid-wire (center tap) N white + Negative L- black + + + +Bibliography + [1] Paul Cook, “Harmonised colours and alphanumeric marking”, IEE Wiring Matters, Spring + 2004 at http://www.iee.org/Publish/WireRegs/IEE Harmonized colours.pdf + + [2] John Wiles, “Photovoltaic Power Systems and the National Electrical Code: Suggested + Practices”, Southwest Technology Development Institute, New Mexico State University, + March 2001 at http://www.re.sandia.gov/en/ti/tu/Copy%20of%20NEC2000.pdf + Chapter 3 + +CONDUCTOR AND INSULATOR +TABLES + +Contents + 3.1 Copper wire gage table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 + 3.2 Copper wire ampacity table . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 + 3.3 Coefficients of specific resistance . . . . . . . . . . . . . . . . . . . . . . . . . 23 + 3.4 Temperature coefficients of resistance . . . . . . . . . . . . . . . . . . . . . 26 + 3.5 Critical temperatures for superconductors . . . . . . . . . . . . . . . . . . 26 + 3.6 Dielectric strengths for insulators . . . . . . . . . . . . . . . . . . . . . . . . 27 + 3.7 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 + + + + +3.1 Copper wire gage table +Soild copper wire table: 3.1 + + +3.2 Copper wire ampacity table +Ampacities of copper wire: 3.2 + * = estimated values; normally, these small wire sizes are not manufactured with these +insulation types, 3.2. + + +3.3 Coefficients of specific resistance +Specific resistance table: 3.3 + + 23 + 24 CHAPTER 3. CONDUCTOR AND INSULATOR TABLES + + + Table 3.1: Soild copper wire table: + Size Diameter Cross-sectional area Weight + AWG inches cir. mils sq. inches lb/1000 ft + 4/0 0.4600 211,600 0.1662 640.5 + 3/0 0.4096 167,800 0.1318 507.9 + 2/0 0.3648 133,100 0.1045 402.8 + 1/0 0.3249 105,500 0.08289 319.5 + 1 0.2893 83,690 0.06573 253.5 + 2 0.2576 66,370 0.05213 200.9 + 3 0.2294 52,630 0.04134 159.3 + 4 0.2043 41,740 0.03278 126.4 + 5 0.1819 33,100 0.02600 100.2 + 6 0.1620 26,250 0.02062 79.46 + 7 0.1443 20,820 0.01635 63.02 + 8 0.1285 16,510 0.01297 49.97 + 9 0.1144 13,090 0.01028 39.63 + 10 0.1019 10,380 0.008155 31.43 + 11 0.09074 8,234 0.006467 24.92 + 12 0.08081 6,530 0.005129 19.77 + 13 0.07196 5,178 0.004067 15.68 + 14 0.06408 4,107 0.003225 12.43 + 15 0.05707 3,257 0.002558 9.858 + 16 0.05082 2,583 0.002028 7.818 + 17 0.04526 2,048 0.001609 6.200 + 18 0.04030 1,624 0.001276 4.917 + 19 0.03589 1,288 0.001012 3.899 + 20 0.03196 1,022 0.0008023 3.092 + 21 0.02846 810.1 0.0006363 2.452 + 22 0.02535 642.5 0.0005046 1.945 + 23 0.02257 509.5 0.0004001 1.542 + 24 0.02010 404.0 0.0003173 1.233 + 25 0.01790 320.4 0.0002517 0.9699 + 26 0.01594 254.1 0.0001996 0.7692 + 27 0.01420 201.5 0.0001583 0.6100 + 28 0.01264 159.8 0.0001255 0.4837 + 29 0.01126 126.7 0.00009954 0.3836 + 30 0.01003 100.5 0.00007894 0.3042 + 31 0.008928 79.70 0.00006260 0.2413 + 32 0.007950 63.21 0.00004964 0.1913 + 33 0.007080 50.13 0.00003937 0.1517 + 34 0.006305 39.75 0.00003122 0.1203 + 35 0.005615 31.52 0.00002476 0.09542 + 36 0.005000 25.00 0.00001963 0.07567 + 37 0.004453 19.83 0.00001557 0.06001 + 38 0.003965 15.72 0.00001235 0.04759 + 39 0.003531 12.47 0.000009793 0.03774 + 40 0.003145 9.888 0.000007766 0.02993 + 41 0.002800 7.842 0.000006159 0.02374 + 42 0.002494 6.219 0.000004884 0.01882 + 43 0.002221 4.932 0.000003873 0.01493 + 44 0.001978 3.911 0.000003072 0.01184 + 3.3. COEFFICIENTS OF SPECIFIC RESISTANCE 25 + + + + Table 3.2: Ampacities of copper wire, in free air at 30o C: + INSULATION TYPE: + RUW, T THW, THWN FEP, FEPB + TW RUH THHN, XHHW + Size Current Rating Current Rating Current Rating + AWG @ 60 degrees C @ 75 degrees C @ 90 degrees C + 20 *9 *12.5 + 18 *13 18 + 16 *18 24 + 14 25 30 35 + 12 30 35 40 + 10 40 50 55 + 8 60 70 80 + 6 80 95 105 + 4 105 125 140 + 2 140 170 190 + 1 165 195 220 + 1/0 195 230 260 + 2/0 225 265 300 + 3/0 260 310 350 + 4/0 300 360 405 + + + + + Table 3.3: Specific resistance at 20o C: + Material Element/Alloy (ohm-cmil/ft) (ohm-cm·10−6 ) + Nichrome Alloy 675 112.2 + Nichrome V Alloy 650 108.1 + Manganin Alloy 290 48.21 + Constantan Alloy 272.97 45.38 + Steel* Alloy 100 16.62 + Platinum Element 63.16 10.5 + Iron Element 57.81 9.61 + Nickel Element 41.69 6.93 + Zinc Element 35.49 5.90 + Molybdenum Element 32.12 5.34 + Tungsten Element 31.76 5.28 + Aluminum Element 15.94 2.650 + Gold Element 13.32 2.214 + Copper Element 10.09 1.678 + Silver Element 9.546 1.587 + * = Steel alloy at 99.5% iron, 0.5% carbon + 26 CHAPTER 3. CONDUCTOR AND INSULATOR TABLES + +3.4 Temperature coefficients of resistance +Temperature coefficient table: 3.4 + + + Table 3.4: Temperature coefficient (α) per degree C: + Material Element/Alloy Temp. coefficient + Nickel Element 0.005866 + Iron Element 0.005671 + Molybdenum Element 0.004579 + Tungsten Element 0.004403 + Aluminum Element 0.004308 + Copper Element 0.004041 + Silver Element 0.003819 + Platinum Element 0.003729 + Gold Element 0.003715 + Zinc Element 0.003847 + Steel* Alloy 0.003 + Nichrome Alloy 0.00017 + Nichrome V Alloy 0.00013 + Manganin Alloy 0.000015 + Constantan Alloy ±0.000074 + * = Steel alloy at 99.5% iron, 0.5% carbon + + + + +3.5 Critical temperatures for superconductors +Critical temperature, superconductors 3.5 + + + Table 3.5: Critical temperatures given in Kelvins + Material Element or Alloy Critical temperature(K) + Aluminum Element 1.20 + Cadmium Element 0.56 + Lead Element 7.2 + Mercury Element 4.16 + Niobium Element 8.70 + Thorium Element 1.37 + Tin Element 3.72 + Titanium Element 0.39 + Uranium ELement 1.0 + Zinc Element 0.91 + Niobium/Tin Alloy 18.1 + Cupric sulphide Compound 1.6 + 3.6. DIELECTRIC STRENGTHS FOR INSULATORS 27 + + + Table 3.6: Critical temperatures, high temperature superconuctors in Kelvins + Material Critical temperature(K) + HgBa2 Ca2 Cu3 O8+d 150 (23.5 GPa pressure) + HgBa2 Ca2 Cu3 O8+d 133 + Tl2 Ba2 Ca2 Cu3 O10 125 + YBa2 Cu3 O7 90 + La1.85 Sr0.15 CuO4 40 + Cs3 C60 40(15 Kbar pressure) + Ba0.6 K0.4 BiO3 30 + Nd1.85 Ce0.15 CuO4 22 + K3 C60 19 + PbMo6 S8 12.6 + + + Critical temperatures, high temperature superconuctors 3.6 + Note: all critical temperatures given at zero magnetic field strength, 3.6. + + +3.6 Dielectric strengths for insulators +Dielectric strength: 3.7 + + + Table 3.7: Dielectric strength in kilovolts per inch (kV/in): + Material* Dielectric strength + Vacuum 20 + Air 20 to 75 + Porcelain 40 to 200 + Paraffin Wax 200 to 300 + Transformer Oil 400 + Bakelite 300 to 550 + Rubber 450 to 700 + Shellac 900 + Paper 1250 + Teflon 1500 + Glass 2000 to 3000 + Mica 5000 + + * = Materials listed are specially prepared for electrical use, 3.7. + + +3.7 Data +Tables of specific resistance and temperature coefficient of resistance for elemental materials +(not alloys) were derived from figures found in the 78th edition of the CRC Handbook of Chem- + 28 CHAPTER 3. CONDUCTOR AND INSULATOR TABLES + +istry and Physics. Superconductivity data from Collier’s Encyclopedia (volume 21, 1968, page +640). + Chapter 4 + +ALGEBRA REFERENCE + +Contents + 4.1 Basic identities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 + 4.2 Arithmetic properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 + 4.2.1 The associative property . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 + 4.2.2 The commutative property . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 + 4.2.3 The distributive property . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 + 4.3 Properties of exponents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 + 4.4 Radicals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 + 4.4.1 Definition of a radical . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 + 4.4.2 Properties of radicals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 + 4.5 Important constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 + 4.5.1 Euler’s number . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 + 4.5.2 Pi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 + 4.6 Logarithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 + 4.6.1 Definition of a logarithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 + 4.6.2 Properties of logarithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 + 4.7 Factoring equivalencies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 + 4.8 The quadratic formula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 + 4.9 Sequences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 + 4.9.1 Arithmetic sequences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 + 4.9.2 Geometric sequences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 + 4.10 Factorials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 + 4.10.1 Definition of a factorial . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 + 4.10.2 Strange factorials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 + 4.11 Solving simultaneous equations . . . . . . . . . . . . . . . . . . . . . . . . . 35 + 4.11.1 Substitution method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 + 4.11.2 Addition method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 + 4.12 Contributors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 + + + + 29 + 30 CHAPTER 4. ALGEBRA REFERENCE + +4.1 Basic identities +a+0=a 1a = a 0a = 0 + + a =a 0 =0 a =1 + 1 a a + a = undefined + 0 + Note: while division by zero is popularly thought to be equal to infinity, this is not techni- +cally true. In some practical applications it may be helpful to think the result of such a fraction +approaching positive infinity as a positive denominator approaches zero (imagine calculating +current I=E/R in a circuit with resistance approaching zero – current would approach infinity), +but the actual fraction of anything divided by zero is undefined in the scope of either real or +complex numbers. + + + +4.2 Arithmetic properties +4.2.1 The associative property +In addition and multiplication, terms may be arbitrarily associated with each other through +the use of parentheses: + a + (b + c) = (a + b) + c a(bc) = (ab)c + + +4.2.2 The commutative property +In addition and multiplication, terms may be arbitrarily interchanged, or commutated: + a+b=b+a ab=ba + + +4.2.3 The distributive property +a(b + c) = ab + ac + + +4.3 Properties of exponents +aman = am+n (ab)m = ambm + + am +(am)n = amn = am-n + an + 4.4. RADICALS 31 + +4.4 Radicals + +4.4.1 Definition of a radical +When people talk of a ”square root,” they’re referring to a radical with a root of 2. This is +mathematically equivalent to a number raised to the power of 1/2. This equivalence is useful +to know when using a calculator to determine a strange root. Suppose for example you needed +to find the fourth root of a number, but your calculator lacks a ”4th root” button or function. If +it has a yx function (which any scientific calculator should have), you can find the fourth root +by raising that number to the 1/4 power, or x0.25 . + x + a = a1/x + It is important to remember that when solving for an even root (square root, fourth root, +etc.) of any number, there are two valid answers. For example, most people know that the +square root of nine is three, but negative three is also a valid answer, since (-3)2 = 9 just as 32 += 9. + + + +4.4.2 Properties of radicals + + x x x + a =a ax = a + + + x x x + ab = a b + + + x x + a a + = x + b b + + + +4.5 Important constants + +4.5.1 Euler’s number +Euler’s constant is an important value for exponential functions, especially scientific applica- +tions involving decay (such as the decay of a radioactive substance). It is especially important +in calculus due to its uniquely self-similar properties of integration and differentiation. +e approximately equals: +2.71828 18284 59045 23536 02874 71352 66249 77572 47093 69996 + 32 CHAPTER 4. ALGEBRA REFERENCE + + + + + e= 1 + k! + k=0 + + + 1 1 1 1 ... 1 + 0! + 1! + 2! + 3! + n! + + + + +4.5.2 Pi + +Pi (π) is defined as the ratio of a circle’s circumference to its diameter. +Pi approximately equals: +3.14159 26535 89793 23846 26433 83279 50288 41971 69399 37511 + + + + Note: For both Euler’s constant (e) and pi (π), the spaces shown between each set of five +digits have no mathematical significance. They are placed there just to make it easier for your +eyes to ”piece” the number into five-digit groups when manually copying. + + + + +4.6 Logarithms + +4.6.1 Definition of a logarithm + + If: + by = x + +Then: + logb x = y + + +Where, + b = "Base" of the logarithm + ”log” denotes a common logarithm (base = 10), while ”ln” denotes a natural logarithm (base += e). + 4.7. FACTORING EQUIVALENCIES 33 + +4.6.2 Properties of logarithms + +(log a) + (log b) = log ab + +(log a) - (log b) = log a + b + log am = (m)(log a) + + a(log m) = m + These properties of logarithms come in handy for performing complex multiplication and +division operations. They are an example of something called a transform function, whereby +one type of mathematical operation is transformed into another type of mathematical operation +that is simpler to solve. Using a table of logarithm figures, one can multiply or divide numbers +by adding or subtracting their logarithms, respectively. then looking up that logarithm figure +in the table and seeing what the final product or quotient is. + Slide rules work on this principle of logarithms by performing multiplication and division +through addition and subtraction of distances on the slide. + + Slide rule + Cursor + + + Slide + + + + Numerical quantities are represented by + the positioning of the slide. + Marks on a slide rule’s scales are spaced in a logarithmic fashion, so that a linear posi- +tioning of the scale or cursor results in a nonlinear indication as read on the scale(s). Adding +or subtracting lengths on these logarithmic scales results in an indication equivalent to the +product or quotient, respectively, of those lengths. + Most slide rules were also equipped with special scales for trigonometric functions, powers, +roots, and other useful arithmetic functions. + + + +4.7 Factoring equivalencies + +x2 - y2 = (x+y)(x-y) + +x3 - y3 = (x-y)(x2 + xy + y2) + 34 CHAPTER 4. ALGEBRA REFERENCE + +4.8 The quadratic formula + +For a polynomial expression in +the form of: ax2 + bx + c = 0 + + + + x = -b - b2 - 4ac + 2a + + + +4.9 Sequences + +4.9.1 Arithmetic sequences + +An arithmetic sequence is a series of numbers obtained by adding (or subtracting) the same +value with each step. A child’s counting sequence (1, 2, 3, 4, . . .) is a simple arithmetic +sequence, where the common difference is 1: that is, each adjacent number in the sequence +differs by a value of one. An arithmetic sequence counting only even numbers (2, 4, 6, 8, . . .) +or only odd numbers (1, 3, 5, 7, 9, . . .) would have a common difference of 2. + In the standard notation of sequences, a lower-case letter ”a” represents an element (a +single number) in the sequence. The term ”an ” refers to the element at the nth step in the +sequence. For example, ”a3 ” in an even-counting (common difference = 2) arithmetic sequence +starting at 2 would be the number 6, ”a” representing 4 and ”a1 ” representing the starting +point of the sequence (given in this example as 2). + A capital letter ”A” represents the sum of an arithmetic sequence. For instance, in the same +even-counting sequence starting at 2, A4 is equal to the sum of all elements from a1 through +a4 , which of course would be 2 + 4 + 6 + 8, or 20. + an = an-1 + d an = a1 + d(n-1) + + Where: + d = The "common difference" + + + Example of an arithmetic sequence: + -7, -3, 1, 5, 9, 13, 17, 21, 25 . . . + + + An = a1 + a2 + . . . an + + An = n (a1 + an) + 2 + 4.10. FACTORIALS 35 + +4.9.2 Geometric sequences +A geometric sequence, on the other hand, is a series of numbers obtained by multiplying (or +dividing) by the same value with each step. A binary place-weight sequence (1, 2, 4, 8, 16, 32, +64, . . .) is a simple geometric sequence, where the common ratio is 2: that is, each adjacent +number in the sequence differs by a factor of two. + an = r(an-1) an = a1(rn-1) + + Where: + r = The "common ratio" + + + Example of a geometric sequence: + 3, 12, 48, 192, 768, 3072 . . . + + + An = a1 + a2 + . . . an + a1(1 - rn) + An = + 1-r + + +4.10 Factorials +4.10.1 Definition of a factorial +Denoted by the symbol ”!” after an integer; the product of that integer and all integers in +descent to 1. + Example of a factorial: + 5! = 5 x 4 x 3 x 2 x 1 + + 5! = 120 + + +4.10.2 Strange factorials +0! = 1 1! = 1 + + +4.11 Solving simultaneous equations +The terms simultaneous equations and systems of equations refer to conditions where two or +more unknown variables are related to each other through an equal number of equations. +Consider the following example: + 36 CHAPTER 4. ALGEBRA REFERENCE + + x + y = 24 + 2x - y = -6 + For this set of equations, there is but a single combination of values for x and y that will +satisfy both. Either equation, considered separately, has an infinitude of valid (x,y) solutions, +but together there is only one. Plotted on a graph, this condition becomes obvious: + + + + (6,18) + + + x + y = 24 + + + + + 2x - y = -6 + + + + + Each line is actually a continuum of points representing possible x and y solution pairs for +each equation. Each equation, separately, has an infinite number of ordered pair (x,y) solu- +tions. There is only one point where the two linear functions x + y = 24 and 2x - y = -6 +intersect (where one of their many independent solutions happen to work for both equations), +and that is where x is equal to a value of 6 and y is equal to a value of 18. + Usually, though, graphing is not a very efficient way to determine the simultaneous solution +set for two or more equations. It is especially impractical for systems of three or more variables. +In a three-variable system, for example, the solution would be found by the point intersection +of three planes in a three-dimensional coordinate space – not an easy scenario to visualize. + + +4.11.1 Substitution method +Several algebraic techniques exist to solve simultaneous equations. Perhaps the easiest to +comprehend is the substitution method. Take, for instance, our two-variable example problem: + x + y = 24 + 2x - y = -6 + In the substitution method, we manipulate one of the equations such that one variable is +defined in terms of the other: + 4.11. SOLVING SIMULTANEOUS EQUATIONS 37 + + x + y = 24 + + + + y = 24 - x + + Defining y in terms of x + Then, we take this new definition of one variable and substitute it for the same variable in +the other equation. In this case, we take the definition of y, which is 24 - x and substitute +this for the y term found in the other equation: + y = 24 - x + substitute + 2x - y = -6 + + + + + 2x - (24 - x) = -6 + Now that we have an equation with just a single variable (x), we can solve it using ”normal” +algebraic techniques: + 2x - (24 - x) = -6 + + Distributive property + + 2x - 24 + x = -6 + + Combining like terms + + 3x -24 = -6 + + Adding 24 to each side + + 3x = 18 + + Dividing both sides by 3 + + x=6 + Now that x is known, we can plug this value into any of the original equations and obtain +a value for y. Or, to save us some work, we can plug this value (6) into the equation we just +generated to define y in terms of x, being that it is already in a form to solve for y: + 38 CHAPTER 4. ALGEBRA REFERENCE + + x=6 + substitute + + y = 24 - x + + + + y = 24 - 6 + + + + y = 18 + Applying the substitution method to systems of three or more variables involves a similar +pattern, only with more work involved. This is generally true for any method of solution: +the number of steps required for obtaining solutions increases rapidly with each additional +variable in the system. + To solve for three unknown variables, we need at least three equations. Consider this +example: + x - y + z = 10 + 3x + y + 2z = 34 + -5x + 2y - z = -14 + Being that the first equation has the simplest coefficients (1, -1, and 1, for x, y, and z, +respectively), it seems logical to use it to develop a definition of one variable in terms of the +other two. In this example, I’ll solve for x in terms of y and z: + x - y + z = 10 + Adding y and subtracting z + from both sides + x = y - z + 10 + Now, we can substitute this definition of x where x appears in the other two equations: + x = y - z + 10 x = y - z + 10 + substitute substitute + + 3x + y + 2z = 34 -5x + 2y - z = -14 + + + + 3(y - z + 10) + y + 2z = 34 -5(y - z + 10) + 2y - z = -14 + Reducing these two equations to their simplest forms: + 4.11. SOLVING SIMULTANEOUS EQUATIONS 39 + + 3(y - z + 10) + y + 2z = 34 -5(y - z + 10) + 2y - z = -14 + + Distributive property + + 3y - 3z + 30 + y + 2z = 34 -5y + 5z - 50 + 2y - z = -14 + + Combining like terms + + 4y - z + 30 = 34 -3y + 4z - 50 = -14 + + Moving constant values to right + of the "=" sign + 4y - z = 4 -3y + 4z = 36 + So far, our efforts have reduced the system from three variables in three equations to two +variables in two equations. Now, we can apply the substitution technique again to the two +equations 4y - z = 4 and -3y + 4z = 36 to solve for either y or z. First, I’ll manipulate +the first equation to define z in terms of y: + 4y - z = 4 + Adding z to both sides; + subtracting 4 from both sides + z = 4y - 4 + Next, we’ll substitute this definition of z in terms of y where we see z in the other equation: + z = 4y - 4 + substitute + -3y + 4z = 36 + + + -3y + 4(4y - 4) = 36 + + Distributive property + -3y + 16y - 16 = 36 + + Combining like terms + 13y - 16 = 36 + + Adding 16 to both sides + 13y = 52 + Dividing both sides by 13 + y=4 + Now that y is a known value, we can plug it into the equation defining z in terms of y and + 40 CHAPTER 4. ALGEBRA REFERENCE + +obtain a figure for z: + y=4 + substitute + z = 4y - 4 + + + z = 16 - 4 + + + z = 12 + Now, with values for y and z known, we can plug these into the equation where we defined +x in terms of y and z, to obtain a value for x: + y=4 + + substitute z = 12 + substitute + x = y - z + 10 + + + x = 4 - 12 + 10 + + + x=2 + In closing, we’ve found values for x, y, and z of 2, 4, and 12, respectively, that satisfy all +three equations. + + +4.11.2 Addition method +While the substitution method may be the easiest to grasp on a conceptual level, there are +other methods of solution available to us. One such method is the so-called addition method, +whereby equations are added to one another for the purpose of canceling variable terms. + Let’s take our two-variable system used to demonstrate the substitution method: + x + y = 24 + 2x - y = -6 + One of the most-used rules of algebra is that you may perform any arithmetic operation you +wish to an equation so long as you do it equally to both sides. With reference to addition, this +means we may add any quantity we wish to both sides of an equation – so long as its the same +quantity – without altering the truth of the equation. + An option we have, then, is to add the corresponding sides of the equations together to form +a new equation. Since each equation is an expression of equality (the same quantity on either + 4.11. SOLVING SIMULTANEOUS EQUATIONS 41 + +side of the = sign), adding the left-hand side of one equation to the left-hand side of the other +equation is valid so long as we add the two equations’ right-hand sides together as well. In our +example equation set, for instance, we may add x + y to 2x - y, and add 24 and -6 together +as well to form a new equation. What benefit does this hold for us? Examine what happens +when we do this to our example equation set: + x + y = 24 + + 2x - y = -6 + 3x + 0 = 18 + Because the top equation happened to contain a positive y term while the bottom equation +happened to contain a negative y term, these two terms canceled each other in the process of +addition, leaving no y term in the sum. What we have left is a new equation, but one with only +a single unknown variable, x! This allows us to easily solve for the value of x: + 3x + 0 = 18 + + Dropping the 0 term + + 3x = 18 + + Dividing both sides by 3 + x=6 + Once we have a known value for x, of course, determining y’s value is a simply matter of +substitution (replacing x with the number 6) into one of the original equations. In this example, +the technique of adding the equations together worked well to produce an equation with a +single unknown variable. What about an example where things aren’t so simple? Consider the +following equation set: + 2x + 2y = 14 + 3x + y = 13 + We could add these two equations together – this being a completely valid algebraic opera- +tion – but it would not profit us in the goal of obtaining values for x and y: + 2x + 2y = 14 + + 3x + y = 13 + 5x + 3y = 27 + The resulting equation still contains two unknown variables, just like the original equations +do, and so we’re no further along in obtaining a solution. However, what if we could manipulate +one of the equations so as to have a negative term that would cancel the respective term in the +other equation when added? Then, the system would reduce to a single equation with a single +unknown variable just as with the last (fortuitous) example. + If we could only turn the y term in the lower equation into a - 2y term, so that when the +two equations were added together, both y terms in the equations would cancel, leaving us +with only an x term, this would bring us closer to a solution. Fortunately, this is not difficult to +do. If we multiply each and every term of the lower equation by a -2, it will produce the result + 42 CHAPTER 4. ALGEBRA REFERENCE + +we seek: + -2(3x + y) = -2(13) + + Distributive property + -6x - 2y = -26 + Now, we may add this new equation to the original, upper equation: + 2x + 2y = 14 + + -6x - 2y = -26 + -4x + 0y = -12 + Solving for x, we obtain a value of 3: + -4x + 0y = -12 + + Dropping the 0 term + + -4x = -12 + + Dividing both sides by -4 + + x=3 + Substituting this new-found value for x into one of the original equations, the value of y is +easily determined: + x=3 + substitute + + 2x + 2y = 14 + + + 6 + 2y = 14 + + Subtracting 6 from both sides + 2y = 8 + + Dividing both sides by 2 + y=4 + Using this solution technique on a three-variable system is a bit more complex. As with +substitution, you must use this technique to reduce the three-equation system of three vari- +ables down to two equations with two variables, then apply it again to obtain a single equation +with one unknown variable. To demonstrate, I’ll use the three-variable equation system from +the substitution section: + 4.11. SOLVING SIMULTANEOUS EQUATIONS 43 + + x - y + z = 10 + 3x + y + 2z = 34 + -5x + 2y - z = -14 + + + + + Being that the top equation has coefficient values of 1 for each variable, it will be an easy +equation to manipulate and use as a cancellation tool. For instance, if we wish to cancel the 3x +term from the middle equation, all we need to do is take the top equation, multiply each of its +terms by -3, then add it to the middle equation like this: + + + + + x - y + z = 10 + + Multiply both sides by -3 + -3(x - y + z) = -3(10) + Distributive property + -3x + 3y - 3z = -30 + + + + -3x + 3y - 3z = -30 + (Adding) + + 3x + y + 2z = 34 + 0x + 4y - z = 4 + or + 4y - z = 4 + + + + + We can rid the bottom equation of its -5x term in the same manner: take the original +top equation, multiply each of its terms by 5, then add that modified equation to the bottom +equation, leaving a new equation with only y and z terms: + 44 CHAPTER 4. ALGEBRA REFERENCE + + x - y + z = 10 + + Multiply both sides by 5 + 5(x - y + z) = 5(10) + + Distributive property + 5x - 5y + 5z = 50 + + + + 5x - 5y + 5z = 50 + (Adding) + + -5x + 2y - z = -14 + 0x - 3y + 4z = 36 + or + -3y + 4z = 36 + At this point, we have two equations with the same two unknown variables, y and z: + 4y - z = 4 + -3y + 4z = 36 + By inspection, it should be evident that the -z term of the upper equation could be leveraged +to cancel the 4z term in the lower equation if only we multiply each term of the upper equation +by 4 and add the two equations together: + 4y - z = 4 + + Multiply both sides by 4 + + 4(4y - z) = 4(4) + + Distributive property + + 16y - 4z = 16 + + + + 16y - 4z = 16 + (Adding) + + -3y + 4z = 36 + 13y + 0z = 52 + or + 13y = 52 + Taking the new equation 13y = 52 and solving for y (by dividing both sides by 13), we get +a value of 4 for y. Substituting this value of 4 for y in either of the two-variable equations + 4.12. CONTRIBUTORS 45 + +allows us to solve for z. Substituting both values of y and z into any one of the original, three- +variable equations allows us to solve for x. The final result (I’ll spare you the algebraic steps, +since you should be familiar with them by now!) is that x = 2, y = 4, and z = 12. + + +4.12 Contributors +Contributors to this chapter are listed in chronological order of their contributions, from most +recent to first. See Appendix 2 (Contributor List) for dates and contact information. + Chirvasuta Constantin (April 2, 2003): Pointed out error in quadratic equation formula. + 46 CHAPTER 4. ALGEBRA REFERENCE + Chapter 5 + +TRIGONOMETRY REFERENCE + +Contents + 5.1 Right triangle trigonometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 + 5.1.1 Trigonometric identities . