Approximation of Fractional Capacitors(1/s)^(1/n)by a Regular Newton Process

Abstract

This paper exhibits a third-order Newton process for approximating(l/s)^{1/n}, the general fractional capacitor, for any integern> 1. The approximation is based on predistortion of the algebraic expressionf(x) = x^{n} - a = 0. The resulting approximation in real variables (resistive networks) has the unique property of preserving upper and lower approximations to thenth root of the real numbera. Any Newton process which possesses this property is regular. The real variable theory of regular Newton processes is presented because motivation lies in the real variable domain. Realizations of 1/3 and 1/4 order fractional capacitor approximations are presented.