Index

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Index

Note: Page numbers followed by f or t represent figures or tables respectively.

A

ABCD parameters, 866 Abc sequence, 505, 505f ac (alternating current), 7–8, 7f, 368, 369 ac bridge circuit, 396–400 Acb sequence, 505, 505f ac circuits, 369 AC power analysis, 455–486 apparent power, 468–471 average power, 457–462 complex power, 471–475 conservation of ac power, 475–478 effective value, 465–466 electricity consumption cost, 484–486 instantaneous power, 456–457 maximum average power transfer, 462–465 power factor, 469–471 power factor correction, 479–481 power measurement, 481–484 rms value, 466–468 Active element, 14 Active filters, 635, 640–646 AC voltage, 10 Additivity property, 127 Admittance, 385–387 Admittance parameters, 857–860 Air-core transformers, 566 Alexander, Charles K., 125, 311 Alternating current (ac), 7–8, 7f, 368, 369 American Institute of Electrical Engineers (AIEE), 13 Ampere, Andre-Marie, 7 Amplitude modulation (AM), 820–821, 838–840 Amplitude-phase form, 761 Amplitude spectrum, 762, 814 Analog computers, 235–238 Apparent power, 468–471 Audio transformers, 566f Automobile ignition circuit, 296–297, 296f Automobile ignition system, 351–353 Autotransformers, 579–582, 579f Average power, 780–783 Axial lead inductor, 224f

B

Bacon, Francis, 3 Bailey, P. J., 251 Balanced, 156 Balanced delta-delta connection, 512–514 Balanced delta-wye circuit, 391 Balanced delta-wye connection, 514–517 Balanced load, 506 Balanced networks, 53 Balanced three-phase voltages, 503–506 Balanced wye-delta connection, 510–512 Balanced wye-wye connection, 507–510 Band-pass filters, 636, 636f, 637–638, 641–643, 642f Band-reject filter, 643–644, 643f Band-stop filters, 636, 636f, 638 Bandwidth, 629 Bandwidth of rejection, 638 Bardeen, John, 106 Barkhausen criteria, 437–438 Bell, Alexander Graham, 616 Bell Laboratories, 106, 143 Binary weighted ladder, 194 Bipolar junction transistor (BJT), 105–106 Bode plots, 615, 617–627 Branch, 35, 35f Brattain, Walter, 106 Braun, Karl Ferdinand, 17 Break frequency, 619 Brush Electric Company, 13 Bunsen, Robert, 38 Buxton, W. J. Wilmont, 79 Byron, Lord, 173

C

Capacitance, 215 Capacitance multiplier, 435–437, 435f Capacitors, 214–223. See also Inductors analog computer, 235–238 characteristics, 230 current-voltage relationship, 216–217 defined, 214 differentiator, 233–234 integrator, 232–233

I-2 Index

Capacitors (continued) properties, 232 series and parallel, 220–223 types, 216 Careers communications systems, 811 in computer engineering, 251 in control systems, 611 in education, 851–852 in electromagnetics, 553 in electronic instrumentation, 173 in electronics, 79 engineering, 311 in power systems, 455 in software engineering, 411 Cascaded networks, 875 Cascaded op amp circuits, 189–192 Cathode-ray tube (CRT), 16, 17f Cesium, 38 Characteristic equation, 318 Charge. See Electric charge Chassis ground, 81, 81f Choke, 224 Circuit analysis, 720–723 Circuit applications, 776–780, 831–833 Circuit element models, 715–720 Circuit theorems, 125–158 linearity, 126–127 maximum power transfer, 148–150 Norton’s theorem, 143–148 with PSpice, 150–153 resistance measurement, 156–158 source modeling, 153–155 source transformation, 133–136 superposition principle, 129–133 Thevenin’s theorem, 137–143, 147–148 Closed-loop gain, 176 Coefficient of coupling, 563–564 Coil, 224 Common-base current gain, 107 Common-emitter current gain, 107 Communication skills, 125 Communications systems, careers in, 811 Complete response, 273–274 Completing the square, 690 Complex amplitude spectrum, 784 Complex conjugate, A–12 Complex numbers, 374, A–9 to A–15 Complex phase spectrum, 784 Complex poles, 690–691 Complex power, 471–475 Computer engineering careers, 251 Conductance, 33, 386 Conductance matrix, 99 Conductively coupled, 554 Conservation of ac power, 475–478 Consumption cost, electricity, 484–486 Control systems, career in, 611