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 + 5.1.2 The Pythagorean theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 + 5.2 Non-right triangle trigonometry . . . . . . . . . . . . . . . . . . . . . . . . . 48 + 5.2.1 The Law of Sines (for any triangle) . . . . . . . . . . . . . . . . . . . . . . 48 + 5.2.2 The Law of Cosines (for any triangle) . . . . . . . . . . . . . . . . . . . . . 49 + 5.3 Trigonometric equivalencies . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 + 5.4 Hyperbolic functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 + 5.5 Contributors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 + + + + +5.1 Right triangle trigonometry + + + + + Hypotenuse (H) + Opposite (O) + + + + Angle 90o + x + + Adjacent (A) +A right triangle is defined as having one angle precisely equal to 90o (a right angle). + + 47 + 48 CHAPTER 5. TRIGONOMETRY REFERENCE + +5.1.1 Trigonometric identities + + sin x = O cos x = A tan x = O sin x + tan x = cos x + H H A + + +csc x = H sec x = H cot x = A cot x = cos x + sin x + O A O + H is the Hypotenuse, always being opposite the right angle. Relative to angle x, O is the +Opposite and A is the Adjacent. + ”Arc” functions such as ”arcsin”, ”arccos”, and ”arctan” are the complements of normal +trigonometric functions. These functions return an angle for a ratio input. For example, if +the tangent of 45o is equal to 1, then the ”arctangent” (arctan) of 1 is 45o . ”Arc” functions are +useful for finding angles in a right triangle if the side lengths are known. + + + +5.1.2 The Pythagorean theorem + +H 2 = A2 + O2 + + + +5.2 Non-right triangle trigonometry + + + b + + + + C A + + + + + a c + B +5.2.1 The Law of Sines (for any triangle) + + sin a = sin b = sin c + A B C + 5.3. TRIGONOMETRIC EQUIVALENCIES 49 + +5.2.2 The Law of Cosines (for any triangle) +A2 = B2 + C2 - (2BC)(cos a) +B2 = A2 + C2 - (2AC)(cos b) +C2 = A2 + B2 - (2AB)(cos c) + + +5.3 Trigonometric equivalencies +sin -x = -sin x cos -x = cos x tan -t = -tan t + +csc -t = -csc t sec -t = sec t cot -t = -cot t + +sin 2x = 2(sin x)(cos x) cos 2x = (cos2 x) - (sin2 x) + + 2(tan x) +tan 2t = + 1 - tan2 x + + + sin2 x = 1 - cos 2x cos2 x = 1 + cos 2x + 2 2 2 2 + + +5.4 Hyperbolic functions + ex - e-x + sinh x = + 2 + ex + e-x +cosh x = + 2 + + sinh x +tanh x = + cosh x + Note: all angles (x) must be expressed in units of radians for these hyperbolic functions. +There are 2π radians in a circle (360o ). + + +5.5 Contributors +Contributors to this chapter are listed in chronological order of their contributions, from most +recent to first. See Appendix 2 (Contributor List) for dates and contact information. + 50 CHAPTER 5. TRIGONOMETRY REFERENCE + + Harvey Lew (??? 2003): Corrected typographical error: ”tangent” should have been ”cotan- +gent”. + Chapter 6 + +CALCULUS REFERENCE + +Contents + 6.1 Rules for limits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 + 6.2 Derivative of a constant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 + 6.3 Common derivatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 + 6.4 Derivatives of power functions of e . . . . . . . . . . . . . . . . . . . . . . . 52 + 6.5 Trigonometric derivatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 + 6.6 Rules for derivatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 + 6.6.1 Constant rule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 + 6.6.2 Rule of sums . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 + 6.6.3 Rule of differences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 + 6.6.4 Product rule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 + 6.6.5 Quotient rule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 + 6.6.6 Power rule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 + 6.6.7 Functions of other functions . . . . . . . . . . . . . . . . . . . . . . . . . . 54 + 6.7 The antiderivative (Indefinite integral) . . . . . . . . . . . . . . . . . . . . . 55 + 6.8 Common antiderivatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 + 6.9 Antiderivatives of power functions of e . . . . . . . . . . . . . . . . . . . . . 56 + 6.10 Rules for antiderivatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 + 6.10.1 Constant rule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 + 6.10.2 Rule of sums . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 + 6.10.3 Rule of differences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 + 6.11 Definite integrals and the fundamental theorem of calculus . . . . . . . . 56 + 6.12 Differential equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 + + + + + 51 + 52 CHAPTER 6. CALCULUS REFERENCE + +6.1 Rules for limits +lim [f(x) + g(x)] = lim f(x) + lim g(x) +x→a x→a x→a + +lim [f(x) - g(x)] = lim f(x) - lim g(x) +x→a x→a x→a + +lim [f(x) g(x)] = [lim f(x)] [lim g(x)] +x→a x→a x→a + + +6.2 Derivative of a constant + If: + f(x) = c + +Then: + d f(x) = 0 + dx + (”c” being a constant) + + +6.3 Common derivatives + d xn = nxn-1 + dx + + d ln x = 1 + dx x + + d ax = (ln a)(ax) + dx + + +6.4 Derivatives of power functions of e + If: If: + x + f(x) = e f(x) = eg(x) + +Then: Then: + d f(x) = ex d f(x) = eg(x) d g(x) + dx dx dx + 6.5. TRIGONOMETRIC DERIVATIVES 53 + + Example: + 2 + f(x) = e(x + 2x) + + + d f(x) = e(x2 + 2x) d (x2 + 2x) + dx dx + + d f(x) = (e(x2 + 2x))(2x + 2) + dx + + + +6.5 Trigonometric derivatives + + d sin x = cos x d cos x = -sin x + dx dx + + d tan x = sec2 x d cot x = -csc2 x + dx dx + + d sec x = (sec x)(tan x) d csc x = (-csc x)(cot x) + dx dx + + + +6.6 Rules for derivatives +6.6.1 Constant rule + d [cf(x)] = c d f(x) + dx dx + + +6.6.2 Rule of sums + d [f(x) + g(x)] = d f(x) + d g(x) + dx dx dx + + +6.6.3 Rule of differences + d [f(x) - g(x)] = d f(x) - d g(x) + dx dx dx + 54 CHAPTER 6. CALCULUS REFERENCE + +6.6.4 Product rule + + d [f(x) g(x)] = f(x)[ d g(x)] + g(x)[ d f(x)] + dx dx dx + + + + +6.6.5 Quotient rule + + + f(x) g(x)[ d f(x)] - f(x)[ d g(x)] + d = dx dx + dx g(x) [g(x)] 2 + + + + +6.6.6 Power rule + + d f(x)a = a[f(x)]a-1 d f(x) + dx dx + + + + +6.6.7 Functions of other functions + + d f[g(x)] + dx + + Break the function into two functions: + + u = g(x) and y = f(u) + + Solve: + dy f[g(x)] = dy f(u) du g(x) + dx du dx + 6.7. THE ANTIDERIVATIVE (INDEFINITE INTEGRAL) 55 + +6.7 The antiderivative (Indefinite integral) + +If: + d f(x) = g(x) + dx + +Then: + g(x) is the derivative of f(x) + f(x) is the antiderivative of g(x) + + +∫g(x) dx = f(x) + c + Notice something important here: taking the derivative of f(x) may precisely give you g(x), +but taking the antiderivative of g(x) does not necessarily give you f(x) in its original form. +Example: + f(x) = 3x2 + 5 + + d f(x) = 6x + dx + + ∫6x dx = 3x2 + c + Note that the constant c is unknown! The original function f(x) could have been 3x2 + 5, +3x + 10, 3x2 + anything, and the derivative of f(x) would have still been 6x. Determining the + 2 + +antiderivative of a function, then, is a bit less certain than determining the derivative of a +function. + + + +6.8 Common antiderivatives + +∫xn dx = xn+1 + c + n+1 + + +∫ 1x dx = (ln |x|) + c + + +Where, + c = a constant + + + ∫ax dx = ax + c + ln a + 56 CHAPTER 6. CALCULUS REFERENCE + +6.9 Antiderivatives of power functions of e + +∫ex dx = ex + c + Note: this is a very unique and useful property of e. As in the case of derivatives, the +antiderivative of such a function is that same function. In the case of the antiderivative, a +constant term ”c” is added to the end as well. + + + +6.10 Rules for antiderivatives +6.10.1 Constant rule +∫cf(x) dx = c ∫f(x) dx + + +6.10.2 Rule of sums +∫[f(x) + g(x)] dx = [∫f(x) dx ] + [∫g(x) dx ] + + +6.10.3 Rule of differences +∫[f(x) - g(x)] dx = [∫f(x) dx ] - [∫g(x) dx ] + + + +6.11 Definite integrals and the fundamental theorem of + calculus +If: + ∫f(x) dx = g(x) or d g(x) = f(x) + dx + + +Then: + b + ∫f(x) dx = g(b) - g(a) + a + + +Where, + a and b are constants + 6.12. DIFFERENTIAL EQUATIONS 57 + + If: + ∫f(x) dx = g(x) and a=0 + + + + Then: + x + ∫f(x) dx = g(x) + 0 + + + + +6.12 Differential equations +As opposed to normal equations where the solution is a number, a differential equation is one +where the solution is actually a function, and which at least one derivative of that unknown +function is part of the equation. + As with finding antiderivatives of a function, we are often left with a solution that encom- +passes more than one possibility (consider the many possible values of the constant ”c” typically +found in antiderivatives). The set of functions which answer any differential equation is called +the ”general solution” for that differential equation. Any one function out of that set is re- +ferred to as a ”particular solution” for that differential equation. The variable of reference for +differentiation and integration within the differential equation is known as the ”independent +variable.” + 58 CHAPTER 6. CALCULUS REFERENCE + Chapter 7 + +USING THE SPICE CIRCUIT +SIMULATION PROGRAM + +Contents + 7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 + 7.2 History of SPICE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 + 7.3 Fundamentals of SPICE programming . . . . . . . . . . . . . . . . . . . . . 61 + 7.4 The command-line interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 + 7.5 Circuit components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 + 7.5.1 Passive components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 + 7.5.2 Active components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 + 7.5.3 Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 + 7.6 Analysis options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 + 7.7 Quirks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 + 7.7.1 A good beginning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 + 7.7.2 A good ending . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 + 7.7.3 Must have a node 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 + 7.7.4 Avoid open circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 + 7.7.5 Avoid certain component loops . . . . . . . . . . . . . . . . . . . . . . . . . 79 + 7.7.6 Current measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 + 7.7.7 Fourier analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 + 7.8 Example circuits and netlists . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 + 7.8.1 Multiple-source DC resistor network, part 1 . . . . . . . . . . . . . . . . . 86 + 7.8.2 Multiple-source DC resistor network, part 2 . . . . . . . . . . . . . . . . . 87 + 7.8.3 RC time-constant circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 + 7.8.4 Plotting and analyzing a simple AC sinewave voltage . . . . . . . . . . . 89 + 7.8.5 Simple AC resistor-capacitor circuit . . . . . . . . . . . . . . . . . . . . . 91 + 7.8.6 Low-pass filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 + 7.8.7 Multiple-source AC network . . . . . . . . . . . . . . . . . . . . . . . . . . 94 + + 59 + 60 CHAPTER 7. USING THE SPICE CIRCUIT SIMULATION PROGRAM + + 7.8.8 AC phase shift demonstration . . . . . . . . . . . . . . . . . . . . . . . . . 95 + 7.8.9 Transformer circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 + 7.8.10 Full-wave bridge rectifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 + 7.8.11 Common-base BJT transistor amplifier . . . . . . . . . . . . . . . . . . . 99 + 7.8.12 Common-source JFET amplifier with self-bias . . . . . . . . . . . . . . . 102 + 7.8.13 Inverting op-amp circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 + 7.8.14 Noninverting op-amp circuit . . . . . . . . . . . . . . . . . . . . . . . . . . 106 + 7.8.15 Instrumentation amplifier . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 + 7.8.16 Op-amp integrator with sinewave input . . . . . . . . . . . . . . . . . . . 108 + 7.8.17 Op-amp integrator with squarewave input . . . . . . . . . . . . . . . . . . 110 + + + + +7.1 Introduction + ”With Electronics Workbench, you can create circuit schematics that look just the + same as those you’re already familiar with on paper – plus you can flip the power + switch so the schematic behaves like a real circuit. With other electronics simulators, + you may have to type in SPICE node lists as text files – an abstract representation of + a circuit beyond the capabilities of all but advanced electronics engineers.” + (Electronics Workbench User’s guide – version 4, page 7) + + This introduction comes from the operating manual for a circuit simulation program called +Electronics Workbench. Using a graphic interface, it allows the user to draw a circuit schematic +and then have the computer analyze that circuit, displaying the results in graphic form. It is a +very valuable analysis tool, but it has its shortcomings. For one, it and other graphic programs +like it tend to be unreliable when analyzing complex circuits, as the translation from picture +to computer code is not quite the exact science we would want it to be (yet). Secondly, due to its +graphics requirements, it tends to need a significant amount of computational ”horsepower” to +run, and a computer operating system that supports graphics. Thirdly, these graphic programs +can be costly. + However, underneath the graphics skin of Electronics Workbench lies a robust (and free!) +program called SPICE, which analyzes a circuit based on a text-file description of the circuit’s +components and connections. What the user pays for with Electronics Workbench and other +graphic circuit analysis programs is the convenient ”point and click” interface, while SPICE +does the actual mathematical analysis. + By itself, SPICE does not require a graphic interface and demands little in system re- +sources. It is also very reliable. The makers of Electronic Workbench would like you to think +that using SPICE in its native text mode is a task suited for rocket scientists, but I’m writing +this to prove them wrong. SPICE is fairly easy to use for simple circuits, and its non-graphic +interface actually lends itself toward the analysis of circuits that can be difficult to draw. I +think it was the programming expert Donald Knuth who quipped, ”What you see is all you get” +when it comes to computer applications. Graphics may look more attractive, but abstracted +interfaces (text) are actually more efficient. + 7.2. HISTORY OF SPICE 61 + + This document is not intended to be an exhaustive tutorial on how to use SPICE. I’m merely +trying to show the interested user how to apply it to the analysis of simple circuits, as an +alternative to proprietary ($$$) and buggy programs. Once you learn the basics, there are +other tutorials better suited to take you further. Using SPICE – a program originally intended +to develop integrated circuits – to analyze some of the really simple circuits showcased here +may seem a bit like cutting butter with a chain saw, but it works! + All options and examples have been tested on SPICE version 2g6 on both MS-DOS and +Linux operating systems. As far as I know, I’m not using features specific to version 2g6, so +these simple functions should work on most versions of SPICE. + + + +7.2 History of SPICE +SPICE is a computer program designed to simulate analog electronic circuits. It original intent +was for the development of integrated circuits, from which it derived its name: Simulation +Program with Integrated Circuit Emphasis. + The origin of SPICE traces back to another circuit simulation program called CANCER. +Developed by professor Ronald Rohrer of U.C. Berkeley along with some of his students in the +late 1960’s, CANCER continued to be improved through the early 1970’s. When Rohrer left +Berkeley, CANCER was re-written and re-named to SPICE, released as version 1 to the public +domain in May of 1972. Version 2 of SPICE was released in 1975 (version 2g6 – the version +used in this book – is a minor revision of this 1975 release). Instrumental in the decision +to release SPICE as a public-domain computer program was professor Donald Pederson of +Berkeley, who believed that all significant technical progress happens when information is +freely shared. I for one thank him for his vision. + A major improvement came about in March of 1985 with version 3 of SPICE (also released +under public domain). Written in the C language rather than FORTRAN, version 3 incorpo- +rated additional transistor types (the MESFET, for example), and switch elements. Version 3 +also allowed the use of alphabetical node labels rather than only numbers. Instructions written +for version 2 of SPICE should still run in version 3, though. + Despite the additional power of version 3, I have chosen to use version 2g6 throughout +this book because it seems to be the easiest version to acquire and run on different computer +systems. + + + +7.3 Fundamentals of SPICE programming +Programming a circuit simulation with SPICE is much like programming in any other com- +puter language: you must type the commands as text in a file, save that file to the computer’s +hard drive, and then process the contents of that file with a program (compiler or interpreter) +that understands such commands. + In an interpreted computer language, the computer holds a special program called an inter- +preter that translates the program you wrote (the so-called source file) into the computer’s own +language, on the fly, as its being executed: + 62 CHAPTER 7. USING THE SPICE CIRCUIT SIMULATION PROGRAM + + Computer + + Source Interpreter + software Output + File + + + In a compiled computer language, the program you wrote is translated all at once into the +computer’s own language by a special program called a compiler. After the program you’ve +written has been ”compiled,” the resulting executable file needs no further translation to be un- +derstood directly by the computer. It can now be ”run” on a computer whether or not compiler +software has been installed on that computer: + + Computer + + Source Compiler + File software + + + Computer + + Executable Executable + File File + + + + + Output + + SPICE is an interpreted language. In order for a computer to be able to understand the +SPICE instructions you type, it must have the SPICE program (interpreter) installed: + + Computer + Source + File SPICE + software Output + "netlist" + SPICE source files are commonly referred to as ”netlists,” although they are sometimes +known as ”decks” with each line in the file being called a ”card.” Cute, don’t you think? Netlists +are created by a person like yourself typing instructions line-by-line using a word processor +or text editor. Text editors are much preferred over word processors for any type of computer +programming, as they produce pure ASCII text with no special embedded codes for text high- + 7.3. FUNDAMENTALS OF SPICE PROGRAMMING 63 + +lighting (like italic or boldface fonts), which are uninterpretable by interpreter and compiler +software. + As in general programming, the source file you create for SPICE must follow certain con- +ventions of programming. It is a computer language in itself, albeit a simple one. Having +programmed in BASIC and C/C++, and having some experience reading PASCAL and FOR- +TRAN programs, it is my opinion that the language of SPICE is much simpler than any of +these. It is about the same complexity as a markup language such as HTML, perhaps less so. + There is a cycle of steps to be followed in using SPICE to analyze a circuit. The cycle starts +when you first invoke the text editing program and make your first draft of the netlist. The +next step is to run SPICE on that new netlist and see what the results are. If you are a novice +user of SPICE, your first attempts at creating a good netlist will be fraught with small errors +of syntax. Don’t worry – as every computer programmer knows, proficiency comes with lots of +practice. If your trial run produces error messages or results that are obviously incorrect, you +need to re-invoke the text editing program and modify the netlist. After modifying the netlist, +you need to run SPICE again and check the results. The sequence, then, looks something like +this: + + • Compose a new netlist with a text editing program. Save that netlist to a file with a name + of your choice. + + • Run SPICE on that netlist and observe the results. + + • If the results contain errors, start up the text editing program again and modify the + netlist. + + • Run SPICE again and observe the new results. + + • If there are still errors in the output of SPICE, re-edit the netlist again with the text + editing program. Repeat this cycle of edit/run as many times as necessary until you are + getting the desired results. + + • Once you’ve ”debugged” your netlist and are getting good results, run SPICE again, only + this time redirecting the output to a new file instead of just observing it on the computer + screen. + + • Start up a text editing program or a word processor program and open the SPICE output + file you just created. Modify that file to suit your formatting needs and either save those + changes to disk and/or print them out on paper. + + To ”run” a SPICE ”program,” you need to type in a command at a terminal prompt interface, +such as that found in MS-DOS, UNIX, or the MS-Windows DOS prompt option: + +spice < example.cir + + The word ”spice” invokes the SPICE interpreting program (providing that the SPICE soft- +ware has been installed on the computer!), the ”<” symbol redirects the contents of the source +file to the SPICE interpreter, and example.cir is the name of the source file for this circuit +example. The file extension ”.cir” is not mandatory; I have seen ”.inp” (for ”input”) and just + 64 CHAPTER 7. USING THE SPICE CIRCUIT SIMULATION PROGRAM + +plain ”.txt” work well, too. It will even work when the netlist file has no extension. SPICE +doesn’t care what you name it, so long as it has a name compatible with the filesystem of +your computer (for old MS-DOS machines, for example, the filename must be no more than 8 +characters in length, with a 3 character extension, and no spaces or other non-alphanumerical +characters). + When this command is typed in, SPICE will read the contents of the example.cir file, +analyze the circuit specified by that file, and send a text report to the computer terminal’s +standard output (usually the screen, where you can see it scroll by). A typical SPICE out- +put is several screens worth of information, so you might want to look it over with a slight +modification of the command: + + +spice < example.cir | more + + + This alternative ”pipes” the text output of SPICE to the ”more” utility, which allows only one +page to be displayed at a time. What this means (in English) is that the text output of SPICE +is halted after one screen-full, and waits until the user presses a keyboard key to display the +next screen-full of text. If you’re just testing your example circuit file and want to check for +any errors, this is a good way to do it. + + +spice < example.cir > example.txt + + + This second alternative (above) redirects the text output of SPICE to another file, called +example.txt, where it can be viewed or printed. This option corresponds to the last step +in the development cycle listed earlier. It is recommended by this author that you use this +technique of ”redirection” to a text file only after you’ve proven your example circuit netlist to +work well, so that you don’t waste time invoking a text editor just to see the output during the +stages of ”debugging.” + Once you have a SPICE output stored in a .txt file, you can use a text editor or (better +yet!) a word processor to edit the output, deleting any unnecessary banners and messages, +even specifying alternative fonts to highlight the headings and/or data for a more polished +appearance. Then, of course, you can print the output to paper if you so desire. Being that the +direct SPICE output is plain ASCII text, such a file will be universally interpretable on any +computer whether SPICE is installed on