# Nilsson Riedel Electric Circuits 10th Edition, Study notes for Electronics. Adams State College (CO)

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A List of Tables

Table No. Title Page No.

1.1 The International System of Units (SI) 9 1.2 Derived Units in SI 9 1.3 Standardized Prefixes to Signify Powers of 10 9 1.4 Interpretation of Reference Directions in Fig. 1.5 13 4.1 Terms for Describing Circuits 91 4.2 PSpice Sensitivity Analysis Results 128 6.1 Terminal Equations for Ideal Inductors and Capacitors 203 6.2 Equations for Series- and Parallel-Connected Inductors and Capacitors 203 7.1 Value of for t Equal to Integral Multiples of 217 8.1 Natural Response Parameters of the Parallel RLC Circuit 269 8.2 The Response of a Second-Order Circuit is Overdamped, Underdamped, or Critically Damped 295 8.3 In Determining the Natural Response of a Second-Order Circuit, We First Determine Whether

it is Over-, Under-, or Critically Damped, and Then We Solve the Appropriate Equations 295 8.4 In Determining the Step Response of a Second-Order Circuit, We Apply the Appropriate

Equations Depending on the Damping 296 9.1 Impedance and Reactance Values 318 9.2 Admittance and Susceptance Values 322 9.3 Impedance and Related Values 345

10.1 Annual Energy Requirements of Electric Household Appliances 365 10.2 Three Power Quantities and Their Units 368 12.1 An Abbreviated List of Laplace Transform Pairs 435 12.2 An Abbreviated List of Operational Transforms 440 12.3 Four Useful Transform Pairs 451 13.1 Summary of the s-Domain Equivalent Circuits 468 13.2 Numerical Values of 492 14.1 Input and Output Voltage Magnitudes for Several Frequencies 527 15.1 Normalized (so that ) Butterworth Polynomials up to the Eighth Order 577 17.1 Fourier Transforms of Elementary Functions 653 17.2 Operational Transforms 658 18.1 Parameter Conversion Table 682 18.2 Terminated Two-Port Equations 688

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ELECTRIC CIRCUITS TENTH EDITION

ELECTRIC CIRCUITS TENTH EDITION

James W. Nilsson Professor Emeritus

Iowa State University

Susan A. Riedel Marquette University

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ISBN-13: 978-0-13-376003-3 ISBN-10: 0-13-376003-0

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Executive Editor: Andrew Gilfillan Editorial Assistant: Sandra Rodriguez Marketing Manager: Tim Galligan Senior Managing Editor: Scott Disanno Production Editor: Rose Kernan

Cover Design: Black Horse Designs Cover Art: Inverter 04 Oil painting by Ben Leone

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Credits and acknowledgments borrowed from other sources and reproduced, with permission, in this textbook appear on appropriate page within text.

Copyright © 2015, 2008, 2005 Pearson Education, Inc., publishing as Prentice Hall, One Lake Street, Upper Saddle River, New Jersey, 07458. All rights reserved. Manufactured in the United States of America. This publication is protected by Copyright, and permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. To obtain permission(s) to use material from this work, please submit a written request to Pearson Education, Inc., Permissions Department, One Lake Street, Upper Saddle River, New Jersey, 07458.

Library of Congress Cataloging-in-Publication Data Nilsson, James William.

Electric circuits / James W. Nilsson, Professor Emeritus, Iowa State University, Susan A. Riedel, Marquette University.—Tenth edition.

pages cm ISBN-13: 978-0-13-376003-3 ISBN-10: 0-13-376003-0

1. Electric circuits. I. Riedel, Susan A. II. Title. TK545.N54 2015 621.319'2—dc23

2013037725

10 9 8 7 6 5 4 3 2

To Anna

vii

Brief Contents List of Examples xiii Preface xvii

Chapter 1 Circuit Variables 2 Chapter 2 Circuit Elements 24 Chapter 3 Simple Resistive Circuits 56 Chapter 4 Techniques of Circuit Analysis 88 Chapter 5 The Operational Amplifier 144 Chapter 6 Inductance, Capacitance, and Mutual Inductance 174 Chapter 7 Response of First-Order RL and RC Circuits 212 Chapter 8 Natural and Step Responses of RLC Circuits 264 Chapter 9 Sinusoidal Steady-State Analysis 304 Chapter 10 Sinusoidal Steady-State Power Calculations 358 Chapter 11 Balanced Three-Phase Circuits 396 Chapter 12 Introduction to the Laplace Transform 426 Chapter 13 The Laplace Transform in Circuit Analysis 464 Chapter 14 Introduction to Frequency Selective Circuits 520 Chapter 15 Active Filter Circuits 556 Chapter 16 Fourier Series 602 Chapter 17 The Fourier Transform 642 Chapter 18 Two-Port Circuits 676 Appendix A The Solution of Linear Simultaneous Equations 703 Appendix B Complex Numbers 723 Appendix C More on Magnetically Coupled Coils and Ideal Transformers 729 Appendix D The Decibel 737 Appendix E Bode Diagrams 739 Appendix F An Abbreviated Table of Trigonometric Identities 757 Appendix G An Abbreviated Table of Integrals 759 Appendix H Common Standard Component Values 761

