Exact solutions for a generalized class of non-uniform transmission lines†

†Communicated by the Authors.

Abstract

Exact solutions for general non-uniform lines, whose patterns of non-uniformity for series impedauce Z(x) and shunt admittance Y(x) are arbitrary and independent of each other, have not been obtained (Gough and Gould 1996, Protonotarios and Wing 1965). This paper presents a voltage-solution for a general non-uniform line for which f(x) and y(x) defining the distributions of non-uniformity of Z(x) and Y(x) respectively, satisfy the relationship :

g(x) = k₂ f(x) { k₁ − a ∫ f(x) dx }^u.

Here k₁, a and n are arbitrary constants and k₂ is any constant≠0, with f(x) an arbitrary function of the distance variable x. Besides making available the solutions for a wide range of non-uniformities, it has been shown that most of the solvable non-uniformities described in the previous literature (Dutta Roy 1963, 1965, Hellstrom 1962, Holt and Ahmed 1968 b, Jacob 1959, Swamy and Bhattacharyya 1960 a) are obtainable as special cases for the generalized results presented here.

Notes

†Communicated by the Authors.