Dielectric measurements using an open resonator
This thesis describes a new method of measuring dielectric constants and loss tangents using an open resonator. The dielectric constant measurement method consists basically of perturbing the resonant frequency of an open resonator by placing a dielectric sample at the centre of the resonator normal to its axis. By measuring the resonant frequency of a symmetrical mode and of the adjacent lower-frequency asymmetrical mode, the dielectric constant can be determined. Based on the Gaussian beam theory, a pair of transcendental equations, one for each mode, are derived by assuming first the surfaces of the dielectric sample are spherical and coincident with the phase fronts of the resonator modes. These equations can easily be solved for the refractive index n, by using a computer. When sample in sheet form is measured, the results can be corrected to account for the error so introduced. The formula giving this correction is derived by using the perturbational technique. From these two equations, two sets of approximate formulas are also derived for the determination of the dielectric constant. An important feature of these formulas is that they are algebraic expressions, but reduction in their accuracy occurs if the sample is nearly a multiple of half wavelengths thick. The loss tangent is determined by the measurements of Q of the perturbed and the unperturbed resonator. Based on the usual definition of Q, an algebraic-expression is derived relating the loss tangent to the experimentally measurable quantities. Measurements of dielectric constants and loss tangents of polystyrene and perspex have been made at X-band frequencies and the results are presented. It is on these results that the accuracy of ±0.25% for measuring dielectric constant is claimed. The accuracy of the loss tangent measurement is estimated to be about ±10%. The method is applicable to the measurements of both low-loss and high-loss materials, and becomes more accurate at shorter wavelengths.