Electric Circuits, 9th Edition P82 potx

786 Index
Impulse function K8(t) (Continued)
unit 5(0,433-434,459
variable-parameter function, 433-434
Impulsive sources, 501-504
Independent sources, 26,29,47
Indirect approach, step response analysis, 281
Inductance (L), 174,176-182,189-200,203-204
circuit parameter of, 174,176,203
Faraday's law, 193-194
mutual, 176,189-200,203-204
self,
176-182,193-194,203
Inductors, 174,176-182,187-200,203,318-319,468-469,
499-501,506
behavior of, 174
circuit symbol for, 176
current (i) in, 111-119,203
energy (vv) in, 179-181,203
frequency domain, 318-319
impulse function (I) in, 499-501
Laplace transform used for, 468-469,499-501,506
power (p) in, 179-181,203
i-domain,
468-469,506
series-parallel combinations, 187-188,203
switching operation, 499-501
terminal equations for, 176-181,203,468-469,506
voltage (v) in, 176-177,203
voltage to current (v-i) relationships, 176-177,
318-319

Infinite frequency, 530
Initial-value theorem, Laplace transform, 455-457
Input constraints, 147-148,165
Instantaneous power, 362-363,386,412,419
Integer power of complex numbers, 729
Integrals, 646-650,761-762
Integrating amplifiers, 241-244,246,289-293,297
cascading connections, 289-293,297
feedback resistors and, 291-293,297
first-order circuits with, 241-246
response analysis of, 241-244,246
second-order circuits with, 289-293,297
sequential switching and, 243
Integration, operational transforms for, 439-440,658
Integrodifferential equations, 442-443
Interconnected two-port circuits, 694-697
International System of Units (SI), 8-10
Inverse Fourier transform, 647
Inverse Laplace transforms, 444-454,459
distinct complex roots of D(s), 447-449
distinct real roots of £)(5), 445-446
improper rational function, 444,453-454
partial fraction expansion, 444-454
proper rational functions, 444-453,459
rational function F(s), 444,459
repeated complex roots of D(s), 451-453
repeated real roots of D(s), 449^451
Inverse of a matrix, 716
Inverse phasor transform, 314-316,347
Inverting-amplifier circuit, 150-152,160,164

K
Kirchhoff s laws, 37-41,48,321-322,471
closed loop (path) for application of, 38
current (KCL), 37-41,48,321-322
frequency domain, 321-322
nodes,
37-38
s-domain
applications of, 471
voltage (KVL), 38,40-41,48,321
L
Laplace transform, 428-521,650-653
applications of, 442-444,472-484
circuit analysis and, 466-521
complete circuit response using, 429,458^159
convolution integral, 489-495,506
defined, 430,459
final-value theorem, 455^4-57
Fourier transforms found using, 650-653
frequency domain and, 441
functional transforms, 431,436-437,459
impulse function K8(t), 433-435,459,498-504,506
initial-value theorem, 455-457
inverse, 444-454,459
lumped-parameter circuit applications, 442-444,459
mutual inductance, analysis of a circuit with, 480-481
natural response using, 472-473
one-sided, 430-431
operational transforms, 431,437^442,459
pairs,

436-437
partial fraction expansion, 444-454,459,486-489,506
poles (roots), 454-455,486
rational functions F(s), 444-454,459
s-domain,
443-455,468-489,506
sinusoidal sources and, 429,458-459
steady-state sinusoidal response, 495-497,505-506
step function Ku(t), 431-432,459
step response using, 473-478
superposition, use of in .s-domain, 482-484
surge suppressors, 467,505
Thevenin equivalent, use of in
s-domain,
479-480
time domain translation in, 440-443
time-invariant circuits and, 488,506
transfer function H(s), 484^197,506
transient response using, 475—476,506
unilateral, 430-431
unit impulse function 5(0,433-434,459
unit step function KK(0,431,459
zeros (roots), 454-455,486
Line current, 405
Line spectra, 630
Line voltage, 404-405
Linear simultaneous equations, 705-724
Cramer's method,706
determinants, 706-709
matrices, 709-724

solution of, 705-724
Index 787
Loads, 62,410-414
balanced three-phase circuits and, 410-414
defined, 62
delta (A) connected,411-413
power calculations and, 410-414
unspecified, 414
wye (Y) connected, 410-411,413
Loop,
38,48,90-91
closed, 38,48
defined, 90-91
Low-pass filters, 524-532,550,560-562,574-584,594-595
active filter circuits, 560-562,578-584,594
Butterworth, 578-584,594-595
cascading identical, 574-577,594-595
cutoff frequency
(<w
c
),
527-529
frequency regions, 530
frequency response plots, 524-525
operational amplifier (op amp), 560-562,578-584,594
passive filter circuits, 524-532,550
qualitative analysis, 526-527
quantitative analysis, 528-529
relationship between frequency and time domains, 531
series RC circuits, 530-531

