Electric circuits 10th nilsson

www.downloadslide.com Electric Circuits For these Global Editions, the editorial team at Pearson has collaborated with educators across the world to address a wide range of subjects and requirements, equipping students with the best possible learning tools This Global Edition preserves the cutting-edge approach and pedagogy of the original, but also features alterations, customization, and adaptation from the North American version TENTH edition Nilsson • Riedel This is a special edition of an established title widely used by colleges and universities throughout the world Pearson published this exclusive edition for the benefit of students outside the United States and Canada If you purchased this book within the United States or Canada you should be aware that it has been imported without the approval of the Publisher or Author Pearson Global Edition Global edition Global edition Global edition ISBN-13: 978-1-292-06054-5 ISBN-10: 1-292-06054-9 0 0 781292 060545 Electric Circuits tenth edition James W Nilsson • Susan A Riedel A01_NILS0545_10_GE_FM.qxd 4/9/14 3:53 PM Page www.downloadslide.com ELECTRIC CIRCUITS TENTH EDITION GLOBAL EDITION A01_NILS0545_10_GE_FM.qxd 4/9/14 3:53 PM Page www.downloadslide.com This page is intentionally left blank A01_NILS0545_10_GE_FM.qxd 4/9/14 3:53 PM Page www.downloadslide.com ELECTRIC CIRCUITS TENTH EDITION GLOBAL EDITION James W Nilsson Professor Emeritus Iowa State University Susan A Riedel Marquette University Boston Columbus Indianapolis New York San Francisco Upper Saddle River Amsterdam Cape Town Dubai London Madrid Milan Munich Paris Montréal Toronto Delhi Mexico City São Paulo Sydney Hong Kong Seoul Singapore Taipei Tokyo A01_NILS0545_10_GE_FM.qxd 4/9/14 3:53 PM Page www.downloadslide.com Vice President and Editorial Director: Marcia J Horton Acquisitions Editor: Andrew Gilfillan Editorial Assistant: William Opaluch Marketing Manager, Global Edition: Bram Van Kempen Senior Managing Editor: Scott Disanno Production Editor: Rose Kernan Head, Learning Asset Acquisition, Global Edition: Laura Dent Acquisitions Editor, Global Edition: Karthik Subramaniun Project Editor, Global Edition: Aaditya Bugga Cover Photograph: oksana2010 / Shutterstock Senior Manufacturing Controller, Global Edition: Trudy Kimber Media Producer, Global Edition: Anuprova Dey Chowdhuri Senior Operations Supervisor: Alan Fischer Design Manager: Kenny Beck Manager, Rights and Permissions: Zina Arabia Full-Service Project Management: Integra Publishing Services Cover Printer: Courier Kendallville Pearson Education Limited Edinburgh Gate Harlow Essex CM20 2JE England and Associated Companies throughout the world Visit us on the World Wide Web at: www.pearsonglobaleditions.com © Pearson Education Limited, 2015 The rights of James W Nilsson and Susan A Riedel to be identified as the authors of this work have been asserted by them in accordance with the Copyright, Designs and Patents Act 1988 Authorized adaptation from the United States edition, entitled Electric Circuits, 10th edition, ISBN 978-0-13-376003-3, by James W Nilsson and Susan A Riedel, published by Pearson Education © 2015 All rights reserved No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without either the prior written permission of the publisher or a license permitting restricted copying in the United Kingdom issued by the Copyright Licensing Agency Ltd, Saffron House, 6–10 Kirby Street, London EC1N 8TS All trademarks used herein are the property of their respective owners The use of any trademark in this text does not vest in the author or publisher any trademark ownership rights in such trademarks, nor does the use of such trademarks imply any affiliation with or endorsement of this book by such owners ISBN 10: 1-292-06054-9 ISBN 13: 978-1-292-06054-5 (Print) ISBN 13: 978-1-292-06547-2 (PDF) British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library 10 14 13 12 11 10 Typeset in 10/12 TimesTen-Roman by Integra Publishing Services Printed and bound by Courier Kendallville in the United States of America A01_NILS0545_10_GE_FM.qxd 4/9/14 3:53 PM Page www.downloadslide.com To Anna A01_NILS0545_10_GE_FM.qxd 4/9/14 3:53 PM Page www.downloadslide.com This page is intentionally left blank A01_NILS0545_10_GE_FM.qxd 4/9/14 3:54 PM Page www.downloadslide.com Brief Contents Chapter Chapter Chapter Chapter Chapter Chapter Chapter Chapter Chapter Chapter 10 Chapter 11 Chapter 12 Chapter 13 Chapter 14 Chapter 15 Chapter 16 Chapter 17 Chapter 18 Appendix A Appendix B Appendix C Appendix D Appendix E Appendix F Appendix G Appendix H List of Examples 13 Preface 17 Circuit Variables 24 Circuit Elements 46 Simple Resistive Circuits 78 Techniques of Circuit Analysis 110 The Operational Amplifier 166 Inductance, Capacitance, and Mutual Inductance 196 Response of First-Order RL and RC Circuits 234 Natural and Step Responses of RLC Circuits 286 Sinusoidal Steady-State Analysis 326 Sinusoidal Steady-State Power Calculations 380 Balanced Three-Phase Circuits 418 Introduction to the Laplace Transform 448 The Laplace Transform in Circuit Analysis 486 Introduction to Frequency Selective Circuits 542 Active Filter Circuits 578 Fourier Series 624 The Fourier Transform 664 Two-Port Circuits 698 The Solution of Linear Simultaneous Equations 725 Complex Numbers 745 More on Magnetically Coupled Coils and Ideal Transformers 751 The Decibel 759 Bode Diagrams 761 An Abbreviated Table of Trigonometric Identities 779 An Abbreviated Table of Integrals 781 Common Standard Component Values 783 Answers to Selected Problems 785 Index 797 A01_NILS0545_10_GE_FM.qxd 4/9/14 3:54 PM Page