Electromagnetic Modeling and Simulation

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.

• Preface xvii About the Author xxviiAcknowledgments xxix1 Introduction to MODSIM 11.1 Models and Modeling, 21.2 Validation, Verifi cation, and Calibration, 51.3 Available Core Models, 71.4 Model Selection Criteria, 91.5 Graduate Level EM MODSIM Course, 111.5.1 Course Description and Plan, 111.5.2 Available Virtual EM Tools, 121.6 EM-MODSIM Lecture Flow, 121.7 Two Level EM Guided Wave Lecture, 171.8 Conclusions, 19References, 192 Engineers Speak with Numbers 232.1 Introduction, 232.2 Measurement, Calculation, and Error Analysis, 242.3 Significant Digits, Truncation, and Round-Off Errors, 272.4 Error Propagation, 282.5 Error and Confi dence Level, 292.5.1 Predicting the Population’s Confidence Interval, 332.6 Hypothesis Testing, 362.6.1 Testing Population Mean, 382.6.2 Testing Population Proportion, 392.6.3 Testing Two Population Averages, 392.6.4 Testing Two Population Proportions, 392.6.5 Testing Paired Data, 402.7 Hypothetical Tests on Cell Phones, 412.8 Conclusions, 45References, 453 Numerical Analysis in Electromagnetics 473.1 Taylor’s Expansion and Numerical Differentiation, 473.1.1 Taylor’s Expansion and Ordinary Differential Equations, 503.1.2 Poisson and Laplace Equations, 523.1.3 An Iterative (Finite-Difference) Solution, 533.2 Numerical Integration, 583.2.1 Rectangular Method, 583.3 Nonlinear Equations and Root Search, 623.4 Linear Systems of Equations, 64References, 694 Fourier Transform and Fourier Series 714.1 Introduction, 714.2 Fourier Transform, 724.2.1 Fourier Transform (FT), 724.2.2 Discrete Fourier Transform (DFT), 744.2.3 Fast Fourier Transform (FFT), 764.2.4 Aliasing, Spectral Leakage, and Scalloping Loss, 774.2.5 Windowing and Window Functions, 804.3 Basic Discretization Requirements, 814.4 Fourier Series Representation, 854.5 Rectangular Pulse and Its Harmonics, 924.6 Conclusions, 92References, 945 Stochastic Modeling in Electromagnetics 955.1 Introduction, 955.2 Radar Signal Environment, 985.2.1 Random Number Generation, 985.2.2 Noise Generation, 1015.2.3 Signal Generation, 1085.2.4 Clutter Generation, 1085.3 Total Radar Signal, 1115.4 Decision Making and Detection, 1145.4.1 Hypothesis Operating Characteristics (HOCs), 1155.4.2 A Communication/Radar Receiver, 1195.5 Conclusions, 129References, 1306 Electromagnetic Theory: Basic Review 1336.1 Maxwell Equations and Reduction, 1336.2 Waveguiding Structures, 1346.3 Radiation Problems and Vector Potentials, 1366.4 The Delta Dirac Function, 1386.5 Coordinate Systems and Basic Operators, 1396.6 The Point Source Representation, 1416.7 Field Representation of a Point/Line Source, 1426.8 Alternative Field Representations, 1436.9 Transverse Electric/Magnetic Fields, 1456.9.1 The 3D TE/TM Waves, 1456.9.2 The 2D TE/TM Waves, 1466.10 The TE/TM Source Injection, 1516.11 Second-Order EM Differential Equations, 1546.12 EM Wave–Transmission Line Analogy, 1556.13 Time Dependence in Maxwell Equations, 1576.14 Physical Fundamentals, 158References, 1587 Sturm–Liouville Equation: The Bridge between Eigenvalue and Green’s Function Problems 1617.1 Introduction, 1617.2 Guided Wave Scenarios, 1627.3 The Sturm–Liouville Equation, 1657.3.1 The Eigenvalue Problem, 