series RL circuits, 526-529
transfer function H(s) for, 531,550
Lumped-parameter system,
6-7,442-444,459
M
Magnetic coupling, see Mutual inductance
Magnetically coupled coils, 235-236,338,731-738
equivalent circuits for, 731,735-738
ideal transformers and, 338,731-738
^-equivalent circuit, 732-735
step response of, 235-236
T-equivalent
circuit, 731-732
Magnitude plot, 524
Magnitude scaling (k
m
), 564,594
Matrices, 709-724
Maximum power transfer, 120-122,129,378-384,386
average power (P
ms
.
x
) absorbed, 380-382
circuit analysis and, 120-122,129
ideal transformer, 383-384
impedance (Z) restricted, 380-381
sinusoidal steady-state analysis and, 378-384,386
Measurement,
8-10,66-70,76

ammeter, 66-67,76
analog meters, 67,76
current, 66-69
d'Arsonval
meter movement, 67-68
digital meters, 67,76
International System of Units (SI), 8-10
resistance, 69-70
voltage, 66-69,76
voltmeter, 66-67,76
Wheats tone bridge, 69-70,76
Memory, transfer function concept of, 494-495
Mesh, defined, 90-91
Mesh circuit, step response of, 476-478
Mesh-current method, 90,99-109,129,190-192,333-334
amplifier circuit analysis using, 105-106
circuit analysis using, 90,99-109,129
defined, 100
dependent sources and, 102-103
equations, 99-102,190,192
frequency-domain circuits, 333-334
mutual inductance (M) and, 190-192
node-voltage method, comparison of, 106-109
sinusoidal steady-state analysis using, 333-334
special cases of, 103-104
supermesh, 104
Meters, see Measurement
mho,
unit of, 31
Models, 10-11,17-18,34-36. See also Equivalent circuits

circuit, 17-18,34-36
conception of, 10-11
construction of, 34-36
flashlight, 34-35
mathematical (circuit), 11
physical prototypes, 11
Moment function (unit doublet), 435
Mutual inductance (M), 176,189-200,203-204,480-481
Laplace transform analysis of a circuit with, 480-481
circuit parameters of, 189-190,194-196,203-204
coefficient of coupling and, 197,204
dot convention for polarity, 190-192,195-196,204
energy (w) storage and, 197-200,204
mesh-current equations for, 190-192
self-inductance and, 196-197,204
N
Narrowband filters, 586-591,595
bandpass filters, 586-588
bandreject, 588-591
quality factor (Q) and, 586-587
twin-T notch, 588-589
Natural response, 212,214-224,231-236,246,266-279,
285-289,297,472-473
critically damped voltage, 269,277-278,286,297
defined, 212,246
forms of RLC circuit, 270-279
general solution for, 231-236
Laplace transform, using, 472-473
method of calculating, 232
overdamped voltage, 269,271-273,286,297

parallel RLC circuit, 266-279
resistor-capacitor (RC) circuits, 220-224,231-236,246,
472-473
resistor-inductor (RL) circuits, 214-220,231-236,246
resistor-inductor-capacitor (RLC) circuits, 266-279
series RLC circuits, 285-289
time constant, 216-217,221-222,246
underdamped voltage, 269,274-277,286-288,297
Negative (acb) phase sequence, 400
Negative feedback, op amps, 147-148
788 Index
Neper frequency (a), 268,286
Neutral terminal, 401
Nodes, 37-38,48,90-91
circuit description by, 37-38,48
defined, 90-91
essential, 91
Node-voltage equation (V
N
), 402-403
Node-voltage method, 90,93-99,106-109,129,332-333
amplifier circuit analysis using, 98-99
circuit analysis using, 90,93-99,106-109,129
defined, 93
dependent sources and, 95-96
equations, 93-94
frequency-domain circuits, 332-333
mesh-current method, comparison of, 106-109
sinusoidal steady-state analysis using, 332-333
special cases for, 96-97

