Introduction to Electric Circuits-------------------------------------------------------EIGHTH EDITION

Richard C. DorfU n iv e rs ity o f C a lifo rn ia

James A. SvobodaC la rk s o n U n iv e rs ity

WILEY

John Wiley & Sons, Inc.

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Donald Fowley Dan Sayre Katie Singleton Dorothy Sinclair Janet Foxman Christopher Ruel Harry Nolan Jim OShea 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. 8 th ed. p. cm. ISBN 978-0-470-52157-1 (cloth : alk. paper) 1. 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 9 8 7 6 5 4 3 2

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 ra 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 ra 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

About the AuthorsRichard 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 Universitys 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.

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 NThis 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 1 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 8 TH E D I T I O N Increased use of PSpice K and MATLABHSignificantly 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 5 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 do the

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Color Code

Matrices, Determinants ----"A.

1ELECTRIC CIRCUIT VARIABLES

2CIRCUIT ELEMENTS

3RESISTIVE CIRCUITS

4METHODS OF ANALYSIS OF RESISTIVE CIRCUITS

W'

Complex Numbers

FIGURE 1 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, theres 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 ClarityChapter 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 ProblemsThe 8 th edition contains 1 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:

Preface

PSpice

16FILTER CIRCUITS 1

13FREQUENCY RESPONCE

14THE LAPLACE TRANSFORM

15FOURIER SERIES AND FOURIER TRANSFORM TWO-PORT NETWORKS

4 17THE OPERATIONAL AMPLIFIER TWO-PORT NETWORKS

Legend: ...

Primary flow

OAppendix

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.

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 IntroductionEach chapter begins with an introduction that motivates consideration o f the material o f that chapter.

ExamplesBecause 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 . . . " SectionsEach 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 1 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 FormulasYou 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 FiguresThe 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.

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 3. 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 .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 textbooks companion site, www.wiley. com/dorf. Figure 2 illustrates the relationship between the textbook example and the computerized example available on the Web-Site. Figure 2a shows an example from Chapter 3. The problem presented by the interactive example shown in Figure 2b is similar to the textbook example but different in several ways: 1 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.

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(a)

Calculator

Show Answer

The voltmeter measures a voltage in volts. What is the value of the resistance, R, in Q?

(b)Worked Examples

Calculator

|

New Problem

Show Answer

The ammeter measures a current in amps. What is the value of the current measured by the ammeter?

j 1 J

(c)F IG U R E 2 (a) The circuit considered Example 3.2-5. ( b ) A corresponding interactive example, (c) A corresponding

interactive exercise.

The interactive example poses a problem and then accepts and checks the users answer. Students are provided with immediate feedback regarding the correctness o f their work. The interactive exam ple chooses parameter values somewhat randomly, providing a seemingly endless supply o f problem s. This pairing of a solution to a particular problem with an endless supply o f sim ilar problem s is an effective aid for learning about electric circuits. The interactive exercise shown in Figure 2c considers a similar, but different, circuit. Like the interactive example, the interactive exercise poses a problem and then accepts and checks the users answer. Student learning is further supported by extensive help in the form o f worked exam ple problems, available from within the interactive exercise, using the W orked Exam ple button. Variations o f this problem are obtained using the New Problem button. We can peek at the answer, using the Show Answer button. The interactive examples and exercises provide hundreds o f additional practice problems with countless variations, all with answers that are checked im m ediately by the computer.

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SUPPLEMENTS AND WEB-SITE MATERIALThe almost ubiquitous use of computers and the Web have provided an exciting opportunity to rethink supplementary material. The supplements available have been greatly enhanced.

Book Companion SiteAdditional student and instructor resources can be found on the John Wiley & Sons textbook companion site at www.wiley.com/college/dorf.S tu d e n t

Interactive Examples The interactive examples and exercises are powerful support resources for students. They were created as tools to assist students in mastering skills and building their confidence. The examples selected from the text and included on the Web give students options for navigating through the problem. They can immediately request to see the solution or select a more gradual approach to help. Then they can try their hand at a similar problem by simply electing to change the values in the problem. By the time students attempt the homework, they have built the confidence and skills to complete their assignments successfully. Its a virtual homework helper. MATLAB Tutorial, by Gary Ybarra and Michael Gustafson of Duke University, builds upon the MATLAB examples in the text. By providing these additional examples, the authors show how this powerful tool is easily used in appropriate areas of introductory circuit analysis. Ten example problems are created in HTML. M-files for the computer-based examples are available for download on the Student Companion site. PowerPoints for note taking Historical information PSpice fo r Linear Circuits, available for purchase WileyPLUS optionInstru cto r

Solutions manual PowerPoint slides WileyPLUS option W iley PL U S Pspice fo r Linear Circuits is a student supplement available for purchase. The PSpice fo r Linear Circuits manual describes in careful detail how to incorporate this valuable tool in solving problems. This manual emphasizes the need to verify the correctness o f computer output. No example is finished until the simulation results have been checked to ensure that they are correct.

