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 |  موضوع: كتاب Engineering Circuit Analysis السبت 06 فبراير 2021, 11:30 am | |
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أحضرت لكم كتاب
Engineering Circuit Analysis
Eighth Edition
William H. Hayt, Jr. (deceased)
Purdue University
Jack E. Kemmerly (deceased)
California State University
Steven M. Durbin
University at Buffalo
The State University of New York
و المحتوى كما يلي :
Contents
Xi
Chapter 1
Introduction 1
1.1 Overview of Text 2
1.2 Relationship of Circuit Analysis to Engineering 4
1.3 Analysis and Design 5
1.4 Computer-aided Analysis 6
1.5 Successful Problem-solving Strategies 7
Reading Further 8
Chapter 2
Basic Components and Electric Circuits 9
2.1 Units and Scales 9
2.2 Charge, Current, Voltage, and Power 11
2.3 Voltage and Current Sources 17
2.4 Ohm’s Law 22
SUMMARY AND REVIEW 28
READING FURTHER 29
EXERCISES 29
CHAPTER 3
VOLTAGE AND CURRENT LAWS 39
3.1 Nodes, Paths, Loops, and Branches 39
3.2 Kirchhoff’s Current Law 4
3.3 Kirchhoff’s Voltage Law 42
3.4 The Single-Loop Circuit 46
3.5 The Single-Node-Pair Circuit 49
3.6 Series and Parallel Connected Sources 51
3.7 Resistors in Series and Parallel 55
3.8 Voltage and Current Division 61
SUMMARY AND REVIEW 66
READING FURTHER 67
EXERCISES 67
CHAPTER 4
BASIC NODAL AND MESH ANALYSIS 79
4.1 Nodal Analysis 8
4.2 The Supernode 89
4.3 Mesh Analysis 92
4.4 The Supermesh 98
4.5 Nodal vs. Mesh Analysis: A Comparison 1 1
4.6 Computer-Aided Circuit Analysis 1 3
SUMMARY AND REVIEW 1 7
READING FURTHER 1 9
EXERCISES 1 9
CHAPTER 5
HANDY CIRCUIT ANALYSIS TECHNIQUES 123
5.1 Linearity and Superposition 123
5.2 Source Transformations 133
5.3 Thévenin and Norton Equivalent Circuits 141
5.4 Maximum Power Transfer 152
5.5 Delta-Wye Conversion 154
5.6 Selecting an Approach: A Summary of Various
Techniques 157
SUMMARY AND REVIEW 158
READING FURTHER 159
EXERCISES 159
CHAPTER 6
THE OPERATIONAL AMPLIFIER 175
6.1 Background 175
6.2 The Ideal Op Amp: A Cordial Introduction 176
6.3 Cascaded Stages 184
6.4 Circuits for Voltage and Current Sources 188
6.5 Practical Considerations 192
6.6 Comparators and the Instrumentation Amplifier 2 3
SUMMARY AND REVIEW 2 6
READING FURTHER 2 7
EXERCISES 2 8
CHAPTER 7
CAPACITORS AND INDUCTORS 217
7.1 The Capacitor 217
7.2 The Inductor 225
7.3 Inductance and Capacitance Combinations 235
7.4 Consequences of Linearity 238
7.5 Simple Op Amp Circuits with Capacitors 24
7.6 Duality 242xii CONTENTS
7.7 Modeling Capacitors and Inductors
with PSpice 245
SUMMARY AND REVIEW 247
READING FURTHER 249
EXERCISES 249
CHAPTER 8
BASIC RL AND RC CIRCUITS 261
8.1 The Source-Free RL Circuit 261
8.2 Properties of the Exponential Response 268
8.3 The Source-Free RC Circuit 272
8.4 A More General Perspective 275
8.5 The Unit-Step Function 282
8.6 Driven RL Circuits 286
8.7 Natural and Forced Response 289
8.8 Driven RC Circuits 295
8.9 Predicting the Response of Sequentially Switched
Circuits 3
SUMMARY AND REVIEW 3 6
READING FURTHER 3 8
EXERCISES 3 9
CHAPTER 9
THE RLC CIRCUIT 321
9.1 The Source-Free Parallel Circuit 321
9.2 The Overdamped Parallel RLC Circuit 326
9.3 Critical Damping 334
9.4 The Underdamped Parallel RLC Circuit 338
9.5 The Source-Free Series RLC Circuit 345
9.6 The Complete Response of the RLC Circuit 351
9.7 The Lossless LC Circuit 359
SUMMARY AND REVIEW 361
READING FURTHER 363
EXERCISES 363
CHAPTER 1
SINUSOIDAL STEADY-STATE ANALYSIS 371
1 .1 Characteristics of Sinusoids 371
1 .2 Forced Response to Sinusoidal Functions 374
1 .3 The Complex Forcing Function 378
1 .4 The Phasor 383
1 .5 Impedance and Admittance 389
1 .6 Nodal and Mesh Analysis 394
1 .7 Superposition, Source Transformations and
Thévenin’s Theorem 397
1 .8 Phasor Diagrams 4 6
SUMMARY AND REVIEW 4 9
READING FURTHER 41
EXERCISES 41
CHAPTER 11
AC CIRCUIT POWER ANALYSIS 421
11.1 Instantaneous Power 422
11.2 Average Power 424
11.3 Effective Values of Current and Voltage 433
11.4 Apparent Power and Power Factor 438
11.5 Complex Power 441
SUMMARY AND REVIEW 447
READING FURTHER 449
EXERCISES 449
CHAPTER 12
POLYPHASE CIRCUITS 457
12.1 Polyphase Systems 458
12.2 Single-Phase Three-Wire Systems 46
12.3 Three-Phase Y-Y Connection 464
12.4 The Delta () Connection 47
12.5 Power Measurement in Three-Phase Systems 476
SUMMARY AND REVIEW 484
READING FURTHER 486
EXERCISES 486
CHAPTER 13
MAGNETICALLY COUPLED CIRCUITS 493
13.1 Mutual Inductance 493
13.2 Energy Considerations 5 1
13.3 The Linear Transformer 5 5
13.4 The Ideal Transformer 512
SUMMARY AND REVIEW 522
READING FURTHER 523
EXERCISES 523
CHAPTER 14
COMPLEX FREQUENCY AND THE LAPLACE
TRANSFORM 533
14.1 Complex Frequency 533
14.2 The Damped Sinusoidal Forcing Function 537
14.3 Definition of the Laplace Transform 54
14.4 Laplace Transforms of Simple Time Functions 543
14.5 Inverse Transform Techniques 546
14.6 Basic Theorems for the Laplace Transform 553CONTENTS xiii
14.7 The Initial-Value and Final-Value Theorems 561
SUMMARY AND REVIEW 564
READING FURTHER 565
EXERCISES 565
CHAPTER 15
CIRCUIT ANALYSIS IN THE s-DOMAIN 571
15.1 Z(s) and Y(s) 571
15.2 Nodal and Mesh Analysis in the s-Domain 578
15.3 Additional Circuit Analysis Techniques 585
15.4 Poles, Zeros, and Transfer Functions 588
15.5 Convolution 589
15.6 The Complex-Frequency Plane 598
15.7 Natural Response and the s Plane 6 2
15.8 A Technique for Synthesizing the Voltage Ratio
H(s) = Vout/Vin 6 6
SUMMARY AND REVIEW 61
READING FURTHER 612
EXERCISES 612
CHAPTER 16
FREQUENCY RESPONSE 619
16.1 Parallel Resonance 619
16.2 Bandwidth and High-Q Circuits 627
16.3 Series Resonance 633
16.4 Other Resonant Forms 637
16.5 Scaling 644
16.6 Bode Diagrams 648
16.7 Basic Filter Design 664
16.8 Advanced Filter Design 672
SUMMARY AND REVIEW 677
READING FURTHER 679
EXERCISES 679
CHAPTER 17
TWO-PORT NETWORKS 687
17.1 One-Port Networks 687
17.2 Admittance Parameters 692
17.3 Some Equivalent Networks 699
17.4 Impedance Parameters 7 8
17.5 Hybrid Parameters 713
17.6 Transmission Parameters 716
SUMMARY AND REVIEW 72
READING FURTHER 721
EXERCISES 722
CHAPTER 18
FOURIER CIRCUIT ANALYSIS 733
18.1 Trigonometric Form of the Fourier Series 733
18.2 The Use of Symmetry 743
18.3 Complete Response to Periodic Forcing
Functions 748
18.4 Complex Form of the Fourier Series 75
18.5 Definition of the Fourier Transform 757
18.6 Some Properties of the Fourier Transform 761
18.7 Fourier Transform Pairs for Some Simple Time
Functions 764
18.8 The Fourier Transform of a General Periodic Time
Function 769
18.9 The System Function and Response in the Frequency
Domain 77
18.1 The Physical Significance of the System
Function 777
SUMMARY AND REVIEW 782
READING FURTHER 783
EXERCISES 783
APPENDIX 1 AN INTRODUCTION TO NETWORK
TOPOLOGY 791
APPENDIX 2 SOLUTION OF SIMULTANEOUS
EQUATIONS 8 3
APPENDIX 3 A PROOF OF THÉVENIN’S
THEOREM 811
APPENDIX 4 A PSPICE TUTORIAL 813
APPENDIX 5 COMPLEX NUMBERS 817
APPENDIX 6 A BRIEF MATLAB TUTORIAL 827
APPENDIX 7 ADDITIONAL LAPLACE TRANSFORM
THEOREMS 833
INDEX 839
A A1
and A2 values
critical damping and, 335
overdamped parallel RLC circuit,
326–327
μA741 op amp, 193–194, 195, 198
ABCD parameters, two-port networks,
716–72 , 73 –731
abc phase sequence, 464–465
Absorbed power, 16, 19, 48–49
by element, 48–49
in resistors, 23–27
ac circuit analysis. See ac circuit power
analysis; Circuit analysis
ac circuit power analysis, 421–456.
