A01 HAMB6646 06 SE FM - Higher Education | Pearson€¦ · 2.6 Thévenin and Norton Equivalent ... 4.4 RC and RL Circuits with General ... “A01_HAMB6646_06_SE_FM” — 2012/9/28

“A01_HAMB6646_06_SE_FM” — 2012/9/28 — 14:36 — page i — #1

Electrical EngineeringPrinciples and Applications

©2014 Pearson Education, Inc., Upper Saddle River, NJ 07458. All Rights Reserved

“A01_HAMB6646_06_SE_FM” — 2012/9/28 — 14:36 — page ii — #2


“A01_HAMB6646_06_SE_FM” — 2012/9/28 — 14:36 — page iii — #3

Electrical EngineeringPrinciples and Applications

SIXTH EDITION

Allan R. HambleyDepartment of Electrical and Computer Engineering

Michigan Technological [email protected]

Upper Saddle River Boston Columbus San Francisco New YorkIndianapolis London Toronto Sydney Singapore Tokyo Montreal

Dubai Madrid Hong Kong Mexico City Munich Paris Amsterdam Cape Town


“A01_HAMB6646_06_SE_FM” — 2012/9/28 — 14:36 — page iv — #4

Vice President and Editorial Director, ECS: Marcia J. HortonSenior Editor: Andrew GilfillanAssociate Editor: Alice DworkinEditorial Assistant: William OpaluchVice President, Production: Vince O’BrienSenior Managing Editor: Scott DisannoProduction Editor: Pavithra Jayapaul, Jouve IndiaSenior Operations Supervisor: Alan FischerSenior Marketing Manager: Tim GalliganMarketing Assistant: Mack PattersonArt Director: Kenny BeckCover Art Director: Kristine CarneyCover Designer: Black Horse DesignsCover Image: Tom Mareschal/Stone/Getty Images, Inc.Art Editor: Greg DullesMedia Editor: Daniel SandinMedia Project Manager: Danielle LeoneComposition/Full-Service Project Management: Jouve India

LabVIEW and NI Multisim are trademarks of National Instruments. MATLAB is a registered trademarkof The MathWorks. Mylar is a registered trademark of DuPont Teijin Films. OrCAD and PSpice areregistered trademarks of Cadence Design Systems.

Copyright © 2011, 2008, 2005, 2002, 1997 by Pearson Education, Inc., Upper Saddle River, New Jersey07458. All rights reserved. Manufactured in the United States of America. This publication is protected byCopyright and permissions 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, pho-tocopying, recording, or likewise. To obtain permission(s) to use materials from this work, please submita written request to Pearson Higher Education, Permissions Department, 1 Lake Street, Upper SaddleRiver, NJ 07458.

The author and publisher of this book have used their best efforts in preparing this book. These effortsinclude the development, research, and testing of the theories and programs to determine their effective-ness. The author and publisher make no warranty of any kind, expressed or implied, with regard to theseprograms or the documentation contained in this book. The author and publisher shall not be liable inany event for incidental or consequential damages in connection with, or arising out of, the furnishing,performance, or use of these programs.

CIP data is on file and available upon request.

10 9 8 7 6 5 4 3 2 1

ISBN-13: 978-0-13-311664-9ISBN-10: 0-13-311664-6


“A01_HAMB6646_06_SE_FM” — 2012/9/28 — 14:36 — page v — #5

To Judy, Tony, Pam, and Mason


“A01_HAMB6646_06_SE_FM” — 2012/9/28 — 14:36 — page vi — #6

Practical Applicationsof Electrical Engineering Principles

1.1Using Resistance to Measure Strain 29

2.1An Important Engineering Problem: Energy-Storage Systems for Electric Vehicles 100

3.1Electronic Photo Flash 145

4.1Electronics and the Art of Automotive Maintenance 190

6.1Active Noise Cancellation 287

7.1Biomedical Engineering Application of Electronics: Cardiac Pacemaker 385

8.1Fresh Bread Anyone? 408

9.1The Virtual First-Down Line 444

11.1Electronic Stud Finder 549

12.1Where Did Those Trout Go? 593

13.1Soup Up Your Automobile by Changing Its Software? 618

14.1Mechanical Application of Negative Feedback: Power Steering 666

16.1Magnetic Flowmeters, Faraday, and The Hunt for Red October 768

vi ©2014 Pearson Education, Inc., Upper Saddle River, NJ 07458. All Rights Reserved

