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Circuit Analysis

Circuit Analysisby John M. Santiago, Jr., PhDProfessor of Electrical and SystemsEngineering, Colonel (Ret) USAF

Circuit Analysis For Dummies Published byJohn Wiley & Sons, Inc.111 River St.Hoboken, NJ 07030-5774www.wiley.comCopyright 2013 by John Wiley & Sons, Inc., Hoboken, New JerseyPublished by John Wiley & Sons, Inc., Hoboken, New JerseyPublished simultaneously in CanadaNo part of this publication may be reproduced, stored in a retrieval system or transmitted in any formor by any means, electronic, mechanical, photocopying, recording, scanning or otherwise, except aspermitted under Sections 107 or 108 of the 1976 United States Copyright Act, without the prior writtenpermission of the Publisher. Requests to the Publisher for permission should be addressed to thePermissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, (201) 748-6011,fax (201) 748-6008, or online at http://www.wiley.com/go/permissions.Trademarks: Wiley, the Wiley logo, For Dummies, the Dummies Man logo, A Reference for the Rest of Us!,The Dummies Way, Dummies Daily, The Fun and Easy Way, Dummies.com, Making Everything Easier,and related trade dress are trademarks or registered trademarks of John Wiley & Sons, Inc., and/or itsaffiliates in the United States and other countries, and may not be used without written permission. Allother trademarks are the property of their respective owners. John Wiley & Sons, Inc., is not associatedwith any product or vendor mentioned in this book.LIMIT OF LIABILITY/DISCLAIMER OF WARRANTY: THE PUBLISHER AND THE AUTHOR MAKE NOREPRESENTATIONS OR WARRANTIES WITH RESPECT TO THE ACCURACY OR COMPLETENESSOF THE CONTENTS OF THIS WORK AND SPECIFICALLY DISCLAIM ALL WARRANTIES, INCLUDINGWITHOUT LIMITATION WARRANTIES OF FITNESS FOR A PARTICULAR PURPOSE. NO WARRANTYMAY BE CREATED OR EXTENDED BY SALES OR PROMOTIONAL MATERIALS. THE ADVICE ANDSTRATEGIES CONTAINED HEREIN MAY NOT BE SUITABLE FOR EVERY SITUATION. THIS WORK ISSOLD WITH THE UNDERSTANDING THAT THE PUBLISHER IS NOT ENGAGED IN RENDERING LEGAL,ACCOUNTING, OR OTHER PROFESSIONAL SERVICES. IF PROFESSIONAL ASSISTANCE IS REQUIRED,THE SERVICES OF A COMPETENT PROFESSIONAL PERSON SHOULD BE SOUGHT. NEITHER THEPUBLISHER NOR THE AUTHOR SHALL BE LIABLE FOR DAMAGES ARISING HEREFROM. THE FACTTHAT AN ORGANIZATION OR WEBSITE IS REFERRED TO IN THIS WORK AS A CITATION AND/ORA POTENTIAL SOURCE OF FURTHER INFORMATION DOES NOT MEAN THAT THE AUTHOR OR THEPUBLISHER ENDORSES THE INFORMATION THE ORGANIZATION OR WEBSITE MAY PROVIDE ORRECOMMENDATIONS IT MAY MAKE. FURTHER, READERS SHOULD BE AWARE THAT INTERNETWEBSITES LISTED IN THIS WORK MAY HAVE CHANGED OR DISAPPEARED BETWEEN WHEN THISWORK WAS WRITTEN AND WHEN IT IS READ.For general information on our other products and services, please contact our Customer CareDepartment within the U.S. at 877-762-2974, outside the U.S. at 317-572-3993, or fax 317-572-4002.For technical support, please visit www.wiley.com/techsupport.Wiley publishes in a variety of print and electronic formats and by print-on-demand. Some materialincluded with standard print versions of this book may not be included in e-books or in print-on-demand.If this book refers to media such as a CD or DVD that is not included in the version you purchased, youmay download this material at http://booksupport.wiley.com. For more information about Wileyproducts, visit www.wiley.com.Library of Congress Control Number: 2013932101ISBN 978-1-118-49312-0 (pbk); ISBN 978-1-118-59050-8 (ebk); ISBN 978-1-118-59052-2 (ebk);ISBN 978-1-118-59056-0 (ebk)Manufactured in the United States of America10 9 8 7 6 5 4 3 2 1