supernode, 97-98
Noninverting-amplifier circuit, 153-154,160-161,164
Nonplanar circuits, 90-91
Norton equivalent circuits, 115,129,329-330
circuit analysis of, 115,129
defined, 115
frequency-domain, 329-330
impedance (Z) in, 329-330
source transformations used for, 115,329-330
Numerator determinant, 706-707
0
Odd-function symmetry, 612-613,616,634
Ohm (O), unit of, 31
Ohm's law, 30-33,47-48,470-471
electrical resistance and, 30-33,47-48
s-domain
applications of, 470^471
Ohmmeter, 145
One-sided Laplace transform, 430-431
Open circuit, 35
Operational amplifiers (op amps), 144-173,560-586,
594-595
bandpass filters, 566-570,585,594
bandreject filters, 570-573,585,594
broadband filters, 567-573,594
Butterworth filters, 578-586,594-595
cascading identical filters, 574-577,594-595
circuit symbol for, 146
currents
(/),146-150

difference-amplifier circuit, 155-159,164
dual in-line package (DIP), 146
equivalent (realistic model), 159-162,164
feedback, 147-148,164
filters,
560-577,594
first-order filters, 560-564
gain (/1), 147,151
high-pass filters, 562-563,585,594
higher-order filters, 573-591,594
input constraints of, 147-148
inverting-amplifier circuit, 150-152,160,164
low-pass filters, 560-562,578-584,594
noninverting-amplifier circuit, 153-154,160-161,164
resistance, 145,162-163
scaling, design of using, 565-566
simplified, 146-159,164
strain gages for, 145,162-163
summing-amplifier circuit, 152-153,164
terminals, 146-150
transfer characteristics of, 146-147,165
voltages (v), 146-150,164
Operational transforms, 431,437-442,459,657-661
addition, 438,658
amplitude modulation, 659
convolution, 659-660
defined, 431
differentiation, 438-439,658
Fourier, 657-661
frequency domain functions, 441,659-660

integration, 439-440,658
Laplace, 431,437-442,459
multiplication by a constant, 437,657
scale changing, 441,659
subtraction, 438,658
time domain functions, 440-441,659-660
translation, 440-441,659
types of, 442,660
Overdamped responses, 269,271-273,282,286,297-298
P
Parallel-connected circuits, 59-61,76,187-189,203
capacitors, 188-189,203
inductors, 187-188,203
resistors, 59-61,76
Parallel RLC circuits, 266-285,297-298
characteristic equation for, 267,269-270,297
circuit symbols for, 266,280
critically damped responses, 269,277-278,283,297-298
direct approach for, 281-282
indirect approach for, 281
natural response, 266-279,297
Neper frequency (a) for, 268
overdamped responses, 269,271-273,282,297-298
resonant radian frequency (wo), 268-269
step response, 280-285,298
underdamped responses, 269,274-277,283,297-298
Parameters of two-port circuits, 680-688,698
Parseval's theorem, 664-672
filter applications of, 667-668
Fourier transform and, 664-672

rectangular voltage pulse application of, 668-670
time-domain energy and, 664-672
Partial fraction expansion, 444^154,459,486-489,506
distinct complex roots of D(s),
AA1-AA9
distinct real roots of D(s), 445-446
improper rational function, 444,453-454
inverse Laplace transforms in, 444-454,459
repeated complex roots of D(s), 451-453
Index 789
repeated real roots of D(s), 449-451
time invariant circuits, 488-489
transfer function H(s) in, 486-489,506
Partitioned matrices, 717-719
Passband frequencies, 524-525,550
Passive circuit elements, 27,176,203,317-320
frequency domain, 317-320
ideal sources, 27
inductors and capacitors as, 176,203
Passive filter circuits, 522-557
bandpass filters, 525,536-545,551
bandreject filters, 525,545-549,551
bandwidth (0), 537,539-540,546-548,551
center (resonant) frequency
(o)
a
),
536-540,546-548,551
cutoff frequency
(<u

c
),
524-525,527-528,538-540,550
defined, 525-526
filtering capabilities of, 525-526
frequency response and, 522
frequency response plots, 524-525
high-pass filters, 524-525,532-536,551
low-pass filters, 524-532,550
magnitude plot, 524
passband, 524-525,550
phase angle plot, 524
pushbutton telephones, 523,550
quality factor (Q), 537,540,546-548,551
relationship between frequency and time domains,
531,545
stopband, 524-525,550
transfer function H(s) for, 531,536,544,549,551
Passive sign convention, 13,176
Path, 38,48,90-91
closed, 38,48
defined, 90-91
Period, sinusoidal sources, 308
Periodic function, 604-607,611-616,619-627,630-632,
634-635
amplitude of, 630-632
average-power calculations with, 623-627,635
defined, 604,607
excitation, 619
Fourier coefficients in, 607,611-627