it or not. Also, the plain text format ensures that the +file will be very small compared to the graphic screen-shot files generated by ”point-and-click” +simulators. + The netlist file format required by SPICE is quite simple. A netlist file is nothing more +than a plain ASCII text file containing multiple lines of text, each line describing either a +circuit component or special SPICE command. Circuit architecture is specified by assigning +numbers to each component’s connection points in each line, connections between components +designated by common numbers. Examine the following example circuit diagram and its cor- +responding SPICE file. Please bear in mind that the circuit diagram exists only to make the +simulation easier for human beings to understand. SPICE only understands netlists: + 7.3. FUNDAMENTALS OF SPICE PROGRAMMING 65 + + + 1 1 R2 + 2 + 3.3 kΩ + 15 V R1 2.2 kΩ R3 + 150 Ω + + 0 0 0 + +Example netlist +v1 1 0 dc 15 +r1 1 0 2.2k +r2 1 2 3.3k +r3 2 0 150 +.end + + Each line of the source file shown above is explained here: + + • v1 represents the battery (voltage source 1), positive terminal numbered 1, negative ter- + minal numbered 0, with a DC voltage output of 15 volts. + • r1 represents resistor R1 in the diagram, connected between points 1 and 0, with a value + of 2.2 kΩ. + • r2 represents resistor R2 in the diagram, connected between points 1 and 2, with a value + of 3.3 kΩ. + • r3 represents resistor R3 in the diagram, connected between points 2 and 0, with a value + of 150 kΩ. + + Electrically common points (or ”nodes”) in a SPICE circuit description share common num- +bers, much in the same way that wires connecting common points in a large circuit typically +share common wire labels. + To simulate this circuit, the user would type those six lines of text on a text editor and +save them as a file with a unique name (such as example.cir). Once the netlist is composed +and saved to a file, the user then processes that file with one of the command-line statements +shown earlier (spice < example.cir), and will receive this text output on their computer’s +screen: + +1*******10/10/99 ******** spice 2g.6 3/15/83 ********07:32:42***** +0example netlist +0**** input listing temperature = 27.000 deg c +v1 1 0 dc 15 +r1 1 0 2.2k +r2 1 2 3.3k +r3 2 0 150 +.end + 66 CHAPTER 7. USING THE SPICE CIRCUIT SIMULATION PROGRAM + +*****10/10/99 ********* spice 2g.6 3/15/83 ******07:32:42****** +0example netlist +0**** small signal bias solution temperature = 27.000 deg c +node voltage node voltage +( 1) 15.0000 ( 2) 0.6522 +voltage source currents +name current +v1 -1.117E-02 +total power dissipation 1.67E-01 watts +job concluded +0 total job time 0.02 +1*******10/10/99 ******** spice 2g.6 3/15/83 ******07:32:42***** +0**** input listing temperature = 27.000 deg c + + SPICE begins by printing the time, date, and version used at the top of the output. It then +lists the input parameters (the lines of the source file), followed by a display of DC voltage +readings from each node (reference number) to ground (always reference number 0). This is +followed by a list of current readings through each voltage source (in this case there’s only one, +v1). Finally, the total power dissipation and computation time in seconds is printed. + All output values provided by SPICE are displayed in scientific notation. + The SPICE output listing shown above is a little verbose for most peoples’ taste. For a final +presentation, it might be nice to trim all the unnecessary text and leave only what matters. +Here is a sample of that same output, redirected to a text file (spice < example.cir > +example.txt), then trimmed down judiciously with a text editor for final presentation and +printed: + +example netlist +v1 1 0 dc 15 +r1 1 0 2.2k +r2 1 2 3.3k +r3 2 0 150 +.end + +node voltage node voltage +( 1) 15.0000 ( 2) 0.6522 + +voltage source currents +name current +v1 -1.117E-02 + +total power dissipation 1.67E-01 watts + + One of the very nice things about SPICE is that both input and output formats are plain- +text, which is the most universal and easy-to-edit electronic format around. Practically any +computer will be able to edit and display this format, even if the SPICE program itself is not +resident on that computer. If the user desires, he or she is free to use the advanced capabilities +of word processing programs to make the output look fancier. Comments can even be inserted +between lines of the output for further clarity to the reader. + 7.4. THE COMMAND-LINE INTERFACE 67 + +7.4 The command-line interface +If you’ve used DOS or UNIX operating systems before in a command-line shell environment, +you may wonder why we have to use the ”<” symbol between the word ”spice” and the name +of the netlist file to be interpreted. Why not just enter the file name as the first argument +to the command ”spice” as we do when we invoke the text editor? The answer is that SPICE +has the option of an interactive mode, whereby each line of the netlist can be interpreted as +it is entered through the computer’s Standard Input (stdin). If you simple type ”spice” at the +prompt and press [Enter], SPICE will begin to interpret anything you type in to it (live). + For most applications, its nice to save your netlist work in a separate file and then let SPICE +interpret that file when you’re ready. This is the way I encourage SPICE to be used, and so +this is the way its presented in this lesson. In order to use SPICE this way in a command-line +environment, we need to use the ”<” redirection symbol to direct the contents of your netlist +file to Standard Input (stdin), which SPICE can then process. + + +7.5 Circuit components +Remember that this tutorial is not exhaustive by any means, and that all descriptions for +elements in the SPICE language are documented here in condensed form. SPICE is a very +capable piece of software with lots of options, and I’m only going to document a few of them. + All components in a SPICE source file are primarily identified by the first letter in each +respective line. Characters following the identifying letter are used to distinguish one compo- +nent of a certain type from another of the same type (r1, r2, r3, rload, rpullup, etc.), and need +not follow any particular naming convention, so long as no more than eight characters are used +in both the component identifying letter and the distinguishing name. + For example, suppose you were simulating a digital circuit with ”pullup” and ”pulldown” +resistors. The name rpullup would be valid because it is seven characters long. The name +rpulldown, however, is nine characters long. This may cause problems when SPICE inter- +prets the netlist. + You can actually get away with component names in excess of eight total characters if there +are no other similarly-named components in the source file. SPICE only pays attention to the +first eight characters of the first field in each line, so rpulldown is actually interpreted as +rpulldow with the ”n” at the end being ignored. Therefore, any other resistor having the +first eight characters in its first field will be seen by SPICE as the same resistor, defined twice, +which will cause an error (i.e. rpulldown1 and rpulldown2 would be interpreted as the same +name, rpulldow). + It should also be noted that SPICE ignores character case, so r1 and R1 are interpreted by +SPICE as one and the same. + SPICE allows the use of metric prefixes in specifying component values, which is a very +handy feature. However, the prefix convention used by SPICE differs somewhat from stan- +dard metric symbols, primarily due to the fact that netlists are restricted to standard ASCII +characters (ruling out Greek letters such as µ for the prefix ”micro”) and that SPICE is case- +insensitive, so ”m” (which is the standard symbol for ”milli”) and ”M” (which is the standard +symbol for ”Mega”) are interpreted identically. Here are a few examples of prefixes used in +SPICE netlists: + 68 CHAPTER 7. USING THE SPICE CIRCUIT SIMULATION PROGRAM + + r1 1 0 2t (Resistor R1 , 2t = 2 Tera-ohms = 2 TΩ) + r2 1 0 4g (Resistor R2 , 4g = 4 Giga-ohms = 4 GΩ) + r3 1 0 47meg (Resistor R3 , 47meg = 47 Mega-ohms = 47 MΩ) + r4 1 0 3.3k (Resistor R4 , 3.3k = 3.3 kilo-ohms = 3.3 kΩ) + r5 1 0 55m (Resistor R5 , 55m = 55 milli-ohms = 55 mΩ) + r6 1 0 10u (Resistor R6 , 10u = 10 micro-ohms 10 µΩ) + r7 1 0 30n (Resistor R7 , 30n = 30 nano-ohms = 30 nΩ) + r8 1 0 5p (Resistor R8 , 5p = 5 pico-ohms = 5 pΩ) + r9 1 0 250f (Resistor R9 , 250f = 250 femto-ohms = 250 fΩ) + + Scientific notation is also allowed in specifying component values. For example: + + r10 1 0 4.7e3 (Resistor R10 , 4.7e3 = 4.7 x 103 ohms = 4.7 kilo-ohms = 4.7 kΩ) + r11 1 0 1e-12 (Resistor R11 , 1e-12 = 1 x 10−12 ohms = 1 pico-ohm = 1 pΩ) + + The unit (ohms, volts, farads, henrys, etc.) is automatically determined by the type of +component being specified. SPICE ”knows” that all of the above examples are ”ohms” because +they are all resistors (r1, r2, r3, . . . ). If they were capacitors, the values would be interpreted +as ”farads,” if inductors, then ”henrys,” etc. + + +7.5.1 Passive components +CAPACITORS + +General form: c[name] [node1] [node2] [value] ic=[initial voltage] +Example 1: c1 12 33 10u +Example 2: c1 12 33 10u ic=3.5 + +Comments: The ”initial condition” (ic=) variable is the capacitor’s voltage in units of volts at +the start of DC analysis. It is an optional value, with the starting voltage assumed to be zero if +unspecified. Starting current values for capacitors are interpreted by SPICE only if the .tran +analysis option is invoked (with the ”uic” option). + + +INDUCTORS + +General form: l[name] [node1] [node2] [value] ic=[initial current] +Example 1: l1 12 33 133m +Example 2: l1 12 33 133m ic=12.7m + +Comments: The ”initial condition” (ic=) variable is the inductor’s current in units of amps at +the start of DC analysis. It is an optional value, with the starting current assumed to be zero +if unspecified. Starting current values for inductors are interpreted by SPICE only if the .tran +analysis option is invoked. + 7.5. CIRCUIT COMPONENTS 69 + +INDUCTOR COUPLING (transformers) +General form: k[name] l[name] l[name] [coupling factor] +Example 1: k1 l1 l2 0.999 + +Comments: SPICE will only allow coupling factor values between 0 and 1 (non-inclusive), +with 0 representing no coupling and 1 representing perfect coupling. The order of specifying +coupled inductors (l1, l2 or l2, l1) is irrelevant. + +RESISTORS +General form: r[name] [node1] [node2] [value] +Example: rload 23 15 3.3k + +Comments: In case you were wondering, there is no declaration of resistor power dissipation +rating in SPICE. All components are assumed to be indestructible. If only real life were this +forgiving! + + +7.5.2 Active components +All semiconductor components must have their electrical characteristics described in a line +starting with the word ”.model”, which tells SPICE exactly how the device will behave. What- +ever parameters are not explicitly defined in the .model card will default to values pre- +programmed in SPICE. However, the .model card must be included, and at least specify the +model name and device type (d, npn, pnp, njf, pjf, nmos, or pmos). + +DIODES +General form: d[name] [anode] [cathode] [model] +Example: d1 1 2 mod1 + +DIODE MODELS: +General form: .model [modelname] d [parmtr1=x] [parmtr2=x] . . . +Example: .model mod1 d +Example: .model mod2 d vj=0.65 rs=1.3 + + ¡hypertarget¿diodeparameter¡/hypertarget¿ + Parameter definitions: + is = saturation current in amps + rs = junction resistance in ohms + n = emission coefficient (unitless) + tt = transit time in seconds + cjo = zero-bias junction capacitance in farads + vj = junction potential in volts + m = grading coefficient (unitless) + eg = activation energy in electron-volts + 70 CHAPTER 7. USING THE SPICE CIRCUIT SIMULATION PROGRAM + + xti = saturation-current temperature exponent (unitless) + kf = flicker noise coefficient (unitless) + af = flicker noise exponent (unitless) + fc = forward-bias depletion capacitance coefficient (unitless) + bv = reverse breakdown voltage in volts + ibv = current at breakdown voltage in amps + + Comments: The model name must begin with a letter, not a number. If you plan to specify +a model for a 1N4003 rectifying diode, for instance, you cannot use ”1n4003” for the model +name. An alternative might be ”m1n4003” instead. + +TRANSISTORS, bipolar junction – BJT +General form: q[name] [collector] [base] [emitter] [model] +Example: q1 2 3 0 mod1 + +BJT TRANSISTOR MODELS: +General form: .model [modelname] [npn or pnp] [parmtr1=x] . . . +Example: .model mod1 pnp +Example: .model mod2 npn bf=75 is=1e-14 + + The model examples shown above are very nonspecific. To accurately model real-life tran- +sistors, more parameters are necessary. Take these two examples, for the popular 2N2222 and +2N2907 transistors (the ”+”) characters represent line-continuation marks in SPICE, when you +wish to break a single line (card) into two or more separate lines on your text editor: + +Example: .model m2n2222 npn is=19f bf=150 vaf=100 ikf=.18 ++ ise=50p ne=2.5 br=7.5 var=6.4 ikr=12m ++ isc=8.7p nc=1.2 rb=50 re=0.4 rc=0.4 cje=26p ++ tf=0.5n cjc=11p tr=7n xtb=1.5 kf=0.032f af=1 + +Example: .model m2n2907 pnp is=1.1p bf=200 nf=1.2 vaf=50 ++ ikf=0.1 ise=13p ne=1.9 br=6 rc=0.6 cje=23p ++ vje=0.85 mje=1.25 tf=0.5n cjc=19p vjc=0.5 ++ mjc=0.2 tr=34n xtb=1.5 + + Parameter definitions: + is = transport saturation current in amps + bf = ideal maximum forward Beta (unitless) + nf = forward current emission coefficient (unitless) + vaf = forward Early voltage in volts + ikf = corner for forward Beta high-current rolloff in amps + ise = B-E leakage saturation current in amps + ne = B-E leakage emission coefficient (unitless) + br = ideal maximum reverse Beta (unitless) + nr = reverse current emission coefficient (unitless) + 7.5. CIRCUIT COMPONENTS 71 + + bar = reverse Early voltage in volts + ikrikr = corner for reverse Beta high-current rolloff in amps + iscisc = B-C leakage saturation current in amps + nc = B-C leakage emission coefficient (unitless) + rb = zero bias base resistance in ohms + irb = current for base resistance halfway value in amps + rbm = minimum base resistance at high currents in ohms + re = emitter resistance in ohms + rc = collector resistance in ohms + cje = B-E zero-bias depletion capacitance in farads + vje = B-E built-in potential in volts + mje = B-E junction exponential factor (unitless) + tf = ideal forward transit time (seconds) + xtf = coefficient for bias dependence of transit time (unitless) + vtf = B-C voltage dependence on transit time, in volts + itf = high-current parameter effect on transit time, in amps + ptf = excess phase at f=1/(transit time)(2)(pi) Hz, in degrees + cjc = B-C zero-bias depletion capacitance in farads + vjc = B-C built-in potential in volts + mjc = B-C junction exponential factor (unitless) + xjcj = B-C depletion capacitance fraction connected in base node (unitless) + tr = ideal reverse transit time in seconds + cjs = zero-bias collector-substrate capacitance in farads + vjs = substrate junction built-in potential in volts + mjs = substrate junction exponential factor (unitless) + xtb = forward/reverse Beta temperature exponent + eg = energy gap for temperature effect on transport saturation current in electron-volts + xti = temperature exponent for effect on transport saturation current (unitless) + kf = flicker noise coefficient (unitless) + af = flicker noise exponent (unitless) + fc = forward-bias depletion capacitance formula coefficient (unitless) + + Comments: Just as with diodes, the model name given for a particular transistor type +must begin with a letter, not a number. That’s why the examples given above for the 2N2222 +and 2N2907 types of BJTs are named ”m2n2222” and ”q2n2907” respectively. + As you can see, SPICE allows for very detailed specification of transistor properties. Many +of the properties listed above are well beyond the scope and interest of the beginning electronics +student, and aren’t even useful apart from knowing the equations SPICE uses to model BJT +transistors. For those interested in learning more about transistor modeling in SPICE, consult +other books, such as Andrei Vladimirescu’s The Spice Book (ISBN 0-471-60926-9). + +JFET, junction field-effect transistor +General form: j[name] [drain] [gate] [source] [model] +Example: j1 2 3 0 mod1 + 72 CHAPTER 7. USING THE SPICE CIRCUIT SIMULATION PROGRAM + +JFET TRANSISTOR MODELS: +General form: .model [modelname] [njf or pjf] [parmtr1=x] . . . +Example: .model mod1 pjf +Example: .model mod2 njf lambda=1e-5 pb=0.75 + + Parameter definitions: + vto = threshold voltage in volts + beta = transconductance parameter in amps/volts2 + lambda = channel length modulation parameter in units of 1/volts + rd = drain resistance in ohms + rs = source resistance in ohms + cgs = zero-bias G-S junction capacitance in farads + cgd = zero-bias G-D junction capacitance in farads + pb = gate junction potential in volts + is = gate junction saturation current in amps + kf = flicker noise coefficient (unitless) + af = flicker noise exponent (unitless) + fc = forward-bias depletion capacitance coefficient (unitless) + + +MOSFET, transistor + +General form: m[name] [drain] [gate] [source] [substrate] [model] +Example: m1 2 3 0 0 mod1 + +MOSFET TRANSISTOR MODELS: +General form: .model [modelname] [nmos or pmos] [parmtr1=x] . . . +Example: .model mod1 pmos +Example: .model mod2 nmos level=2 phi=0.65 rd=1.5 +Example: .model mod3 nmos vto=-1 (depletion) +Example: .model mod4 nmos vto=1 (enhancement) +Example: .model mod5 pmos vto=1 (depletion) +Example: .model mod6 pmos vto=-1 (enhancement) + + Comments: In order to distinguish between enhancement mode and depletion-mode (also +known as depletion-enhancement mode) transistors, the model parameter ”vto” (zero-bias +threshold voltage) must be specified. Its default value is zero, but a positive value (+1 volts, +for example) on a P-channel transistor or a negative value (-1 volts) on an N-channel transis- +tor will specify that transistor to be a depletion (otherwise known as depletion-enhancement) +mode device. Conversely, a negative value on a P-channel transistor or a positive value on an +N-channel transistor will specify that transistor to be an enhancement mode device. + Remember that enhancement mode transistors are normally-off devices, and must be turned +on by the application of gate voltage. Depletion-mode transistors are normally ”on,” but can +be ”pinched off ” as well as enhanced to greater levels of drain current by applied gate voltage, +hence the alternate designation of ”depletion-enhancement” MOSFETs. The ”vto” parameter +specifies the threshold gate voltage for MOSFET conduction. + 7.5. CIRCUIT COMPONENTS 73 + +7.5.3 Sources +AC SINEWAVE VOLTAGE SOURCES (when using .ac card to specify frequency): +General form: v[name] [+node] [-node] ac [voltage] [phase] sin +Example 1: v1 1 0 ac 12 sin +Example 2: v1 1 0 ac 12 240 sin (12 V 6 240o ) + Comments: This method of specifying AC voltage sources works well if you’re using multi- +ple sources at different phase angles from each other, but all at the same frequency. If you need +to specify sources at different frequencies in the same circuit, you must use the next method! + + AC SINEWAVE VOLTAGE SOURCES (when NOT using .ac card to specify fre- +quency): +General form: v[name] [+node] [-node] sin([offset] [voltage] ++ [freq] [delay] [damping factor]) +Example 1: v1 1 0 sin(0 12 60 0 0) + Parameter definitions: + offset = DC bias voltage, offsetting the AC waveform by a specified voltage. + voltage = peak, or crest, AC voltage value for the waveform. + freq = frequency in Hertz. + delay = time delay, or phase offset for the waveform, in seconds. + damping factor = a figure used to create waveforms of decaying amplitude. + Comments: This method of specifying AC voltage sources works well if you’re using multi- +ple sources at different frequencies from each other. Representing phase shift is tricky, though, +necessitating the use of the delay factor. + + DC VOLTAGE SOURCES (when using .dc card to specify voltage): +General form: v[name] [+node] [-node] dc +Example 1: v1 1 0 dc + Comments: If you wish to have SPICE output voltages not in reference to node 0, you must +use the .dc analysis option, and to use this option you must specify at least one of your DC +sources in this manner. + + DC VOLTAGE SOURCES (when NOT using .dc card to specify voltage): +General form: v[name] [+node] [-node] dc [voltage] +Example 1: v1 1 0 dc 12 + Comments: Nothing noteworthy here! + + PULSE VOLTAGE SOURCES +General form: v[name] [+node] [-node] pulse ([i] [p] [td] [tr] ++ [tf] [pw] [pd]) + Parameter definitions: + i = initial value + p = pulse value + td = delay time (all time parameters in units of seconds) + tr = rise time + tf = fall time + 74 CHAPTER 7. USING THE SPICE CIRCUIT SIMULATION PROGRAM + + pw = pulse width + pd = period +Example 1: v1 1 0 pulse (-3 3 0 0 0 10m 20m) + Comments: Example 1 is a perfect square wave oscillating between -3 and +3 volts, with +zero rise and fall times, a 20 millisecond period, and a 50 percent duty cycle (+3 volts for 10 +ms, then -3 volts for 10 ms). + + AC SINEWAVE CURRENT SOURCES (when using .ac card to specify frequency): +General form: i[name] [+node] [-node] ac [current] [phase] sin +Example 1: i1 1 0 ac 3 sin (3 amps) +Example 2: i1 1 0 ac 1m 240 sin (1 mA 6 240o ) + Comments: The same comments apply here (and in the next example) as for AC voltage +sources. + + AC SINEWAVE CURRENT SOURCES (when NOT using .ac card to specify fre- +quency): +General form: i[name] [+node] [-node] sin([offset] ++ [current] [freq] 0 0) +Example 1: i1 1 0 sin(0 1.5 60 0 0) + + DC CURRENT SOURCES (when using .dc card to specify current): +General form: i[name] [+node] [-node] dc +Example 1: i1 1 0 dc + + DC CURRENT SOURCES (when NOT using .dc card to specify current): +General form: i[name] [+node] [-node] dc [current] +Example 1: i1 1 0 dc 12 + Comments: Even though the books all say that the first node given for the DC current +source is the positive node, that’s not what I’ve found to be in practice. In actuality, a DC +current source in SPICE pushes current in the same direction as a voltage source (battery) +would with its negative node specified first. + + PULSE CURRENT SOURCES +General form: i[name] [+node] [-node] pulse ([i] [p] [td] [tr] ++ [tf] [pw] [pd]) + Parameter definitions: + i = initial value + p = pulse value + td = delay time + tr = rise time + tf = fall time + pw = pulse width + pd = period +Example 1: i1 1 0 pulse (-3m 3m 0 0 0 17m 34m) + 7.6. ANALYSIS OPTIONS 75 + + Comments: Example 1 is a perfect square wave oscillating between -3 mA and +3 mA, +with zero rise and fall times, a 34 millisecond period, and a 50 percent duty cycle (+3 mA for +17 ms, then -3 mA for 17 ms). + + VOLTAGE SOURCES (dependent): +General form: e[name] [out+node] [out-node] [in+node] [in-node] ++ [gain] +Example 1: e1 2 0 1 2 999k + Comments: Dependent voltage sources are great to use for simulating operational ampli- +fiers. Example 1 shows how such a source would be configured for use as a voltage follower, +inverting input connected to output (node 2) for negative feedback, and the noninverting input +coming in on node 1. The gain has been set to an arbitrarily high value of 999,000. One word +of caution, though: SPICE does not recognize the input of a dependent source as being a load, +so a voltage source tied only to the input of an independent voltage source will be interpreted +as ”open.” See op-amp circuit examples for more details on this. + + CURRENT SOURCES (dependent): + + +7.6 Analysis options +AC ANALYSIS: +General form: .ac [curve] [points] [start] [final] +Example 1: .ac lin 1 1000 1000 + Comments: The [curve] field can be ”lin” (linear), ”dec” (decade), or ”oct” (octave), specify- +ing the (non)linearity of the frequency sweep. ¡points¿ specifies how many points within the +frequency sweep to perform analyses at (for decade sweep, the number of points per decade; +for octave, the number of points per octave). The [start] and [final] fields specify the starting +and ending frequencies of the sweep, respectively. One final note: the ”start” value cannot be +zero! + + DC ANALYSIS: +General form: .dc [source] [start] [final] [increment] +Example 1: .dc vin 1.5 15 0.5 + Comments: The .dc card is necessary if you want to print or plot any voltage between +two nonzero nodes. Otherwise, the default ”small-signal” analysis only prints out the voltage +between each nonzero node and node zero. + + TRANSIENT ANALYSIS: +General form: .tran [increment] [stop time] [start time] ++ [comp interval] +Example 1: .tran 1m 50m uic +Example 2: .tran .5m 32m 0 .01m + Comments: Example 1 has an increment time of 1 millisecond and a stop time of 50 mil- +liseconds (when only two parameters are specified, they are increment time and stop time, + 76 CHAPTER 7. USING THE SPICE CIRCUIT SIMULATION PROGRAM + +respectively). Example 2 has an increment time of 0.5 milliseconds, a stop time of 32 mil- +liseconds, a start time of 0 milliseconds (no delay on start), and a computation interval of 0.01 +milliseconds. + Default value for start time is zero. Transient analysis always beings at time zero, but +storage of data only takes place between start time and stop time. Data output interval is +increment time, or (stop time - start time)/50, which ever is smallest. However, the computing +interval variable can be used to force a computational interval smaller than either. For large +total interval counts, the itl5 variable in the .options card may be set to a higher number. +The ”uic” option tells SPICE to ”use initial conditions.” + + PLOT OUTPUT: +General form: .plot [type] [output1] [output2] . . . [output n] +Example 1: .plot dc v(1,2) i(v2) +Example 2: .plot ac v(3,4) vp(3,4) i(v1) ip(v1) +Example 3: .plot tran v(4,5) i(v2) + Comments: SPICE can’t handle more than eight data point requests on a single .plot or +.print card. If requesting more than eight data points, use multiple cards! + Also, here’s a major caveat when using SPICE version 3: if you’re performing AC analysis +and you ask SPICE to plot an AC voltage as in example #2, the v(3,4) command will only +output the real component of a rectangular-form complex number! SPICE version 2 outputs +the polar magnitude of a complex number: a much more meaningful quantity if only a single +quantity is asked for. To coerce SPICE3 to give you polar magnitude, you will