Date of Award

Fall 1995

Document Type

Thesis

Degree Name

Master of Science in Electrical Engineering - (M.S.)

Department

Electrical and Computer Engineering

First Advisor

Edip Niver

Second Advisor

Gerald Martin Whitman

Third Advisor

Ali N. Akansu

Abstract

The Gabor representation in the context of an aperture problem is an expansion of a radiated field in terms of a discrete set of linearly shifted and spatially rotated elementary Gaussian beams. The parameters that can be varied in this summation are the number of beams and corresponding beam widths. As the difficulty associated with the unique determination of the expansion coefficients was alleviated, the method has been successfully applied to one and two dimensional apertures. Although, the asymptotic evaluation of expansion functions has reduced the computational burden drasticallym it was at the expense of some loss in accuracy. The numerical experiments have established that the narrow beam algorithm with almost a priori predictability can be used in a variety of problems. Here, the Gabor representation has been applied to a narrow rectangular aperture illuminated with a sinusoidal field. The narrow aperture (height >> width) excited by sinusoidal field distribution approximates an equivalent dipole with a similar current distribution with only exception that aperture radiates into a half-space whereas 'the dipole covers the entire space. Utilizing the narrow beam algorithm, once the expansion coefficients were determined, the radiated electric field potential in near, mid and far zones were evaluated. The criteria in determining the number of expansion coefficients was based on re-generation of the aperture field distribution with sufficient accuracy. It was observed that even though wide beam algorithm was applied, less number of terms resulted in erroneous side lobes and higher number of terms caused Gibbs phenomena in the region close to the aperture plane. The numerical evaluations are carried out for the half-wavelength high narrow aperture. Far zone numerical results of radiated potential utilizing Gabor expansion are compared to analytical expressions determined via Fourier transform. The unique application developed in this work in expressing the radiated field of an equivalent dipole antenna revealed that Gabor expansion can be a valuable tool in studying practical radiation and propagation problems.

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