Answers to Selected Problems 763 Index 775

ix

Contents List of Examples xiii

Preface xvii

Chapter 1 Circuit Variables 2 Practical Perspective: Balancing Power 3

1.1 Electrical Engineering: An Overview 4 1.2 The International System of Units 8 1.3 Circuit Analysis: An Overview 10 1.4 Voltage and Current 11 1.5 The Ideal Basic Circuit Element 12 1.6 Power and Energy 14

Practical Perspective: Balancing Power 17 Summary 18 Problems 19

Chapter 2 Circuit Elements 24 Practical Perspective: Heating with Electric Radiators 25

2.1 Voltage and Current Sources 26 2.2 Electrical Resistance (Ohm’s Law) 30 2.3 Construction of a Circuit Model 34 2.4 Kirchhoff’s Laws 37 2.5 Analysis of a Circuit Containing Dependent

Sources 42 Practical Perspective: Heating with Electric Radiators 46 Summary 48 Problems 48

Chapter 3 Simple Resistive Circuits 56 Practical Perspective: Resistive Touch Screens 57

3.1 Resistors in Series 58 3.2 Resistors in Parallel 59 3.3 The Voltage-Divider and Current-Divider

Circuits 61 3.4 Voltage Division and Current Division 64 3.5 Measuring Voltage and Current 66 3.6 Measuring Resistance—The Wheatstone

Bridge 69 3.7 Delta-to-Wye (Pi-to-Tee) Equivalent

Circuits 71 Practical Perspective: Resistive Touch Screens 73 Summary 75 Problems 76

Chapter 4 Techniques of Circuit Analysis 88

Practical Perspective: Circuits with Realistic Resistors 89

4.1 Terminology 90 4.2 Introduction to the Node-Voltage

Method 93 4.3 The Node-Voltage Method and Dependent

Sources 95 4.4 The Node-Voltage Method: Some Special

Cases 96 4.5 Introduction to the Mesh-Current

Method 99 4.6 The Mesh-Current Method and Dependent

Sources 102 4.7 The Mesh-Current Method: Some Special

Cases 103 4.8 The Node-Voltage Method Versus the

Mesh-Current Method 106 4.9 Source Transformations 109 4.10 Thévenin and Norton Equivalents 113 4.11 More on Deriving a Thévenin

Equivalent 117 4.12 Maximum Power Transfer 120 4.13 Superposition 122

Practical Perspective: Circuits with Realistic Resistors 125 Summary 129 Problems 130

Chapter 5 The Operational Amplifier 144

Practical Perspective: Strain Gages 145 5.1 Operational Amplifier Terminals 146 5.2 Terminal Voltages and Currents 146 5.3 The Inverting-Amplifier Circuit 150 5.4 The Summing-Amplifier Circuit 152 5.5 The Noninverting-Amplifier

Circuit 153 5.6 The Difference-Amplifier Circuit 155 5.7 A More Realistic Model for the Operational

Amplifier 159 Practical Perspective: Strain Gages 162 Summary 164 Problems 165

x Contents

Chapter 6 Inductance, Capacitance, and Mutual Inductance 174

Practical Perspective: Capacitive Touch Screens 175

6.1 The Inductor 176 6.2 The Capacitor 182 6.3 Series-Parallel Combinations of Inductance

and Capacitance 187 6.4 Mutual Inductance 189 6.5 A Closer Look at Mutual Inductance 193

Practical Perspective: Capacitive Touch Screens 200 Summary 202 Problems 204

Chapter 7 Response of First-Order RL and RC Circuits 212

Practical Perspective: Artificial Pacemaker 213 7.1 The Natural Response of an RL Circuit 214 7.2 The Natural Response of an RC Circuit 220 7.3 The Step Response of RL and RC Circuits 224 7.4 A General Solution for Step and Natural

Responses 231 7.5 Sequential Switching 236 7.6 Unbounded Response 240 7.7 The Integrating Amplifier 241

Practical Perspective: Artificial Pacemaker 245 Summary 246 Problems 247

Chapter 8 Natural and Step Responses of RLC Circuits 264

Practical Perspective: Clock for Computer Timing 265

8.1 Introduction to the Natural Response of a Parallel RLC Circuit 266

8.2 The Forms of the Natural Response of a Parallel RLC Circuit 270

8.3 The Step Response of a Parallel RLC Circuit 280 8.4 The Natural and Step Response of a Series RLC

Circuit 285 8.5 A Circuit with Two Integrating Amplifiers 289

Practical Perspective: Clock for Computer Timing 293 Summary 295 Problems 296

Chapter 9 Sinusoidal Steady-State Analysis 304

Practical Perspective: A Household Distribution Circuit 305

9.1 The Sinusoidal Source 306 9.2 The Sinusoidal Response 309 9.3 The Phasor 310 9.4 The Passive Circuit Elements in the Frequency

