Interpolation of amplitude-only S-parameter data of passive integrated devices in the frequency domain using the Cauchy Method

This paper deals with the application of the Cauchy Method to interpolate the S-parameter of a passive integrated device of which amplitude-only data over a given frequency band are known. An approximation of the amplitude-only data by a ratio of two polynomials is done. The coefficients of the polynomials depend on the data set itself. 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 a Singular Value Decomposition (SVD) is used to properly estimate the dimension of the null space, and hence calculate the value of the coefficients. Once these coefficients are computed using the amplitude-only S-parameter data, the response can be interpolated over other frequencies of interest. A numerical example is provided to show the applicability of the Cauchy Method in interpolating the amplitude-only S-parameter data over a whole frequency band.