www.EngineeringEBooksPdf.com Introduction to Electric Circuits EIGHTH EDITION Richard C Dorf U n iv e rs ity o f C a lifo rn ia James A Svoboda C la rk s o n U n iv e rs ity WILEY John Wiley & Sons, Inc www.EngineeringEBooksPdf.com VICE PRESIDENT AND EXECUTIVE PUBLISHER ASSOCIATE PUBLISHER SENIOR EDITORIAL ASSISTANT PRODUCTION SERVICES MANAGER PRODUCTION EDITOR EXECUTIVE MARKETING MANAGER CREATIVE DIRECTOR DESIGNER MEDIA EDITOR PRODUCTION SERVICES Donald Fowley Dan Sayre Katie Singleton Dorothy Sinclair Janet Foxman Christopher Ruel Harry Nolan Jim O’Shea Lauren Sapira Elm Street Publishing Services COVER IMAGES: Main Image: © Science Photo Library/Getty Images, Inc.; inset © SuperStock Inset images: C SuperStock; Goodshot/Jupiter/Getty Images, Inc.; Stockbyte/SuperStock This book was set in 10/12 pt in Times New Roman by Thomson Digital, and printed and bound by RRD Jefferson City The cover was printed by RRD Jefferson City This book is printed on acid-free paper @ Copyright c 2010, 2006, 2004, 2001 John Wiley & Sons, Inc 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, scanning or otherwise, except as permitted under Sections 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, website w\w.copyright.com Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., Ill River Street, Hoboken, NJ 07030-5774, (201) 748-6011, fax (201) 748-6008, website wmv.wiley.com/go/permissions Evaluation copies are provided to qualified academics and professionals for review purposes only, for use in their courses during the next academic year These copies are licensed and may not be sold or transferred to a third party Upon completion of the review period, please return the evaluation copy to Wiley Return instructions and a free of charge return shipping label are available at wr\irw.wiley.com/go/returnlabel Outside of the United States, please contact your local representative Library of Congress Cataloging-in-Publication Data Dorf, Richard C Introduction to electric circuits / Richard C Dorf & James A Svoboda.— th ed p cm ISBN 978-0-470-52157-1 (cloth : alk paper) Electric circuits I Svoboda, James A II Title TK454-.D67 2010 621.319'24— dc22 2009047257 ISBN 978-0-470-52157-1 Printed in the United States of America 10 www.EngineeringEBooksPdf.com T h e scien tific n a tu re o f th e o rd in a ry m a n Is to go o n o u t a n d d o th e b e st he can —John Prine B ut, C a p ta in , I c a n n o t c h a n g e th e la w s o f p h y sics —Lt Cmdr Montogomery Scott (Scotty), USS Enterprise D e d ic a te d to o u r g n d c h ild re n : Ian C h risto p h e r B o ila rd , K y le E v e re tt S c h a fer, a n d G h a m H e n ry S c h a fe r an d H e a th e r L y n n S v o b o d a , Ja m e s H u g h S v o b o d a , Ja c o b A rth u r L eis, M a x w e ll A n d re w L e is, a n d J a c k M a n d lin L e ffle r www.EngineeringEBooksPdf.com About the Authors Richard C Dorf, professor of electrical and computer engineering at the University of California, Davis, teaches graduate and undergraduate courses in electrical engineering in the fields of circuits and control systems He earned a PhD in electrical engineering from the U.S Naval Postgraduate School, an MS from the University of Colorado, and a BS from Clarkson University Highly concerned with the discipline of electrical engineering and its wide value to social and economic needs, he has written and lectured internationally on the contributions and advances in electrical engineering Professor Dorf has extensive experience with education and industry and is professionally active in the fields of robotics, automation, electric circuits, and communications He has served as a visiting professor at the University of Edinburgh, Scotland, the Massachusetts Institute of Technology, Stanford University, and the University of California at Berkeley A Fellow of the Institute of Electrical and Electronic Engineers and the American Society for Engineering Education, Dr Dorf is widely known to the profession for his Modern Control Systems, eleventh edition (Prentice Hall, 2008) and The International Encyclopedia o f Robotics (Wiley, 1988) Dr Dorf is also the coauthor of Circuits, Devices and Systems (with Ralph Smith), fifth edition (Wiley, 1992) Dr Dorf editedthewidely used Electrical Engineering Handbook, third edition (CRC Press and IEEE press), published in 2008 Hislatest work is Technology Ventures, third edition (McGraw-Hill 2010) James A Svoboda is an