Surface wave transmission line theory for single and many wire systems

Abstract

Examining cables using the many conductor transmission line theory has shed light on the modes supported by various cable types. However, so far, the theory disregards the fundamental surface wave mode whose lateral confinement increases with frequency and hence is expected to play an important role in high-frequency applications. To address this issue, we propose an extension to the theory that incorporates surface waves on uncoated, cylindrical wires. Crucially, this requires new definitions of the per unit length transmission line parameters, which are derived using the single wire surface wave solution. By closely examining a two-wire and a three-wire system, we show that these new parameters can predict surface waves as well as modes found using conventional many conductor transmission line theory. Furthermore, all calculated modes are validated experimentally by diagonalization of a measured coupling matrix. Additionally, the propagation constants for the modes predicted by the model are validated against full numerical simulations. Good agreement is observed when proximity effects can be neglected.