ACKNOWLEDGMENTS AND C O M M IT M E N T TOACCURACY ---------- -- ---------------------------------------- ----------------------------------We are grateful to many people whose efforts have gone into the making of this textbook. We are especially grateful to our Associate Publisher Daniel Sayre, Executive Marketing Manager Chris Ruel

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and Marketing Assistant Diana Smith for their support and enthus.asm. W e are grateful to Janet Foxm an and Dorothy Sinclair o f Wiley and Heather Johnson o f Elm Street Publishing Services tor their e o s m producing this textbook. We wish to thank Lauren Sapira, Carolyn W eisman, and Andre Legaspi to rth eir S'gnifi^ a r e particularly grateful to the team o f reviewerswho checked the problem s and solutions to ensure their accuracy:

Accuracy CheckersKhalid Al-Olimat, Ohio Northern University Lisa Anneberg, Lawrence Technological University Horace Gordon, University o f South Florida Lisimachos Kondi, SUNY, Buffalo Michael Polis, Oakland University Sannasi Ramanan, Rochester Institute of Technology W illiam Robbins, U niversity o f M innesota James Rowland, University o f Kansas Mike Shen, Duke University Thyagarajan Srinivasan, W ilkes University Aaron Still, U.S. Naval Academ y Howard W einert, Johns Hopkins U niversity Xiao-Bang Xu, Clem son U niversity Jiann Shiun Yuan, U niversity o f Central Florida

ReviewersRehab Abdel-Kader, Georgia Southern University Said Ahmed-Zaid, Boise State University Farzan Aminian, Trinity University Constantin Apostoaia, Purdue University Calumet Jonathon Bagby, Florida Atlantic University Carlotta Berry. Tennessee State University Kiron Bordoloi, University o f Louisville Mauro Caputi, Hofstra University Edward Collins, Clemson University Glen Dudevoir, U.S. Miliary Academy Malik Elbuluk, University o f Akron Prasad Enjeti, Texas A&M University Ali Eydgahi, University o f Maryland Eastern Shore Carlos Figueroa, Cabrillo College Walid Hubbi, New Jersey Institute o f Technology Brian Huggins, Bradley University Chris Ianello, University o f Central Florida Simone Jarzabek, ITT Technical Institute James Kawamoto, Mission College Rasool Kenarangui, University of Texas Arlington Jumoke Ladeji-Osias, Morgan State University Mark Lau, Universidad del Turabo Seyed M ousavinezhad, W estern M ichigan U niversity Philip M unro, Y oungstow n State U niversity Ahm ad Nafisi, California Polytechnic State U niversity A m ost N eugroschel, U niversity o f Florida Tokunbo Ogunfunm i, Santa Clara U niversity Gary Perks, C alifornia Polytechnic State University, San Luis Obispo Owe Petersen, M ilwaukee School o f Engineering Ron Pieper, U niversity o f Texas, Tyler Teodoro Robles, M ilw aukee School o f Engineering Pedda Sannuti, Rutgers U niversity M arcelo Simoes, Colorado School o f M ines Ralph Tanner, W estern M ichigan U niversity Tristan Tayag, Texas Christian U niversity Jean-Claude Thom assian, Central M ichigan University John Ventura, Christian Brothers U niversity Annette von Jouanne, Oregon State U niversity Ravi W arrier, Kettering U niversity Gerald Woelfl, M ilwaukee School o f Engineering Hewlon Zim m er, U.S. M erchant Marine Academ y

Contents

CHAPTER 1

Electric Circuit Variables............................................................................... ..................... 11.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 Introduction....................................................................................................................................... 1 Electric Circuits and Current............................................................................................................ 1 Systems of Units................................................................................................................................5 Voltage.............................................................................................................................................. 7 Power and Energy............................................................................................................................ 7 Circuit Analysis and Design........................................................................................................... 11 How Can We Check . . . ? ............................................................................................................13 Design ExampleJet Valve Controller........................................................................................14 Summary............... ..........................................................................................................................15 Problems...... ........................................................ ........................................................................ 15 Design Problems........................................................................................................................... 19

CHAPTER 2

Circuit Elements..................................................................................................................202.1 2.2 2.3 2.4 2.5 2.6 2.72.8

