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# Electromagnetic Modeling and Simulation

 Copyright Year: 2014 Author(s): Levent Sevgi Publisher: Wiley-IEEE Press Content Type : Books & eBooks Topics: Computing & Processing ;  Fields, Waves & Electromagnetics

• ### Front Matter

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The prelims comprise:
Half-Title Page
Series Page
Title Page
Dedication
Contents
Preface
Acknowledgments View full abstract»

• ### Introduction to MODSIM

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Computer simulations, either in-house prepared or commercially available, have been effectively used in electromagnetics (EMs). Key issues are model validation, code verification, and calibration (VV&C) and physical interpretation of the numbers obtained. The four critical words are mathematics, physics, experience, and practice. A good EM modeling and simulation (EM-MODSIM) course should cover them all. When not measuring or soldering, engineers continuously deal with models when analyzing, designing, and implementing. The two phases in modeling are utilization and creation. Maxwell's well-known equations establish the physics of electrical engineering (EE), well define the interaction of electromagnetic waves with matter, and form the basis for a real understanding of EE problems and their solutions. Well-known and widely used EM-MODSIM models are finite element model (FEM), method of moments (MoM), parabolic equation (PE), finite-difference time-domain (FDTD), and transmission line matrix (TLM). Guided wave problems are important in teaching EM. View full abstract»

• ### Engineers Speak with Numbers

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Numbers are expressed using figures (numerals). The first nonzero numeral at the left of a number (which contributes the largest amount to the number) is called the most-significant digit. The first nonzero numeral at the right of a number (which contributes the least amount) is the least-significant digit. All nonzero digits beyond the number of significant digits at the right of a number are removed in one of two ways: truncation or round off. Error propagates because of model-based derived quantities. A method or a result may become unstable due to the propagated error if the errors are magnified continuously during multiple derivations or iterative processes. Confidence levels can be defined through a good understanding of the nature (probabilistic distributions) of the errors. Designing a hypothesis testing starts with the choice of the level of significance since it directly affects whether to accept or reject a null hypothesis. View full abstract»

• ### Numerical Analysis in Electromagnetics

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EM modeling and simulation (EM-MODSIM) necessitates a good understanding and use of numerical analysis. Built-in MATLAB functions such as roots(), diff(), gradient(), trapz(), and inv() can be used for most of numerical analysis jobs. Although MATLAB makes life easy for engineers, EM-MODSIM people should always depend on their own codes; at least aware of and well understand what is going on behind these built-in commands. This chapter reviews briefly some numerical analysis fundamentals which are essential for EM-MODSIM studies. Taylor's expansion is one of a few important methods for the numerical solution of ordinary differential equations (ODEs). An important topic in numerical analysis is the root finding of a given nonlinear function. Method of moments (MoM) is used to solve linear systems of equations. Multiloop circuits are also solved using linear systems of equations. View full abstract»

• ### Fourier Transform and Fourier Series

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The Fourier transform (FT) has been widely used in circuit analysis and synthesis, from filter design to signal processing, image reconstruction, and so on. Fourier transform is used for energy signal which contain finite energy. The discrete Fourier transform (DFT) and fast Fourier transform (FFT) are discrete tools to analyze time domain signals. One needs to know the problems caused by discretization and specify the parameters accordingly to avoid nonphysical and nonmathematical results. Mathematically, FT is defined for continuous time signals, and in order to go to frequency domain, the time signal must be observed from an infinite-extend time window. This chapter lists a simple MATLAB code for the Fourier series representation of a given function. The number of terms required in the Fourier series representation depends on the smoothness of the function and the specified accuracy. View full abstract»

• ### Stochastic Modeling in Electromagnetics

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Performance tests of multisensor systems with tens even hundreds of targets can only be done in a synthetic environment so computer simulations are almost mandatory. A radar signal usually contains echoes from objects under investigation (targets), unwanted objects echoes (clutter), noise, and other interfering signals. The process of extracting target information from the total echo is called (stochastic) signal processing and performed via powerful, intelligent algorithms. Total radar signal is the addition of signal, noise, and clutter. This chapter illustrates the total signal environment in the time and frequency domains, respectively. Detection is the first task in establishing a communication link or tracking a target with a radar system. This is a decision making problem and is performed through a hypothesis testing procedure. View full abstract»

