ac (alternating current) signal, see waveforms Across variable (voltage), 8 ADC, see Analog-to-digital converter Active circuit, 151 Active device: dependent source, 151 OP AMP, 171 transistor, 168 transducer, 203 Active filters: second-order BP 730, BS 732 basics, 720 Butterworth, LP 745, HP 763 Chebyshev, LP 751, HP 769 design, 721 First-Order Cascade, LP 741, HP 762 Sallen-Key, LP 721, HP, 726 Adapter, 300Ω to 75Ω, photo, 129 Additive property (sinusoids), 250 Additivity property (superposition), 98, 102 Admittance (Y): Laplace, 503 matrix [y], WC6 parallel connection, 400, 509 parameters, WC5 phasors, 391 transfer, 558 two-port y-parameters, WC6 Aliasing, 712 Ampere (A) (unit), 5 Ampère, André-Marie, 1 Amplifier: differential, 187, 192 ideal OP AMP model, 173 inverting, 181 inverting summer, 184 instrumentation, 192, 212 logarithmic, 224 noninverting, 175 noninverting summer, 185 real OP AMPs (GBW), 628 subtractor-double, 190 subtractor-single, 187 transistor, 168 voltage follower, 179 Amplitude: descriptors, 260 functions, 235, 240, 245 Amplitude spectrum, 695 Analog computer, 294 Analog-to-digital converter: flash, 216, photo 217 full-scale input, 216 resolution, 216 sample-hold, 281, photo 281 Analysis, definition, 2 Angular or radian frequency (ω), 247 Aperiodic waveform, 250 Apparent power, 815 Applications: 300-Ω to 75-Ω adapter, 127 analog switch, 19 analog-to-digital converter (ADC), 280 attenuation pad, 130 autotransformer, 799 band-limited differentiator, 295 batteries, 48 binary current divider, 49 BJT transistor, 168 Cathode ray tube (CRT), 6 clock waveform, 263 damped sinusoidal waveform, 255 dc power supply (full-wave rectifier), 705 decibels, 620 digital clock detection, 328 digital clock skew, 603 digital multimeters (DMM), 180 dynamic OP AMP circuits, 295 ECG waveform, 264 exponential waveform, 243 filter LP (using phasors), 407 gain-bandwidth product, 628 impedance bridge, 399 instrumentation amplifier, 212 isolation transformer, 804 L-pad, 126 loading, 129 Maxwell bridge, 399 non-inverting summer, 185 oscilloscope, 243, 244, 248, 255 potentiometer, 44 power distribution, 797 resonance, 405 sample-and-hold circuit, 280, 378 signal bandwidth, 710 signal sampling, 710 sinusoidal waveform, 248 step response descriptors, 575 Thévenin measurements with DMM, 108 time-limited integrator, 295 Assigning reference marks, 32 Asymptotically stable, 570 Average power (P), 437, 812 of a periodic signal, 707 COPYRIGHTED MATERIAL Attenuator, in-line 130, photo, 130 Austin, Arthur O., 805 Average value: of a signal (V avg ), 260 of a periodic signal (a 0 ), 688 of sinusoidal signal, 262 B (susceptance) (S), 400 B (bandwidth) (Hz, rad/s), 644, 650, 710, 731, 734, 773 Balanced three-phase: basics, 825, 828 Δ-Δ connection, 828 Δ-Y connection, 828 Y-Δ connection, 828 Y-Y connection, 828 Ballantine, Stuart, WC1 Bandpass filter: basics, 637 cascade design, 637, 773 narrow band, see tuned parallel RLC, 649 second order, 730 series RLC, 643 tuned, 643, 649, 731, 735 using first-order circuits, 637 using phasor analysis, 429 wide band, 644, 773 Bandstop filter: basics, 637, 732, 774 narrow band, see notch notch, 647, 733, 735 parallel design, 641, 774 second order, 647, 733, 735 series RLC, 647 using first-order circuits, 641 Bandwidth, 644, 650, 731, 773 Battery, 20, 48 Bell, Alexander Graham, footnote 620 Bessel filter, 782 Bilateral, 17 Bipolar power, 813 Biquad filter, 784 Black, Harold S, 150 Block diagrams: differential amplifier, 187 differentiator, 289 integrator, 289 instrumentation system, 202 gain, 98, 151, 175, 181 network function, 555 of sinusoidal steady-stare response, 578 proportionality constant (K), 98 881
882 INDEX Block diagrams: (Continued) summary table basic, 188, 290, inside front cover summing point, 102, 184 Blocking capacitor, 574 Bode, Hendrik, 554, 616 Bode diagram: basics, 619 complex poles and zeros, 661, 665 first order, LP 622, HP 630 real poles and zeros, 652 straight-line approximation (SL), 654, 659 using Multisim, 658, Web using MATLAB, 634, 656, Web Bridge circuits: basic, 100 bridge-t, 130, 146 impedance, 399, 418 Maxwell, 399 reference bridge, 208, 210, 211 Wheatstone, 100, 135, 137, 144 Bromwich, Thomas John, 453, 498 Brune, Otto, 554 Budak, Aram, footnote 752 Buffer (see also OP AMP circuits), 179 Bus, 841 Butterworth, Stephen, 740 Butterworth: discussion of poles, 497, Web App B high-pass response, 763 low-pass response, 745 overview, 739 pole-zero diagram, 758 polynomials, 747, inside rear cover step response, 758 third-order filter, 783 C (capacitor), 275 Capacitance (C) definition, 275 Campbell, George A, 