“A01_HAMB6646_06_SE_FM” — 2012/9/25 — 17:49 — page vii — #1

Contents

Practical Applications ofElectrical Engineering Principles vi

Preface xi

1Introduction 1

1.1 Overview of Electrical Engineering 21.2 Circuits, Currents, and Voltages 61.3 Power and Energy 131.4 Kirchhoff’s Current Law 161.5 Kirchhoff’s Voltage Law 191.6 Introduction to Circuit Elements 221.7 Introduction to Circuits 30

Summary 34Problems 35

2Resistive Circuits 46

2.1 Resistances in Series and Parallel 472.2 Network Analysis by Using Series

and Parallel Equivalents 512.3 Voltage-Divider and Current-Divider

Circuits 552.4 Node-Voltage Analysis 602.5 Mesh-Current Analysis 792.6 Thévenin and Norton Equivalent

Circuits 882.7 Superposition Principle 1012.8 Wheatstone Bridge 104


3Inductance and Capacitance 124

3.1 Capacitance 1253.2 Capacitances in Series and Parallel 132

3.3 Physical Characteristics ofCapacitors 134

3.4 Inductance 1383.5 Inductances in Series

and Parallel 1433.6 Practical Inductors 1443.7 Mutual Inductance 1473.8 Symbolic Integration and

Differentiation Using MATLAB 148Summary 152Problems 153

4Transients 162

4.1 First-Order RC Circuits 1634.2 DC Steady State 1674.3 RL Circuits 1694.4 RC and RL Circuits with General

Sources 1734.5 Second-Order Circuits 1794.6 Transient Analysis Using the MATLAB

Symbolic Toolbox 192Summary 197Problems 198

5Steady-State Sinusoidal Analysis 209

5.1 Sinusoidal Currents and Voltages 2105.2 Phasors 2165.3 Complex Impedances 2225.4 Circuit Analysis with Phasors and

Complex Impedances 2255.5 Power in AC Circuits 2315.6 Thévenin and Norton Equivalent

Circuits 2445.7 Balanced Three-Phase Circuits 249

vii©2014 Pearson Education, Inc., Upper Saddle River, NJ 07458. All Rights Reserved

“A01_HAMB6646_06_SE_FM” — 2012/9/25 — 17:49 — page viii — #2

viii Contents

5.8 AC Analysis Using MATLAB 261Summary 265Problems 266

6Frequency Response, Bode Plots,and Resonance 278

6.1 Fourier Analysis, Filters, and TransferFunctions 279

6.2 First-Order Lowpass Filters 2876.3 Decibels, the Cascade Connection,

and Logarithmic Frequency Scales 2926.4 Bode Plots 2966.5 First-Order Highpass Filters 2996.6 Series Resonance 3036.7 Parallel Resonance 3086.8 Ideal and Second-Order Filters 3116.9 Transfer Functions and Bode Plots

with MATLAB 3176.10 Digital Signal Processing 322


7Logic Circuits 347

7.1 Basic Logic Circuit Concepts 3487.2 Representation of Numerical Data

in Binary Form 3517.3 Combinatorial Logic Circuits 3597.4 Synthesis of Logic Circuits 3667.5 Minimization of Logic Circuits 3737.6 Sequential Logic Circuits 377


8Computers and Microcontrollers 400

8.1 Computer Organization 4018.2 Memory Types 4048.3 Digital Process Control 4068.4 Programming Model for the HCS12/9S12

Family 4098.5 The Instruction Set and Addressing

Modes for the CPU12 4138.6 Assembly-Language Programming 422


9Computer-Based Instrumentation Systems 433

9.1 Measurement Conceptsand Sensors 434

9.2 Signal Conditioning 4399.3 Analog-to-Digital Conversion 4469.4 LabVIEW 449


10Diodes 467

10.1 Basic Diode Concepts 46810.2 Load-Line Analysis of Diode

Circuits 47110.3 Zener-Diode Voltage-Regulator

Circuits 47410.4 Ideal-Diode Model 47810.5 Piecewise-Linear Diode Models 48010.6 Rectifier Circuits 48310.7 Wave-Shaping Circuits 48810.8 Linear Small-Signal Equivalent