About the AuthorJohn Santiago retired from the military in 2003 with 26 years of service inthe United States Air Force (USAF). John has served in a variety of leadershippositions in technical program management, acquisition development,and operation research support. While assigned in Europe for three yearswith the USAF, he spearheaded more than 40 international scientific andengineering conferences/workshops as a steering committee member.John has experience in many engineering disciplines and missions, includingcontrol and modeling of large, flexible space structures; communicationssystems; electro-optics; high-energy lasers; missile seekers/sensors forprecision-guided munitions; image processing/recognition; informationtechnologies; space, air, and missile warning; missile defense; and homelanddefense.One of John’s favorite assignments was serving as an associate professor atthe USAF Academy during his tour from 1984 through 1989. John is currentlya professor of Electrical and Systems Engineering at Colorado TechnicalUniversity, where he has taught 26 different undergraduate and graduatecourses in electrical and systems engineering.Some of his awards include Faculty of the Year at Colorado TechnicalUniversity in 2008; USAF Academy Outstanding Military Educator in 1989; andUSAF Academy Outstanding Electrical Engineering Educator in 1998.During his USAF career, John received his PhD in Electrical Engineering fromthe University of New Mexico; his Master of Science in Resource Strategy atthe Industrial College of the Armed Forces; his Master of Science in ElectricalEngineering from the Air Force Institute of Technology, specializing inelectro-optics; and his Bachelor of Science from the University of California,Los Angeles.On February 14, 1982, John married Emerenciana F. Manaois.More information about John’s background and experience is available atwww.FreedomUniversity.TV.

DedicationTo my heavenly Father, thank you for all the many blessings, especially thegift of family and friends.To my lovely Emily, thank you for your loving and continued support, alwaysand forever.To my parents, who bravely immigrated here from the Philippines to live inthis great nation.To the Founding Fathers, who were engineers and visionary leaders increating this great country called the United States. To their creative geniusand to all those standing on their shoulders, especially the next generation ofengineers.To all those who wondered if there’s anything more to circuit analysis thanOhm’s law and Kirchhoff’s laws.Author’s AcknowledgmentsMany people have been involved in this book, and I thank them all. First, toall the former cadets at the United States Air Force Academy, the students atthe University of West Florida, and the students at the Colorado TechnicalUniversity who endured my class lessons and asked a gazillion questionsover the years as I continued to learn to become a better teacher.I’d like to thank a team of players who’ve made my writing presentable.First, I’d like to thank Matt Wagner, my agent, who contacted me aboutwriting this book. I’d also especially like to thank the folks at Wiley who madethis book possible: Erin Mooney, my acquisitions editor; Jennifer Tebbe, myproject editor; and Danielle Voirol, my copy editor.I’d again like to thank my wife for her encouragement and for keeping mestraight about the things going on at home and in the community as I wentthrough this writing adventure.

Publisher’s AcknowledgmentsWe’re proud of this book; please send us your comments at http://dummies.custhelp.com. Forother comments, please contact our Customer Care Department within the U.S. at 877-762-2974,outside the U.S. at 317-572-3993, or fax 317-572-4002.Some of the people who helped bring this book to market include the following:Acquisitions, Editorial, andVertical WebsitesComposition ServicesProject Editor: Jennifer TebbeAcquisitions Editor: Erin Calligan MooneySenior Copy Editor: Danielle VoirolAssistant Editor: David LuttonEditorial Program Coordinator: Joe NiesenProject Coordinator: Katherine CrockerLayout and Graphics: Carl Byers,Carrie A. Cesavice, Amy Hassos,Joyce Haughey, Christin SwinfordProofreaders: Tricia Liebig, Dwight RamseyIndexer: Ty KoontzTechnical Editor: Chang Liu, Dan MooreEditorial Manager: Christine Meloy BeckEditorial Assistant: Alexa Koschier,Rachelle S. AmickCover Photo: VOLODYMYR GRINKO/iStockphoto.comPublishing and Editorial for Consumer DummiesKathleen Nebenhaus, Vice President and Executive PublisherDavid Palmer, Associate PublisherKristin Ferguson-Wagstaffe, Product Development DirectorPublishing for Technology DummiesAndy Cummings, Vice President and PublisherComposition ServicesDebbie Stailey, Director of Composition Services