www.downloadslide.com This page is intentionally left blank A01_NILS0545_10_GE_FM.qxd 4/9/14 3:54 PM Page www.downloadslide.com Contents Chapter Techniques of Circuit Analysis 110 List of Examples 13 Preface 17 Chapter Circuit Variables 24 1.1 1.2 1.3 1.4 1.5 1.6 4.1 4.2 Practical Perspective: Balancing Power 25 Electrical Engineering: An Overview 26 The International System of Units 30 Circuit Analysis: An Overview 32 Voltage and Current 33 The Ideal Basic Circuit Element 34 Power and Energy 36 Practical Perspective: Balancing Power 39 Summary 40 Problems 41 4.3 4.4 4.5 4.6 4.7 Chapter Circuit Elements 46 2.1 2.2 2.3 2.4 2.5 Practical Perspective: Heating with Electric Radiators 47 Voltage and Current Sources 48 Electrical Resistance (Ohm’s Law) 52 Construction of a Circuit Model 56 Kirchhoff’s Laws 59 Analysis of a Circuit Containing Dependent Sources 64 Practical Perspective: Heating with Electric Radiators 68 Summary 70 Problems 70 Chapter Simple Resistive Circuits 3.1 3.2 3.3 3.4 3.5 3.6 3.7 Practical Perspective: Resistive Touch Screens 79 Resistors in Series 80 Resistors in Parallel 81 The Voltage-Divider and Current-Divider Circuits 83 Voltage Division and Current Division 86 Measuring Voltage and Current 88 Measuring Resistance—The Wheatstone Bridge 91 Delta-to-Wye (Pi-to-Tee) Equivalent Circuits 93 Practical Perspective: Resistive Touch Screens 95 Summary 97 Problems 98 78 4.8 4.9 4.10 4.11 4.12 4.13 Practical Perspective: Circuits with Realistic Resistors 111 Terminology 112 Introduction to the Node-Voltage Method 115 The Node-Voltage Method and Dependent Sources 117 The Node-Voltage Method: Some Special Cases 118 Introduction to the Mesh-Current Method 121 The Mesh-Current Method and Dependent Sources 124 The Mesh-Current Method: Some Special Cases 125 The Node-Voltage Method Versus the Mesh-Current Method 128 Source Transformations 131 Thévenin and Norton Equivalents 135 More on Deriving a Thévenin Equivalent 139 Maximum Power Transfer 142 Superposition 144 Practical Perspective: Circuits with Realistic Resistors 147 Summary 151 Problems 152 Chapter The Operational Amplifier 166 5.1 5.2 5.3 5.4 5.5 5.6 5.7 Practical Perspective: Strain Gages 167 Operational Amplifier Terminals 168 Terminal Voltages and Currents 168 The Inverting-Amplifier Circuit 172 The Summing-Amplifier Circuit 174 The Noninverting-Amplifier Circuit 175 The Difference-Amplifier Circuit 177 A More Realistic Model for the Operational Amplifier 181 Practical Perspective: Strain Gages 184 Summary 186 Problems 187 Z10_NILS0545_10_GE_IDX.qxd 4/7/14 4:15 PM Page 806 www.downloadslide.com 806 Index N O Narrowband filters, 606–611, 615 bandpass filters, 606–608 bandreject, 608–611 quality factor (Q) and, 606–611 twin-T notch filter, 608–611 Natural response, 234, 236–246, 253–258, 268, 288–301, 307–311, 317, 492–493 critically damped voltage, 291, 299–300, 308, 317 current (i) determined for, 236–238, 308 defined, 234, 268 first-order circuits, 234, 236–246, 253–258, 268 forms of in RLC circuits, 292–301 general solution for, 253–258, 268, 288–292 Laplace transform analysis and, 492–493 method of calculating, 254 overdamped voltage, 291, 293–295, 308, 317 parallel RLC circuit, 288–301, 317 resistor-capacitor (RC) circuits, 242–246, 253–258, 268, 492–493 resistor-inductor (RL) circuits, 236–242, 253–258, 268 resistor-inductor-capacitor (RLC) circuits, 288–301, 307–311, 317 series RLC circuits, 307–311, 317 time constant (t), 238–239, 243, 268 underdamped voltage, 291, 296–299, 308–310, 317 voltage (v) determined for, 243 Negative (acb) phase voltage sequence, 420 Neper frequency (a) for, 290–291, 308 Neutral terminal, 421 Node-voltage equation (VN), 422–423 Node-voltage method, 112, 115–121, 128–131, 151, 352–353 amplifier circuit analysis using, 120–121 circuit analysis using, 112, 115–121, 128–131, 151 dependent sources and, 117–118 equations, 115–116, 151 essential nodes and, 118–119 frequency-domain circuits, 352–353 mesh-current method, comparison of, 128–131 sinusoidal steady-state analysis using, 352–353 special cases for, 118–121 supernode, 119–120 Nodes, 59–60, 70, 112–113, 115–116 circuit element, 59–60, 70 defined, 59, 112–113 essential, 113 voltage, 115–116 Noninverting-amplifier circuit, 175–176, 182–183, 186 Nonplanar circuits, 112–113 Norton equivalent circuits, 137, 151, 349 analysis of, 137, 151 defined, 137 frequency-domain source transformations, 349 impedance (Z) in, 349 source transformations used for, 137 Numerator determinant, 726–727 Octave, 766 Odd-function symmetry, 632–633, 636, 654 Ohm’s law, 52–53, 70, 81, 490–491 electrical resistance and, 52–53, 70, 81 s-domain applications of, 490–491 One-sided (unilateral) Laplace transform, 450–451 Open circuit, 57 Open-loop gain (A), 173, 186 Operational amplifiers (op amps), 166–195, 578–623 bandpass filters, 586–590, 605–608, 614–615 bandreject filters, 590–593, 605, 608–611, 614–615 bass volume control, 579, 611–613 broadband filters, 587–593, 614 Butterworth filters, 598–606, 614–615 cascading, 586–596, 614 circuit symbol for, 168 currents (i), 168–172 difference-amplifier circuit, 177–181, 186 dual in-line package (DIP), 168 equivalent (realistic model), 181–184, 186 negative feedback, 169–170, 186 filters, 578–623 first-order filters, 580–584 gain (A), 169, 173, 179–180, 186 high-pass filters, 582–583, 605, 614 higher-order filters, 593–606, 614–615 input constraints, 169–170,186 inverting-amplifier circuit, 172–174, 182, 186 low-pass filters, 580–582, 598–604, 614–615 noninverting-amplifier circuit, 175–176, 182–183, 186 realistic model (equivalent), 181–184, 186 resistance (R) and, 167, 184–185 scaling, design of using, 