Title

Computation of the resonant frequency of a dielectrometer by the method of moments

Date of Award

2005

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Electrical Engineering and Computer Science

Advisor(s)

Ercument Arvas

Keywords

Resonant frequency, Dielectrometer, Method of moments, Body of revolution

Subject Categories

Electrical and Computer Engineering | Engineering

Abstract

In this thesis, a method of obtaining the dielectric constant (relative permittivity) of a sample of dielectric material is described. Insertion of a dielectric sample into an empty cavity will lower the resonant frequency of the cavity. In the method, a new numerical solution by the method of moments is programmed on a digital computer to calculate the resonant frequency of the cavity when it contains a hypothetical sample whose dielectric constant is an arbitrarily chosen number. This numerical solution is then used to plot a curve of the resonant frequency versus the dielectric constant of the hypothetical inserted sample for the range of dielectric constant in which the dielectric constant of the actual sample is thought to be. The dielectric constant for which the resonant frequency is equal to the resonant frequency that is measured when the actual sample is inserted into the cavity is then the dielectric constant of the actual sample.

Called the dielectrometer, the cavity possesses the rotational symmetry of a body of revolution. The resonant field in it is assumed to be not much different from the TE 011 circular cavity mode. A gap in the perfectly conducting walls allows for insertion of the dielectric sample. After the dielectric sample is inserted, the interior of the cavity is divided into three regions: the dielectric region and two separate regions outside the dielectric. In the numerical solution by the method of moments, the electromagnetic field in each region is produced by surface currents on the boundary of each region. Boundary conditions give surface integral equations which are solved by the method of moments. Advantage is taken of both rotational symmetry and symmetry about a central plane. Dielectric constants obtained by using the method described in this thesis are in excellent agreement with other results.

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