2.9 2.10 2 .11 2.12

Introduction....................................................................................................................................20 Engineering and Linear M odels.................................................................................................... 20 Active and Passive Circuit Elem ents........................................................................................... 24 Resistors..........................................................................................................................................25 Independent Sources............... ...................................................................................................... 28 Voltmeters and Ammeters..............................................................................................................31 Dependent Sources......................................................................................................................... 33 Transducers.................................................................................................................................... 37 Switches.......................................................................................................................................... 39 How Can We Check . . . ? ......................................... Design ExampleTemperature Sensor....................................................................................... 42 Summary.......................................................................................................................... 44 Problems.................................................................................................................................... 44 Design Problems..................... ........................................................................... 52

C o n te nts

CHAPTER 3

...........................................................5 3

Resistive Circuits...............................................................................3.1 3.23.3 3 4 3 5 3 .6 3 .7

53

Introduction................................................................................................................. 53 KirchhofTs Laws....................... ...................................................................................................... 61 Series Resistors and Voltage D ivision................................................................................................^ Parallel Resistors and Current D iv isio n . Series Voltage Sources and Parallel Current so u rc e s ..................................................................... Circuit Analysis....................................................................................................................................... 7 8 Analyzing Resistive Circuits Using M A T L A B .................................................................................... How Can We Check . . . .......................................................................................................................... Design Example Adjustable Voltage S o u rce................................................................................. ^ Sum m ary...................................................................................................................... *........................ Problem s.........................................................................................................* ..........* ......................... * Design Problem s................................................................................................................................

3.8 3.9 3.10

CHAPTER 4

Methods of Analysis of Resistive Circuits........................................................................... 1084.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 4.10 4.1 1 4.12 4.13 Introduction...........................................................................................................................................*08 Node Voltage Analysis o f Circuits with Current Sources........................................................... 109 Node Voltage Analysis o f Circuits with Current and Voltage S o u rces...................................115 Node Voltage Analysis with Dependent Sources..........................................................................120 Mesh Current Analysis with Independent Voltage Sources....................................................... 122 Mesh Current Analysis with Current and Voltage Sources.........................................................127 Mesh Current Analysis with Dependent Sources.......................................................................... 131 The Node Voltage Method and Mesh Current M ethod C om pared ........................................... 134 Mesh Current Analysis Using M A T L A B ......................................................................................... 136 Using PSpice to Determine Node Voltages and Mesh C urren ts....................................................138 How Can We Check . . . ? .................................................................................................................. 140 Design Example Potentiometer Angle D isplay............................................................................. 143 Sum m ary.................................................................................................................................................. 146 P roblem s..................... ...........................................................................................................................147 PSpice P roblem s................................................................................................................................... 160 Design Problem s................................................................................................................................... 160

CHAPTER 5

Circuit Theorem s........................................................................................................................ 16 25.1 5.2 5.3 5.4 5.5 5.6 5.8 5.9 5.10 5.11 Introduction................................................................................................................. Source Transform ations..................................................................................................... 152 Superposition.............................................................................................. jg y Thevenins T h eo rem ................................................................................... jy j Nortons Equivalent C ircu it................................................................. j 75 Maximum Power T ra n sfe r....................................................................... ........................... Using MATLAB to Determine the Thevenin Equivalent C ircu it............................................... 182 Using PSpice to Determine the Thevenin Equivalent Circuit 1 How Can We Check . . . ? ................................................................ ..................................................jJjJ Design Example Strain Gauge B rid g e .................................... ' * * * *1.................................. 189 ** Sum m ary......... .................................................................. J ............................................................................................... 1Q9 P roblem s............................................... .................................. PSpice Problem s............................................. ................................................................... Design Problem s......... .............................................................................

206

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CHAPTER 6

The Operational Amplifier.............................................................................................. ....6.1 6.2 6.3 6.4 6.56.6

6.76.8

6.9 6.10 6 .11 6.12

Introduction........................................................................................................................................ The Operational Amplifier...........................................................................................................208 The Ideal Operational Amplifier................................................................................................. 210 Nodal Analysis of Circuits Containing Ideal Operational Amplifiers.....................................212 Design Using Operational Amplifiers......................................................................................... 217 Operational Amplifier Circuits and Linear Algebraic Equations............................................. 222 Characteristics of Practical Operational Amplifiers.................................................................. 227 Analysis of Op Amp Circuits Using MATLAB.........................................................................234 Using PSpice to Analyze Op Amp Circuits...............................................................................236 How Can We Check . . . ? ......................................................................................................... 237 Design ExampleTransducer Interface Circuit....................................................................... 239 Summary....................................................................................................................................... 24 * Problems..................................................................................................................................... 242 PSpice Problems.........................................................................................................................255 Design Problems........................................................................................................................ 256