585–586 simplified, 168–181, 186 strain gages for, 167, 184–185 summing-amplifier circuit, 174–175, 186 terminals, 168–172 transfer characteristics, 169 voltages (v), 168–172, 186 Operational transforms, 451, 457–462, 479, 677–681 addition, 458, 678 amplitude modulation, 679 convolution, 679–680 defined, 451 differentiation, 458–459, 678 Fourier, 677–681 frequency domain functions, 461, 679–680 integration, 459–460, 678 Laplace, 453, 459–464, 481 modulation, 679 multiplication by a constant, 457, 677 scale changing, 461, 679 subtraction, 458, 678 time domain functions, 460–461, 677–681 translation, 460–461, 679 types of, 462, 680 Z10_NILS0545_10_GE_IDX.qxd 4/7/14 4:15 PM Page 807 www.downloadslide.com Index Overdamped responses, 291, 293–295, 304, 308, 317–318 natural response equations, 293–295, 317 parallel RLC circuits, 291, 293–295, 304, 317 series RLC circuits, 308, 317 step response equations, 308, 318 P Pacemaker circuits responses, 235, 267–268 Parallel-connected circuits, 81–83, 97, 209–211, 225, 344–345, 714 See also Parallel RLC circuits capacitors, 210–211, 225 impedances combined in, 344–345 inductors, 209–210, 225 Kirchhoff’s law for, 81, 83 Ohm’s law for, 81 resistors, 81–83, 97 two-port circuits, 714 Parallel RLC circuits, 288–307, 317–318, 493–496 characteristic equation for, 289, 291–292, 317 circuit symbols for, 288, 302 critically damped responses, 291, 299–300, 305, 317 direct approach for, 303–304 general solution of differential equations, 288–292 indirect approach for, 303 Laplace transform analysis of, 493–496 natural response, 288–301, 317 Neper frequency (a) for, 290–291 overdamped responses, 291, 293–295, 304, 317 resonant radian frequency (v0), 290–291 s-domain, 493–496 step response, 302–307, 317–318, 493–495 transient response, 495–496 underdamped responses, 291, 296–299, 305, 317 Parallel-series two-port circuit connection, 714 Parameters of two-port circuits, 701–708, 718 Parseval’s theorem, 684–691 filter applications of, 687–688 Fourier transform and, 684–691 graphic interpretation of, 685–686 rectangular voltage pulse analysis using, 688–690 time-domain energy calculations, 684–690 Partial fraction expansion, 464–474, 479, 506–509, 526 distinct complex roots of D(s), 467–469 distinct real roots of D(s), 465–466 improper rational function, 464, 473–474 inverse Laplace transforms in, 464–474, 479 Laplace transform analysis and, 506–509, 526 Laplace transform pairs for, 473 proper rational functions, 464–465, 479 repeated complex roots of D(s), 471–473 repeated real roots of D(s), 469–471 time invariant circuits, 508–509, 526 transfer function H(s) in, 506–509, 526 Partitioned matrix, 737–739 Passband frequencies, 544–545, 570 807 Passive current elements, 49, 198, 224, 337–340 capacitors, 198, 224, 339–340 defined, 49 frequency domain, 337–340 ideal sources, 49 impedance (Z), 340 inductors, 198, 224, 338–339 reactance, 340 resistors, 337–338 voltage to current (v–i) relationships, 337–340 Passive filter circuits, 542–577 bandpass filters, 545, 556–565, 571 bandreject filters, 545, 565–569, 571 bandwidth ( b ), 557, 559, 567–568, 571 center (resonant) frequency (vo), 556–558, 567–568, 571 cutoff frequency (vc), 544–545, 547–548, 553, 555, 559, 567–568, 570 defined, 545–546 filtering capabilities of, 545–546 frequency response and, 542, frequency response plots, 544–545 high-pass filters, 544–545, 552–556, 571 low-pass filters, 544–552, 570 magnitude plot, 544 qualitative analysis, 546–547 quantitative analysis, 548–549 passband frequencies, 544–545, 570 phase angle plot, 544 pushbutton telephones, 543, 570 quality factor (Q), 557, 560, 567, 571 relationship between frequency and time domains, 551, 565 stopband frequencies, 544–545, 570 transfer function H(s) for, 544, 551, 555–556, 564, 566–567, 569–571 Passive sign convention, 35, 40 Path, defined, 112–113 Per-phase quantity (f), 425 Period, sinusoidal sources, 328 Periodic functions, 624–627, 631–636, 639–647, 650–652, 654–655, 666–668 amplitude spectrum of, 650–652 aperiodic function transition from, 666–668 average-power calculations, 643–646, 655 defined, 624, 654 Fourier coefficients and, 627, 631–636 Fourier series application of, 639–643 Fourier series representation of, 627 Fourier transforms and, 666–668 phase spectrum of, 650–652 root-mean-square (rms) value, 646–647, 655 steady-state response using, 639–643 symmetry effects, 631–636, 654 waveforms, 624–626 Phase angle (f), 328 Phase angle plots, 544, 767–496, 775–777 Phase current, 425, 427–429 Phase spectrum, 650–652 Z10_NILS0545_10_GE_IDX.qxd 4/7/14 4:15 PM Page 808 www.downloadslide.com 808 Index Phase voltage, 420, 424–426 Phasor diagrams, 364–366, 425, 428 Phasors, 332–337, 367 defined, 332 frequency domain and, 333, 367 inverse transform, 334–336, 367 sinusoidal steady-state analysis and, 332–337, 367 transform, 333, 367 Pi (p)-equivalent circuit, 752–754 Pi (p) interconnection, 93 Pi to tee (p to T) equivalent circuit, 93–95 Planar circuits, 112–113 Polar form of complex numbers, 745–746 Polarity, 37–38, 212–214, 217–218, 225, 361–362 dot convention for, 212–214, 217–218, 225, 363–364 ideal transformers, 361–362 mutual inductance, 212–214, 217–218, 225 power references, 37–38 voltage and current ratios, 361–362 Poles (roots), 474–475, 480, 506, 761–762, 769–771 Bode plots and, 761–762, 769–771 complex, 769–771 defined, 474 rational function F(s), 474–475, 479 real, first order, 761–762 transfer function H(s), 506 Ports, 698 Positive (abc) phase voltage sequence, 420 Potential coil, 435 Power (p), 36–40, 53–54, 70, 142–144, 151, 201–203, 205–208, 224, 381, 404–405, 419, 435–437, 439, 759–760 algebraic signs