Convolution, 823–826 Convolution integral, 695–703 Copper wound dry power transformer, 566f Corner frequency, 619 Cramer’s rule, 80, A to A–4 Critically damped case source-free parallel RLC circuits, 325 source-free series RLC circuit, 319–320 step response of parallel RLC circuits, 335 step response series RLC circuits, 330 Crossover network, 659–661, 660f Current divider, 46 Current-division principle, 390 Cutoff frequency, 636–637 Cyclic frequency, 370

D

DAC (digital-to-analog converter), 194–195, 194f, 195t Damped frequency, 321 Damped natural frequency, 321, 352 d’Arsonval meter movement, 60, 60f Darwin, Francis, 213 Datum node, 81 dc (direct current), 7–8, 7f, 368 DC meters, design of, 59–62 DC transistor circuits (application), 105–107 DC voltage, 10 Decibel scale, 615–617 Definite integrals, A–19 to A–20 Delay circuits, 291–293 Delta function, 265 Delta to wye conversion, 52–53, 390 Demodulation, 838 Derivatives, A–17 to A–18 Deschemes, Marc-Antoine Parseval, 781 Difference op amp, 185–188, 185f Differential equations, 674 Differentiator, 233–234 Digital meter, 61–62 Digital-to-analog converter (DAC), 194–195, 194f, 195t Dinger, J. E., 411 Direct current (dc), 7–8, 7f, 368 Dirichlet, P. G. L., 760 Dirichlet conditions, 760 Discrete Fourier Transform (DFT), 789–790 Dot convention, 557–558 Driving-point impedances, 854 Duality, 348–350, 823

E

Earth ground, 81 Edison, Thomas Alva, 13, 57, 368, 502, 503 Education, careers in, 851–852 Effective value, 465–466 Electrical engineer, 79

Electrical isolation, 579, 590 Electrical lighting systems (application), 57–58 Electric charge, 6 Electric circuits, 4–5, 4–5f elements in, 14–16 Electric current, 6–7, 6f flow of, 8, 8f Electricity bills (application), 18, 18t Electricity consumption cost, 484–486 Electrolytic capacitors, 216, 216f Electromagnetic induction, 215 Electromagnetics, careers in, 553 Electronic instrumentation, career in, 173 Electronics, 79 Elements, 4, 14–16 Energy, 10–12 Energy sink, 59 Energy source, 59 Equivalent capacitance of parallel-connected capacitors, 221 of series-connected capacitors, 222 Equivalent conductance, 45 Equivalent impedance, 388–390 Equivalent inductance of parallel inductors, 229 of series-connected inductors, 229 Equivalent resistance of parallel resistors, 45 of series resistors, 44 Ethics, 501 Euler’s formula, A–14 to A–15 Euler’s identity, 321, 783 Even symmetry, 766–768 Excitation, 126 Exponential form, A–10 Exponential Fourier series, 783–789 External electromotive force (emf), 9

F

Faraday, Michael, 215, 455 Faraday’s law, 572 Fast Fourier Transform (FFT), 790–791 Field-effect transistors (FETs), 105–106 Film capacitors, 216, 216f Filters active, 635, 640–646 band-pass, 636, 636f, 637–638 band-stop, 538, 636, 636f defined, 635 design of, 795–798 high-pass, 636, 636f, 637 low-pass, 636–637, 636f passive, 635–640 First-order circuits, 251–297 automobile ignition circuit, 296–297, 296f defined, 252

