org Circuit Analysis Demystified Demystified Series Accounting Demystified Macroeconomics Demystified Advanced Calculus Demystified Management Accounting Demystified Advanced Physics Demystified Math Proofs Demystified Advanced Statistics Demystified Math Word Problems Demystified r Algebra Demystified MATLAB Demystified Alternative Energy Demystified Medical Billing and Coding Anatomy Demystified Demystified asp.0 Demystified Medical Terminology Demystified Astronomy Demystified Meteorology Demystified Audio Demystified Microbiology Demystified Biology Demystified Microeconomics Demystified Biotechnology Demystified Nanotechnology Demystified Business Calculus Demystified Nurse Management Demystified Business Math Demystified OOP Demystified Business Statistics Demystified Options Demystified C++ Demystified Organic Chemistry Demystified Calculus Demystified Personal Computing Demystified Chemistry Demystified Pharmacology Demystified Circuit Analysis Demystified Physics Demystified College Algebra Demystified Physiology Demystified Corporate Finance Demystified Pre-Algebra Demystified Databases Demystified Precalculus Demystified Data Structures Demystified Probability Demystified Differential Equations Demystified Project Management Demystified Digital Electronics Demystified Psychology Demystified Earth Science Demystified Quality Management Demystified Electricity Demystified Quantum Mechanics Demystified Electronics Demystified Real Estate Math Demystified Engineering Statistics Demystified Relativity Demystified Environmental Science Demystified Robotics Demystified Everyday Math Demystified Sales Management Demystified Fertility Demystified Signals and Systems Demystified Financial Planning Demystified Six Sigma Demystified Forensics Demystified Spanish Demystified French Demystified sql Demystified Genetics Demystified Statics and Dynamics Demystified Geometry Demystified Statistics Demystified German Demystified Technical Analysis Demystified Home Networking Demystified Technical Math Demystified Investing Demystified Trigonometry Demystified Italian Demystified uml Demystified Java Demystified Visual Basic 2005 Demystified JavaScript Demystified Visual C# 2005 Demystified Lean Six Sigma Demystified Vitamins and Minerals Demystified Linear Algebra Demystified xml Demystified www.org Circuit Analysis Demystified David McMahon New York Chicago San Francisco Lisbon London Madrid Mexico City Milan New Delhi San Juan Seoul Singapore Sydney Toronto Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved. Manufactured in the United States of America. Except as permitted under the United States Copyright Act of 1976, no part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without the prior written permission of the publisher. 0-07-151086-9 The material in this eBook also appears in the print version of this title: 0-07-148898-7. All trademarks are trademarks of their respective owners. Rather than put a trademark symbol after every occurrence of a trademarked name, we use names in an editorial fashion only, and to the benefit of the trademark owner, with no intention of infringement of the trademark. Where such designations appear in this book, they have been printed with initial caps. McGraw-Hill eBooks are available at special quantity discounts to use as premiums and sales promotions, or for use in corporate training programs. For more information, please contact George Hoare, Special Sales, at george_hoare@mcgraw-hill. TERMS OF USE This is a copyrighted work and The McGraw-Hill Companies, Inc. (“McGraw-Hill”) and its licensors reserve all rights in and to the work. Use of this work is subject to these terms. Except as permitted under the Copyright Act of 1976 and the right to store and retrieve one copy of the work, you may not decompile, disassemble, reverse engineer, reproduce, modify, create derivativeworks based upon, transmit, distribute, disseminate, sell, publish or sublicense the work or any part of it without McGraw-Hill’s prior consent. You may use the work for your own noncommercial and personal use; any other use of the work is strictly prohibited. Your right to use the work may be terminated if you fail to comply with these terms. THE WORK IS PROVIDED “AS IS.” McGRAW-HILL AND ITS LICENSORS MAKE NO GUARANTEES OR WARRANTIES AS TO THE ACCURACY, ADEQUACY OR COMPLETENESS OF OR RESULTS TO BE OBTAINED FROM USING THE WORK, INCLUDING ANY INFORMATION