of, 37–38 balancing, model for, 39–40 capacitors, 205–208, 224 defined, 37, 40 decibel (dB) used for, 759–760 electrical, transmission and distribution of, 419, 438–439 energy (w) and, 36–39 inductors, 201–203, 224 maximum transfer, 142–144, 151 measurement of, 435–737, 439, 759–760 polarity references, 37–38 resistors and, 53–54, 70 standby (vampire), 381, 404–405 wattmeter, 435–437, 439 Power calculations, 380–417, 430–435, 439, 643–646, 655 apparent power, 390, 406 appliance ratings, 387 average (real) power (P), 383–387, 393–395, 406, 430–431, 643–646, 655 balanced three-phase circuits, 430–435, 439 balancing from an ac circuit, 396–397 capacitive circuits, 385 complex power (S), 390–394, 406, 431 delta ( ¢ ) connected loads, 431–432 equations for, 391–398 inductive circuits, 384–385 instantaneous power, 382–383, 406 maximum power transfer, 398–404, 406 parallel loads, 395–396 periodic functions and, 643–646, 655 power factor (pf), 385, 406 reactive factor (rf), 385, 406 reactive power (Q), 383–387, 393–395, 406 resistive circuits, 384 root-mean-square (rms) value, 388–389 sinusoidal steady-state analysis, 380–417 three-phase circuits, 430–435, 439 standby (vampire) power, 381, 404–405 wye (Y) connected loads, 430–431 unspecified loads, 434 Power equation, 37 Power factor (pf), 385, 406 Power systems, 27 Primary winding, transformers, 355 Problem solving strategy, 25, 29–30 Pushbutton telephone circuits, 543, 570 Q Qualitative analysis, 546–547, 553, 557–558, 566 bandpass filters, 557–558 bandreject filters, 566 high-pass filters, 553 low-pass filters, 546–547 Quality factor (Q), 559, 561, 567, 571, 606–607 active (narrowband) filter circuits, 606–607 passive filter circuits, 559, 561, 567, 571 Quantitative analysis, 548–549, 552–553, 558–560, 566–569 bandpass filters, 558–560 bandreject filters, 566–569 high-pass filters, 552–553 low-pass filters, 548–549 Quarter-wave symmetry, 634–635, 654 R Rational function F(s), 464–475, 479–480 defined, 464 partial fraction expansion of, 464–474, 479 poles of, 474–475, 480 zeros of, 474–475, 480 RC circuits, see Resistor-capacitor (RC) circuits Reactance, impedance and, 340 Reactive factor (rf), 385, 406 Reactive power (Q), 383–387, 393–395, 406 See also Power calculations Real first-order poles and zeros, 761–762 Real models, see Equivalent circuits Real power, see Average power Reciprocal two-port circuits, 707–708, 718 Rectangular (Cartesian) form of complex numbers, 745 Reflected impedance (Zr), 356, 367 Z10_NILS0545_10_GE_IDX.qxd 4/7/14 4:15 PM Page 809 www.downloadslide.com Index Resistance (R), 52–55, 70, 91–92, 135–137, 167, 184–185 conductance (G) and, 53, 82 equivalent, 80–82, 86–87 measurement of, 91–92 Ohm’s law, 52–53, 70 operational amplifiers (op amps), 167, 184–185 resistors as models of, 52–55, 70 strain gages for, 167, 184–185 Thévenin equivalent (RTh), 135–137 Resistive circuits, 78–109, 384 constant (dc) sources, 78 current-divider, 85, 97 current-division analysis, 86–88, 97–98 delta to wye ( ¢ to Y) equivalent, 93–95, 98 load, 84 measurement of voltage and current in, 88–91, 98 parallel-connected (in parallel), 81–83, 97 pi to tee (p to T) equivalent, 93–95 power calculations for, 384 resistors, 80–83, 97 series-connected (in series), 80, 97 touch screens, 79, 95–97 voltage-divider, 83–84, 97 voltage-division analysis, 86–88, 97 Wheatstone bridge, 91–92, 98 Resistor-capacitor (RC) circuits, 234, 236, 242–246, 251–258, 261, 268, 492–493, 550–556 circuit symbols for, 236, 242 cutoff frequency, 553, 555 defined, 234 frequency response plot of, 553 general solution for responses of, 253–258, 268 high-pass filters, behavior of as, 552–556 Laplace transform analysis of, 492–493 low-pass filters, behavior of as, 550–551 natural response of, 242–246, 253–258, 268, 492–493 qualitative analysis of series, 552–553 quantitative analysis of series, 553 s-domain, 492–493 sequential switching, 258, 261 step response, 251–258, 268 time constant (t), 243, 268 unbounded response, 262–263 voltage (v), deriving expression for, 243 Resistor-inductor (RL) circuits, 234, 236–242, 246–250, 253–260, 268, 546–549, 554–556 circuit symbol for, 236 current (i), deriving expression for, 236–238 cutoff frequency, 547–549, 555 defined, 234 frequency response plots of, 546–547 general solution for responses of, 253–258, 268 high-pass filters, behavior of as, 552–556 low-pass filters, behavior of as, 546–549 natural response of, 236–242, 253–258, 268 809 qualitative analysis of series, 546–547 quantitative analysis of series, 548–549 sequential switching, 258–260 steady-state response, 239 step response, 246–250, 253–258, 268 time constant (t), 238–239, 268 transient response, 239 Resistor-inductor-capacitor (RLC) circuits, 286–325, 493–496, 557–569 bandpass filters, behavior of as, 557–565 bandreject filters, behavior of as, 565–569 characteristic equation for, 289, 291–292, 308, 317 circuit symbols for, 288, 307–308 critically damped voltage responses, 291, 299–300, 305, 308, 317–318 cutoff frequency (vc), 559, 567–568 clock for computer timing, 287, 315–316 frequency response plots, 557–558, 566 frequency selective circuits, 557–569 Laplace transform, analysis of using, 493–496 natural response of, 288–301, 307–311, 317 Neper frequency (a) for, 290–291, 308 overdamped voltage responses, 291, 293–295, 304, 308, 317–318 parallel, 288–307, 317, 493–496 qualitative analysis of series, 557–558, 566 quantitative analysis of series, 558–560, 566–569 resonant radian frequency (v0), 290–291, 308 s-domain, 493–496 series, 307–311, 317–318 step response of, 302–311, 317–318, 493–495 transfer function H(s) for, 564, 566–567, 569, 571 transient