associate professor of electrical and computer engineering at Clarkson University,where he teaches courses on topics such as circuits, electronics, and computer programming He earned a PhD in electrical engineering from the University of Wisconsin at Madison, an MS from the University of Colorado, and a BS from General Motors Institute Sophomore Circuits is one of Professor Svoboda's favorite courses He has taught this course to 5,500 undergraduates at Clarkson University over the past 30 years In 1986, he received Clarkson University’s Distinguished Teaching Award Professor Svoboda has written several research papers describing the advantages of using nullors to model electric circuits for computer analysis He is interested in the way technology affects engineering education and has developed several software packages for use in Sophomore Circuits www.EngineeringEBooksPdf.com Preface The central theme of Introduction to Electric Circuits is the concept that electric circuits are part of the basic fabric of modem technology Given this theme, we endeavor to show how the analysis and design of electric circuits are inseparably intertwined with the ability of the engineer to design complex electronic, communication, computer, and control systems as well as consumer products APPROACH & O R G A N IZ A T IO N This book is designed for a one- to three-term course in electric circuits or linear circuit analysis and is structured for maximum flexibility The flowchart in Figure demonstrates alternative chapter organizations that can accommodate different course outlines without disrupting continuity The presentation is geared to readers who are being exposed to the basic concepts of electric circuits for the first time, and the scope of the work is broad Students should come to the course with the basic knowledge of differential and integral calculus This book endeavors to prepare the reader to solve realistic problems involving electric circuits Thus, circuits are shown to be the results of real inventions and the answers to real needs in industry, the office, and the home Although the tools of electric circuit analysis may be partially abstract, electric circuits are the building blocks of modem society The analysis and design of electric circuits are critical skills for all engineers W H A T ' S N E W IN THE TH E D I T I O N Increased use of PSpice K and MATLABH Significantly more attention has been given to using PSpice and MATLAB to solve circuits problems It starts with two new appendixes, one introducing PSpice and the other introducing MATLAB These appendixes briefly describe the capabilities of the programs and illustrate the steps needed to get started using them Next, PSpice and MATLAB are used throughout the text to solve various circuit analysis and design problems For example, PSpice is used in Chapter to find a Thevenin equivalent circuit and in Chapter 15 to represent circuit inputs and outputs as Fourier series MATLAB is frequently used to obtain plots of circuit inputs and outputs that help us see what our equations are telling us MATLAB also helps us with some long and tedious arithmetic For example, in Chapter 10, MATLAB helps us the www.EngineeringEBooksPdf.com — - P r e fa c e Matrices, Determinants Color Code "A ELECTRIC CIRCUIT VARIABLES RESISTIVE CIRCUITS CIRCUIT ELEMENTS METHODS OF ANALYSIS OF RESISTIVE CIRCUITS W' Complex Numbers FIGURE Flow chart showing alternative paths through the topics in this textbook complex arithmetic to analyze ac circuits and, in Chapter 14, MATLAB helps with the partial fraction required to find inverse Laplace transforms O f course, there’s more to using PSpice and MATLAB than simply running the programs W e pay particular attention to interpreting the output o f these computer programs and checking it to m ake sure it is correct Frequently, this is done in the section called, “ How Can We Check ” included in every chapter For example, Section 8.9 shows how to interpret and check a PSpice transient response, and Section 13.7 shows how to interpret and check a frequency response produced using M ATLAB or PSpice Revisions to Improve Clarity Chapter 15 covering the Laplace transform and the Fourier series and transform , Chapters 14 and 15, have been largely rewritten, both to improve clarity o f exposition and to significantly increase coverage of MATLAB and PSpice In addition, revisions have been made throughout the text to