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Electromagnetic Modeling and Simulation

ISBN: 978-1-118-71618-2
696 pages
April 2014, Wiley-IEEE Press
Electromagnetic Modeling and Simulation (1118716183) cover image

This unique book presents simple, easy-to-use, but effective short codes as well as virtual tools that can be used by electrical, electronic, communication, and computer engineers in a broad range of electrical engineering problems

Electromagnetic modeling is essential to the design and modeling of antenna, radar, satellite, medical imaging, and other applications. In this book, author Levent Sevgi explains techniques for solving real-time complex physical problems using MATLAB-based short scripts and comprehensive virtual tools.

Unique in coverage and tutorial approach, Electromagnetic Modeling and Simulation covers fundamental analytical and numerical models that are widely used in teaching, research, and engineering designs—including mode and ray summation approaches with the canonical 2D nonpenetrable parallel plate waveguide as well as FDTD, MoM, and SSPE scripts. The book also establishes an intelligent balance among the essentials of EM MODSIM: The Problem (the physics), The Theory and Models (mathematical background and analytical solutions), and The Simulations (code developing plus validation, verification, and calibration).

Classroom tested in graduate-level and short courses, Electromagnetic Modeling and Simulation:

  • Clarifies concepts through numerous worked problems and quizzes provided throughout the book
  • Features valuable MATLAB-based, user-friendly, effective engineering and research virtual design tools
  • Includes sample scenarios and video clips recorded during characteristic simulations that visually impact learning—available on wiley.com
  • Provides readers with their first steps in EM MODSIM as well as tools for medium and high-level code developers and users

Electromagnetic Modeling and Simulation thoroughly covers the physics, mathematical background, analytical solutions, and code development of electromagnetic modeling, making it an ideal resource for electrical engineers and researchers.