See also Complex power
apparent power/power factor,
438–441, 453–454
average power. See Average power
instantaneous power, 422–424, 447,
45 –451
maximum average power, 431
RMS values of current/voltage,
433–438, 447
average power computations, 435
multiple-frequency circuits,
435–436
periodic waveform values,
433–434
sinusoidal waveform values,
434–435
sinusoidal excitation, instantaneous
power, 423, 45 –451
sinusoidal steady state theorem,
43 –431
Active element, 217
Active filters, 669–67
Active network, 21
AD549K op amp, 193, 195
AD622 op amp, 2 6
Addition, Laplace transform
operation, 561
Additive fluxes, 497
Additive property, of the Laplace
transform, 546
Admittance, 239, 572
parameters. See Two-port networks
in sinusoidal steady-state, 394
Algebraic alternatives, complex forcing
functions, 38 –381
American Wire Gauge (AWG), 26
Ampère, A.M., 12
Amperes, 1 , 11, 12
Amplifiers, equivalent networks and,
7 4–7 6
Amplitude
exponential form of complex number,
822–824
of response, proportional forcing
function, 376
of sinusoids, 371
Amprobe, 443
Analysis
of circuits. See Circuit analysis
computer-aided. See Computer-aided
analysis
defined, 5–6
Fourier circuit. See Fourier circuit
analysis
mesh. See Nodal and mesh analysis
nodal. See Nodal and mesh analysis
power. See ac circuit power analysis
PSpice Type command, 1 5
sinusoidal steady-state. See Sinusoidal
steady-state analysis
transient, 3, 4, 27 –272
Analytical Engine, 6
Angles, exponential complex numbers,
822–824
Angular frequency, of sinusoids, 371
Anode, 189
Apparent power, 439, 443, 447
power factor and, 438–441, 453–454
Argand diagram, 817–818
Argument
exponential form of complex number,
822–824
of sinusoids, 371
Arrows, for current, 9, 13
Asymptotes, Bode diagrams and, 65 –651
Attenuator, 178, 6 9
Automotive suspensions, modeling, 358
Auxiliary equation, 323
Average power, 443, 447
ac circuits, 424–433, 447, 45 –452
ideal resistor absorption of, 428
maximum, 431
maximum transfer of, 43 –432
nonperiodic functions, 431–433
periodic waveforms, 425–426
reactive element absorption of,
428–429
RMS value and, 435
in the sinusoidal steady state, 426–427
superposition and, 433
12AX7A vacuum tube, 176
B B
1 and B2 values, 339–34
Babbage, Charles, 6
Balanced load, 458
Balanced three-phase system, 458
Bandpass filters, 665, 667–669
Band-reject filters, 673
Bandstop filters, 665
Bandwidth, and high-Q circuits, 628–633,
68 –681
Base, of transistors, 715
Basic components and electric circuits,
9–38
charge, 11–12, 3 –33
current. See Current
Ohm’s law. See Ohm’s law
power. See Power
units and scales, 9–11, 29–3
voltage. See Voltage
INDEX
•
839
Note: Page numbers followed by an “n” refer to footnotes.84 INDEX
Bass, treble, and midrange filters,
671–672
Beaty, H. Wayne, 29
Bias Point command (PSpice), 1 5
Bilateral circuit, 698
Bilateral element, 698
Bode, Hendrik W., 649
Bode diagrams/plots, 648–664, 683–684
additional considerations, 653–657
asymptotes, determining, 65 –651
complex conjugate pairs, 658–661
computer-aided analysis for, 661–664
decibel (dB) scale, 649
higher-order terms and, 657
multiple terms in, 651
phase response and, 652–653
smoothing of, 651
Bossanyi, E., 486
Boyce, W.E., 3 8
Branch current, 94
Branches, defined, 791
Break frequency, 651
Buffer design, 18
Burton, T., 486
Butterworth filters, 673–674
Butterworth polynomials, 673
C
Candela, 1
Capacitors, 217–225
defined, 218
duality. See Duality
energy storage, 222–224
ideal, 217–22 , 225
integral voltage-current relationships,
22 –222, 249–252
linearity, consequences of, 238–24 ,
254–257
modeling
of ideal capacitors, 217–22
with PSpice, 245–247, 259–26
in the s-domain, 575–576
op amp circuits with, 24 –241,
257–258
in parallel, 237–238
phasor relationships for, 387–388
s-domain circuits and, 575–577
in series, 236–237
Cartesian form, complex numbers, 818
Cascaded op amps, 184–187, 21 –212, 6 9
Cathode, 189
Cavendish, Henry, 22
cba phase sequence, 464–465
Characteristic equation, 265–267, 323
Charge, 11–12, 3 –33
conservation of, 11, 157
distance and, 5
Chassis ground, 65–66
Chebyshev filters, 673–674
Chebyshev polynomials, 673
Chua, L.O., 234
Circuit analysis. See also Circuit analysis
techniques
engineering and, 4–5
linear. See Linear circuits
nonlinear. See Nonlinear circuit
analysis
in the s-domain. See s-domain circuit
analysis
software, 7. See also Computer-aided
analysis
Circuit analysis techniques, 123–174
delta-wye conversion, 154–156,
17 –172
linearity and superposition, 123–133,
159–162
maximum power transfer, 152–154,
168–17
Norton equivalent circuits. See
Thévenin/Norton equivalent
circuits
selection process for, 157–158,
172–173
source transformations. See Source
transformations
superposition. See Superposition
Thévenin equivalent circuits. See
Thévenin/Norton equivalent
circuits
Circuits
analysis of. See Circuit analysis
components of. See Basic components
and electric circuits
elements of, 17–18, 21
networks and, 21–22
response résumé, source-free series
RLC, 346–347
transfer functions for, 499
Clayton, G., 612
Closed-loop operation, op amps, 2 3
Closed-loop voltage gain, 193
Closed paths, 43, 92
Coefficient of mutual inductance, 494
Coils, in wattmeters, 476–477
Collectors, 715
Column matrix, 8 4
Common-emitter configuration, 715
Common mode rejection ratio (CMRR),
op amps, 195–196
Comparators, 2 3–2 4, 214–215
Complementary function, source-free RL
circuits, 262
Complementary solution. See Natural
responses
Complete response, 733–734
driven RL circuits, 291–295, 317–319
to periodic forcing functions, 748–75
of RLC circuits. See RLC circuits
Complex conjugate pairs, Bode diagrams
and, 658–661
Complex forcing function. See Sinusoidal
steady-state analysis
Complex form, of Fourier series, 75 –757
Complex frequency, 324
dc case, 535
defined, 533–537
exponential case, 535
exponentially damped sinusoids, 536
general form, 534–535, 565–566
neper frequency, 534, 537
radian frequency, 537
s-domain circuit analysis and,
598–6 6
at complex frequencies, 6 3
graphing and, 599, 617–618
natural response and, 6 2–6 6, 618
general perspective, 6 4
special case, 6 5
operating at complex
frequencies, 6 3
pole-zero constellations, 6 –6 2
response as a function of σ,
598–599
s in relation to reality, 536–537
sinusoidal case, 535
Complex numbers, 819–828
arithmetic operations for, 818–82
described, 817–818
Euler’s identity, 82 –821
exponential form of, 822–824INDEX 841
imaginary unit (operator), 817
polar form of, 824–826
rectangular (cartesian) form of, 818
Complex plane, 817–818
s-domain circuit analysis and.
