Levent Sevgi
Electromagnetic Modeling and Simulation (eBook, PDF)
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Levent Sevgi
Electromagnetic Modeling and Simulation (eBook, PDF)
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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…mehr
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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.
Produktdetails
- Produktdetails
- Verlag: John Wiley & Sons
- Seitenzahl: 696
- Erscheinungstermin: 17. März 2014
- Englisch
- ISBN-13: 9781118716441
- Artikelnr.: 40614007
- Verlag: John Wiley & Sons
- Seitenzahl: 696
- Erscheinungstermin: 17. März 2014
- Englisch
- ISBN-13: 9781118716441
- Artikelnr.: 40614007
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 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
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
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
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