response of, 495–496 underdamped voltage response, 291, 296–299, 305, 308–310, 317–318 Resistors, 52–55, 70, 80–83, 97, 111, 147–150, 313–315, 337–338, 488, 526, 783 black box, 80 circuit symbol for, 53 component values, 783 conductance (G) and, 53 defined, 52, 70 electrical resistance and, 52–55, 69–70 feedback, 313–315 frequency domain, 337–338 integrating amplifiers with, 313–315 Laplace transforms for analysis of, 488, 526 parallel-connected (in parallel), 81–83, 97 power terminals of, 53–54, 70 resistance (R) and, 52–55, 70 s-domain, 488, 526 sensitivity analysis, 111, 147–150 series-connected (in series), 80, 97 time and frequency domain elements, 488 voltage to current (v–i) relationships, 337–338 Resonant radian frequency (vo), 290–291, 308 See also Center frequency (v0) Z10_NILS0545_10_GE_IDX.qxd 4/7/14 4:15 PM Page 810 www.downloadslide.com 810 Index Response, 234–325, 331–332, 367, 449, 478–479, 492–504, 515–517, 525–526, 542, 681–683 clock for computer timing, 287, 315–316 complete, 449, 478–479 first-order circuits, 234–285 Fourier transform for, 681–683 frequency, 542 general solutions for, 253–258, 268 integrating amplifiers, 263–266, 268, 311–315, 317 Laplace transform used for, 449, 478–479, 492–504, 517–519, 525 multiple mesh circuits, 496–498 natural, 234, 236–246, 253–258, 268, 288–301, 307–311, 317, 492–493 pacemaker circuits, 235, 267–268 parallel RLC circuits, 288–307, 317–318, 493–496 resistor-capacitor (RC) circuits, 234, 236, 242–246, 251–258, 261, 268, 492–493 resistor-inductor (RL) circuits, 234, 236–242, 246–250, 253–260, 268 resistor-inductor-capacitor (RLC) circuits, 286–325, 493–496 second-order circuits, 286–325 sequential switching, 258–262, 265, 268 series RLC circuits, 307–311, 317–318 sinusoidal, 331–332, 367, 515–517, 525–526, 683 steady-state, 239, 449, 515–517, 525–526, 683 step, 234, 246–258, 268, 302–311, 317–318, 493–498 transfer function and, 515–517, 525–526, 683 transient, 239, 449, 495–496, 681–682 unbounded, 262–263, 268 RL circuits, see Resistor-inductor (RL) circuits RLC circuits, see Resistor-inductor-capacitor (RLC) circuits Root-mean-square (rms) value, 329–331, 388–389, 646–647, 655 effective value (eff) as, 388–389 periodic functions, 646–647, 655 power calculations and, 388–389 sinusoidal sources, 329–331 Roots, 465–475, 480, 749–750 complex numbers, 465–473, 749–750 distinct complex, 467–469 distinct real, 465–466 Laplace transform pairs for, 473 partial fraction expansion of D(s), 464–473, 480 repeated complex, 471–473 poles (denominator polynomial), 474–475, 480 repeated real, 469–471 zeros (numerator polynomial), 474–475, 480 Row matrix, 730 S s-domain, 463–477, 479–480, 488–524, 526 capacitor in, 489–490, 526 circuit analysis in, 490–504, 526 circuit symbols for, 488–489, 492–493, 497, 499, 501–502 final-value theorem, 475–477, 480 impulse function Kd(t) in, 518–524, 526 inductor in, 488–489, 526 initial-value theorem, 475–477, 480 inverse Laplace transform and, 464–474, 479 Kirchhoff’s laws and, 491 Laplace transform and, 463–477, 479–480, 488–509, 526 mutual inductance in, 500–501 notation of in Laplace transforms, 463–464 Ohm’s law in, 490–491 partial fraction expansion, 464–474, 479, 506–509, 526 poles (denominator polynomial), 474–475, 480 resistor in, 488, 526 responses of circuits in, 492–504 superposition, use of in, 502–504 terminal voltage-current equations in, 488–490, 526 Thévenin equivalent, use of in, 499–500 transfer function H(s) in, 504–517, 526 zeros (numerator polynomial), 474–475, 480 Scale-changing property, operational transforms, 461, 679 Scaling, 584–586, 614 frequency factor (kf), 584, 614 magnitude factor (km), 584, 614 op-amp filter design using, 585–586 Second-order circuits, 286–325 defined, 288 general solution of differential equations, 288–292 integrating amplifiers, 311–315, 317 natural response of, 288–301, 307–311, 317 resistor-inductor-capacitor (RLC), 286–325 step response of, 302–311, 317–318 Secondary winding, transformers, 355 self-impedance (Z), 355–356 Self-inductance, 215–216, 218–219, 225 Sensitivity analysis, resistors, 111, 147–150 Sequential switching, 258–262, 265, 268 first-order circuit responses and, 258–262, 265, 268 integrating amplifier with, 265 resistor-capacitor (RC) circuits, 258, 261 resistor-inductor (RL) circuits, 258–260 Series-connected (in series) circuits, 61, 70, 80, 97, 209–211, 225, 342–346, 714 See also Series RLC Circuits black box concept, 80 capacitors, 210–211, 225 impedances combined in, 342–346 inductors, 209–210, 225 Kirchhoff’s current law for, 61, 70, 80 node positions, 61, 70 resistors, 80, 97 two-port circuits, 714 Series-parallel two-port circuit connection, 714 Series RLC circuits, 307–311, 317–318 capacitor voltage in, 308–309 characteristic equation of, 308, 317 circuit symbols for, 307–308 critically damped response, 308 natural response, 307–311 Z10_NILS0545_10_GE_IDX.qxd 4/7/14 4:15 PM Page 811 www.downloadslide.com Index Neper frequency (a), 308 overdamped response, 308 resonant radian frequency (v0), 308 step response, 307–311, 317–318 underdamped responses, 308–310 Short circuit, 57 Sifting property, 454 Signal-processing systems, 27–28 Signed minor, 727–728 Signum function, Fourier transform of, 673 Simultaneous equations, 113–115, 725–744 characteristic determinant, 726 circuit analysis using, 113–115 Cramer’s method, 726 determinant evaluation for, 727–730 determination of number of, 113–114 matrices for, 729–730, 734–739 matrix algebra for, 730–734, 740–744 numerator determinant, 726–727 solution of, 725–744 systematic approach using, 114–115 Sine functions, 637–638 Single-phase equivalent circuits, 424–425, 