See Complex frequency
Complex power, 441–447, 454–455
apparent power, 439, 443, 447
and power factor, 438–441,
453–454
average power, 443
complex power, 441, 443
formula, 441–442
measuring, 443–444
power factor, 438–441, 453–454
correction, 444–445
power factor (PF)
lagging, 439
leading, 439
power triangle, 442–443
quadrature component, 443
quadrature power, 443
reactive power, 441, 442–443, 447
terminology, 447
volt-ampere (VA), 439
volt-ampere-reactive (VAR) units, 442
watt (W), 447
Complex representation, phasor as
abbreviation for, 383
Components. See Basic components and
electric circuits
Computer-aided analysis, 6–7, 13 –133.
See also MATLAB; PSpice
Bode diagrams and, 661–664
fast Fourier Transform, 774–777
Laplace transforms and, 551–553
magnetically coupled circuits,
51 –512
nodal and mesh analysis, 1 3–1 7,
12 –121, 578–58
op amps, 2 –2 3
s-domain nodal and mesh analysis,
578–58
sinusoidal steady-state analysis,
4 4–4 5
source-free parallel RLC circuits,
344–345
source-free RL circuits, 27 –272
system function, 774–777
for two port networks, 719–72
Conductance, 27–28, 394
Conformal matrices, 8 5
Conservation of charge, 11, 157
Conservation of energy, 14, 48, 157
Constant charge, 12
Controlled sources, of voltage/current,
18, 19–21
Convolution
Laplace transform operation, 561,
595–596
s-domain circuit analysis and,
589–598
convolution integral, 591
four-step process for analysis, 589
graphical methods of, 592–593
impulse response, 589–59 , 617
Laplace transform and, 595–596
realizable systems and, 591–592
transfer function comments, 597
Cooper, George R., 544n
Corner frequency, 651
Cosines, sines converted to, 373
Cotree, 792–793
Coulomb, 11
Coupling coefficient, 5 4
Cramer’s rule, 84, 8 9–81
Create command (PSpice), 1 5
Critical frequencies, s-domain circuit
analysis, 589
Critically damped response, RLC circuits
form of, 334–335
graphical representation, 336–337
source-free circuits
parallel, 325, 347
series, 346–347
Current, 9, 11, 12–13, 3 –33
actual direction vs. convention, 13
branch current, 94
capacitor voltage-current
relationships, 22 –222,
249–252
coil, 476
current-controlled current source,
18, 19–21
current-controlled voltage source,
18, 19–21
effective values of, 433–438, 452–453
gain, amplifiers, 7 4
graphical symbols for, 13
laws. See Voltage and current laws
mesh, 92, 93–95, 5 5
response, resonance and, 622
sources
controlled, 18, 19–21
practical, 135, 139–14
reliable, op amps, 19 –192,
212–213
series/parallel connections,
51–55, 74
and voltage. See Voltage
superposition applicable to, 433
types of, 13
and voltage division, 61–64, 76–77
Current level adjustment, ideal
transformers for, 517
Cutoff frequency, transistor amplifier,
398–399
D
Damped sinusoidal forcing function,
537–54 , 566
Damped sinusoidal response, 338
Damping factor, parallel resonance and,
625–627
Damping out, of transients, 332
Davies, B., 565
3 dB frequency, 651
dc (direct current)
analysis, 3
case, complex frequency, 535
current source, 19
parameter sweep, 13 –133
short circuits to, 226
sources, 19, 175
Dead network, 144, 147
Decade (of frequencies), 65
DeCarlo, R.A., 1 9, 159, 41 , 721
Decibel (dB) scale, Bode diagrams, 649
Delivered power, 19
Delta () connection, 47 –476, 489–49
connected sources, 473–476
Y-connected loads vs., 473
Delta () of impedances, equivalent
networks, 7 –7 2
Delta-wye conversion, 154–156, 17 –172
Dependent sources
linear, 124
Thévenin/Norton equivalent circuits,
147–149
of voltage/current, 18, 19–21Derivative of the current voltage, 18
Design, defined, 5–6
Determinants, 8 7–8 9
Difference amplifier, 181–184, 195–196
summary, 182
Difference Engine, 6
Differential equations
algebraic alternative, sinusoidal
steady-state, 38 –381
for source-free parallel RLC circuits,
322–324
Differential input voltage, 195
Digital integrated circuits, frequency
limits in, 3 6–3 7
Digital multimeter (DMM), 15 –151
DiPrima, R.C., 3 8
Direct approach, source-free RL circuits,
262–263
Direction of travel, current, 12
Direct procedure, driven RL circuits,
287–289
Discrete spectrum, 742
Dissipation of power, 49
Distance, charge and, 5
Distinct poles, method of residues and,
548–549
Distributed-parameter networks, 39
Dot convention
circuit transfer function, 499
mutual inductance, 495–499, 523–527
physical basis of, 497–5
power gain, 499
Double-subscript notation, polyphase
circuits, 459–46
Drexler, H.B., 249
Driven RC circuits, 295–3
Driven RL circuits, 286–289, 315–316
complete response determination,
291–295, 317–319
direct procedure, 287–289
intuitive understanding of, 289
natural and forced response, 288,
289–295, 316–317
Duality, 233, 242–245, 258–259
E
Earth ground, 65–66
Edison, Thomas, 457
Effective (RMS) value. See RMS value
Electric circuits. See Circuits
Emitters, 715
Energy, 14
accounting, source-free RL
circuits, 267
conservation of, 14, 48, 157
density, 763
instantaneous, stored, 624
magnetically coupled circuits. See
Magnetically coupled circuits
storage capacitors, 222–224
storage inductors, 231–233
work units, 1
Engineering, circuit analysis and, 4–5
Engineering units, 11
ENIAC, 6
Equivalent circuits, ideal transformers,
519–521
Equivalent combinations, frequency
response and, 639–644
Equivalent networks, two-port. See
Two-port networks
Equivalent practical sources, 135–138
Equivalent resistance, 56, 144
Equivalent voltage sources, 133
Euler’s identity, 38 , 383, 441
Even functions, 745n
Even harmonics, 745, 745n
Even symmetry, Fourier series analysis,
743, 747
Exponential case, complex frequency, 535
Exponential damping coefficient,
324, 621
Exponential form, complex numbers,
822–824
Exponential function eαt, 545
Exponentially damped sinusoids, 536
Exponential response, RL circuits,
268–272, 31
F
Fairchild Corp., 175, 193
Fall time, of wave forms, 3
farad (F), 218
Faraday, Michael, 218n, 225, 226
Fast Fourier transform (FFT), 772,
774–777
image processing example, 78
Feedback control, 5
Feynman. R., 67
Fiber optic intercom, 183–184
Filters (frequency), 664–672, 684–685
active, 669–67
bandpass, 665, 667–669
band-reject, 673
bandstop, 665
bass/treble/midrange adjustment,
671–672
Butterworth, 673–674
Chebyshev, 673–674
higher order, 672–677, 685
high-pass, 665–666, 676
low-pass, 665–666, 674
multiband, 665
notch, 665
passive
defined, 669
low-pass and high-pass, 665–666
practical application, 671–672
Final-value, Laplace transforms, 562–563
Finite resistance, underdamped sourcefree parallel RLC, 34 –342
Finite wire impedance, 461
Fink, Donald G., 29
Flowchart, for problem-solving, 8
Force, voltage and, 5
Forced responses, 371, 733–734
driven RL circuits, 288, 316–317
to sinusoids. See Sinusoidal steadystate analysis
source-free RL circuits, 262
Forcing functions, 124
sinusoidal waveform as, 371
source-free RL circuits, 262
Forms of responses
critically damped RLC circuits,
334–335
underdamped source-free parallel RLC
circuits, 338–339
Fourier circuit analysis, 4, 733–79 . See
also Fourier series; Fourier
transform
complete response to periodic forcing
functions, 748–75
image processing, 78 –781
practical application, 78 –781
Fourier series
coefficients, 737–738
complex form, 75 –757
sampling function, 754–757
symmetry, use of, 743–747
842 INDEXINDEX 843
even and odd symmetry, 743, 747
Fourier terms and, 743–745
half-wave symmetry, 745–746, 747
for simplification purposes, 747
trigonometric form of, 733–743
coefficients, evaluating, 737–738
derived, 735–736
equation for, 736
harmonics, 734–735
integrals, useful, 736–737
line spectra, 741–742
phase spectra, 742–743
Fourier transform. See also Fourier
transform pairs
defined, 757–761
fast Fourier transform (FFT), 772,
774–777
image processing example, 78
of general periodic time function,
769–77
physical significance of, 762–763
properties of, 761–764
system function, frequency domain.