CHAPTER 7

Energy Storage Elements.................................................................................................. 2577.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 7.10 7.11 1.12 7.13 Introduction.................................................................................................................................. 257 Capacitors..................................................................................................................................... 258 Energy Storage in a Capacitor.....................................................................................................264 Series and Parallel Capacitors..................................................................................................... 267 Inductors....................................................................................................................................... 269 Energy Storage in an Inductor.....................................................................................................274 Series and Parallel Inductors....................................................................................................... 276 Initial Conditions of Switched Circuits...................................................................................... 277 Operational Amplifier Circuits and Linear Differential Equations.......................................... 281 Using MATLAB to Plot Capacitor or Inductor Voltage and Current..................................... 287 How Can We Check . . . ? ......................................................................................................... 289 Design ExampleIntegrator and Switch...................................................................................290 Summary.......................................................................................................................................293 Problems..................................................................................................................................... 294 Design Problems........................................................................................................................ 309

CHAPTER 8

The Complete Response of RL And RC Circuits........................................................... 3118.1

8.2 8.3 8.4 8.58.6

8.78.8

8.98.10 8 .11

Introduction................................................................................................................................. 311 First-Order Circuits..................................................................................................................... 311 The Response of a First-Order Circuit toa Constant Input...................................................... 314 Sequential Switching.................................................................................................................. 327 Stability of First-Order Circuits.................................................................................................329 The Unit Step Source............................................................................................. 331 The Response of a First-Order Circuit toa Nonconstant Source............................................. 335 Differential Operators................................................................................................................ Using PSpice to Analyze First-Order Circuits......................................................................... 342 How Can We Check . . . ? .............................................................. 345 Design ExampleA Computer and Printer.............................................................................. 3 4 9

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8.12

........................................... 352 Sum m ary.................................................................................... ........................................................... 3 5 3 Problem s................................................................................................. 355 PSpice Problem s.............................................................................................................................. Design Problem s......................................................................................................................

CHAPTER 9 The Complete Response of Circuits With Two Energy Storage Elements............. ............................................................9.1 9.2 9.39 .4 9 .5

.

....................................368

36g

9.6 9.7 9.8 9.9 9.10 9.11 9.12 9.13

Introduction.................................................................................................................................................... Differential Equation for Circuits with Two Energy Storage E lem en ts........................................... Solution o f the Second-Order Differential Equation The Natural R esponse......................... 373 Natural Response o f the Unforced Parallel RLC C ircuit.......................... ..... ............................ 376 Natural Response o f the Critically Damped Unforced Parallel R LC C ircu it...........................379 Natural Response o f an Underdamped Unforced Parallel RLC C irc u it....................................380 Forced Response o f an RLC C ircu it................................................................................................. 3 8 2 Complete Response o f an RLC C irc u it........................................................................................... 3 ^ 6 State Variable Approach to Circuit A n aly sis................................................................................... 389 Roots in the Complex P lan e............................................................................................................ . 393 How Can We Check . . . .. .................................................................................................................. 3 9 4 Design Example Auto Airbag Igniter............................................................................................. 397 Sum m ary............................................................................................................................................... 3 99 P roblem s.................................................................................................................................................401 PSpice P roblem s...................................................................................................................................412 Design Problem s...................................................................................................................................413

CHAPTER 10

Sinusoidal Steady-State Analysis...................................................................................... . 41510.1 10 .2 10.3 10.4 10.5 10.6 10.7 10.8 10.910.10

10.11 10.12 10.13 10.14 10.15 10.16 10.17 10.18

Introduction............................................................................................................................................ 415 Sinusoidal S o u rces................................................................................................................................416 Steady-State Response o f an RL Circuit for a Sinusoidal Forcing F unction.............................421 Complex Exponential Forcing F u nction.......................................................................................... 422 The Phasor..............................................................................................................................................426 Phasor Relationships for R, I , and C Elem ents...............................................................................430 Impedance and A dm ittance................................................................................................................. 4 3 4 K irchhoffs Laws Using Phasors....................................................................................................... 4 3 3 Node Voltage and Mesh Current Analysis Using Phasors............................................................. 4 4 3 Superposition, Thevenin and Norton Equivalents, and Source T ransform ations..................... 4 4 9 Phasor D iag ram s............................................................................................ 454 Phasor Circuits and the Operational A m plifier...................................................................... 455 The Complete R esponse..................................................................... 4*7 Using MATLAB for Analysis o f Steady-State Circuits with Sinusoidal Inputs......................464 Using PSpice to Analyze AC Circuits........................................................ 4 ^/. How Can We Check . . . ? ........................................... ................................ 4 ^ Design Example Op Amp C irc u it................................................. ........................................ A1\ Sum m ary............................. ...........................................* * Problem s..................................................... ............................................... ................................................. 4Q1 PSpice Problem s............. ...................................................................................... Design Problem s........... ................................. .................................................................................................................. 494