improve clarity Sometimes these revisions are small, involving sentences or paragraphs O ther, larger revisions involve pages or even entire sections More Problems The th edition contains 20 new problems, bringing the total number o f problems to more than 1,3 50 This edition uses a variety of problem types and they range in difficulty from simple to challenging, including: www.EngineeringEBooksPdf.com Preface PSpice 16 FILTER CIRCUITS 13 14 FREQUENCY RESPONCE THE LAPLACE TRANSFORM 15 TWO-PORT NETWORKS FOURIER SERIES AND FOURIER TRANSFORM 17 THE OPERATIONAL AMPLIFIER TWO-PORT NETWORKS Legend: Primary flow O Appendix Chapter Optional flow Straightforward analysis problems Analysis of complicated circuits Simple design problems (For example, given a circuit and the specified response, determine the required RLC values.) Compare and contrast, multipart problems that draw attention to similarities or differences between two situations www.EngineeringEBooksPdf.com • MATLAB and PSpice problems Design problems (Given some specifications, devise a circuit that satisfies those specifications.) How Can We Check ? (Verify that a solution is indeed correct.) FEATURES RETAINED FROM PREVIOUS EDITION S Introduction Each chapter begins with an introduction that motivates consideration o f the material o f that chapter Examples Because this book is oriented toward providing expertise in problem solving, we have included m ore than 260 illustrative examples Also, each example has a title that directs the student to exactly w hat is being illustrated in that particular example Various methods o f solving problems are incorporated into select exam ples These cases show students that multiple methods can be used to derive sim ilar solutions or, in some cases, that m ultiple solutions can be correct This helps students build the critical thinking skills necessary to discern the best choice between multiple outcomes Design Examples, a Problem-Solving Method, and "How Can We Check " Sections Each chapter concludes with a design example that uses the methods o f that chapter to solve a design problem A formal, five-step problem-solving method is introduced in Chapter and then used in each o f the design examples An important step in the problem-solving method requires you to check your results to verify that they are correct Each chapter includes a section entitled ‘ ‘How Can We Check ” that illustrates how the kind o f results obtained in that chapter can be checked to ensure correctness Key Equations and Formulas You will find that key equations, formulas, and important notes have been called out in a shaded box to help you pinpoint critical information Summarizing Tables and Figures The procedures and m ethods developed in this text have been sum m arized in certain key tables and hgures Students will find these to be an im portant problem -solving resource • Table 1.5-1 The passive convention • Figure 2.7-1 and Table 2.7-1 Dependent sources • Table 3.10-1 Series and parallel sources • Table 3.10-1 Series and parallel elements Voltage and current division Figure 4.2-3 Node voltages versus element currents and voltages www.EngineeringEBooksPdf.com • Figure 4.5-4 Mesh currents versus element currents and voltages • Figures 5.4-3 and 5.4-4 Thevenin equivalent circuits • Figure 6.3-1 The ideal op amp • Figure 6.5-1 A catalog of popular op amp circuits • Table 7.8-1 Capacitors and inductors • Table 7.13-2 Series and parallel capacitors and inductors • Table 8.11-1 First-order circuits • Tables 9.13-1, 2, and Second-order circuits • Table 10.6-1 AC circuits in the frequency domain (phasors and impedances) • Table 10.8-1 Voltage and current division for AC circuits • Table 11.5-1 Power formulas for AC circuits • Tables 11.13-1 and 11.13-2 Coupled inductors and ideal transformers • Table 13.4-1 Resonant circuits • Tables 14.2-1 and 14.2-2 Laplace transform tables • Table 14.7-1 s-domain models of circuit elements • Table 15.4-1 Fourier series of selected periodic waveforms In tro d u ctio n to S ignal P ro c e ssin g Signal processing is an important application of electric circuits This book introduces signal processing in two ways First, two sections (Sections 6 and 7.9) describe methods to design electric circuits that implement algebraic and differential equations Second, numerous examples and problems throughout this book illustrate signal processing The input and output signals of an electric