have to re-write +the .print or .plot argument as such: vm(3,4). + + PRINT OUTPUT: +General form: .print [type] [output1] [output2] . . . [output n] +Example 1: .print dc v(1,2) i(v2) +Example 2: .print ac v(2,4) i(vinput) vp(2,3) +Example 3: .print tran v(4,5) i(v2) + Comments: SPICE can’t handle more than eight data point requests on a single .plot or +.print card. If requesting more than eight data points, use multiple cards! + + FOURIER ANALYSIS: +General form: .four [freq] [output1] [output2] . . . [output n] +Example 1: .four 60 v(1,2) + Comments: The .four card relies on the .tran card being present somewhere in the +deck, with the proper time periods for analysis of adequate cycles. Also, SPICE may ”crash” if +a .plot analysis isn’t done along with the .four analysis, even if all .tran parameters are +technically correct. Finally, the .four analysis option only works when the frequency of the +AC source is specified in that source’s card line, and not in an .ac analysis option line. + It helps to include a computation interval variable in the .tran card for better analysis +precision. A Fourier analysis of the voltage or current specified is performed up to the 9th +harmonic, with the [freq] specification being the fundamental, or starting frequency of the +analysis spectrum. + + MISCELLANEOUS: + 7.6. ANALYSIS OPTIONS 77 + +General form: .options [option1] [option2] +Example 1: .options limpts=500 +Example 2: .options itl5=0 +Example 3: .options method=gear +Example 4: .options list +Example 5: .options nopage +Example 6: .options numdgt=6 + Comments: There are lots of options that can be specified using this card. Perhaps the one +most needed by beginning users of SPICE is the ”limpts” setting. When running a simulation +that requires more than 201 points to be printed or plotted, this calculation point limit must +be increased or else SPICE will terminate analysis. The example given above (limpts=500) +tells SPICE to allocate enough memory to handle at least 500 calculation points in whatever +type of analysis is specified (DC, AC, or transient). + In example 2, we see an iteration variable (itl5) being set to a value of 0. There are +actually six different iteration variables available for user manipulation. They control the +iteration cycle limits for solution of nonlinear equations. The variable itl5 sets the maximum +number of iterations for a transient analysis. Similar to the limpts variable, itl5 usually +needs to be set when a small computation interval has been specified on a .tran card. Setting +itl5 to a value of 0 turns off the limit entirely, allowing the computer infinite iteration cycles +(infinite time) to compute the analysis. Warning: this may result in long simulation times! + Example 3 with ”method=gear” sets the numerical integration method used by SPICE. The +default is ”trapezoid” rather than ”gear,” trapezoid being a simple geometric approximation of +area under a curve found by slicing up the curve into trapezoids to approximate the shape. The +”gear” method is based on second-order or better polynomial equations and is named after C.W. +Gear (Numerical Integration of Stiff Ordinary Equations, Report 221, Department of Computer +Science, University of Illinois, Urbana). The Gear method of integration is more demanding of +the computer (computationally ”expensive”) and will sometimes give slightly different results +from the trapezoid method. + The ”list” option shown in example 4 gives a verbose summary of all circuit components +and their respective values in the final output. + By default, SPICE will insert ASCII page-break control codes in the output to separate +different sections of the analysis. Specifying the ”nopage” option (example 5) will prevent +such pagination. + The ”numdgt” option shown in example 6 specifies the number of significant digits out- +put when using one of the ”.print” data output options. SPICE defaults at a precision of 4 +significant digits. + + + WIDTH CONTROL: +General form: .width in=[columns] out=[columns] +Example 1: .width out=80 + Comments: The .width card can be used to control the width of text output lines upon +analysis. This is especially handy when plotting graphs with the .plot card. The default +value is 120, which can cause problems on 80-character terminal displays unless set to 80 with +this command. + 78 CHAPTER 7. USING THE SPICE CIRCUIT SIMULATION PROGRAM + +7.7 Quirks + ”Garbage in, garbage out.” + Anonymous + SPICE is a very reliable piece of software, but it does have its little quirks that take some +getting used to. By ”quirk” I mean a demand placed upon the user to write the source file in a +particular way in order for it to work without giving error messages. I do not mean any kind +of fault with SPICE which would produce erroneous or misleading results: that would be more +properly referred to as a ”bug.” Speaking of bugs, SPICE has a few of them as well. + Some (or all) of these quirks may be unique to SPICE version 2g6, which is the only version +I’ve used extensively. They may have been fixed in later versions. + +7.7.1 A good beginning +SPICE demands that the source file begin with something other than the first ”card” in the +circuit description ”deck.” This first character in the source file can be a linefeed, title line, or +a comment: there just has to be something there before the first component-specifying line of +the file. If not, SPICE will refuse to do an analysis at all, claiming that there is a serious error +(such as improper node connections) in the ”deck.” + +7.7.2 A good ending +SPICE demands that the .end line at the end of the source file not be terminated with a line- +feed or carriage return character. In other words, when you finish typing ”.end” you should +not hit the [Enter] key on your keyboard. The cursor on your text editor should stop imme- +diately to the right of the ”d” after the ”.end” and go no further. Failure to heed this quirk +will result in a ”missing .end card” error message at the end of the analysis output. The actual +circuit analysis is not affected by this error, so I normally ignore the message. However, if +you’re looking to receive a ”perfect” output, you must pay heed to this idiosyncrasy. + +7.7.3 Must have a node 0 +You are given much freedom in numbering circuit nodes, but you must have a node 0 some- +where in your netlist in order for SPICE to work. Node 0 is the default node for circuit ground, +and it is the point of reference for all voltages specified at single node locations. + When simple DC analysis is performed by SPICE, the output will contain a listing of volt- +ages at all non-zero nodes in the circuit. The point of reference (ground) for all these voltage +readings is node 0. For example: + +node voltage node voltage +( 1) 15.0000 ( 2) 0.6522 + + In this analysis, there is a DC voltage of 15 volts between node 1 and ground (node 0), and +a DC voltage of 0.6522 volts between node 2 and ground (node 0). In both these cases, the +voltage polarity is negative at node 0 with reference to the other node (in other words, both +nodes 1 and 2 are positive with respect to node 0). + 7.7. QUIRKS 79 + +7.7.4 Avoid open circuits +SPICE cannot handle open circuits of any kind. If your netlist specifies a circuit with an open +voltage source, for example, SPICE will refuse to perform an analysis. A prime example of this +type of error is found when ”connecting” a voltage source to the input of a voltage-dependent +source (used to simulate an operational amplifier). SPICE needs to see a complete path for +current, so I usually tie a high-value resistor (call it rbogus!) across the voltage source to act +as a minimal load. + + + +7.7.5 Avoid certain component loops +SPICE cannot handle certain uninterrupted loops of components in a circuit, namely voltage +sources and inductors. The following loops will cause SPICE to abort analysis: + + Parallel inductors + + 2 2 2 + + + L1 10 mH L2 50 mH L3 25 mH + + + 4 4 4 +netlist +l1 2 4 10m +l2 2 4 50m +l3 2 4 25m + + + + Voltage source / inductor loop + + 1 1 + + V1 12 V L1 150 mH + + + 0 0 +netlist +v1 1 0 dc 12 +l1 1 0 150m + 80 CHAPTER 7. USING THE SPICE CIRCUIT SIMULATION PROGRAM + + Series capacitors + 5 + + + C1 33 µF + + + 6 + + C2 47 µF + + + + 7 + + +netlist +c1 5 6 33u +c2 6 7 47u + + + + + The reason SPICE can’t handle these conditions stems from the way it performs DC anal- +ysis: by treating all inductors as shorts and all capacitors as opens. Since short-circuits (0 Ω) +and open circuits (infinite resistance) either contain or generate mathematical infinitudes, a +computer simply cannot deal with them, and so SPICE will discontinue analysis if any of these +conditions occur. + + + In order to make these component configurations acceptable to SPICE, you must insert +resistors of appropriate values into the appropriate places, eliminating the respective short- +circuits and open-circuits. If a series resistor is required, choose a very low resistance value. +Conversely, if a parallel resistor is required, choose a very high resistance value. For example: + + + To fix the parallel inductor problem, insert a very low-value resistor in series with each +offending inductor. + 7.7. QUIRKS 81 + + Original circuit + 2 2 2 + + + L1 10 mH L2 50 mH L3 25 mH + + + 4 4 4 + + "Fixed" circuit + 3 Rbogus1 2 Rbogus2 5 + + + L1 10 mH L2 50 mH L3 25 mH + + + 4 4 4 + +original netlist +l1 2 4 10m +l2 2 4 50m +l3 2 4 25m + + + + +fixed netlist +rbogus1 2 3 1e-12 +rbogus2 2 5 1e-12 +l1 3 4 10m +l2 2 4 50m +l3 5 4 25m + + + + + The extremely low-resistance resistors Rbogus1 and Rbogus2 (each one with a mere 1 pico-ohm +of resistance) ”break up” the direct parallel connections that existed between L1 , L2 , and L3 . It +is important to choose very low resistances here so that circuit operation is not substantially +impacted by the ”fix.” + + To fix the voltage source / inductor loop, insert a very low-value resistor in series with the +two components. + 82 CHAPTER 7. USING THE SPICE CIRCUIT SIMULATION PROGRAM + + Original circuit + 1 1 + + + V1 12 V L1 150 mH + + + 0 0 + + + "Fixed" circuit + Rbogus + 1 2 + + + V1 12 V L1 150 mH + + + 0 0 + +original netlist +v1 1 0 dc 12 +l1 1 0 150m + + + + +fixed netlist +v1 1 0 dc 12 +l1 2 0 150m +rbogus 1 2 1e-12 + + + + + As in the previous example with parallel inductors, it is important to make the correction +resistor (Rbogus ) very low in resistance, so as to not substantially impact circuit operation. + + To fix the series capacitor circuit, one of the capacitors must have a resistor shunting across +it. SPICE requires a DC current path to each capacitor for analysis. + 7.7. QUIRKS 83 + + Original circuit "Fixed" circuit + 5 5 + + + C1 33 µF C1 33 µF + + + 6 6 + 6 + + C2 47 µF C2 47 µF Rbogus + + + 7 + 7 7 +original netlist +c1 5 6 33u +c2 6 7 47u + +fixed netlist +c1 5 6 33u +c2 6 7 47u +rbogus 6 7 9e12 + + The Rbogus value of 9 Tera-ohms provides a DC current path to C1 (and around C2 ) without +substantially impacting the circuit’s operation. + + +7.7.6 Current measurement +Although printing or plotting of voltage is quite easy in SPICE, the output of current values is +a bit more difficult. Voltage measurements are specified by declaring the appropriate circuit +nodes. For example, if we desire to know the voltage across a capacitor whose leads connect +between nodes 4 and 7, we might make out .print statement look like this: + + C1 + 4 7 + + 22 µF +c1 4 7 22u +.print ac v(4,7) + + However, if we wanted to have SPICE measure the current through that capacitor, it wouldn’t +be quite so easy. Currents in SPICE must be specified in relation to a voltage source, not any +arbitrary component. For example: + 84 CHAPTER 7. USING THE SPICE CIRCUIT SIMULATION PROGRAM + + Vinput C1 + 6 4 7 + + I 22 µF +c1 4 7 22u +vinput 6 4 ac 1 sin +.print ac i(vinput) + + This .print card instructs SPICE to print the current through voltage source Vinput , which +happens to be the same as the current through our capacitor between nodes 4 and 7. But what +if there is no such voltage source in our circuit to reference for current measurement? One +solution is to insert a shunt resistor into the circuit and measure voltage across it. In this case, +I have chosen a shunt resistance value of 1 Ω to produce 1 volt per amp of current through C1 : + + Rshunt C1 + 6 4 7 + 1Ω 22 µF + I +c1 4 7 22u +rshunt 6 4 1 +.print ac v(6,4) + + However, the insertion of an extra resistance into our circuit large enough to drop a mean- +ingful voltage for the intended range of current might adversely affect things. A better solution +for SPICE is this, although one would never seek such a current measurement solution in real +life: + + Vbogus C1 + 6 4 7 + + 0V 22 µF + I +c1 4 7 22u +vbogus 6 4 dc 0 +.print ac i(vbogus) + + Inserting a ”bogus” DC voltage source of zero volts doesn’t affect circuit operation at all, yet +it provides a convenient place for SPICE to take a current measurement. Interestingly enough, +it doesn’t matter that Vbogus is a DC source when we’re looking to measure AC current! The +fact that SPICE will output an AC current reading is determined by the ”ac” specification in +the .print card and nothing more. + It should also be noted that the way SPICE assigns a polarity to current measurements is +a bit odd. Take the following circuit as an example: + 7.7. QUIRKS 85 + + R1 + 1 2 + 5 kΩ + + V1 10 V R2 5 kΩ + + + 0 0 +example +v1 1 0 +r1 1 2 5k +r2 2 0 5k +.dc v1 10 10 1 +.print dc i(v1) +.end + + With 10 volts total voltage and 10 kΩ total resistance, you might expect SPICE to tell you +there’s going to be 1 mA (1e-03) of current through voltage source V1 , but in actuality SPICE +will output a figure of negative 1 mA (-1e-03)! SPICE regards current out of the negative end +of a DC voltage source (the normal direction) to be a negative value of current rather than a +positive value of current. There are times I’ll throw in a ”bogus” voltage source in a DC circuit +like this simply to get SPICE to output a positive current value: + + R1 + 1 2 + 5 kΩ + + V1 10 V R2 5 kΩ + Vbogus + + 0 3 + 0V +example +v1 1 0 +r1 1 2 5k +r2 2 3 5k +vbogus 3 0 dc 0 +.dc v1 10 10 1 +.print dc i(vbogus) +.end + + Notice how Vbogus is positioned so that the circuit current will enter its positive side (node +3) and exit its negative side (node 0). This orientation will ensure a positive output figure for +circuit current. + 86 CHAPTER 7. USING THE SPICE CIRCUIT SIMULATION PROGRAM + +7.7.7 Fourier analysis +When performing a Fourier (frequency-domain) analysis on a waveform, I have found it neces- +sary to either print or plot the waveform using the .print or .plot cards, respectively. If you +don’t print or plot it, SPICE will pause for a moment during analysis and then abort the job +after outputting the ”initial transient solution.” + Also, when analyzing a square wave produced by the ”pulse” source function, you must +give the waveform some finite rise and fall time, or else the Fourier analysis results will be +incorrect. For some reason, a perfect square wave with zero rise/fall time produces significant +levels of even harmonics according to SPICE’s Fourier analysis option, which is not true for +real square waves. + + +7.8 Example circuits and netlists +The following circuits are pre-tested netlists for SPICE 2g6, complete with short descriptions +when necessary. Feel free to ”copy” and ”paste” any of the netlists to your own SPICE source file +for analysis and/or modification. My goal here is twofold: to give practical examples of SPICE +netlist design to further understanding of SPICE netlist syntax, and to show how simple and +compact SPICE netlists can be in analyzing simple circuits. + All output listings for these examples have been ”trimmed” of extraneous information, giv- +ing you the most succinct presentation of the SPICE output as possible. I do this primarily +to save space on this document. Typical SPICE outputs contain lots of headers and summary +information not necessarily germane to the task at hand. So don’t be surprised when you run +a simulation on your own and find that the output doesn’t exactly look like what I have shown +here! + + +7.8.1 Multiple-source DC resistor network, part 1 + + R1 2 R2 + 1 3 + 10 kΩ 8.1 kΩ + + V1 24 V R3 4.7 kΩ V2 15 V + + + 0 0 0 +Without a .dc card and a .print or .plot card, the output for this netlist will only display +voltages for nodes 1, 2, and 3 (with reference to node 0, of course). + + Netlist: +Multiple dc sources +v1 1 0 dc 24 +v2 3 0 dc 15 + 7.8. EXAMPLE CIRCUITS AND NETLISTS 87 + +r1 1 2 10k +r2 2 3 8.1k +r3 2 0 4.7k +.end + + Output: +node voltage node voltage node voltage +( 1) 24.0000 ( 2) 9.7470 ( 3) 15.0000 + +voltage source currents +name current +v1 -1.425E-03 +v2 -6.485E-04 + +total power dissipation 4.39E-02 watts + +7.8.2 Multiple-source DC resistor network, part 2 + + R1 2 R2 + 1 3 + 10 kΩ 8.1 kΩ + + V1 24 V R3 4.7 kΩ V2 15 V + + + 0 0 0 +By adding a .dc analysis card and specifying source V1 from 24 volts to 24 volts in 1 step +(in other words, 24 volts steady), we can use the .print card analysis to print out voltages +between any two points we desire. Oddly enough, when the .dc analysis option is invoked, +the default voltage printouts for each node (to ground) disappears, so we end up having to +explicitly specify them in the .print card to see them at all. + + Netlist: +Multiple dc sources +v1 1 0 +v2 3 0 15 +r1 1 2 10k +r2 2 3 8.1k +r3 2 0 4.7k +.dc v1 24 24 1 +.print dc v(1) v(2) v(3) v(1,2) v(2,3) +.end + + Output: + 88 CHAPTER 7. USING THE SPICE CIRCUIT SIMULATION PROGRAM + +v1 v(1) v(2) v(3) v(1,2) v(2,3) +2.400E+01 2.400E+01 9.747E+00 1.500E+01 1.425E+01 -5.253E+00 + + +7.8.3 RC time-constant circuit + + 1 1 1 + + + V1 10 V C1 C2 + 47 µF 22 µF + R1 + 0 2 2 + 3.3 kΩ +For DC analysis, the initial conditions of any reactive component (C or L) must be specified +(voltage for capacitors, current for inductors). This is provided by the last data field of each +capacitor card (ic=0). To perform a DC analysis, the .tran (”transient”) analysis option must +be specified, with the first data field specifying time increment in seconds, the second specifying +total analysis timespan in seconds, and the ”uic” telling it to ”use initial conditions” when +analyzing. + + Netlist: +RC time delay circuit +v1 1 0 dc 10 +c1 1 2 47u ic=0 +c2 1 2 22u ic=0 +r1 2 0 3.3k +.tran .05 1 uic +.print tran v(1,2) +.end + + Output: +time v(1,2) +0.000E+00 7.701E-06 +5.000E-02 1.967E+00 +1.000E-01 3.551E+00 +1.500E-01 4.824E+00 +2.000E-01 5.844E+00 +2.500E-01 6.664E+00 +3.000E-01 7.322E+00 +3.500E-01 7.851E+00 +4.000E-01 8.274E+00 +4.500E-01 8.615E+00 +5.000E-01 8.888E+00 +5.500E-01 9.107E+00 + 7.8. EXAMPLE CIRCUITS AND NETLISTS 89 + +6.000E-01 9.283E+00 +6.500E-01 9.425E+00 +7.000E-01 9.538E+00 +7.500E-01 9.629E+00 +8.000E-01 9.702E+00 +8.500E-01 9.761E+00 +9.000E-01 9.808E+00 +9.500E-01 9.846E+00 +1.000E+00 9.877E+00 + +7.8.4 Plotting and analyzing a simple AC sinewave voltage + + 1 1 + V1 + 15 V Rload 10 kΩ + 60 Hz + 0 0 +This exercise does show the proper setup for plotting instantaneous values of a sine-wave +voltage source with the .plot function (as a transient analysis). Not surprisingly, the Fourier +analysis in this deck also requires the .tran (transient) analysis option to be specified over +a suitable time range. The time range in this particular deck allows for a Fourier analysis +with rather poor accuracy. The more cycles of the fundamental frequency that the transient +analysis is performed over, the more precise the Fourier analysis will be. This is not a quirk of +SPICE, but rather a basic principle of waveforms. + + Netlist: +v1 1 0 sin(0 15 60 0 0) +rload 1 0 10k +* change tran card to the following for better Fourier precision +* .tran 1m 30m .01m and include .options card: +* .options itl5=30000 +.tran 1m 30m +.plot tran v(1) +.four 60 v(1) +.end + + Output: +time v(1) -2.000E+01 -1.000E+01 0.000E+00 1.000E+01 +- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - +0.000E+00 0.000E+00 . . * . . +1.000E-03 5.487E+00 . . . * . . +2.000E-03 1.025E+01 . . . * . +3.000E-03 1.350E+01 . . . . * . +4.000E-03 1.488E+01 . . . . *. + 90 CHAPTER 7. USING THE SPICE CIRCUIT SIMULATION PROGRAM + +5.000E-03 1.425E+01 . . . . * . +6.000E-03 1.150E+01 . . . . * . +7.000E-03 7.184E+00 . . . * . . +8.000E-03 1.879E+00 . . . * . . +9.000E-03 -3.714E+00 . . * . . . +1.000E-02 -8.762E+00 . . * . . . +1.100E-02 -1.265E+01 . * . . . . +1.200E-02 -1.466E+01 . * . . . . +1.300E-02 -1.465E+01 . * . . . . +1.400E-02 -1.265E+01 . * . . . . +1.500E-02 -8.769E+00 . . * . . . +1.600E-02 -3.709E+00 . . * . . . +1.700E-02 1.876E+00 . . . * . . +1.800E-02 7.191E+00 . . . * . . +1.900E-02 1.149E+01 . . . . * . +2.000E-02 1.425E+01 . . . . * . +2.100E-02 1.489E+01 . . . . *. +2.200E-02 1.349E+01 . . . . * . +2.300E-02 1.026E+01 . . . * . +2.400E-02 5.491E+00 . . . * . . +2.500E-02 1.553E-03 . . * . . +2.600E-02 -5.514E+00 . . * . . . +2.700E-02 -1.022E+01 . * . . . +2.800E-02 -1.349E+01 . * . . . . +2.900E-02 -1.495E+01 . * . . . . +3.000E-02 -1.427E+01 . * . . . . +- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + + + + +fourier components of transient response v(1) +dc component = -1.885E-03 +harmonic frequency fourier normalized phase normalized +no (hz) component component (deg) phase (deg) +1 6.000E+01 1.494E+01 1.000000 -71.998 0.000 +2 1.200E+02 1.886E-02 0.001262 -50.162 21.836 +3 1.800E+02 1.346E-03 0.000090 102.674 174.671 +4 2.400E+02 1.799E-02 0.001204 -10.866 61.132 +5 3.000E+02 3.604E-03 0.000241 160.923 232.921 +6 3.600E+02 5.642E-03 0.000378 -176.247 -104.250 +7 4.200E+02 2.095E-03 0.000140 122.661 194.658 +8 4.800E+02 4.574E-03 0.000306 -143.754 -71.757 +9 5.400E+02 4.896E-03 0.000328 -129.418 -57.420 +total harmonic distortion = 0.186350 percent + 7.8. EXAMPLE CIRCUITS AND NETLISTS 91 + +7.8.5 Simple AC resistor-capacitor circuit + + R1 + 1 2 + 30 Ω + + V1 12 V C1 100 µF + 60 Hz + + 0 0 +The .ac card specifies the points of ac analysis from 60Hz to 60Hz, at a single point. This card, +of course, is a bit more useful for multi-frequency analysis, where a range of frequencies can +be analyzed in steps. The .print card outputs the AC voltage between nodes 1 and 2, and the +AC voltage between node 2 and ground. + + Netlist: +Demo of a simple AC circuit +v1 1 0 ac 12 sin +r1 1 2 30 +c1 2 0 100u +.ac lin 1 60 60 +.print ac v(1,2) v(2) +.end + + Output: +freq v(1,2) v(2) +6.000E+01 8.990E+00 7.949E+00 + +7.8.6 Low-pass filter + + L1 L2 + 2 3 4 + 100 mH 250 mH + + V1 24 V + + 1 C1 100 µF Rload 1 kΩ + + + V2 24 V + + + + 0 0 0 + 92 CHAPTER 7. USING THE SPICE CIRCUIT SIMULATION PROGRAM + +This low-pass filter blocks AC and passes DC to the Rload resistor. Typical of a filter used to +suppress ripple from a rectifier circuit, it actually has a resonant frequency, technically making +it a band-pass filter. However, it works well anyway to pass DC and block the high-frequency +harmonics generated by the AC-to-DC rectification process. Its performance is measured with +an AC source sweeping from 500 Hz to 15 kHz. If desired, the .print card can be substituted +or supplemented with a .plot card to show AC voltage at node 4 graphically. + + Netlist: +Lowpass filter +v1 2 1 ac 24 sin +v2 1 0 dc 24 +rload 4 0 1k +l1 2 3 100m +l2 3 4 250m +c1 3 0 100u +.ac lin 30 500 15k +.print ac v(4) +.plot ac v(4) +.end + +freq v(4) +5.000E+02 1.935E-01 +1.000E+03 3.275E-02 +1.500E+03 1.057E-02 +2.000E+03 4.614E-03 +2.500E+03 2.402E-03 +3.000E+03 1.403E-03 +3.500E+03 8.884E-04 +4.000E+03 5.973E-04 +4.500E+03 4.206E-04 +5.000E+03 3.072E-04 +5.500E+03 2.311E-04 +6.000E+03 1.782E-04 +6.500E+03 1.403E-04 +7.000E+03 1.124E-04 +7.500E+03 9.141E-05 +8.000E+03 7.536E-05 +8.500E+03 6.285E-05 +9.000E+03 5.296E-05 +9.500E+03 4.504E-05 +1.000E+04 3.863E-05 +1.050E+04 3.337E-05 +1.100E+04 2.903E-05 +1.150E+04 2.541E-05 +1.200E+04 2.237E-05 +1.250E+04 1.979E-05 + 7.8. EXAMPLE CIRCUITS AND NETLISTS 93 + +1.300E+04 1.760E-05 +1.350E+04 1.571E-05 +1.400E+04 1.409E-05 +1.450E+04 1.268E-05 +1.500E+04 1.146E-05 + + + + +freq v(4) 1.000E-06 1.000E-04 1.000E-02 1.000E+00 +- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - +5.000E+02 1.935E-01 . . . * . +1.000E+03 3.275E-02 . . . * . +1.500E+03 1.057E-02 . . * . +2.000E+03 4.614E-03 . . * . . +2.500E+03 2.402E-03 . . * . . +3.000E+03 1.403E-03 . . * . . +3.500E+03 8.884E-04 . . * . . +4.000E+03 5.973E-04 . . * . . +4.500E+03 4.206E-04 . . * . . +5.000E+03 3.072E-04 . . * . . +5.500E+03 2.311E-04 . . * . . +6.000E+03 1.782E-04 . . * . . +6.500E+03 1.403E-04 . .