Matrix Approximation Techniques for Symbolic Extraction of Poles and Zeros

Several recently published approaches to symbolic pole/zero analysis of analog circuits exploit the order reduction effect of Simplification Before Generation (SBG) techniques 1]. SBG methods allow the extraction of symbolic expressions for poles and zeros by computing local low-order approximations of transfer functions whose roots can be calculated analytically. In this article we present a new matrix-based SBG method for pole/zero analysis which simplifies a symbolic generalized eigenvalue problem with respect to a selected root. The method uses a fast linear error estimation formula based on eigenvalue sensitivities to obtain a term ranking. Accurate and efficient error control is achieved by tracking eigenvalue shifts numerically using an iterative generalized eigenvalue solver. The new algorithm is capable of computing real and complex dominant as well as unobservable poles and zeros.