ABSTRACT

Since the first studies developed by S. B. Cohn in the late 1960s, high-Q dielectric resonators have been employed to design
microwave bandpass filters. Once new dielectric materials with suitable electrical properties and temperature
stability were proposed in the 1970s, dielectric resonators became a key element in many filtering applications.
Indeed, dielectric-loaded waveguide filters are frequently found in satellite and mobile communication systems, due to their advantages in terms of mass and volume reduction, low losses, and thermal stability. For these reasons, the full-wave analysis and design of such filters has deserved considerable attention in the technical literature.

The main objective of this PhD thesis is the development of an efficient modal technique to characterise the electromagnetic behaviour of dielectric-loaded cavity resonators. For such purpose, a new state-space integral-equation (SS-IE) formulation in the $s$-domain, based on the boundary integral-resonant mode expansion (BI-RME) method, is presented. In order to solve the volume integral equation proposed, the dielectric resonator is rigorously characterized by means of the electric equivalent polarization charge and current densities defined in the volume of the dielectric object. Following this method, the resonant modes of the considered cavities are obtained through the solution of a linear matrix eigenvalue problem. Furthermore, a pole expansion of the generalized admittance matrix of the dielectric-loaded cavity is obtained in the domain of the Laplace variable. Hence, the electromagnetic behaviour of the cavity resonators can be solved in a wide and dense frequency range with a very reduced computational effort, avoiding to perform intensive computations at each frequency point.

The formulation developed has been applied to analyse rectangular cavities loaded with cylindrical dielectric resonators. The implemented code has been integrated into a Computer Aided Engineering (CAE) tool for the analysis and design of passive microwave and millimetre waves components. This CAE tool is a general purpose electromagnetic solver based on adevanced modal techniques. Thus, a very efficient software tool for the full-wave analysis of dielectric resonator filters has been developed. Indeed, different bandpass and stopband single-mode filters have been designed using the new software tool. The numerical results provided by this tool have been successfully compared with those included in the technical literature, as well as with those provided by a well-known commercial code based on the finite-element  method. It has been proved that the implemented method is very accurate and computationally efficient, thus making it very suitable for the optimized design of waveguide filters including dielectric resonators.