Electrical and Computer Engineering ETDs

Publication Date

5-5-1972

Abstract

This dissertation presents a general theory for the solution of electromagnetic boundary value problems for regions which are not homogeneous. The theory begins with the wave equation in Fourier frequency domain for the electric field in the interior of a closed volume; the electromagnetic property parameters, specifically conductivity and dielectric constant, are written as functions of position. The wave equation, which holds throughout the interior of the closed volume, is then converted to an integral equation by use of a Green's function for the same volume containing a homogeneous medium. Boundary conditions between homogeneous regions inside the closed volume appear as sources in the integral equation. The same theory applies to a closed region in which the parameters vary smoothly, rather than discontinuously, as a function of position. The theoretical development is first presented, and the remainder of the paper illustrates the theory in the solution of a problem arising from the study of internal electromagnetic pulse phenomena. The problem consists of determining the electric field in the interior of a two­dimensional rectangular cavity excited by a source current density specified throughout the cavity. The walls of the cavity are assumed to be perfectly conducting. The cavity contains a single rectangular inhomogeneity, or object. The example problem is worked in rectangular coordinates for clarity of presentation. Although the object treated in the presentation is rectangular, any other object of regular shape could be treated just as well in this coordinate system. The choice of coordinate system is determined by the homogeneous cavity walls. In rectangular coordinates, the integral equation for each component of the electric field reduces to an algebraic equation. In this paper, the algebraic equations are solved by an iterative process which requires that the parameter changes in the inhomogeneity be small. Results are presented for the cavity containing a conductive inhomogeneity and for the cavity containing a dielectric inhomogeneity with a higher dielectric constant than the rest of the cavity. Further applications of the theory are suggested.

Document Type

Dissertation

Language

English

Degree Name

Electrical Engineering

Level of Degree

Doctoral

Department Name

Electrical and Computer Engineering

First Committee Member (Chair)

Ahmed Erteza

Second Committee Member

Martin D. Bradshaw

Third Committee Member

David E. Merewether

Fourth Committee Member

Shlomo Karni

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