The Synthesis of Nonuniform Lines of Finite Length-Part I

The class of lossless, nonuniform transmission lines having an absolutely continuous characteristic impedance is considered. It is shown that an integral representation for the solution of such a line is possible when the line is terminated in a matched load. The principal contribution of this paper is the derivation of a linear integral equation in the kernel function of this representation. It is shown that the solution to this integral equation constitutes a unique solution to the synthesis problem for lines of the class considered. Necessary and sufficient conditions for realizability are also given.