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

This paper exhibits a third-order Newton process for approximating
(l/s)^{1/n}
, the general fractional capacitor, for any integer
n
> 1. The approximation is based on predistortion of the algebraic expression
f(x) = x^{n} - a = 0
. The resulting approximation in real variables (resistive networks) has the unique property of preserving upper and lower approximations to the
n
th root of the real number
a
. 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.