Orthogonal Rational Approximation of Transfer Functions for High-Frequency Circuits

TL;DR

This paper introduces Orthogonal Rational Approximation (ORA), a stabilized and efficient method for high-frequency circuit transfer function approximation that ensures real coefficients and stable poles.

Contribution

It extends the stabilized Sanathanan-Koerner iteration with an orthogonal basis to improve approximation stability and realizability in high-frequency circuit modeling.

Findings

Ensures real polynomial coefficients in approximations.

Provides stable poles for electrical network realizability.

Offers an efficient multi-port network implementation.

Abstract

Rational function approximations find applications in many areas including macro-modeling of high-frequency circuits, model order reduction for controller design, interpolation and extrapolation of system responses, surrogate models for high-energy physics, and approximation of elementary mathematical functions. The unknown denominator polynomial of the model results in a non-linear 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 Orthogonal Rational Approximation (ORA), which ensures real polynomial coefficients and stable poles for realizability of electrical networks. We also introduce an efficient implementation of ORA for multi-port networks based on a block QR decomposition.