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.