719 Capacitive load, 816 Capacitive reactance (X C ), 395 power-factor correction, 823 Capacitor (C): average power, 437 basics, 275 blocking, 574 bypass (for BJT), 553 dc response, 299 energy (w C (t)), 276, 436 photos, 275, 276 impedance, 391, 502 i-v relationships, 275 parallel connection, 296 power (p C (t)), 276, 436 series connection, 297 standard values, see inside rear cover super capacitor, 307, 378, footnote 596 two-wire feed through, 305 Cascade connection, 189, 566, 590, 720 Cascade design: dc OP AMP, 193 transfer function, 590 first-order filters, 637, 741, 762 multiple-order filters, 720 Cauer, Wilhelm, 554, 740 Cauer or Elliptic filter, 739 Causal waveform, 260, footnote 584 Center frequency (ω 0 ), 643, 650, 731 Chain rule, 188, 566 Chapter Learning Objectives (CLOs), 3 Characteristic equation: first order, 313 second order, series 346, parallel 354 Charge (q(t)), 5, 276 Charging exponential, see exponential rise Chebyshev Type 1: discussion of poles, Web App B high-pass response, 769 low-pass response, 751 overview, 739 pole-zero diagram, 758 polynomials, 754, inside rear cover step response, 758 Chebychev Type 2, 739 Chen, Wai Kai, footnote 731 Circuit (definition), 2, 17, 22 Circuit analysis: combined constraints (dc), 28 computer aided, 11, 54, Web definition, 2 dependent sources, 152 phasor domain, 394, using Multisim 404 phasor domain, mesh current, 423 phasor domain, node voltage, 422 single phase, 817 three-phase, 830 using Laplace transforms, 480, 508, 523 using Fourier series, 699 using Fourier transforms, Web Circuit design: ac voltage divider (phasor), 395 bandpass filter, 429, 637, 639, 731, 773 bandstop filter, 638, 734, 774 Bode plot, 656 Butterworth, LP 745, HP 763 concepts, 122 Chebyshev, LP 751, HP 769 comparator, 214 complex poles, 529 DAC, 200, 201 dc voltage divider, 42 differential equation, 293, 294 discussion, 2, 193 First-Order Cascade, LP 741, HP 762 first-order step response, 333, 574, 602 first-order voltage divider, 590 high-pass filters, 632, 761 input-output relationship, 197, 293 low-pass filters, 413, 624, 628, 739 interface circuits (dc), 122 to 132 interface circuit (ac) (phasors), 421 inverting OP AMP network, 594 network function, 590, 592, 594, 598, 595, 599 OP AMP inverter, 182, 594 OP AMP interface circuit, 202, 208 OP AMP non-inverter, 178 OP AMP subtractor (difference amp), 187, 190 OP AMP summer, 184, 185 OP AMP transducer interface, 205, 208, 210, 212 passive notch filter, 648 phasor load design, 416 poles and zeros, 466, 529, 538 power factor correction, 824 RC circuit, 333 RLC circuits, 366, 367, 598, 599, 602, 646, 648 sample-hold, 378 second-order active filters, 637, 723, 727 second-order step response, 366, 600 second-order network function, 593, 595, 599 transfer function, 563 transistor inverter, 171 transformer maximum power transfer, 798 using MATLAB, 602, 666, 734, Web using Multisim, 645, 666, 734, Web voltage divider and OP AMP, 592 Circuit determinant, 434, 526, 529, 537, 539 Circuit reduction, 50, 409, 508 Circuit theorems: maximum power transfer, 119, 438 maximum signal transfer, 118 proportionality, 98, 409, 513 superposition, 102, 410, 514 Thévenin/Norton, 107, 415, 520 Circuit variables, 5 Clock waveform, 263 Common mode rejection ratio (CMRR), 212 Combined constraints, 28, 499 Comparator: basics, 214 flash ADC, 216 zero-crossing detector, 215 Complex frequency (s= α ±jβ), 350, also footnote 351 Complex frequency variable s (Laplace), 454 Complex numbers: Arithmetic operations, App A conjugate, App A exponential form, App A imaginary part, App A real part, App A Complex poles, 471 Complex power: and load impedance, 816 basics, 814 conservation of, 817
Composite waveforms: basics, 252 damped ramp, 254 damped sinusoid, 255 double exponential, 257 double-sided exponential, 254 exponential rise, 253 signal s fundamental frequency, 259 signal s harmonic frequencies, 259 signum function, 253 Computer tools: basics, 11, 54, Web comparison between tools, 58 Excel, 241, 342, 528, 706 MATLAB, 11, Web Multisim, 56, Web Conductance (G), 17, 400, 503 Conjugate match (max power), 439 Connections models, 22 Connection constraints: definition, 22 using phasors, 389 using Laplace transforms, 499 using Fourier transforms, Web Continuity: capacitor voltage, 277, 330 inductor current, 284, 330 Convolution: applications of, 589 basics, 583 equivalence between t- and s- domains, 586 graphical approach, 587 integral, 584 using MATLAB, 585, Web Corner frequency, 622 Coulomb (unit), 5 Coupled inductors: basics, 786 energy, 790 dot convention, 788 i-v relationships, 786 mutual inductance, 786 