Analytical and Computational Methods in Electromagnetics

by Ramesh Garq

Overview

Achieve optimal microwave system performance by mastering the principles and methods underlying today's powerful computational tools and commercial software in electromagnetics. This authoritative resource offers you clear and complete explanation of this essential electromagnetics knowledge, providing you with the analytical background you need to understand such key approaches as MoM (method of moments), FDTD (Finite Difference Time Domain) and FEM (Finite Element Method), and Green's functions. This comprehensive book includes all math necessary to master the material. Moreover, it features numerous solved problems that help ensure your understanding of key concepts throughout the book.

To keep you from being bogged down with complex mathematical details (vector calculus) and coding, this comprehensive volume places emphasis on the analysis of the scalar wave equation in Cartesian coordinates. The book also includes multiple choice questions, appropriate for self study or courses, that help clarify concepts without any mathematical burden. Packed with over 1,300 equations, most of the problems presented in the book can be solved using nothing more than calculator.

CD-ROM-Included! Includes time-saving Matlab® source code for the problems presented in the book which can be easily modified to help you solve similar problems in the field.

Product Details

ISBN-13:	9781596933859
Publisher:	Artech House, Incorporated
Publication date:	09/30/2008
Series:	Artech House Electromagnetic Analysis Series
Pages:	528
Product dimensions:	7.20(w) x 10.20(h) x 1.30(d)

About the Author

Ramesh Garg is a professor in the Electronics and Electrical Communication Engineering Department at the Indian Institute of Technology, Kharagpur, India. He earned his M.Sc. and Ph.D. in physics at Panjab University and the Indian Institute of Technology, respectively.

Table of Contents

Basic Principles of Electromagnetic Theory - Maxwell's Equations. Constitutive Relations. Electrical Properties of the Medium. Interface and Boundary Conditions. Skin Depth. Poynting Vector and Power Flow. Image Currents and Equivalence Principle. Reciprocity Theorem. Differential Equations in Electromagnetics. Vector Potentials. Phase Velocity, Group Velocity and Dispersion, Characteristics of Transmission Lines. Charge and Current Singularities. Classification of Methods of Analysis. Mathematical Framework in Electromagnetics. Overview of Analytical and Computational Methods.

Analytical Methods and Orthogonal Functions - Introduction. Method of Separation of Variables. Orthogonality Condition. Sturn-Liouville Differential Equation. Eigenfunction Expansion Method. Vector Space/Function Space. Operators and their Matrix Representation. Delta-Function and Source Representations.

Green's Functions - Introduction. Direct Construction Approach for Green's Function. Eigenfunction Expansion of Green's Function. Green's Function in Spectral Domain. Examples. Green's Function for Unbounded Region.

Contour Integration and Conformal Mapping - Introduction. Calculus of Residues. Evaluation of Definite Improper Integrals. Conformal Mapping of Complex Functions. Schwarz-Christoffel Transformation. Quasi-Static Analysis of Planar Transmission Lines. Some Useful Mappings for Planar Transmission Lines.

Fourier Transform Method - Introduction. Reduction of PDE to Ordinary Differential Equation/Algebraic Equation. Solution of Differential Equations with Unbounded Regions. Radiation from Two-Dimensional Apertures. Stationary Phase Method. Green's Function for the Quasi-Static Analysis of Microstrip Line.

Introduction to Computational Methods - Elements of Computational Methods. Basis Functions. Convergence and Discretization Error. Stability of Numerical Solutions. Accuracy of Numerical Solutions. Spurious Solutions. Formulations for the Computational Methods.

Method of Finite Differences - Finite Difference Approximations. Treatment of Interface and Boundary Conditions. Numerical Dispersion. Finite Difference Analysis of Guiding Structures: Microstrip Line, Ridge Waveguide, etc.

Finite Difference Time Domain Analysis - Pulse Propagation in a Transmission Line. FDTD Analysis in One-Dimension. Applications of One-Dimension Analysis to Reflection at an Interface, Propagation Constant Determination, Material Absorber Design. FDTD Analysis in Two- and Three- Dimensions. Implementation of Boundary Conditions in FDTD. Advances in FDTD.

Variational Methods - Calculus of Variations. Stationary Functional and Euler Equations. The Ritz Variational Method and its Applications to the Solution of Laplace Equation. Waveguide Modes and Resonant Frequencies of Cavities. Construction of Functionals from PDE. Method of Weighed Residuals.

Finite Element Method - Basic Steps in Finite Element Analysis. FEM Analysis in One- and Two-Dimensions. Rectangular and Triangular Elements. Mesh Generation. Weighted Residual Formulation for FEM. Examples: Inhomogeneously Filled Capacitor, Cut-off Frequency of Waveguide Modes, etc.

Method of Moments - Introduction. Solution of Integral Equations Using MoM. Fast Multipole Solution Methods for MoM. Comparison of FDM, FDTD, FEM, and MoM. Hybrid Computational Methods. Examples: Charge Distribution on a Wire, Stripline Analysis, Wire Dipole Antenna, Scattering from a Conducting Cylinder, etc.

Appendices. About the Author. Index.