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Fundamentals of Electromagnetics for Electrical and Computer Engineering

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Fundamentals of Electromagnetics for Electrical and Computer Engineering Rao Fundamentals of for Electrical and Computer Engineering Fundamentals of Electromagnetics Electromagnetics for Fundamentals of Electrical and Electromagnetics for Computer Engineering Nannapaneni Narayana Rao Electrical and This compact, one-semester textbook introduces the fundamental concepts of electromagnetics for the technologies of electrical and computer engineering. It combines the approach of beginning Computer Engineering with Maxwell’s equations for time-varying fields with the treatment of the different categories of fields as solutions to Maxwell’s equations and uses the thread of statics-quasistatics-waves to bring out the frequency behavior of physical structures. The text develops the bulk of the material through the use of the Cartesian coordinate system to Nannapaneni Narayana Rao keep the geometry simple and compassionate, yet sufficient to learn the physical concepts and mathematical tools, while employing other coordinate systems where necessary. HIGHLIGHTS INCLUDE: • A unique introduction of Maxwell’s equations for time-varying fields collectively, first in integral form and then in differential form • Introduction of uniform plane wave propagation in free space following Maxwell’s equations, and then introducing materials by considering their interaction with uniform plane wave fields • Development of the transmission line and the distributed circuit concept following from the dis- cussion of the frequency behavior of physical structures • Coverage of the essentials of transmission line analysis in one chapter both in frequency domain, including Smith Chart, and in time domain • A chapter on waveguide principles for both metallic waveguides and dielectric waveguides • Coverage of antenna basics, beginning with obtaining complete solution to the Hertzian dipole fields through a successive extension of the quasistatic fields • A chapter on supplementary topics for optional coverage ISBN-13: 978-0-13-601333-4 ISBN-10: 0-13-601333-3 90000 Upper Saddle River, NJ 07458 ILLINOIS ECE SERIES www.prenhall.com 9 780136 013334 A01_RAO3333_1_SE_FM.QXD 4/15/08 10:37 AM Page i Fundamentals of Electromagnetics for Electrical and Computer Engineering Nannapaneni Narayana Rao Edward C. Jordan Professor Emeritus of Electrical and Computer Engineering University of Illinois at Urbana–Champaign, USA Distinguished Amrita Professor of Engineering Amrita Vishwa Vidyapeetham (Amrita University), India Previously published by Pearson Education, Inc. A01_RAO3333_1_SE_FM.QXD 4/9/08 12:28 PM Page ii Library of Congress Cataloging-in-Publication Data Narayana Rao, Nannapaneni. Fundamentals of electromagnetics for electrical and computer engineering / Nannapaneni Narayana Rao. p. cm. Includes index. ISBN 0-13-601333-3 1. Electromagnetic theory. 2. Electric engineering. 3. Computer engineering. I. Title. QC670.N32 2004 621.3—dc22 About the Front Cover Image: Figure 7.14 (right), application of Smith Chart in transmission-line analysis, and its mirror image (left), inside the circles of Figure 9.5(c), the field intensity radiation pattern of the Hertzian dipole antenna, superimposed on a historic depiction of the two hemispheres of the globe, reflecting the spirit of the dedication. © 2018 Nannapaneni Narayana Rao Pearson Education, Inc. has transferred the rights of this 2009 edition to the author in December 2017. The author has decided to make the book available on the web free of charge to the teachers, students, and others all over the world for the purpose of teaching and learning the fundamentals of electromagnetics. Any use involving monetary transaction violates the spirit of this decision. There is a Subhashitam (Worthy Saying) in Sanskrit, which says: Annadaanam param daanam Vidyadaanam atahparam Annena kshanikam triptih yaavajjiivamcha vidyayaa. The gift of food is a great gift Greater still is the gift of knowledge While food provides a momentary contentment, knowledge provides a lasting fulfillment. This “webook (web + book)” constitutes the gift, by the author and his department, of the knowledge of the subject of electromagnetics, based on Maxwell’s equations, which “today underpin all modern information and communication technologies.” 