Fourier series application of, 619-623
phase spectra of, 630-632
root-mean-square (rms) value of, 626-627,635
steady-state response using, 619-627
symmetry, 611-616,634
waveforms, 604-606
Periodic waveforms, 604-606
Phase angle
(</>),
308
Phase angle plots, 524,747-749,755-757
Phase spectrum, Fourier series and, 630-632
Phasor diagrams, 344-346
Phasors, 312-317,347
defined, 311
inverse transform, 314-316,347
transform, 313-317,347
7t-equivalent circuit, 732-735
Pi (77-) interconnection, 71
Pi to tee (77 to T) equivalent circuits, 71-73
Planar circuits, 90-91
Polarity, 15-16,190-192,195-196,204,341-342
algebraic references, 15-16
dot convention for, 190-192,195-196,204,341-342
ideal transformers, 341-342
mutual inductance, 190-192,195-196,204
voltage and current ratios, 341-342
Poles (roots), 454-455,486,741-742,749-751
Bode plots and, 741-742,749-751
complex, 749-751

rational function F(s), 454-455
real, first order, 741-742
transfer function H(s), 486
Ports,
defined, 678
Positive (abc) phase sequence, 400
Potential coil, 415
Power (/?), 14-17,31-32,48,179-181,183-186,203,
410-415,419
algebraic signs of, 15-16
average (P), 410-411,415-417,419
balanced three-phase circuit calculations for, 410-415
capacitors, 183-186,203
complex (S), 411,419
delta (A) loads and, 411-413
energy and, 14-17
inductors, 179-181,203
measurement of, 415-417,419
polarity references, 15-16
resistors and, 31-32,48
wattmeter, 415-417,419
wye (Y) loads and, 410-411,413
Power calculations, 360-397,445^146,452-454,623-627,635
apparent power, 370,386
average (real) power (P), 363-367,373-375,386,
623-627,635
capacitive circuits, 365
complex power
(5"),
370-374,386

heating appliances, 361,384-385
inductive circuits, 364-365
instantaneous power, 362-363,386
maximum power transfer, 378-384,386
periodic functions, 623-627,635
power factor (pf), 365,386
reactive factor (rf), 365,386
reactive power (£?), 363-367,373-375,386
resistive circuits, 364
root-mean-square (rms) value, 368-369
sinusoidal steady-state analysis, 360-397
three-phase circuits, 445-446,452-454
Power factor (pf), 365,386
Power systems, see Balanced three-phase circuits
Primary winder, transformers, 335
Proper rational functions, 444-453,459
Prototype filters, 561-566,594
Proximity switches, 175,200-202
Pushbutton telephone circuits, 523,550
790 Index
Q
Quality factor (£>), 537,540,546-548,551,586-587
active (narrowband) filter circuits, 586-587
passive filter circuits, 537,540,546-548,551
Quarter-wave symmetry, 614-615,634
R
Rational functions F(s), 444-455,459. See also Partial
fraction expansion
defined, 444
improper, 444,453-454,459

inverse Laplace transform using, 444-455,459
partial fraction expansion of, 444-454,459
poles of, 454-455
proper, 444-453,459
zeros of, 454-455
RC circuits, see Resistor-capacitor (RC) circuits
Reactance, 320
Reactive factor (rf), 365,386
Reactive power (0,363-367,373-375,386
Real models, see Equivalent circuits
Real power, see Average power
Real, first order poles and zeros, 741-742
Reciprocal two-port circuits, 687-688,698
Rectangular-pulse waveforms, 604,606
Rectangular voltage pulse, 668-670
Reflected impedance (Z,.), 336,347
Resistance (R), 30-33,47-48,69-70,113-115,145,162-163
conductance (G) and, 31
measurement of, 69-70
Ohm's law, 30-31,47
operational amplifiers (op amps), 145,162-163
resistors as models of, 30-33,47-48
strain gages for, 145,162-163
Thevenin equivalent (Rjh), 113-115
Resistive circuits, 56-87
constant (dc) sources, 56
current-divider, 63,76
current-division analysis, 64-66,76
delta to wye (A to Y) equivalent, 71-73,76
load. 62

measurement of voltage and current in, 66-69
parallel-connected (in parallel), 59-61,76
pi to tee
(IT
to T) equivalent, 71-73
rear window defroster grid, 57,73-75
resistors, 58-61
series-connected (in series), 39,58,76
voltage-divider, 61-62,76
voltage division analysis, 64-66,76
Wheatstone bridge, 69-70,76
Resistor-capacitor (RC) circuits, 212,214,220-224,
229-236,239,246,472-473,530-536
circuit symbol for, 214
cutoff frequency, 533
defined, 212
general solution for responses of, 231-236,246
high-pass filters, behavior of as, 532-536
Laplace transform, using for analysis of, 472-473
low-pass filters, behavior of
as,
530-531
natural response of, 220-224,231-236,246,472^173
qualitative analysis of series, 532-533
quantitative analysis of series, 533-536
s-domain,
472-473
sequential switching, 236,239
step response, 229-236,246
time constant