Circuits 493Summary 499Problems 499

11Amplifiers: Specifications and ExternalCharacteristics 511

11.1 Basic Amplifier Concepts 51211.2 Cascaded Amplifiers 51711.3 Power Supplies and Efficiency 52011.4 Additional Amplifier Models 52311.5 Importance of Amplifier Impedances

in Various Applications 52611.6 Ideal Amplifiers 52911.7 Frequency Response 53011.8 Linear Waveform Distortion 53511.9 Pulse Response 539

11.10 Transfer Characteristic and NonlinearDistortion 542

11.11 Differential Amplifiers 54411.12 Offset Voltage, Bias Current,

and Offset Current 548Summary 553Problems 554


“A01_HAMB6646_06_SE_FM” — 2012/9/25 — 17:49 — page ix — #3

Contents ix

12Field-Effect Transistors 566

12.1 NMOS and PMOS Transistors 56712.2 Load-Line Analysis of a Simple NMOS

Amplifier 57412.3 Bias Circuits 57712.4 Small-Signal Equivalent Circuits 58012.5 Common-Source Amplifiers 58512.6 Source Followers 58812.7 CMOS Logic Gates 593


13Bipolar Junction Transistors 607

13.1 Current and Voltage Relationships 60813.2 Common-Emitter Characteristics 61113.3 Load-Line Analysis of a

Common-Emitter Amplifier 61213.4 pnp Bipolar Junction Transistors 61813.5 Large-Signal DC Circuit Models 62013.6 Large-Signal DC Analysis of BJT

Circuits 62313.7 Small-Signal Equivalent Circuits 63013.8 Common-Emitter Amplifiers 63313.9 Emitter Followers 638


14Operational Amplifiers 655

14.1 Ideal Operational Amplifiers 65614.2 Inverting Amplifiers 65714.3 Noninverting Amplifiers 66414.4 Design of Simple Amplifiers 66714.5 Op-Amp Imperfections in the Linear

Range of Operation 67214.6 Nonlinear Limitations 67614.7 DC Imperfections 68114.8 Differential and Instrumentation

Amplifiers 68514.9 Integrators and Differentiators 687

14.10 Active Filters 690Summary 694Problems 695

15Magnetic Circuits andTransformers 708

15.1 Magnetic Fields 70915.2 Magnetic Circuits 71815.3 Inductance and Mutual Inductance 72315.4 Magnetic Materials 72715.5 Ideal Transformers 73115.6 Real Transformers 738


16DC Machines 754

16.1 Overview of Motors 75516.2 Principles of DC Machines 76416.3 Rotating DC Machines 76916.4 Shunt-Connected and Separately Excited

DC Motors 77516.5 Series-Connected DC Motors 78016.6 Speed Control of DC Motors 78416.7 DC Generators 788


17AC Machines 803

17.1 Three-Phase Induction Motors 80417.2 Equivalent-Circuit and Performance

Calculations for InductionMotors 812

17.3 Synchronous Machines 82117.4 Single-Phase Motors 83317.5 Stepper Motors and Brushless

DC Motors 836Summary 838Problems 839

APPENDICES

AComplex Numbers 845



“A01_HAMB6646_06_SE_FM” — 2012/9/25 — 17:49 — page x — #4

x Contents

BNominal Values and the Color Code forResistors 854

CThe Fundamentals of EngineeringExamination 856

DAnswers for the Practice Tests 860

EOn-Line Student Resources 868

Index 000


“A01_HAMB6646_06_SE_FM” — 2012/9/28 — 14:36 — page xi — #7

Preface

As in the previous editions, my guiding philosophy in writing this book has threeelements. The first element is my belief that in the long run students are best servedby learning basic concepts in a general setting. Second, I believe that students need tobe motivated by seeing how the principles apply to specific and interesting problemsin their own fields. The third element of my philosophy is to take every opportunityto make learning free of frustration for the student.