self-inductance, 786 Coupling coefficient (k), 791, 800 Course learning objectives (CLOs): basics, 2 intro to each chapter with each problem set Cover-up algorithm, 470 Cramer's rule, 79, Web App A Critical frequencies (ω C ), 466 Critically damped, 352 Crystal filters, 784 Current: definition, 5 lag, lead, 390, 391 line, 830 mesh, 89 Norton, 107 phase, 833 short circuit, 108 Current division: basics, 46, 400, 509 binary, 49 phasor, 400 two path, 47 Current gain (β), 151, two-port T I, WC15 Current source: dependent, 151, 501 Fourier representation of, Web ideal, 20, 500 i-v characteristics, 20 Laplace representation of, 500 phasor representation, 383 practical, 21 symbol, 20 Current transfer function, 558 Cutoff frequency, 617, 644, see also respective filters Cyclic frequency (f), 247 Δ-connection, 828 Δ-Y transformation, 829 DAC, see Digital-to-analog converter Damped ramp, 254 Damped sinusoid, 255 Damping: cases (RLC), series 352, parallel 355 Damping ratio (ζ), 352, 359, 529, 541, 644, 721 Darlington, Sidney, 554 D Arsonval meter, 71 dc (direct current): current source, 20 signal, 234 voltage source, 20 dc equivalent circuits, C and L, 299 dc steady-state response, 572 Decade, 619 Decibel, 619 Defibrillation waveform, 264 Delay time, 575 Delyannis-Friend circuit, footnote 731 Dependent source: analysis, 152 basics, 151 CCCS, 151 CCVS, 151 Laplace representation of, 501 parameters, μ, β, g, r, 151 Thévenin/Norton, 166 VCCS, 151 VCVS, 151 Design, introduction, 2, see also Circuit design Determinant, Web App A circuit, 526 Device, 17 Differential amplifier basics, 173 one-stage, 187 two-stage, 190 instrumentation, 192, 212 Differential equation: 883 classical solution first order, 310 classical solution second order, 344, 353 solution by Laplace transforms, 480 solution by Fourier transforms, Web Differentiator: band-limited, 295 definition, 289 Differentiation property: Laplace, 461 Digital-to-analog converter: discussion of, 199 full-scale output, 200 photos, 200 R-2R ladder, 201 resolution, 200 weighted summer, 200 Digital Multimeter (DMM), 108, 180 Dirac, Paul, footnote 237 Dirichlet, P.G.L., 686 Dirichlet conditions, 697 Dot convention, 788 Double exponential, 257 Double-sided exponential, 254 Driving function, 20 Driving-point impedance, 558 Duality: definition, 288 examples: footnote 36, 47, 288, 311, 354, 650 Duality property, Web Dynamic OP AMP circuits, 288 ECG waveform, 264 Edison, Thomas, 811 Effective value, see Root-mean-square Electric field (E) (V/m), 275 Element, 17 Element constraints: basics, 17 using phasors, 391 using Laplace transforms, 500 using Fourier transforms, Web Elliptic or Cauer filter, 739 Energy (w): capacitor, 276 coupled inductors, 790 definition, 6 inductor, 283 phasors, 436 signal, Web Energy spectral density, Web Equal-capacitor method, BP 731, BR 733 Equal-element method, LP 723, HP 727 Equiripple filters, 740 Equivalent circuits: admittance, 503 capacitance, 296 definition, 34 of C and L at dc, 299 impedance, 508 inductance, 298
884 INDEX Equivalent circuits: (Continued) resistance, 35 sources, 38 summary of, 40, (Table) 41 Thévenin/Norton, 107, 415, 520, 809 transformer, 810 Euler's relationship, 383, 814 Evaluation: bandpass circuits, 646 bandstop circuits, 641, 737 basic design concepts, 126 cascade connections, 567, 568, 768, 770 design evaluation, 600 eliminate 60 Hz hum, 579 high-pass filters, 428, 634 high fidelity filter, 759 interface circuits (active), 191, 193, 196, 197, 205 interface circuits (passive), 125, 127, 132 introduction, 2 loading, 567 low-pass filters, 413, 757, 759 notch filter, 670 pressure transducers, 672 RC circuits, 334 Residential power distribution, 820 RLC bandpass filter circuit, 646 second-order LP filter, 723 step response designs, 334, 600 transfer function designs, 567, 600, 601 Even symmetry, 697 Exponential order (Laplace), 455 Exponential waveform: basics, 240 double, 257 double-sided, 254 properties of, 242 rise, 253 Laplace transform of, 456 Fan-out, 614 Farad (F) (unit), 275 Faraday, Michael, 274, 309, 785 Feedback, 181 Filter: 60 Hz notch, 452, 734, 737 active, 720 active LP filter overview, 739 bandpass, 429, 638, 773 bandstop, 638, 732, 774 basics, 617 Bessel, 782 biquad, 784 Butterworth, LP 745, HP 763 Chebyshev, LP 751, HP 769 crystal, 784 First-Order Cascade, LP 741, HP 762 high pass, 428, 630, 726, 761, 762, 763, 769 low pass, 408, 413, 621, 721, 739, 741, 745, 751 notch, 648, 733, 735 passive, 720 summary of second-order filters, 721 tuned, see notch using MATLAB, 413, 429, 668, 743, 765, Web using Multisim, 645, 658, 737, 748, 760, 768, Web Final conditions, 