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CHAPTER 11

. qfi

AC Steady-State Power...................................................................................................11.1

11.2 1 1.3 11.4 1 1.5 11.6 11.7 1 1.8 11 .9 11.10 11.11 11.12 11.13

Introduction........................................................................................................................................ dUn Electric Power.................................................................................................................................... ~ Instantaneous Power and Average Power.................................................................................... 49 Effective Value of a Periodic Waveform.................................................................................... 501 Complex Power............................................................................................................................ 503 Power Factor.................................................................................................................................511 The Power Superposition Principle.............................................................................................519 The Maximum Power Transfer Theorem................................................................................... 522 Coupled Inductors........................................................................................................................523 The Ideal Transformer.................................................................................................................. 531 How Can We Check . . . ? ......................................................................................................... -36 Design ExampleMaximum Power Transfer...........................................................................538 Summary...................................................................................................................................... 540 Problems..................................................................................................................................... 542 PSpice Problems........................................................................................................................ 556 Design Problems........................................................................................................................ 556

CHAPTER 12

Three-Phase Circuits....................................................................................................... 55812.1 12.2 12.3 12.4 12.5 12.6 12.7 12.8 12.9 12.10 12.11 Introduction.................................................................................................................................. 558 Three-Phase Voltages.................................................................................................................. 559 The Y-to-Y Circuit.......................................................................................... ............................ 562 The A-Connected Source and L o ad ............................................................................................571 The Y-to-A Circuit.......................................................................................................................573 Balanced Three-Phase Circuits...................................................................................................576 Instantaneous and Average Power in a Balanced Three-Phase L o ad ..................................... 578 Two-Wattmeter Power Measurement.........................................................................................581 How Can We Check . . . ? ......................................................................................................... 584 Design ExamplePower Factor Correction..............................................................................587 Summary...................................................................................................................................... 588 Problems..................................................................................................................................... 589 PSpice Problems.........................................................................................................................593 Design Problems......................................................................................................................... 593

CHAPTER 13

Frequency Response..................................................................................................... 59413.1 13.2 13.3 13.4 13.5 13.6 13.7 13.8 Introduction................................................................................................................................. 5 94 Gain, Phase Shift, and the Network Function........................................................................... 594 Bode Plots........................... ...................................................................................................... 606 Resonant Circuits............................................................................................................. 623 Frequency Response of Op Amp Circuits................................................................................630 Plotting Bode Plots Using MATLAB...................................................................................... 632 Using PSpice to Plot a Frequency Response............................................................................634 How Can We Check . . . ?............................

C o n te nts

13.9 13.10

_ ............................................ 640 Design Example Radio T u ner............................................................ ^ 2 Sum m ary................................................................................................................... 643 Problem s........................................................................................................................ 656 PSpice Problem s.................................................................................................................................. 6 5 8 Design P roblem s................................................................................................................................

CHAPTER 14

6g0

The Laplace Transform.......................................................................................................14.1 14.2 14.3 14.4 14.5 14.6 14.7 14.8 14.9 14.10 14.11 14.12 14.13 14.14

660

Introduction.................................................................................................................................................... Laplace T ransform ....................................................................................................................................... * T . .............................. 0 0 / Pulse In p u ts......................................................................................................... Inverse Laplace T ran sfo rm ......................................................................................................................... Initial and Final Value T heorem s........................................................................................................ 6 7 7 Solution o f Differential Equations Describing a C ircu it................................................................. 680 Circuit Analysis Using Impedance and Initial C onditions.............................................................. 681 Transfer Function and Im pedance.......................................................................................................692 Convolution............................................................................................................................................. ^ 5 Stability....................................................................................................................................................^99 Partial Fraction Expansion Using M A T L A B ................................................................................... 702 How Can We Check . . . ? .................................................................................................................. 707 Design Example Space Shuttle Cargo D o o r.................................................................................710 Sum m ary........................................................................... ......................................................................713 P roblem s................................................................................................................................................714 PSpice P roblem s...................................................................................................................... ..........728 Design Problem s................................................................................................. .................................729