circuit are explicitly identified in each of these examples and problems These examples and problems investigate the relationship between the input and output signals that is imposed by the circuit Interactive E x am p les an d E xercises Numerous examples throughout this book are labeled as interactive examples This label indicates that computerized versions of that example are available at the textbook’s companion site, www.wiley com/dorf Figure illustrates the relationship between the textbook example and the computerized example available on the Web-Site Figure 2a shows an example from Chapter The problem presented by the interactive example shown in Figure 2b is similar to the textbook example but different in several ways: • he values of the circuit parameters have been randomized • The independent and dependent sources may be reversed • The reference direction of the measured voltage may be reversed A different question is asked Here, the student is asked to work the textbook problem backward, using the measured voltage to determine the value of a circuit parameter www.EngineeringEBooksPdf.com 872 J— Mathematical Formulas - d du dv — (uv) = — v + w — dx dx dx du dv V) — sin (ax + b) — a cos (ax + b) dx dx C.3 = ^ INDEFINITE I NTEGRALS The letters u and v represent functions of x, whereas a and b are constants J au dx = a J u dx J (u + v)d x = J ud x + J vdx r J m+ 10 f dv f du dx J dx / u — dx = u v — / v — dx / f h W J / sin ax dx = —- cos ax a [ cos ax dx = - sin ax J a , x sin ax dx = - ~ sin 2ax x sin 2ax cos ax dx = - -\ 4a aax r sin2 / cos ax sin ax dx = sin ax —ax cos ax x sin a x d x = "• J / / S ' xm+1 xm dx = - when m / —1 / a2 www.EngineeringEBooksPdf.com I n d e f i n i t e I n t e g r a l s i nI cos ax + ax sin ax x cos ax dx = a1 f i / sin a* sin J 13 j sin ( a - b ) x sin (a + b)x dx = —— - — — - — (a - b) (a + b) , sin (a - b)x sin (a + b)x , ,9 , cos ax cos to dx = — h —— —— when bl ± a / 2(a - b) / 16 17 (a + b) cos (a - b)x cos (a + b)x , , sin ax cos bx dx = -— — - —when bL ^ a2 (a - b) (a + b) I eaxdx = - e ax a nr , ax — _Y I x e dx = z— e a- !■ I^ j* jax sina2bx-f- b2b cos foe) e ^ ia cos bx / _ _ _ b sin for) _ www.EngineeringEBooksPdf.com when bz ^ a2 873 Stm,dmd W V Appendix V Resistor Color Code I— -y Low-power resistors have a standard set of values Color-band codes indicate the resistance value as well as a tolerance The most common types of resistors are the carbon composition and carbon film resistors The color code for the resistor value uses two digits and a multiplier digit, in that order, as shown in Figure D A fourth band designates the tolerance Standard values for the first two digits are listed in Table D.l The resistance of a resistor with the four bands of color may be written as R = (a x 10 + b)m ± tolerance where a and b are the values of the first and second bands, respectively, and m is a multiplier These resistance values are for percent and percent tolerance resistors, as listed in Tables D.l The color code is listed in Table D.2 The multiplier and tolerance color codes are listed in Tables D.3 and D.4, respectively Consider a resistor with the four bands, yellow, violet, orange, and gold We write the resistance as R = (4 x 10+ 7) kfi ±5% = 47 kfi ±5% 2nd digit Tolerance FIGURE D.l Resistor with four color bands St a n d a r d V alues for First Two Digits for P e rc e n t and P e rc e n t T o le n c e R esisto rs www.EngineeringEBooksPdf.com S ta n d a r d R e sisto r C olor C o d e Table D-3 Multiplier Color Code Color Code black brown red orange yellow green blue violet gray white silver gold black brown red orange yellow green blue violet 0.01 0.1 10 100 1k 10k 100 k 1M 10 M Table 0-4 Tolerance Band Code red gold silver none 2% 5% 10% 20% www.EngineeringEBooksPdf.com R eferences A dler, Jerry, ‘'A nother Bright Idea,” N ew sw eek, June 15, 1992, p 67 A lbean, D L., “ Single Pot Swings Amplifier Gain Positive or N egative,” Electronic Design Januarv 1997, p 153 ' Barnes, R., and W ong, K T., “ Unbalanced and Harmonic Studies for the Channel Tunnel Railway S ystem ,’’ IE E Proceedings, M arch 1991, pp 41-50 B ernstein, Theodore, “ Electrical Shock H azards,” IEEE Transactions on Education August 1991 pp 216-222 Brown, S F., “ Predicting Earthquakes,” P opular Science, June 1989, pp 124-125 B utterw orth, S “ On the Theory o f Filters,” Wireless World, Vol 7, October 1930, pp 536-541 C oltm an, John W , “ The T ransform