MATLAB-Based Electromagnetics

Series
Prentice Hall
Author
Branislav M. Notaros  
Publisher
Pearson
Cover
Softcover
Edition
1
Language
English
Total pages
416
Pub.-date
May 2013
ISBN13
9780132857949
ISBN
0132857944
Related Titles



Description

 

Can be used to either complement available electromagnetics text, or as an independent resource. Designed primarily for undergraduate electromagnetics, but can also be used in follow-up courses on antennas, propagation, microwaves, advanced electromagnetic theory, computational electromagnetics, electrical machines, signal integrity, etc.


MATLAB-Based Electromagentics provides engineering and physics students and other users with an operational knowledge and firm grasp of electromagnetic fundamentals aimed toward practical engineering applications, by teaching them “hands on” electromagnetics through a unique and comprehensive collection of MATLAB computer exercises and projects. Essentially, the book unifies two themes: it presents and explains electromagnetics using MATLAB on one side, and develops and discusses MATLAB for electromagnetics on the other.

 

MATLAB codes described (and listed) in TUTORIALS or proposed in other exercises provide prolonged benefits of learning. By running codes; generating results, figures, and diagrams; playing movies and animations; and solving a large variety of problems in MATLAB, in class, with peers in study groups, or individually, students gain a deep understanding of electromagnetics.

Features

Designed to support a variety of courses

MATLAB-Based Electromagnetics covers all important theoretical concepts, methodological procedures, and solution tools in electromagnetic fields and waves for undergraduates—organized in 12 chapters on electrostatic fields; steady electric currents; magnetostatic fields; time-varying electromagnetic fields; uniform plane electromagnetic waves; transmission lines; waveguides and cavity resonators; and antennas and wireless communication systems.

  • The book provides two interwoven themes: presentation and study of electromagnetics using MATLAB and development and discussion of MATLAB for electromagnetics
  • Provides a theoretical overview at the start of each section within each chapter of the book
  • Can be used to either complement another electromagnetics text, or as an independent resource
  • Designed primarily for undergraduate electromagnetics, but can also be used in follow-up courses on antennas, propagation, microwaves, advanced electromagnetic theory, computational electromagnetics, electrical machines, signal integrity, etc.
  • Allows for flexibility in coverage of the material, including the transmission-lines-early and transmission-lines-first approaches

Spark independent learning and classroom discussion

Assignments of computer exercises along with traditional “by hand” problems help students develop a stronger intuition and a deeper understanding of electromagnetics. Moreover, this approach actively challenges and involves the student, providing additional benefit as compared to a passive computer demonstration. This book provides abundant opportunities for instructors to assign in-class and homework projects, and for students to engage in independent learning. MATLAB exercises are also ideal for interactive in-class explorations and discussions (active teaching and learning), and for teamwork and peer instruction (collaborative teaching/learning).

  • Contains 389 MATLAB computer exercises and projects, covering and reinforcing practically all important theoretical concepts, methodologies, and problem-solving techniques in electromagnetic fields and waves
  • Maintains a favorable balance of MATLAB exercises between static (one third) and dynamic (two thirds) topics
  • Offers MATLAB exercises at all levels of difficulty, from a few lines of MATLAB code, to those requiring a great deal of initiative and exploration
  • Contains 125 TUTORIALS with detailed solutions merged with listings of MATLAB codes (m files); a demo tutorial for every class of MATLAB problems and projects is provided
  • Gives 98 HINTS with guidance on the solution, equations, and programming, often with portions of the code and/or resulting graphs and movie snapshots for validation
  • Features 48 3-D and 2-D movies developed and played in MATLAB, which are extremely valuable for interactive visualizations of fields and waves
  • Displays 133 figures generated in MATLAB with plots of geometries of structures, vector fields, guided and unbounded waves, wave polarization curves, Smith charts, transient signals, antenna patterns, etc.
  • Presents 16 graphical user interfaces (GUIs) built in MATLAB to calculate and display parameters and characteristics of various electromagnetic structures, materials, and systems, selected from a pop-up menu
  • Offers 130 MATLAB exercises recommended to be done also “by hand” – i.e., not using MATLAB, thus serving as traditional written problems