(T),
221-222,246
unbounded response, 240-241
voltage (v), deriving expression for, 221-222
Resistor-inductor (RL) circuits, 212,214-220,224-228,
236-238,246,526-529
circuit symbol for, 214
current (/), deriving expression for, 214-216
cutoff frequency, 527-529
defined, 212
general solution for responses of, 231-236,246
low-pass filters, behavior of as, 526-529
natural response of, 214-220,231-236,246
qualitative analysis of series, 526-527
quantitative analysis of series, 528-529
sequential switching, 236-238
steady-state response, 217
step response, 224-228,231-236,246
time constant (r), 216-217,246
transient response, 217
Resistor-inductor-capacitor (RLC) circuits, 264-305,
473-476,537-549
bandpass filters, behavior of as, 537-545
bandreject filters, analysis of as, 546-549
characteristic equation for, 267,269-270,297
critically damped voltage response, 269,277-278
cutoff frequency, 538-539,547-548
ignition circuit, 265,294-296
Laplace transform, analysis of using, 473-476
natural response of, 266-279,285-289,297

overdamped voltage response, 269,271-273,297
parallel, 266-279,473-476
qualitative analysis of series, 537-538,546
quantitative analysis of series, 538-544,546-549
.v-domain, 473-476
series,
285-289
step response of, 287-289,297-298,473-475
transient response of, 475-476
underdamped voltage response, 269,274-277,297
Resistors, 30-33,47^18,58-61,76,89,125-128,291-293,
297,317-318,468,506
black box, 58
circuit symbol for, 30
electrical resistance and ,30-33,47-48
feedback, 291-293,297
frequency domain, 317-318
integrating amplifiers with, 291-293,297
Laplace transform used for, 468,506
parallel-connected (in parallel), 59-61,76
power terminals of, 31-32,48
Index 791
s-domain,
468,506
sensitivity analysis, 89,125-128
series-connected (in series), 58,76
voltage to current (v-i) relationships, 317-318
Resonant frequency, see Center frequency (o)
0
)

Resonant radian frequency
(co
()
),
268-269,286
Response, 212-305,429,458-459,472-478,495-497,
505-506,522,661-663
complete, 429,458-459
first-order circuits, 212-263
flashing light circuit, 213,245-246
Fourier transform for, 661-663
frequency, 522
general solutions for, 231-236,246
ignition circuit, 265,294-296
integrating amplifiers, 241-244,246,289-293,297
Laplace transform used for, 429,458-459,472-478,
495-497,505-506
multiple mesh circuits, 476-478
natural, 212,214-224,231-236,246,266-279,285-289,
472^173
parallel RLC circuits, 266-279,473^176
resistor-capacitor (RC) circuits, 212,214,220-224,
229-236,239,246,472-473
resistor-inductor (RL) circuits, 212,214-220,224-228,
236-238,246
resistor-inductor-capacitor (RLC) circuits, 264-305,
473^175
second-order circuits, 264-305
sequential switching, 236-240,246
series RLC circuits, 285-289

sinusoidal, 495-497,505-506,663
steady-state, 217,495^197,505-506,663
step,
212,224-236,246,280-289,297-298,473^178
transfer function and, 495^197,505-506
transient, 217,475-476,506,662
unbounded, 240-241,246
RL circuits, see Resistor-inductor (RL) circuits
RLC
circuits,
.see
Resistor-inductor-capacitor (RLC) circuits
Root-mean-square (rms) value, 309-311,368-369,
626-627,635
periodic functions, 626-627,635
power calculations and, 368-369
sinusoidal sources, 309-311
Roots of complex numbers, 729-730. See also Poles; Zeros
S
.y-domain, 443-455,468-489,506
capacitor in, 469-470,506
circuit analysis in, 470-489,506
circuit symbols for, 468^-70
inductor in, 468-469,506
inverse Laplace transform and, 443-444,506
Kirchhoff s laws and, 471
Laplace transform and, 443-444,468^184,506
mutual inductance in,480-481
Ohm's law in, 470-471
partial fraction expansion in, 444-454,486-489,506

