Measurement of the Dielectric Constant of Anisotropic Dielectric Materials Using the Degenerated Modes of a Spherical Cavity

A spherical resonator has many advantages for measuring the dielectric constant of anisotropic dielectric materials. It is a resonator of high Q-factor, it can be excited easily, it has threefold degenerated eigenfrequencies, which split up if an anisotropic spherical probe is inserted into the cavity, and it is the only type of cavity which can be calculated exactly under consideration of the losses in its walls. An exact theory has been derived for a three-layer spherical cavity with arbitrary isotropic materials. Using this theory a measuring equipment is described to measure the complex dielectric constant of isotropic dielectric materials. Using the field solutions of the isotropic resonator it can be shown that the resonances of the spherical cavity with an anisotropic material probe can be described by coupled field modes of the isotropic resonator. The measurement equipment and the evaluation procedure of the measurements of the permittivity tensor of uniaxial anisotropic materials will be described.