Table of Contents

1 Electrostatic Field in Free Space 1
1.1 Coulomb’s Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Electric Field Intensity Vector Due to Given Charge Distributions . . . . . . . . . 9
1.3 Electric Scalar Potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
1.4 Differential Relationship Between the Field and Potential in Electrostatics, Gradient 26
1.5 Electric Dipole . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
1.6 Gauss’ Law in Integral Form . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
1.7 Differential Form of Gauss’ Law, Divergence . . . . . . . . . . . . . . . . . . . . . . 31
1.8 Method of Moments for Numerical Analysis of Charged Metallic Bodies . . . . . . 33
2 Electrostatic Field in Dielectrics 41
2.1 Characterization of Dielectric Materials . . . . . . . . . . . . . . . . . . . . . . . . 41
2.2 Dielectric—Dielectric Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . 46
2.3 Poisson’s and Laplace’s Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
2.4 Finite-Difference Method for Numerical Solution of Laplace’s Equation . . . . . . . 51
2.5 Evaluation of Capacitances of Capacitors and Transmission Lines . . . . . . . . . . 59
2.6 Capacitors with Inhomogeneous Dielectrics . . . . . . . . . . . . . . . . . . . . . . 69
2.7 Dielectric Breakdown in Electrostatic Systems . . . . . . . . . . . . . . . . . . . . . 70
3 Steady Electric Currents 73
3.1 Continuity Equation, Conductivity, and Ohm’s Law in Local Form . . . . . . . . . 73
3.2 Boundary Conditions for Steady Currents . . . . . . . . . . . . . . . . . . . . . . . 79
3.3 Relaxation Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
3.4 Resistance and Ohm’s Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
4 Magnetostatic Field in Free Space 86
4.1 Magnetic Force and Magnetic Flux Density Vector . . . . . . . . . . . . . . . . . . 86
4.2 Magnetic Field Computation Using Biot—Savart Law . . . . . . . . . . . . . . . . . 92
4.3 Ampere’s Law in Integral Form . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
4.4 Differential Form of Ampere’s Law, Curl . . . . . . . . . . . . . . . . . . . . . . . . 102
4.5 Magnetic Vector Potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
4.6 Magnetic Dipole . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
5 Magnetostatic Field in Material Media 106
5.1 Permeability of Magnetic Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
5.2 Boundary Conditions for the Magnetic Field . . . . . . . . . . . . . . . . . . . . . . 108
5.3 Magnetic Circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
vi Contents, Preface, and m Files on Instructor Resources
6 Time-Varying Electromagnetic Field 118
6.1 Faraday’s Law of Electromagnetic Induction . . . . . . . . . . . . . . . . . . . . . . 118
6.2 Self-Inductance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
6.3 Mutual Inductance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
6.4 Displacement Current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
6.5 Maxwell’s Equations for the Time-Varying Electromagnetic Field . . . . . . . . . . 130
6.6 Boundary Conditions for the Time-Varying Electromagnetic Field . . . . . . . . . . 132
6.7 Time-Harmonic Electromagnetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
6.8 Complex Representatives of Time-Harmonic Field and Circuit Quantities . . . . . 137
6.9 Instantaneous and Complex Poynting Vector . . . . . . . . . . . . . . . . . . . . . 144
7 Uniform Plane Electromagnetic Waves 146
7.1 Time-Harmonic Uniform Plane Waves and Complex-Domain Analysis . . . . . . . 146
7.2 Arbitrarily Directed Uniform Plane Waves . . . . . . . . . . . . . . . . . . . . . . . 151
7.3 Theory of Time-Harmonic Waves in Lossy Media . . . . . . . . . . . . . . . . . . . 153
7.4 Wave Propagation in Good Dielectrics . . . . . . . . . . . . . . . . . . . . . . . . . 158
7.5 Wave Propagation in Good Conductors . . . . . . . . . . . . . . . . . . . . . . . . 158
7.6 Skin Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
7.7 Wave Propagation in Plasmas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