CHAPTER 15

Fourier Series and Fourier Transform ....................................................................................73015.1 15.2 15.3 15.4 15.5 15.6 15.7 15.8 15.9 15.10 15.11 15.12 15.13 15.14 15.15 15.16 Introduction............................................................................................................................................730 The Fourier S eries................................................................................................................................. 731 Symmetry o f the Functionf (t) ........................................................................................................... 739 Fourier Series o f Selected W aveform s..............................................................................................744 Exponential Form o f the Fourier S e rie s........................................................................................... 746 The Fourier Spectrum........................................................................................................................... 7 5 4 Circuits and Fourier Series.................................................................................................................. 758 Using PSpice to Determine the Fourier S eries................................................................................ 761 The Fourier Transform ...................................................................................................................... 7 5 6 Fourier Transform Properties..............................................................................................................769 The Spectrum o f S ignals................................................................................ 773 Convolution and Circuit Response...................................................................... 774 The Fourier Transform and the Laplace Transform ......................... 777 How Can We Check . . . ? ................................................................................................................. 7 7 9 ............................... 701 Design Example DC Power S u p p ly .......................................................... * * Sum m ary.................. ...................................nQA r> ................................................................................................................................784 P roblem s.................................................................................. 7J. . PSpice Problem s.............................................................. ............................. ^ Design Problem s................................................................ .....................................................

C ontents

CHAPTER 16

Filter Circuits...................................................................................................................16.1 16.2 16.3 16.4 16.5 16.6 16.7 16.8 16.9 Introduction................................................................................................................................ The Electric Filter..................................................................................................................... 793 Filters........................................... .............................................................................................. 794 Second-Order Filters................................................................................................................. 797 High-Order Filters..................................................................................................................... ^05 Simulating Filter Circuits Using PSpice..................................................................................811 How Can We Check . . . ? ......................................................................................................815 Design ExampleAnti-Aliasing Filter....................................................................................817 Summary....................................................................................................................................820 Problems...................................................................................................................................820 PSpice Problems........................................................................................................................ 825 Design Problems........................................................................................................................ 828

CHAPTER 17

Two-Port and Three-Port Networks................................................................................82917.1 17.2 17.3 17.4 17.5 17.6 17.7 17.8 17.9 17.10 Introduction................................................................................................................................829T -to -n Transformation and Two-Port Three-Terminal Networks........................................ 830

Equations of Two-Port Networks............................................................................................. 832 Z and Y Parameters for a Circuit with Dependent Sources....................................................835 Hybrid and Transmission Parameters......................................................................................837 Relationships Between Two-Port Parameters......................................................................... 839 Interconnection of Two-Port Networks....................................................................................841 How Can We Check . . . ? .......................................................................................................844 Design ExampleTransistor Amplifier..................................................................................846 Summary.................................................................................................................................... 848 Problems................................................................................................................................... 848 Design Problems.......................................................................................................................852

APPENDIX A

Getting Started with PSpice..............................................................................................853APPENDIX B

MATLAB, Matricies and Complex Arithmetic..................................................................860APPENDIX C

Mathematical Formulas..................................................................................................... 871APPENDIX D

Standard Resistor Color Code......................................................................................... 874 References......................................................................... lndex...................................................................................................................................879

VariablesIN THI S C H A P T E R1.1 1.2 1.3 1.4 1 .5.6

L\

Introduction Electric Circuts and Current Systems of Units Voltage Power and Energy Circuit Analysis and Design

1.7 How Can We Check . . . ? 1.8DESIGN EXAMPLEJet Valve Controller 1.9 Summary Problems Design Problems

1.1

INTRODUCTION

A circuit consists of electrical elements connected together. Engineers use electric circuits to solve problems that are important to modem society. In particular: 1. Electric circuits are used in the generation, transmission, and consumption of electric power and energy. 2. Electric circuits are used in the encoding, decoding, storage, retrieval, transmission, and processing of information. In this chapter, we will do the following: Represent the current and voltage of an electric circuit element, paying particular attention to the reference direction of the current and to the reference direction or polarity of the voltage Calculate the power and energy supplied or received by a circuit element Use the passive convention to determine whether the product of the current and voltage of a circuit element is the power supplied by that element or the power received by the element Use scientific notation to represent electrical quantities with a wide range of magnitudes

1.2

ELECTRIC CI R CU I TS AND C U R R E N T

The outstanding characteristics o f electricity when compared with other power sources are its mobility and flexibility. Electrical energy can be moved to any point along a couple of wires and, depending on the users requirements, converted to light, heat, or motion.

( D

-

Electric C i r c u i t V a r i a b l e s

An electric circuit or electric network is an interconnection o f electrical elem ents linked together in a closed path so that an electric current may flow continuously. C onsider a s.m ple circuit consisting o f tw o w ell-know n electrical elem ents, a b a ttery and a resistor, as shown in Figure 1.2-1. Each elem ent is represented by the tw o-term inal elem ent shown in Figure 1.2-2. E lem ents are som etim es called devices, and term in als are som e im es called nodes.Wire

Battery

l t t LWire

Resistor

FIGURE

1.2-2

A

general

two-terminal

electrical

FIGURE 1.2-1 A simple circuit.

element with terminals a and b.

