Jacek Gulgowski

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 Laplaces 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.

Approximation of solutions to second order nonlinear Picard problems with Carathéodory right-hand side

We present an approximation method for Picard second order boundary value problems with Carathéodory righthand side. The method is based on the idea of replacing a measurable function in the right-hand side of the problem with its Kantorovich polynomial. We will show that this approximation scheme recovers essential solutions to the original BVP. We also consider the corresponding finite dimensional problem. We suggest a suitable mapping of solutions to finite dimensional problems to piecewise constant functions so that the later approximate a solution to the original BVP. That is why the presented idea may be used in numerical computations.

Influence of number of frequency points on rational function's zeroes and poles reliability in microwave filter tuning

In this paper it is investigated how the number of measured frequency points of reflection characteristics influences the behavior of its coefficients in the process of microwave filter tuning. The method used to identify the rational function corresponding to the reflection characteristics is Least Squares version of Cauchy interpolation technique. The number of frequency points required in the process must exceed certain level but there is no upper limit on the number of frequency points used. So the question appears how many points should be taken to have results that may be used in a reasonable way in the microwave filter tuning process. The certain measure of the quality of such approximations (stability of coefficients of scattering characteristics; stability of zeroes and poles of this characteristics) is suggested and experiment is described showing how this measure behaves in the process of microwave filter tuning. The stability measure for the sets of zeroes and poles is based on the Hausdorff distance of the finite subsets of the Euclidean space.