er,” Scientific American, January 1988, pp 86-95 D oebelin, E O., M easurem ent Systems, M cGraw-Hill, New York, 1966 D ordick, Herbert S., U nderstanding M odern Telecommunications, McGraw-Hill, New York, 1986 Dorf, Richard, The E lectrical Engineering Handbook, CRC Press, 1988 Dorf, Richard C., Technology, Society and Man, Boyd and Fraser, San Francisco, 1974 Edelson, Edw ard, “ Solar Cell U pdate,” Popular Science, June 1992, pp 95-99 G ardner, Dana, “ The W alking Piano,” Design News, D ecem ber 11, 1988, pp 60-65 G arnett, G H., “ A H igh-Resolution, M ultichannel Digital-to-Analog Converter,” Hewlett-Packard Journal, February 1992, pp 48-52 G raem e, J., “ A ctive Potentiom eter Tunes Com m on-M ode Rejection,” Electronics, June 1982, p 119 G raham , Dunstan, Analysis o f N onlinear Control Systems, Dover Publishing, New York, 1971 Halliday, D., Resnick, R and W alker, J., Fundamentals o f Physics, John Wiley and Sons, New York, 2001 H anselm an, D., and Littlefield, B„ M astering M ATLAB®, Prentice Hall, Upper Saddle River, NJ, 2005 Jurgen, Ronald, “ Electronic Handgun Trigger Proposed,” IEEE Institute, February 1989, p Lam arre, Leslie, “ Problem s with Power Q uality,” E P R I Journal, August 1991, pp 14-23 Lenz, Jam es E., “ A Review o f M agnetic Sensors,” Proceedings o f the IEEE June 1990, pp 973-989 Lewis, Raym ond, “ A Com pensated A ccelerom eter,” IEEE Transactions on Vehicular Technology, August 1988, pp 174-178 Loeb, Gerald E., “ The Functional Replacement o f the Ear,” Scientific American, February 1985, pp 104-108 M ackay, Lionel, “ Rural Electrification in N epal,” Power Engineering Journal, September 1990, pp 223-231 M athcad U se r’s G uide, M athSoft Inc., Cambridge, MA, 1991 McCarty, Lyle H„ “ Catheter Clears Coronary Arteries,” Design News, September 23,1991, pp 88-92 M cM ahon, A M „ The M aking o f a Profession: A Century o f Electrical Engineering in America, IEEE Press, New York, 1984 Nahin Paul J., “ O liver H eaviside,” Scientific American, June 1990, pp 122-129 Perry T S., “ Donald Pederson: The Father o f SPICE,“ IEEE Spectrum, June 1998 www.EngineeringEBooksPdf.com R eferen ces Sallen, R P., and Key, E L., “ A Practical Method of Designing RC Active Filters,” IRE Transactions on Circuit Theory, Vol CT-2, March 1955, pp 74-85 Smith, E D., “ Electric Shark Barrier,” Power Engineering Journal, July 1991, pp 167-177 Svoboda, J A., “ Elab, A Circuit Analysis Program for Engineering Education,” Computer Appli cations in Engineering Education, Vol 5, No 2, 1997, pp 135-149 Svoboda, J A., PSpice fo r Linear Circuits, John Wiley and Sons, New York, 2007 Trotter, D M., “ Capacitors,” Scientific American, Vol 259, No 1, 1988, pp 86-90 Tuinenga, P W., SPICE: A Guide to Circuit Simulation & Analysis Using PSpice, Prentice-Hall, Englewood Cliffs, New Jersey, 1988 Williams, E R., “ The Electrification o f Thunderstorms,” Scientific American, November 1988, pp 88-99 Wright, A., “ Construction and Application o f Electric Fuses,” Power Engineering Journal, Vol 4, No 3, 1990, pp 141-148 www.EngineeringEBooksPdf.com www.EngineeringEBooksPdf.com Index 2D gel electrophoresis, 18 abc phase sequence, 560 Active element, 25 Admittance, 434, 693 Admittance parameters, 833 Alternating current (ac), Ammeter, 31 Ampere, Amplifier, 143, 189 Amplitude spectrum, 754 Amplitude-phase Fourier series, 736 Analog-to-digital converter (ADC), 239 Anti-aliasing filter, 817 Asymptotic Bode plot, 609 Average power, 499 three phase-circuit, 579 Balanced three-phase circuits, 576 Balanced three-phase load, 562 Balanced three-phase source, 560 Band-pass filter, 794 Bandwidth, 625 Bell, Alexander Graham, 607 Block diagram, 223, 224, 281 Bode, H.W., 606 Bode plot, 606 asymptotic, 609 complex poles, 617 Break frequency, 610 Bridge, 189, 214 Buffer amplifier, 217 Butterworth transfer function, 795 Capacitor, 258, 314, 347 complex-frequency domain, 682 dc circuit, 279 element equation, 293 two-port networks, 842 Cascade, 805, 808 CCCS, 35 CCVS, 35 Characteristic equation, 374 Characteristic roots, 375 Charge, Circuit drawing, 54 Coaxial cable, 349 Color-code probes, 32, 33 Column vector, 862 Complete response, 313, 337, 386 first-order circuits, 314 switched ac circuits, 457 Complex arithmetic, 867 MATLAB, 869 Complex exponential, 422 Complex frequency, 394, 662 Complex number, 866, 868 conjugate, 867 MATLAB, 868 polar form, 866 rectangular form, 866 Complex plane, 393 Complex poles, 