See System function
Fourier transform pairs, 759
for constant forcing function, 766
for signum function, 766–767
summary of, 768
for unit-impulse function, 764–766
for unit step function, 767
Free response, source-free RL circuits, 262
Frequency
angular, of sinusoids, 371
complex. See Complex frequency
cutoff, transistor amplifier, 398–399
differentiation, Laplace transforms,
561, 836–837
domain. See Frequency domain
fundamental frequency, 734
integration, Laplace transforms,
561, 837
limits, digital integrated circuits,
3 6–3 7
multiple, RMS value with, 435–436
natural resonant, 338–339
op amps and, 199–2
radian, of sinusoids, 371
response. See Frequency response
scaling, 644–648, 682–683
selectivity, parallel resonance and, 629
shift, Laplace transforms, 561,
835–836
of sinusoids, 372–373
source-free parallel RLC circuits,
324–325
unit definitions for, 324
Frequency domain
phasor representation, 384
system function and, 77 –777
time domain converted to, 539
V-I expressions, phasor relationships
and, 387
Frequency response, 3, 4, 619–686
Bode diagrams. See Bode
diagram/plots
equivalent series/parallel
combinations, 639–644
filters. See Filters (frequency)
parallel resonance. See Parallel
resonance
resonant forms, other, 637–644, 682
scaling, 644–648, 682–683
series resonance, 633–636, 681
Friction coefficient, 5
Fundamental frequency, 734
G
Gain, of op amps, 6 7
General Conference on Weights and
Measures, 9–1
General form, complex frequency,
534–535, 565–566
General practical voltage source, 134
General RC circuits, 279–282
General RL circuits, 275–276, 312–315
General solution, source-free RL circuits,
264–265
George A. Philbrick Researches, Inc., 2 8
Global positioning systems (GPS), 6 7
Goody, R.W., 363, 816
Graphics/Graphical
on complex-frequency (s) plane, 599,
617–618
of convolution, s-domain analysis,
592–593
of critically damped response, RLC
circuits, 336–337
of current, symbols for, 13
overdamped response, RLC circuits,
331–332
underdamped response, RLC
circuits, 34
Ground (neutral) connection, 65–66, 458
Groups, of independent sources, 125
H
Half-power frequency, 651
Half-wave symmetry, Fourier,
745–746, 747
Hanselman, D.C., 832
Harmonics, Fourier, 734–735
Harper, C.A., 249
Hartwell, F.P., 67
Hayt, W.H., Jr., 2 7, 41 , 721
Heathcote, M., 523
henry (H), 225
Henry, Joseph, 225
Higher order filters, 672–677, 685
Higher-order terms, Bode diagrams, 657
High-pass filters, 665, 676
passive, 665–666
High-Q circuits
approximations for, 629–633
bandwidth and, 629–633, 68 –681
Hilburn, J.L., 679
Homogeneity property, Laplace
transforms, 546
Homogeneous linear differential
equations, 261–262
H(s) Vout/Vin, synthesizing, 6 6–61 ,
618
Huang, Q., 679
Huelsman, L.P., 679
Hybrid parameters, two-port networks,
713–716, 729–73
I
Ideal capacitor model, 217–22
Ideal inductor model, 225–229
Ideal operational amplifiers.
See Operational amplifiers
Ideal resistor, average power,
absorption, 428
Ideal sources, of voltage, 18
Ideal transformers, 512–522
for current level adjustment, 517
equivalent circuits, 519–521
for impedance matching, 514
step-down transformers, 516
step-up transformers, 516turns ratio of, 512–514
for voltage level adjustment, 515–516
voltage relationship in the time
domain, 517–521, 53 –532
Ideal voltage sources, 133–135
Image processing, Fourier analysis and,
78 –781
Imaginary sources → imaginary
responses, 379–38
Imaginary unit (operator)/component, 817
of complex forcing function, 378
of complex power, 441
imaginary sources → imaginary
responses, 379–38
Immittance, 394
Impedance, 239, 571–572
input, 587
matching, 514
sinusoidal steady-state, 389–394,
414–415
defined, 389
parallel impedance
combinations, 388
reactance and, 357
resistance and, 39
series impedance combinations, 389
Impulse response, convolution and,
589–59 , 617
Inactive network, 147
Independent current sources, 18, 19
Independent voltage sources, 18–19
Inductors/Inductance, 225–234,
252–254, 493
characteristics, ideal, 233
defined, 225
duality. See Duality
energy storage, 231–233
in the frequency domain, 572, 577
ideal inductor model, 225–229
inductive reactance, 376
infinite voltage spikes, 229
integral voltage-current relationships,
229–231
linearity, consequences of, 238–24 ,
254–257
modeled, 245–247, 259–26 , 572–575
in parallel, 236
phasor relationships for, 386, 413–414
in series, 235–236
in the time domain, 577
Infinite voltage spikes, inductors and, 229
Initial value, Laplace transforms, 561–562
In-phase sinusoids, 372–373
Input bias, 195
Input impedance, 587
amplifiers, 7 4–7 6
one-port networks, 688–692
Input offset voltage, op amps, 198
Instantaneous charge, 12
Instantaneous power, 422–424, 447,
45 –451
Instantaneous stored energy, parallel
resonance and, 624
Instrumentation amplifier, 2 4–2 6,
214–215
Integral of the current voltage, 18
Integral voltage-current relationships
capacitors, 22 –222, 249–252
inductors, 229–231
Internal generated voltage, 474
Internal resistance, 134
International System of Units (SI), 9–1
Intuitive understanding, driven RL
circuits, 289
Inverse transforms. See Laplace
transform(s)
Inversion, of matrices, 8 6–8 7
Inverting amplifier, 177, 182
Inverting input, 176
J
Jenkins, N., 486
Johnson, D.E., 679
Joules, 1
Jung, W.G., 2 7, 249
K
K2-W op amp, 176
Kaiser, C.J., 249
kelvin, 1
Kennedy, B.K., 523
Kilograms, 1
kilowatthour (kWh), 438
Kirchhoff, Gustav Robert, 4
Kirchhoff’s laws
current law (KCL), 39, 4 –42, 68–7
nodal analysis and, 8 , 157
phasors and, 387–388
voltage law (KVL), 39, 42–46, 7 –72
circuit analysis and, 157
in mesh analysis, 98
order of elements and, 55
Korn, G.A., 679
L
Lagging power factor, 439
Lagging sinusoids, 372–373
Lancaster, D., 679
Laplace analysis, 4
Laplace transform(s), 533–57
computer-aided analysis, 551–553
convolution and, 595–596
damped sinusoidal forcing function,
537–54 , 566
defined, 54 –543, 567
for exponential function eατ, 545
frequency-differentiation theorem,
836–837
frequency-integration theorem, 837
frequency-shift theorem, 835–836
initial-value/final-value theorems,
561–563, 569–57
inverse transform techniques,
546–551, 568
distinct poles/method of residues,
548–549
linearity theorem, 546–547
for rational functions, 547–548
repeated poles, 55
one-sided, 542–543
operations, table of, 561
pairs, 559
of periodic time functions, 833–835
for ramp function tu(t), 545
sifting property, 545
of simple time functions, 543–546, 567
sinusoid theorem, 558
system stability theorem, 56
theorems for, 553–561, 568–569
time differentiation theorem, 553–554
time-integration theorem, 555–556
time-scaling theorem, 838
time-shift theorem, 558, 833–835
two-sided inverse Laplace
transform, 542
two-sided Laplace transform, 541
for unit-impulse function α(t t ),
544–545
for unit-step function u(t), 544
LC circuit, lossless, 359–361, 369–37
844 INDEXINDEX 845
Leading sinusoids, 372–373
Leighton, R.B., 67
LF411 op amp, 193, 2
Lin, P.M., 1 9, 159, 41 , 721
Linden, D., 159
Linear circuits, 2–4
complex forcing functions, 379–38
conservation laws, 157
dc analysis, 3
frequency response analysis, 3, 4
linear voltage-current relationships,
123–124
transient analysis, 3, 4
Linear dependent source, 124
Linear elements, 123–124
Linear homogeneous differential
equations, 261–262
Linearity, 123–124
consequences, capacitors/inductors,
238–24 , 254–257
inverse transform theorem, 546–547
Linear resistor, 23
Linear transformers, 5 5–512, 528–53
primary mesh current, 5 5
reflected impedance, 5 5–5 6
secondary mesh current, 5 5
T and equivalent networks, 5 7–51
Linear voltage-current relationship,
123–124
Line spectra, Fourier series analysis,
741–742
Line terminals, 464
Line-to-line voltages, three-phase Y-Y
connection, 465–466
Links, 792–793
loop analysis and, 797–8 2
Littlefield, B.L., 832
LM324 op amp, 193
LM741 op amp, 2
LMC6 35 op amp, 176
LMV321 dual op amp, 176
Loop
analysis, links and, 797–8 2
defined, 792
mesh analysis and, 92
Lossless LC circuit, 359–361, 369–37
Lower half-power frequency, 628
Low-pass filters, 665, 674
passive, 665–666
Lumped-parameter networks, 39
M
M, upper limit for, 5 3
M12/M21 equality, magnetically coupled
circuits, 5 2–5 3
Magnetically coupled circuits, 493–532.
