Fundamentals Of Electromagnetics With MATLAB

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lonngren frontmatter.fm Page i Wednesday, April 6, 2011 7:13 AMFundamentals ofElectromagneticswith MATLAB Second Edition

lonngren frontmatter.fm Page ii Wednesday, April 6, 2011 7:13 AMTo our wives: Vicki, Rossi, and Vickie

lonngren frontmatter.fm Page iii Wednesday, April 6, 2011 7:13 AMFundamentals ofElectromagneticswith MATLAB Second EditionKarl E. LonngrenDepartment of Electrical and Computer EngineeringThe University of IowaIowa City, IowaSava V. SavovDepartment of Electronic EngineeringTechnical University of VarnaVarna, BulgariaRandy J. JostSpace Dynamics LaboratoryDepartment of Electrical and Computer EngineeringDepartment of PhysicsUtah State UniversityLogan, UtahRaleigh, NCwww.scitechpub.com

lonngren frontmatter.fm Page iv Wednesday, April 6, 2011 7:13 AM 2007 by SciTech Publishing, Inc.All rights reserved. No part of this book may be reproduced or used in any form whatsoever without writtenpermission except in the case of brief quotations embodied in critical articles and reviews. For information,contact SciTech Publishing.Printed in Taiwan10 9 8 7 6 5 4 3Hardcover ISBN: 978-1-891121-58-6Paperback IBSN: 978-1-61353-000-9Publisher and Editor: Dudley R. KayProduction Director: Susan ManningProduction Assistant: Robert LawlessProduction and Design Services: AptaraCopyeditor: Deborah StirlingCover Design: Kathy GagneCover Illustration: NASAIllustration Reviewer: Michael GeorgievSciTech Publishing, Inc.911 Paverstone Drive, Suite BRaleigh, NC 27615Phone: (919) 847-2434 Fax: (919) 847-2568Email: info@scitechpub.comUpdates: www.scitechpub.com/lonngren2e.htmInformation contained in this work has been obtained from sources believed to be reliable. However, neitherSciTech Publishing nor its authors guarantee the accuracy or completeness of any information publishedherein, and neither SciTech Publishing nor its authors shall be responsible for any errors, omissions, ordamages arising out of use of this information. This work is published with the understanding that SciTechPublishing and its authors are supplying information but are not attempting to render engineering or otherprofessional services. If such services are required the assistance of an appropriate professional should besought.Library of Congress Cataloging-in-Publication DataLonngren, Karl E. (Karl Erik), 1938Fundamentals of electromagnetics with MATLAB / Karl E. Lonngren, Sava V. Savov, Randy J. Jost.p. cm.Includes bibliographical references and index.ISBN-13: 978-1-891121-58-6 (hardback : alk. paper)ISBN-10: 1-891121-58-8 (hardback : alk. paper)1. Electromagnetic theory. 2. Electric engineering. 3. MATLAB. I.Savov, Sava Vasilev. II. Jost, Randy J. III. Title.QC670.6.L56 2007537–dc222006101377

lonngren frontmatter.fm Page v Wednesday, April 6, 2011 7:13 AMvPublisher’s Note to the Second PrintingThe diligent efforts of many dedicated individuals to help eliminate errata andimprove fine points of this text bear special commendation. In barely six monthsfrom the first printing, the authors, SciTech advisors, adopting instructors, their students, and very talented teaching assistants went through every page, figure,example, equation and problem to bring subsequent students and users this remarkably clean printing. Among the improvements that will benefits students and readersare the following: Chapter One – MATLAB, Vectors, and Phasors was rewritten to provide aneven better review of vector analysis and a more detailed introduction tophasors and phasor notation. Sixteen new problems were added to Chapter Two – Electrostatic Fields All problems were checked for clarity and 100% accurate answers inAppendix G Highly detailed Solutions were derived for instructors in editable Word files Short sections were added on topics of EMF, power flow and energy deposition,and complex vectorsWe continue to encourage submission of errata and suggestions for improvements.We welcome Dr. Jonathan Bagby of Florida Atlantic University to the authorteam. Though Dr. Bagby is primarily concerned with the Optional Topics on theStudent CD that will evolve into the Intermediate Electromagnetics with MATLABtext, his strong background in Mathematics was ideal in strengthening Chapter 1 andoverseeing numerous improvements in Chapter 7’s Transmission Lines notation.Prof. Sven Bilen and his colleague Prof. Svetla Jivkova of Pennsylvania StateUniversity used their teaching experience from the text and invited student feedbackto submit numerous corrections and suggested improvements to factual and conceptual aspects of the book. In addition, their student Mickey Rhoades had a keeneye for errors that went undetected by others. Taken all together, a profound debt ofgratitude is owed to the PSU spring 2007 EM course team. Similarly, Prof. DoranBaker and Prof. Donald Cripps at Utah State gathered student feedback and submitted a summary for our reprint consideration.The accuracy checks of problems and their selected answers in Appendix G, plusthe improvements to the detailed steps in the Solutions Manual for instructors, arethe work of three talented PhD honors students: David Padgett of North CarolinaState University, Zhihong Hu of the University of Iowa, and Avinash Uppuluri of