7.8 Polarization of Electromagnetic Waves . . . . . . . . . . . . . . . . . . . . . . . . . 163
8 Reflection and Transmission of Plane Waves 173
8.1 Normal Incidence on a Perfectly Conducting Plane . . . . . . . . . . . . . . . . . . 173
8.2 Normal Incidence on a Penetrable Planar Interface . . . . . . . . . . . . . . . . . . 180
8.3 Oblique Incidence on a Perfect Conductor . . . . . . . . . . . . . . . . . . . . . . . 189
8.4 Oblique Incidence on a Dielectric Boundary . . . . . . . . . . . . . . . . . . . . . . 192
8.5 Wave Propagation in Multilayer Media . . . . . . . . . . . . . . . . . . . . . . . . . 202
9 Field Analysis of Transmission Lines 204
9.1 Field Analysis of Lossless Transmission Lines . . . . . . . . . . . . . . . . . . . . . 204
9.2 Transmission Lines with Small Losses . . . . . . . . . . . . . . . . . . . . . . . . . 207
9.3 Evaluation of Primary and Secondary Circuit Parameters of Transmission Lines . . 212
9.4 Transmission Lines with Inhomogeneous Dielectrics . . . . . . . . . . . . . . . . . . 213
9.5 Multilayer Printed Circuit Board . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213
10 Circuit Analysis of Transmission Lines 222
10.1 Telegrapher’s Equations and Their Solution . . . . . . . . . . . . . . . . . . . . . . 222
10.2 Reflection Coefficient for Transmission Lines . . . . . . . . . . . . . . . . . . . . . . 225
10.3 Transmission-Line Impedance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232
10.4 Complete Solution for Line Voltage and Current . . . . . . . . . . . . . . . . . . . 233
10.5 Short-Circuited, Open-Circuited, and Matched Transmission Lines . . . . . . . . . 235
10.6 Impedance-Matching Using Short- and Open-Circuited Stubs . . . . . . . . . . . . 237
10.7 The Smith Chart — Construction and Basic Properties . . . . . . . . . . . . . . . . 241
10.8 Circuit Analysis of Transmission Lines Using the Smith Chart . . . . . . . . . . . . 247
10.9 Transient Analysis of Transmission Lines . . . . . . . . . . . . . . . . . . . . . . . . 263
10.10 Step Response of Transmission Lines with Purely Resistive Terminations . . . . . 267
10.11 Analysis of Transmission Lines with Pulse Excitations . . . . . . . . . . . . . . . . 272
10.12 Bounce Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279
10.13 Transient Response for Reactive Terminations . . . . . . . . . . . . . . . . . . . . 286
11 Waveguides and Cavity Resonators 291
11.1 Analysis of Rectangular Waveguides Based on Multiple Reflections of Plane Waves 291
11.2 Arbitrary TE and TM Modes in a Rectangular Waveguide . . . . . . . . . . . . . . 299
11.3 Wave Impedances of TE and TM Waves . . . . . . . . . . . . . . . . . . . . . . . . 306
11.4 Power Flow Along a Waveguide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 307
11.5 Waveguides With Small Losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 310
11.6 Waveguide Dispersion and Group Velocity . . . . . . . . . . . . . . . . . . . . . . . 312
11.7 Rectangular Cavity Resonators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314
11.8 Electromagnetic Energy Stored in a Cavity Resonator . . . . . . . . . . . . . . . . 316
11.9 Quality Factor of Rectangular Cavities with Small Losses . . . . . . . . . . . . . . 319
12 Antennas and Wireless Communication Systems 321
12.1 Electromagnetic Field due to a Hertzian Dipole . . . . . . . . . . . . . . . . . . . . 321
12.2 Far Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323
12.3 Steps in Far Field Evaluation of an Arbitrary Antenna . . . . . . . . . . . . . . . . 326
12.4 Radiation and Ohmic Resistances of an Antenna . . . . . . . . . . . . . . . . . . . 328
12.5 Antenna Radiation Patterns, Directivity, and Gain . . . . . . . . . . . . . . . . . . 331
12.6 Wire Dipole Antennas of Arbitrary Lengths . . . . . . . . . . . . . . . . . . . . . . 337
12.7 Theory of Receiving Antennas. Wireless Links with Nonaligned Wire Antennas . . 344
12.8 Friis Transmission Formula for a Wireless Link . . . . . . . . . . . . . . . . . . . . 350
12.9 Antenna Arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 352