This book covers circuit analysis, digital systems, electronics, and electromechan-ics at a level appropriate for either electrical-engineering students in an introductorycourse or nonmajors in a survey course. The only essential prerequisites are basicphysics and single-variable calculus. Teaching a course using this book offers opportu-nities to develop theoretical and experimental skills and experiences in the followingareas:

Basic circuit analysis and measurementFirst- and second-order transientsSteady-state ac circuitsResonance and frequency responseDigital logic circuitsMicrocontrollersComputer-based instrumentation, including LabVIEWDiode circuitsElectronic amplifiersField-effect and bipolar junction transistorsOperational amplifiersTransformersAc and dc machinesComputer-aided circuit analysis using MATLAB

While the emphasis of this book is on basic concepts, a key feature is the inclusionof short articles scattered throughout showing how electrical-engineering conceptsare applied in other fields. The subjects of these articles include anti-knock signalprocessing for internal combustion engines, a cardiac pacemaker, active noise control,and the use of RFID tags in fisheries research, among others.

I welcome comments from users of this book. Information on how the book couldbe improved is especially valuable and will be taken to heart in future revisions. Mye-mail address is [email protected]

xi©2014 Pearson Education, Inc., Upper Saddle River, NJ 07458. All Rights Reserved

“A01_HAMB6646_06_SE_FM” — 2012/9/28 — 14:36 — page xii — #8

xii Preface

ON-LINE STUDENT RESOURCES

The Companion Website contains an abundance of additional resources for students.The site is located at

www.pearsonhighered.com/hambley

An access code is included with the purchase of every new book or can be purchasedseparately at the website. These resources include:

Pearson eText, which is a complete on-line version of the book that includeshighlighting, note-taking, and search capabilities.Video Solutions that provide complete, step-by-step solution walkthroughs ofrepresentative homework problems from each chapter.A Student Solutions Manual. A PDF file for each chapter includes full solutionsfor the in-chapter exercises, answers for the end-of-chapter problems that aremarked with asterisks, and full solutions for the Practice Tests.A MATLAB folder that contains the m-files discussed in the book.A Multisim folder that contains tutorials on the basic features of Multisim andcircuit simulations for a wide variety of circuits from the book.A Virtual Instruments folder, which contains the LabVIEW programs discussedin Section 9.4.

INSTRUCTOR RESOURCES

Resources for instructors include:

A complete Instructor’s Solutions ManualPowerPoint Lecture slides with all the figures from the book

Instructor Resources are available for download by adopters of this book at thePearson Higher Education website: www.pearsonhighered.com. If you are in needof a login and password, please contact your local Pearson representative.

WHAT’S NEW IN THIS EDITION

We have continued the popular Practice Tests that students can use in preparingfor course exams at the end of each chapter. Answers for the Practice Testsappear inAppendix D and complete solutions are included in the on-line StudentSolutions Manual files.We have updated the coverage of MATLAB and the Symbolic Toolbox fornetwork analysis in Chapters 2 through 6.Approximately 200 problems are new to this edition, replacing some of theproblems from the previous edition, and many other problems have beenmodified.In Chapter 2, we have added an explanation of how the Wheatstone bridge isused in strain measurements.Sections 3.8 and 4.6 have been updated, deleting the coverage of piecewise linearfunctions which are problematic with recent versions of the Symbolic Toolbox.


“A01_HAMB6646_06_SE_FM” — 2012/9/28 — 14:36 — page xiii — #9

Preface xiii

Practical Application 5.1 on the LORAN system has been deleted.Chapter 8 has been extensively updated and now uses the Freescale Semi-conductor HCS12/9S12 family as an example of microcontrollers.Section 9.4 has been updated to the most recent version of LabVIEWRelatively minor corrections and improvements appear throughout the book.

PREREQUISITES

The essential prerequisites for a course from this book are basic physics and single-variable calculus. A prior differential equations course would be helpful but is notessential. Differential equations are encountered in Chapter 4 on transient analysis,but the skills needed are developed from basic calculus.

PEDAGOGICAL FEATURES

The book includes various pedagogical features designed with the goal of stimulat-ing student interest, eliminating frustration, and engendering an awareness of therelevance of the material to their chosen profession. These features are:

Statements of learning objectives open each chapter.Comments in the margins emphasize and summarize important points or indicatecommon pitfalls that students need to avoid.Short boxed articles demonstrate how electrical-engineering principles areapplied in other fields of engineering. For example, see the articles on activenoise cancellation (page 287) and electronic pacemakers (starting on page 385).Step-by-step problem solving procedures. For example, see the step-by-step sum-mary of node-voltage analysis (on pages 76–77) or the summary of Théveninequivalents (on page 95).A Practice Test at the end of each chapter gives students a chance to test theirknowledge. Answers appear in Appendix D.Complete solutions to the in-chapter exercises and Practice Tests, included asPDF files on-line, build student confidence and indicate where additional studyis needed.Summaries of important points at the end of each chapter provide references forstudents.Key equations are highlighted in the book to draw attention to important results.