* . . +7.000E+03 1.124E-04 . * . . +7.500E+03 9.141E-05 . * . . +8.000E+03 7.536E-05 . *. . . +8.500E+03 6.285E-05 . *. . . +9.000E+03 5.296E-05 . * . . . +9.500E+03 4.504E-05 . * . . . +1.000E+04 3.863E-05 . * . . . +1.050E+04 3.337E-05 . * . . . +1.100E+04 2.903E-05 . * . . . +1.150E+04 2.541E-05 . * . . . +1.200E+04 2.237E-05 . * . . . +1.250E+04 1.979E-05 . * . . . +1.300E+04 1.760E-05 . * . . . +1.350E+04 1.571E-05 . * . . . +1.400E+04 1.409E-05 . * . . . +1.450E+04 1.268E-05 . * . . . +1.500E+04 1.146E-05 . * . . . +- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + 94 CHAPTER 7. USING THE SPICE CIRCUIT SIMULATION PROGRAM + +7.8.7 Multiple-source AC network + + L1 L2 + 1 2 3 + 450 mH 150 mH + + + + + + V1 55 V C1 330 µF V2 43 V + 30 Hz 30 Hz + - 0o - 25o + + + + + 0 0 0 +One of the idiosyncrasies of SPICE is its inability to handle any loop in a circuit exclusively +composed of series voltage sources and inductors. Therefore, the ”loop” of V1 -L1 -L2 -V2 -V1 is +unacceptable. To get around this, I had to insert a low-resistance resistor somewhere in that +loop to break it up. Thus, we have Rbogus between 3 and 4 (with 1 pico-ohm of resistance), and +V2 between 4 and 0. The circuit above is the original design, while the circuit below has Rbogus +inserted to avoid the SPICE error. + L1 L2 + 1 2 3 + 450 mH 150 mH + Rbogus 1 pΩ + + + V1 55 V C1 330 µF 4 + 30 Hz + + - 0o V2 43 V + 30 Hz + - 25o + + + 0 0 0 + + Netlist: +Multiple ac source +v1 1 0 ac 55 0 sin +v2 4 0 ac 43 25 sin +l1 1 2 450m +c1 2 0 330u +l2 2 3 150m + 7.8. EXAMPLE CIRCUITS AND NETLISTS 95 + +rbogus 3 4 1e-12 +.ac lin 1 30 30 +.print ac v(2) +.end + + Output: +freq v(2) +3.000E+01 1.413E+02 + + +7.8.8 AC phase shift demonstration + + 1 1 1 + + + Rshunt1 1 Ω Rshunt2 1Ω + + 2 3 + + L1 1H R1 6.3 kΩ + + + 0 0 0 +The currents through each leg are indicated by the voltage drops across each respective shunt +resistor (1 amp = 1 volt through 1 Ω), output by the v(1,2) and v(1,3) terms of the .print +card. The phase of the currents through each leg are indicated by the phase of the voltage +drops across each respective shunt resistor, output by the vp(1,2) and vp(1,3) terms in the +.print card. + + Netlist: +phase shift +v1 1 0 ac 4 sin +rshunt1 1 2 1 +rshunt2 1 3 1 +l1 2 0 1 +r1 3 0 6.3k +.ac lin 1 1000 1000 +.print ac v(1,2) v(1,3) vp(1,2) vp(1,3) +.end + + Output: +freq v(1,2) v(1,3) vp(1,2) vp(1,3) +1.000E+03 6.366E-04 6.349E-04 -9.000E+01 0.000E+00 + 96 CHAPTER 7. USING THE SPICE CIRCUIT SIMULATION PROGRAM + +7.8.9 Transformer circuit + + 2 + Rbogus0 L2 R1 + 1 1H + L1 4 + V1 3 + 100 H L3 + 0 R2 + 25 H + 5 + Rbogus1 Rbogus2 + 0 0 + +SPICE understands transformers as a set of mutually coupled inductors. Thus, to simulate +a transformer in SPICE, you must specify the primary and secondary windings as separate +inductors, then instruct SPICE to link them together with a ”k” card specifying the coupling +constant. For ideal transformer simulation, the coupling constant would be unity (1). However, +SPICE can’t handle this value, so we use something like 0.999 as the coupling factor. + Note that all winding inductor pairs must be coupled with their own k cards in order for +the simulation to work properly. For a two-winding transformer, a single k card will suffice. +For a three-winding transformer, three k cards must be specified (to link L1 with L2 , L2 with +L3 , and L1 with L3 ). + The L1 /L2 inductance ratio of 100:1 provides a 10:1 step-down voltage transformation ratio. +With 120 volts in we should see 12 volts out of the L2 winding. The L1 /L3 inductance ratio +of 100:25 (4:1) provides a 2:1 step-down voltage transformation ratio, which should give us 60 +volts out of the L3 winding with 120 volts in. + + Netlist: +transformer +v1 1 0 ac 120 sin +rbogus0 1 6 1e-3 +l1 6 0 100 +l2 2 4 1 +l3 3 5 25 +k1 l1 l2 0.999 +k2 l2 l3 0.999 +k3 l1 l3 0.999 +r1 2 4 1000 +r2 3 5 1000 +rbogus1 5 0 1e10 +rbogus2 4 0 1e10 +.ac lin 1 60 60 +.print ac v(1,0) v(2,0) v(3,0) +.end + 7.8. EXAMPLE CIRCUITS AND NETLISTS 97 + + Output: +freq v(1) v(2) v(3) +6.000E+01 1.200E+02 1.199E+01 5.993E+01 + In this example, Rbogus0 is a very low-value resistor, serving to break up the source/inductor +loop of V1 /L1 . Rbogus1 and Rbogus2 are very high-value resistors necessary to provide DC paths +to ground on each of the isolated circuits. Note as well that one side of the primary circuit is +directly grounded. Without these ground references, SPICE will produce errors! + + +7.8.10 Full-wave bridge rectifier + + 1 1 + D1 D3 + Rload + V1 15 V 2 + - 3 + 60 Hz 10 kΩ + D2 D4 + + 0 0 +Diodes, like all semiconductor components in SPICE, must be modeled so that SPICE knows +all the nitty-gritty details of how they’re supposed to work. Fortunately, SPICE comes with +a few generic models, and the diode is the most basic. Notice the .model card which simply +specifies ”d” as the generic diode model for mod1. Again, since we’re plotting the waveforms +here, we need to specify all parameters of the AC source in a single card and print/plot all +values using the .tran option. + + Netlist: +fullwave bridge rectifier +v1 1 0 sin(0 15 60 0 0) +rload 1 0 10k +d1 1 2 mod1 +d2 0 2 mod1 +d3 3 1 mod1 +d4 3 0 mod1 +.model mod1 d +.tran .5m 25m +.plot tran v(1,0) v(2,3) +.end + + Output: +legend: +*: v(1) ++: v(2,3) +time v(1) + 98 CHAPTER 7. USING THE SPICE CIRCUIT SIMULATION PROGRAM + +(*)--------- -2.000E+01 -1.000E+01 0.000E+00 1.000E+01 2.000E+01 +(+)--------- -5.000E+00 0.000E+00 5.000E+00 1.000E+01 1.500E+01 +- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - +0.000E+00 0.000E+00 . + * . . +5.000E-04 2.806E+00 . . + . * . . +1.000E-03 5.483E+00 . . + * . . +1.500E-03 7.929E+00 . . . + * . . +2.000E-03 1.013E+01 . . . +* . +2.500E-03 1.198E+01 . . . . * + . +3.000E-03 1.338E+01 . . . . * + . +3.500E-03 1.435E+01 . . . . * +. +4.000E-03 1.476E+01 . . . . * + +4.500E-03 1.470E+01 . . . . * + +5.000E-03 1.406E+01 . . . . * + . +5.500E-03 1.299E+01 . . . . * + . +6.000E-03 1.139E+01 . . . . *+ . +6.500E-03 9.455E+00 . . . + *. . +7.000E-03 7.113E+00 . . . + * . . +7.500E-03 4.591E+00 . . +. * . . +8.000E-03 1.841E+00 . . + . * . . +8.500E-03 -9.177E-01 . . + *. . . +9.000E-03 -3.689E+00 . . *+ . . . +9.500E-03 -6.380E+00 . . * . + . . +1.000E-02 -8.784E+00 . . * . + . . +1.050E-02 -1.075E+01 . *. . .+ . +1.100E-02 -1.255E+01 . * . . . + . +1.150E-02 -1.372E+01 . * . . . + . +1.200E-02 -1.460E+01 . * . . . + +1.250E-02 -1.476E+01 .* . . . + +1.300E-02 -1.460E+01 . * . . . + +1.350E-02 -1.373E+01 . * . . . + . +1.400E-02 -1.254E+01 . * . . . + . +1.450E-02 -1.077E+01 . *. . .+ . +1.500E-02 -8.726E+00 . . * . + . . +1.550E-02 -6.293E+00 . . * . + . . +1.600E-02 -3.684E+00 . . x . . . +1.650E-02 -9.361E-01 . . + *. . . +1.700E-02 1.875E+00 . . + . * . . +1.750E-02 4.552E+00 . . +. * . . +1.800E-02 7.170E+00 . . . + * . . +1.850E-02 9.401E+00 . . . + *. . +1.900E-02 1.146E+01 . . . . *+ . +1.950E-02 1.293E+01 . . . . * + . +2.000E-02 1.414E+01 . . . . * +. +2.050E-02 1.464E+01 . . . . * + +2.100E-02 1.483E+01 . . . . * + + 7.8. EXAMPLE CIRCUITS AND NETLISTS 99 + +2.150E-02 1.430E+01 . . . . * +. +2.200E-02 1.344E+01 . . . . * + . +2.250E-02 1.195E+01 . . . . *+ . +2.300E-02 1.016E+01 . . . +* . +2.350E-02 7.917E+00 . . . + * . . +2.400E-02 5.460E+00 . . + * . . +2.450E-02 2.809E+00 . . + . * . . +2.500E-02 -8.297E-04 . + * . . +- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + +7.8.11 Common-base BJT transistor amplifier + + Q1 + β = 50 + 3 2 + + Re 100 Ω Rc 800 Ω + Vin Vsupply + 4 0 1 + 0 to 5 V 24 V +This analysis sweeps the input voltage (Vin) from 0 to 5 volts in 0.1 volt increments, then prints +out the voltage between the collector and emitter leads of the transistor v(2,3). The transistor +(Q1) is an NPN with a forward Beta of 50. + + Netlist: +Common-base BJT amplifier +vsupply 1 0 dc 24 +vin 0 4 dc +rc 1 2 800 +re 3 4 100 +q1 2 0 3 mod1 +.model mod1 npn bf=50 +.dc vin 0 5 0.1 +.print dc v(2,3) +.plot dc v(2,3) +.end + + Output: +vin v(2,3) +0.000E+00 2.400E+01 +1.000E-01 2.410E+01 +2.000E-01 2.420E+01 +3.000E-01 2.430E+01 +4.000E-01 2.440E+01 + 100 CHAPTER 7. USING THE SPICE CIRCUIT SIMULATION PROGRAM + +5.000E-01 2.450E+01 +6.000E-01 2.460E+01 +7.000E-01 2.466E+01 +8.000E-01 2.439E+01 +9.000E-01 2.383E+01 +1.000E+00 2.317E+01 +1.100E+00 2.246E+01 +1.200E+00 2.174E+01 +1.300E+00 2.101E+01 +1.400E+00 2.026E+01 +1.500E+00 1.951E+01 +1.600E+00 1.876E+01 +1.700E+00 1.800E+01 +1.800E+00 1.724E+01 +1.900E+00 1.648E+01 +2.000E+00 1.572E+01 +2.100E+00 1.495E+01 +2.200E+00 1.418E+01 +2.300E+00 1.342E+01 +2.400E+00 1.265E+01 +2.500E+00 1.188E+01 +2.600E+00 1.110E+01 +2.700E+00 1.033E+01 +2.800E+00 9.560E+00 +2.900E+00 8.787E+00 +3.000E+00 8.014E+00 +3.100E+00 7.240E+00 +3.200E+00 6.465E+00 +3.300E+00 5.691E+00 +3.400E+00 4.915E+00 +3.500E+00 4.140E+00 +3.600E+00 3.364E+00 +3.700E+00 2.588E+00 +3.800E+00 1.811E+00 +3.900E+00 1.034E+00 +4.000E+00 2.587E-01 +4.100E+00 9.744E-02 +4.200E+00 7.815E-02 +4.300E+00 6.806E-02 +4.400E+00 6.141E-02 +4.500E+00 5.657E-02 +4.600E+00 5.281E-02 +4.700E+00 4.981E-02 +4.800E+00 4.734E-02 +4.900E+00 4.525E-02 +5.000E+00 4.346E-02 + 7.8. EXAMPLE CIRCUITS AND NETLISTS 101 + +vin v(2,3) 0.000E+00 1.000E+01 2.000E+01 3.000E+01 +- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - +0.000E+00 2.400E+01 . . . * . +1.000E-01 2.410E+01 . . . * . +2.000E-01 2.420E+01 . . . * . +3.000E-01 2.430E+01 . . . * . +4.000E-01 2.440E+01 . . . * . +5.000E-01 2.450E+01 . . . * . +6.000E-01 2.460E+01 . . . * . +7.000E-01 2.466E+01 . . . * . +8.000E-01 2.439E+01 . . . * . +9.000E-01 2.383E+01 . . . * . +1.000E+00 2.317E+01 . . . * . +1.100E+00 2.246E+01 . . . * . +1.200E+00 2.174E+01 . . . * . +1.300E+00 2.101E+01 . . .* . +1.400E+00 2.026E+01 . . * . +1.500E+00 1.951E+01 . . *. . +1.600E+00 1.876E+01 . . * . . +1.700E+00 1.800E+01 . . * . . +1.800E+00 1.724E+01 . . * . . +1.900E+00 1.648E+01 . . * . . +2.000E+00 1.572E+01 . . * . . +2.100E+00 1.495E+01 . . * . . +2.200E+00 1.418E+01 . . * . . +2.300E+00 1.342E+01 . . * . . +2.400E+00 1.265E+01 . . * . . +2.500E+00 1.188E+01 . . * . . +2.600E+00 1.110E+01 . . * . . +2.700E+00 1.033E+01 . * . . +2.800E+00 9.560E+00 . *. . . +2.900E+00 8.787E+00 . * . . . +3.000E+00 8.014E+00 . * . . . +3.100E+00 7.240E+00 . * . . . +3.200E+00 6.465E+00 . * . . . +3.300E+00 5.691E+00 . * . . . +3.400E+00 4.915E+00 . * . . . +3.500E+00 4.140E+00 . * . . . +3.600E+00 3.364E+00 . * . . . +3.700E+00 2.588E+00 . * . . . +3.800E+00 1.811E+00 . * . . . +3.900E+00 1.034E+00 .* . . . +4.000E+00 2.587E-01 * . . . +4.100E+00 9.744E-02 * . . . +4.200E+00 7.815E-02 * . . . +4.300E+00 6.806E-02 * . . . + 102 CHAPTER 7. USING THE SPICE CIRCUIT SIMULATION PROGRAM + +4.400E+00 6.141E-02 * . . . +4.500E+00 5.657E-02 * . . . +4.600E+00 5.281E-02 * . . . +4.700E+00 4.981E-02 * . . . +4.800E+00 4.734E-02 * . . . +4.900E+00 4.525E-02 * . . . +5.000E+00 4.346E-02 * . . . +- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + +7.8.12 Common-source JFET amplifier with self-bias + + 3 3 + + Rdrain 10 kΩ + + J1 2 + 1 VDD 20 V + 4 + Vin 1V + 60 Hz Vout + Rsource 1 kΩ + + 0 0 0 +Netlist: +common source jfet amplifier +vin 1 0 sin(0 1 60 0 0) +vdd 3 0 dc 20 +rdrain 3 2 10k +rsource 4 0 1k +j1 2 1 4 mod1 +.model mod1 njf +.tran 1m 30m +.plot tran v(2,0) v(1,0) +.end + + Output: +legend: +*: v(2) ++: v(1) +time v(2) +(*)--------- 1.400E+01 1.600E+01 1.800E+01 2.000E+01 2.200E+01 +(+)--------- -1.000E+00 -5.000E-01 0.000E+00 5.000E-01 1.000E+00 +- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + 7.8. EXAMPLE CIRCUITS AND NETLISTS 103 + +0.000E+00 1.708E+01 . . * + . . +1.000E-03 1.609E+01 . .* . + . . +2.000E-03 1.516E+01 . * . . . + . +3.000E-03 1.448E+01 . * . . . + . +4.000E-03 1.419E+01 .* . . . + +5.000E-03 1.432E+01 . * . . . +. +6.000E-03 1.490E+01 . * . . . + . +7.000E-03 1.577E+01 . * . . +. . +8.000E-03 1.676E+01 . . * . + . . +9.000E-03 1.768E+01 . . + *. . . +1.000E-02 1.841E+01 . + . . * . . +1.100E-02 1.890E+01 . + . . * . . +1.200E-02 1.912E+01 .+ . . * . . +1.300E-02 1.912E+01 .+ . . * . . +1.400E-02 1.890E+01 . + . . * . . +1.500E-02 1.842E+01 . + . . * . . +1.600E-02 1.768E+01 . . + *. . . +1.700E-02 1.676E+01 . . * . + . . +1.800E-02 1.577E+01 . * . . +. . +1.900E-02 1.491E+01 . * . . . + . +2.000E-02 1.432E+01 . * . . . +. +2.100E-02 1.419E+01 .* . . . + +2.200E-02 1.449E+01 . * . . . + . +2.300E-02 1.516E+01 . * . . . + . +2.400E-02 1.609E+01 . .* . + . . +2.500E-02 1.708E+01 . . * + . . +2.600E-02 1.796E+01 . . + * . . +2.700E-02 1.861E+01 . + . . * . . +2.800E-02 1.900E+01 . + . . * . . +2.900E-02 1.916E+01 + . . * . . +3.000E-02 1.908E+01 .+ . . * . . +- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + +7.8.13 Inverting op-amp circuit + + R2 1 R1 + 2 3 + 1.18 kΩ 3.29 kΩ + V1 0 to 3.5 V 1 − + (e) 3 + + + 0 + 0 + 104 CHAPTER 7. USING THE SPICE CIRCUIT SIMULATION PROGRAM + +To simulate an ideal operational amplifier in SPICE, we use a voltage-dependent voltage source +as a differential amplifier with extremely high gain. The ”e” card sets up the dependent voltage +source with four nodes, 3 and 0 for voltage output, and 1 and 0 for voltage input. No power +supply is needed for the dependent voltage source, unlike a real operational amplifier. The +voltage gain is set at 999,000 in this case. The input voltage source (V1 ) sweeps from 0 to 3.5 +volts in 0.05 volt steps. + + Netlist: +Inverting opamp +v1 2 0 dc +e 3 0 0 1 999k +r1 3 1 3.29k +r2 1 2 1.18k +.dc v1 0 3.5 0.05 +.print dc v(3,0) +.end + + Output: +v1 v(3) +0.000E+00 0.000E+00 +5.000E-02 -1.394E-01 +1.000E-01 -2.788E-01 +1.500E-01 -4.182E-01 +2.000E-01 -5.576E-01 +2.500E-01 -6.970E-01 +3.000E-01 -8.364E-01 +3.500E-01 -9.758E-01 +4.000E-01 -1.115E+00 +4.500E-01 -1.255E+00 +5.000E-01 -1.394E+00 +5.500E-01 -1.533E+00 +6.000E-01 -1.673E+00 +6.500E-01 -1.812E+00 +7.000E-01 -1.952E+00 +7.500E-01 -2.091E+00 +8.000E-01 -2.231E+00 +8.500E-01 -2.370E+00 +9.000E-01 -2.509E+00 +9.500E-01 -2.649E+00 +1.000E+00 -2.788E+00 +1.050E+00 -2.928E+00 +1.100E+00 -3.067E+00 +1.150E+00 -3.206E+00 +1.200E+00 -3.346E+00 +1.250E+00 -3.485E+00 +1.300E+00 -3.625E+00 + 7.8. EXAMPLE CIRCUITS AND NETLISTS 105 + +1.350E+00 -3.764E+00 +1.400E+00 -3.903E+00 +1.450E+00 -4.043E+00 +1.500E+00 -4.182E+00 +1.550E+00 -4.322E+00 +1.600E+00 -4.461E+00 +1.650E+00 -4.600E+00 +1.700E+00 -4.740E+00 +1.750E+00 -4.879E+00 +1.800E+00 -5.019E+00 +1.850E+00 -5.158E+00 +1.900E+00 -5.297E+00 +1.950E+00 -5.437E+00 +2.000E+00 -5.576E+00 +2.050E+00 -5.716E+00 +2.100E+00 -5.855E+00 +2.150E+00 -5.994E+00 +2.200E+00 -6.134E+00 +2.250E+00 -6.273E+00 +2.300E+00 -6.413E+00 +2.350E+00 -6.552E+00 +2.400E+00 -6.692E+00 +2.450E+00 -6.831E+00 +2.500E+00 -6.970E+00 +2.550E+00 -7.110E+00 +2.600E+00 -7.249E+00 +2.650E+00 -7.389E+00 +2.700E+00 -7.528E+00 +2.750E+00 -7.667E+00 +2.800E+00 -7.807E+00 +2.850E+00 -7.946E+00 +2.900E+00 -8.086E+00 +2.950E+00 -8.225E+00 +3.000E+00 -8.364E+00 +3.050E+00 -8.504E+00 +3.100E+00 -8.643E+00 +3.150E+00 -8.783E+00 +3.200E+00 -8.922E+00 +3.250E+00 -9.061E+00 +3.300E+00 -9.201E+00 +3.350E+00 -9.340E+00 +3.400E+00 -9.480E+00 +3.450E+00 -9.619E+00 +3.500E+00 -9.758E+00 + 106 CHAPTER 7. USING THE SPICE CIRCUIT SIMULATION PROGRAM + +7.8.14 Noninverting op-amp circuit + + + + R2 1 R1 + 3 + 10 kΩ 20 kΩ + 0 + 1 − + 2 (e) 3 + 2 + + + Rbogus 10 kΩ + V1 5V + + 0 0 + +Another example of a SPICE quirk: since the dependent voltage source ”e” isn’t considered a +load to voltage source V1 , SPICE interprets V1 to be open-circuited and will refuse to analyze +it. The fix is to connect Rbogus in parallel with V1 to act as a DC load. Being directly connected +across V1 , the resistance of Rbogus is not crucial to the operation of the circuit, so 10 kΩ will +work fine. I decided not to sweep the V1 input voltage at all in this circuit for the sake of +keeping the netlist and output listing simple. + + + + + Netlist: + +noninverting opamp +v1 2 0 dc 5 +rbogus 2 0 10k +e 3 0 2 1 999k +r1 3 1 20k +r2 1 0 10k +.end + + + + + Output: + +node voltage node voltage node voltage +( 1) 5.0000 ( 2) 5.0000 ( 3) 15.0000 + 7.8. EXAMPLE CIRCUITS AND NETLISTS 107 + +7.8.15 Instrumentation amplifier + + 1 1 + R3 R4 + 3 7 9 + (e1) + 2 − 10 kΩ 10 kΩ + Rbogus1 V1 + 0 to 10 V + R1 10 kΩ + 0 0 + 2 + 7 − + Rgain 10 kΩ (e3) 9 + 8 + + 5 Rload 10 kΩ + + R2 10 kΩ 0 + + 5 − R5 R6 + 4 (e2) 0 + 4 + 6 10 kΩ 8 10 kΩ + + + Rbogus2 V2 5V + + + 0 0 + +Note the very high-resistance Rbogus1 and Rbogus2 resistors in the netlist (not shown in schematic +for brevity) across each input voltage source, to keep SPICE from thinking V1 and V2 were +open-circuited, just like the other op-amp circuit examples. + + Netlist: +Instrumentation amplifier +v1 1 0 +rbogus1 1 0 9e12 +v2 4 0 dc 5 +rbogus2 4 0 9e12 +e1 3 0 1 2 999k +e2 6 0 4 5 999k +e3 9 0 8 7 999k +rload 9 0 10k +r1 2 3 10k +rgain 2 5 10k +r2 5 6 10k +r3 3 7 10k +r4 7 9 10k +r5 6 8 10k +r6 8 0 10k +.dc v1 0 10 1 +.print dc v(9) v(3,6) +.end + + Output: + 108 CHAPTER 7. USING THE SPICE CIRCUIT SIMULATION PROGRAM + +v1 v(9) v(3,6) +0.000E+00 1.500E+01 -1.500E+01 +1.000E+00 1.200E+01 -1.200E+01 +2.000E+00 9.000E+00 -9.000E+00 +3.000E+00 6.000E+00 -6.000E+00 +4.000E+00 3.000E+00 -3.000E+00 +5.000E+00 9.955E-11 -9.956E-11 +6.000E+00 -3.000E+00 3.000E+00 +7.000E+00 -6.000E+00 6.000E+00 +8.000E+00 -9.000E+00 9.000E+00 +9.000E+00 -1.200E+01 1.200E+01 +1.000E+01 -1.500E+01 1.500E+01 + +7.8.16 Op-amp integrator with sinewave input + + R1 C1 + 1 2 3 + 10 kΩ 100 µF + 15 V 2 − + Vin + 60 Hz (e) + 0 + + + 0 Vout + + 0 + + 0 + +Netlist: +Integrator with sinewave input +vin 1 0 sin (0 15 60 0 0) +r1 1 2 10k +c1 2 3 150u ic=0 +e 3 0 0 2 999k +.tran 1m 30m uic +.plot tran v(1,0) v(3,0) +.end + + Output: +legend: +*: v(1) ++: v(3) +time v(1) + 7.8. EXAMPLE CIRCUITS AND NETLISTS 109 + +(*)-------- -2.000E+01 -1.000E+01 0.000E+00 1.000E+01 +(+)-------- -6.000E-02 -4.000E-02 -2.000E-02 0.000E+00 +- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - +0.000E+00 6.536E-08 . . * + . +1.000E-03 5.516E+00 . . . * +. . +2.000E-03 1.021E+01 . . . + * . +3.000E-03 1.350E+01 . . . + . * . +4.000E-03 1.495E+01 . . + . . *. +5.000E-03 1.418E+01 . . + . . * . +6.000E-03 1.150E+01 . + . . . * . +7.000E-03 7.214E+00 . + . . * . . +8.000E-03 1.867E+00 .+ . . * . . +9.000E-03 -3.709E+00 . + . * . . . +1.000E-02 -8.805E+00 . + . * . . . +1.100E-02 -1.259E+01 . * + . . . +1.200E-02 -1.466E+01 . * . + . . . +1.300E-02 -1.471E+01 . * . +. . . +1.400E-02 -1.259E+01 . * . . + . . +1.500E-02 -8.774E+00 . . * . + . . +1.600E-02 -3.723E+00 . . * . +. . +1.700E-02 1.870E+00 . . . * + . +1.800E-02 7.188E+00 . . . * + . . +1.900E-02 1.154E+01 . . . + . * . +2.000E-02 1.418E+01 . . .+ . * . +2.100E-02 1.490E+01 . . + . . *. +2.200E-02 1.355E+01 . . + . . * . +2.300E-02 1.020E+01 . + . . * . +2.400E-02 5.496E+00 . + . . * . . +2.500E-02 -1.486E-03 .+ . * . . +2.600E-02 -5.489E+00 . + . * . . . +2.700E-02 -1.021E+01 . + * . . . +2.800E-02 -1.355E+01 . * . + . . . +2.900E-02 -1.488E+01 . * . + . . . +3.000E-02 -1.427E+01 . * . .+ . . +- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + 110 CHAPTER 7. USING THE SPICE CIRCUIT SIMULATION PROGRAM + +7.8.17 Op-amp integrator with squarewave input + + R1 C1 + 1 2 3 + 10 kΩ 100 µF + 1V 2 − + Vin + 50 Hz (e) + 0 + + + 0 Vout + + 0 + + 0 + +Netlist: +Integrator with squarewave input +vin 1 0 pulse (-1 1 0 0 0 10m 20m) +r1 1 2 1k +c1 2 3 150u ic=0 +e 3 0 0 2 999k +.tran 1m 50m uic +.plot tran v(1,0) v(3,0) +.end + + Output: +legend: +*: v(1) ++: v(3) +time v(1) +(*)-------- -1.000E+00 -5.000E-01 0.000E+00 5.000E-01 1.000E+00 +(+)-------- -1.000E-01 -5.000E-02 0.000E+00 5.000E-02 1.000E-01 +- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - +0.000E+00 -1.000E+00 * . + . . +1.000E-03 1.000E+00 . . + . * +2.000E-03 1.000E+00 . . + . . * +3.000E-03 1.000E+00 . . + . . * +4.000E-03 1.000E+00 . . + . . * +5.000E-03 1.000E+00 . . + . . * +6.000E-03 1.000E+00 . . + . . * +7.000E-03 1.000E+00 . . + . . * +8.000E-03 1.000E+00 . .+ . . * +9.000E-03 1.000E+00 . +. . . * + 7.8. EXAMPLE CIRCUITS AND NETLISTS 111 + +1.000E-02 1.000E+00 . + . . . * +1.100E-02 1.000E+00 . + . . . * +1.200E-02 -1.000E+00 * + . . . . +1.300E-02 -1.000E+00 * + . . . . +1.400E-02 -1.000E+00 * +. . . . +1.500E-02 -1.000E+00 * .+ . . . +1.600E-02 -1.000E+00 * . + . . . +1.700E-02 -1.000E+00 * . + . . . +1.800E-02 -1.000E+00 * . + . . . +1.900E-02 -1.000E+00 * . + . . . +2.000E-02 -1.000E+00 * . + . . . +2.100E-02 1.000E+00 . . + . . * +2.200E-02 1.000E+00 . . + . . * +2.300E-02 1.000E+00 . . + . . * +2.400E-02 1.000E+00 . . + . . * +2.500E-02 1.000E+00 . . + . . * +2.600E-02 1.000E+00 . .+ . . * +2.700E-02 1.000E+00 . +. . . * +2.800E-02 1.000E+00 . + . . . * +2.900E-02 1.000E+00 . + . . . * +3.000E-02 1.000E+00 . + . . . * +3.100E-02 1.000E+00 . + . . . * +3.200E-02 -1.000E+00 * + . . . . +3.300E-02 -1.000E+00 * + . . . . +3.400E-02 -1.000E+00 * + . . . . +3.500E-02 -1.000E+00 * + . . . . +3.600E-02 -1.000E+00 * +. . . . +3.700E-02 -1.000E+00 * .+ . . . +3.800E-02 -1.000E+00 * . + . . . +3.900E-02 -1.000E+00 * . + . . . +4.000E-02 -1.000E+00 * . + . . . +4.100E-02 1.000E+00 . . + . . * +4.200E-02 1.000E+00 . . + . . * +4.300E-02 1.000E+00 . . + . . * +4.400E-02 1.000E+00 . .+ . . * +4.500E-02 1.000E+00 . +. . . * +4.600E-02 1.000E+00 . + . . . * +4.700E-02 1.000E+00 . + . . . * +4.800E-02 1.000E+00 . + . . . * +4.900E-02 1.000E+00 . + . . . * +5.000E-02 1.000E+00 + . . . * +- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + 112 CHAPTER 7. USING THE SPICE CIRCUIT SIMULATION PROGRAM + Chapter 8 + +TROUBLESHOOTING – THEORY +AND PRACTICE + +Contents + 8.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 + 8.2 Questions to ask before proceeding . . . . . . . . . . . . . . . . . . . . . . . 115 + 8.3 General troubleshooting tips . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 + 8.3.1 Prior occurrence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 + 8.3.2 Recent alterations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 + 8.3.3 Function vs. non-function . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 + 8.3.4 Hypothesize . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 + 8.4 Specific troubleshooting techniques . . . . . . . . . . . . . . . . . . . . . . . 117 + 8.4.1 Swap identical components . . . . . . . . . . . . . . . . . . . . . . . . . . 117 + 8.4.2 Remove parallel components . . . . . . . . . . . . . . . . . . . . . . . . . . 119 + 8.4.3 Divide system into sections and test those sections . . . . . . . . . . . . . 119 + 8.4.4 Simplify and rebuild . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 + 8.4.5 Trap a signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 + 8.5 Likely failures in proven systems . . . . . . . . . . . . . . . . . . . . . . . . . 121 + 8.5.1 Operator error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 + 8.5.2 Bad wire connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122 + 8.5.3 Power supply problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122 + 8.5.4 Active components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122 + 8.5.5 Passive components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 + 8.6 Likely failures in unproven systems . . . . . . . . . . . . . . . . . . . . . . . 123 + 8.6.1 Wiring problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 + 8.6.2 Power supply problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 + 8.6.3 Defective components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 + 8.6.4 Improper system configuration . . . . . . . . . . . . . . . . . . . . . . . . 124 + 8.6.5 Design error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 + + 113 + 114 CHAPTER 8. TROUBLESHOOTING – THEORY AND PRACTICE + + 8.7 Potential pitfalls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 + 8.8 Contributors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 + + + + +8.1 +Perhaps the most valuable but difficult-to-learn skill any technical person could have is the +ability to troubleshoot a system. For those unfamiliar with the term, troubleshooting means +the act of pinpointing and correcting problems in any kind of system. For an auto mechanic, +this means determining and fixing problems in cars based on the car’s behavior. For a doctor, +this means correctly diagnosing a patient’s malady and prescribing a cure. For a business +expert, this means identifying the source(s) of inefficiency in a corporation and recommending +corrective measures. + Troubleshooters must be able to determine the cause or causes of a problem simply by +examining its effects. Rarely does the source of a problem directly present itself for all to see. +Cause/effect relationships are often complex, even for seemingly simple systems, and often +the proficient troubleshooter is regarded by others as something of a miracle-worker for their +ability to quickly discern the root cause of a problem. While some people are gifted with a +natural talent for troubleshooting, it is a skill that can be learned like any other. + Sometimes the system to be analyzed is in so bad a state of affairs that there is no hope +of ever getting it working again. When investigators sift through the wreckage of a crashed +airplane, or when a doctor performs an autopsy, they must do their best to determine the +cause of massive failure after the fact. Fortunately, the task of the troubleshooter is usually +not this grim. Typically, a misbehaving system is still functioning to some degree and may +be stimulated and adjusted by the troubleshooter as part of the diagnostic procedure. In this +sense, troubleshooting is a lot like scientific method: determining cause/effect relationships by +means of live experimentation. + Like science, troubleshooting is a mixture of standard procedure and personal creativity. +There are certain procedures employed as tools to discern cause(s) from effects, but they are +impotent if not coupled with a creative and inquisitive mind. In the course of troubleshooting, +the troubleshooter may have to invent their own specific technique – adapted to the particular +system they’re working on – and/or modify tools to perform a special task. Creativity is nec- +essary in examining a problem from different perspectives: learning to ask different questions +when the ”standard” questions don’t lead to fruitful answers. + If there is one personality trait I’ve seen positively associated with excellent troubleshooting +more than any other, its technical curiosity. People fascinated by learning how things work, +and who aren’t discouraged by a challenging problem, tend to be better at troubleshooting than +others. Richard Feynman, the late physicist who taught at Caltech for many years, illustrates +to me the ultimate troubleshooting personality. Reading any of his (auto)biographical books +is both educating and entertaining, and I recommend them to anyone seeking to develop their +own scientific reasoning/troubleshooting skills. + 8.2. QUESTIONS TO ASK BEFORE PROCEEDING 115 + +8.2 Questions to ask before proceeding + • Has the system ever worked before? If yes, has anything happened to it since then that + could cause the problem? + + • Has this system proven itself to be prone to certain types of failure? + + • How urgent is the need for repair? + + • What are the safety concerns, before I start troubleshooting? + + • What are the process quality concerns, before I start troubleshooting (what can I do with- + out causing interruptions in production)? + + These preliminary questions are not trivial. Indeed, they are essential to expedient and +safe troubleshooting. They are especially important when the system to be trouble-shot is +large, dangerous, and/or expensive. + Sometimes the troubleshooter will be required to work on a system that is still in full op- +eration (perhaps the ultimate example of this is a doctor diagnosing a live patient). Once the +cause or causes are determined to a high degree of certainty, there is the step of corrective ac- +tion. Correcting a system fault without significantly interrupting the operation of the system +can be very challenging, and it deserves thorough planning. + When there is high risk involved in taking corrective action, such as is the case with per- +forming surgery on a patient or making repairs to an operating process in a chemical plant, +it is essential for the worker(s) to plan ahead for possible trouble. One question to ask before +proceeding with repairs is, ”how and at what point(s) can I abort the repairs if something goes +wrong?” In risky situations, it is vital to have planned ”escape routes” in your corrective action, +just in case things do not go as planned. A surgeon operating