Pole and zero estimation in linear circuits

Abstract

A unified method for fast, accurate estimation of dominant and nondominant poles and zeros of linear active circuit transfer functions is presented. The basis for both pole and zero estimates is an efficiently computed time-constant matrix. The major computation in the estimation process involves only the solution of linear equations, which are independent of capacitor values. This feature permits the implementation of fast real-time dominant pole-zero design based on capacitor variation. Formulas with concomitant applicability criteria are developed for estimating the four most dominant poles and zeros of a transfer function. A broad range of circuit examples is included to demonstrate the power and relative accuracy of different orders of approximation through fourth order.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>