poles (roots) in, 454-455,486
resistor in, 468,506
responses of circuits in, 472-484
superposition, use of in, 482-484
terminal voltage-current equations in, 468-470,506
Thevenin equivalent, use of in, 479-480
transfer function H(s) in, 484-489,506
zeros (roots) in, 454-455,486
Safety, electrical circuits, 25,46-74
Scale-change property, operational transforms, 441,659
Scaling, 564-566,594
frequency (k
f
), 564,594
magnitude
(k,
n
),
564,594
op-amp filter design using, 565-566
Second-order circuits, 264-305
characteristic equation for, 267,269-270,286,297
critically damped responses, 269,277-278,283,286,
297-298
defined, 266,
general solution for responses of, 266-270
ignition, example of, 265,294-296
integrating amplifiers and, 289-293,297
natural response of, 266-279,285-289,297
overdamped responses, 269,271-273,282,286,297-298

parallel RLC, 266-285,297
resistor-inductor-capacitor (RLC) circuits, 264-305
second-order differential equation for, 266-270
series RLC, 285-289,297-298
step response of, 281-289,297
underdamped responses, 269,274-277,283,286-288,
297-298
Second-order differential equations, 266-270
Secondary winder, transformers, 335
Self-inductance, 176-182,193-194,204
Sensitivity analysis, resistors, 89,125-128
Sequential switching, 236-240,246
resistor-capacitor (RC) circuits, 236,239
resistor-inductor (RL) circuits, 236-238
Series-connected (in series) circuits, 37-39,48,58,76,
187-189,203
capacitors, 188-189,203
inductors, 187,203
nodes,
37-39,48
resistors, 58,76
Series RLC circuits, 285-289
characteristic equation of, 286
circuit symbols for, 285-286
critically damped response, 286
natural response, 285-289
Neper frequency (a), 286
overdamped response, 286
resonant radian frequency (w
0

), 286
step response, 285-289,297-298
underdamped responses, 286-288
Short circuit, 35
Siemens (S), unit of, 31
Sifting property, 434
792 Index
Signum function, Fourier transform of, 653
Simultaneous equations, 91-93
current analysis using, 92-93
determination of number of, 91-92
systematic approach using, 92-93
Single-phase equivalent circuits, 403-404,419
Sinusoidal response, 311-312,347,495-497,505-506,663
Fourier transform for, 663
steady-state analysis and, 311-312,347
steady-state component of, 31
surge suppressors, 505
transfer function H(s) and, 495-497,506
transient component of, 312
Sinusoidal sources, 308-311,347,429,458-459
complete circuit response and, 429,458-459
current, 308-309
period, 308
phase angle
(<£),
308
root-mean-square (rms) value of, 309-311
sources, 308-311,347
steady-state analysis, 308-311,347

voltage, 308-310
Sinusoidal steady-state analysis, 306-359,360-397
delta-to-wye (A-to-Y) transformations, 326-328
frequency domain, 312-322,329-343
heating appliances, 361,384-385
household distribution circuit, 307,346
ideal transformer, 338-343,347
impedance (Z), 320,322-332,336,343,347
Kirchhoff's laws, 321-322
mesh-current method, 333-334
node-voltage method, 332-333
Norton equivalent circuit, 329-330
passive circuit elements, 317-320
phasor diagrams for, 344-346
phasors, 312-317,347
power calculations, 360-397
reactance, 320
response, 311-312,347
source transformations, 329-332
sources, 308-311,347
Thevenin equivalent circuit, 329-332
transformers, 334-343,347
voltage-to-current (V-I) relationships, 317-320
Sinusoidal voltage phases, 400-401,419
Source transformations, 71-73,109-116,129,326-332
circuit analysis using, 109-116,129
defined, 110
delta-to-wye (A to Y), 326-328
equivalent circuits, 71-73
frequency domain, 326-332

impedance (Z) and, 326-332
Norton equivalent circuits, 115,329-330
Thevenin equivalent circuit, 115-116,329-332
Sources, 26-29,42-45,47,56,401^102,429,458-459,501-504
active element of, 27
complete circuit response and, 429,458-459
constant (dc),56
controlled, 27
dependent, 26-27,29,42^15,47
ideal current, 26-29,47
ideal voltage, 26-29,47
impulsive, 501-504
independent, 26,29,47
interconnection of, 28-29
Laplace transform and, 429,458-459,501-504
passive element of, 27
sinusoidal, 429,458-459
three-phase voltage, 401-402
Square waves, 604-606,632-634
formation of, 604,606
sinusoid input as, 605,632-634
Steady-state analysis, see Sinusoidal steady-state analysis
Steady-state response, 217,467,495-*97,505-506,619-627.
635,663
direct approach to, 621-623
first-order circuits, 217
Fourier series analysis, 619-627,635
Fourier transform for, 663
Laplace transform analysis and, 467,495-497,505-506
periodic functions used for, 619-627