on a patient knows if there are +any ”points of no return” in such a procedure, and stops to re-check the patient before proceed- +ing past those points. He or she also knows how to ”back out” of a surgical procedure at those +points if needed. + + + +8.3 General troubleshooting tips +When first approaching a failed or otherwise misbehaving system, the new troubleshooter often +doesn’t know where to begin. The following strategies are not exhaustive by any means, but +provide the troubleshooter with a simple checklist of questions to ask in order to start isolating +the problem. + As tips, these troubleshooting suggestions are not comprehensive procedures: they serve +as starting points only for the troubleshooting process. An essential part of expedient trou- +bleshooting is probability assessment, and these tips help the troubleshooter determine which +possible points of failure are more or less likely than others. Final isolation of the system +failure is usually determined through more specific techniques (outlined in the next section – +Specific Troubleshooting Techniques). + 116 CHAPTER 8. TROUBLESHOOTING – THEORY AND PRACTICE + +8.3.1 Prior occurrence +If this device or process has been historically known to fail in a certain particular way, and +the conditions leading to this common failure have not changed, check for this ”way” first. A +corollary to this troubleshooting tip is the directive to keep detailed records of failure. Ideally, +a computer-based failure log is optimal, so that failures may be referenced by and correlated +to a number of factors such as time, date, and environmental conditions. + + Example: The car’s engine is overheating. The last two times this happened, the cause was +low coolant level in the radiator. + What to do: Check the coolant level first. Of course, past history by no means guarantees +the present symptoms are caused by the same problem, but since this is more likely, it makes +sense to check this first. + If, however, the cause of routine failure in a system has been corrected (i.e. the leak causing +low coolant level in the past has been repaired), then this may not be a probable cause of +trouble this time. + + + +8.3.2 Recent alterations +If a system has been having problems immediately after some kind of maintenance or other +change, the problems might be linked to those changes. + + Example: The mechanic recently tuned my car’s engine, and now I hear a rattling noise +that I didn’t hear before I took the car in for repair. + What to do: Check for something that may have been left loose by the mechanic after his or +her tune-up work. + + + +8.3.3 Function vs. non-function +If a system isn’t producing the desired end result, look for what it is doing correctly; in other +words, identify where the problem is not, and focus your efforts elsewhere. Whatever compo- +nents or subsystems necessary for the properly working parts to function are probably okay. +The degree of fault can often tell you what part of it is to blame. + + Example: The radio works fine on the AM band, but not on the FM band. + What to do: Eliminate from the list of possible causes, anything in the radio necessary for +the AM band’s function. Whatever the source of the problem is, it is specific to the FM band +and not to the AM band. This eliminates the audio amplifier, speakers, fuse, power supply, and +almost all external wiring. Being able to eliminate sections of the system as possible failures +reduces the scope of the problem and makes the rest of the troubleshooting procedure more +efficient. + 8.4. SPECIFIC TROUBLESHOOTING TECHNIQUES 117 + +8.3.4 Hypothesize +Based on your knowledge of how a system works, think of various kinds of failures that would +cause this problem (or these phenomena) to occur, and check for those failures (starting with +the most likely based on circumstances, history, or knowledge of component weaknesses). + + Example: The car’s engine is overheating. + What to do: Consider possible causes for overheating, based on what you know of engine +operation. Either the engine is generating too much heat, or not getting rid of the heat well +enough (most likely the latter). Brainstorm some possible causes: a loose fan belt, clogged +radiator, bad water pump, low coolant level, etc. Investigate each one of those possibilities +before investigating alternatives. + + + +8.4 Specific troubleshooting techniques +After applying some of the general troubleshooting tips to narrow the scope of a problem’s +location, there are techniques useful in further isolating it. Here are a few: + + +8.4.1 Swap identical components +In a system with identical or parallel subsystems, swap components between those subsystems +and see whether or not the problem moves with the swapped component. If it does, you’ve just +swapped the faulty component; if it doesn’t, keep searching! + This is a powerful troubleshooting method, because it gives you both a positive and a neg- +ative indication of the swapped component’s fault: when the bad part is exchanged between +identical systems, the formerly broken subsystem will start working again and the formerly +good subsystem will fail. + I was once able to troubleshoot an elusive problem with an automotive engine ignition +system using this method: I happened to have a friend with an automobile sharing the exact +same model of ignition system. We swapped parts between the engines (distributor, spark +plug wires, ignition coil – one at a time) until the problem moved to the other vehicle. The +problem happened to be a ”weak” ignition coil, and it only manifested itself under heavy load +(a condition that could not be simulated in my garage). Normally, this type of problem could +only be pinpointed using an ignition system analyzer (or oscilloscope) and a dynamometer +to simulate loaded driving conditions. This technique, however, confirmed the source of the +problem with 100% accuracy, using no diagnostic equipment whatsoever. + Occasionally you may swap a component and find that the problem still exists, but has +changed in some way. This tells you that the components you just swapped are somehow +different (different calibration, different function), and nothing more. However, don’t dismiss +this information just because it doesn’t lead you straight to the problem – look for other changes +in the system as a whole as a result of the swap, and try to figure out what these changes tell +you about the source of the problem. + An important caveat to this technique is the possibility of causing further damage. Suppose +a component has failed because of another, less conspicuous failure in the system. Swapping + 118 CHAPTER 8. TROUBLESHOOTING – THEORY AND PRACTICE + +the failed component with a good component will cause the good component to fail as well. For +example, suppose that a circuit develops a short, which ”blows” the protective fuse for that +circuit. The blown fuse is not evident by inspection, and you don’t have a meter to electrically +test the fuse, so you decide to swap the suspect fuse with one of the same rating from a working +circuit. As a result of this, the good fuse that you move to the shorted circuit blows as well, +leaving you with two blown fuses and two non-working circuits. At least you know for certain +that the original fuse was blown, because the circuit it was moved to stopped working after the +swap, but this knowledge was gained only through the loss of a good fuse and the additional +”down time” of the second circuit. + Another example to illustrate this caveat is the ignition system problem previously men- +tioned. Suppose that the ”weak” ignition coil had caused the engine to backfire, damaging +the muffler. If swapping ignition system components with another vehicle causes the prob- +lem to move to the other vehicle, damage may be done to the other vehicle’s muffler as well. +As a general rule, the technique of swapping identical components should be used only when +there is minimal chance of causing additional damage. It is an excellent technique for isolating +non-destructive problems. + + + Example 1: You’re working on a CNC machine tool with X, Y, and Z-axis drives. The Y axis +is not working, but the X and Z axes are working. All three axes share identical components +(feedback encoders, servo motor drives, servo motors). + What to do: Exchange these identical components, one at a time, Y axis and either one of +the working axes (X or Z), and see after each swap whether or not the problem has moved with +the swap. + + + Example 2: A stereo system produces no sound on the left speaker, but the right speaker +works just fine. + What to do: Try swapping respective components between the two channels and see if the +problem changes sides, from left to right. When it does, you’ve found the defective component. +For instance, you could swap the speakers between channels: if the problem moves to the other +side (i.e. the same speaker that was dead before is still dead, now that its connected to the right +channel cable) then you know that speaker is bad. If the problem stays on the same side (i.e. +the speaker formerly silent is now producing sound after having been moved to the other side +of the room and connected to the other cable), then you know the speakers are fine, and the +problem must lie somewhere else (perhaps in the cable connecting the silent speaker to the +amplifier, or in the amplifier itself). + If the speakers have been verified as good, then you could check the cables using the same +method. Swap the cables so that each one now connects to the other channel of the amplifier +and to the other speaker. Again, if the problem changes sides (i.e. now the right speaker is +now ”dead” and the left speaker now produces sound), then the cable now connected to the right +speaker must be defective. If neither swap (the speakers nor the cables) causes the problem +to change sides from left to right, then the problem must lie within the amplifier (i.e. the left +channel output must be ”dead”). + 8.4. SPECIFIC TROUBLESHOOTING TECHNIQUES 119 + +8.4.2 Remove parallel components +If a system is composed of several parallel or redundant components which can be removed +without crippling the whole system, start removing these components (one at a time) and see +if things start to work again. + + Example 1: A ”star” topology communications network between several computers has +failed. None of the computers are able to communicate with each other. + What to do: Try unplugging the computers, one at a time from the network, and see if +the network starts working again after one of them is unplugged. If it does, then that last +unplugged computer may be the one at fault (it may have been ”jamming” the network by +constantly outputting data or noise). + + Example 2: A household fuse keeps blowing (or the breaker keeps tripping open) after a +short amount of time. + What to do: Unplug appliances from that circuit until the fuse or breaker quits interrupting +the circuit. If you can eliminate the problem by unplugging a single appliance, then that +appliance might be defective. If you find that unplugging almost any appliance solves the +problem, then the circuit may simply be overloaded by too many appliances, neither of them +defective. + + + +8.4.3 Divide system into sections and test those sections +In a system with multiple sections or stages, carefully measure the variables going in and out +of each stage until you find a stage where things don’t look right. + + Example 1: A radio is not working (producing no sound at the speaker)) + What to do: Divide the circuitry into stages: tuning stage, mixing stages, amplifier stage, +all the way through to the speaker(s). Measure signals at test points between these stages and +tell whether or not a stage is working properly. + + Example 2: An analog summer circuit is not functioning properly. + + Analog summer circuit + + R 2R + + + − + R Vout + Vin1 + + R + Vin2 + R + Vin3 + 120 CHAPTER 8. TROUBLESHOOTING – THEORY AND PRACTICE + + What to do: I would test the passive averager network (the three resistors at the lower-left +corner of the schematic) to see that the proper (averaged) voltage was seen at the noninverting +input of the op-amp. I would then measure the voltage at the inverting input to see if it was the +same as at the noninverting input (or, alternatively, measure the voltage difference between +the two inputs of the op-amp, as it should be zero). Continue testing sections of the circuit (or +just test points within the circuit) to see if you measure the expected voltages and currents. + + + +8.4.4 Simplify and rebuild +Closely related to the strategy of dividing a system into sections, this is actually a design and +fabrication technique useful for new circuits, machines, or systems. It’s always easier begin +the design and construction process in little steps, leading to larger and larger steps, rather +than to build the whole thing at once and try to troubleshoot it as a whole. + Suppose that someone were building a custom automobile. He or she would be foolish to bolt +all the parts together without checking and testing components and subsystems as they went +along, expecting everything to work perfectly after its all assembled. Ideally, the builder would +check the proper operation of components along the way through the construction process: +start and tune the engine before its connected to the drivetrain, check for wiring problems +before all the cover panels are put in place, check the brake system in the driveway before +taking it out on the road, etc. + Countless times I’ve witnessed students build a complex experimental circuit and have +trouble getting it to work because they didn’t stop to check things along the way: test all +resistors before plugging them into place, make sure the power supply is regulating voltage +adequately before trying to power anything with it, etc. It is human nature to rush to comple- +tion of a project, thinking that such checks are a waste of valuable time. However, more time +will be wasted in troubleshooting a malfunctioning circuit than would be spent checking the +operation of subsystems throughout the process of construction. + Take the example of the analog summer circuit in the previous section for example: what +if it wasn’t working properly? How would you simplify it and test it in stages? Well, you +could reconnect the op-amp as a basic comparator and see if its responsive to differential input +voltages, and/or connect it as a voltage follower (buffer) and see if it outputs the same analog +voltage as what is input. If it doesn’t perform these simple functions, it will never perform its +function in the summer circuit! By stripping away the complexity of the summer circuit, paring +it down to an (almost) bare op-amp, you can test that component’s functionality and then build +from there (add resistor feedback and check for voltage amplification, then add input resistors +and check for voltage summing), checking for expected results along the way. + + + +8.4.5 Trap a signal +Set up instrumentation (such as a datalogger, chart recorder, or multimeter set on ”record” +mode) to monitor a signal over a period of time. This is especially helpful when tracking down +intermittent problems, which have a way of showing up the moment you’ve turned your back +and walked away. + 8.5. LIKELY FAILURES IN PROVEN SYSTEMS 121 + + This may be essential for proving what happens first in a fast-acting system. Many fast +systems (especially shutdown ”trip” systems) have a ”first out” monitoring capability to provide +this kind of data. + + Example #1: A turbine control system shuts automatically in response to an abnormal con- +dition. By the time a technician arrives at the scene to survey the turbine’s condition, however, +everything is in a ”down” state and its impossible to tell what signal or condition was responsi- +ble for the initial shutdown, as all operating parameters are now ”abnormal.” + What to do: One technician I knew used a videocamera to record the turbine control panel, +so he could see what happened (by indications on the gauges) first in an automatic-shutdown +event. Simply by looking at the panel after the fact, there was no way to tell which signal shut +the turbine down, but the videotape playback would show what happened in sequence, down +to a frame-by-frame time resolution. + + Example #2: An alarm system is falsely triggering, and you suspect it may be due to a +specific wire connection going bad. Unfortunately, the problem never manifests itself while +you’re watching it! + What to do: Many modern digital multimeters are equipped with ”record” settings, whereby +they can monitor a voltage, current, or resistance over time and note whether that measure- +ment deviates substantially from a regular value. This is an invaluable tool for use in ”inter- +mittent” electronic system failures. + + + + +8.5 Likely failures in proven systems +The following problems are arranged in order from most likely to least likely, top to bottom. +This order has been determined largely from personal experience troubleshooting electrical +and electronic problems in automotive, industry, and home applications. This order also as- +sumes a circuit or system that has been proven to function as designed and has failed after +substantial operation time. Problems experienced in newly assembled circuits and systems do +not necessarily exhibit the same probabilities of occurrence. + + +8.5.1 Operator error +A frequent cause of system failure is error on the part of those human beings operating it. +This cause of trouble is placed at the top of the list, but of course the actual likelihood depends +largely on the particular individuals responsible for operation. When operator error is the +cause of a failure, it is unlikely that it will be admitted prior to investigation. I do not mean +to suggest that operators are incompetent and irresponsible – quite the contrary: these people +are often your best teachers for learning system function and obtaining a history of failure – +but the reality of human error cannot be overlooked. A positive attitude coupled with good +interpersonal skills on the part of the troubleshooter goes a long way in troubleshooting when +human error is the root cause of failure. + 122 CHAPTER 8. TROUBLESHOOTING – THEORY AND PRACTICE + +8.5.2 Bad wire connections +As incredible as this may sound to the new student of electronics, a high percentage of electrical +and electronic system problems are caused by a very simple source of trouble: poor (i.e. open +or shorted) wire connections. This is especially true when the environment is hostile, including +such factors as high vibration and/or a corrosive atmosphere. Connection points found in any +variety of plug-and-socket connector, terminal strip, or splice are at the greatest risk for failure. +The category of ”connections” also includes mechanical switch contacts, which can be thought +of as a high-cycle connector. Improper wire termination lugs (such as a compression-style +connector crimped on the end of a solid wire – a definite faux pas) can cause high-resistance +connections after a period of trouble-free service. + It should be noted that connections in low-voltage systems tend to be far more troublesome +than connections in high-voltage systems. The main reason for this is the effect of arcing across +a discontinuity (circuit break) in higher-voltage systems tends to blast away insulating layers +of dirt and corrosion, and may even weld the two ends together if sustained long enough. Low- +voltage systems tend not to generate such vigorous arcing across the gap of a circuit break, +and also tend to be more sensitive to additional resistance in the circuit. Mechanical switch +contacts used in low-voltage systems benefit from having the recommended minimum wetting +current conducted through them to promote a healthy amount of arcing upon opening, even if +this level of current is not necessary for the operation of other circuit components. + Although open failures tend to more common than shorted failures, ”shorts” still constitute +a substantial percentage of wiring failure modes. Many shorts are caused by degradation of +wire insulation. This, again, is especially true when the environment is hostile, including +such factors as high vibration, high heat, high humidity, or high voltage. It is rare to find a +mechanical switch contact that is failed shorted, except in the case of high-current contacts +where contact ”welding” may occur in overcurrent conditions. Shorts may also be caused by +conductive buildup across terminal strip sections or the backs of printed circuit boards. + A common case of shorted wiring is the ground fault, where a conductor accidently makes +contact with either earth or chassis ground. This may change the voltage(s) present between +other conductors in the circuit and ground, thereby causing bizarre system malfunctions and/or +personnel hazard. + + +8.5.3 Power supply problems +These generally consist of tripped overcurrent protection devices or damage due to overheating. +Although power supply circuitry is usually less complex than the circuitry being powered, and +therefore should figure to be less prone to failure on that basis alone, it generally handles more +power than any other portion of the system and therefore must deal with greater voltages +and/or currents. Also, because of its relative design simplicity, a system’s power supply may +not receive the engineering attention it deserves, most of the engineering focus devoted to more +glamorous parts of the system. + + +8.5.4 Active components +Active components (amplification devices) tend to fail with greater regularity than passive +(non-amplifying) devices, due to their greater complexity and tendency to amplify overvolt- + 8.6. LIKELY FAILURES IN UNPROVEN SYSTEMS 123 + +age/overcurrent conditions. Semiconductor devices are notoriously prone to failure due to elec- +trical transient (voltage/current surge) overloading and thermal (heat) overloading. Electron +tube devices are far more resistant to both of these failure modes, but are generally more prone +to mechanical failures due to their fragile construction. + + +8.5.5 Passive components +Non-amplifying components are the most rugged of all, their relative simplicity granting them +a statistical advantage over active devices. The following list gives an approximate relation of +failure probabilities (again, top being the most likely and bottom being the least likely): + + • Capacitors (shorted), especially electrolytic capacitors. The paste electrolyte tends to lose + moisture with age, leading to failure. Thin dielectric layers may be punctured by over- + voltage transients. + + • Diodes open (rectifying diodes) or shorted (Zener diodes). + + • Inductor and transformer windings open or shorted to conductive core. Failures related + to overheating (insulation breakdown) are easily detected by smell. + + • Resistors open, almost never shorted. Usually this is due to overcurrent heating, al- + though it is less frequently caused by overvoltage transient (arc-over) or physical damage + (vibration or impact). Resistors may also change resistance value if overheated! + + +8.6 Likely failures in unproven systems + ”All men are liable to error;” + John Locke + + Whereas the last section deals with component failures in systems that have been success- +fully operating for some time, this section concentrates on the problems plaguing brand-new +systems. In this case, failure modes are generally not of the aging kind, but are related to +mistakes in design and assembly caused by human beings. + + +8.6.1 Wiring problems +In this case, bad connections are usually due to assembly error, such as connection to the wrong +point or poor connector fabrication. Shorted failures are also seen, but usually involve miscon- +nections (conductors inadvertently attached to grounding points) or wires pinched under box +covers. + Another wiring-related problem seen in new systems is that of electrostatic or electromag- +netic interference between different circuits by way of close wiring proximity. This kind of +problem is easily created by routing sets of wires too close to each other (especially routing +signal cables close to power conductors), and tends to be very difficult to identify and locate +with test equipment. + 124 CHAPTER 8. TROUBLESHOOTING – THEORY AND PRACTICE + +8.6.2 Power supply problems +Blown fuses and tripped circuit breakers are likely sources of trouble, especially if the project in +question is an addition to an already-functioning system. Loads may be larger than expected, +resulting in overloading and subsequent failure of power supplies. + + +8.6.3 Defective components +In the case of a newly-assembled system, component fault probabilities are not as predictable +as in the case of an operating system that fails with age. Any type of component – active or +passive – may be found defective or of imprecise value ”out of the box” with roughly equal prob- +ability, barring any specific sensitivities in shipping (i.e fragile vacuum tubes or electrostati- +cally sensitive semiconductor components). Moreover, these types of failures are not always as +easy to identify by sight or smell as an age- or transient-induced failure. + + +8.6.4 Improper system configuration +Increasingly seen in large systems using microprocessor-based components, ”programming” +issues can still plague non-microprocessor systems in the form of incorrect time-delay relay +settings, limit switch calibrations, and drum switch sequences. Complex components having +configuration ”jumpers” or switches to control behavior may not be ”programmed” properly. + Components may be used in a new system outside of their tolerable ranges. Resistors, for +example, with too low of power ratings, of too great of tolerance, may have been installed. +Sensors, instruments, and controlling mechanisms may be uncalibrated, or calibrated to the +wrong ranges. + + +8.6.5 Design error +Perhaps the most difficult to pinpoint and the slowest to be recognized (especially by the chief +designer) is the problem of design error, where the system fails to function simply because +it cannot function as designed. This may be as trivial as the designer specifying the wrong +components in a system, or as fundamental as a system not working due to the designer’s +improper knowledge of physics. + I once saw a turbine control system installed that used a low-pressure switch