674 MATLAB, 705 www.EngineeringEBooksPdf.com 880 V - Index Complex-frequency domain, 684 Conductance, 26, 436 Conservation of complex power, 507 Controlled source, 33 Convolution, 695, 774 MATLAB, 697 Comer frequency, 609, 610 Coulomb, Coupled coils, 523 Coupled inductors, 523 dot convention, 524 element equation, 541 Coupling coefficient, 526 Cramer’s rule, 865 Critically damped, 377, 394 natural response, 379 Current, Current divider, 67, 87 design, 70 frequency domain, 439 Current source, 29 nonideal, 163 parallel, 73 Cutoff frequency, 794 Damped resonant frequency, 380, 397 Damping coefficient, 380 Decibel, 607 Delay, 596, 669 Delta-connected three phase source, 561 Delta-Y transformation, 571 Dependent source, 33, 35 gain, 34 node equations, 120 power, 36 Design Example ac circuit with op amp, 471 adjustable voltage source, 84 airbag igniter, 397 anti-aliasing filter, 817 computer and printer, 349 dc power supply, 781 integrator and switch, 290 jet valve controller, 14 maximum power transfer, 538 potentiometer angle display, 143 power factor correction, 587 radio tuner, 640 space shuttle cargo door, 710 strain gauge bridge, 189 temperature sensor, 42 transducer interface circuit, 239 transistor amplifier, 846 Determinant, 865 Device, Dielectric constant, 258 Difference amplifier, 213, 217 Differential equation, 315 direct method, 369, 370 first-order circuits, 314 integrating factor, 335 Laplace transform, 680 operator method, 370, 371 state variable method, 389 Differential operator, 371 Differentiator, 282 Digital signal processing, 817 Dirchlet conditions, 732 Direct current (dc), Dot convention, 524 Effective value, 501 EFS, 750 Electric field, 258, 264 Element, Element equation (constitutive equation) 20 capacitor, 293 complex-frequency domain, 684 coupled inductors, 541 frequency domain, 433 ideal transformers, 541 inductors, 293 Energy, stored in a capacitor, 264 stored in an inductor, 274 stored in coupled coils, 526 www.EngineeringEBooksPdf.com Equivalent circuit, 73 coupled inductors, 525 frequency-dependent op amp, 630 hybrid parameters, 837 ideal transformer, 532 inverse hybrid parameters, 837 per-phase, 564, 576 Equivalent resistance, 78, 87 parallel resistors, 67 series resistors, 63 Euler’s formula, 868 Even function, 739 Exponential Fourier series, 747 MATLAB, 749 Farad, 258 Faraday, Michael, 258 FFT, 750 Filter, 794 Filter circuits, 793 PSpice, 811 Final value theorem, 678, 708 First-order circuit, 312, 314 network functions, 605 summary, 352 First-order filters, 808 Forced response, 313, 336, 339, 382 Fourier, Jean-Baptise-Joseph, 731 Fourier series, 731 exponential, 746, 748 full-wave rectified cosine, 732 MATLAB, 734 PSpice, 761 triangle waveform, 741 trigonometric, 731, 744 Fourier spectrum, 754, 773 MATLAB, 757 Fourier transform, 766 Laplace transform, 777 properties, 769, 770 table, 771 Franklin, Benjamin, Frequency, 416 Frequency domain, 427 table, 433 Frequency response, 599 PSpice, 634 Frequency scaling, 796 Fundamental frequency, 731 Gain, 220, 594 Gain-bandwidth-product, 632 Ground node, 110, 209 Guidelines for labeling circuit variables, 81 h parameters, 845, 846 Harmonics, 731 Heaviside, Oliver, 374 Henry, Joseph, 270 Hertz, 5, 416 Hertz, Heinrich, 416 High-order filters, 805 High-pass filter, 794 Homogeneity, 21 “How can we check ?” , 13 ac analysis, 469 AC power, 536 balanced three phase circuits, 584 band-pass filter, 815 capacitor voltage and current, 289 complex arithmetic, 469 first-order circuits, 345 Fourier series, 779 frequency response, 636, 815 gain, 637 hybrid parameters, 844 initial and final values, 708 Kirchhoff s law's, 82 mesh currents, 142 node voltages, 140 Ohm’s law, 41 www.EngineeringEBooksPdf.com 882 ) - I n d e x “ How can we check ?” (C on tin u ed ) operational amplifier, 237 passive convention, 13 phase shift, 637 second-order circuits, 394 Thevenin equivalent, 188 unbalanced three phase circuits, 585 Hybrid parameters, 837 Ideal filter, 794 Ideal operational amplifier, 210 Ideal source, 29 Ideal transformers, 531 element equation, 541 lossless, 533 Impedance, 434, 693 complex-frequency domain, 681 Impedance parameters, 833 Impluse function, 667, 693 Independent source, 29 Inductor, 269, 315, 346 complex-frequency domain, 683 dc circuit, 278 element equation, 293 Initial condition, 316, 681 capacitor, 259 inductor, 270 second-order circuits, 377 switched dc circuits, 277 Initial value theorem, 677, 708 Input