Stabilized Sanathanan-Koerner Iteration for Rational Transfer Function Approximation of Scattering Parameters

Abstract

The vector-fitting algorithm has been the predominant method of macromodeling of high-frequency circuits for the past 20 years. Vector fitting is based on a partial-fractions basis to avoid the ill-conditioning of the Vandermonde matrices in direct fitting of the polynomial coefficients of a rational function. In a recent formulation of the Sanathanan- Koerner iteration, an orthogonal basis is obtained using the Arnoldi iteration significantly improving the conditioning and accuracy of rational approximation. This Stabilized Sanathanan-Koerner (SSK) iteration has been mostly applied on closed-form functions or data with no noise. We will utilize this SSK formulation for high-frequency package interconnect macromodeling. The method will be tested using empirical scattering parameters on a noisy transmission line system. The resultant curve fit will then be compared to several other polynomial and rational linear approximation methods, including the standard polynomial approximation. We show that the SSK method compares favorably to these different methods and provide a curve fit that can provide a reasonable approximation over different frequency ranges.