Computer Techniques for Electromagnetics

Preface


1. A Brief Preview

References


2. Wire Antennas


2.1. Introduction


2.2. Integral Equations for Wire Antennas


2.2.1. A Volume Equivalence Theorem


2.2.2. Pocklington's Integral Equation


2.2.3. Hallen's Integral Equation


2.3. Method of Moments


2.3.1. Galerkin's Method


2.3.2. Point-matching


2.4. Bases


2.4.1. Entire-domain Bases


2.4.2. Sub-domain Bases (Segmentation)


2.4.3. Some Common Basis Functions


2.4.4. A Basis Transformation Method


2.4.5. Piecewise-sinusoidal Basis: Reaction-matching


2.4.6. Characteristic Mode Currents: An Eigenvalue Problem


2.4.7. The Stability Problem


2.5. Calculation of Antenna Characteristics


2.5.1. Current Distribution, Impedance and Lumped Loading


2.5.2. Radiation Patterns, Gain and Efficiency


2.6. The Yagi—Uda Array


2.6.1. The Integral Operator


2.6.2. Matrix Formulation


2.6.3. Far-zone Radiation


2.6.4. Current Distributions


2.6.5. Array Input Impedance


2.7. Electrically Small Antennas


2.7.1. Multiturn Loop Antenna


2.7.2. TEM-line Antenna with Loading


2.8. Modeling of Wire Antennas on Metallic Bodies


2.8.1. Monopole or Circular Slot in the Base of a Cone


2.8.2. Small Loops of TEl Line on an Aircraft


2.9. Conclusions and Acknowledgment


2.10. Exercises

Appendix I. Fields of a Magnetic Frill Current

Appendix II. Calculation of Characteristic Mode Currents

Appendix III. Fortran IV Program for Wire Antennas on Metallic Bodies

References


3. Numerical Solution of Electromagnetic Scattering Problems


3.1. Introduction


3.1.1. General Discussion


3.1.2. Computational Aspects


3.2. Theory


3.2.1. Matrix Formulation


3.2.2. Evaluation of the Transition Matrix


3.2.3. Application to Special Geometries


3.2.4. Results for Finite Cylinders and a Cone—Sphere


3.3. Organization of the Computer Program


3.3.1. Introduction


3.3.2. Glossary of the Subroutines


3.3.3. The Input Routine


3.3.4. Calculation of End Points and Spacing for Integration


3.3.5. The First Control Routine


3.3.6. Associated Legendre Functions


3.3.7. Bessel Functions


3.3.8. Recursion Relationships for Bessel and Neumann Functions


3.3.9. Generating the Body Shape


3.3.10. First Matrix Printout


3.3.11. Printout of an Array


3.3.12. Generating the Q Matrix and the T Matrix


3.3.13. Normalizing Matrices


3.3.14. Conditioning Matrices


3.3.15. Printing the [Ti Matrix


3.3.16. Final Control Routine


3.3.17. Multiplying a Matrix Times a Vector


3.3.18. Core Dump


3.3.19. Storage Arrangements

Appendix I. The Fortran IV Program Listing

References


4. Integral Equation Solutions of Three-dimensional Scattering Problems


4.1. Introduction


4.2. The Integral Equations of Electromagnetic Theory


4.2.1. The Derivation of Space-Frequency Domain Integral Equations


4.2.2. The Derivation of Space—Time Domain Integral Equations


4.2.3. Tabulation of Integral Equations


4.3. Numerical Solution Methods


4.3.1. Frequency Domain Solutions


4.3.2. Time-Domain Solutions


4.3.3. Additional Considerations


4.4. Applications


4.4.1. Frequency-Domain Examples


4.4.2. Time-Domain Examples


4.5. Concluding Remarks

References


5. Variational and Iterative Methods for Waveguides and Arrays


5.1. Scattering from an Infinite Grating of Metallic Strips


5.2. Variational Principle, Method of Moments and Iterative Methods


5.2.1. Variational Principle


5.2.2. Method of Moments


5.2.3. Iterative Methods


5.3. Step Discontinuity in Circular Waveguides (Mode Conversion Applications)


5.4. Transition Between a Straight and a Continuously Curved Waveguide


5.4.1. Waveguide Modes in Curved Waveguides


5.4.2. Formulation of the Integral Equation


5.4.3. Application of the Moments Method


5.4.4. Special Computational Problems


5.5. Dielectric Slab-Covered Waveguide Antenna


5.6. Double Discontinuity Problems


5.6.1. Coupled Integral Equations for Double Discontinuity Problems


5.6.2. Band Rejection Filter in Coaxial Waveguides


5.7. Concluding Remarks

Appendix. Convergence Test and the Relative Convergence Problem

References


6. Some Numerically Efficient Methods


6.1. Introduction


6.2. Analysis of Microstrip Lines


6.2.1. Introduction and Description of the Problem


6.2.2. Formulation of a Boundary Value Problem in Spectral Domain


6.2.3. Modified Residue Calculus Technique


6.2.4. Numerical Computation


6.2.5. Numerical Results


6.3. Diffraction Grating


6.3.1. Description of the Problem


6.3.2. Formulation in the Spectral Domain


6.3.3. MRCT Method of Solution


6.3.4. Numerical Procedure


6.3.5. Numerical Results


6.4. Dielectric Step in a Waveguide


6.4.1. Introduction and Problem Description


6.4.2. Formulation of the Problem


6.4.3. Method of Solution


6.4.4. Numerical Considerations


6.4.5. Numerical Results


6.5. The Generalized Scattering Matrix Method for Solving Discontinuity Problems


6.5.1. Introduction


6.5.2. Generalized Scattering Matrix Analysis of a Thick-Walled Phase Array


6.5.3. Method of Solution for the Thick-Walled Phased Array


6.5.4. Considerations for the Numerical Calculation


6.5.5. Numerical Results

References

Problems


7. Inverse Scattering and Remote Probing


7.1. Introduction


7.2. The Two-Dimensional Inverse Scattering Problem


7.2.1. Statement of the Problem and Preliminaries


7.2.2. Numerical Processing of Pattern Function to Derive Object Shape


7.2.3. Summary of Computational Procedure for Inverse Scattering


7.2.4. Numerical Results


7.3. Remote Probing of Antenna Apertures by Holographic Techniques


7.3.1. Description of the Problem


7.3.2. Analytical Development


7.3.3. Numerical Procedure


7.3.4. Numerical Results


7.4. Antenna Power Pattern Synthesis


7.4.1. Introduction and Description of Problem


7.4.2. Formulation of Problem


7.4.3. Numerical Considerations


7.4.4. Numerical Results


7.5. Remote Probing of Inhomogeneous Media


7.5.1. Introduction


7.5.2. Linear Approach


7.5.3. Parameter Optimization Method of Solution


7.5.4. Numerical Considerations


7.5.5. Numerical Results


7.6. Numerical Aspects of Wavefront Reconstruction Using Matrix Methods


7.6.1. Introduction


7.6.2. Analytical Background


7.6.3. Numerical Experiment


7.6.4. Numerical Results

Appendix A. Optimization Methods

Appendix B. The Use of the Fast Fourier Transform Algorithm

References

Index