439 Sinusoidal response, 331–332, 367, 487, 517–519, 525, 528, 683 Fourier transform for, 683 Laplace transform for, 487, 517–519, 525 steady-state analysis and, 331–332, 367 steady-state component of, 332 surge suppressors, 487, 525 transfer function H(s) and, 517–519, 528 transient component of, 334 Sinusoidal sources, 328–331, 367, 449, 478–479 complete circuit response of, 449, 478–479 current (i), 328–329, 367 Laplace transforms for, 449, 478–479 period, 328 phase angle (f), 328 root-mean-square (rms) value of, 329–331 steady-state analysis, 328–331, 367 voltage (v), 328–330, 367 Sinusoidal steady-state analysis, 326–417 delta-to-wye ( ¢ -to-Y) transformations, 346–348 frequency domain, 333, 337–342, 349–363, 367 household distribution circuit, 327, 366 ideal transformer, 358–363, 367 impedance (Z), 340, 342–352, 356, 363, 367 Kirchhoff’s laws, 341–342 mesh-current method, 353–354 node-voltage method, 352–353 Norton equivalent circuit, 349 passive circuit elements, 337–340 phasor diagrams for, 364–366 phasors, 332–337, 367 power calculations, 380–417 reactance, 340 response, 331–332, 367 source transformations, 349–352 811 sources, 328–331, 367 standby (vampire) power, 381, 404–405 Thévenin equivalent circuit, 349–352 transformers, 354–363, 367 voltage to current (v-i) relationships, 337–340 Source transformations, 131–135, 137–138, 151, 349–352 circuit analysis using, 131–135, 137–138, 151 defined, 132 frequency domain, 349–352 impedance (Z) and, 349–352 Norton equivalent circuits, 137, 349 Thévenin equivalent circuit, 137–138, 349–351 Sources, 48–51, 64–67, 70, 78, 328–331, 367, 421–422, 449, 478–479, 521–524 active element of, 49 complete circuit response and, 449, 478–479 constant (dc), 78 controlled, 49 delta ( ¢ ) configurations, 421–422 dependent, 48–49, 51, 64–67, 70 ideal current, 48–51, 70 ideal voltage, 48–51, 70 impulsive, 521–524 independent, 48, 51, 70 interconnection of, 50–51 Laplace transform and, 449, 478–479, 521–524 passive element of, 49 sinusoidal, 328–331, 367, 449, 478–479 three-phase voltage, 421–422 wye (Y) configurations, 421–422 Square matrix, 730 Square wave input of sinusoids, 625, 652–654 Standby (vampire) power, 381, 404–405 Steady-state analysis, see Sinusoidal steady-state analysis Steady-state response, 239, 449, 478–479, 515–517, 525–526, 639–643, 655, 683 defined, 239 direct approach to, 641–643 first-order circuits, 239 Fourier series analysis, 639–643, 655 Fourier transform for, 683 Laplace transform analysis and, 515–517, 526 periodic functions used for, 639–643 sinusoidal, 515–517, 525–526, 683 surge suppressors and, 487, 525 transfer function H(s) and, 515–517, 526 transient effects and, 449, 478–479 Step function Ku(t), 451–452, 479 Step response, 234, 246–258, 268, 302–311, 317–318, 493–498 capacitor voltage in series RLC circuits, 308–309 critically damped voltage, 305, 317–318 defined, 234, 268 direct approach, 303–304 first-order circuits, 234, 246–258, 268 general solution for, 253–258, 268 indirect approach, 303 Laplace transform analysis and, 493–498 Z10_NILS0545_10_GE_IDX.qxd 4/7/14 4:15 PM Page 812 www.downloadslide.com 812 Index Step response (Continued) magnetically coupled coils and, 257–258 method of calculating, 254 multiple mesh circuit, 496–498 overdamped voltage, 304, 317–318 parallel RLC circuits, 302–307, 317–318, 493–495 resistor-capacitor (RC) circuits, 251–258, 268 resistor-inductor (RL) circuits, 246–250, 253–258, 268 resistor-inductor-capacitor (RLC) circuits, 302–311, 317–318 series RLC circuits, 307–311, 317–318 underdamped, 305, 310, 317–318 Stopband frequencies, 544–545, 570 Straight-line amplitude plots, 762–766, 772–774 Straight-line phase angle plots, 767–769 Strain gages, 167, 184–185 Summing-amplifier circuit, 174–175, 186 Supermesh, 126 Supernode, 119–120 Superposition, 144–147, 151, 502–504 circuit analysis using, 144–147, 151 defined, 144 Laplace transform analysis and, 502–504 s-domain, 502–504 Surge suppressors, 487, 525 Susceptance (B), 344 Switches, 198, 254–262, 265, 487, 518–521, 525 arcing, 198 capacitor circuits, 518–519 inductor circuits, 198, 519–521 impulse functions created by, 518–521 integrating amplifier with, 265 Laplace transform analysis and, 487, 518–521, 525 RL and RC circuits, 254–262, 268 sequential switching, 258–262, 268 surge suppressors, 487, 525 Symmetric two-port circuits, 708, 718 Symmetry, 631–636, 654 even-function, 631–632, 654 Fourier coefficients, effects on, 631–636, 654 half-wave, 633–634, 654 odd-function, 632–633, 636, 654 quarter-wave, 634–635, 654 T T-equivalent circuit, 751–752 Tee (T) interconnection, 93 Terminals, 53–54, 58, 168–172, 186, 204–208, 225, 488–490, 700 capacitor equations, 204–208, 225, 489–490 current (i) input constraints, 170–171, 186 inductor equations, 198–203, 225, 488–489 measurements for circuit construction, 58 operation amplifiers (op amps), 168–172, 186 resistor power at, 53–54 two-port circuits, 700 variable characteristics (voltage and current), 168–172, 186 voltage (v) input constraints, 169–170, 186 Terminated two-port circuits, 709–713 Thévenin equivalent circuits, 135–141, 151, 349–351, 499–500 amplifier circuit using, 140–141 analysis of, 135–141, 151 defined, 135 dependent sources, 138, 140 finding equivalent of, 136–137 frequency-domain, 349–351 impedance (Z) in, 349–351 independent sources, 139–140 Laplace transform analysis and, 499–500 resistance source (RTh), 135–137 s-domain, use of in, 499–500 source transformations used for, 137–138, 349–351 voltage source (VTh), 135–137 test source for, 140 Three-phase circuits, see Balanced three-phase circuits Time constant (t), 238–239, 243, 268 resistor-capacitor (RC) circuits, 243, 268 resistor-inductor (RL) circuits, 238–239, 268 Time domain, 333–335, 367, 460–464, 551, 565, 668–670, 677–681, 684–690 convergence of Fourier transform integral and, 668–670 convolution in, 679–680 differentiation in, 678 energy calculations, 684–690 Fourier transform and, 668–670, 677–681, 686–692 frequency domain relationships, 551, 565, 679 frequency domain transformations, 333–335, 367 integration in, 678 integrodifferential equations for, 462–464 inverse phasor transformation, 334–335, 367 Laplace transform and, 460–464 operational transforms for, 460–461, 677–681 Parseval’s theorem for, 684–690 passive-filter circuits and, 551, 565 phasor transformation, 333, 367 scale change in, 679 translation in, 460–461, 679 Time-invariant circuits, 508–509, 526 Tolerance, 84 Touch screens, 79, 95–97, 197, 222–224 capacitance of, 197, 222–224 resistive circuits of, 79, 95–97 Transducers (strain gages), 167, 184–185 Transfer function H(s), 504–517, 526, 551, 555–556, 566–567, 569–571, 591, 594–601, 605–606, 614 active-filter circuits, 591, 594–599, 606, 614 bandpass filters, 564, 571, 591, 606 bandreject filters, 566–567, 569, 571 Z10_NILS0545_10_GE_IDX.qxd 4/7/14 4:15 PM Page 813 www.downloadslide.com Index Butterworth filters, 598–601, 605, 614 cascading identical filters and, 594–597 circuit analysis, 504–517, 526 convolution integral and, 509–515, 526 defined, 504 high-pass filters, 555–556, 571 Laplace transform circuit analysis and, 504–517, 526 low-pass filters, 551, 570 memory and, 514–515 partial fraction expansion, use of in, 506–509, 526 passive-filter circuits and, 551, 555–556, 564, 566–567, 569–571 poles of, 506 steady-state sinusoidal response and, 515–517, 526 time-invariant circuits, 508–509, 526 weighting function, 514–515 zeros of, 506 Transformations, see Circuit transformations Transformers, 354–363, 367, 751–758 defined, 354 dot convention for, 361–362 equivalent circuits and, 751–758 frequency domain and, 354–363, 367 ideal, 355, 358–363, 367, 751–758 self-impedance (Z), 355–356 limiting values of, 358–360 linear, 355–358, 367 winding (primary and secondary), 355 reflected impedance (Zr), 356, 367 sinusoidal steady-state analysis, 354–363, 367 voltage and current ratios, 360–362, 367 Transient effects on circuits, 449, 478–479 Transient response, 239, 495–496, 681–682 defined, 239 Laplace transform for, 495–496 Fourier transform for, 681–682 Translation, operational transforms for, 460–461, 679 Transmission parameters, 703 Transpose of a matrix, 734 Trigonometric identities, 779 Twin-T notch filter, 608–611 Two-port circuits, 698–723 analysis of, 709–713 black box amplifier, 699, 717 conversion of parameters, 706–708 hybrid parameters, 703 interconnected, 714–717 intermittence, 702–703 parameter conversion for, 704–706 parameters of, 701–708, 718 ports, 698 reciprocal, 707–708, 718 symmetric, 708, 718 terminal equations for, 700 terminated, 709–713 transmission parameters, 703 z parameters, 701–702, 709–713 813 U Unbounded response, 262–263, 268 Underdamped responses, 291, 296–299, 305, 308–310, 317–318 characteristics of, 298 damped radian frequency, 296 damping factor (coefficient), 297 natural response equations, 296–297, 317 parallel RLC circuits, 291, 296–299, 305, 317 series RLC circuits, 308–310, 317 step response equations, 308, 318 Unilateral (one-sided) Laplace transform, 450–451 Unit impulse function d(t), 453, 479 Unit step function u(t), 451, 479, 674 V Vampire (standby) power, 381, 404–405 Variable-parameter function, 453–454 Volt-amp reactive (VAR), unit of, 385, 406 Volt-amps (VA), unit of, 390, 406 Voltage (v), 33–35, 40, 48–51, 54–55, 60, 62–63, 70, 88–91, 98, 135–137, 168–172, 186, 198–201, 205–208, 210, 224–225, 243, 308–309, 328–330, 341, 360–362, 367, 420–427, 439, 488–491, 526 a-, b-, and c-phase, 420, 439 capacitors, 205–208, 224–225, 308–309, 489–490, 526 current (i) and, 33–35, 199–201, 490–491 defined, 34, 40 determination of, 198–199 electric charge and, 33–34 equivalent capacitance in, 210 frequency domain, 341, 360–362, 367 gain (A), 169 inductors, 198–201, 224, 488–489, 526 input constraints, 169–170, 186 Kirchhoff’s law (KVL), 60–63, 70, 341, 424–425 line, 424–426 measurement of, 88–91, 98 natural response and, 243 negative (acb) phase sequence, 420 node-voltage equation (VN), 422–423 operational amplifiers (op amps), 168–172, 186 phase, 420, 424–426 polarity of, 361–362 positive (abc) phase sequence, 420 power in a resistor, 54–55, 70 RC circuits, deriving expression for, 243 reference direction, 35 resistors, 488, 526 s-domain equations for, 488–491, 526 series RLC capacitor step response, 308–309 sinusoidal phase sequences, 420–421 sinusoidal source, 328–330, 367 sources, 48–51, 70, 421–422 terminal variable characteristics, 168–172, 186 Z10_NILS0545_10_GE_IDX.qxd 4/7/14 4:15 PM Page 814 www.downloadslide.com 814 Index Voltage (v) (Continued) Thévenin equivalent (VTh), 135–137 three-phase, 420–427, 439 transfer characteristics of, 168–169, 186 transformer ratio, 360–362, 367 wye (Y) and delta ( ¢ ) configurations, 421–422 wye-wye (Y-Y) circuit analysis and, 422–427, 439 Voltage-divider circuits, 83–84, 97 Voltage-division circuit analysis, 86–88, 97 Voltage drop, 79, 86–87 Voltage pulse analysis, 667, 688–690 Voltage to current (v–i) relationships, 198–199, 205, 337–340, 367 capacitors, 205, 339–340 frequency domain, 337–340 impedance (Z) of, 340 inductors, 198–199, 338–339 reactance of, 340 resistors, 337–338 sinusoidal steady-state analysis and, 337–338, 367 Voltmeter, 88–89, 98 W Watt (W), unit of, 385, 406 Wattmeter, 435–437, 439 Waveforms, 624–626 Weighting function, memory