sinusoidal, 495-497,505-506,663
surge suppressors and, 467,505
transfer function H(s) and, 495-497
Step function Ku(t), Laplace transform, 431-432,459
Step response, 212,224-236,246,297-289,297-298,473^78
critically damped, 283,298
defined, 212,246
direct approach, 281-282
general solution for, 231-236,246
indirect approach, 281
Laplace transform, analysis of using, 473^178
magnetically coupled coils and, 235-236
method of calculating, 232-235
multiple mesh circuit, 476^478
overdamped, 282,298
parallel RLC circuits, 280-285,473^75
resistor-capacitor (RC) circuits, 229-236,246
resistor-inductor (RL) circuits, 224-228,231-236,246
resistor-inductor-capacitor (RLC) circuits, 280-285
series RLC circuits, 285-289
underdamped, 283,288,298
Stopband frequencies, 524-525,550
Summing-amplifier circuit, 152-153,164
Supermesh, 104
Supernode, 97-98
Superposition, 122-125,129,482^184
circuit analysis using, 122-125,129
defined, 122
Laplace transform and, 482-484
Surge suppressors, 467,505

Susceptance, 324
Switches, 175,200-202,236-240,246,467,498-505
arcing, 176
Index 793
capacitor circuit operation, 498^99
first-order circuits, 236-240,246
impulse functions created by, 498-504
impulsive sources for, 501-504
inductor circuit operation, 499-501
Laplace transform and, 467,498-505
proximity, 175,200-202
sequential switching, 236-240,246
surge suppressors, 467,505
Symmetry, 611-616,634,688,698
even-function, 611-612,634
Fourier coefficients, effects of on, 611-616,634
half-wave, 613-614,634
odd-function, 612-613,616,634
quarter-wave, 614-615,634
reciprocal two-port circuits, 688,698
T
T-equivalent
circuit, 731-732
Tee (T) interconnection, 71
Telephone line frequency response, 645,672
Terminals, 30-33,35-36,146-150,164,680
circuit connections, 35-36
current (/) input constraints, 147-148,164
operation amplifiers (op amps), 146-150,164
resistor power and, 31-32

two-port circuits, 680
variables (voltage and current), 146-147
voltage (v) input constraints, 147-148,165
Terminated two-port circuits, 689-693
Thevenin equivalent circuits, 113-119,129,329-332,479-480
amplifier circuit using, 118-119
circuit analysis of, 113-119,129
defined, 113
finding equivalent of, 114-115
frequency-domain, 329-332
impedance (Z) in, 329-332
independent sources used for, 117-118
Laplace transform, analysis of using, 479^180
resistance source (/?jh), 113-115
s-domain,
use of in, 479-480
source transformations used for, 115-116,329-332
voltage source (Vn,), 113-115
Three-phase circuits, see Balanced three-phase circuits
Time constant
(T),
216-217,221-222,246
resistor-capacitor (RC) circuits, 221-222,246
resistor-inductor (RL) circuits, 216-217,246
Time domain, 440-443,531,545,648-650,659-660,664-672
convolution in, 659-660
energy, 664-671
Fourier transform and, 648-650,659-660,664-672
frequency domain, relationship to, 531,545
integral for, 648-650,672

integrodifferential equations for, 442-443
Laplace transform and, 440-443
operational transforms, 440-441,659-660
Parseval's theorem for, 664-672
passive-filter circuits and, 531,545
translation in, 440-441,659
Time invariant circuits, 488-489,506
Transducers, 145
Transfer function H(s), 484-497,506,531,536,544,549,
551,578-579
active-filter circuits, 578-579
Butterworth filters, 578-579
circuit analysis, 488^197,506
convolution integral and, 489-495,506
defined, 484
Laplace transform circuit analysis and, 484-497,506
memory and, 494-495
partial fraction expansion, use of in, 486-489,506
passive-filter circuits and, 531,536,544,549,551
poles and zeros of, 486
steady-state sinusoidal response and, 495^-97,506
time invariant circuits, 488-489,506
weighting function, 494-495
Transformation, see Source transformation
Transformers, 334-343,347,731-738
defined, 335
dot convention for, 341-342
equivalent circuits and, 731-738
frequency domain and, 334-343
ideal, 335,338-343,347,731-738

