5.1 Introduction

The simple cylindrical dielectric resonator (DR) models described in Ch. 4 are approximate, since they postulate non-Maxwellian fields as the point of departure. Although these simple models are useful as aids in understanding the principles of operation of DRs, and they may be helpful at initial stages of the analysis or design process, they fail to provide the high accuracy usually required in present-day microwave circuit design. As a result, more sophisticated (and accurate), rigorous techniques have been recently developed which allow one to take into account the influence of the environment on the characteristics of a DR. These techniques are rigorous in the sense that the solution is obtained in the form of successive approximations converging toward the exact solution. Therefore, at least in principle, they allow one to compute both the resonant frequency and the field distribution to any desired accuracy.

The purpose of this chapter is twofold: first, to survey the rigorous techniques available for the analysis of DRs and, second, to present selected numerical results obtained by these techniques. We only consider circular-cylindrical (pillbox or disc) and tubular (ring) resonators, since these are the shapes most often encountered in practice. Also, we direct most of the attention to the analysis of shielded DRs, i.e., resonators placed in a parallel-plate waveguide or in a cylindrical cavity (possibly on a substrate), as illustrated in Fig. 5.1. (Since this structure exhibits rotational symmetry with respect to the z axis, only one half of the...