See also Transformers
computer-aided analysis, 51 –512
coupling coefficient, 5 4
energy considerations, 5 1–5 4,
527–528
equality of M12 and M21, 5 2–5 3
ideal transformers. See Ideal
transformers
linear transformers, 5 5–512, 528–53
magnetic flux, 493, 494, 497
mutual inductance. See Mutual
inductance
upper limit for M, establishing, 5 3
Magnetic flux, 493, 494, 497
Magnitude
exponential form of complex number,
822–824
scaling, 644–648, 682–683
Mancini, R., 2 7, 249, 612
MATLAB, 85, 551–553
tutorial, 827–832
Matrices
determinants of, 8 7–8 9
inversion of, 8 6–8 7
matrix form of equations, 85
simultaneous equations, solving,
8 4–81
Maximum average power, 431
Maximum power transfer, 152–154,
168–17 , 43 –432
Maxwell, James Clerk, 218
McGillem, Clare D., 544n
McLyman, W.T., 523
McPartland, B.J., 67
McPartland, J.P., 67
Memristor, 234
Mesh. See Nodal and mesh analysis
Meters, 1
Method of residues, 548–549
Metric system of units, 1
microfarads (μF), 219
MicroSim Corporation, 1 3
Midrange filters, 671–672
Models/Modeling, 3
of automotive suspension systems, 358
of ideal capacitors, 217–22
of inductors
ideal inductors, 225–229
with PSpice, 245–247, 259–26
in the s-domain, 572–575
of op amps, detailed, 192–194
Moles, 1
MOSFET, 22
Multiband filters, 665
Multiple-frequency circuits, RMS value
with, 435–436
Multiple terms, in Bode diagrams, 651
Multiport network, 687. See also
Two-port networks
Mutual inductance, 493–5 1
additive fluxes, 497
coefficient of, 494
dot convention, 495–499, 523–527
circuit transfer function, 499
physical basis of, 497–5
power gain, 499
magnetic flux, 493, 494, 497
self-inductance added to, 496
N
1N75 Zener diode, 189–19
2N39 4, ac parameters, 716
Nanotechnology, 234
Napier, John, 534
NASA Dryden Space Flight Center, 6
National Bureau of Standards, 9
National Semiconductor Corp., 176, 2
Natural resonant frequency, 338–339, 622
Natural responses, 282, 371, 374,
733–734
and the complex-frequency (s) plane,
6 2–6 6, 618
driven RL circuits, 288, 289–295,
316–317
source-free RL circuits, 262
Negative charge, 11
Negative feedback
op amps, 196–197
path, 6 7
Negative phase sequence, 464–465
Negative (absorbed) power, 16, 19
Negative resistances, 692
Neper frequency, 537
defined, 324
Nepers (Np), 534Networks, 21–22
active, 21
passive, 21
topology. See Network topology
two-port. See Two-port networks
Network topology, 791–8 2
links and loop analysis, 797–8 2
trees and general nodal analysis,
791–797
Neudeck, G.W., 2 7, 41 , 721
Neutral (ground) connection, 458, 464
New Simulation Profile command
(PSpice), 1 5
Nodal and mesh analysis, 3, 79–122
compared, 1 1–1 3, 119–12
computer-aided, 1 3–1 7, 12 –121,
578–58
location of sources and, 1 1
mesh analysis, 92–98, 114–117, 157
Kirchhoff’s voltage law applied
to, 98
mesh current, 92, 93–95, 5 5
mesh defined, 792
procedure, summarized, 98
supermesh, 98, 1 –1 1, 117–118
nodal analysis, 3, 8 –89, 1 9–112, 157
basic procedure, summary, 88–89
Kirchhoff s current law and, 8
nodes defined, 4 , 791
procedure, summarized, 98
reference node, 8
sinusoidal steady-state analysis,
394–397, 415–417
supermesh, 98, 1 –1 1, 117–118
supernodes, 89–91, 112–114
trees and, 791–797
voltage source effects, 89–91,
112–114
node-base PSpice schematics, 1 6–1 7
s-domain circuit analysis and,
578–584, 613–615
computer-aided, 578–58
of sinusoidal steady-states, 394–397,
415–417
Noninverting amplifier circuit, 182
output waveform, 178–179
Noninverting input, 176
Nonlinear circuit analysis, 2
Nonperiodic functions, average power
for, 431–433
Nonplanar circuit, defined, 792
Norton, E.L., 141
Norton equivalents. See Thévenin/Norton
equivalent circuits
Notch filters, 665
Number systems, units and scales, 9
Numerical value, of current, 12
O
Octave (of frequencies), 65
Odd functions, 745n
Odd harmonics, 745n
Odd symmetry, Fourier series analysis,
743, 747
Øersted, Hans Christian, 225
Ogata, K., 565, 612
Ohm, Georg Simon, 22
Ohms (), 22
Ohm’s law, 22–28, 34–36
conductance, 27–28
defined, 22
power absorption in resistors, 23–27
practical application, 25–26
resistance units defined, 22
One-port networks, 687–692, 722–723
input impedance calculations for,
688–692
One-sided Laplace transform,
542–543
OPA69 op amp, 193, 199
Op amps. See Operational amplifiers
Open circuit, 27–28
to dc, 219
impedance parameters, 7 8–7 9
Open-loop
configuration, op amps, 2 3
voltage gain, 192–193
Operating at complex frequencies, 6 3
Operational amplifiers, 175–216
μA741 op amp, 193–194, 195, 198
AD549K op amp, 193, 195
AD622 op amp, 2 6
capacitors with, 24 –241, 257–258
cascaded stages, 184–187, 21 –212
common mode rejection, 195–196
comparators, 2 3–2 4, 214–215
computer-aided analysis, 2 –2 3
frequency and, 199–2
ideal, 176–184, 2 8–21
derivation of, 194–195
difference amplifier, 181–184,
195–196
inverting amplifier, 177, 182
noninverting amplifier circuit,
178–179, 182
rules, 176
summary, 182
summing amplifier, 18 –181, 182
voltage follower circuit, 179, 182
input offset voltage, 198
instrumentation amplifier, 2 4–2 6,
214–215
LF411 op amp, 193, 2
LM324 op amp, 193
LM741 op amp, 2
LMC6 35 op amp, 176
LMV321 dual op amp, 176
modeling, 192–194
negative feedback, 196–197
OPA69 op amp, 193, 199
outputs depending on inputs, 176
packaging, 2
parameter values, typical, 193
Philbrick K2-W op amp, 176
positive feedback, 197
practical considerations,
192–2 3, 213
reliable current sources, 19 –192,
212–213
reliable voltage sources, 188–19 ,
212–213
saturation, 197–198
slew rate, 199–2
tank pressure monitoring system,
186–187
Operations, Laplace transform,
table of, 561
Order of elements, KVL and, 55
Oscillator, 6 7
circuit design, 6 7–6 8
function, 34
Out-of-phase sinusoids, 372–373
Output impedance, amplifiers, 7 5
Output resistance, 134
Overdamped response
source-free parallel RLC circuits, 325,
326–333, 347, 363–365
A1 and A2 values, finding,
326–327
graphical representation of,
331–332
source-free series RLC circuits,
346–347
846 INDEXINDEX 847
P
Packages, op amp, 2
Pairs, Laplace transform, 559
Palm, W.J., III, 832
and T equivalent networks, 5 7–51
Parallel element combinations, 49
capacitors, 237–238
impedance combinations, 389–39
inductors, 236
series/parallel combination
equivalents, 639–644
Parallel resonance, 619–627, 636,
679–68
bandwidth and high-Q circuits,
628–633, 68 –681
current response and, 622
damping
exponential coefficient, 621
factor, 625–627
defined, 62 –622
frequency selectivity, 629
instantaneous stored energy, 624
key conclusions on, 633
natural resonant frequency, 622
quality factor (Q), 623–627
bandwidth and, 628–633,
68 –681
damping factor and, 625–627
other interpretations of Q, 625
summary of, 636
voltage response and, 622–623
Parameter values, op amps, 193
Parseval-Deschenes, Marc Antione, 762
Particular integral, 291
Particular solution, 291
source-free RL circuits, 262
Passband, 665
Passive element, 217
Passive filters
defined, 669
low-pass and high-pass, 665–666
Passive network, 21
Passive sign convention, 16
Path
defined, 791
mesh analysis, 92
voltage, 14
Periodic functions/waveforms, 432.