Domain 315 9.5 Kirchhoff’s Laws in the Frequency

Domain 319 9.6 Series, Parallel, and Delta-to-Wye

Simplifications 320 9.7 Source Transformations and Thévenin-Norton

Equivalent Circuits 327 9.8 The Node-Voltage Method 330 9.9 The Mesh-Current Method 331 9.10 The Transformer 332 9.11 The Ideal Transformer 336 9.12 Phasor Diagrams 342

Practical Perspective: A Household Distribution Circuit 344 Summary 345 Problems 346

Chapter 10 Sinusoidal Steady-State Power Calculations 358

Practical Perspective: Vampire Power 359

10.1 Instantaneous Power 360 10.2 Average and Reactive Power 361 10.3 The rms Value and Power Calculations 366 10.4 Complex Power 368 10.5 Power Calculations 369 10.6 Maximum Power Transfer 376

Practical Perspective: Vampire Power 382 Summary 384 Problems 385

Chapter 11 Balanced Three-Phase Circuits 396

Practical Perspective: Transmission and Distribution of Electric Power 397

11.1 Balanced Three-Phase Voltages 398 11.2 Three-Phase Voltage Sources 399 11.3 Analysis of the Wye-Wye Circuit 400 11.4 Analysis of the Wye-Delta Circuit 405 11.5 Power Calculations in Balanced Three-Phase

Circuits 408 11.6 Measuring Average Power in Three-Phase

Circuits 413 Practical Perspective: Transmission and Distribution of Electric Power 416 Summary 417 Problems 418

Contents xi

Chapter 12 Introduction to the Laplace Transform 426

Practical Perspective: Transient Effects 427 12.1 Definition of the Laplace Transform 428 12.2 The Step Function 429 12.3 The Impulse Function 431 12.4 Functional Transforms 434 12.5 Operational Transforms 435 12.6 Applying the Laplace Transform 440 12.7 Inverse Transforms 442 12.8 Poles and Zeros of F(s) 452 12.9 Initial- and Final-Value Theorems 453

Practical Perspective: Transient Effects 456 Summary 457 Problems 458

Chapter 13 The Laplace Transform in Circuit Analysis 464

Practical Perspective: Surge Suppressors 465 13.1 Circuit Elements in the s Domain 466 13.2 Circuit Analysis in the s Domain 468 13.3 Applications 470 13.4 The Transfer Function 482 13.5 The Transfer Function in Partial Fraction

Expansions 484 13.6 The Transfer Function and the Convolution

Integral 487 13.7 The Transfer Function and the Steady-State

Sinusoidal Response 493 13.8 The Impulse Function in Circuit

Analysis 496 Practical Perspective: Surge Suppressors 503 Summary 504 Problems 505

Chapter 14 Introduction to Frequency Selective Circuits 520

Practical Perspective: Pushbutton Telephone Circuits 521

14.1 Some Preliminaries 522 14.2 Low-Pass Filters 524 14.3 High-Pass Filters 530 14.4 Bandpass Filters 534 14.5 Bandreject Filters 543

Practical Perspective: Pushbutton Telephone Circuits 548 Summary 548 Problems 549

Chapter 15 Active Filter Circuits 556 Practical Perspective: Bass Volume Control 557

15.1 First-Order Low-Pass and High-Pass Filters 558

15.2 Scaling 562 15.3 Op Amp Bandpass and Bandreject Filters 564 15.4 Higher Order Op Amp Filters 571 15.5 Narrowband Bandpass and Bandreject

Filters 584 Practical Perspective: Bass Volume Control 589 Summary 592 Problems 593

Chapter 16 Fourier Series 602 Practical Perspective: Active High-Q Filters 603

16.1 Fourier Series Analysis: An Overview 605 16.2 The Fourier Coefficients 606 16.3 The Effect of Symmetry on the Fourier

Coefficients 609 16.4 An Alternative Trigonometric Form of the

Fourier Series 615 16.5 An Application 617 16.6 Average-Power Calculations with Periodic

Functions 621 16.7 The rms Value of a Periodic Function 624 16.8 The Exponential Form of the Fourier

Series 625 16.9 Amplitude and Phase Spectra 628

Practical Perspective: Active High-Q Filters 630 Summary 632 Problems 633

Chapter 17 The Fourier Transform 642 Practical Perspective: Filtering Digital Signals 643

17.1 The Derivation of the Fourier Transform 644 17.2 The Convergence of the Fourier Integral 646 17.3 Using Laplace Transforms to Find Fourier

Transforms 648 17.4 Fourier Transforms in the Limit 651 17.5 Some Mathematical Properties 653 17.6 Operational Transforms 655 17.7 Circuit Applications 659 17.8 Parseval’s Theorem 662

Practical Perspective: Filtering Digital Signals 669 Summary 670 Problems 670

xii Contents

Chapter 18 Two-Port Circuits 676 Practical Perspective: Characterizing an Unknown Circuit 677

