مرکز منطقه ای اطلاع رساني علوم و فناوري - Approximation of Fractional Capacitors <img src="/images/tex/213.gif" alt="(1/s)^(1/n)"> by a Regular Newton Process

DocumentCode :

1158860

Title :

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

Author :

Carlson, G.E. ; Halijak, C.

Volume :

Issue :

fYear :

1964

fDate :

6/1/1964 12:00:00 AM

Firstpage :

210

Lastpage :

213

Abstract :

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.