See also Sinusoidal steadystate analysis; Sinusoidal
waveforms
ac average power of, 425–426
complete response to,
748–75
fall time of, 3
as forcing functions, 371
Laplace transforms of, 833–835
as output, noninverting amplifiers,
178–179
period T of, 3 , 372
pulse width of, 3
rise time of, 3
RMS values for, 433–434
time delay of, 3
Perry, T., 816
Peterson, Donald O., 813
Phase angle θ, 372
Phase comparison, sinusoidal
waves, 373
Phase response, Bode diagrams and,
652–653
Phase spectra, Fourier series analysis,
742–743
Phase voltages, 464
Phasor(s), 4, 384, 413–414, 571. See
also Phasor relationships
for R, L, and C
diagrams, sinusoidal steady-states,
4 6–4 8, 419
Phasor relationships for R, L, and C
as abbreviated complex
representation, 383
capacitors, 387–388
frequency-domain representation, 384
frequency-domain V-I expressions, 387
impedance defined from. See Sinusoidal
steady-state analysis
inductors, 386, 413–414
Kirchhoff’s laws using, 387–388
phasor representation, 384
resistors, 385–386
time-domain representation, 384
time-domain V-I expressions, 387
Philbrick, George A., 2 8
Philbrick K2-W op amp, 176
Philbrick Researches, Inc., 175
Physically realizable systems,
591–592
Physical significance, of Fourier
transforms, 762–763
Physical sources, unit-step function and,
284–285
Pinkus, A., 565, 783
Planar circuit, 92, 1 1
defined, 792
Polar form, of complex numbers,
824–826
Poles, 547
method of residues and, 548–549
pole-zero constellations, 6 –6 2
repeated, inverse transforms, 55
zeros, and transfer functions, 588–589,
616–617
Polya, G., 8
Polyphase circuits, 457–492
delta () connection, 47 –476,
489–49
of sources, 473–476
Y-connected loads vs., 473
double-subscript notation, 459–46
polyphase systems, 458–46 ,
486–487
single-phase three-wire systems,
46 –464, 487
three-phase Y-Y connection. See
Three-phase Y-Y connection
Port, 687
Positive charge, 11
Positive feedback, 197, 6 7
Positive phase sequence, 464–465
Positive power, 16, 18
Potential coil, 476
Potential difference, 14
Potentiometer, 671
Power, 9, 15–17, 3 –33. See also ac
circuit power analysis
absorbed. See Absorbed power
average. See Average power
dissipation, 49
expression for, 15
factor. See Power factor
gain, 499, 7 4
generating systems, 474–475
maximum transfer of, 152–154,
168–17
measuring. See Power measurement
negative. See Absorbed power
positive, 16, 18
reactive, 442, 447
superposition applicable to, 433
terminology recap, 447
triangle, 442–443
units, 1 Power factor (PF), 447
apparent power and, 438–441, 453–454
complex power, 438–441, 453–454
correction, 444–445
lagging, 439
leading, 439
Power factor (PF) angle, 439
Power measurement, 443–444
three-phase systems, 476–484,
49 –491
two-wattmeter method, 481–483
wattmeters, use of, 476–478
wattmeter theory and formulas,
478–481
Practical current sources, 135, 139–14
Practical voltage sources, 133–135,
139–14
Prefixes, SI, 1 –11
Primary mesh current, 5 5
Prime mover, 474
Probe software, 344–345
Problem-solving strategies, 1, 7–8
PSpice, 1 3, 1 5–1 7, 13 –133
Bias Point command, 1 5
capacitors modeled with, 245–247,
259–26
Create command, 1 5
inductors modeled with, 245–247,
259–26
New Simulation Profile command, 1 5
node-base schematics, 1 6–1 7
Run command, 1 5
for sinusoidal steady-state analysis,
4 4–4 5
for transient analysis, 27 –272
tutorial, 813–816
Type command, 1 5
Pulse width (PW), of waveforms, 3
Purely reactive elements, average power
absorption, 428–429
Q
Quadrature power, 443
Quality factor (Q). See Parallel resonance
R
Radian frequency, 371, 537
Ragazzini, J.R., 2 7
Ramp function tu(t), Laplace transform
for, 545
Randall, R.M., 2 7
Rational functions, inverse transforms for,
547–548
Rawlins, C.B., 25n, 26n
RC circuits
driven, 295–3
general, 279–282
sequentially switched, 3 –3 5, 319
I: time to fully charge/fully
discharge, 3 2–3 3, 3 4
II: time to fully charge but not fully
discharge, 3 3, 3 4
III: no time to fully charge but time
to fully discharge, 3 3, 3 4
IV: no time to fully charge or fully
discharge, 3 4–3 5
source-free, 272–275, 311–312
time constant (τ), 274
unit-step function, 282–286, 315
Reactance
impedance and, 39
inductive, 376
synchronous, 474
Reactive elements, average power
absorption, 428–429
Reactive power, 442–443, 447
Realizable systems, s-domain analysis,
591–592
Real portion, of complex forcing
function, 378
Real sources → real responses, complex
forcing functions, 379–38
Reciprocity theorem, 698
Rectangular form, complex numbers, 818
Rectangular pulse function, 285–286
Rectifiers/Rectification, 459, 493
Reference node, 8
Reflected impedance, 5 5–5 6
Reliable current sources, op amps,
19 –192, 212–213
Reliable voltage sources, op amps,
188–19 , 212–213
Repeated poles, inverse transform
techniques, 55
Resistance/Resistors/Resistivity, 9, 25.