lonngren frontmatter.fm Page vi Wednesday, April 6, 2011 7:13 AMviUtah State University. The feedback of a remarkable undergraduate student who provided avoice to the eyes and mind of the typical neophyte reader must also be acknowledged:David Ristov of South Dakota State University.We like to call our textbook and its supplements “organic” because they are continuallygrowing and being nurtured by those who are passionate about the subject and teachingundergraduates. Using book reprintings and the electronic opportunities of CDs and theinternet, our authors and contributors are dedicated to fixing flaws and adding helpfulresources whenever they present themselves. We gratefully thank all who share our dedication to the subject, the process, and the delight in learning.Dudley R. Kay – President and FounderSciTech Publishing, Inc.Raleigh, NCJuly, 2007

lonngren frontmatter.fm Page vii Wednesday, April 6, 2011 7:13 AMContentsxPrefaceChapter 1Editorial Advisory Board in ElectromagneticsxxNotation Tablexxi1.11.21.31.41.51.61.7Chapter 2Understanding Vectors Using MATLABCoordinate Systems 17Integral Relations for Vectors 29Differential Relations for Vectors 37Phasors 52Conclusion 56Problems 56461Electrostatic Fields2.12.22.32.42.52.62.72.82.92.10Chapter 33MATLAB, Vectors, and PhasorsCoulomb’s Law 61Electric Field 67Superposition Principles 69Gauss’s Law 77Potential Energy and Electric PotentialNumerical Integration 100Dielectric Materials 109Capacitance 114Conclusion 118Problems 11985123Magnetostatic Fields3.13.23.33.43.53.6Electrical Currents 123Fundamentals of Magnetic Fields 128Magnetic Vector Potential and the Biot-Savart LawMagnetic Forces 146Magnetic Materials 157Magnetic Circuits 162138vii

lonngren frontmatter.fm Page viii Wednesday, April 6, 2011 7:13 AMContentsviii3.73.83.9Chapter 44.44.54.64.74.84.94.10257Faraday’s Law of Induction 257Equation of Continuity 270Displacement Current 274Maxwell’s Equations 280Poynting’s Theorem 285Time-Harmonic Electromagnetic FieldsConclusion 293Problems 294290297Electromagnetic Wave Propagation6.16.26.36.46.56.66.7Chapter 7Boundary Conditions for Electric and Magnetic Fields 178Poisson’s and Laplace’s Equations 186Analytical Solution in One Dimension—Direct IntegrationMethod 191Numerical Solution of a One-Dimensional Equation—FiniteDifference Method 201Analytical Solution of a Two-Dimensional Equation—Separation of variables 211Finite Difference Method Using MATLAB 220Finite Element Method Using MATLAB 226Method of Moments Using MATLAB 241Conclusion 251Problems 252Time-Varying Electromagnetic Fields5.15.25.35.45.55.65.75.8Chapter 6177Boundary Value Problems Using MATLAB4.14.24.3Chapter 5Inductance 166Conclusion 171Problems 172Wave Equation 297One-Dimensional Wave Equation 302Time-Harmonic Plane Waves 318Plane Wave Propagation in a Dielectric Medium 325Reflection and Transmission of an Electromagnetic WaveConclusion 349Problems 349Transmission Lines7.17.2Equivalent Electrical Circuits 354Transmission Line Equations 357335353

lonngren frontmatter.fm Page ix Wednesday, April 6, 2011 7:13 er 8Sinusoidal Waves 362Terminations 367Impedance and Matching of a Transmission LineSmith Chart 381Transient Effects and the Bounce Diagram 390Pulse Propagation 397Lossy Transmission Lines 402Dispersion and Group Velocity 406Conclusion 414Problems 414373419Radiation of Electromagnetic Waves8.18.28.38.48.58.68.78.8Radiation Fundamentals 419Infinitesimal Electric Dipole AntennaFinite Electric Dipole Antenna 434Loop Antennas 440Antenna Parameters 443Antenna Arrays 455Conclusion 466Problems 467427Appendix AMathematical Formulas469Appendix BMaterial Parameters474Appendix CMathematical Foundation of the FiniteElement Method477Appendix DTransmission Line Parameters of Two Parallel Wires483Appendix EPlasma Evolution Adjacent to a Metallic Surface487Appendix FBibliography490Appendix GSelected Answers493Appendix HGreek Alphabet523Index524