Contents at a GlanceIntroduction. 1Part I: Getting Started with Circuit Analysis. 5Chapter 1: Introducing Circuit Analysis. 7Chapter 2: Clarifying Basic Circuit Concepts and Diagrams. 15Chapter 3: Exploring Simple Circuits with Kirchhoff’s Laws. 25Chapter 4: Simplifying Circuit Analysis with Source Transformationand Division Techniques. 41Part II: Applying Analytical Methodsfor Complex Circuits. 65Chapter 5: Giving the Nod to Node-Voltage Analysis. 67Chapter 6: Getting in the Loop on Mesh Current Equations. 83Chapter 7: Solving One Problem at a Time Using Superposition. 95Chapter 8: Applying Thévenin’s and Norton’s Theorems. 113Part III: Understanding Circuits with Transistorsand Operational Amplifiers. 131Chapter 9: Dependent Sources and the Transistors That Involve Them. 133Chapter 10: Letting Operational Amplifiers Do the Tough Math Fast. 155Part IV: Applying Time-Varying Signalsto First- and Second-Order Circuits. 173Chapter 11: Making Waves with Funky Functions. 175Chapter 12: Spicing Up Circuit Analysis with Capacitors and Inductors. 193Chapter 13: Tackling First-Order Circuits. 211Chapter 14: Analyzing Second-Order Circuits. 233Part V: Advanced Techniques andApplications in Circuit Analysis. 253Chapter 15: Phasing in Phasors for Wave Functions. 255Chapter 16: Predicting Circuit Behavior with Laplace Transform Techniques. 273Chapter 17: Implementing Laplace Techniques for Circuit Analysis. 295Chapter 18: Focusing on the Frequency Responses. 313

Part VI: The Part of Tens. 335Chapter 19: Ten Practical Applications for Circuits. 337Chapter 20: Ten Technologies Affecting Circuits. 341Index. 345

Table of ContentsIntroduction. 1About This Book. 1Conventions Used in This Book. 1What You’re Not to Read. 2Foolish Assumptions. 2How This Book Is Organized. 2Part I: Getting Started with Circuit Analysis. 2Part II: Applying Analytical Methods for Complex Circuits. 3Part III: Understanding Circuits with Transistorsand Operational Amplifiers.3Part IV: Applying Time-Varying Signalsto First- and Second-Order Circuits. 3Part V: Advanced Techniques andApplications in Circuit Analysis. 3Part VI: The Part of Tens. 3Icons Used in This Book. 4Where to Go from Here. 4Part I: Getting Started with Circuit Analysis. 5Chapter 1: Introducing Circuit Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 7Getting Started with Current and Voltage. 7Going with the flow with current. 8Recognizing potential differences with voltage. 9Staying grounded with zero voltage. 9Getting some direction with the passive sign convention. 10Beginning with the Basic Laws. 11Surveying the Analytical Methods for More-Complex Circuits. 11Introducing Transistors and Operational Amplifiers. 12Dealing with Time-Varying Signals, Capacitors, and Inductors. 13Avoiding Calculus with Advanced Techniques. 13Chapter 2: Clarifying Basic Circuit Concepts and Diagrams . . . . . . . . 15Looking at Current-Voltage Relationships. 15Absorbing energy with resistors. 16Applying Ohm’s law to resistors. 16Calculating the power dissipated by resistors. 18Offering no resistance: Batteries and short circuits. 18Batteries: Providing power independently. 19Short circuits: No voltage, no power. 19