See also Ohm’s law
equivalent, 56
in the frequency domain, 571–572
ideal, average power absorption, 428
impedance and, 39 , 391
internal, 134
linear, 23
output, 134
phasor relationships for, 385–386
in s-domain circuit analysis,
571–572, 577
in series and parallel, 55–61, 75–76
in the time domain, 577
variable. See Potentiometer
Resonance, 324
current response and, 622
parallel. See Parallel resonance
series, 633–636, 681
summary table for, 636
voltage response and, 622–623
Resonant frequency, 324
Response, 123
in the frequency domain, 77 –777
as a function of the σ s-domain,
598–599
functions, 124
source-free series RLC circuits,
346–347
Ripple factor, 673, 677
Rise time (TR), of waveforms, 3
RLC circuits, 321–37
automotive suspensions modeled, 358
complete response of, 351–359,
368–369
complicated part, 352–357
uncomplicated part, 351–352
lossless LC circuit, 359–361, 369–37
phasor relationships for. See Phasor
relationships for R, L, and C
solution process summary, 357–359
source-free critical damping, 334–338,
365–366
A1 and A2 values, 335
form of critically damped response,
334–335
graphical representation of,
336–337
source-free parallel circuits,
321–325, 363
computer-aided analysis, 344–345
critically damped response,
325, 347
differential equation for, 322–324
equations summary, 347
frequency terms defined, 324–325
848 INDEXoverdamped response, 325,
326–333, 347, 363–365
A1 and A2 values, 326–327
graphical representation,
331–332
underdamped response, 325,
338–345, 347, 366–367
B1 and B2 values, 339–34
finite resistance, role of,
34 –342
form of, 338–339
graphical representation, 34
source-free series circuits, 345–351,
367–368
circuit response résumé, 346–347
critically damped response,
346–347
equations summary, 347
overdamped response, 346–347
underdamped response, 346–347
RL circuits
driven. See Driven RL circuits
exponential response properties,
268–272, 31
exponential response time constant
(τ), 268–269
general, 275–276, 312–315
natural response. See Natural
responses
sequentially switched, 3 –3 5, 319
I: time to fully charge/fully
discharge, 3 2–3 3, 3 4
II: time to fully charge but not fully
discharge, 3 3, 3 4
III: no time to fully charge but time
to fully discharge, 3 3, 3 4
IV: no time to fully charge or fully
discharge, 3 4–3 5
slicing thinly: vs. , 276–279
source-free, 261–268, 3 9–31
alternative approach, 264
complementary function, 262
computer-aided analysis, 27 –272
direct approach, 262–263
energy, accounting for, 267
forced response, 262
forcing function, 262
free response, 262
general solution approach,
264–265
natural response, 262
the particular solution, 262
the steady-state response, 262
transient response, 262
unit-step function, 282–286, 315
RMS value
for average power, 435
for current and voltage, 433–438, 447
with multiple-frequency circuits,
435–436
for periodic waveforms, 433–434
for sinusoidal waveforms, 434–435
Robotic manipulator, 5
Root-mean-square (RMS) value. See
RMS value
Rotor, 474
Row vector, 8 4
Run command (PSpice), 1 5
Russell, F.A., 2 7
S
s, defined, 536–537
Sallen-key amplifier, 673–677
Sampling function, Fourier series,
754–757
Sands, M.L., 67
Saturation, op amp, 197–198
Scalar multiplication, 561
Scales, units and, 9–11, 29–3
Scaling
and frequency response, 644–648,
682–683
Laplace transform operation, 561
Scientific calculators, 8 3–8 4
s-domain circuit analysis, 571–618
additional techniques, 585–589,
615–616
complex frequency and. See Complex
frequency
convolution and. See Convolution
H(s) Vout/Vin voltage ratio,
synthesized, 6 6–61 , 618
nodal and mesh analysis in, 578–584,
613–615
computer-aided analysis, 578–58
poles, zeros, and transfer functions,
588–589, 616–617
Thévenin equivalent technique,
587–588
Z(s) and Y(s), 571–577, 612–613
capacitors
in frequency domain, 577
modeled in the s domain,
575–576
in time domain, 577
inductors
in frequency domain, 572, 577
modeled in the s domain,
572–575
in time domain, 577
resistors
in frequency domain,
571–572, 577
in time domain, 577
summary of element
representations, 577
Secondary mesh current, 5 5
Seconds, 1
Self-inductance, 493
added to mutual inductance, 496
Sequentially switched RL or RC circuits.
See RC circuits; RL circuits
Series connections, 46
capacitors, 236–237
impedance combinations, 389
inductors in, 235–236
and parallel combinations. See also
Source transformations
connected sources, 51–55, 74,
139–14
other resonant forms, 639–644
Series resonance, 633–636, 681
Settling time, 332
Sharpe, D., 486
Short circuit(s), 27–28
admittance and, 7 8–7 9
for equivalent networks, 699–7
input admittance, 693–694
output admittance, 694
transfer admittance, 694
two-port networks, 694
to dc, 226
SI base units, 1
siemen (S), 572
Sifting property, 545
Signal ground, 65–66
Signs
passive convention, 16
for voltages, 9, 14
Simon, Paul-René, 29
INDEX 84985 INDEX
Simple time functions, Laplace
transforms of, 543–546, 567
Simulation Program with Integrated
Circuit Emphasis, 1 3
Simultaneous equations, solving,
8 3–81
Cramer’s rule, 8 9–81
determinants and, 8 7–8 9
matrices, 8 4–81
scientific calculators and, 8 3–8 4
Sines, converted to cosines, 373
Single-loop circuit, 46–49, 72–73
Single-node-pair circuit, 49–51, 73
Single-phase three-wire systems,
46 –464, 487
Singularity functions, 283
Sinusoids
complex frequency case, 535
as forcing functions, 619–62
Laplace transforms of, 558
Sinusoidal steady-state analysis, 3, 371–42
ac circuit average power, 426–427
admittance, 394
amplitude, 371
angular frequency, 371
argument, 371
characteristics of sinusoids, 371–374,
41 –411
complex forcing function, 378–382,
412–413
algebraic alternative to differential
equations, 38 –381
applying, 379–38
imaginary part, 378
imaginary sources → imaginary
responses, 379–38
real part, 378
real sources → real responses,
379–38
superposition theorem, 379–38
computer-aided analysis, 4 4–4 5
conductance, 394
cutoff frequency, transistor amplifier,
398–399
forced responses to sinusoids, 371,
374–377, 411–412
alternative form of, 375–376
amplitude, response vs. forcing
function, 376
steady-state, 374–375
frequency, 372–373
immittance, 394
impedance. See Impedance
lagging and leading, 372–373
natural response, 371
nodal and mesh analysis, 394–397,
415–417
out-of-phase, 372–373
period, 372
in phase, 372–373
phase comparison requirements, 373
phasor diagrams, 4 6–4 8, 419
phasor relationships and. See Phasor
relationships for R, L and C
radian frequency, 371
sines converted to cosines, 373
sinusoidal waveform forcing
function, 371
superposition, source transformations,
and, 397–4 5, 417–418
susceptance, 394
Sinusoidal waveforms
as forcing functions, 371
oscillator circuit design and,
6 7–6 8
phase comparison, 373
RMS values of current/voltage,
434–435
SI prefixes, 1 –11
Slew rate, op amps, 199–2
Slicing thinly: vs. , RL circuits,
276–279
Smoothing, of Bode diagrams, 651
Snider, G.S., 234n
Solve() routine, 86
Source-free RC circuits, 272–275,
311–312
Source-free RLC circuits. See RLC
circuits
Source-free RL circuits. See RL circuits
Source transformations, 3, 133–14 , 157,
162–165
equivalent practical sources,
135–138
key concept requirements,
139–14
practical current sources, 135,
139–14
practical voltage sources, 133–135,
139–14
and sinusoidal steady-state analysis,
397–4 5, 417–418
summary, 14
SPICE, 6, 1 3. See also PSpice
Square matrix, 8 4
Squire, J., 783
Stability, of a system, 56
Stator, 474
Steady-state analysis/response, 291. See
also Sinusoidal steady-state
analysis
source-free RL circuits, 262
Step-down transformers, 516
Step-up transformers, 516
Stewart, D.R., 234n
Stopband, 665
Structure (programming), 86
Strukov, D.B., 234n
Summing amplifier, 18 –181, 182
Superconducting transformers, 518–519