delay circuits, 291–293 natural response, 253–254 op amp, 282–287 photoflash unit, 293–294 relay circuits, 294–296 singularity functions, 263–271 source-free RC circuit, 253–257 source-free RL circuit, 257–263 step response of an RC circuit, 271–277 step response of an RL circuit, 278–282 time constant, 254–255 transient analysis with PSpice, 287–291 First-order differential equation, 253 First-order high-pass filters, 641 First-order low-pass filter, 641 Fixed capacitor, 216 Fixed resistors, 32, 32f Forced response, 273 Fourier, Jean Baptiste Joseph, 758 Fourier analysis, 369, 760 Fourier coefficients, 759 Fourier cosine series, 767 Fourier series, 757–798 average power, 780–783 circuit applications, 776–780 defined, 759 exponential, 783–789 filters, 795–798 Gibbs phenomenon, 764 Parseval’s theorem, 781 PSpice, 789–794 RMS value, 780–783 sinc function, 785 sine, 769 spectrum analyzers, 795 symmetry considerations. See Symmetry trigonometric series, 759–766 Fourier theorem, 759 Fourier transform, 811–841 amplitude modulation, 820–821, 838–840 circuit applications, 831–833 convolution, 823–826 defined, 812–818 duality, 823 frequency shifting, 820–821 inverse, 814 linearity, 818 pairs, 827t Parseval’s theorem, 834–837 reversal, 822–823 time differentiation, 821–822 time integration, 822 time scaling, 818–819 time shifting, 819–820 vs. Laplace transform, 837 Franklin, Benjamin, 6, 611 Frequency differentiation, 682 Frequency domain, 378, 387–388

I-4 Index

Frequency mixer, 656 Frequency of rejection, 638 Frequency response, 611–661 active filters, 640–646 bode plots, 617–627 crossover network, 659–661, 660f decibel scale, 615–617 defined, 612 MATLAB, 653–655 parallel resonance, 632–635 passive filters, 635–640 radio receiver, 655–657 scaling, 646–649 series resonance, 627–632 touch-tone telephone, 658–659 transfer function, 612–615 using PSpice, 650–653 Frequency scaling, 648–649 Frequency shift/shifting, 679–680, 820–821 Frequency spectrum, 762 Full-wave rectified sine, 772 Fundamental angular frequency, 759

G

Ganged tuning, 656 Gate function, 267 Generalized node, 87 General second-order circuits, 337–341 Gibbs, Josiah Willard, 764 Gibbs phenomenon, 764 Ground, 81, 81f Ground-fault circuit interrupter (GFCI), 540 Györgyi, Albert Szent, 757

H

Half-power frequencies, 629 Half-wave rectified sine, 772 Half-wave symmetry, 770–776 Heaviside’s theorem, 689 Henry, Joseph, 224, 225 Herbert, G., 501 Hertz, Heinrich Rudorf, 370 Heterodyne circuit, 656 Higher potential, in resistor, 81 High-pass filters, 636, 636f, 637 High-Q circuit, 630 Homogeneity property, 126 Hybrid parameters, 860–865 Hyperbolic functions, A–17 Hysteresis, 375

I

Ibn, Al Halif Omar, 455 Ideal autotransformers, 579–582, 579f Ideal dependent/controlled source, 15, 15f Ideal independent source, 14, 15f Ideal op amp, 178–179, 178f Ideal transformers, 571–578 IEEE (Institute of Electrical and Electronics Engineers), 13, 79, 251, 375, 554 Imaginary part, A–9 Immittance parameters, 857 Impedance, 385–387 combinations, 388–394 Impedance matching, 574, 591 Impedance parameters, 853–856 Impedance triangle, 473, 473f Indefinite integrals, A–18 to A–19 Inductance, 224 Inductance, mutual, 555–561 Inductive, 385 Inductors, 224–231, 224f. See also Capacitors analog computer, 235–238 characteristics, 230 defined, 224 differentiator, 233–234 integrator, 232–233 linear, 225 nonlinear, 225 parallel, 228–231 properties, 232 series, 228–231 Inspection, of circuit, 98–99 Instantaneous power, 11, 456–457 Institute of Electrical and Electronics Engineers (IEEE), 13, 79, 251, 375, 554 Institute of Radio Engineers (IRE), 13 Instrumentation amplifier (IA), 185, 187–188, 188f, 196–197, 196f Integral transform, 812 Integrator, 232–233 Integrodifferential equations, 703–705 International Electrical Exhibition, 13 International System of Units (SI), 5, 5t Inverse Fourier transform, 814 Inverse hybrid parameters, 861 Inverse Laplace transform, 676, 688–695 Inverse transmission, 867 Inverting op amp, 179–181 Isolation transformer, 573

