Interpolation and Extrapolation of S-Parameter Data of a Microwave Filter in the Frequency Domain Using the Cauchy Method

The interpolation and extrapolation of complex S-parameter data using the Cauchy method is described. An approximation of the complex S-parameter data is accomplished by a ratio of two polynomials. By applying the Cauchy method, an electromagnetic system is represented by a set of poles and zeros in the s-plane. The Total Least Squares (TLS) implementation of the Singular Value Decomposition (SVD) is used to estimate the dimension of the null space and hence calculate the value of the coefficients of the polynomials. Once these coefficients are computed, the complex S-parameter data can be interpolated or extrapolated over other frequencies of interest. A numerical example is provided to show the applicability of the Cauchy method in interpolating or extrapolating the complex S-parameter data over a whole frequency band including the pass and the stop bands.