Surface Wave Transmission Line Theory for Single and Many Wire Systems

TL;DR

This paper extends the traditional transmission line theory to include surface wave modes on cylindrical wires, providing improved predictions for high-frequency cable behavior validated through experiments and simulations.

Contribution

It introduces new definitions of transmission line parameters that incorporate surface waves, enhancing the modeling of multi-wire systems at high frequencies.

Findings

Surface wave modes are successfully predicted by the extended theory.

Experimental validation confirms the accuracy of the new parameters.

Good agreement with numerical simulations when proximity effects are negligible.

Abstract

Examining cables using 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 which 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 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 channel transfer matrix. Additionally, the theoretically predicted propagation constants for the modes are validated against full numerical simulation for the two wire case and good agreement is observed when proximity effects can be neglected.