J

Jefferson, Thomas, 851

K

Kirchhoff, Gustav Robert, 38 Kirchhoff’s current law (KCL), 37–39, 81–82, 97, 412–415 Kirchhoff’s voltage law (KVL), 39–40, 87, 92, 96, 387–388, 415–419

Knowledge capturing integrated design environment” (KCIDE), see the web site associated with this book.

L

Lagging power factor, 469 Lamme, B. G., 368 Laplace, Pierre Simon, 674 Laplace transform, 673–705, 714 circuit analysis, 720–723 circuit element models, 715–720 convolution integral, 695–703 defined, 675 Fourier transform vs., 837 frequency differentiation, 682 frequency shift, 679–680 integrodifferential equations, 703–705 inverse, 676, 688–695 linearity, 678 network stability, 735–738 network synthesis, 738–743 one-sided, 676 properties of, 677–688, 685t sampling, 840–841 scaling, 678 state variables, 728–735 steps in applying, 715 time differentiation, 680 time integration, 681–682 time periodicity, 682–684 time shift, 678–679 transfer functions, 724–728 two-sided, 676 Law of conservation of charge, 6 Law of conservation of energy, 11 Law of cosines, A–16 Law of sines, A–16 Law of tangents, A–16 Leading power factor, 469 Least significant bit (LSB), 194 L’Hopital’s rule, 786, A–20 Lighting systems (application), 57–58 Linear capacitor, 216 Linear circuit, 127, 127f Linearity, 126–127, 678, 818 Linear resistor, 33, 33f Linear transformers, 565–571, 566f Line spectra, 786 Line-to-line voltages, 508 Load, 59, 137 Loading effect, 154 Local oscillator, 656 Loop analysis. See Mesh analysis Loops, 35f, 36 Loosely coupled, 564 Lower potential, in resistor, 81 Low-pass filters, 636–637, 636f

M

Magnetically coupled circuits, 553–594 energy in coupled circuit, 562–565 ideal autotransformers, 579–582 linear transformers, 565–571 mutual inductance, 555–561 power distribution, 593–594 PSpice, 584–589 three-phase transformers, 582–584 Magnitude scaling, 647 Maple, 82, 760 Mathcad, 82, 760 MATLAB, 80, 653–655 Maximum average power transfer, 462–465 Maximum power theorem, 148 Maximum power transfer, 148–150 Maxwell, James Clerk, 370, 554 Megger tester, 156 Mesh, defined, 91 Mesh analysis, 91–93 with current sources, 96–98 by inspection, 98–99 KVL and, 415–419 nodal analysis vs., 102–103 steps, 92 Mesh-current method. See Mesh analysis Method of algebra, 691 Milliohmmeter, 156 Morse, Samuel F. B., 62 Most significant bit (MSB), 194 Multidisciplinary teams, 367 Multimeter, 59 Mutual inductance, 555–561 Mutual voltage, 556

N

Natural frequencies, 319 Natural response, 253–254 Negative current flow, 8, 8f Negative sequence, 505, 505f Neper frequency, 319 Network function. See Transfer function Network stability, 735–738 Network synthesis, 738–743 Nodal analysis by inspection, 98–99 KCL and, 412–415 steps, 80–82 with voltage sources, 86–87 vs. mesh analysis, 102–103 Nodes, 35–36, 35f Node-voltage method, 80–82 Noninverting op amp, 181–183 Nonlinear capacitor, 216 Nonlinear resistor, 33, 33f

