Mode Matching Solvers for Filters and Cavities

Over the past decades computational electromagnetics tools have become an indispensable aid for engineers and scientists. Partial Differential Equation techniques, with the Finite Element method being an example, are recognised as being the standard approach for the electromagnetic analysis of closed structures such as waveguide components and cavities. A major drawback of these techniques results from the fact that they require a spacesegmentation of the domain under consideration. If complex geometries or structures with dimensions exceeding few wavelengths are to be solved, the resulting meshes tend to become very large, which is undesirable in terms of memory requirements and computation time. In contrast, a striking feature of the Mode Matching technique discussed in this thesis is its ability to efficiently solve the field problem imposed by such structures, provided they can be decomposed into sub-domains whose spectrum of Eigenmodes is known analytically. Using the Mode Matching technique, orthogonal expansion of the yet unknown tangential fields at the interfaces between these sub-domains is performed, which leads to a system of equations that can be solved for the Eigenmodes' amplitudes. Several applications such as waveguide filter design strongly benefit from the Mode Matching technique's computational efficiency rather than they suffer from the geometric limitations resulting from the method's quasi-analytical approach. The present thesis provides a complete treatise of the Mode Matching technique. While literature has focused almost exclusively on the method's underlying electromagnetic concept, this work offers in-depth insights into implementation-related aspects such as efficient matrix population and proper scattering parameter calculation. To illustrate the advantages of the Mode Matching technique, the solvers developed in the scope of this thesis are used to analyse problems from two fields of application: The analysis of waveguide filters repre