limiting values of, 338-340
linear, 335-338,347
primary and secondary winders for, 335
reflected impedance (Z
r
), 336,347
sinusoidal steady-state analysis, 334-343,347
voltage and current ratios. 340-342
Transient response, 217,475-476,506,662
circuit analysis of, 212
Fourier transform for, 662
Laplace transform for, 475-476,506
Translation, operational transforms for, 440-441,659
Transmission parameters, two-port circuits, 683
Triangular waves, 604,606
Trigonometric form of Fourier series, 617-618,634
Trigonometric identities, 759
Twin-T notch filter, 588-589
Two-port circuits, 678-703
analysis of, 689-693
black box amplifier, 679,697
conversion of parameters, 684-686
hybrid parameters, 683
interconnected, 694-697
parameters of, 680-688,698
reciprocal, 687-688,698
symmetric, 688,698
terminal equations for, 680
terminated, 689-693
transmission parameters, 683

z parameters, 681,689-692
Two-wattmeter method, three-phase circuits, 415^117,419
794 Index
U
Unbounded response, 240-241,246
Underdamped responses, 269,274-277,283,286-288,
297-298
parallel RLC circuits, 269,274-277,283,297-298
series RLC circuits, 286-288
Unilateral Laplace transform, 430-431
Unit doublet (moment function), 435
Unit impulse function 8(/), 433-434,459
Unit step function Ku(t), 431,459,654
Laplace transform of, 431,459,654
Fourier transform of, 654
V
Variable-parameter function, 433-434
Voltage (v), 11-13,26-29,38,40-41,47,66-69,113-115,
146-150,164,176-177,184-186,203,221-222,
308-310,347,400-405,419,468-470,506
a-, b-, and c-phase, 400,419
capacitors, 183-186,203,469-470,506
defined, 11-12
electric charge and, 11-13
gain (,4), 147
inductors, 176-177,203,468-469,506
input constraints, 147-148,165
Kirchhoff s law (KVL), 38,40-41
line,
404-405

measurement of, 66-69
negative (acb) phase sequence, 400
node-voltage equation (V
N
), 402^103
operational amplifiers (op amps), 146-150,164
positive (abc) phase sequence, 400
RC circuits, deriving expression for, 221-222
reference direction, 13
resistors, 468,506
s-domain
equations for, 468-470,506
sinusoidal phases, 400-401,419
sinusoidal source, 308-310,347
sources, 26-29,47,401-402
terminal variables, 146
Thevenin equivalent (^
Th
), 113-115
three-phase, 401^105
transfer characteristics of, 146-147,164
Voltage-divider circuits, 61-62,76
Voltage division circuit analysis, 64-66,76
Voltage ratios, transformers, 340-342
Voltage to current (v-i) relationships, 176-177,183,317-320
capacitors, 183,319-320
frequency domain, 317-320
impedance (Z) of, 320
inductors, 176-177,318-319
reactance of, 320

resistors, 317-318
Volt-amp reactive (VAR), unit of, 365,386
Voltmeter, 66-67,76
W
Watt (W), unit of, 365,386
Wattmeter, defined, 415,419
Waveforms, 604-606
Wavelength (y), defined, 7
Weighting function, transfer function concept of, 494-495
Wheatstone bridge, 69-70,76
Wye (Y) connected loads, 410^111,413,419
Wye (Y) interconnection, 71
Wye-delta (Y-A) circuit, analysis of, 407-409
Wye-wye (Y-Y) circuit, analysis of, 402^407
Z
z parameters, two-port circuits, 681,689-692
Zero frequency, 530
Zeros (roots), 454-455,486,741-742,749-751
Bode plots and, 741-742,749-751
complex, 749-751
rational function F(s), 454-455
real, first order, 741-742
transfer function H(s), 486
Periodic Functions
/(0
A -
Triangular Wave
7/2 7 37/2
Half-wave rectified sine
/(0

/i "
0
A
T
27
Square Wave
7/2 7 37/2
Full-wave rectified sine
27
Fourier Series
/(o
=
— S
17
«=1.3,5.
Triangular wave
sin
nojQt
A A . 2A ^, cos /10),,(
/(0 =
—
+ T
sm
w
<>'
^ ~J—r
77
* ^ /»=2.4,6. " ~~ 1
Half-wave rectified sine
/YA

4/1*1,
/(0 = — 2i r,
sm IH0
"
1
/(0
2 A
«=1.3,5,
4/1 ^ cos no)
0
t
Square wave
TT TT f=\ (4/r - 1)
Full-wave rectified sine