• ### Electromagnetic Theory: Basic Review

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This chapter brings together fundamental electromagnetic (EM) concepts, mathematical relations, and physical meanings. It illustrates three well-known coordinate systems and discusses the relations among them. Electromagnetic problems such as antenna radiation or radar crosssection prediction are better modeled via vector (and scalar) potentials. The concept of delta function is used in EM source representations. Guided wave propagation problems in telecommunications media are best treated using reduced equations obtained from the longitudinal and transverse decomposition of Maxwell equations. This yields the well-known transverse electric (TE), transverse magnetic (TM), and transverse EM (TEM) field representations under different polarizations. Electromagnetic problems involve linear, second-order differential equations. Any linear, second-order PDE can be classified as elliptic, hyperbolic, or parabolic. View full abstract»

• ### Sturm-Liouville Equation: The Bridge between Eigenvalue and Green's Function Problems

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Guided wave problems can be grouped into two: eigenvalue (EV) problems (i.e., the effects of the environment on to the propagating waves) and the Green's function (GF) problem (the effects of the excitation in the environment). This chapter reviews guided wave theory (GWT) in one dimension (1D) which is represented by the Sturm-Liouville (SL) equation. In GWT, SL equation establishes a bridge between source-free (homogeneous) and source-driven (nonhomogeneous) wave equations. The GF problem in the physical domain differs from the EV problem due to the presence of the delta function (i.e., source terms) on the right-hand side. View full abstract»

• ### The 2D Nonpenetrable Parallel Plate Waveguide

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This chapter deals with high frequency electromagnetic wave propagation in guiding environments. After an introductory overview of issues and physical interpretations pertaining to this broad subject area, detailed attention is given to the simplest canonical, thoroughly familiar, test environment: a (time-harmonic) line-source-excited two-dimensional (2D) infinite waveguide with perfectly electrical conducting (PEC) plane-parallel boundaries. After formulating the Green's function (GF) problem within the framework of Maxwell equations, alternative field representations are presented and interpreted in physical terms, highlighting two complementary phenomenologies: progressing (ray-type) and oscillatory (mode-type), culminating in the self-consistent hybrid ray-mode scheme which is usually not included in conventional treatments at this level. This provides the analytical background for two educational MATLAB packages which explore the dynamics of ray fields, mode fields, and the ray-mode interplay: RAYMODE package and HYBRID package. Finally, the chapter focuses on eigenvalue extraction from propagation characteristics and tilted beam excitation. View full abstract»

• ### Wedge Waveguide with Nonpenetrable Boundaries

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Many natural or man-made guiding environments are characterized by physical parameters that render the wave equation nonseparable in any of the standard coordinate systems. Adiabatic modes (AMs) fail in cutoff regions and can be uniformized there by intrinsic modes (IMs), which are synthesized by a spectral continuum of AM. In this chapter, the problem, in general, is defined and formulated. A special test case of a wedge waveguide with nonpenetrable boundaries, under line source excitation (Green's function (GF) problem), is formulated and solved rigorously (in cylindrical coordinates) and approximately in terms of local rectangular mode superposition. The chapter then describes a self-contained MATLAB-based visualization package WedgeGUIDE. Numerical tests and illustrations are also presented, followed by a discussion on the method of moments (MoM) modeling. View full abstract»

• ### High Frequency Asymptotics: The 2D Wedge Diffraction Problem

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In this chapter, high frequency asymptotics (HFA) techniques are reviewed through a classical, canonical problem: EM wave scattering from a wedge shaped object with perfectly electrical conductor (PEC) boundaries. A MATLAB-based virtual diffraction tool WedgeGUI, using analytical exact as well as well-known HFA techniques, is also introduced. Mathematical equations of different models are included for both line source (LS) and plane wave (PW) illuminations. The PW models presented are exact by series summation, PO, PTD, UTD, and PE models. View full abstract»