18.1 The Terminal Equations 678 18.2 The Two-Port Parameters 679 18.3 Analysis of the Terminated Two-Port

Circuit 687 18.4 Interconnected Two-Port Circuits 692

Practical Perspective: Characterizing an Unknown Circuit 695 Summary 696 Problems 696

Appendix A The Solution of Linear Simultaneous Equations 703

A.1 Preliminary Steps 703 A.2 Cramer’s Method 704 A.3 The Characteristic Determinant 704 A.4 The Numerator Determinant 704 A.5 The Evaluation of a Determinant 705 A.6 Matrices 707 A.7 Matrix Algebra 708 A.8 Identity, Adjoint, and Inverse Matrices 712 A.9 Partitioned Matrices 715 A.10 Applications 718

Appendix B Complex Numbers 723 B.1 Notation 723 B.2 The Graphical Representation of a Complex

Number 724 B.3 Arithmetic Operations 725 B.4 Useful Identities 726 B.5 The Integer Power of a Complex

Number 727 B.6 The Roots of a Complex Number 727

Appendix C More on Magnetically Coupled Coils and Ideal Transformers 729

C.1 Equivalent Circuits for Magnetically Coupled Coils 729

C.2 The Need for Ideal Transformers in the Equivalent Circuits 733

Appendix D The Decibel 737

Appendix E Bode Diagrams 739 E.1 Real, First-Order Poles and Zeros 739 E.2 Straight-Line Amplitude Plots 740 E.3 More Accurate Amplitude Plots 744 E.4 Straight-Line Phase Angle Plots 745 E.5 Bode Diagrams: Complex Poles and Zeros 747 E.6 Amplitude Plots 749 E.7 Correcting Straight-Line Amplitude Plots 750 E.8 Phase Angle Plots 753

Appendix F An Abbreviated Table of Trigonometric Identities 757

Appendix G An Abbreviated Table of Integrals 759

Appendix H Common Standard Component Values 761

Index 775

xiii

List of Examples Chapter 1 1.1 Using SI Units and Prefixes for Powers of 10 10 1.2 Relating Current and Charge 14 1.3 Relating Voltage, Current, Power, and Energy 16

Chapter 2 2.1 Testing Interconnections of Ideal Sources 28 2.2 Testing Interconnections of Ideal Independent

and Dependent Sources 29 2.3 Calculating Voltage, Current, and Power for a

Simple Resistive Circuit 33 2.4 Constructing a Circuit Model of a Flashlight 34 2.5 Constructing a Circuit Model Based on Terminal

Measurements 36 2.6 Using Kirchhoff’s Current Law 39 2.7 Using Kirchhoff’s Voltage Law 40 2.8 Applying Ohm’s Law and Kirchhoff’s Laws to

Find an Unknown Current 40 2.9 Constructing a Circuit Model Based on Terminal

Measurements 41 2.10 Applying Ohm’s Law and Kirchhoff’s Laws to

Find an Unknown Voltage 44 2.11 Applying Ohm’s Law and Kirchhoff’s Law in an

Amplifier Circuit 45

Chapter 3 3.1 Applying Series-Parallel Simplification 60 3.2 Analyzing the Voltage-Divider Circuit 62 3.3 Analyzing a Current-Divider Circuit 63 3.4 Using Voltage Division and Current Division to

Solve a Circuit 66 3.5 Using a d’Arsonval Ammeter 68 3.6 Using a d’Arsonval Voltmeter 68 3.7 Applying a Delta-to-Wye Transform 72

Chapter 4 4.1 Identifying Node, Branch, Mesh and Loop in a

Circuit 90 4.2 Using the Node-Voltage Method 94 4.3 Using the Node-Voltage Method with

Dependent Sources 95 4.4 Using the Mesh-Current Method 101 4.5 Using the Mesh-Current Method with

Dependent Sources 102

4.6 Understanding the Node-Voltage Method Versus Mesh-Current Method 107

4.7 Comparing the Node-Voltage and Mesh-Current Methods 108

4.8 Using Source Transformations to Solve a Circuit 110

4.9 Using Special Source Transformation Techniques 112

4.10 Finding the Thévenin Equivalent of a Circuit with a Dependent Source 116

4.11 Finding the Thévenin Equivalent Using a Test Source 118

4.12 Calculating the Condition for Maximum Power Transfer 121

4.13 Using Superposition to Solve a Circuit 124

Chapter 5 5.1 Analyzing an Op Amp Circuit 149 5.2 Designing an Inverting Amplifier 151 5.3 Designing a Noninverting Amplifier 154 5.4 Designing a Difference Amplifier 155

Chapter 6 6.1 Determining the Voltage, Given the Current,

at the Terminals of an Inductor 177 6.2 Determining the Current, Given the Voltage,

at the Terminals of an Inductor 178 6.3 Determining the Current, Voltage, Power,

and Energy for an Inductor 180 6.4 Determining Current, Voltage, Power, and

Energy for a Capacitor 184 6.5 Finding , , and Induced by a Triangular

Current Pulse for a Capacitor 185 6.6 Finding Mesh-Current Equations for a Circuit

with Magnetically Coupled Coils 192

Chapter 7 7.1 Determining the Natural Response of an

RL Circuit 218 7.2 Determining the Natural Response of an

RL Circuit with Parallel Inductors 219 7.3 Determining the Natural Response of an

