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 K K ( 0 , 4 3 1 , 4 5 9 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
Trang 2Loads, 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 (<wc), 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
Trang 3Neper 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 (VN), 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
Trang 4repeated 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 (<uc), 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
Trang 5Q
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
Trang 6s-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 (w0), 286 step response, 285-289,297-298 underdamped responses, 286-288 Short circuit, 35
Siemens (S), unit of, 31 Sifting property, 434
Trang 7Signum 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
Trang 8capacitor 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 (Zr), 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
Trang 9U
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 (VN), 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 (^T h), 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
Trang 10/(0
A
-Triangular Wave
7/2 7 37/2 Half-wave rectified sine
/(0
/ i "
0
A
Square Wave
7/2 7 37/2 Full-wave rectified sine
27
Fourier Series
/(o = — S
1 7 «=1.3,5
Triangular wave
sin nojQt A A 2A ^ , cos /10),,(
/(0 = — + T sm w<>' ^ ~ J — r
7 7 * ^ /»=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