Supermesh, 98, 1 –1 1, 117–118
Supernodes, 89–91, 112–114
Superposition, 3, 123–133, 158, 159–162,
379–38
applicable to current, 433
applicable to power, 433
basic procedure, 13
limitations of, 133
sinusoidal steady-state analysis,
397–4 5, 417–418
superposition theorem, 125
Supplied power, 16
equaling absorbed power, 49
Susceptance, 394
Suspension systems, automotive,
modeling of, 358
Symmetrical components, 47
Symmetry, use of, Fourier series analysis,
743–747
Synchronous generator, 474
Synchronous reactance, 474
System function, 589
computer-aided analysis, 774–777
fast Fourier transform (FFT), 772,
774–777
image processing example, 78
physical significance of, 777–779
response, in frequency domain, 77 –777
Systems, stability of, 56
Szwarc, Joseph, 29INDEX 851
T
T and equivalent networks, 5 7–51
Tank pressure monitoring system.,
186–187
Taylor, Barry N., 29
Taylor, J.T., 679
Tesla, Nikola, 457
Thévenin, L.C., 141
Thévenin/Norton equivalent circuits, 3–4,
141–151, 157–158,
165–168, 172–173
Norton’s theorem, 3–4, 145–147,
157–158, 172–173
linearity for capacitors/
inductors, 24
resistance, 144, 157–158, 172–173
s-domain circuit analysis, 587–588
Thévenin’s theorem, 3, 141, 143–145,
157–158, 172–173
linearity for capacitors/
inductors, 24
proof of, 811–812
and sinusoidal steady-state
analysis, 397–4 5, 417–418
two-port networks, 7 5–7 6
when dependent sources are present,
147–149
Thompson, Ambler, 29
Three-phase system, balanced, 458
Three-phase Y-Y connection, 464–47 ,
488–489
abc phase sequence, 464–465
cba phase sequence, 464–465
Delta () connection vs., 473
line-to-line voltages, 465–466
negative phase sequence, 464–465
positive phase sequence, 464–465
power measurement in. See Power
measurement
total instantaneous power,
467–468
with unbalanced load, 47
Tightly coupled coils, 5 4
Time constant (τ)
exponential response of RL circuits,
268–269
RC circuits, 274
Time delay (TD) of waveforms, 3
Time differentiation, Laplace transforms
and, 553–554, 561
Time domain
capacitors in, 577
converted to frequency domain, 539
ideal transformer voltage relationships
in, 517–521, 53 –532
inductors in, 577
representation, phasors, 384
resistors in, 577
V-I expressions, phasor relationships
and, 387
Time functions, simple, Laplace
transforms of, 543–546, 567
Time integration, Laplace transforms and,
555–556, 561
Time periodicity, Laplace transforms and,
561, 833–835
Time-scaling theorem, Laplace
transforms and, 838
Time shift, Laplace transforms and, 558,
561, 833–835
Topology, 791. See also Network
topology
Total instantaneous power, three-phase,
458, 467–468
T parameters, two-port networks,
716–72 , 73 –731
Transconductance, 21
Transfer functions, 499, 588, 597
Transfer of charge, 12
Transformations
source. See Source transformations
between y, z, h, and t parameters, 7 9
Transformers, 493. See also Magnetically
coupled circuits
ideal. See Ideal transformers
linear. See Linear transformers
superconducting, 518–519
Transient analysis, 3, 4
PSpice capability for, 27 –272
Transient response, 289
source-free RL circuits, 262
Transistors, 22, 398–399,
715–716
Transmission parameters, two-port
networks, 716–72 ,
73 –731
Treble filters, 671–672
Trees, 791–797
Trigonometric form, of Fourier series. See
Fourier series
Trigonometric integrals, Fourier series
analysis, 736–737
Tuinenga, P., 1 9, 816
Turns ratio, ideal transformers, 512–514
Two-port networks, 687–732
ABCD parameters, 716–72 , 73 –731
admittance parameters, 692–699,
723–725
bilateral circuit, 698
bilateral element, 698
reciprocity theorem, 698
short-circuit admittance
parameters, 694
short-circuit input admittance,
693–694
short-circuit output admittance, 694
short-circuit transfer admittance, 694
y parameters, 694–695, 7 6–7 7
computer-aided analysis for, 719–72
equivalent networks, 699–7 7,
725–727
amplifiers, 7 4–7 6
of impedances method, 7 –7 2
Norton equivalent method, 7 5–7 6
short-circuit admittance method,
699–7
Thevenin equivalent method,
7 5–7 6
Y- not applicable, 7 2
yV subtraction/addition method,
699
hybrid parameters, 713–716, 729–73
impedance parameters, 7 8–712,
727–728
one-port networks. See One-port
networks
t parameters, 716–72 , 73 –731
transistors, characterizing, 715–716
transmission parameters, 716–72 ,
73 –731
Two-sided inverse Laplace transform, 542
Two-sided Laplace transform, 541
U
Unbalanced Y-connected loads, 47
Underdamped response
source-free parallel RLC circuits. See
RLC circuits
source-free series RLC circuits,
346–347Unit-impulse function, 283
Laplace transform for, 544–545
Units and scales, 9–11, 29–3
Unit-step function u(t), 282–286, 315
Fourier transform pairs for, 767
Laplace transforms for, 544
and physical sources, 284–285
RC circuits, 282–286, 315
rectangular, 285–286
RL circuits, 282–286, 315
Unity gain amplifier, 182
Upper half-power frequency, 628
V
Vectors, 85, 8 4
Volta, Alessandro Giuseppe Antonio
Anastasio, 14n
Voltage, 9, 14–15, 3 –33
actual polarity vs. convention, 14
current sources and, 17–22, 33–34,
51–55, 74
active elements, 21
circuit element, 21
dependent sources of
voltage/current, 18, 19–21
derivative of the current voltage, 18
independent current sources, 19
independent voltage sources, 18–19
integral of the current voltage, 18
networks and circuits, 21–22
passive elements, 21
effective values of, 433–438,
452–453
force and, 5
input offset, op amps, 198
integral voltage-current relationships,
for capacitors, 22 –222,
249–252
internally generated, 474
laws. See Voltage and current laws
sources. See Voltage sources
voltage and current division, 61–64,
76–77
Voltage amplifier, 178
Voltage and current division, 61–64,
76–77
Voltage and current laws, 39–78
branches, 39–4 , 67–68
equivalent resistance, 55
Kirchhoff’s current law (KCL), 39,
4 –42, 68–7
Kirchhoff’s voltage law (KVL), 39,
42–46, 7 –72
order of elements and, 55
loops, 39–4 , 67–68
nodes, 39–4 , 67–68
paths, 39–4 , 67–68
resistors in series and parallel, 55–61,
75–76
series and parallel connected sources,
51–55, 74
single-loop circuit, 46–49, 72–73
single-node-pair circuit, 49–51, 73
voltage and current division, 61–64,
76–77
Voltage coil, 476
Voltage-controlled current source, 19
Voltage-controlled voltage source, 19–2
Voltage follower circuit, 179, 182
Voltage gain, amplifiers, 7 4
Voltage level adjustment, ideal
transformers for, 515–516
Voltage ratio H(s) Vout/Vin,
synthesizing, 6 6–61 , 618
Voltage regulation, 475
Voltage relationship, ideal transformers,
time domain, 517–521,
53 –532
Voltage response, resonance and,
622–623
Voltage sources
ideal, 133–135
practical, 133–135
reliable, op amps, 188–19 , 212–213
series and parallel connected sources,
51–55, 74
source effects, nodal and mesh
analysis, 89–91, 112–114
Volt-ampere-reactive (VAR) units, 442
complex power, 441
Volt-amperes (VA), 439
W
Wait, J.V., 679
Wattmeters, for three-phase systems
theory and formulas, 478–481
two wattmeter method, 481–483
use, 476–478
Watts (W), 1 , 447
Weber, E., 3 8, 363
Weedy, B.M., 449, 486
Westinghouse, George, 457
Wheeler, H.A., 534
Wien-bridge oscillator, 6 7
Williams, R.S., 234n
Winder, S., 612
Wire gauges, 25–26
Work (energy) units, 1
Y
Y parameters, two-port networks,
694–695, 7 6–7 7
Y(s) and Z(s). See s-domain circuit
analysis
YV method, for equivalent networks, 699
Z
Zafrany, S., 565, 783
Zandman, Felix, 29
Zener diode, 188–19 , 212–213
Zener voltage, 189
Zeros, 547
s-domain circuit analysis
pole-zero constellations, 6 –6 2
zeros, poles, and transfer functions,
588–589
Zero vs. Zero, slicing thinly: RL
circuits, 276–279
Zeta (ζ) damping factor, 626
Z parameters, 7 8–712, 727–728
Z(s), Y(s) and. See s-domain circuit
analysis
852 INDEX
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