RC Circuit 222 7.4 Determining the Natural Response of an

RC Circuit with Series Capacitors 223

wpv

xiv List of Examples

7.5 Determining the Step Response of an RL Circuit 227

7.6 Determining the Step Response of an RC Circuit 230

7.7 Using the General Solution Method to Find an RC Circuit’s Step Response 233

7.8 Using the General Solution Method with Zero Initial Conditions 234

7.9 Using the General Solution Method to Find an RL Circuit’s Step Response 234

7.10 Determining the Step Response of a Circuit with Magnetically Coupled Coils 235

7.11 Analyzing an RL Circuit that has Sequential Switching 237

7.12 Analyzing an RC Circuit that has Sequential Switching 239

7.13 Finding the Unbounded Response in an RC Circuit 241

7.14 Analyzing an Integrating Amplifier 243 7.15 Analyzing an Integrating Amplifier that has

Sequential Switching 243

Chapter 8 8.1 Finding the Roots of the Characteristic

Equation of a Parallel RLC Circuit 269 8.2 Finding the Overdamped Natural Response of a

Parallel RLC Circuit 272 8.3 Calculating Branch Currents in the Natural

Response of a Parallel RLC Circuit 273 8.4 Finding the Underdamped Natural Response of

a Parallel RLC Circuit 275 8.5 Finding the Critically Damped Natural

Response of a Parallel RLC Circuit 278 8.6 Finding the Overdamped Step Response of a

Parallel RLC Circuit 282 8.7 Finding the Underdamped Step Response of a

Parallel RLC Circuit 283 8.8 Finding the Critically Damped Step Response

of a Parallel RLC Circuit 283 8.9 Comparing the Three-Step Response Forms 284 8.10 Finding Step Response of a Parallel RLC Circuit

with Initial Stored Energy 284 8.11 Finding the Underdamped Natural Response of

a Series RLC Circuit 287 8.12 Finding the Underdamped Step Response of a

Series RLC Circuit 288 8.13 Analyzing Two Cascaded Integrating

Amplifiers 290 8.14 Analyzing Two Cascaded Integrating Amplifiers

with Feedback Resistors 293

Chapter 9 9.1 Finding the Characteristics of a Sinusoidal

Current 307 9.2 Finding the Characteristics of a Sinusoidal

Voltage 308 9.3 Translating a Sine Expression to a Cosine

Expression 308 9.4 Calculating the rms Value of a Triangular

Waveform 308 9.5 Adding Cosines Using Phasors 314 9.6 Combining Impedances in Series 321 9.7 Combining Impedances in Series and in

Parallel 323 9.8 Using a Delta-to-Wye Transform in the

Frequency Domain 325 9.9 Performing Source Transformations in the

Frequency Domain 327 9.10 Finding a Thévenin Equivalent in the

Frequency Domain 328 9.11 Using the Node-Voltage Method in the

Frequency Domain 330 9.12 Using the Mesh-Current Method in the

Frequency Domain 331 9.13 Analyzing a Linear Transformer in the

Frequency Domain 335 9.14 Analyzing an Ideal Transformer Circuit in the

Frequency Domain 340 9.15 Using Phasor Diagrams to Analyze a

Circuit 342 9.16 Using Phasor Diagrams to Analyze Capacitive

Chapter 10 10.1 Calculating Average and Reactive Power 364 10.2 Making Power Calculations Involving

Household Appliances 365 10.3 Determining Average Power Delivered to a

Resistor by Sinusoidal Voltage 367 10.4 Calculating Complex Power 369 10.5 Calculating Average and Reactive Power 372 10.6 Calculating Power in Parallel Loads 373 10.7 Balancing Power Delivered with Power

Absorbed in an ac Circuit 374 10.8 Determining Maximum Power Transfer without

Load Restrictions 378 10.9 Determining Maximum Power Transfer with

Load Impedance Restriction 379 10.10 Finding Maximum Power Transfer with

Impedance Angle Restrictions 380 10.11 Finding Maximum Power Transfer in a Circuit

with an Ideal Transformer 381

List of Examples xv

Chapter 11 11.1 Analyzing a Wye-Wye Circuit 403 11.2 Analyzing a Wye-Delta Circuit 406 11.3 Calculating Power in a Three-Phase Wye-Wye

Circuit 411 11.4 Calculating Power in a Three-Phase Wye-Delta

Circuit 411 11.5 Calculating Three-Phase Power with

Circuits 415

Chapter 12 12.1 Using Step Functions to Represent a Function

of Finite Duration 430

Chapter 13 13.1 Deriving the Transfer Function of a Circuit 483 13.2 Analyzing the Transfer Function

of a Circuit 485 13.3 Using the Convolution Integral to Find

an Output Signal 491 13.4 Using the Transfer Function to Find

Chapter 14 14.1 Designing a Low-Pass Filter 527 14.2 Designing a Series RC Low-Pass Filter 528 14.3 Designing a Series RL High-Pass Filter 532 14.4 Loading the Series RL High-Pass Filter 532 14.5 Designing a Bandpass Filter 538 14.6 Designing a Parallel RLC Bandpass Filter 539 14.7 Determining Effect of a Nonideal Voltage

