Orthogonal rational approximation of transfer functions for high‐frequency circuits

Abstract

SummaryThis paper introduces the orthogonal rational approximation (ORA) algorithm for rational function approximation of transfer functions, based on data available from simulations or measurements. A rational function allows integration of such data in transient solvers for analysis of high‐frequency circuits. In rational function approximation, the unknown denominator polynomial of the model results in a nonlinear problem, which can be replaced with successive solutions of linearized problems following the Sanathanan–Koerner (SK) iteration. An orthogonal basis can be obtained based on Arnoldi resulting in a stabilized SK iteration. We present an extension of the stabilized SK, called ORA, which ensures real polynomial coefficients and stable poles for realizability of electrical networks. We also introduce an efficient implementation of ORA for multiport networks based on a block QR decomposition.