Electromagnetic Modeling and Simulation

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