Source on a RLC Bandpass Filter 540 14.8 Designing a Series RLC Bandreject Filter 546

Chapter 15 15.1 Designing a Low-Pass Op Amp Filter 559 15.2 Designing a High-Pass Op Amp Filter 561 15.3 Scaling a Series RLC Circuit 563 15.4 Scaling a Prototype Low-Pass Op Amp

Filter 563 15.5 Designing a Broadband Bandpass Op Amp

Filter 567 15.6 Designing a Broadband Bandreject Op Amp

Filter 570 15.7 Designing a Fourth-Order Low-Pass Op Amp

Filter 574 15.8 Calculating Butterworth Transfer

Functions 577

15.9 Designing a Fourth-Order Low-Pass Butterworth Filter 579

15.10 Determining the Order of a Butterworth Filter 582

15.11 An Alternate Approach to Determining the Order of a Butterworth Filter 582

15.12 Designing a High-Q Bandpass Filter 586 15.13 Designing a High-Q Bandreject Filter 588

Chapter 16 16.1 Finding the Fourier Series of a Triangular

Waveform with No Symmetry 607 16.2 Finding the Fourier Series of an Odd Function

with Symmetry 614 16.3 Calculating Forms of the Trigonometric Fourier

Series for Periodic Voltage 616 16.4 Calculating Average Power for a Circuit

with a Periodic Voltage Source 623 16.5 Estimating the rms Value of a Periodic

Function 625 16.6 Finding the Exponential Form of the Fourier

Series 627

Chapter 17 17.1 Using the Fourier Transform to Find

the Transient Response 660 17.2 Using the Fourier Transform to Find the

Sinusoidal Steady-State Response 661 17.3 Applying Parseval’s Theorem 664 17.4 Applying Parseval’s Theorem to an Ideal

Bandpass Filter 665 17.5 Applying Parseval’s Theorem to a Low-Pass

Filter 666

Chapter 18 18.1 Finding the z Parameters of a Two-Port

Circuit 679 18.2 Finding the a Parameters from

Measurements 681 18.3 Finding h Parameters from Measurements

and Table 18.1 684 18.4 Analyzing a Terminated Two-Port Circuit 690 18.5 Analyzing Cascaded Two-Port Circuits 694

The first edition of Electric Circuits, an introductory circuits text, was pub- lished in 1983. It included 100 worked examples and about 600 problems. It did not include a student workbook, supplements for PSpice or MultiSim, or any web support. Support for instructors was limited to a solution man- ual for the problems and enlarged copies of many text figures, suitable for making transparencies.

Much has changed in the 31 years since Electric Circuits first appeared, and during that time this text has evolved to better meet the needs of both students and their instructors. As an example, the text now includes about 150 worked examples, about 1850 problems, and extensive supplements and web content. The tenth edition is designed to revise and improve the material presented in the text, in its supplements, and on the web. Yet the fundamental goals of the text are unchanged. These goals are:

• To build an understanding of concepts and ideas explicitly in terms of previous learning. Students are constantly challenged by the need to layer new concepts on top of previous concepts they may still be struggling to master.This text provides an important focus on helping students understand how new concepts are related to and rely upon concepts previously presented.

• To emphasize the relationship between conceptual understanding and problem-solving approaches. Developing problem-solving skills continues to be the central challenge in a first-year circuits course. In this text we include numerous Examples that present problem- solving techniques followed by Assessment Problems that enable students to test their mastery of the material and techniques intro- duced. The problem-solving process we illustrate is based on con- cepts rather than the use of rote procedures. This encourages students to think about a problem before attempting to solve it.

• To provide students with a strong foundation of engineering prac- tices. There are limited opportunities in a first-year circuit analysis course to introduce students to realistic engineering experiences. We continue to take advantage of the opportunities that do exist by including problems and examples that use realistic component values and represent realizable circuits. We include many problems related to the Practical Perspective problems that begin each chapter. We also include problems intended to stimulate the students’ interest in engineering, where the problems require the type of insight typical of a practicing engineer.

WHY THIS EDITION? The tenth edition revision of Electric Circuits began with a thorough review of the text. This review provided a clear picture of what matters most to instructors and their students and led to the following changes:

• Problem solving is fundamental to the study of circuit analysis. Having a wealth of new problems to assign and work is a key to suc- cess in any circuits course. Therefore, existing end-of-chapter prob- lems were revised, and new end-of-chapter problems were added. As a result, more than 40% of the problems in the tenth edition have never appeared in any previous edition of the text.

xvii

Preface

xviii Preface

• Both students and instructors want to know how the generalized techniques presented in a first-year circuit analysis course relate to problems faced by practicing engineers. The Practical Perspective problems provide this connection between circuit analysis and the real world. We have created new Practical Perspective problems for Chapters 2, 3, 6, 7, 8, and 10. Many of the new problems represent the world of the 21st century. Each Practical Perspective problem is solved, at least in part, at the end of the chapter, and additional end- of-chapter problems can be assigned to allow students to explore the Practical Perspective topic further.