lonngren frontmatter.fm Page x Wednesday, April 6, 2011 7:13 AMPrefaceOverviewProfessors ask, “Why another textbook (edition)?” while students ask, “Why do Ineed to study electromagnetics?” The concise answers are that today’s instructorneeds more flexible options in topic selection, and students will better understanda difficult subject in their world of microelectronics and wireless if offered theopportunity to apply their considerable computer skills to problems and applications. We see many good textbooks but none with the built-in flexibility forinstructors and computer-augmented orientation that we have found successfulwith our own students.Virtually every four-year electrical and computer engineering programrequires a course in electromagnetic fields and waves encompassing Maxwell’sequations. Understanding and appreciating the laws of Nature that govern thespeed of even the smallest computer chip or largest power line is fundamental forevery electrical and computer engineer. Practicing engineers review these principles constantly, many regretting either their inattention as undergrads or thecondensed, rushed nature of the single course. What used to be two or more termsof required study has been whittled down to one very intense term, with variationsof emphasis and order. Recently, there has been a resurgence of the two-termcourse, or at least an elective second term, that is gathering momentum as a desirable, career-enhancing option in a wireless world. Students today have grown upwith computers; they employ sophisticated simulation and calculation programsquite literally as child’s play. When one considers the difficult challenges of thisfield of study, the variation among schools and individual instructors in coursestructure and emphasis, and the diverse backgrounds and abilities of students, youhave the reason for another textbook in electromagnetics: learning by doing onthe computer, using the premier software tool available in electrical engineeringeducation today: MATLAB.x

lonngren frontmatter.fm Page xi Wednesday, April 6, 2011 7:13 AMPrefacexiTextbook and Supplements on CDActually, this is much more than a mere textbook. The book itself offers a structural framework of principles, key equations, illustrations, and problems. With that crucial supportingstructure, each instructor, student, or reader can turn to the supplemental files provided withthis book or available online to customize and decorate each topic room. The entire learningpackage is “organic” as we the authors, contributing EM instructors, and SciTech Publishing strive to bring you an array of supporting material through the CD, the Internet, and filesstored on your computer. It is very important, therefore, that you register your book andbookmark the URL that will always be available as a starting and reference point for everchanging supplementary materials: www.scitechpub.com/lonngren2e.htm.Approach Using MATLAB 1Our underlying philosophy is that you can learn and apply this subject’s difficult principlesmuch more easily, and possibly even enjoyably, using MATLAB. Numerical computationsare readily solved using MATLAB. Also, abstract theory of unobservable waves can bestrikingly visualized using MATLAB. Perhaps you are either familiar with MATLABthrough personal use or through a previous course and can immediately apply it to yourstudy of electromagnetics. However, if you are unfamiliar with MATLAB, you can learn touse it on your own very quickly. A MATLAB Tutorial is supplied on the book’s enclosedstudent CD. The extensive Lesson 0 is all you really need to establish a solid starting pointand build on it. If you do not have the CD or a computer handy, Chapter One provides abrief overview of MATLAB operations and a review of vector analysis. For more information and instruction on using MATLAB, SciTech Publishing provides a list of MATLABbooks and CDs in Appendix F, available at special discount prices to registered users of thisbook. If your book came without the CD (a used book purchase, perhaps), or even if youwant to be sure of obtaining the latest files, you can purchase an electronic license for ayear’s access to all files at the URL shown above.Within the book, MATLAB is used numerous ways. You will always be able to seewhere MATLAB is either applied or has the potential to be applied by the universal iconfurnished by MATLAB’s parent company MathWorks. Each time this icon appears, youwill know that either MATLAB’s M-files of program code are supplied on your student CDor else your instructor or TA has them, most typically on Problem solutions. Use and distribution of these solution M-files are at the discretion of individual instructors and are not,therefore, furnished to students. Non-student readers can contact the publisher for selectedsolutions and M-files if registered.1MATLAB is a registered trademark of The MathWorks, Inc. For MATLAB product information and cool user code contributions, go to www.mathworks.com, write The MathWorks, Inc., 3 Apple Hill Dr., Natick, MA 01760-2098 or call (508)647-7101.