Appendix 1: Quantities, Symbols, Units, and Constants A-1
Appendix 2: Mathematical Facts and Identities A-4
A2.1 Trigonometric Identities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-4
A2.2 Exponential, Logarithmic, and Hyperbolic Identities . . . . . . . . . . . . . . . . . A-4
A2.3 Solution of Quadratic Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-5
A2.4 Approximations for Small Quantities . . . . . . . . . . . . . . . . . . . . . . . . . A-5
A2.5 Derivatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-5
A2.6 Integrals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-5
A2.7 Vector Algebraic Identities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-5
A2.8 Vector Calculus Identities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-6
A2.9 Gradient, Divergence, Curl, and Laplacian in Orthogonal Coordinate Systems . . A-6
A2.10 Vector Algebra and Calculus Index . . . . . . . . . . . . . . . . . . . . . . . . . . A-7
Appendix 3: List of MATLAB Exercises A-8
Bibliography A-22
Index A-25

Author

Branislav M. Notaroš received the Dipl.Ing. (B.Sc.), M.Sc., and Ph.D. degrees in electrical engineering from the University of Belgrade, Belgrade, Yugoslavia, in 1988, 1992, and 1995, respectively. From 1996 to 1998, he was an Assistant Professor in the Department of Electrical Engineering at the University of Belgrade, and before that, from 1989 to 1996, a Teaching and Research Assistant (faculty position) in the same department.  He spent the 1998-1999 academic year as a Research Associate at the University of Colorado at Boulder. He was an Assistant Professor, from 1999 to 2004, and Associate Professor (with Tenure), from 2004 to 2006, in the Department of Electrical and Computer Engineering at the University of Massachusetts Dartmouth. He is currently an Associate Professor (with Tenure) of electrical and computer engineering at Colorado State University.

 

Research activities of Prof. Notaroš are in applied computational electromagnetics, antennas, and microwaves. His research publications so far include 22 journal papers, 58 conference papers and abstracts, and a chapter in a monograph. His main contributions are in higher order computational electromagnetic techniques based on the method of moments, finite element method, physical optics, domain decomposition method, and hybrid methods as applied to modeling and design of antennas and microwave circuits and devices for wireless technology. He has produced several Ph.D. and M.S. graduates. Prof. Notaroš’ teaching activities are in theoretical, computational, and applied electromagnetics. He is the author of the Electromagnetics Concept Inventory (EMCI), an assessment tool for electromagnetic fields and waves. He has published 3 workbooks in electromagnetics and in fundamentals of electrical engineering (basic circuits and fields). He has taught a variety of undergraduate and graduate courses in electromagnetic theory, antennas and propagation, computational electromagnetics, fundamentals of electrical engineering, electromagnetic compatibility, and signal integrity. He has been consistently extremely highly rated by his students in all courses, and most notably in undergraduate electromagnetics courses (even though undergraduates generally find these mandatory courses quite difficult and challenging).

 

Dr. Notaroš was the recipient of the 2005 IEEE MTT-S Microwave Prize, Microwave Theory and Techniques Society of the Institute of Electrical and Electronics Engineers (best-paper award for IEEE Transactions on MTT), 1999 IEE Marconi Premium, Institution of Electrical Engineers, London, UK (best-paper award for IEE Proceedings on Microwaves, Antennas and Propagation), 1999 URSI Young Scientist Award, International Union of Radio Science, Toronto, Canada, 2005 UMD Scholar of the Year Award, University of Massachusetts Dartmouth, 2004 Dean’s Recognition Award, College of Engineering, University of Massachusetts Dartmouth, 2009 and 2010 ECE Excellence in Teaching Awards (by nominations and votes of ECE students), Colorado State University, and 2010 George T. Abell Outstanding Teaching and Service Faculty Award, College of Engineering, Colorado State University.