Charge may flow in an electric circuit. Current is the time rate o f change o f charge p a st a given point. Charge is the intrinsic property o f m atter responsible for electric phenom ena. The quantity o f charge q can be expressed in terms o f the charge on one electron, which is -1 .6 0 2 x 10 y coulom bs. Thus, - 1 coulomb is the charge on 6.24 x 10 18 electrons. The current through a specified area is defined by the electric charge passing through the area per unit o f time. Thus, q is defined as the charge expressed in coulombs (C).

C harge is the quantity o f electricity responsible for electric phenom ena.

Then we can express current as i dq

dt

( 1.2- 1)

The unit o f current is the ampere (A); an ampere is 1 coulomb per second.

C u rre n t is the time rate o f flow o f electric charge past a given point.

Note that throughout this chapter we use a lowercase letter, such as q , to denote a variable that is a function o f time, q(t). We use an uppercase letter, such as Q, to represent a constant. The flow o f current is conventionally represented as a flow o f positive charges. This convention was initiated by Benjamin Franklin, the first great American electrical scientist. O f course, we now know that charge flow in metal conductors results from electrons with a negative charge. Nevertheless, we will conceive o f current as the flow o f positive charge, according to accepted convention.a

-------

-b

FIGURE 1.2-3 Current in a circuit element.

Figure 1 .2-3 shows the notation that we use to describe a current. There are two parts to thls notation: a value (perhaps represented by a variable name) and an assigned direction. As a matter ot vocabulary, we say that a current exists in or through an element. Figure 1 .2-3 shows that there are two ways to assign the direction o f the current through an elem ent. The current /, ls the rate ot flow o f electric charge from terminal a to terminal b. On the other hand the current i2 is the flow o f electric charge from terminal b to terminal a. The currents i, and i2 are

Ele c tr ic C ir c u it s and C u r r e n t

i I --------------------------------------

0

/

FIG URE 1.2-4 A direct current of magnitude /.

similar but different. They are the same size but have different directions. Therefore, i2 is the negative of i\ andll = - 12

We always associate an arrow with a current to denote its direction. A complete description of current requires both a value (which can be positive or negative) and a direction (indicated by an arrow). If the current flowing through an element is constant, we represent it by the constant /, as shown in Figure 1.2-4. A constant current is called a direct current (dc). A direct current (dc) is a current of constant magnitude. A time-varying current /(/) can take many forms, such as a ramp, a sinusoid, or an exponential, as shown in Figure 1.2-5. The sinusoidal current is called an alternating current (ac).

FIGURE 1.2-5 (a) A ramp with a slope M. (6 ) A sinusoid, (c) An exponential. / is a constant. The current / is zero for t < 0.

If the charge q is known, the current i is readily found using Eq. 1.2-1. Alternatively, if the current i is known, the charge q is readily calculated. Note that from Eq. 1.2-1, we obtainq= fJ c o

id x=

[ i d z + q(0)Jo

( 1 .2 - 2 )

where 1

tered a circuit element is q{t) 4 sin 31 C when = 0 when , < 0 , D etem , the c t in this crcu i, element for , > 0,

Answer: i{t) = - 4 sin 3/ = 12 cos 31A

S y s t e m s o f U n it s

1.3

S Y S T E M S OF U N I T S

In representing a circuit and its elements, we must define a consistent system of units for the quantities occurring in the circuit. At the 1960 meeting of the General Conference of Weights and Measures, the representatives modernized the metric system and created the Systeme International dUnites, commonly called SI units. SI is Systeme International d Unites or the International System of Units. The fundamental, or base, units of SI are shown in Table 1.3-1. Symbols for units that represent proper (persons) names are capitalized; the others are not. Periods are not used after the symbols, and the symbols do not take on plural forms. The derived units for other physical quantities are obtained by combining the fundamental units. Table 1.3-2 shows the more common derived units along with their formulas in terms of the fundamental units or preceding derived units. Symbols are shown for the units that have them.Table 1.3-1 SI Base UnitsSI UNIT QUANTITY NAME SYMBOL

Length Mass Time Electric current Thermodynamic temperature Amount of substance Luminous intensity

meter kilogram second ampere kelvin mole candela

m kg s A K mol cd

Table 1 3 2 Derived Units in SIQUANTITY UNIT NAME FORMULA SYMBOL

Acceleration linear Velocity linear Frequency Force Pressure or stress Density Energy or work Power Electric charge Electric potential Electric resistance Electric conductance Electric capacitance Magnetic flux Inductance

meter per second per second meter per second hertz newton pascal kilogram per cubic meter joule watt coulomb volt ohm siemens farad weber henry

m/s2 m/s s- kg m/s2 N/m2 kg/m3 N m J/s A s W/A V/A A/VC/V

Hz N Pa Jw c v a s

F Wb H

V -s Wb/A

0

-

E le ctric C irc u it V a ria b le s

SI Prefixes

MULTIPLE1012 109 106 103 10~2

PREFIX tera giga mega kilo centi milli micro nano pico femto

SYMBOL T G M k c m M n P f

i 0, FIGI RE 1.8-1 The circuit to control and the voltage across the second element is v2(f) = a V for t> 0. The maximum magnitude o f the jet valve for a space rocket. current, A is limited to 1 mA. Determine the required constants D and B and describe the required battery.

|

E _3

Describe the Situation and the A ssum ptions1.

