A Theoretical Synthesis of Coupling Matrix by Eigen Mode Expansion Method and Householder Transform

This paper presents a new theoretical synthesis method for the coupling matrix strictly based on the classical network synthesis theory. While the classical network synthesis theory based on the real rational functions is a well-established rigorous process, the coupling matrix method becomes popular, and is being widely used because of its flexible design capabilities. The coupling matrix method has, however, relatively ambiguous adaptability to the classical scheme, although many studies have been carried out to relate them to each other. This paper shows that the Eigen mode expansion method in corporation with the orthogonal symmetric transform by the Householder method enables an exact correspondence between them. To generalize and extend this process further, the Householder method is modified to be applicable to general cross coupling configurations. Finally, some design examples are provided.