• The PSpice and Multisim manuals have been revised to include screenshots from the most recent versions of these software simula- tion applications. Each manual presents the simulation material in the same order as the material is presented in the text. These manu- als continue to include examples of circuits to be simulated that are drawn directly from the text. The text continues to indicate end-of- chapter problems that are good candidates for simulation using either PSpice or Multisim.

• Students who could benefit from additional examples and practice problems can use the Student Workbook, which has been revised to reflect changes to the tenth edition of the text. This workbook has examples and problems covering the following material: balancing power, simple resistive circuits, node voltage method, mesh current method, Thévenin and Norton equivalents, op amp circuits, first- order circuits, second-order circuits, AC steady-state analysis, and Laplace transform circuit analysis.

• The Student Workbook now includes access to Video Solutions, complete, step-by-step solution walkthroughs to representative homework problems.

• Learning Catalytics, a “bring your own device” student engagement, assessment, and classroom intelligence system is now available with the tenth edition. With Learning Catalytics you can: • Use open-ended questions to get into the minds of students to

understand what they do or don’t know and adjust lectures accordingly.

• Use a wide variety of question types to sketch a graph, annotate a circuit diagram, compose numeric or algebraic answers, and more.

• Access rich analytics to understand student performance. • Use pre-built questions or add your own to make Learning

• MasteringEngineering is an online tutorial and assessment program that provides students with personalized feedback and hints and instructors with diagnostics to track students’ progress. With the tenth edition, MasteringEngineering will offer new tutorial homework prob- lems, Coaching Activities, and Adaptive Follow-Up assignments. Visit www.masteringengineering.com for more information.

HALLMARK FEATURES Chapter Problems Users of Electric Circuits have consistently rated the Chapter Problems as one of the book’s most attractive features. In the tenth edition, there are over 1650 end-of-chapter problems with approximately 40% that have never appeared in a previous edition. Problems are organized at the end of each chapter by section.

Preface xix

Practical Perspectives The tenth edition continues the use of Practical Perspectives introduced with the chapter openers.They offer examples of real-world circuits, taken from real-world devices. The Practical Perspectives for six of the chapters are brand new to this edition. Every chapter begins with a brief descrip- tion of a practical application of the material that follows. Once the chap- ter material is presented, the chapter concludes with a quantitative analysis of the Practical Perspective application. A group of end-of-chap- ter problems directly relates to the Practical Perspective application. Solving some of these problems enables you to understand how to apply the chapter contents to the solution of a real-world problem.

Assessment Problems Each chapter begins with a set of chapter objectives. At key points in the chapter, you are asked to stop and assess your mastery of a particular objective by solving one or more assessment problems. The answers to all of the assessment problems are given at the conclusion of each problem, so you can check your work. If you are able to solve the assessment problems for a given objective, you have mastered that objective. If you need more practice, several end-of-chapter problems that relate to the objective are suggested at the conclusion of the assessment problems.

Examples Every chapter includes many examples that illustrate the concepts presented in the text in the form of a numeric example. There are nearly 150 examples in this text. The examples are intended to illus- trate the application of a particular concept, and also to encourage good problem-solving skills.

Fundamental Equations and Concepts Throughout the text, you will see fundamental equations and concepts set apart from the main text.This is done to help you focus on some of the key principles in electric circuits and to help you navigate through the important topics.

Integration of Computer Tools Computer tools can assist students in the learning process by providing a visual representation of a circuit’s behavior, validating a calculated solu- tion, reducing the computational burden of more complex circuits, and iterating toward a desired solution using parameter variation.This compu- tational support is often invaluable in the design process.The tenth edition includes the support of PSpice® and Multisim®, both popular computer tools for circuit simulation and analysis. Chapter problems suited for exploration with PSpice and Multisim are marked accordingly.

Design Emphasis The tenth edition continues to support the emphasis on the design of cir- cuits in many ways. First, many of the Practical Perspective discussions focus on the design aspects of the circuits. The accompanying Chapter Problems continue the discussion of the design issues in these practical examples. Second, design-oriented Chapter Problems have been labeled explicitly, enabling students and instructors to identify those problems with a design focus. Third, the identification of problems suited to explo- ration with PSpice or Multisim suggests design opportunities using these

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software tools. Fourth, some problems in nearly every chapter focus on the use of realistic component values in achieving a desired circuit design. Once such a problem has been analyzed, the student can proceed to a lab- oratory to build and test the circuit, comparing the analysis with the meas- ured performance of the actual circuit.

Accuracy All text and problems in the tenth edition have undergone our strict hallmark accuracy checking process, to ensure the most error-free book possible.