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Preface xvii

About the Author xxvii

Acknowledgments xxix

1 Introduction to MODSIM 1

1.1 Models and Modeling, 2

1.2 Validation, Verifi cation, and Calibration, 5

1.3 Available Core Models, 7

1.4 Model Selection Criteria, 9

1.5 Graduate Level EM MODSIM Course, 11

1.5.1 Course Description and Plan, 11

1.5.2 Available Virtual EM Tools, 12

1.6 EM-MODSIM Lecture Flow, 12

1.7 Two Level EM Guided Wave Lecture, 17

1.8 Conclusions, 19

References, 19

2 Engineers Speak with Numbers 23

2.1 Introduction, 23

2.2 Measurement, Calculation, and Error Analysis, 24

2.3 Significant Digits, Truncation, and Round-Off Errors, 27

2.4 Error Propagation, 28

2.5 Error and Confi dence Level, 29

2.5.1 Predicting the Population’s Confidence Interval, 33

2.6 Hypothesis Testing, 36

2.6.1 Testing Population Mean, 38

2.6.2 Testing Population Proportion, 39

2.6.3 Testing Two Population Averages, 39

2.6.4 Testing Two Population Proportions, 39

2.6.5 Testing Paired Data, 40

2.7 Hypothetical Tests on Cell Phones, 41

2.8 Conclusions, 45

References, 45

3 Numerical Analysis in Electromagnetics 47

3.1 Taylor’s Expansion and Numerical Differentiation, 47

3.1.1 Taylor’s Expansion and Ordinary Differential Equations, 50

3.1.2 Poisson and Laplace Equations, 52

3.1.3 An Iterative (Finite-Difference) Solution, 53

3.2 Numerical Integration, 58

3.2.1 Rectangular Method, 58

3.3 Nonlinear Equations and Root Search, 62

3.4 Linear Systems of Equations, 64

References, 69

4 Fourier Transform and Fourier Series 71

4.1 Introduction, 71

4.2 Fourier Transform, 72

4.2.1 Fourier Transform (FT), 72

4.2.2 Discrete Fourier Transform (DFT), 74

4.2.3 Fast Fourier Transform (FFT), 76

4.2.4 Aliasing, Spectral Leakage, and Scalloping Loss, 77

4.2.5 Windowing and Window Functions, 80

4.3 Basic Discretization Requirements, 81

4.4 Fourier Series Representation, 85

4.5 Rectangular Pulse and Its Harmonics, 92

4.6 Conclusions, 92

References, 94

5 Stochastic Modeling in Electromagnetics 95

5.1 Introduction, 95

5.2 Radar Signal Environment, 98

5.2.1 Random Number Generation, 98

5.2.2 Noise Generation, 101

5.2.3 Signal Generation, 108

5.2.4 Clutter Generation, 108

5.3 Total Radar Signal, 111

5.4 Decision Making and Detection, 114

5.4.1 Hypothesis Operating Characteristics (HOCs), 115

5.4.2 A Communication/Radar Receiver, 119

5.5 Conclusions, 129

References, 130

6 Electromagnetic Theory: Basic Review 133

6.1 Maxwell Equations and Reduction, 133

6.2 Waveguiding Structures, 134

6.3 Radiation Problems and Vector Potentials, 136

6.4 The Delta Dirac Function, 138

6.5 Coordinate Systems and Basic Operators, 139

6.6 The Point Source Representation, 141

6.7 Field Representation of a Point/Line Source, 142

6.8 Alternative Field Representations, 143

6.9 Transverse Electric/Magnetic Fields, 145

6.9.1 The 3D TE/TM Waves, 145

6.9.2 The 2D TE/TM Waves, 146

6.10 The TE/TM Source Injection, 151

6.11 Second-Order EM Differential Equations, 154

6.12 EM Wave–Transmission Line Analogy, 155

6.13 Time Dependence in Maxwell Equations, 157

6.14 Physical Fundamentals, 158

References, 158

7 Sturm–Liouville Equation: The Bridge between Eigenvalue and Green’s Function Problems 161

7.1 Introduction, 161

7.2 Guided Wave Scenarios, 162

7.3 The Sturm–Liouville Equation, 165

7.3.1 The Eigenvalue Problem, 167

7.3.2 The Green’s Function (GF) Problem, 168

7.3.3 Finite z-Domain Problem, 169

7.3.4 Infi nite z-Domain Problem, 170

7.3.5 Relation between Eigenvalue and Green’s Function Problems, 171

7.4 Conclusions, 172

References, 173

8 The 2D Nonpenetrable Parallel Plate Waveguide 175

8.1 Introduction, 176

8.2 Propagation Inside a 2D-PEC Parallel Plate Waveguide, 177

8.2.1 Formulation of the TE- and TM-Type Problems, 178

8.2.2 The Green’s Function Problem, 181

8.2.3 Accessing the Spectral Domain: Separation of Variables, 182

8.2.4 Spectral Representations: Eigenvalue Problems, 183

8.2.5 Spectral Representations: 1D Characteristic Green’s Functions, 184

8.2.6 The 2D Green’s Function Problem: Alternative Representations, 185

8.3 Alternative Representation: Eigenray Solution, 187

8.3.1 Relation between Eigenmode and Eigenray Representations, 191

8.3.2 2D GF and Hybrid Ray-Mode Decomposition, 192

8.4 A 2D-PEC Parallel Plate Waveguide Simulator, 194

8.4.1 Representations Used for Mode, Ray, and Hybrid Solutions, 195

8.4.2 MATLAB Packages: RayMode and Hybrid, 207

8.4.3 Numerical Examples, 210

8.5 Eigenvalue Extraction from Propagation Characteristics, 215

8.5.1 Longitudinal Correlation Function, 215

8.5.2 Numerical Illustrations, 217

8.6 Tilted Beam Excitation, 221

8.7 Conclusions, 223

References, 225

9 Wedge Waveguide with Nonpenetrable Boundaries 227

9.1 Introduction, 228

9.2 Statement of the Problem: Physical Configuration and Ray-Asymptotic Guided Wave Schematizations, 229

9.3 Source-Free Solutions, 230

9.3.1 Separable Coordinates: Conventional NM, 230

9.3.2 Weakly Nonseparable Coordinates: AM, 231

9.3.3 Uniformizing the AM Near Caustics: IM, 232

9.4 Test Problem: The 2D Line-Source-Excited Nonpenetrable Wedge Waveguide, 234

9.4.1 Exact Solution in Cylindrical Coordinate, 234

9.4.2 Approximate Solutions in Rectangular Coordinates, 241

9.4.3 IM Spectral Representation, 244

9.5 The MATLAB Package “WedgeGUIDE,” 247

9.6 Numerical Tests and Illustrations, 249

9.7 Conclusions, 256

Appendix 9A: Formation of the Spectral IM Integral in Section 9.3.3, 257