on the lubri- +cation oil tubing to shut down the turbine if oil pressure dropped to an insufficient level. The +oil pressure for lubrication was supplied by an oil pump turned by the turbine. When installed, +the turbine refused to start. Why? Because when it was stopped, the oil pump was not turning, +thus there was no oil pressure to lubricate the turbine. The low-oil-pressure switch detected +this condition and the control system maintained the turbine in shutdown mode, preventing +it from starting. This is a classic example of a design flaw, and it could only be corrected by a +change in the system logic. + While most design flaws manifest themselves early in the operational life of the system, +some remain hidden until just the right conditions exist to trigger the fault. These types of +flaws are the most difficult to uncover, as the troubleshooter usually overlooks the possibility +of design error due to the fact that the system is assumed to be ”proven.” The example of the +turbine lubrication system was a design flaw impossible to ignore on start-up. An example of + 8.7. POTENTIAL PITFALLS 125 + +a ”hidden” design flaw might be a faulty emergency coolant system for a machine, designed to +remain inactive until certain abnormal conditions are reached – conditions which might never +be experienced in the life of the system. + + +8.7 Potential pitfalls +Fallacious reasoning and poor interpersonal relations account for more failed or belabored trou- +bleshooting efforts than any other impediments. With this in mind, the aspiring troubleshooter +needs to be familiar with a few common troubleshooting mistakes. + + Trusting that a brand-new component will always be good. While it is generally true +that a new component will be in good condition, it is not always true. It is also possible that +a component has been mis-labeled and may have the wrong value (usually this mis-labeling is +a mistake made at the point of distribution or warehousing and not at the manufacturer, but +again, not always!). + + Not periodically checking your test equipment. This is especially true with battery- +powered meters, as weak batteries may give spurious readings. When using meters to safety- +check for dangerous voltage, remember to test the meter on a known source of voltage both +before and after checking the circuit to be serviced, to make sure the meter is in proper operat- +ing condition. + + Assuming there is only one failure to account for the problem. Single-failure sys- +tem problems are ideal for troubleshooting, but sometimes failures come in multiple numbers. +In some instances, the failure of one component may lead to a system condition that damages +other components. Sometimes a component in marginal condition goes undetected for a long +time, then when another component fails the system suffers from problems with both compo- +nents. + + Mistaking coincidence for causality. Just because two events occurred at nearly the +same time does not necessarily mean one event caused the other! They may be both conse- +quences of a common cause, or they may be totally unrelated! If possible, try to duplicate the +same condition suspected to be the cause and see if the event suspected to be the coincidence +happens again. If not, then there is either no causal relationship as assumed. This may mean +there is no causal relationship between the two events whatsoever, or that there is a causal +relationship, but just not the one you expected. + + Self-induced blindness. After a long effort at troubleshooting a difficult problem, you +may become tired and begin to overlook crucial clues to the problem. Take a break and let +someone else look at it for a while. You will be amazed at what a difference this can make. +On the other hand, it is generally a bad idea to solicit help at the start of the troubleshooting +process. Effective troubleshooting involves complex, multi-level thinking, which is not easily +communicated with others. More often than not, ”team troubleshooting” takes more time and +causes more frustration than doing it yourself. An exception to this rule is when the knowledge +of the troubleshooters is complementary: for example, a technician who knows electronics + 126 CHAPTER 8. TROUBLESHOOTING – THEORY AND PRACTICE + +but not machine operation, teamed with an operator who knows machine function but not +electronics. + + Failing to question the troubleshooting work of others on the same job. This may +sound rather cynical and misanthropic, but it is sound scientific practice. Because it is easy to +overlook important details, troubleshooting data received from another troubleshooter should +be personally verified before proceeding. This is a common situation when troubleshooters +”change shifts” and a technician takes over for another technician who is leaving before the +job is done. It is important to exchange information, but do not assume the prior techni- +cian checked everything they said they did, or checked it perfectly. I’ve been hindered in my +troubleshooting efforts on many occasions by failing to verify what someone else told me they +checked. + + Being pressured to ”hurry up.” When an important system fails, there will be pressure +from other people to fix the problem as quickly as possible. As they say in business, ”time +is money.” Having been on the receiving end of this pressure many times, I can understand +the need for expedience. However, in many cases there is a higher priority: caution. If the +system in question harbors great danger to life and limb, the pressure to ”hurry up” may +result in injury or death. At the very least, hasty repairs may result in further damage when +the system is restarted. Most failures can be recovered or at least temporarily repaired in +short time if approached intelligently. Improper ”fixes” resulting in haste often lead to damage +that cannot be recovered in short time, if ever. If the potential for greater harm is present, the +troubleshooter needs to politely address the pressure received from others, and maintain their +perspective in the midst of chaos. Interpersonal skills are just as important in this realm as +technical ability! + + Finger-pointing. It is all too easy to blame a problem on someone else, for reasons of +ignorance, pride, laziness, or some other unfortunate facet of human nature. When the respon- +sibility for system maintenance is divided into departments or work crews, troubleshooting +efforts are often hindered by blame cast between groups. ”It’s a mechanical problem . . . its +an electrical problem . . . its an instrument problem . . .” ad infinitum, ad nauseum, is all too +common in the workplace. I have found that a positive attitude does more to quench the fires +of blame than anything else. + On one particular job, I was summoned to fix a problem in a hydraulic system assumed to +be related to the electronic metering and controls. My troubleshooting isolated the source of +trouble to a faulty control valve, which was the domain of the millwright (mechanical) crew. I +knew that the millwright on shift was a contentious person, so I expected trouble if I simply +passed the problem on to his department. Instead, I politely explained to him and his super- +visor the nature of the problem as well as a brief synopsis of my reasoning, then proceeded +to help him replace the faulty valve, even though it wasn’t ”my” responsibility to do so. As a +result, the problem was fixed very quickly, and I gained the respect of the millwright. + + +8.8 Contributors +Contributors to this chapter are listed in chronological order of their contributions, from most +recent to first. See Appendix 2 (Contributor List) for dates and contact information. + 8.8. CONTRIBUTORS 127 + + Alejandro Gamero Divasto (January 2002): contributed troubleshooting tips regarding +potential hazards of swapping two similar components, avoiding pressure placed on the trou- +bleshooter, perils of ”team” troubleshooting, wisdom of recording system history, operator error +as a cause of failure, and the perils of finger-pointing. + 128 CHAPTER 8. TROUBLESHOOTING – THEORY AND PRACTICE + Chapter 9 + +CIRCUIT SCHEMATIC SYMBOLS + +Contents + 9.1 Wires and connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 + 9.2 Power sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 + 9.3 Resistors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 + 9.4 Capacitors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 + 9.5 Inductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 + 9.6 Mutual inductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 + 9.7 Switches, hand actuated . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 + 9.8 Switches, process actuated . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 + 9.9 Switches, electrically actuated (relays) . . . . . . . . . . . . . . . . . . . . . 136 + 9.10 Connectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 + 9.11 Diodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 + 9.12 Transistors, bipolar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138 + 9.13 Transistors, junction field-effect (JFET) . . . . . . . . . . . . . . . . . . . . 138 + 9.14 Transistors, insulated-gate field-effect (IGFET or MOSFET) . . . . . . . . 139 + 9.15 Transistors, hybrid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 + 9.16 Thyristors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 + 9.17 Integrated circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 + 9.18 Electron tubes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144 + + + + + 129 + 130 CHAPTER 9. CIRCUIT SCHEMATIC SYMBOLS + +9.1 Wires and connections + + + Older convention + + Connected Not connected + + + + + Newer convention + + Connected Not connected + + + + +Older electrical schematics showed connecting wires crossing, while non-connecting wires ”jumped” +over each other with little half-circle marks. Newer electrical schematics show connecting +wires joining with a dot, while non-connecting wires cross with no dot. However, some peo- +ple still use the older convention of connecting wires crossing with no dot, which may create +confusion. + + For this reason, I opt to use a hybrid convention, with connecting wires unambiguously +connected by a dot, and non-connecting wires unambiguously ”jumping” over one another with +a half-circle mark. While this may be frowned upon by some, it leaves no room for interpreta- +tional error: in each case, the intent is clear and unmistakable: + + + Convention used in this book + + Connected Not connected + 9.2. POWER SOURCES 131 + +9.2 Power sources + + DC voltage DC voltage AC voltage + + + − + + + + Variable + DC voltage DC current + A diagonal arrow + + represents variability + for any component! - + + Generator AC current + + Gen + + + + +9.3 Resistors + + Fixed-value Rheostat + + + + + Potentiometer Tapped Thermistor + + to + + + + Photoresistor + 132 CHAPTER 9. CIRCUIT SCHEMATIC SYMBOLS + +9.4 Capacitors + + + + + Non-polarized Polarized (top positive) + + + + + + + + Variable + + + + +9.5 Inductors + + + + + Fixed-value Iron core + + + + + Variable Variac Tapped + 9.6. MUTUAL INDUCTORS 133 + +9.6 Mutual inductors + + + + + Step-up/step-down + Transformer transformer Variac + + + + + Saturable + Transformer Transformer Transformer reactor + + + + + Synchro + Synchro + 134 CHAPTER 9. CIRCUIT SCHEMATIC SYMBOLS + +9.7 Switches, hand actuated + + + + + SPST toggle Pushbutton + normally open DPST toggle normally open + + + + SPST toggle Pushbutton + normally closed normally closed + DPDT toggle + + + + + SPDT toggle SPST joystick + position of dot + on circle indicates + joystick direction + 4PDT toggle + 9.8. SWITCHES, PROCESS ACTUATED 135 + +9.8 Switches, process actuated + + + + + Normally open shown on top; normally closed on bottom + + + + Level Pressure Flow Temperature + + + F + + + + + Electronic R + Limit Limit Speed + F + + + + + R + + + + +It is very important to keep in mind that the ”normal” contact status of a process-actuated +switch refers to its status when the process is absent and/or inactive, not ”normal” in the sense +of process conditions as expected during routine operation. For instance, a normally-closed +low-flow detection switch installed on a coolant pipe will be maintained in the actuated state +(open) when there is regular coolant flow through the pipe. If the coolant flow stops, the flow +switch will go to its ”normal” (unactuated) status of closed. + + + + A limit switch is one actuated by contact with a moving machine part. An electronic limit +switch senses mechanical motion, but does so using light, magnetic fields, or other non-contact +means. + 136 CHAPTER 9. CIRCUIT SCHEMATIC SYMBOLS + +9.9 Switches, electrically actuated (relays) + + + Relay components, "ladder logic" notation style + + + + + Generic Electronic Relay coil, Relay coil, + electromechanical electronic + + + + + Relays, electronic schematic notation style + + + + +9.10 Connectors + + + + Plug Jack Plug & Jack + (male) (female) connected + + + + + Receptacle Household Multi-conductor + (female) power plug/jack set + connectors + Plug Jack + + Plug + (male) + 9.11. DIODES 137 + +9.11 Diodes + + + + + Generic Schottky Shockley Constant current + A K A K A K A K + + + + + Zener Light-emitting Photo- Step recovery + A K A K A K A K + + + + + Tunnel Varactor PIN Vacuum tube + P + A K A K A K + + + + + A = Anode + K = Cathode + C + H1 H2 + 138 CHAPTER 9. CIRCUIT SCHEMATIC SYMBOLS + +9.12 Transistors, bipolar + + + . . . with case + Bipolar NPN Bipolar PNP + B B + + + E C E C + + + + + Photo- + Dual-emitter NPN Dual-emitter PNP + B B + + + E C E1 C E1 C + E2 E2 + + + + + Darlington pair E = Emitter Sziklai pair + B B + B = Base + C = Collector + + C C + E E + + + + +9.13 Transistors, junction field-effect (JFET) + + + N-channel P-channel . . . with case + G G + + + + + S D S D + + + + + S = Source + G = Gate + D = Drain + 9.14. TRANSISTORS, INSULATED-GATE FIELD-EFFECT (IGFET OR MOSFET) 139 + +9.14 Transistors, insulated-gate field-effect (IGFET or MOS- + FET) + + N-channel P-channel N-channel P-channel + depletion depletion enhancement enhancement + G G G G + + + + + S D S D S D S D + + + SS SS SS SS + + + + + N-channel P-channel N-channel P-channel + depletion depletion enhancement enhancement + G G G G + + + + + S D S D S D S D + + + + + S = Source . . . with case + + G = Gate + D = Drain + SS = Substrate + + +9.15 Transistors, hybrid + + . . . with case + IGBT (NPN) IGBT (PNP) + G G + + + + E C E C + + + + + . . . with case + IGBT (N-channel) IGBT (P-channel) + G G + + + + + E C E C + + + + + E = Emitter + G = Gate + C = Collector + 140 CHAPTER 9. CIRCUIT SCHEMATIC SYMBOLS + +9.16 Thyristors + + + + + Shockley DIAC SCR LASCR + A K A K A K + + + G G + + + + TRIAC Opto-TRIAC GA SCS GCS + MT2 MT1 MT2 MT1 A K A K + + + G G GK G + + + + + GTO UJT B1 A = Anode + A K + E K = Cathode + G G = Gate + B2 + MT = Main Terminal + E = Emitter + B = Base + 9.17. INTEGRATED CIRCUITS 141 + +9.17 Integrated circuits + + + + + Operational amplifier (alternative) Norton op-amp + − - − + + + + + + + + Inverter AND gate OR gate XOR gate + + + + + Inverter NAND gate NOR gate XNOR gate + + + + Negative-AND Negative-OR + Buffer gate gate + + + + Gate with open- Gate with Schmitt + collector output trigger input + 142 CHAPTER 9. CIRCUIT SCHEMATIC SYMBOLS + + S-R Latch Enabled S-R Latch S-R Flip-flop + + S Q S Q S Q + + E C + + R Q R Q R Q + + + + + D Latch D Flip-flop J-K Flip-flop + + D Q D Q J Q + + E C C + + Q Q K Q + 9.17. INTEGRATED CIRCUITS 143 + 144 CHAPTER 9. CIRCUIT SCHEMATIC SYMBOLS + +9.18 Electron tubes + Diode Glow tube Phototube + P P C + + + + + C C A + H1 H2 + + + + + Triode Tetrode Beam tetrode + P P P + + + + + S + G S + G G + + + + + C C C + H1 H2 H1 H2 H1 H2 + + + + + Pentode Pentode Thyratron + P P P + + + + + Sup + S S G + G G + + + + C C C + H1 H2 H1 H2 H1 H2 + + + + + Ignitron Cathode Ray Tube + A + + + + + I H V + + + + + C + + + + + P = Plate S = Screen + G = Grid A = Anode + C = Cathode H = Heater + I = Ignitor Sup = Suppressor + Chapter 10 + +PERIODIC TABLE OF THE +ELEMENTS + +Contents + 10.1 Table (landscape view) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 + 10.2 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 + + + + +10.1 Table (landscape view) +See Figure 10.1. + + +10.2 Data +Atomic masses shown in parentheses indicate the most stable isotope (longest half-life) known. + Electron configuration data was taken from Douglas C. Giancoli’s Physics, 3rd edition. Av- +erage atomic masses were taken from Kenneth W. Whitten’s, Kenneth D. Gailey’s, and Ray- +mond E. Davis’ General Chemistry, 3rd edition. In the latter book, the masses were specified +as 1985 IUPAC values. + + + + + 145 + 146 + + 1 IA 13 VIIIA + H 1 He 2 + Hydrogen Periodic Table of the Elements Helium + 1.00794 4.00260 + Group old Metalloids Nonmetals + 1s1 2 IIA Group new 1 IA 13 IIIA 14 IVA 15 VA 16 VIA 17 VIIA 1s2 + Li 3 Be 4 Symbol K 19 Atomic number B 5 C 6 N 7 O 8 F 9 Ne 10 + Lithium Beryllium Potassium Boron Carbon Nitrogen Oxygen Fluorine Neon + 6.941 9.012182 Name 39.0983 10.81 12.011 14.0067 15.9994 18.9984 20.179 + Atomic mass + 2s1 2s2 4s1 (averaged according to 2p1 2p2 2p3 2p4 2p5 2p6 + Electron occurence on earth) + Na 11 Mg 12 configuration Al 13 Si 14 P 15 S 16 Cl 17 Ar 18 + Sodium Magnesium Aluminum Silicon Phosphorus Sulfur Chlorine Argon + 22.989768 24.3050 26.9815 28.0855 30.9738 32.06 35.453 39.948 + Metals + 3s1 3s2 3 IIIB 4 IVB 5 VB 6 VIB 7 VIIB 8 VIIIB 9 VIIIB 10 VIIIB 11 IB 12 IIB 3p1 3p2 3p3 3p4 3p5 3p6 + K 19 Ca 20 Sc 21 Ti 22 V 23 Cr 24 Mn 25 Fe 26 Co 27 Ni 28 Cu 29 Zn 30 Ga 31 Ge 32 As 33 Se 34 Br 35 Kr 36 + Potassium Calcium Scandium Titanium Vanadium Chromium Manganese Iron Cobalt Nickel Copper Zinc Gallium Germanium Arsenic Selenium Bromine Krypton + 39.0983 40.078 44.955910 47.88 50.9415 51.9961 54.93805 55.847 58.93320 58.69 63.546 65.39 69.723 72.61 74.92159 78.96 79.904 83.80 + 4s1 4s2 3d14s2 3d24s2 3d34s2 3d54s1 3d54s2 3d64s2 3d74s2 3d84s2 3d104s1 3d104s2 4p1 4p2 4p3 4p4 4p5 4p6 + Rb 37 Sr 38 Y 39 Zr 40 Nb 41 Mo 42 Tc 43 Ru 44 Rh 45 Pd 46 Ag 47 Cd 48 In 49 Sn 50 Sb 51 Te 52 I 53 Xe 54 + Rubidium Strontium Yttrium Zirconium Niobium Molybdenum Technetium Ruthenium Rhodium Palladium Silver Cadmium Indium Tin Antimony Tellurium Iodine Xenon + 85.4678 87.62 88.90585 91.224 92.90638 95.94 (98) 101.07 102.90550 106.42 107.8682 112.411 114.82 118.710 121.75 127.60 126.905 131.30 + 5s1 5s2 4d15s2 4d25s2 4d45s1 4d55s1 4d55s2 4d75s1 4d85s1 4d105s0 4d105s1 4d105s2 5p1 5p2 5p3 5p4 5p5 5p6 + Cs 55 Ba 56 57 - 71 Hf 72 Ta 73 W 74 Re 75 Os 76 Ir 77 Pt 78 Au 79 Hg 80 Tl 81 Pb 82 Bi 83 Po 84 At 85 Rn 86 + Cesium Barium Lanthanide Hafnium Tantalum Tungsten Rhenium Osmium Iridium Platinum Gold Mercury Thallium Lead Bismuth Polonium Astatine Radon + 132.90543 137.327 series 178.49 180.9479 183.85 186.207 190.2 192.22 195.08 196.96654 200.59 204.3833 207.2 208.98037 (209) (210) (222) + 6s1 6s2 5d26s2 5d36s2 5d46s2 5d56s2 5d66s2 5d76s2 5d96s1 5d106s1 5d106s2 6p1 6p2 6p3 6p4 6p5 6p6 + Fr 87 Ra 88 89 - 103 Unq 104 Unp 105 Unh 106 Uns 107 108 109 + Francium Radium Actinide Unnilquadium Unnilpentium Unnilhexium Unnilseptium + (223) (226) series (261) (262) (263) (262) + 1 2 2 2 3 2 4 2 + 7s 7s 6d 7s 6d 7s 6d 7s + + + + La 57 Ce 58 Pr 59 Nd 60 Pm 61 Sm 62 Eu 63 Gd 64 Tb 65 Dy 66 Ho 67 Er 68 Tm 69 Yb 70 Lu 71 + Lanthanide Lanthanum Cerium Praseodymium Neodymium Promethium Samarium Europium Gadolinium Terbium Dysprosium Holmium Erbium Thulium Ytterbium Lutetium + series 138.9055 140.115 140.90765 144.24 (145) 150.36 151.965 157.25 158.92534 162.50 164.93032 167.26 168.93421 173.04 174.967 + + + + +Figure 10.1: Periodic table of chemical elements. + 5d16s2 4f15d16s2 4f36s2 4f46s2 4f56s2 4f66s2 4f76s2 4f75d16s2 4f96s2 4f106s2 4f116s2 4f126s2 4f136s2 4f146s2 4f145d16s2 + + + + Ac 89 Th 90 Pa 91 U 92 Np 93 Pu 94 Am 95 Cm 96 Bk 97 Cf 98 Es 99 Fm 100 Md 101 No 102 Lr 103 + Actinide Actinium Thorium Protactinium Uranium Neptunium Plutonium Americium Curium Berkelium Californium Einsteinium Fermium Mendelevium Nobelium Lawrencium + series (227) 232.0381 231.03588 238.0289 (237) (244) (243) (247) (247) (251) (252) (257) (258) (259) (260) + 6d17s2 6d27s2 5f26d17s2 5f36d17s2 5f46d17s2 5f66d07s2 5f76d07s2 5f76d17s2 5f96d07s2 5f106d07s2 5f116d07s2 5f126d07s2 5f136d07s2 6d07s2 6d17s2 + CHAPTER 10. PERIODIC TABLE OF THE ELEMENTS + Appendix A-1 + + ABOUT THIS BOOK + + + +A-1.1 Purpose +They say that necessity is the mother of invention. At least in the case of this book, that adage +is true. As an industrial electronics instructor, I was forced to use a sub-standard textbook +during my first year of teaching. My students were daily frustrated with the many typograph- +ical errors and obscure explanations in this book, having spent much time at home struggling +to comprehend the material within. Worse yet were the many incorrect answers in the back of +the book to selected problems. Adding insult to injury was the $100+ price. + Contacting the publisher proved to be an exercise in futility. Even though the particular +text I was using had been in print and in popular use for a couple of years, they claimed my +complaint was the first they’d ever heard. My request to review the draft for the next edition +of their book was met with disinterest on their part, and I resolved to find an alternative text. + Finding a suitable alternative was more difficult than I had imagined. Sure, there were +plenty of texts in print, but the really good books seemed a bit too heavy on the math and the +less intimidating books omitted a lot of information I felt was important. Some of the best +books were out of print, and those that were still being printed were quite expensive. + It was out of frustration that I compiled Lessons in Electric Circuits from notes and ideas I +had been collecting for years. My primary goal was to put readable, high-quality information +into the hands of my students, but a secondary goal was to make the book as affordable as +possible. Over the years, I had experienced the benefit of receiving free instruction and encour- +agement in my pursuit of learning electronics from many people, including several teachers +of mine in elementary and high school. Their selfless assistance played a key role in my own +studies, paving the way for a rewarding career and fascinating hobby. If only I could extend +the gift of their help by giving to other people what they gave to me . . . + So, I decided to make the book freely available. More than that, I decided to make it ”open,” +following the same development model used in the making of free software (most notably the +various UNIX utilities released by the Free Software Foundation, and the Linux operating + + 147 + 148 APPENDIX A-1. ABOUT THIS BOOK + +system, whose fame is growing even as I write). The goal was to copyright the text – so as to +protect my authorship – but expressly allow anyone to distribute and/or modify the text to suit +their own needs with a minimum of legal encumbrance. This willful and formal revoking of +standard distribution limitations under copyright is whimsically termed copyleft. Anyone can +”copyleft” their creative work simply by appending a notice to that effect on their work, but +several Licenses already exist, covering the fine legal points in great detail. + The first such License I applied to my work was the GPL – General Public License – of the +Free Software Foundation (GNU). The GPL, however, is intended to copyleft works of computer +software, and although its introductory language is broad enough to cover works of text, its +wording is not as clear as it could be for that application. When other, less specific copyleft +Licenses began appearing within the free software community, I chose one of them (the Design +Science License, or DSL) as the official notice for my project. Once the author of the DSL said +it was obsolete, I moved on to Creative Commons (CC BY License). + In ”copylefting” this text, I guaranteed that no instructor would be limited by a text insuffi- +cient for their needs, as I had been with error-ridden textbooks from major publishers. I’m sure +this book in its initial form will not satisfy everyone, but anyone has the freedom to change it, +leveraging my efforts to suit variant and individual requirements. For the beginning student +of electronics, learn what you can from this book, editing it as you feel necessary if you come +across a useful piece of information. Then, if you pass it on to someone else, you will be giving +them something better than what you received. For the instructor or electronics professional, +feel free to use this as a reference manual, adding or editing to your heart’s content. The +only ”catch” is this: if you plan to distribute your modified version of this text, you must give +credit where credit is due (to me, the original author, and anyone else whose modifications are +contained in your version), and you must ensure that whoever you give the text to is aware of +their freedom to similarly share and edit the text. The next chapter covers this process in more +detail. + It must be mentioned that although I strive to maintain technical accuracy in all of this +book’s content, the subject matter is broad and harbors many potential dangers. Electricity +maims and kills without provocation, and deserves the utmost respect. I strongly encourage +experimentation on the part of the reader, but only with circuits powered by small batteries +where there is no risk of electric shock, fire, explosion, etc. High-power electric circuits should +be left to the care of trained professionals! The CC BY License clearly states that neither I nor +any contributors to this book bear any liability for what is done with its contents. + + +A-1.2 The use of SPICE +One of the best ways to learn how things work is to follow the inductive approach: to observe +specific instances of things working and derive general conclusions from those observations. +In science education, labwork is the traditionally accepted venue for this type of learning, al- +though in many cases labs are designed by educators to reinforce principles previously learned +through lecture or textbook reading, rather than to allow the student to learn on their own +through a truly exploratory process. + Having taught myself most of the electronics that I know, I appreciate the sense of frustra- +tion students may have in teaching themselves from books. Although electronic components +are typically inexpensive, not everyone has the