MEETING ABET-DIRECTED OUTCOMES

Courses based on this book provide excellent opportunities to meet many of thedirected outcomes for accreditation. The Criteria for Accrediting Engineering Pro-grams require that graduates of accredited programs have “an ability to applyknowledge of mathematics, science, and engineering” and “an ability to identify,formulate, and solve engineering problems.” This book, in its entirety, is aimed atdeveloping these abilities.


“A01_HAMB6646_06_SE_FM” — 2012/9/28 — 14:36 — page xiv — #10

xiv Preface

Also, graduates must have “an ability to design and conduct experiments, as wellas analyze and interpret data.” Chapter 9, Computer-Based Instrumentation Systems,helps to develop this ability. If the course includes a laboratory, this ability can bedeveloped even further.

Furthermore, the criteria require “an ability to function on multi-disciplinaryteams” and “an ability to communicate effectively.” Courses based on this bookcontribute to these abilities by giving nonmajors the knowledge and vocabu-lary to communicate effectively with electrical engineers. The book also helps toinform electrical engineers about applications in other fields of engineering. Toaid in communication skills, end-of-chapter problems that ask students to explainelectrical-engineering concepts in their own words are included.

CONTENT AND ORGANIZATION

Basic Circuit Analysis

Chapter 1 defines current, voltage, power, and energy. Kirchhoff’s laws areintroduced. Voltage sources, current sources, and resistance are defined.

Chapter 2 treats resistive circuits. Analysis by network reduction, node volt-ages, and mesh currents is covered. Thévenin equivalents, superposition, and theWheatstone bridge are treated.

Capacitance, inductance, and mutual inductance are treated in Chapter 3.Transients in electrical circuits are discussed in Chapter 4. First-order RL and

RC circuits and time constants are covered, followed by a discussion of second-ordercircuits.

Chapter 5 considers sinusoidal steady-state circuit behavior. (A review of com-plex arithmetic is included in Appendix A.) Power calculations, ac Thévenin andNorton equivalents, and balanced three-phase circuits are treated.

Chapter 6 covers frequency response, Bode plots, resonance, filters, and digitalsignal processing. The basic concept of Fourier theory (that signals are composedof sinusoidal components having various amplitudes, phases, and frequencies) isqualitatively discussed.

Digital Systems

Chapter 7 introduces logic gates and the representation of numerical data in binaryform. It then proceeds to discuss combinatorial and sequential logic. Boolean algebra,De Morgan’s laws, truth tables, Karnaugh maps, coders, decoders, flip-flops, andregisters are discussed.

Chapter 8 treats microcomputers with emphasis on embedded systems using theFreescale Semiconductor HCS12/9S12 as the primary example. Computer organiza-tion and memory types are discussed. Digital process control using microcontrollersis described in general terms. Finally, selected instructions and addressing modes forthe CPU12 are described. Assembly language programming is treated very briefly.

Chapter 9 discusses computer-based instrumentation systems including mea-surement concepts, sensors, signal conditioning, and analog-to-digital conversion.The chapter ends with a discussion of LabVIEW, including an example virtualinstrument that students can duplicate using an evaluation version on their owncomputers.


“A01_HAMB6646_06_SE_FM” — 2012/9/28 — 14:36 — page xv — #11

Preface xv

Electronic Devices and Circuits

Chapter 10 presents the diode, its various models, load-line analysis, and diodecircuits, such as rectifiers, Zener-diode regulators, and wave shapers.

In Chapter 11, the specifications and imperfections of amplifiers that need tobe considered in applications are discussed from a users perspective. These includegain, input impedance, output impedance, loading effects, frequency response, pulseresponse, nonlinear distortion, common-mode rejection, and dc offsets.

Chapter 12 covers the MOS field-effect transistor, its characteristic curves, load-line analysis, large-signal and small-signal models, bias circuits, the common-sourceamplifier, and the source follower.

