The synthesis of infinite lines

Abstract

The class of nonuniform lines having solutions which exhibit an out-going wave behavior at infinity and which have a rational input admittance is considered. Necessary and sufficient conditions are given for a rational function to be realizable as the input admittance of an infinite line. A closed-form expression is derived by means of which the characteristic impedance Z 0 ( x ) {Z_0}\left ( x \right ) of a line in this class can be constructed from its input admittance. It is shown that this solution to the synthesis problem is unique once the limiting value of Z 0 ( x ) {Z_0}\left ( x \right ) at infinity or at the input is specified. An example in the application of the technique is presented.