and output impedance, 807 Instantaneous power, 498 three phase circuit, 578 Integrator, 282, 290 Interactive Example, xi AC power, 516 Bode plot, 613, 615 capacitors, 261, 262 complete response, 685, 687 coupled inductors, 528, 529, 530 equivalent resistance, 75 inductors, 272 Kirchhoffs laws, 57 Kirchhoffs and Ohm’s laws, 59, 60 mesh equations, 132 network functions, 600, 601, 602 op amp circuit, 215, 216 parallel resistors, 69 RC circuit, 317, 319, 334 RL circuit, 318, 320, 332 series resistors, 64 simple AC circuits, 440, 441, 442 Thevenin equivalent circuit, 172, 174 transformers, 534, 535 Inverse Fourier transform, 767 Inverse hybrid parameters, 837 Inverse Laplace transform, 662, 671 Inverting amplifier, 217, 220, 229, 240 in frequency domain, 456 Joule, Kilo, Kirchhoff, Gustav Robert, 56 Kirchhoff s Current Law (KCL), 56, 83 in frequency domain, 438 Kirchhoffs Laws, 53 Kirchhoffs Voltage Law (KVL), 57, 83 in frequency domain, 438 Laplace, Pierre-Simon, 662 Laplace transform, 661 properties, 665 table, 665 Line current, 573 Line losses, 567 Linear element, 21 Line-to-line voltage, 561 Loading, 218, 805 Loop, 57, 122 Low-pass filter, 794 Magnetic field, 269, 274 MathCad, 82, 238, 779 Kirchhoffs Laws, 82 Fourier series, 779 simultaneous equations, 238 www.EngineeringEBooksPdf.com MATLAB, 860 ac circuits, 464 Bode plot, 632 capacitors and inductors, 287 complex arithmetic, 869 complex numbers, 868 consecutive equations, 78 convolution, 697 exponential Fourier series, 749 Fourier spectrum, 757 frequency response, 632 functions, 861 matrices, 184, 863 mesh equations, 136 node equations, 115 operational amplifiers, 234 operations, 861 partial fraction expansion, 702 plotting functions, 870 simultaneous equations, 78, 183 Thevenin equivalent circuit, 182 Trigonometric Fourier series, 734 Matrix, 862 Maximum power transfer, 179,180, 522, 534 ac circuits, 538 Mega, Mesh, 122 Mesh current, 123 element currents and voltages, 124 PSpice, 138 Mesh equations, 123, 134, 146 dependent sources, 131, 146 frequency domain, 443 MATLAB, 136 PSpice, 138 Mho, 26 Micro, Milli, Model, 20, 30, 234 Multiplicity, 675 Mutual inductance, 524 element equation, 541 my_periodic_ftinction, 750 Nano, Natural frequencies, 375 Natural response, 313, 336 critically damped, 379 overdamped, 376 second-order circuits, 373 underdamped, 380 Network function, 598 Node, Node equations, 110, 134, 146 dependent sources, 120, 146 frequency domain, 443 MATLAB, 115 op amp circuits, 212 PSpice, 138 Node voltages, 110 element currents and voltages, 111 PSpice, 138 Nodes, 54, 109 Nonideal op amps, 227 Noninverting amplifier, 217, 220 in frequency domain, 456 Noninverting summing amplifier, 224 Norton, E.L., 175 Norton equivalent circuit, 175, 312, 315 in the frequency domain, 452 Notch filter, 794 Odd function, 739 Ohm, 5, 26 Ohm, Georg Simon, 25 Ohmmeter, 75 Ohm’s law, 26, 44 Op amp amplifiers, 220 Op amp circuits, 208 AC circuits, 455 DC circuits, 217 differential equations, 281 differentiator, 282 first order circuits, 605 first order filters, 808 integrator, 282 linear algebraic equations, 222 www.EngineeringEBooksPdf.com Index Op amp circuits ( Continued) linear differential equations, 281 node equations, 212 poles and zeros, 622 PSpice, 236 Sallen-Key filters, 799 summing integrator, 283 Open circuit, 44, 347 capacitor in a dc circuit, 278 ideal voltmeter, 31 Open-circuit voltage, 171 Operational amplifier, 208 bias current, 227, 229 catalog of op amp circuits, 217 circuits having poles or zeros, 622 common-mode rejection ratio, 233 first-order low-pass filters, 605 frequency-dependent gain, 630 gain-bandwidth product, 233 ideal operational amplifier, 210 input resistance, 227 models, 227, 234 offset voltage, 227, 229 output resistance, 227 saturation current, 210 saturation voltage, 210, 234 slew rate limit, 210 typical parameters, 228 voltage gain, 227, 231 Operator, 340 Overdamped, 377, 394 Parallel, 66 admittances, 439, 465 capacitors, 267, 294 current sources, 73 inductors, 276, 294 resistors, 66, 87 two-port networks, 841 voltage sources, 87 Partial fraction expansion, 672 MATLAB, 702 Pass-band, 794 Passive convention, 8, 26, 44, 500 Passive element, 24 resistor, 28 Periodic function, 416, 731 Permeability, 269 Per-phase equivalent circuit, 564 Phase angle, 417, 420 Phase current, 573 Phase shift, 594 Phase spectrum, 754 Phase voltage, 561 Phasor diagram, 454 Phasors, 426 RLC elements, 430 Pico, Planar