1677.3.2 The Green’s Function (GF) Problem, 1687.3.3 Finite z-Domain Problem, 1697.3.4 Infi nite z-Domain Problem, 1707.3.5 Relation between Eigenvalue and Green’s Function Problems, 1717.4 Conclusions, 172References, 1738 The 2D Nonpenetrable Parallel Plate Waveguide 1758.1 Introduction, 1768.2 Propagation Inside a 2D-PEC Parallel Plate Waveguide, 1778.2.1 Formulation of the TE- and TM-Type Problems, 1788.2.2 The Green’s Function Problem, 1818.2.3 Accessing the Spectral Domain: Separation of Variables, 1828.2.4 Spectral Representations: Eigenvalue Problems, 1838.2.5 Spectral Representations: 1D Characteristic Green’s Functions, 1848.2.6 The 2D Green’s Function Problem: Alternative Representations, 1858.3 Alternative Representation: Eigenray Solution, 1878.3.1 Relation between Eigenmode and Eigenray Representations, 1918.3.2 2D GF and Hybrid Ray-Mode Decomposition, 1928.4 A 2D-PEC Parallel Plate Waveguide Simulator, 1948.4.1 Representations Used for Mode, Ray, and Hybrid Solutions, 1958.4.2 MATLAB Packages: RayMode and Hybrid, 2078.4.3 Numerical Examples, 2108.5 Eigenvalue Extraction from Propagation Characteristics, 2158.5.1 Longitudinal Correlation Function, 2158.5.2 Numerical Illustrations, 2178.6 Tilted Beam Excitation, 2218.7 Conclusions, 223References, 2259 Wedge Waveguide with Nonpenetrable Boundaries 2279.1 Introduction, 2289.2 Statement of the Problem: Physical Configuration and Ray-Asymptotic Guided Wave Schematizations, 2299.3 Source-Free Solutions, 2309.3.1 Separable Coordinates: Conventional NM, 2309.3.2 Weakly Nonseparable Coordinates: AM, 2319.3.3 Uniformizing the AM Near Caustics: IM, 2329.4 Test Problem: The 2D Line-Source-Excited Nonpenetrable Wedge Waveguide, 2349.4.1 Exact Solution in Cylindrical Coordinate, 2349.4.2 Approximate Solutions in Rectangular Coordinates, 2419.4.3 IM Spectral Representation, 2449.5 The MATLAB Package “WedgeGUIDE,” 2479.6 Numerical Tests and Illustrations, 2499.7 Conclusions, 256Appendix 9A: Formation of the Spectral IM Integral in Section 9.3.3, 257References, 26210 High Frequency Asymptotics: The 2D Wedge Diffraction Problem 26510.1 Introduction, 26610.2 Plane Wave Illumination and HFA Models, 26810.2.1 Exact Solution by Series Summation, 26810.2.2 The Physical Optics (PO) Solution, 27010.2.3 The PTD Solution, 27210.2.4 The UTD Solution, 27310.2.5 The Parabolic Equation (PE) Solution, 27510.3 HFA Models under Line Source (LS) Excitations, 27510.3.1 Exact Solution by Series Summation, 27610.3.2 Exact Solution by Integral, 27710.3.3 The Parabolic Equation (PE) Solution, 27710.4 Basic MATLAB Scripts, 27810.5 The WedgeGUI Virtual Tool and Some Examples, 29110.6 Conclusions, 297References, 29811 Antennas: Isotropic Radiators and Beam Forming/Beam Steering 30111.1 Introduction, 30111.2 Arrays of Isotropic Radiators, 30311.3 The ARRAY Package, 30611.4 Beam Forming/Steering Examples, 31011.5 Conclusions, 317References, 31812 Simple Propagation Models and Ray Solutions 31912.1 Introduction, 32012.2 Ray-Tracing Approaches, 32112.3 A Ray-Shooting MATLAB Package, 32312.4 Characteristic Examples, 32912.5 Flat-Earth Problem and 2Ray Model, 33312.6 Knife-Edge Problem and 4Ray Model, 33812.7 Ray Plus Diffraction Models, 34812.8 Conclusions, 351References, 35113 Method of