and, 514–515 Wheatstone bridge, 91–92, 98 Winding (primary and secondary), 355 Wye (Y) connected loads, power in, 430–431 Wye (Y) interconnection, 93 Wye (Y) source configurations, 421–422 Wye-delta (Y- ¢ ) circuit analysis, 427–429 Wye-wye (Y-Y) circuit analysis, 422–427, 439 Z z parameters, two-port circuits, 701–702, 709–713 Zero frequency, 550 Zeros (roots), 474–475, 480, 506, 761–762, 769–771 Bode plots and, 761–762, 769–771 complex, 769–771 defined, 474 rational function F(s), 474–475, 479 real, first order, 761–762 transfer function H(s), 506 Z10_NILS0545_10_GE_IDX.qxd 4/7/14 4:15 PM Page 815 www.downloadslide.com This page is intentionally left blank Z10_NILS0545_10_GE_IDX.qxd 4/7/14 4:15 PM Page 816 www.downloadslide.com This page is intentionally left blank Z11_NILS0545_10_GE_EP.qxd 4/7/14 4:16 PM Page www.downloadslide.com A List of Tables Table No Title 1.1 1.2 1.3 1.4 4.1 4.2 6.1 6.2 7.1 8.1 8.2 8.3 Page No The International System of Units (SI) Derived Units in SI Standardized Prefixes to Signify Powers of 10 Interpretation of Reference Directions in Fig 1.5 Terms for Describing Circuits PSpice Sensitivity Analysis Results Terminal Equations for Ideal Inductors and Capacitors Equations for Series- and Parallel-Connected Inductors and Capacitors Value of e - t>t for t Equal to Integral Multiples of t Natural Response Parameters of the Parallel RLC Circuit The Response of a Second-Order Circuit is Overdamped, Underdamped, or Critically Damped In Determining the Natural Response of a Second-Order Circuit, We First Determine Whether it is Over-, Under-, or Critically Damped, and Then We Solve the Appropriate Equations In Determining the Step Response of a Second-Order Circuit, We Apply the Appropriate Equations Depending on the Damping Impedance and Reactance Values Admittance and Susceptance Values Impedance and Related Values Annual Energy Requirements of Electric Household Appliances Three Power Quantities and Their Units An Abbreviated List of Laplace Transform Pairs An Abbreviated List of Operational Transforms Four Useful Transform Pairs Summary of the s-Domain Equivalent Circuits Numerical Values of vo(t) Input and Output Voltage Magnitudes for Several Frequencies Normalized (so that vc = rad>s) Butterworth Polynomials up to the Eighth Order Fourier Transforms of Elementary Functions Operational Transforms Parameter Conversion Table Terminated Two-Port Equations 8.4 9.1 9.2 9.3 10.1 10.2 12.1 12.2 12.3 13.1 13.2 14.1 15.1 17.1 17.2 18.1 18.2 31 31 31 35 113 150 225 225 239 291 317 317 318 340 344 367 387 390 457 462 473 490 514 549 599 675 680 704 710 Greek Alphabet A a Alpha I i Iota P r Rho B b Beta K k Kappa © s Sigma ≠ g Gamma ¶ l Lambda T t Tau ¢ d Delta M m Mu ⌼ y Upsilon E P Epsilon N n Nu £ f Phi Z z Zeta ⌶ j Xi X x Chi H h Eta O o Omicron ° c Psi ™ u Theta ß p Pi Æ v Omega Z11_NILS0545_10_GE_EP.qxd 4/7/14 4:16 PM Page www.downloadslide.com An Abbreviated List of Laplace Transform Pairs f (t) (t > – ) Type F(s) d(t) (impulse) u(t) (step) s t (ramp) s2 e - at (exponential) s + a sin vt (sine) v s2 + v2 cos vt (cosine) s s2 + v2 te - at (damped ramp) (s + a)2 e - at sin vt (damped sine) v (s + a)2 + v e - at cos vt (damped cosine) s + a (s + a)2 + v An Abbreviated List of Operational Transforms f (t) F(s) Kf(t) KF(s) f1(t) + f2(t) - f3(t) + Á F1(s) + F2(s) - F3(s) + Á df(t) dt sF(s) - f(0 - ) d2 f(t) dt2 s 2F(s) - sf(0 - ) - df(0 - ) dt n d f(t) dtn t f(x) dx s n F(s) - s n - f(0 - ) - s n - F(s) s L0 f(t - a)u(t - a), a > e - as F(s) e - at f(t) F(s + a) f(at), a > s Fa b a a tf(t) tn f(t) f(t) t - dF(s) ds (- 1) n dn F(s) ds n q Ls F(u) du df(0 - ) df2(0 - ) dn - f(0 - ) Á - s n-3 dt dt2 dtn - Z11_NILS0545_10_GE_EP.qxd 4/7/14 4:16 PM Page www.downloadslide.com Periodic Functions f (t) f(t) A A T 2T t ϪA Triangular Wave f (t) t T T/2 3T/2 Half-wave rectified sine 2T T T/2 3T/2 Full-wave rectified sine 2T f(t) A A T 2T t ϪA Square Wave t Fourier Series 8A np B sin a b R sin nv0t p2 n =a 1,3,5, n q f(t) = Triangular wave f(t) = q cos nv0t A A 2A + sin v0t a p p n = 2,4,6, n2 - Half-wave rectified sine q f(t) = 4A sin nv0t a p n = 1,3,5, n Square wave f(t) - q cos nv0t 2A 4A a p p n = (4n2 - 1) Full-wave rectified sine Z11_NILS0545_10_GE_EP.qxd 4/7/14 4:16 PM Page www.downloadslide.com Fourier Transforms of Elementary Functions f (t) F( V ) d(t) (impulse) A (constant) 2pAd(v) sgn(t) (signum) 2>jv u(t) (step) pd(v) + 1>jv e - atu(t)(positive-time exponential) 1>(a + jv) at e u(- t) (negative-time exponential) e - a|t| (positive- and negative-time exponential) 1>(a - jv) 2a>(a2 + v2) e jv0t (complex exponential) 2pd(v - v0) cos v0t (cosine) p[d(v + v0) + d(v - v0)] sin v0t (sine) jp[d(v + v0) - d(v - v0)] Operational Transforms f (t) F( V ) Kf(t) KF(v) f1(t) - f2(t) + f3(t) n n d f(t)>dt F1(v) - F2(v) + F3(v) ( jv)n F(v) t f(x) dx L- q F(v)>jv f(at) v F a b, a > a a f(t - a) e - jva F(v) e jv0t f(t) f(t) cos v0t F(v - v0) 1 F(v - v0) + F(v + v0) 2 q L- q x (l)h(t - l) dl X(v)H(v) q f1(t) f2(t) F (u)F2(v - u) du 2p L- q tn f(t) ( j)n dn F(v) dvn ... Authorized adaptation from the United States edition, entitled Electric Circuits, 10th edition, ISBN 978-0-13-376003-3, by James W Nilsson and Susan A Riedel, published by Pearson Education © 2015... balancing power, simple resistive circuits, node voltage method, mesh current method, Thévenin and Norton equivalents, op amp circuits, firstorder circuits, second-order circuits, AC steady-state analysis,... Circuit Variables 1.1 Electrical Engineering: An Overview Electrical engineering is the profession concerned with systems that produce, transmit, and measure electric signals Electrical engineering