THAT CAN BE ACCESSED THROUGH THE WORK VIA HYPERLINK OR OTHERWISE, AND EXPRESSLY DISCLAIM ANY WARRANTY, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO IMPLIED WARRANTIES OF MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE. McGraw-Hill and its licensors do not warrant or guarantee that the functions contained in the work will meet your requirements or that its operation will be uninterrupted or error free. Neither McGraw-Hill nor its licensors shall be liable to you or anyone else for any inaccuracy, error or omission, regardless of cause, in the work or for any damages resulting therefrom. McGraw-Hill has no responsibility for the content of any information accessed through the work. Under no circumstances shall McGraw-Hill and/or its licensors be liable for any indirect, incidental, special, punitive, consequential or similar damages that result from the use of or inability to use the work, even if any of them has been advised of the possibility of such damages. This limitation of liability shall apply to any claim or cause whatsoever whether such claim or cause arises in contract, tort or otherwise.1036/0071488987 Professional Want to learn more? We hope you enjoy this McGraw-Hill eBook! If you’d like more information about this book, its author, or related books and websites, please click here.org ABOUT THE AUTHOR David McMahon is a physicist and researcher at a national laboratory. He is the author of Linear Algebra Demystified, Quantum Mechanics Demystified, Relativity Demystified, Signals and Systems Demystified, Statics and Dynamics Demystified, and MATLAB r Demystified. Copyright © 2008 by The McGraw-Hill Companies, Inc. Click here for terms of use. This page intentionally left blank For more information about this title, click here CONTENTS Preface xiii Acknowledgments xv CHAPTER 1 An Introduction to Circuit Analysis 1 What Is Circuit Analysis? 2 Electric Current 2 Current Arrows 9 Voltage 11 Time Varying Voltage and Voltage Sources 13 Dependent Voltage Sources 16 Current Sources 16 Open and Short Circuits 18 Power 19 Conservation of Energy 22 Summary 23 Quiz 23 CHAPTER 2 Kirchhoff’s Laws and Resistance 25 Branches, Nodes, and Loops 25 Kirchhoff’s Current Law 26 Kirchhoff’s Voltage Law 28 The Resistor 31 Power in a Resistor 33 Circuit Analysis with Resistors 34 www.org viii Circuit Analysis Demystified Root Mean Square (RMS) Values 37 Voltage and Current Dividers 41 More Examples 46 Summary 53 Quiz 54 CHAPTER 3 Thevenin’s and Norton’s Theorems 58 Thevenin’s Theorem 59 Step One: Disconnect the Outside Network 60 Step Two: Set Independent Sources to Zero 61 Step Three: Measure the Resistance at Terminals A and B 61 Series and Parallel Circuits 61 Back to Thevenin’s Theorem 67 Thevenin’s Theorem Using the Karni Method 77 Norton’s Theorem and Norton Equivalent Circuits 82 Summary 84 Quiz 84 CHAPTER 4 Network Theorems 86 Superposition 86 Millman’s Theorem 93 Quiz 96 CHAPTER 5 Delta–Wye Transformations and Bridge Circuits 97 Delta–Wye Transformations 97 Bridge Circuits 101 Quiz 102 CHAPTER 6 Capacitance and Inductance 103 The Capacitor 103 Capacitors in Parallel or Series 104 Voltage–Current Relations in a Capacitor 106 Voltage in Terms of Current 107 Contents ix Power and Energy in the Capacitor 109 Time Constants, Zero-Input Response, and First-Order RC Circuits 110 The Inductor 114 Inductors in Series and in Parallel 115 Energy in an Inductor 115 Current in an Inductor 115 Zero-Input Analysis of First-Order RL Circuits 116 Mutual Inductance 117 Zero-Input Response in an RL Circuit 120 Second-Order Circuits 125 Summary 130 Quiz 131 CHAPTER 7 The Phasor Transform 132 Basics on Complex Numbers 132 Polar Representation 134 Sinusoids and Complex Numbers 134 Sinusoidal Sources 137 Leading and Lagging 138 Effective or RMS Values 139 Dynamic Elements and Sinusoidal Sources 139 The Phasor Transform 140 Properties of the Phasor Transform 142 Circuit Analysis Using Phasors 143 Impedance 147 Summary 150 Quiz 151 CHAPTER 8 Frequency Response 152 Natural Frequencies 152 The Frequency Response of a Circuit 156 Filters 164 Summary 169 Quiz 170 x Circuit Analysis Demystified CHAPTER 9 Operational Amplifiers 172 The Noninverting Amplifier 173 Inverting Amplifier 175 The Summing Amplifier 176 Summary 178 Quiz 178 CHAPTER 10 Sinusoidal Steady-State Power Calculations 179 Maximum Power Transfer 179 Instantaneous Power 183 Average and Reactive Power 185 The RMS