I-6 Index

Nonplanar circuit, 91, 91f Norton, E. L., 143 Norton equivalent circuits, 424–428, 424f Norton’s theorem, 143–148 Notch filter, 643–644, 643f npn transistors, 106–107, 106f Nyquist frequency, 841 Nyquist interval, 841

O

Odd symmetry, 768–770 Ohm, Georg Simon, 31 Ohm’s law, 30–34 One-sided Laplace transform, 676 Open circuit, 32, 32f Open-circuit impedance parameters, 854 Open delta, 583 Open-loop voltage gain, 176 Operational amplifier (op amp), 173–197 ac circuit, 429–430 cascaded circuits, 189–192 defined, 174 difference, 185–188, 185f feedback, 176 first-order circuits, 282–287 ideal, 178–179, 178f instrumentation amplifier, 185, 187–188, 188f, 196–197, 196f inverting, 179–181 noninverting, 181–183 parameters, range of, 176t PSpice, analysis with, 192–193 second-order circuits, 342–344 summing, 183–185, 183f terminals, 175 Oscillators, 437–439 Overdamped case source-free parallel RLC circuits, 325 source-free series RLC circuit, 319 step response of parallel RLC circuits, 335 step response series RLC circuits, 330

P

Parallel, electric circuit, 36
Parallel capacitors, 220–223
Parallel inductors, 228–231
Parallel resistors, 44–47, 44f
Parallel resonance, 632–635
Parallel RLC circuits
  source-free, 324–329
  step response, 334–337
Parameters
  ABCD, 866
  admittance, 857–860

hybrid, 860–865 immittance, 857 impedance, 853–856 inverse transmission, 867 relationships between, 870–873 short-circuit admittance, 857 transmission, 865–869 Parseval’s theorem, 781, 834–837 Partial fraction expansion, 688 Passive elements, 14 Passive filters, 635–640 Passive sign convention, 11 Period, 369, 370 Periodic function, 370, 759 Phase sequence, 505 Phase-shifting circuit, 394–396 Phase spectrum, 762, 814 Phase voltages, 504 Phasor diagram, 377, 378f Phasor relationships for circuit elements, 383–384 Phasors, 374–382. See also Sinusoids Photoflash unit, 293–294 Planar circuit, 91, 91f pnp transistors, 106, 106f Poisson, Simeon, 674 Polar form, A–9 Poles, 613, 618 complex, 690–691 first-order, 688–689 repeated, 689–690 Polyester capacitors, 216, 216f Polyphase, 502 Port, 852 Positive current flow, 8, 8f Positive sequence, 505, 505f Potential difference. See Voltage Potentiometer (pot), 32, 32f, 59, 59f Power, 10–12 Power distribution system, 593–594, 593f Power factor, 469–471 Power factor angle, 469 Power factor correction, 479–481 Power grid, 593 Power measurement, 481–484 Power spectrum, 785 Power systems, careers in, 455 Power triangle, 473, 473f Primary winding, 566 Principle of current division, 46 Principle of voltage division, 44 Problem solving technique, 19–20 PSpice, 80 ac analysis using, 431–435 analysis of RLC circuits, 344–347 circuit analysis with, 103–105 circuit theorems with, 150–153 Fourier analysis, 789–794

frequency response, 650–653 magnetically coupled circuits, 584–589 operational amplifier analysis with, 192–193 three-phase circuits, 527–532 transient analysis with, 287–291 two-port networks, 279–282

Q

Quadratic formulas, A–16 Quadrature power, 472 Quality factor, 629–630 Quattro Pro, 82