10987654321 ISBN 10: 0-13-601333-3 ISBN 13: 978-0-13-601333-4 A01_RAO3333_1_SE_FM.QXD 4/9/08 12:28 PM Page iii “Fill your heart with love and express it in everything you do.” —Amma Mata Amritanandamayi Devi, Chancellor, Amrita Vishwa Vidyapeetham To students all over the world, I offer to you this book on Electromagnetics, the “Mother of Electrical and Computer Engineering,” with the spirit of the above message from Amma, the “Mother of Compassion!” A01_RAO3333_1_SE_FM.QXD 4/9/08 12:28 PM Page iv A01_RAO3333_1_SE_FM.QXD 4/9/08 12:28 PM Page v Contents Preface ix About the Author xiii Gratitude and “Grattitude” xv CHAPTER 1 Vectors and Fields 1 1.1 Vector Algebra 1 1.2 Cartesian Coordinate System 9 1.3 Scalar and Vector Fields 13 1.4 Sinusoidally Time-Varying Fields 16 1.5 The Electric Field 21 1.6 The Magnetic Field 27 Summary 31 Review Questions 33 Problems 35 CHAPTER 2 Maxwell’s Equations in Integral Form 38 2.1 The Line Integral 38 2.2 The Surface Integral 43 2.3 Faraday’s Law 49 2.4 Ampere’s Circuital Law 54 2.5 Gauss’ Law for the Electric Field 59 2.6 Gauss’ Law for the Magnetic Field 63 Summary 64 Review Questions 66 Problems 68 v A01_RAO3333_1_SE_FM.QXD 4/9/08 12:28 PM Page vi vi Contents CHAPTER 3 Maxwell’s Equations in Differential Form 71 3.1 Faraday’s Law 71 3.2 Ampere’s Circuital Law 78 3.3 Curl and Stokes’ Theorem 82 3.4 Gauss’ Law for the Electric Field 88 3.5 Gauss’ Law for the Magnetic Field 92 3.6 Divergence and the Divergence Theorem 93 Summary 98 Review Questions 102 Problems 103 CHAPTER 4 Wave Propagation in Free Space 106 4.1 The Infinite Plane Current Sheet 106 4.2 Magnetic Field Adjacent to the Current Sheet 108 4.3 Successive Solution of Maxwell’s Equations 111 4.4 Solution by Wave Equation 115 4.5 Uniform Plane Waves 118 4.6 Poynting Vector and Energy Storage 129 Summary 133 Review Questions 135 Problems 137 CHAPTER 5 Wave Propagation in Material Media 141 5.1 Conductors and Dielectrics 141 5.2 Magnetic Materials 149 5.3 Wave Equation and Solution 154 5.4 Uniform Plane Waves in Dielectrics and Conductors 161 5.5 Boundary Conditions 166 5.6 Reflection and Transmission of Uniform Plane Waves 173 Summary 177 Review Questions 180 Problems 181 CHAPTER 6 Statics, Quasistatics, and Transmission Lines 186 6.1 Gradient and Electric Potential 186 6.2 Poisson’s and Laplace’s Equations 192 6.3 Static Fields and Circuit Elements 197 6.4 Low-Frequency Behavior via Quasistatics 205 6.5 The Distributed Circuit Concept and the Parallel-Plate Transmission Line 211 6.6 Transmission Line with an Arbitrary Cross Section 217 A01_RAO3333_1_SE_FM.QXD 4/9/08 12:28 PM Page vii Contents vii Summary 223 Review Questions 226 Problems 228 CHAPTER 7 Transmission-Line Analysis 232 A. Frequency Domain 232 7.1 Short-Circuited Line and Frequency Behavior 234 7.2 Transmission-Line Discontinuity 241 7.3 The Smith Chart 246 B. Time Domain 254 7.4 Line Terminated by Resistive Load 256 7.5 Lines with Initial Conditions 266 7.6 Interconnections between Logic Gates 272 Summary 278 Review Questions 282 Problems 283 CHAPTER 8 Waveguide Principles 290 8.1 Uniform Plane Wave Propagation in an Arbitrary Direction 290 8.2 Transverse Electric Waves in a Parallel-Plate Waveguide 298 8.3 Dispersion and Group Velocity 304 8.4 Rectangular Waveguide and Cavity Resonator 310 8.5 Reflection and Refraction of Plane Waves 316 8.6 Dielectric Slab Guide 325 Summary 331 Review Questions 334 Problems 335 CHAPTER 9 Antenna Basics 339 9.1 Hertzian Dipole 339 9.2 Radiation Resistance and Directivity 347 9.3 Half-Wave Dipole 353 9.4 Antenna Arrays 357 9.5 Image Antennas 361 9.6 Receiving Properties 363 Summary 368 Review Questions 370 Problems 371 CHAPTER 10 Supplementary Topics 375 10.1 Wave Propagation in Ionized Medium 375 10.2 Wave Propagation in Anisotropic Medium 380 A01_RAO3333_1_SE_FM.QXD 4/9/08 12:28 PM Page viii viii Contents 10.3 Electromagnetic Compatibility and Shielding 387 10.4 Crosstalk on Transmission Lines 395 10.5 Parallel-Plate Waveguide Discontinuity 403 10.6 Magnetic Vector Potential and the Loop Antenna 406 APPENDICES A. Cylindrical and Spherical Coordinate Systems 413 B. Curl,Divergence,and Gradient in Cylindrical and Spherical Coordinate Systems 420 C. Units and Dimensions 427 Suggested Collateral and Further Reading 432 Answers to Odd-Numbered Problems 433 Index 443 A01_RAO3333_1_SE_FM.QXD 4/9/08 12:28 PM Page ix Preface “. I am talking about the areas of science and learning that have been at the heart of what we know and what we do, that which has supported and guided us and which is fundamental to our thinking. It is electromagnetism in all its many forms that has been so basic, that haunts us and guides us. .” —Nick Holonyak, Jr., the John Bardeen Endowed Chair Professor of Electrical and Computer Engineering and Physics at the University of Illinois at Urbana–Champaign, and the inventor of the semiconductor visible LED, laser, and quantum-well laser “The electromagnetic theory, as we know it, is surely one of the supreme accomplish- ments of the human intellect, reason enough to study it. But its usefulness in science and engineering makes it an indispensable tool in virtually any area of technology or physical research.” —George W. Swenson, Jr., Professor Emeritus of Electrical and Computer Engineering, University of Illinois at Urbana–Champaign The above quotes from two of my distinguished colleagues at the University of Illinois underscore the fact that electromagnetics is all around us. In simple terms, every time we turn on a switch for electrical power or for electronic equipment, every time we press a key on our computer keyboard or on our cell phone, or every time we perform a similar action involving an everyday electrical device, electromagnetics comes into play.
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