Network Representation of Exponential Transmission Lines

The purpose of the paper is to show that by the use of the rational fraction expansion of transcendental functions, the exponential transmission line can be represented at all frequencies by networks comprising lumped elements. The open-circuited and the short-circuited exponential lines are first considered; it is shown that there are three forms to represent each of these. In the cases of the open-circuited divergent line and the short-circuited convergent line, all the three forms yield physically realisable elements. But, in the cases of the open-circuited convergent line and the short-circuited divergent line, two forms can be physically realised when the impedance transformation ratio lies below 7.389 and only one form is realisable when it exceeds 7.389. It is shown that the exponential transmission line can be synthesized either by the use of the open-circuit impedance functions or by the shortcircuit admittance functions, taking, in both cases, only the networks whose elements are physically realisable for any length of the line, thus constituting the two basic forms.