Chapter 13 gives a similar treatment for bipolar transistors. If desired, the orderof Chapters 12 and 13 can be reversed. Another possibility is to skip most of bothchapters so more time can be devoted to other topics.

Chapter 14 treats the operational amplifier and many of its applications. Non-majors can learn enough from this chapter to design and use op-amp circuits forinstrumentation applications in their own fields.

Electromechanics

Chapter 15 reviews basic magnetic field theory, analyzes magnetic circuits, andpresents transformers.

DC machines and ac machines are treated in Chapters 16 and 17, respectively.The emphasis is on motors rather than generators because the nonelectrical engineerapplies motors much more often than generators. In Chapter 16, an overall view ofmotors in general is presented before considering DC machines, their equivalentcircuits, and performance calculations. The universal motor and its applications arediscussed.

Chapter 17 deals with AC motors, starting with the three-phase induction motor.Synchronous motors and their advantages with respect to power-factor correction areanalyzed. Small motors including single-phase induction motors are also discussed.A section on stepper motors and brushless dc motors ends the chapter.

ACKNOWLEDGMENTS

I wish to thank my colleagues, past and present, in the Electrical and ComputerEngineering Department at Michigan Technological University, all of whom havegiven me help and encouragement at one time or another in writing this book and inmy other projects.

I have received much excellent advice from professors at other institutionswho reviewed the manuscript in various stages. This advice has improved the finalresult a great deal, and I am grateful for their help.

The reviewers for this edition are:

William Best, Lehigh UniversitySteven Bibyk, Ohio State UniversityKaren Butler-Purry, Texas A&M UniversityWalter Green, University of TennesseeJasmine Henry, University of Western AustraliaIan Hutchinson, MIT


“A01_HAMB6646_06_SE_FM” — 2012/9/28 — 14:36 — page xvi — #12

xvi Preface

David Klemer, University of Wisconsin, MilwaukeeSelahattin Sayil, Lamar UniversityJohn Tyler, Texas A&M UniversitySubbaraya Yuvarajan, North Dakota State University

The reviewers for earlier editions were:

Ibrahim Abdel-Motaled, Northwestern UniversityD. B. Brumm, Michigan Technological UniversityRobert Collin, Case Western UniversityJoseph A. Coppola, Syracuse UniversityNorman R. Cox, University of Missouri at RollaW.T. Easter, North Carolina State UniversityZoran Gajic, Rutgers UniversityEdwin L. Gerber, Drexel UniversityVictor Gerez, Montana State UniversityElmer Grubbs, New Mexico Highlands UniversityRichard S. Marleau, University of WisconsinSunanda Mitra, Texas Tech UniversityPhil Noe, Texas A&M UniversityEdgar A. O’Hair, Texas Tech UniversityJohn Pavlat, Iowa State UniversityClifford Pollock, Cornell UniversityMichael Reed, Carnegie Mellon UniversityGerald F. Reid, Virginia Polytechnic InstituteWilliam Sayle II, Georgia Institute of TechnologyLen Trombetta, University of HoustonBelinda B. Wang, University of TorontoCarl Wells, Washington State UniversityEdward Yang, Columbia UniversityRodger E. Ziemer, University of Colorado, Colorado Springs

I also thank Professor Al Wicks of Virginia Tech who reviewed the manuscriptfor the second edition and supplied excellent suggestions for improvement.

Over the years,many students and faculty using my books at MichiganTechnolog-ical University and elsewhere have made many excellent suggestions for improvingthe books and correcting errors. I thank them very much.

I am indebted toAndrew Gilfillan and Tom Robbins, my present and past editorsat Pearson, for keeping me pointed in the right direction and for many excellentsuggestions that have improved my books a great deal. A very special thank you,also, to Scott Disanno for a great job of managing the production of this and pasteditions of this book.

Thanks are extended to National Instruments which provided many excellentsuggestions. Thanks are also extended to Pavithra Jayapaul of Jouve India for herexcellent work on this edition.

Also, I want to thank Tony and Pam for their continuing encouragement andvaluable insights. I thank Judy for many good things much too extensive to list.

ALLAN R. HAMBLEY


Documents

A01 HAMB6646 06 SE FM - Higher Education | Pearson€¦ · 2.6 Thévenin and Norton Equivalent ... 4.4 RC and RL Circuits with General ... “A01_HAMB6646_06_SE_FM” — 2012/9/28