lonngren frontmatter.fm Page xii Wednesday, April 6, 2011 7:13 AMPrefacexii Examples – Worked-out examples run throughout the text to show how a proof canbe derived or a problem solved in steps. Each is clearly marked with a heading andalso appears in a tinted blue box. When the MATLAB icon appears, it means theworked solution also has an equivalent M-file. Here is how Example sectionsappear:EXAMPLE 7.3The voltage wave that propagates along a transmission line is detected at theindicated points. From this data, write an expression for the wave. Note thatthere is a propagation of the sinusoidal signal to increasing values of thecoordinate z. Figures – Numerous figures within the text were generated using MATLAB.Not only can you obtain and manipulate the program code with its corresponding M-file, but you can also view this figure in full color from the CD. Here ishow a MATLAB-generated figure will appear: j1FIGURE 7–9 j0.5To generator0A Smith chart createdwith MATLAB. j2 j50.20.512–j5To load–j2–j0.5–j1

lonngren frontmatter.fm Page xiii Wednesday, April 6, 2011 7:13 AMPrefacexiii Problems – Each chapter contains numerous problems of varying complexity.Problem numbers correspond to the text sections so you can review any problemsthat prove difficult to handle at first pass. When an icon appears, you will know thisproblem can be solved using your MATLAB skills. Discuss with your instructor ifthe M-files will be made available for checking your work. Answers to selectedproblems are provided in Appendix G7.6.17.6.2RL7.6.3 ANIMATIONSZc1Zc2Animations – It is possible to portray electromagnetic principles in animation, alsosometimes called “movies.” Authors, instructors, and even students have contributed a number of such animations showing principles at work. However, the realfun may be in manipulating the variables to produce different results. Thus the Mfiles become a starting point for that and also an instructive demo for leading you toyour own creations. Animations at the time of this book’s printing are indicated bya “flying disk” in the margin, close to the most pertinent text discussion of theunderlying principle. You can create and submit animations to the publisher forposting and credit to you, using the submission form on the website. Also, checkback for new animations.Student CDThe Student CD enclosed with your textbook is a powerful resource. Not only does it contain files that are immediately and directly related to your course study, but it also offers awealth of supplementary and advanced material for a 2nd term of study or your personalexplorations. By registering your book, any new material produced for future CDs will beoffered to you as web downloads. Here is what the Student CD contains:MATLAB TutorialReaders will come to this book with widely varying exposures to MATLAB. A self-pacedtutorial has been included on the CD. Divided into lessons, MATLAB operations and toolsare introduced within the context of Electromagnetics extensive notation, subject areas,examples, and problems. That is, the MATLAB tutorial gets you started with basics first and

lonngren frontmatter.fm Page xiv Wednesday, April 6, 2011 7:13 AMPrefacexivthen develops text topics incrementally. You will eventually learn to perform relatively complex operations, problem-solving, and visualizations. Your instructor may later choose toassign projects involving multi-step problem-solving in MATLAB. Independent readersseeking these Projects should contact SciTech after registering the book. Also, an array ofhelpful books and tutorials about MATLAB for engineers is kept up to date on the SciTechwebsite, always at discount prices.Optional TopicsSome schools require a second term of Electromagnetics and most at least offer a secondterm as an elective Advanced Electromagnetics course. Most of today’s textbooks containsomewhat more material than can be covered in one term but not enough material for a fulland flexible second term. Therefore, a second textbook is often required for the follow-upcourse, one that is costly, probably does not match the notation of the first textbook, andmay even contradict the first book in places because of the difference in notation. Theseinconveniences are overcome with the CD’s extended topics. Optional Topics are providedin PDF files that match the two-color design of the text, integrate MATLAB throughout,and contain the same array of problems. The book and CD, therefore, satisfy the needs ofmost two-term courses and many elective second-term courses. Additional optional topicsare being added continually, as they are suggested and contributed by instructors withcourse-specific needs, such as biomedical engineering, wireless communications, materialsscience, military applications, and so forth. Contact SciTech Publishing if you wish to suggest or contribute a new topic.ApplicationsWhile brief references are made throughout the text to real-world applications of electromagnetic principles, we have chosen not to interrupt text flow with lengthy applicationdiscussions. Instead, applications are done proper justice in three–five page descriptionswith graphics, in most cases, on the CD in PDF format. These applications point the waytoward the utility of later courses in Microwave and RF, Wireless Communications,Antennas, High-speed Electronics, and many other career and research interests. Theyanswer the age-old student question: “Why do I have to know this stuff?” Instructors,their TAs, and students are encouraged to submit additional applications for inclusion inthe web-based Shareware Community.M-FilesThe Student CD contains M-files for selected examples, figures, and anim

Electromagnetics with MATLAB Second Edition Karl E. Lonngren Department of Electrical and Computer Engineering The University of Iowa Iowa City, Iowa Sava V. Savov Department of Electronic Engineering Technical University of Varna Varna, Bulgaria Randy J. Jost Space Dynamics Laborat

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