Solving the double eigenvalue problem: a study of mode matching in arbitrary-layer dielectric resonators

Abstract

The mode matching method of dielectric resonator analysis is capable of high accuracy calculation of sample permittivity and loss. However, it is generally only used for 3-layer resonators because of difficulties solving an 'internal' eigenvalue problem. Here we show how this may be done and hence extend the method to any number of layers. We achieve this by detailed analysis of the internal secular equation noting the existence of 'false roots' of this equation where the determinant vanishes without yielding a root. (We show how such pitfalls may be avoided.) The resulting algorithm is used, in particular, to model a novel 7-layer 14 GHz split post resonator which is capable of high accuracy measurements of 0-0.5 mm thick samples. This resonator. combined with our new computer simulation technique allows accurate measurement of thin sample permittivity and loss. We also present a comparison of our simulation with other programs to indicate accuracy. Such software validation is important in obtaining traceable, accurate measurements. We restrict analysis to the TE 0np modes and consider only the real eigenvalue problem.