circuits, 122 Poles, 610, 671 MATLAB, 703 stability, 700 Port, 829 Potentiometer, 37, 84, 136, 143 Power, absorbed, apparent, 504 average, 499, 504 complex, 503 instantaneous, 498 reactive, 504 resistor, 27 supplied, table, 505 Power factor, 511 Power factor correction, 512 three phase circuit, 587 Power superposition, 520 Power triangle, 505 Pressure transducer, 239 Primary coil, 527, 531 Problem-solving method, 11 Proper rational function, 671 www.EngineeringEBooksPdf.com PSpice, 853 AC circuits, 466 complete response, 313 filters, 811 first order circuits, 342 Fourier series, 761 frequency response, 634 getting Started, 853 ground node, 856 initial condition, 342 mesh currents, 138 node voltages, 138 Op amp circuits, 236 parts, 855 sources for ac circuits, 467 sources for transient response, 343 Thevenin equivalent circuit, 185 wiring, 858 workspace, 853 Sallen-Key filters, 813 Pulse, 332 Pulse inputs, 667 Quality factor, 625, 797 Radian frequency, 416 Reactance, 435 Rectangular to polar conversion, 736 Reference node, 110 Repeated poles, 675 MATLAB, 704 Residues, 672 MATLAB, 703 Resistance, 25 Resistor, 25 color code, 874 tolerance, 874 Resonant circuit, 623, 640 parallel RLC, 624, 629 series RLC, 626, 629 Resonant frequency, 624 RLC circuit summary, 400 Root-mean-squared, 502 Sallen-Key filters, 799 Saturation nonlinearity, 779 s-domain, 684 Secondary coil, 527, 531 Second-order RLC filters, 798 Sequential Switching, 327, 347 Series, 61 capacitors, 267, 294 current sources, 87 impedances, 438, 465 inductors, 276, 294 resistors, 61, 62, 87 two-port networks, 842 voltage sources, 73 Short circuit, 44, 346 ideal ammeter, 31 inductor in a dc circuit, 278 Short-circuit current, 171 SI Prefixes, SI Units, Siemens, 5, 26 Simple real poles, 672 MATLAB, 703 Simulated inductor, 641 Simultaneous equations, 864 MATLAB, 865 Sine-cosine Fourier series, 736 Sinusoidal sources, 416 Source transformations, 162, 165, 192 in the frequency domain, 451 SPST, SPDT, 39 Stability, 329, 699 impulse response, 700 transfer function, 700 Standard resistor values, 874 State variables, 389 Steady state response, 313, 346, 395 periodic inputs, 759 sinusoidal input, 421 www.EngineeringEBooksPdf.com Index Step function, 331, 667 Step response, 692, 708 Stop-band, 794 Strain gauge, 189 Summing Amplifier, 217, 221, 240 Supermesh, 129, 130 Supemode, 116, 117 Superposition, 21, 167, 168, 229, 759 in the frequency domain, 449 Susceptance, 436 Switched dc circuits, 278 Switches, 39 Symmetry and the Fourier series, 740 Temperature sensor, 37, 42 Terminal, Thevenin and Norton Equivalent Circuits, 192 Thevenin equivalent circuit, 171, 182, 190, 214, 312, 314 in the frequency domain, 452 Thevenin equivalent resistance, 180, 329 maximum power transfer, 522 Thevenin impedance, 452 Thevenin resistance, 171 Thevenin, M.L., 171 Three phase circuit, 560 instaneous power, 578 Three phase source, 561 delta-connected, 561 Y-connected, 561 Time constant, 315, 316, 345 Tow-Thomas filters, 803 T-Pi Converion, 831 Transfer function, 692, 708 Transformer, 527 element equation, 541 ideal, 531 line losses, 568 Transient response, 313 Transmission parameters, 838, 843 Trigonometric formulas, 871 Turns ratio, 527, 532 Two-port network, 829 Two-port parameter conversion, 840 Two-wattmeter power measurement, 581 uA, 741 208, 210, 229 Underdamped, 377, 394 natural response, 380 VCCS, 35 VCVS, 35 Volt, Voltage, Voltage divider, 62, 87, 220 design, 64 frequency domain, 439, 466 Voltage follower, 217, 218, 220, 231, 240 Voltage source, 29 nonideal, 162 series, 73 Voltage-controlled switch, 290 Voltmeter, 31 Watt, Y parameters, 833, 842 Y-connected three phase source, 561 Y-delta circuit, 573 Y-delta transformation, 571 Y-Y circuit, 562 3-wire, 563 4-wire, 562 Z parameters, 833, 842 Zeros, 610, 672 www.EngineeringEBooksPdf.com ... www.EngineeringEBooksPdf.com Preface The central theme of Introduction to Electric Circuits is the concept that electric circuits are part of the basic fabric of modem technology Given this theme, we endeavor to. .. This book endeavors to prepare the reader to solve realistic problems involving electric circuits Thus, circuits are shown to be the results of real inventions and the answers to real needs in industry,... op amp circuits • Table 7.8-1 Capacitors and inductors • Table 7.13-2 Series and parallel capacitors and inductors • Table 8.11-1 First-order circuits • Tables 9.13-1, 2, and Second-order circuits