329 Final-value property, 488 First-order circuit: basics, 311 design with (bandpass), 637 design with (bandstop), 638, 642 design with (high pass), 632 design with (low pass), 624, 628 differential equation, RC 311, RL 311 exponential input transient response, 336 frequency response (high pass), 630 frequency response (low pass), 621 network function design, 590 RC and RL circuits, 310, 312, 321, 329, 336 sinusoidal input transient response, 336 step response, 321 zero-input response, 312, 515 zero-state response, 327, 515 First-Order Cascade filters, LP 741, HP 762 pole-zero diagram, 758 step response, 758 Flash converter (ADC), 217, photo 217 Flux (), 287, 786, 793 Flux linkage (λ): basics, 282 coupled coils, 786 transformers, 793 Follower (see also OP AMP circuits), 179 Forced pole, 526, 555 Forced response, 321, 506, 516, 539 Forcing function, 20 Foster, Ronald M, 554 Fourier, Jean Baptiste, 686 Fourier series: alternative form, 695 amplitude spectrum, 695 average power, 706 coefficients, 687, 688 composite waveforms, 259 fundamental frequency, 687 in circuit analysis, 699 line spectra, 695 overview, 687 phase spectrum, 695 rms value, 706 symmetries, 697 table of common waveforms, 694 using MATLAB, 689, Web Fourier transforms (F(ω)), Web Frequency: angular, 247 center (f 0, ω 0 ), 643, 650, 731 complex (s), 350 corner (f C, ω C ), 622 critical (f C, ω C ), 466 cutoff (f C, ω C ), 617, 644, 648 cyclic (f), 247 damped natural (β), 350 fundamental, 258, 687 harmonic, 258, 687 natural, 350 negative, Web neper (α), 350 notch, 648, 733 radian (β, ω), 350 resonant (ω 0 ), 391, 643, 650, spectrum, 688 undamped natural (ω 0 ), 359 Frequency response: and step response, 667 Bode diagrams, 619 definition, 617 descriptors, 617 first-order bandpass, 539 first-order bandstop, 641 first-order high pass, 630 first-order low pass, 621 of four basic gain responses, 618 RLC circuits bandpass, 429, 643, 649 RLC circuits bandstop, 647 Fundamental frequency, 258, 687 Full-scale output (DAC), 200 G(s) (step response transform), 572 g(t) (step response), 572 Gain (K): current, 151 follower, 179 inverter, 181 non-inverter, 174 proportionality constant, 98, 409, 513 two-port T V or T I, WC15 voltage, 151 Gain-bandwidth product (GBW), 626 Gain function, 617 Gauland, Lucien, 785 Gate function, 239 Gibbs, Josiah, 785 Grapher View (Multisim), 58 Ground, 9 Ground loop, 804 H(s) (impulse response transform), 569 h(t) (impulse response), 569 Half-wave symmetry, 697 Harmonic frequency, 258, 687 Heaviside, Oliver, footnote 335, 382, 453, 498 Henry, Joseph, 274, 785 Henry (H) (unit), 282 Hertz (Hz) (unit), 247 Hidden symmetry, 698 High-pass filter: basics, 630, 761 Butterworth, 763 Chebychev, 769
885 first order, 630 First-Order Cascade, 762 second order equal element, 727 second order unity gain, 727 h-matrix, WC8 Home power distribution, 451 Homogeneity, 97 Homogeneous equation, 312 Hybrid h-parameters, WC7 i (the current variable) (A), 5 i v characteristics, 17 Ideal models: capacitor, 275 current source, 20 dependent source, 151 inductor, 282 OP AMP, 174, and GBW 627 open circuit, 19 resistor, 17 short circuit, 19 switch, 19 BJT transistor, 169 voltage source, 20 Ideal transformer: basics, 792 i-v relationships, 795 input impedance, 796 Impedance (Z): bridge, 399 concept, 391 driving-point, 558 frequency effects on, 391 input, 558 magnitude scaling, 596 matrix [z], WC3 parallel connection Laplace, 509 parallel connection phasor domain, 400 ratio of phasors V and I, 391 ratio of V(s) and I(s), 502 ratio of V(ω) and I(ω), Web resonance (ω 0 ), 391 series connection Laplace, 508 series connection phasor domain, 395 two-port z-parameters, WC3 Improper rational function, 474 Impulse function (δ(t)), 236 Impulse response (h(t)), 569, diagram 573 Impulse response transform (H(s)): and convolution, 583 basics, 569 diagram, 573 from network function, 569 from step response, 572 Inductance (L): definition, 282 mutual (M), 787 self (L), 282, 786 Inductive load, 816 Inductive reactance (X L ), 395 power factor correction, 823 Inductor (L): air-coil design, 308 average power, 436 basics, 282 chokes, footnote 596 coupled, 786 dc equivalence, 299 energy (w L (t)), 283, 436 photos, 282, 283 impedance (Fourier transform), Web impedance (Laplace transform), 502 impedance (phasor domain), 391 i-v relationships, 282 parallel connection, 298 power (p L (t)), 283, 436 series connection, 298 standard values, 596, see inside rear cover Initial conditions, 329, 502, 503 Initial-value property, 488 Input, 98 Input impedance, 558 In phase, 390 Instantaneous power (p(t)): basics, 435, 812 three-phase, 