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

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2 Author(s)

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.

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Circuit Theory, IEEE Transactions on  (Volume:11 ,  Issue: 2 )