RESOURCES FOR STUDENTS MasteringEngineering. MasteringEngineering provides tutorial home- work problems designed to emulate the instructor’s office hour environ- ment, guiding students through engineering concepts with self-paced individualized coaching. These in-depth tutorial homework problems pro- vide students with feedback specific to their errors and optional hints that break problems down into simpler steps. Visit www.masteringengineering .com for more information.

Student Workbook. This resource teaches students techniques for solving problems presented in the text. Organized by concepts, this is a valuable problem-solving resource for all levels of students.

The Student Workbook now includes access to Video Solutions, com- plete, step-by-step solution walkthroughs to representative homework problems.

Introduction to Multisim and Introduction to PSpice Manuals—Updated for the tenth edition, these manuals are excellent resources for those wish- ing to integrate PSpice or Multisim into their classes.

Instructor Solutions Manual—Fully worked-out solutions to Assessment Problems and end-of-chapter problems.

PowerPoint lecture images—All figures from the text are available in PowerPoint for your lecture needs. An additional set of full lecture slides with embedded assessment questions are available upon request.

MasteringEngineering. This online tutorial and assessment program allows you to integrate dynamic homework with automated grading and personalized feedback. MasteringEngineering allows you to easily track the performance of your entire class on an assignment-by-assignment basis, or the detailed work of an individual student. For more information visit www.masteringengineeing.com.

Learning Catalytics—This “bring your own device” student engagement, assessment and classroom intelligence system enables you to measure student learning during class, and adjust your lectures accordingly. A wide variety of question and answer types allows you to author your own questions, or you can use questions already authored into the system. For more information visit www.learningcatalytics.com.

Preface xxi

PREREQUISITES In writing the first 12 chapters of the text, we have assumed that the reader has taken a course in elementary differential and integral calculus. We have also assumed that the reader has had an introductory physics course, at either the high school or university level, that introduces the concepts of energy, power, electric charge, electric current, electric poten- tial, and electromagnetic fields. In writing the final six chapters, we have assumed the student has had, or is enrolled in, an introductory course in differential equations.

COURSE OPTIONS The text has been designed for use in a one-semester, two-semester, or a three-quarter sequence.

Single-semester course: After covering Chapters 1–4 and Chapters 6–10 (omitting Sections 7.7 and 8.5) the instructor can choose from Chapter 5 (operational amplifiers), Chapter 11 (three-phase circuits), Chapters 13 and 14 (Laplace methods), and Chapter 18 (Two-Port Circuits) to develop the desired emphasis.

Two-semester sequence: Assuming three lectures per week, the first nine chapters can be covered during the first semester, leaving Chapters 10–18 for the second semester.

Academic quarter schedule: The book can be subdivided into three parts: Chapters 1–6, Chapters 7–12, and Chapters 13–18.

The introduction to operational amplifier circuits in Chapter 5 can be omitted without interfering with the reading of subsequent chapters. For example, if Chapter 5 is omitted, the instructor can simply skip Section 7.7, Section 8.5, Chapter 15, and those assessment problems and end-of- chapter problems in the chapters following Chapter 5 that pertain to oper- ational amplifiers.

There are several appendixes at the end of the book to help readers make effective use of their mathematical background. Appendix A reviews Cramer’s method of solving simultaneous linear equations and simple matrix algebra; complex numbers are reviewed in Appendix B;Appendix C contains additional material on magnetically coupled coils and ideal trans- formers;Appendix D contains a brief discussion of the decibel;Appendix E is dedicated to Bode diagrams; Appendix F is devoted to an abbreviated table of trigonometric identities that are useful in circuit analysis; and an abbreviated table of useful integrals is given in Appendix G. Appendix H provides tables of common standard component values for resistors, induc- tors, and capacitors, to be used in solving many end-of-chapter problems. Selected Answers provides answers to selected end-of-chapter problems.

ACKNOWLEDGMENTS There were many hard-working people behind the scenes at our pub- lisher who deserve our thanks and gratitude for their efforts on behalf of the tenth edition. At Pearson, we would like to thank Andrew Gilfillan, Rose Kernan, Gregory Dulles, Tim Galligan, and Scott Disanno for their continued support and encouragement, their professional demeanor, their willingness to lend an ear, and their months of long hours and no weekends. The authors would also like to acknowledge the staff at Integra Software Solutions for their dedication and hard work in typeset- ting this text. The authors would also like to thank Kurt Norlin for his help in accuracy checking the text and problems.

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We are very grateful for the many instructors and students who have done formal reviews of the text or offered positive feedback and suggestions for improvement more informally. We are pleased to receive email from instructors and students who use the book, even when they are pointing out an error we failed to catch in the review process. We have been contacted by people who use our text from all over the world, and we thank all of you for taking the time to do so. We use as many of your suggestions as possible to continue to improve the content, the pedagogy, and the presentation in this text. We are privi- leged to have the opportunity to impact the educational experience of the many thousands of future engineers who will use this text.

JAMES W. NILSSON SUSAN A. RIEDEL

ELECTRIC CIRCUITS TENTH EDITION

nice and usefull
Awesome, just what I needed