840 Instantaneous value, 259 Instrumentation systems: active transducers, 203 basics, 201 passive transducers (photos), 207 Instrumentation amplifier, 193, 212 Integration property: Laplace, 459 Integrator: description, 288 time-limited, 295 Interface, 2 Interface circuit design, 121, 196, 201 Inverse Laplace transforms: complex poles, 471 definition, 457, 469 improper rational function, 474 multiple poles, 476 simple poles, 469 sum of residues, 473 table, 464, see table inside rear cover using MATLAB, 479, Web Inverting amplifier, 181 Isolation transformer, 804, photo 804 Joule (J) (unit), 5 K (proportionality constant for gain), see Gain (K) K (scale factor in pole-zero diagrams), 466 k 1, k 2, k M (proportionality constants for inductors), 282, 786 k (coupling coefficient), 791 Kirchhoff, Gustav, 22 Kirchhoff's laws: basics, 22 current (KCL), 23 phasor domain, 389 in Laplace transforms, 499 in Fourier transforms, Web voltage (KVL), 24 L (inductor), 282, 787 L-pad, 121, photo 121 Ladder circuit, 50 Lagging power factor, 815 Laplace, Pierre Simon, 453 Laplace transforms (F(s)): basics, 454 circuit response using Laplace, 480 complex differentiation property, 497 definition, 455 differentiation property, 461 inverse, 457, 469 integration property, 459 linearity, 458 poles and zeros, 466 properties and pairs, 458 relationship to Fourier transforms, Web solving differential/integrodifferential eq, 480 table of pairs, 464, inside back cover table of properties, 464, inside back cover translation properties, 462 uniqueness property, 457 using MATLAB, 466, Web Leading power factor, 815 Linear: circuit, 2, definition, 17 element, 17 Linearity properties: additivity, 97 homogeneity, 97 Laplace, 458 proportionality, 98 superposition, 98 Line current, 825 Line spectra, 695 Line voltage, 826 Load-flow problem: single-phase, 821 three-phase, 836, 841 Loading: definition, 130, 182 follower used to avoid, 179 OP AMP, 178, 189 s domain, 590 Logarithmic amplifier, 224 Lookback impedance, 417 Lookback resistance (R T ), 114 Loop (definition), 22 Low-pass filter: basics, 621, 739 Butterworth, 745 Chebyshev, 751 comparisons, 757
886 INDEX Low-pass filter: (Continued) first order, 621 First-Order Cascade, 741 second order equal element, 723 second order unity gain, 723 M (mutual inductance), 787 Magnitude scaling, 596 Matrix: admittance or [y]matrix, WC6 basics, 76, 89, Web App A hybrid or [h] matrix, WC8 impedance or [z] matrix, WC3 mesh-current analysis, 89 node-voltage analysis, 76 s-domain analysis, 525, 533 symmetrical, 76 transmission or [t] matrix, WC10 using MATLAB, Web using complex numbers (phasors), 433 Matched condition dc, 119 conjugate, 439 MATLAB: applications, throughout text, Web discussion, 11, 54 Maximally flat filters, 740 Maximum signal transfer: basics, 118 current, 119 graph, (120) power, 119, 438 theorem (power), 119 voltage, 118 Maxwell bridge, 399 Maxwell, James Clerk, 233 Mesh-current analysis: basics, 89 by inspection, 92 fundamental property, 90 using Fourier transform analysis, Web using Laplace transform analysis, 532 using MATLAB, 91, 534, Web using phasor analysis, 423 summary of, 97 supermesh, 95 symmetrical matrix Ax=b, 93 with current sources, 94 with dependent sources, 163 Mho ( ) (unit), 17 Multiple poles, 476, filters 740 Multisim: applications, throughout text, Web discussion, 11, 54 Mutual inductance (M), 787, and the dot convention 788 N (coil turns), 282, 786 n (turns ratio) 793, Napier, John, footnote 351 Narrow band, 644 Natural frequencies (s, α, β), 352 Natural pole, 526, 555 Natural response, 321, 506, 539 Neper frequency (s -1 ), 350, also footnote 351 Netlist, 55 Network function: and phasors, 582 definition, 514, 555 design and evaluation of, 589 design comparison, 567, 600 determining, 555 driving-point impedance (Z(s)), 558 importance of cascade connection, 590 impulse response, 569 sinusoidal steady-state response, 576 step response, 572 transfer function (T(s)), 558 with current/voltage dividers, 559, 590 with OP AMPs, 559, 592 Node (definition), 22 Node voltage, 73 Node-voltage analysis: basics, 73 by inspection, 76 fundamental property, 73 using Excel, 525 using Fourier transform analysis, Web using Laplace transform analysis, 523 using MATLAB, 86, Web using Multisim, 82, 159, Web using phasor analysis, 422 summary of, 89 supernode, 83 symmetrical matrix Ax=b, 76 with dependent sources, 154 with OP AMPs, 191 with voltage sources, 82 Non-causal waveform, 260, Web Noninverting amplifier, 178 Nonlinear: analysis, 115 characteristics, 69 element, 17 Nonreciprocal network, WC3 Norton equivalent circuit: applications, 109 basics, 107 phasor domain, 415 s domain, 520 Notch bandwidth, 734 Notch filter, 638, 648, 732, 735 Notch frequency, 648, 734 Nyquist, Harry, footnote 711 Nyquist rate, 711 Octave, 619 Odd symmetry, footnote 17, 697 Ohm (Ω) (unit), 17 Ohm's law, 17 Ohm, Simon Georg, 16 O-pad, 132 OP AMP: basics, 171 closed-loop gain, 175 dependent source model, 173 effect of finite gain, 176 photos, 172 ideal model, 173, 174 in the s domain, 501 notation, 172 open-loop gain (A), footnote 174 operating modes, 173 transfer characteristics, 172 OP AMP circuits: analog-to-digital (ADC) circuit, 216 applications, 199 bandpass filter, 639, 634, 646, 730, 735, 773 bandstop filter, 641, 732, 735, 774 buffer, 179 cascading observation, 189 comparator circuits, 214 design, 193 differential amplifier, 187 differentiator, 289 digital-to-analog circuits, 199, 200, 201 follower, 179 high-pass filter, 633, 636, 726, 762, 763, 769 integrator, 289 instrumentation systems, 201 inverting amplifier, 181 log-amp, 224 low-pass filter, 624, 722, 741, 745, 751 noninverting amplifier, 175 Sallen-Key realization, LP 721, HP 726 subtractor (one-stage), 187 subtractor (two-stage), 190 summary of (Table), 188, 290 summing amplifier (inverting), 184 summing amplifier (non-inverting), 185 voltage follower, 179 Open circuit, 19 Open-circuit voltage (v OC ), 108 Open Loop gain (A) or (μ), footnote 173 Operational amplifier, see OP AMP Oscilloscope probe, 552 Out of phase, 390 Output, 98 Overdamped response, 352 Overshoot, 575 p (the power variable) (W), 6 Parallel connection: admittances, 400, 509 capacitors, 296 current sources, 41 definition, 26 impedances, 400 inductors, 298 resistors, 35 Parseval's theorem, Web Partial fraction expansion: of complex poles, 471 of improper rational functions, 474
of multiple poles, 476 of simple poles, 469 Passband, 617, 740 Passive sign convention, 8, 9 Passive filter, 720 Peak-to-peak value of a signal, 260 Peak value of a signal, 260 Perfect coupling, 791, 793 Period (T 0 ), 245 Periodic waveform, 250, 687 average value of, 260 Fourier series of, rms value of, 261, 706 Permittivity (ε), 275 Phase angle (ϕ), 247 Phase converter, 849 Phase current, 833 Phase function, 617 Phase sequence, 826 Phase spectrum, 695 Phase voltage, 826 Phasor: and network functions, 582 definition, 383 diagram, 383 domain, 394 properties, 384 rotating, 384 Phasor circuit analysis: basics, 389, 394 device constraints, 389 connection constraints, 389 current division, 400 energy and power, 435 filters, 408, 413, 429 frequency vs. impedance, 391 general circuit analysis, 422 impedance concept, 391 in out of phase, lead, lag, 391 phasor domain, 395 proportionality, 409 source transformation, 416 superposition, 410 Thévenin and Norton equivalents, 415 voltage division, 395 Photoresistor: photo, 207 interfacing, 207 Piecewise continuous (Laplace), 455 Piezoelectric transducer, 306 Planar circuit, 90, 422, 532 Pole: basics, 466 circuit determinant, 539 complex, 471, 538 double real, 538 forced, 526, 539 form of filter response, 758 multiple, 476 natural,526, 539 number of, 541 simple, 469, 538 stable, 539 Pole-zero diagram: and circuit response, 538 basics, 466 finding transforms from, 479 left hand plane, 539 of second-order filter types, 758 scale factor (K), 466 software applications, Web Port, 121, 558, WC2 Potentiometer, 44, photos, 44, 45 Power (p(t)): apparent, 815 average (P), 437, 706, 812 complex, 814 definition, 6 flow, single phase 821 gain, 153 instantaneous, 435, 812 maximum, 119, 438 phasors, 435 reactive (Q), 813 three phase, 836, 840, 841 Power factor (pf ): angle, 815 basics, 815 correction, 823 Power triangle, 815 Practical sources current, 21 voltage, 21 Primary winding, 792 Proper rational function, 469 Proportionality property dc circuits, 98 phasor domain, 409 s domain, 513 Prototype, 596 Quality factor (Q), 644, 650, 731 Quantities, table of, 4, see inside front cover Quiescent or Q-point, 117 R (resistor), 17 Radians per second (rad/s) (Unit), 247 Ragazzini, John R., 171 Ramp function (r(t)), 238 Range of practical components, 597, see inside rear cover Rational function, 469, 513 Reactance (X), 395 Reactive power (Q), 813 Reciprocal network, WC3 Reciprocal spreading, 668, Web Reference marks, 8 Relationships between responses in s and t domains, 573 Residue, 469 sums of, 473 Resistance (R), basics, 17 lookback (R T ), 114 real part of impedance, 391, 502 887 Resistor (R): average power, 436 photos, 17, 18 i-v relationships, 17 impedance, 391, 502 linear, 17 parallel connection, 35 power, 18 series connection, 35 standard values, 596, see inside rear