• ### Antennas: Isotropic Radiators and Beam Forming/Beam Steering

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In this chapter, a simple MATLAB package (ARRAY), accommodated with beam steering capabilities, is designed and introduced which plots two-dimensional (2D) and three-dimensional (3D) radiation patterns of a number of selected and user-located isotropic radiators. An isotropic radiator is a hypothetical, lossless antenna occupying a point in space and, when transmitting, radiates uniformly in all directions. The chapter provides geometrical parameters associated with this problem. The ARRAY package allows the user to choose from a popup menu (a) arbitrary, (b) linear, (c) planar, or (d) circular arrays with a number of user-selected and located isotropic radiators. The ARRAY package is used to plot 2D and 3D radiation patterns of various types of antenna arrays, and some examples of these are given in the chapter. View full abstract»

• ### Simple Propagation Models and Ray Solutions

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The topic of electromagnetic (EM) wave propagation through complex environments has been and will continue to be of great interest for communication and radar systems. Simple propagation models are introduced in this chapter. First, a simple ray-shooting MATLAB package is designed and discussed. The package may be used as an educational tool in various EM lectures (e.g., EM wave theory, antennas and propagation, wireless propagation, etc.) as well as a research tool to predict ducting and/or antiducting conditions in the presence of buildings and under various atmospheric refractivity conditions. Then, early analytical ray-based models are discussed. Propagation over nonpenetrable flat earth with the simple two ray (2Ray) model and single knife-edge problem with the four ray (4Ray) model are summarized with basic examples and illustrations. View full abstract»

• ### Method of Moments

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Method of moments (MoM) is a numerical technique used to approximately solve linear operator equations such as differential equations or integral equations. This chapter outlines the steps to approximate the unknown function in linear operator equations in terms of a known finite series. It then presents the Fourier series (FS) expansion of a continuous function in a specified finite region to reinforce the concept of minimizing error or residual. The basics of MoM are presented next. A few simple examples are included to better understand the MoM procedure. Finally, complex radiating and scattering problems that cannot be handled via analytical methods are simulated with MoM and compared with other numerical models. View full abstract»

• ### Finite-Difference Time-Domain Method

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This chapter focuses on the most widely used numerical model: the finite-difference time-domain (FDTD) method. It investigates electromagnetic (EM) plane wave behaviors both in time and frequency domains. A TL made from two conductors (a pair of parallel wires) is accepted as the fundamental structure and the theory is established according to this assumption. The theory, basic concepts, and characteristic equations explained in the chapter may be obtained either from EM wave theory or independently from the circuit theory. The chapter discusses the time-domain reflectometer concept, which has been widely used in fault location and identification in TLs. It then discusses one-dimensional (1D) FDTD with second order differential equations, and moves onto review the plane wave and the transmission line (TL) problems. Finally, the chapter focuses on two-dimensional (2D) FDTD models. Most of EM problems including radiation and beam forming/beam steering, scattering, and propagation modeling are handled in 2D. View full abstract»

• ### Parabolic Equation Method

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Parabolic equation method (PEM) represents one-way propagation and is widely used in two-dimensional (2D) radio wave/ground wave propagation modeling. It takes the earth's curvature, atmospheric refractivity variations, nonflat terrain scattering, and boundary losses into account. This chapter reviews both split-step PE (SSPE)- and finite element method (FEM)-based numerical solution approaches and introduces MATLAB-based simple routines. Canonical test cases are presented and systematic comparisons between the SSPE and FEMPE methods are made, followed by calibration of both the SSPE and FEMPE tools against analytical exact (reference) solutions. Finally, the chapter introduces several simple MATLAB scripts in 2D propagation modeling. View full abstract»

• ### Parallel Plate Waveguide Problem

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This conclusory chapter compares widely used numerical models, finite-difference time-domain (FDTD), method of moments (MoM), and split-step PE (SSPE) models, on a simple, canonical problem: Propagation inside a parallel plate waveguide with perfectly electrical conducting (PEC) boundaries in two-dimension. The same can be applied to wedge waveguide also. Propagation inside a parallel plate waveguide is an interesting EM problem where both analytical and numerical models can be tested one against the others. Analytical reference data can be generated using any of the three models: mode/eigenray summations or image method (IM). View full abstract»

• ### Appendix A: Introduction to MATLAB

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• ### Appendix B: Suggested References

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• ### Appendix C: Suggested Tutorials and Feature Articles

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• ### Index

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