R

Radio receiver, 655–657 Ragazzini, John, 174 RC circuits delay, 291–293 source-free, 253–257 step response, 271–277 RC phase-shifting circuits, 394–396 Reactance, 385 Reactive load, 459 Reactive power, 472 Real part of complex numbers, A–9 Reciprocal network, 854 Rectangular form of complex numbers, A–9 Rectangular pulse train, 772 Reference node, 81, 81f Reflected impedance, 567, 574 Relay circuits, 294–296 Relay delay time, 295 Residential wiring, 538–540, 539f Residue method, 689 Residues, 689 Resistance, 30, 32, 385 equivalent, 44 measurement, 156–158 Resistance bridge, 156 Resistance matrix, 99 Resistive load, 459 Resistivity, 30, 31t Resistors characteristics, 230 fixed, 32, 32f linear, 33, 33f nonlinear, 33, 33f Ohm’s law, 30–34 parallel, 44–47, 44f series, 43–44 variable, 32, 33f Resonance, 627–628 Resonant frequency, 319, 628 Resonant peak, 627

Response, 126 Reversal, 822–823 Right-hand rule, 554 RLC circuits source-free parallel, 324–329 source-free series, 317–324 step response of parallel, 334–337 step response of series, 329–334 RL circuits, 257–263 RMS value, 466–468, 780–783 Rolloff frequency, 637 Rotor, 503 Rubidium, 38

S

Sampling, 266, 840–841 Sampling frequency, 840 Sampling function, 785 Sampling interval, 840 Sampling rate, 840 Sampling theorem, 795 Sawtooth function, 268 Sawtooth wave, 772 Scaling, 646–649, 678 frequency, 648–649 magnitude, 647 Schockley, William, 106 Scott, C. F., 368 Secondary winding, 566 Second-order circuits, 311–354 automobile ignition system, 351–353 characteristic equation, 318 defined, 312 duality, 348–350 general, 337–341 initial/final values, 313–317 op amp circuits, 342–344 PSpice, 344–347 second-order differential equation, 318 smoothing circuits, 353–354 source-free parallel RLC circuits, 324–329 source-free series RLC circuits, 317–324 step response of parallel RLC circuit, 334–337 step response of series RLC circuit, 329–334 Second-order differential equation, 318 Self-inductance, 555 Series, electric circuit, 36 Series capacitors, 220–223 Series inductors, 228–231 Series resistors, 43–44 Series resonance, 627–632 Series RLC circuits source-free, 317–324 step response, 329–334 Short circuit, 32, 32f

I-8 Index

Short-circuit admittance parameters, 857 Sifting, 266 Signal, 9 Simultaneous equations, A to A–4 Sinc function, 785 Single-phase three-wire system, 502, 502f Singularity functions, 263–271 Sinusoidal steady-state analysis, 411–439 capacitance multiplier, 435–437, 435f mesh analysis, 415–419 nodal analysis, 412–415 Norton equivalent circuits, 424–428, 424f op amp ac circuits, 429–430 oscillators, 437–439 PSpice, 431–435 source transformation, 422–424 superposition theorem, 419–422 Thevenin equivalent circuits, 424–428, 424f Sinusoidal steady-state response, 369 Sinusoids, 368–374 SI units, 5, 5t Smoothing circuits, 353–354 Software engineering, career in, 411 Solenoidal wound inductor, 224f Source-free parallel RLC circuits, 324–329 Source-free RC circuit, 253–257 Source-free RL circuit, 257–263 Source-free series RLC circuits, 317–324 Source modeling, 153–155 Source transformation, 133–136, 422–424 Spectrum analyzers, 795 Sprague, Frank, 13 Square wave, 772 Stability, network, 735–738 Standard form, 618 State variables, 728–735 Stator, 503 Steady-state response, 274 Steinmetz, Charles P., 713 Steinmetz, Charles Proteus, 374, 375 Step-down autotransformer, 579, 579f Step-down transformers, 573 Step response of RC circuit, 271–277 of RL circuit, 278–282 Step response of parallel RLC circuits, 334–337 Step response series RLC circuits, 329–334 Step-up autotransformer, 579–580, 579f Step-up transformer, 573 Storage elements, 214 Strength, of impulse function, 265 Summing op amp, 183–185, 183f Superheterodyne receiver, 656 Supermesh, 96 Supernode, 87 Superposition, 129–133 Superposition integral, 698