cover Resolution (DAC), 200 Resonance (ω 0 ), 391, 405, 644 Resonant frequency (ω 0 ), 392, 405, 644, 651 Response: see also transient and frequency responses ac steady state, 340 dc steady state, 340, 572 critically damped, 352 forced, 321, 539 frequency, 617 impulse, 569 narrow band, 644 natural, 321, 539 overdamped, 352 sinusoidal steady state, 340, 576 step, 321, 359, 572 underdamped, 352 wide band, 644 zero frequency (dc), 340 zero input, 312, 345, 515 zero state, 327, 515 Reversal property, Web Ringing, 670, 759 Rise time, 575 RC and RL circuits: characteristic equations, RC 313, RL 313 frequency response, 621, 624, 631, 634 initial and final conditions, 329 step response, 321 zero-input response, 312 zero-state response, 327 RLC circuits: basics, 344 characteristic equation, series 346, parallel 354 frequency response, 643, 647 design, 366, 367, 646, 648, 702 parallel, 353, 647 series, 344, 646 zero-input response: series 345, 348 Root-mean-square (V rms ) value, 261, 707 Rotating phasor, 384 s-plane geometry relationships, 529 Sallen-Key, footnote 729, table 730, LP 721, HP 726 Sample-and-hold circuit, 280, 378 Sampling: aliasing, 712 anti-aliasing, 712 Nyquist rate, footnote 711 strictly band-limited, 711 theorem, 711
888 INDEX Secondary winding, 792 Self-inductance, 282, 787 Scale factor, 466 Scaling property, Web Second-order circuit: bandpass prototype, 730 bandstop prototype, 732 differential equation, 345, 354, 359 integrodifferential equation, 345 high-pass prototype, 726 low-pass prototype, 721 network function design, 598 parallel RLC, 354, 648 Sallen-Key, footnote 729 series RLC, 345, 643 step response, 359 zero-input response, 345, 353 Self-inductance (L), 282, 786 Sensor, see Transducer Series connection: basics, 26 capacitors, 297 impedances, 395, 508 inductors, 298 resistors, 35 voltage sources, 41 Shannon, Claude, footnote 711 Short circuit, 19 Short-circuit current (i SC ), 108 Siemens (S) (unit), 17 Signals: ac, 261 amplification, 151 composite, 252 dc, 234, 261 damped ramp, 254 damped sinusoid, 255 definition, 2 double exponential, 257 double-sided exponential, 254 exponential, 240 exponential rise, 253 introduction, 2, 234 inversion, 154 impulse, 236 ramp, 238 signum (sgn(t)), 253 sinc x (sin x/x), Web sinusoidal, 245 step function, 235 Signum function (sgn(t)), 253 Single-line representation of power systems, 841 Simple pole(s), 469 Single phase circuit analysis, 817 Single phase power flow, 821 Singularity functions, 238 Sinusoidal steady-state response: average power, 437 basics, 340 from network functions, 576, diagram 573 using phasors, 389 relationship with phasors, 582 Sinusoidal waveform: basics, 245 damped, 255 Fourier transform of, Web Laplace transform of, (sin) 459, (cos) 462 properties of, 250, 385 phasor representation, 383 Solving linear algebraic equations, 78, Web App A Source: current (ideal), 20 dependent, 151 equivalent, 38 practical (i and v), 21 three phase, 826 voltage (ideal), 20 Source transformation: dc, 38 phasor domain, 415 s domain, 520 Spectrum, 688 SPICE, 55, 116 Stability: and pole loci, 539, 541 asymptotic, 570 inherently stable, 539 marginally stable, 539, see also footnote, 539 Standard decimal prefixes, Table 1-2, 3 Standard form (second-order eq.), 360 State variable, 277, 284, 311 Steady-state response, 340, 556, 576 Steinmetz, Charles, 382 Step function (u(t)), 235 Step response (g(t)): definition, 572 descriptors, 575 diagram 573 Step-response transform (G(s)): and frequency response, 667 diagram, 573 first-order circuit, 321 from impulse response, 572 from network function, 572 second-order circuit, 359 using MATLAB, in various sections, Web using Multisim, in various sections, Web Step-down transformer, 793 Step-up transformer, 793 Stopband, 617, 740 Strain gauge: photo, 207 interfacing, 208, 210 Subtractor, see differential amplifier Summing amplifier, 184, 185 Super Capacitor, 307, 378 Supermesh, 95 Supernode, 83 Superposition principle dc, 98, 103 ac (phasor domain), 409 s domain, 514 Susceptance (B), 400 Switch: analog, 19 ideal, 19 photos of, 19 models, 20 Symbols and Units, 3, see also Table 1-1, 4 t-parameters, WC10 T(s) (transfer function), 555, 558 T-circuit, 413 Tank circuit, 650, 683 Temporal descriptors, 259 Tesla, Nikola, 811 Test signals, 557 Thévenin, Leon Charles, 72 Thévenin equivalent circuit applications of, 109 basics, 107 derivation of theorem, 113 of a transformer, 810 phasor domain, 415, 426 relationship to Norton, 108 s domain, 520 with dependent sources, 166 with nonlinear loads, 115 Thévenin resistance (R T =R N ), 108 Three-phase power analysis: balanced