The current enters the plus terminal o f the second element. The current leaves the plus terminal o f the first element. The wires are perfect and have no effect on the circuit (they do not absorb energy). The model o f the circuit, as shown in Figure 1.8-1. assumes that the voltage across the two elements is equal; that is, Vj v2. The battery voltage V! is vx= B e~r 60 V where B is the initial voltage o f the battery that will discharge exponentially as it supplies energy' to the valve. The circuit operates from t = 0 to / = 60 s. The current is limited, so D < 1 mA.

2. 3. 4.

5.

6.

7.

State the GoalDetermine the energy supplied by the first elem ent for the one-minute period and then select the constants D and B. Describe the battery selected.

G enerate a PlanFirst, find v , ( 0 and i(t) and then obtain the power, p x(t), supplied by the first elem ent. Next, using /?,(?), find the energy supplied for the first 60 s.G0AL EQUATION NEED INFORMATION

The energy wj for the

y 60

first 60 s

Hi I Jo

P \ v ) dt

p x(t)

V] and j known except for constants D and B

A ct on the P la n First, we need p \(t), so we first calculate p x{t) = ivi = (De~t,6 x 10"3 A ) [Be~t60 V ) = DBe~'/30 x 10 3 W = D B e- //3 mW

P r o b le m s~ o

Second, we need to find w\ for the first 60 s as w, = /*60 60 / {DBe~mX

. DB x 10- 3e - ' / 30 6" 10- 3) t/f = ------ _ 1/3Q -

= - 3 0 DB x 10- 3 (e ' 2 - 1) = 25.9DB x 10~3 J Because we require vti > 40 mJ, 40 < 25.9DB Next, select the limiting value, D = 1, to get 40 B > - -------- - = 1.54 V (2 5 ,.9)(1) Thus, we select a 2-V battery so that the magnitude of the current is less than 1 mA. Verify the Proposed Solution We must verify that at least 40 mJ is supplied using the 2-V battery. Because i = e ~ ' 60 mA and v2 2e~tm V, the energy supplied by the battery is /60 /*60 w= (2 e-/60) ( e - t/6 x 10"3) d t= 2e~tl30 x 10' 3 dt - 51.8 mJ Jo Jo Thus, we have verified the solution, and we communicate it by recording the require ment for a 2-V battery.

1.9

SUMMARY

O Charge is the intrinsic property of matter responsible for electric phenomena. The current in a circuit element is the rate of movement of charge through the element. The voltage across an element indicates the energy available to cause charge to move through the element. O Given the current, i, and voltage, v, of a circuit element, the power, p, and energy, w , are given by >

O Table 1.5-1 summarizes the use of the passive convention when calculating the power supplied or received by a circuit element. O The SI units (Table 1.3-1) are used by todays engineers and scientists. Using decimal prefixes (Table 1.3-3), we may simply express electrical quantities with a wide range of magnitudes.

p = v -i

andJo

pd r

PROBLEMSSection 1.2 Electric Circuits and Current P 1.2-1 The total charge that has entered a circuit element is q ( 0 = 1 25( 1- e 51) when t > 0 and q{t) = 0 when t < 0. Deter mine the current in this circuit element for t > 0 .

Hint: q{0) = f

J 30

i(r) dr = j

J G O

0 dx = 0

Answer: q(t) = 4 1 + 0.8^-5' - 0.8 C for t > 0P 1.2-3 The current in a circuit element is /(f) = 4 sin 5 1 A when t > 0 and i(t) = 0 when t < 0. Determine the total charge that has entered a circuit element for / > 0 .

Answer: i(t) = 6.25e~St AP 1.2-2 The current in a circuit element is i(t) = 4 ( 1- e~5t) A when t > 0 and i(t) 0 when t < 0 . Determine the total charge that has entered a circuit element for t > 0 .

Hint: q( 0) = f

J -O O

i(r) dr = I

J 00

0 dr = 0

E le ctric C irc u it V a ria b le s

P 1.2-4 The current in a circuit element is

Section 1.3 Systems of UnitsP 1.3-1 A constant current of 3.2 flows through an element. What is the charge that has passed through the element in the first millisecond?

0

/