Moments 35313.1 Introduction, 35313.2 Approximating a Periodic Function by Other Functions: Fourier Series Representation, 35413.3 Introduction to the MoM, 35913.4 Simple Applications of MoM, 36113.4.1 An Ordinary Differential Equation, 36113.4.2 The Parallel Plate Capacitor, 36413.4.3 Propagation over PEC Flat Earth, 36613.5 MoM Applied to Radiation and Scattering Problems, 37213.5.1 A Complex Antenna Structure, 37213.5.2 Ground Wave Propagation Modeling, 37313.5.3 EM Scattering from Infinitely Long Cylinder, 37613.5.4 3D RCS Modeling, 38113.6 MoM Applied to Wedge Diffraction Problem, 38613.7 MoM Applied to Wedge Waveguide Problem, 39713.8 Conclusions, 402References, 40214 Finite-Difference Time-Domain Method 40714.1 FDTD Representation of EM Plane Waves, 40714.1.1 Maxwell Equations and Plane Waves, 40814.1.2 FDTD and Discretization, 41014.1.3 A One-Dimensional FDTD MATLAB Script, 41714.1.4 MATLAB-Based FDTD1D Package, 41714.2 Transmission Lines and Time-Domain Reflectometer, 42914.2.1 Transmission Line (TL) Theory, 43014.2.2 Plane Wave–Transmission Line Analogy, 43414.2.3 FDTD Representation of TL Equations, 43714.2.4 MATLAB-Based TDRMeter Package, 44714.2.5 Fourier Analysis and Reflection Characteristics, 45414.2.6 Laplace Analysis and Fault Identification, 45614.2.7 Step Response, 46414.3 1D FDTD with Second-Order Differential Equations, 46814.4 Two-Dimensional (2D) FDTD Modeling, 47214.4.1 Field Components and FDTD Equations, 47614.4.2 FDTD-Based Virtual Tool: MGL2D Package, 47714.4.3 Characteristic Examples, 47914.5 Canonical 2D Wedge Scattering Problem, 49414.5.1 Problem Postulation, 49414.5.2 Review of Analytical Models, 49614.5.3 The FDTD Model, 49914.5.4 Discretization and Dey–Mittra Approach, 50214.5.5 The WedgeFDTD Package and Examples, 50514.5.6 Wedge Diffraction and FDTD versus MoM, 51014.6 Conclusions, 512References, 51215 Parabolic Equation Method 51515.1 Introduction, 51615.2 The Parabolic Equation (PE) Model, 51815.3 The Split-Step Parabolic Equation (SSPE) Propagation Tool, 52015.4 The Finite Element Method-Based PE Propagation Tool, 52815.5 Atmospheric Refractivity Effects, 53115.6 A 2D Surface Duct Scenario and Reference Solutions, 53315.7 LINPE Algorithm and Canonical Tests/Comparisons, 53815.8 The GrSSPE Package, 55815.9 The Single-Knife-Edge Problem, 56615.10 Accurate Source Modeling, 57115.11 Dielectric Slab Waveguide, 58015.11.1 Even and Odd Symmetric Solutions, 58215.11.2 The SSPE Propagator and Eigenvalue Extraction, 58415.11.3 The Matlab-Based DiSLAB Package, 58515.12 Conclusions, 591References, 59116 Parallel Plate Waveguide Problem 59516.1 Introduction, 59516.2 Problem Postulation and Analytical Solutions: Revisited, 59916.2.1 Green’s Function in Terms of Mode Summation, 60216.2.2 Mode Summation for a Tilted/Directive Antenna, 60416.2.3 Eigenray Representation, 60616.2.4 Hybrid Ray + Image Method, 61316.3 Numerical Models, 61316.3.1 Split Step Parabolic Equation Model, 61316.3.2 Finite-Difference Time-Domain Model, 61716.3.3 Method of Moments (MoM), 62216.4 Conclusions, 638References, 639Appendix A Introduction to MATLAB 643Appendix B Suggested References 653Appendix C Suggested Tutorials and Feature Articles 655Index 659

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