connections, 827, 828 basics, 830 instantaneous power, 840 power flow, 836, 841 single-line diagram, 841 using Multisim, 832, 834, Web Y-Δ analysis, 833 Y-Δ connection, 828 Y-Δ conversions, 829 Thermistor, 207, photo, 207 Thermocouple, 205, curves 228, 230 Thermometer code, 217 Time constant: definition, 240 RC circuit, 313 RL circuit, 314 Time shift (T S ): effect on exponential, 242 effect on impulse, 237 effect on ramp, 238 effect on sinusoid, 246 effect on step function, 235 Transconductance (g), 151 Transducers: accelerometer, 229 active, 203 design with, 203 to 213 interface circuit, 202 passive, 207, photos 207 photocell, 203 photoresistor, 207, photo 207 pressure, 229, 672 strain gauge, 207, photo 207
thermistors, 207, photo 207 thermocouples, 205, curves, 228 Transfer characteristics BJT, 171 OP AMP, 172 Transfer function: admittance, 558 current, 558 definition, 558 determining, 559 Fourier domain, Web impedance, 558 voltage, 558 with OP AMPs, 559 Transform pair: Laplace, 455, 464, see table inside rear cover Transformed circuits, 499 Transformers: autotransformer, 799, 802 basics, 792 equivalent circuit, 810 photos, 792 ideal, 792 impedance matching, 798 isolation transformer, 804 i-v characteristics, 795, two-port WC21 linear, 799 maximum power transfer, 798 perfect coupling, 793 phasor model, 799 solution using Multisim 794, 798, Web step down, 793 step up, 793 turns ratio, 793 windings, 792 zero power loss, 795 Transient response: first-order (classical), RC 313, RL 314 second-order (classical), series 344, parallel, 353 using Laplace, 504, 505, 507, 569, 572 using MATLAB, Web using Multisim, Web Transition band, 740 Transistor (BJT): basics, 168 biasing, 69 bypass capacitor, 553 digital switch, 171 models, 170 photos, 169 operating modes, 169 Translation property: Fourier transform, Web Laplace transform, 462 Transmission matrix [t], WC10 Transmission t-parameters, WC10 Transresistance (r), 151 Through variable (current), 8 Tuned filter, 644, 731, 735 Turning off sources, 103 Turns ratio n, 793 Two-port network, 121, 558, WC2 admittance or y-parameters, WC2, WC5 conversion table, WC13 current gain, WC15, table WC16 definition, WC2 hybrid or h-parameters, WC2, WC7 impedance or z-parameters, WC2, WC3 network, WC2 parameters, WC2 transfer function, 558 transmission or t-parameters, WC2, WC10 two-port connections or conversions, WC12 voltage gain, WC13, table WC16 Undamped natural frequency (ω 0 ), 359, 529, 541 Under-damped response, 352 Unilateral two-port network, WC20 Unipolar power, 813 Uniqueness property: Fourier transform, Web Laplace transform, 457 Unit output method, 100, 409 Units, table of, 4, inside front cover Unity gain method, LP 723, HP 727 Unstable circuit, 539 v (the voltage variable) (V), 5 Virtual keyboard, 718 Volt (V) (unit), 6 Volta, Alessandro, footnote 6 Volt-Amperes (VA) (unit), 8152 Volt-Amperes Reactive (VAR) (unit), 813 Voltage: average value (V avg ), 260, a 0, 689 definition, 5 lag, lead, 390, 391 line, 827 maximum value (V MAX ), 260 minimum value (V MIN ), 260 node, 73 open circuit, 108 peak value (V p ), 260 peak-to-peak value (V pp ), 260 root-mean-square value (V rms ), 261 root-mean-square value of periodic functions, 706 Thévenin, 107 phase, 826 Voltage division, 42, 395, 508, 590, 592 Voltage follower, 179 Voltage gain (μ), 151, two-port T V, WC15 Voltage source: ac source symbol, 20 battery symbol, 20 dependent, 151 Fourier representation of, Web i-v characteristics, 20 Laplace representation of, 500 phasor representation, 383 practical, 21 three-phase, 826 Wagner, K.W., 719 Watt (W) (unit), 6 Watt, James, footnote 6 Waveforms: basics, 234 amplitude descriptors, 260 damped ramp, 254 damped sinusoid, 255 dc signals, 234 double exponential, 257 double-sided exponential, 254 exponentials (e t=tc ), 240 generation using MATLAB, Web generation using Multisim, Web impulse (δ(t)), 236 instantaneous value, 259 partial descriptors, 259 ramp (r(t)), 238 signum function (sgn(t)), 253 sinc (sin x/x), Web singularity functions, 238 sinusoids (cos ωt + φ), 245 step (u(t)), 235 temporal descriptors, 259 waveform-transform relationship, 454 Waveform symmetries, 697 Weber, Wilhelm, 282 Weber (Wb) (unit), 282, 786 Weber-turns (Wb-t) (unit), 282, 786 Westinghouse, George, 811 Wide band, 644 X (reactance), 395 Y (admittance), 395 Y-connection, 828 y-parameters, WC5 889 Z (impedance): Laplace, 503 phasors, 391 z-parameters, WC3 Zero, 466, 721 Zero crossing detector, 215 Zero-input response, 312, 327, 345, 348, 515 Zero power loss, 795 Zero state response, 327, 515 Zeta (ζ) damping ratio, 352, 359, 529, 534, 644, 721