Value and Power Calculations 187 Complex Power 194 Summary 195 Quiz 196 CHAPTER 11 Transformers 197 The Dot Convention 198 Summary 200 Quiz 200 CHAPTER 12 Three-Phase Circuits 202 Balanced Sequences 203 Y Loads 204 Summary 205 Quiz 205 CHAPTER 13 Network Analysis Using Laplace Transforms 206 The Laplace Transform 207 Exponential Order 210 The Inverse Laplace Transform 211 Analyzing Circuits Using Laplace Transforms 214 Convolution 218 www.org Contents xi Zero-State Response and the Network Function 221 Poles and Zeros 224 Summary 225 Quiz 226 CHAPTER 14 Circuit Stability 228 Poles and Stability 231 Zero-Input Response Stability 236 Bounded Input-Bounded Output Stability 237 Summary 239 Quiz 240 CHAPTER 15 Bode Plots and Butterworth Filters 241 Asymptotic Behavior of Functions 242 Creating Bode Plots 244 Bode Plot Examples 245 Filters 252 Butterworth Filters 254 Quiz 259 Final Exam 260 Quiz and Exam Solutions 270 References 281 Index 283 This page intentionally left blank PREFACE Circuit analysis is one of the most important courses in electrical engineering, where students learn the basics of the field for the first time. Unfortunately it is also one of the most difficult courses that students face when attempting to learn electrical engineering. At most universities it serves as a “weed out” course, where students not “cut out” for electrical engineering are shown the exit. A friend once referred to the course as “circuit paralysis” because he claimed to freeze up during the exams. The purpose of this book is to make learning circuit analysis easier. It can function as a supplement to just about any electric circuits book and it will serve as a tutorial for just about any circuit analysis class. If you are having trouble with electrical engineering because the books are too difficult or the professor is too hard to understand, this text will help you. This book explains concepts in a clear, matter-of-fact style and then uses solved examples to illustrate how each concept is applied. Quizzes at the end of each chapter include questions similar to the questions solved in the book, allowing you to practice what you have learned. The answer to each quiz question is provided at the end of the book. In addition, a final exam allows you to test your overall knowledge. This book is designed to help students taking a one-year circuit analysis course or professionals looking for a review. The first 10 chapters cover topics typically discussed in a first-semester circuit analysis course, such as voltage and current theorems, Thevenin’s and Norton’s theorems, op amp circuits, capacitance and inductance, and phasor analysis of circuits. The remaining chapters cover more advanced topics typically left to a second- semester course. These include Laplace transforms, filters, Bode plots, and characterization of circuit stability. If you use this book for self-study or as a supplement in your class you will find it much easier to master circuit analysis. Copyright © 2008 by The McGraw-Hill Companies, Inc. Click here for terms of use.org This page intentionally left blank ACKNOWLEDGMENTS I would like to thank Rayjan Wilson for his thorough and thoughtful review of the manuscript. His insightful comments and detailed review were vital to making this book a success. Copyright © 2008 by The McGraw-Hill Companies, Inc. Click here for terms of use. This page intentionally left blank www.org CHAPTER 1 An Introduction to Circuit Analysis An electric circuit is an arrangement into a network of several connected electric components. The components that we will be concerned with are two-terminal components. This means that each component has two connection points or terminals that can be used to connect it with other components in the circuit. Each type of component will have its own symbol. This is illustrated in Fig. 1-1, where we indicate the terminals with two rounded ends or dots and use an empty box to represent a generic electric component. There are several electric components but in this book our primary focus will be on resistors, capacitors, inductors, and operational amplifiers. At this point, we won’t worry about what these components are. We will investigate each one in detail later in the book as the necessary theory is developed. In this chapter we will lay down a few fundamentals. We begin by defining circuit analysis. Copyright © 2008 by The McGraw-Hill Companies, Inc.