References, 262

10 High Frequency Asymptotics: The 2D Wedge Diffraction Problem 265

10.1 Introduction, 266

10.2 Plane Wave Illumination and HFA Models, 268

10.2.1 Exact Solution by Series Summation, 268

10.2.2 The Physical Optics (PO) Solution, 270

10.2.3 The PTD Solution, 272

10.2.4 The UTD Solution, 273

10.2.5 The Parabolic Equation (PE) Solution, 275

10.3 HFA Models under Line Source (LS) Excitations, 275

10.3.1 Exact Solution by Series Summation, 276

10.3.2 Exact Solution by Integral, 277

10.3.3 The Parabolic Equation (PE) Solution, 277

10.4 Basic MATLAB Scripts, 278

10.5 The WedgeGUI Virtual Tool and Some Examples, 291

10.6 Conclusions, 297

References, 298

11 Antennas: Isotropic Radiators and Beam Forming/Beam Steering 301

11.1 Introduction, 301

11.2 Arrays of Isotropic Radiators, 303

11.3 The ARRAY Package, 306

11.4 Beam Forming/Steering Examples, 310

11.5 Conclusions, 317

References, 318

12 Simple Propagation Models and Ray Solutions 319

12.1 Introduction, 320

12.2 Ray-Tracing Approaches, 321

12.3 A Ray-Shooting MATLAB Package, 323

12.4 Characteristic Examples, 329

12.5 Flat-Earth Problem and 2Ray Model, 333

12.6 Knife-Edge Problem and 4Ray Model, 338

12.7 Ray Plus Diffraction Models, 348

12.8 Conclusions, 351

References, 351

13 Method of Moments 353

13.1 Introduction, 353

13.2 Approximating a Periodic Function by Other Functions: Fourier Series Representation, 354

13.3 Introduction to the MoM, 359

13.4 Simple Applications of MoM, 361

13.4.1 An Ordinary Differential Equation, 361

13.4.2 The Parallel Plate Capacitor, 364

13.4.3 Propagation over PEC Flat Earth, 366

13.5 MoM Applied to Radiation and Scattering Problems, 372

13.5.1 A Complex Antenna Structure, 372

13.5.2 Ground Wave Propagation Modeling, 373

13.5.3 EM Scattering from Infinitely Long Cylinder, 376

13.5.4 3D RCS Modeling, 381

13.6 MoM Applied to Wedge Diffraction Problem, 386

13.7 MoM Applied to Wedge Waveguide Problem, 397

13.8 Conclusions, 402

References, 402

14 Finite-Difference Time-Domain Method 407

14.1 FDTD Representation of EM Plane Waves, 407

14.1.1 Maxwell Equations and Plane Waves, 408

14.1.2 FDTD and Discretization, 410

14.1.3 A One-Dimensional FDTD MATLAB Script, 417

14.1.4 MATLAB-Based FDTD1D Package, 417

14.2 Transmission Lines and Time-Domain Reflectometer, 429

14.2.1 Transmission Line (TL) Theory, 430

14.2.2 Plane Wave–Transmission Line Analogy, 434

14.2.3 FDTD Representation of TL Equations, 437

14.2.4 MATLAB-Based TDRMeter Package, 447

14.2.5 Fourier Analysis and Reflection Characteristics, 454

14.2.6 Laplace Analysis and Fault Identification, 456

14.2.7 Step Response, 464

14.3 1D FDTD with Second-Order Differential Equations, 468

14.4 Two-Dimensional (2D) FDTD Modeling, 472

14.4.1 Field Components and FDTD Equations, 476

14.4.2 FDTD-Based Virtual Tool: MGL2D Package, 477

14.4.3 Characteristic Examples, 479

14.5 Canonical 2D Wedge Scattering Problem, 494

14.5.1 Problem Postulation, 494

14.5.2 Review of Analytical Models, 496

14.5.3 The FDTD Model, 499

14.5.4 Discretization and Dey–Mittra Approach, 502

14.5.5 The WedgeFDTD Package and Examples, 505

14.5.6 Wedge Diffraction and FDTD versus MoM, 510

14.6 Conclusions, 512

References, 512

15 Parabolic Equation Method 515

15.1 Introduction, 516

15.2 The Parabolic Equation (PE) Model, 518

15.3 The Split-Step Parabolic Equation (SSPE) Propagation Tool, 520

15.4 The Finite Element Method-Based PE Propagation Tool, 528

15.5 Atmospheric Refractivity Effects, 531

15.6 A 2D Surface Duct Scenario and Reference Solutions, 533

15.7 LINPE Algorithm and Canonical Tests/Comparisons, 538

15.8 The GrSSPE Package, 558

15.9 The Single-Knife-Edge Problem, 566

15.10 Accurate Source Modeling, 571

15.11 Dielectric Slab Waveguide, 580

15.11.1 Even and Odd Symmetric Solutions, 582

15.11.2 The SSPE Propagator and Eigenvalue Extraction, 584

15.11.3 The Matlab-Based DiSLAB Package, 585

15.12 Conclusions, 591

References, 591

16 Parallel Plate Waveguide Problem 595

16.1 Introduction, 595

16.2 Problem Postulation and Analytical Solutions: Revisited, 599

16.2.1 Green’s Function in Terms of Mode Summation, 602

16.2.2 Mode Summation for a Tilted/Directive Antenna, 604

16.2.3 Eigenray Representation, 606

16.2.4 Hybrid Ray + Image Method, 613

16.3 Numerical Models, 613

16.3.1 Split Step Parabolic Equation Model, 613

16.3.2 Finite-Difference Time-Domain Model, 617

16.3.3 Method of Moments (MoM), 622

16.4 Conclusions, 638

References, 639

Appendix A Introduction to MATLAB 643

Appendix B Suggested References 653

Appendix C Suggested Tutorials and Feature Articles 655

Index 659

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LEVENT SEVGI, BSEE, MSEE, PhD, works at the Electronics and Communication Engineering Department at Dogus University in Istanbul, while serving as a full-time faculty member at University of Massachusetts, Lowell (UML) during his sabbatical. A former chair of the Electronic Systems Department in TUBITAK-MRC, Information Technologies Research Institute, Dr. Sevgi is also the author or coauthor of nearly 200 journal, magazine, conference papers, and tutorials; a Fellow of the IEEE; AdCom Member of the IEEE Antennas and Propagation Society (AP-S; 2013-2015); the writer/editor of the “Testing Ourselves” column in the IEEE Antennas and Propagation Magazine; and a member of the IEEE AP-S Education Committee.

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