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

Abstract

Abstract-The idea behind the coupling matrix identification is to find the coupling matrix corresponding to the measured or designed scattering characteristics of the microwave filter. 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 filter without cross-couplings we give fast and simple recursive method of finding such complexvalued 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 find 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.

Diagnosis of Coupled Resonator Bandpass Filters Using Vf and Optimization Method

“…Early filter diagnosis techniques can be traced back to the 1970s and 1980s [1,2]. In the past years, interest is growing on the filter diagnosis methods for extracting the coupling matrix of microwave filters from the measurements (or simulations) with losses [3][4][5][6][7][8][9][10][11][12][13][14][15]. These filter diagnosis or coupling matrix (CM) extraction techniques require two sorts: 1) CM extraction techniques are based on optimization (as in [3][4][5]) for matching the measured scattering parameters, whose elements are the problem unknowns.…”

“…In the past years, interest is growing on the filter diagnosis methods for extracting the coupling matrix of microwave filters from the measurements (or simulations) with losses [3][4][5][6][7][8][9][10][11][12][13][14][15]. These filter diagnosis or coupling matrix (CM) extraction techniques require two sorts: 1) CM extraction techniques are based on optimization (as in [3][4][5]) for matching the measured scattering parameters, whose elements are the problem unknowns. The optimization techniques are either greatly influenced by the initial values assigned to the variables, number of the resonators and topology of the filters, or are time consuming; and 2) CM extraction techniques are based on a polynomial model, which matches the measured (or the simulated) parameters and then extract the CM of the filter with a specified topology (by using well-known established methods as in [16]).…”

New Negative Coupling Structure for Substrate-Integrated Cavity Resonators and Its Application to Design of an Elliptic Response Filter

“…As wireless communications systems have required tighter microwave filter specifications, a tremendous amount of studies has been devoted to developing new filter design theories and topologies [1][2][3][4][5][6][7][8]. Recently, studies on negative coupling structures have presented physical realization of frequency responses with transmission zeros that enhance the frequency selectivity.…”

Filter Tuning Based on Linear Decomposition of Scattering Characteristics

“…The advantage of the coupling matrix is that its entries are directly related to the position of the physically tunable elements. Recently researches have reported new methods of coupling matrix synthesis [12][13][14][15][16][17]. When dealing with (N +2)×(N +2) coupling matrix formulas for reflection S 11 and transmission S 21 are as follows [18]:…”