The Analytic Extraction of the Complex-Valued Coupling Matrix and its Application in the Microwave Filter Modeling

The idea behind the coupling matrix identiflcation is to flnd the coupling matrix corresponding to the measured or designed scattering characteristics of the microwave fllter. The typical attitude towards coupling matrix parameter extraction is to use some optimization methods to minimize the appropriate cost function. In this paper, we concentrate on the analytic solutions | how they may be found and their application in further optimization processes. In general case, the suggested method generates complex-valued coupling matrix. For a special case of the fllter without cross-couplings we give fast and simple recursive method of flnding such complex- valued coupling matrix. The method is based on Laplace's formula for expanding the determinant. The complex-valued coupling matrix is used as a good starting point for the optimization methods to flnd the regular coupling matrix. The examples are presented showing that the optimization arrives to global minimum starting from real parts of complex-valued entries considerably more often than when the starting point is selected randomly.

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