means or opportunity to set up a laboratory + A-1.3. ACKNOWLEDGEMENTS 149 + +in their own homes, and when things go wrong there’s no one to ask for help. Most textbooks +seem to approach the task of education from a deductive perspective: tell the student how +things are supposed to work, then apply those principles to specific instances that the student +may or may not be able to explore by themselves. The inductive approach, as useful as it is, is +hard to find in the pages of a book. + However, textbooks don’t have to be this way. I discovered this when I started to learn a +computer program called SPICE. It is a text-based piece of software intended to model circuits +and provide analyses of voltage, current, frequency, etc. Although nothing is quite as good as +building real circuits to gain knowledge in electronics, computer simulation is an excellent al- +ternative. In learning how to use this powerful tool, I made a discovery: SPICE could be used +within a textbook to present circuit simulations to allow students to ”observe” the phenomena +for themselves. This way, the readers could learn the concepts inductively (by interpreting +SPICE’s output) as well as deductively (by interpreting my explanations). Furthermore, in +seeing SPICE used over and over again, they should be able to understand how to use it them- +selves, providing a perfectly safe means of experimentation on their own computers with circuit +simulations of their own design. + Another advantage to including computer analyses in a textbook is the empirical verifi- +cation it adds to the concepts presented. Without demonstrations, the reader is left to take +the author’s statements on faith, trusting that what has been written is indeed accurate. The +problem with faith, of course, is that it is only as good as the authority in which it is placed and +the accuracy of interpretation through which it is understood. Authors, like all human beings, +are liable to err and/or communicate poorly. With demonstrations, however, the reader can +immediately see for themselves that what the author describes is indeed true. Demonstrations +also serve to clarify the meaning of the text with concrete examples. + SPICE is introduced early in volume I (DC) of this book series, and hopefully in a gentle +enough way that it doesn’t create confusion. For those wishing to learn more, a chapter in this +volume (volume V) contains an overview of SPICE with many example circuits. There may +be more flashy (graphic) circuit simulation programs in existence, but SPICE is free, a virtue +complementing the charitable philosophy of this book very nicely. + + +A-1.3 Acknowledgements +First, I wish to thank my wife, whose patience during those many and long evenings (and +weekends!) of typing has been extraordinary. + I also wish to thank those whose open-source software development efforts have made this +endeavor all the more affordable and pleasurable. The following is a list of various free com- +puter software used to make this book, and the respective programmers: + + • GNU/Linux Operating System – Linus Torvalds, Richard Stallman, and a host of others + too numerous to mention. + + • Vim text editor – Bram Moolenaar and others. + + • Xcircuit drafting program – Tim Edwards. + + • SPICE circuit simulation program – too many contributors to mention. + 150 APPENDIX A-1. ABOUT THIS BOOK + + • TEX text processing system – Donald Knuth and others. + + • Texinfo document formatting system – Free Software Foundation. + • LATEX document formatting system – Leslie Lamport and others. + + • Gimp image manipulation program – too many contributors to mention. + + Appreciation is also extended to Robert L. Boylestad, whose first edition of Introductory +Circuit Analysis taught me more about electric circuits than any other book. Other important +texts in my electronics studies include the 1939 edition of The ”Radio” Handbook, Bernard +Grob’s second edition of Introduction to Electronics I, and Forrest Mims’ original Engineer’s +Notebook. + Thanks to the staff of the Bellingham Antique Radio Museum, who were generous enough +to let me terrorize their establishment with my camera and flash unit. + I wish to specifically thank Jeffrey Elkner and all those at Yorktown High School for being +willing to host my book as part of their Open Book Project, and to make the first effort in con- +tributing to its form and content. Thanks also to David Sweet (website: (http://www.andamooka.org)) +and Ben Crowell (website: (http://www.lightandmatter.com)) for providing encourage- +ment, constructive criticism, and a wider audience for the online version of this book. + Thanks to Michael Stutz for drafting his Design Science License, to Richard Stallman for +pioneering the concept of copyleft, and to Creative Commons for the CC BY License. + Last but certainly not least, many thanks to my parents and those teachers of mine who +saw in me a desire to learn about electricity, and who kindled that flame into a passion for +discovery and intellectual adventure. I honor you by helping others as you have helped me. + + Tony Kuphaldt, July 2001 + + + ”A candle loses nothing of its light when lighting another” + Kahlil Gibran + Appendix A-2 + + CONTRIBUTOR LIST + + + +A-2.1 How to contribute to this book +As a copylefted work, this book is open to revision and expansion by any interested parties. +The only ”catch” is that credit must be given where credit is due. + If you wish to cite portions of this book in a work of your own, you must follow the same +guidelines as for any other copyrighted work. Here is a sample for the CreativeCommons CC +BY License: + +Subject to the terms and conditions of this Public License, the Licensor +hereby grants You a worldwide, royalty-free, non-sublicensable, +non-exclusive, irrevocable license to exercise the Licensed Rights in the +Licensed Material to: +A. reproduce and Share the Licensed Material, in whole or in part; and +B. produce, reproduce, and Share Adapted Material + +No warranties are given. The license may not give you all of the +permissions necessary for your intended use. For example, other rights +such as publicity, privacy, or moral rights may limit how you use the +material. + + If you wish to modify this book in any way, you should document the nature of those modifi- +cations in the ”Credits” section along with your name, and ideally, information concerning how +you may be contacted. Again, the CC BY License: + +You are free to: +(a) Share -- copy and redistribute the material in any medium +or format. + + 151 + 152 APPENDIX A-2. CONTRIBUTOR LIST + +(b) Adapt -- remix, transform, and build upon the material +for any purpose, even commercially. +(c) Attribution -- You must give appropriate credit, provide +a link to the license, and indicate if changes were made. +You may do so in any reasonable manner, but not in any +way that suggests the licensor endorses you or your use. + + Given the complexities and security issues surrounding the maintenance of files comprising +this book, it is recommended that you submit any revisions or expansions to the original author +(Tony R. Kuphaldt). You are, of course, welcome to modify this book directly by editing your +own personal copy, but we would all stand to benefit from your contributions if your ideas were +incorporated into the online ”master copy” where all the world can see it. + + +A-2.2 Credits +All entries arranged in alphabetical order of surname. Major contributions are listed by indi- +vidual name with some detail on the nature of the contribution(s), date, contact info, etc. Minor +contributions (typo corrections, etc.) are listed by name only for reasons of brevity. Please un- +derstand that when I classify a contribution as ”minor,” it is in no way inferior to the effort +or value of a ”major” contribution, just smaller in the sense of less text changed. Any and all +contributions are gratefully accepted. I am indebted to all those who have given freely of their +own knowledge, time, and resources to make this a better book! + + +A-2.2.1 John Anhalt + • Date(s) of contribution(s): December 2008 + + • Nature of contribution: Updated lead-acid cell chemistry, Ch 11 + + • Contact at: jpa@anhalt.org + + +A-2.2.2 Benjamin Crowell, Ph.D. + • Date(s) of contribution(s): January 2001 + + • Nature of contribution: Suggestions on improving technical accuracy of electric field + and charge explanations in the first two chapters. + + • Contact at: crowell01@lightandmatter.com + + +A-2.2.3 Dennis Crunkilton + • Date(s) of contribution(s): January 2006 to present + + • Nature of contribution: Mini table of contents, all chapters except appedicies; html, + latex, ps, pdf; See Devel/tutorial.html; 01/2006. + A-2.2. CREDITS 153 + + • DC network analysis ch, Mesh current section, Mesh current by inspection, new mate- + rial.i DC network analysis ch, Node voltage method, new section. + + • Ch3, Added AFCI paragraphs after GFCI, 10/09/2007. + + • Contact at: liecibiblio(at)gmail.com + + +A-2.2.4 Tony R. Kuphaldt + • Date(s) of contribution(s): 1996 to present + + • Nature of contribution: Original author. + + • Contact at: liec0@lycos.com + + +A-2.2.5 Ron LaPlante + • Date(s) of contribution(s): October 1998 + + • Nature of contribution: Helped create the ”table” concept for use in analysis of series + and parallel circuits. + + +A-2.2.6 Davy Van Nieuwenborgh + • Date(s) of contribution(s): October 2006 + + • Nature of contribution: DC network analysis ch, Mesh current section, supplied solu- + tion to mesh problem, pointed out error in text. + + • Contact at: Theoretical Computer Science laboratory, Department of Computer + Science, Vrije Universiteit Brussel. + + +A-2.2.7 Ray A. Rayburn + • Date(s) of contribution(s): September 2009 + + • Nature of contribution: Nonapplicability of Maximum Power Transfer Theorem to Hi- + Fi audio amplifier. + + • Contact at: http://forum.allaboutcircuits.com/member.php?u=54720 + + +A-2.2.8 Jason Starck + • Date(s) of contribution(s): June 2000 + + • Nature of contribution: HTML formatting, some error corrections. + + • Contact at: jstarck@yhslug.tux.org + 154 APPENDIX A-2. CONTRIBUTOR LIST + +A-2.2.9 Warren Young + • Date(s) of contribution(s): August 2002 + • Nature of contribution: Provided capacitor photographs for chapter 13. + +A-2.2.10 someonesdad@allaboutcircuits.com + • Date(s) of contribution(s): November 2009 + • Nature of contribution: Chapter 8, troublehooting tip end of Kelvin section. + +A-2.2.11 Your name here + • Date(s) of contribution(s): Month and year of contribution + • Nature of contribution: Insert text here, describing how you contributed to the book. + • Contact at: my email@provider.net + +A-2.2.12 Typo corrections and other ”minor” contributions + • The students of Bellingham Technical College’s Instrumentation program. + • anonymous (July 2007) Ch 1, remove :registers. Ch 5, s/figures something/figures is + something/. Ch 6 s/The current/The current. (September 2007) Ch 5, 8, 9, 10, 11, 12, 13, + 15. Numerous typos, clarifications. + • Tony Armstrong (January 2003) Suggested diagram correction in ”Series and Parallel + Combination Circuits” chapter. + • James Boorn (January 2001) Clarification on SPICE simulation. + • Dejan Budimir (January 2003) Clarification of Mesh Current method explanation. + • Sridhar Chitta, Assoc. Professor, Dept. of Instrumentation and Control Engg., Vignan + Institute of Technology and Science, Deshmukhi Village, Pochampally Mandal, Nalgonda + Distt, Andhra Pradesh, India (December 2005) Chapter 13: CAPACITORS, Clarification: + s/note the direction of current/note the direction of electron current/, 2-places + • Colin Creitz (May 2007) Chapters: several, s/it’s/its. + • Larry Cramblett (September 2004) Typographical error correction in ”Nonlinear con- + duction” section. + • Brad Drum (May 2006) Error correction in ”Superconductivity” section, Chapter 12: + PHYSICS OF CONDUCTORS AND INSULATORS. Degrees are not used as a modifier + with kelvin(s), 3 changes. + • Jeff DeFreitas (March 2006)Improve appearance: replace “/” and ”/” Chapters: A1, A2. + Type errors Chapter 3: /am injurious spark/an injurious spark/, /in the even/inthe event/ + A-2.2. CREDITS 155 + + • Sean Donner (December 2004) Typographical error correction in ”Voltage and current” + section, Chapter 1: BASIC CONCEPTS OF ELECTRICITY,(by a the/ by the) (current of + current/ of current). + (January 2005), Typographical error correction in ”Fuses” section, Chapter 12: THE + PHYSICS OF CONDUCTORS AND INSULATORS (Neither fuses nor circuit breakers + were not designed to open / Neither fuses nor circuit breakers were designed to open). + (January 2005), Typographical error correction in ”Factors Affecting Capacitance” sec- + tion, Chapter 13: CAPACITORS, (greater plate area gives greater capacitance; less plate + area gives less capacitance / greater plate area gives greater capacitance; less plate area + gives less capacitance); ”Factors Affecting Capacitance” section, (thin layer if insula- + tion/thin layer of insulation). + (January 2005), Typographical error correction in ”Practical Considerations” section, Chap- + ter 15: INDUCTORS, (there is not such thing / there is no such thing). + (January 2005), Typographical error correction in ”Voltage and current calculations” sec- + tion, Chapter 16: RC AND L/R TIME CONSTANTS (voltage in current / voltage and + current). + + • Manuel Duarte (August 2006): Ch: DC Metering Circuits ammeter images: 00163.eps, + 00164.eps; Ch: RC and L/R Time Constants, simplified ln() equation images 10263.eps, + 10264.eps, 10266.eps, 10276.eps. + + • Aaron Forster (February 2003) Typographical error correction in ”Physics of Conductors + and Insulators” chapter. + + • Bill Heath (September-December 2002) Correction on illustration of atomic structure, + and corrections of several typographical errors. + + • Stefan Kluehspies (June 2003): Corrected spelling error in Andrew Tannenbaum’s + name. + + • David M. St. Pierre (November 2007): Corrected spelling error in Andrew Tanenbaum’s + name (from the title page of his book). + + • Geoffrey Lessel,Thompsons Station, TN (June 2005): Corrected typo error in Ch 1 ”If + this charge (static electricity) is stationary, and you won’t realize–remove If; Ch 2 ”Ohm’s + Law also make intuitive sense if you apply if to the water-and-pipe analogy.” s/if/it; Chap- + ter 2 ”Ohm’s Law is not very useful for analyzing the behavior of components like these + where resistance is varies with voltage and current.” remove ”is”; Ch 3 ”which halts fibril- + lation and and gives the heart a chance to recover.” double ”and”; Ch 3 ”To be safest, you + should follow this procedure is checking, using, and then checking your meter.... s/is/of. + + • LouTheBlueGuru, allaboutcircuits.com, July 2005 Typographical errors, in Ch 6 ”the + current through R1 is half:” s/half/twice; ”current through R1 is still exactly twice that of + R2” s/R3/R2 + + • Norm Meyrowitz , nkm, allaboutcircuits.com, July 2005 Typographical errors, in Ch 2.3 + ”where we don’t know both voltage and resistance:” s/resistance/current + 156 APPENDIX A-2. CONTRIBUTOR LIST + + • Don Stalkowski (June 2002) Technical help with PostScript-to-PDF file format conver- + sion. + • Joseph Teichman (June 2002) Suggestion and technical help regarding use of PNG + images instead of JPEG. + • Derek Terveer (June 2006) Typographical errors, several in Ch 1,2,3. + • Geoffrey Lessel (June 2005) Typographical error, s/It discovered/It was discovered/ in + Ch 1. + • Austin@allaboutcircuits.com (July 2007) Ch 2, units of mass, pound vs kilogram, near + ”units of pound” s/pound/kilogram/. + • CATV@allaboutcircuits.com (April 2007) Telephone ring voltage error, Ch 3. + • line@allaboutcircuits.com (June 2005) Typographical error correction in Volumes 1,2,3,5, + various chapters ,(:s/visa-versa/vice versa/). + • rob843@allaboutcircuits.com (April 2007) Telephone ring voltage error, Ch 3. + • bigtwenty@allaboutcircuits.com (July 2007) Ch 4 near “different metric prefix”, s/right + to left/left to right/. + • jut@allaboutcircuits.com (September 2007) Ch 13 near s/if were we to/if we were to/, + s/a capacitors/a capacitor. + • rxtxau@allaboutcircuits.com (October 2007) Ch 3, suggested, GFCI terminology, non- + US usage. + • Stacy Mckenna Seip (November 2007) Ch 3 s/on hand/one hand, Ch 4 s/weight/weigh, + Ch 8 s/weight/weigh, s/left their/left there, Ch 9 s/cannot spare/cannot afford/, Ch1 Clari- + fication, static electricity. + • Cory Benjamin (November 2007) Ch 3 s/on hand/one hand. + • Larry Weber (Feb 2008) Ch 3 s/on hand/one hand. + • trunks14@allaboutrcircuits.com (Feb 2008) Ch 15 s/of of/of . + • Greg Herrington (Feb 2008) Ch 1, Clarification: no neutron in hydrogen atom. + • mark44 (Feb 2008) Ch 1, s/naturaly/naturally/ + • Unregistered@allaboutcircuits.com (February 2008) Ch 1, s/smokelsee/smokeless , + s/ecconomic/economic/ . + • Timothy Unregistered@allaboutcircuits.com (Feb 2008) Changed default roman font + to newcent. + • Imranullah Syed (Feb 2008) Suggested centering of uncaptioned schematics. + • davidr@insyst ltd.com (april 2008) Ch 5, s/results/result 2plcs. + A-2.2. CREDITS 157 + + • Professor Thom@allaboutcircuits.com (Oct 2008) Ch 6, s/g/c near Ecd and near 00435.png, + 2plcs. + • John Schwab (Dec 2008) Ch 1, Static Electricity, near Charles Coulomb: rearrangement + of text segments. + • Olivier Derewonko (Dec 2008) Ch 4 s/orientation a voltage/orientation of a/. Ch2 s/flow + though/flow through/. Ch Safe meter usage, REVIEW, s/,/./ . Ch5, s/is it/it is/. + • dor@allaboutcircuits.com (June 2009) Ch 1, s/nusiance/nuisance. + • rspuzio@allaboutcircuits.com (September 2009) Ch 8, s/logarithmic/nonlinear , 6-plcs. + • David Lewis@allaboutcircuits.com (September 2009) Ch 1, hide paragraph: Physical + dimension also impacts conductivity. . . etc. + • Walter Odington@allaboutcircuits.com (January 2010) Ch 3, s/hydration another/hydration + is another/ . + • tone b@allaboutcircuits.com (January 2010) Ch 6 , s/must were/were/ . + • Unregistered Guest@allaboutcircuits.com (July 2010) Ch 1 , s/is is/it is/ . + • Unregistered Guest@allaboutcircuits.com (July 2010) Ch 5 , added I2 to image 00090.png + . + • Unregistered Guest@allaboutcircuits.com (August 2010) Ch 1 , s/was one the/was + one of the/ . + • D. Crunkilton (June 2011) hi.latex, header file; updated link to openbookproject.net . + • Bob Arthur (Jan 2012) images: 00046.eps, 00047.eps,00048.eps 00362.eps, graph line + visibility fixed. + • vspriyan@allaboutcircuits.com (Jan 2013) Ch 10, Near: voltages divided by their + s/currents/resistances/ . + • Eugene Smirnoff (Jan 2013) Ch1, s/an hypothetical/a hypothetical/ . Ch 2 s/An his- + toric/A historic/ . + • Gulliveig@allaboutcircuits.com (Jan 2014) Ch4, s/significant digits/mantissa, s/1000/999/ + . + • slidercrank@allaboutcircuits.com (Feb 2014) Ch6, s/both positive/both be positive/ . + • Skfir@allaboutcircuits.com (August 2015) Ch10, s/suppling/supplying/ . + • John Wang (Sept 2017) Ch2, s/points 1 and 4/points 1 and 6/, s/points 2 and 3/3 and 4/ . + • Stewart Todd Morgan (Feb 2020) Ch3, s+http://web.mit.edu/safety+https://ehs.mit.edu/workplace- + safety-program/electr + • DC (Sept 2017) Ch12, Chi3; Reformated various tables to html/latex. + • DC (Nov 2021) ChA1, ChA2, ChA3; Replaced Design Science with Creative Commons CC + BY license + 158 APPENDIX A-2. CONTRIBUTOR LIST + Appendix A-3 + + CC BY License + + + +A-3.1 Creative Commons Attribution 4.0 International (CC + BY 4.0) +This is a human-readable summary of the full license code: + https://creativecommons.org/licenses/by/4.0/legalcode + This page was adapted from: https://creativecommons.org/licenses/by/4.0/ + + +A-3.2 You are free to: + • Share – copy and redistribute the material in any medium or format + + • Adapt – remix, transform, and build upon the material for any purpose, even commer- + cially. + + The licensor cannot revoke these freedoms as long as you follow the license terms. + + +A-3.3 Under the following terms: + • Attribution – You must give appropriate credit, provide a link to the license, and indi- + cate if changes were made. You may do so in any reasonable manner, but not in any way + that suggests the licensor endorses you or your use. + + • No additional restrictions – You may not apply legal terms or technological measures + that legally restrict others from doing anything the license permits./item¿ + + 159 + 160 APPENDIX A-3. CC BY LICENSE + +A-3.4 Notices: +You do not have to comply with the license for elements of the material in the public domain or +where your use is permitted by an applicable exception or limitation. + No warranties are given. The license may not give you all of the permissions necessary for +your intended use. For example, other rights such as publicity, privacy, or moral rights may +limit how you use the material. + The full CC BY 4.0 license is available at Creative Commons: + https://creativecommons.org/licenses/by/4.0/legalcode + + +A-3.5 A simple explanation of your rights +This section was reused from Tony Kuphaldt, “Lessons In Industrial Instrumentation”, Ap- +pendix B at: + https://ibiblio.org/kuphaldt/socratic/sinst/book/liii 0v2.pdf + This is an “open-source” textbook, which means the entirety of it is freely available for +public perusal, reproduction, distribution, and even modification. All digital “source” files com- +prising this textbook reside at the following website: + https://www.ibiblio.org/kuphaldt/electricCircuits + The Creative Commons Attribution license grants you (the recipient), as well as anyone who +might receive my work from you, the right to freely use it. 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It does, however, protect +the investment(s) you make in creating the adaptation by allowing you to release the adapta- +tion under whatever terms you see fit (so long as those terms comply with current intellectual +property laws, of course). + A-3.5. A SIMPLE EXPLANATION OF YOUR RIGHTS 161 + + In summary, the following “legalese”2 is actually a very good thing for you, the reader of +my book. It grants you permission to do so much more with this text than what you would be +legally allowed to do with any other (traditionally copyrighted) book. It also opens the door to +open collaborative development, so it might grow into something far better than what I alone +could create. + 1 + You cannot pass my original work to anyone else under different terms or conditions than +the Attribution license. That is called sublicensing, and the Attribution license forbids it. In +fact, any re-distribution of my original work must come with a notice to the Attribution license, +so anyone receiving the book through you knows their rights. + 2 + “legalese” at https://creativecommons.org/licenses/by/4.0/legalcode + Index + +.end command, SPICE, 78 Derivative of a constant, 52 +Electronics Workbench, 60 Derivative of power and log functions, 52 + Derivative rules, 53 +Addition method, simultaneous equations, 40 Dielectric strength, 27 +Adjacent, 48 Difference, common, 34 +Algebraic identities, 30 Differential Equations, 57 +Ampacity, 23 Diodes, SPICE, 69 +Analysis, AC, SPICE, 75 +Analysis, DC, SPICE, 75 E, symbol for voltage, 2 +Analysis, Fourier, SPICE, 76, 86 +Analysis, transient, SPICE, 75 Factor, conversion, 12 +Antiderivative of e functions, 56 Factorial, 35 +Antiderivatives, 55 Factoring, 33 +Arithmetic sequence, 34 Fault, ground, 122 + FORTRAN, computer language, 61, 62 +BASIC, computer language, 62 + Gage size, wire, 23 +C, computer language, 61 General solution, 57 +Capacitance equation, 4 Geometric sequence, 35 +Capacitors, SPICE, 68 Ground fault, 122 +Common difference, 34 +Common ratio, 35 Hyperbolic functions, 49 +Compiler, 62 Hypotenuse, 48 +Component names, SPICE, 67 +Conductor ampacity, 23 I, symbol for current, 2 +Constants, mathematical, 31 Impedance, 8 +Conversion factor, 12 Independent variable, 57 +Cosines, law of, 49 Inductance equation, 6 +Critical temperature, high temperature super- Inductors, SPICE, 68 + conductors, 26 Integral, definite, 56 +Critical temperature, superconductors, 26 Integral, indefinite, 55 +Current measurement, SPICE, 83 Interpreter, 61 +Current sources, AC, SPICE, 74 +Current sources, DC, SPICE, 74 Joule’s Law, 2 +Current sources, dependent, SPICE, 75 +Current sources, pulse, SPICE, 74 Law of cosines, 49 + Law of sines, 48 +Derivative of e functions, 52 Limits, calculus, 52 + + 162 + INDEX 163 + +Logarithm, 32 Resistors, SPICE, 69 + Resonance, 8 +Metric prefixes, SPICE, 67 Rules for antiderivatives, 56 +Metric system, 12 +Model, SPICE, 69 Scientific notation, SPICE, 68 +Mutual inductance, SPICE, 69 Semiconductor model, SPICE, 69 + Sequences, 34 +Netlist, SPICE, 62 Series circuits, 3 +Nodes, SPICE, 65, 78 Simultaneous equations, 35 + Sines, law of, 48 +Ohm’s Law, 2 Slide rule, 33 +Ohm’s Law, AC, 9 Specific resistance, 23 +Open circuits, SPICE, 79 SPICE, 60 +Opposite, 48 SPICE programming, 61 +Option, itl5, SPICE, 77 SPICE2g6, 61 +Option, limpts, SPICE, 77 Substitution method, simultaneous equations, +Option, list, SPICE, 77 36 +Option, method, SPICE, 77 Superconductivity, 26 +Option, nopage, SPICE, 77 Superconductivity, high temperature, 26 +Option, numdgt, SPICE, 77 Systems of linear equations, 35 +Option, width, SPICE, 77 +Options, miscellaneous, SPICE, 76 Temperature coefficient of resistance, 26 + Temperature, critical, for high temperature su- +P, symbol for power, 2 perconductors, 26 +Parallel circuits, 3 Temperature, critical, for superconductors, 26 +Particular solution, 57 Time constant equations, 7 +PASCAL, computer language, 62 Transform function, definition of, 33 +Periodic table, 145 Transformers, SPICE, 69 +Plot output, SPICE, 76 Transistors, bipolar, SPICE, 70 +Power factor, 8 Transistors, jfet, SPICE, 71 +Prefix, metric, 12 Transistors, mosfet, SPICE, 72 +Print output, SPICE, 76 Trigonometric derivatives , 53 +Programming, SPICE, 61 Trigonometric equivalencies, 49 +Properties, arithmetic, 30 Trigonometric identities, 48 +Properties, exponents, 30 Troubleshooting, 114 +Properties, radicals , 31 +Pythagorean Theorem, 48 Unit, radian, 49 + +Quadratic formula, 34 Voltage sources, AC, SPICE, 73 + Voltage sources, DC, SPICE, 73 +R, symbol for resistance, 2 Voltage sources, dependent, SPICE, 75 +Radian, 49 Voltage sources, pulse, SPICE, 73 +Ratio, common, 35 +Reactance, 8 Wetting current, 122 +Resistance, specific, 23 Wire size, gage scale, 23 +Resistance, temperature coefficient of, 26 +Resistor color codes, 17 + 164 INDEX + + . + \ No newline at end of file