Superposition theorem, 419–422 Susceptance, 386 Switching functions. See Singularity functions Symmetrical network, 854 Symmetry even, 766–768 half-wave, 770–776 odd, 768–770 System, 714 System design, 213

T

Terminals, 175 Tesla, Nikola, 368, 503 Thevenin, M. Leon, 137 Thevenin equivalent circuit, 137, 137f Thevenin equivalent circuits, 424–428, 424f Thevenin’s theorem, 137–143, 147–148 Thompson, Elihu, 13 Three-phase circuits, 501–540 balanced delta-delta connection, 512–514 balanced delta-wye connection, 514–517 balanced three-phase voltages, 503–506 balanced wye-delta connection, 510–512 balanced wye-wye connection, 507–510 importance of, 502–503 power in balanced system, 517–523 power measurement, 533–538 PSpice, 527–532 residential wiring, 538–540, 539f unbalanced three-phase systems, 523–526 Three-phase transformers, 582–584 Three-stage cascaded connection, 189, 189f Three-wattmeter method, 533, 533f Tightly coupled, 564 Time constant, 254–255 Time differentiation, 680, 821–822 Time integration, 681–682, 822 Time periodicity, 682–684 Time scaling, 818–819 Time shift/shifting, 678–679, 819–820 Toroidal inductor, 224f Total response, 273 Touch-tone telephone, 658–659 Transfer functions, 612–615, 724–728 Transfer impedances, 854 Transformation ratio, 572 Transformer bank, 582 Transformers, 555 air-core, 566 ideal, 571–578 isolation, 573 as isolation device, 590–591 linear, 565–571, 566f as matching device, 591–592 step-down, 573

Index I-9

step-up, 573 three-phase, 582–584 Transient analysis with PSpice, 287–291 Transient response, 274 Transistor, 105–107, 106f Transistor circuits, 882–887 Transmission parameters, 865–869 Triangular wave, 772 Trigonometric Fourier series, 759–766 Trigonometric identities, A–16 to A–17 Turns ratio, 572 TV picture tube, 16, 17f Two-phase three-wire system, 502f Two-port networks, 851–891 admittance parameters, 857–860 defined, 852 hybrid parameters, 860–865 impedance parameters, 853–856 interconnection of networks, 873–879 inverse transmission parameters, 867 PSpice, 879–882 reciprocal network, 854 relationships between parameters, 870–873 symmetrical network, 854 transistor circuits, 882–887 transmission parameters, 865–869 Two-sided Laplace transform, 676 Two-wattmeter method, 533–534, 533f

U

Unbalanced three-phase systems, 523–526 Undamped natural frequency, 319 Underdamped case source-free parallel RLC circuits, 325 source-free series RLC circuit, 321–322 step response of parallel RLC circuits, 335 step response series RLC circuits, 330

United States Electric Lighting Company, 13 Unit impulse function, 265, 265f Unit ramp function, 266, 266f Unit step function, 264 Unity gain amplifier, 182 Unloaded source, 154

V

Variable capacitor, 216 Variable resistors, 32, 33f Volta, Alessandro Antonio, 10 Voltage, 9–10, 9f Voltage divider, 44 Voltage-division relationship, 389 Voltage drop, 9, 9f Voltage follower, 182, 182f Voltage rise, 9, 9f Volt-ampere reactive (VAR), 472 Volt-ohm meter (VOM), 59

W

Watson, James A., 713 Watson, Thomas A., 616 Wattmeter, 481–482, 482f, 533 Westinghouse, George, 368 Weston, Edward, 13 Wheatstone, Charles, 156 Wheatstone bridge, 156 Wien-bridge oscillator, 437, 437f Winding capacitance, 226 Winding resistance, 226 Wye-delta transformations, 51–53, 390

Z

Zeros, transfer function, 613, 618 Zworykin, Vladimir K., 17