Electromagnetic propagation along a multiconductor transmission line in a tunnel--approximate analysis

A general approximate formalism is presented which enables one to calculate in a simple manner the electromagnetic propagation characteristics of a multiconductor transmission line in an underground tunnel. This approach circumvents the tedious task of locating the complex roots of the exact mode equation. The formalism is based on an approximate treatment of the single-wire case due to Wait.
\Lambda, \Omega
, and
Z_{s}
in Wait's single wire formula for the propagation constant are replaced with corresponding quadratic forms in the eigenmodal wire currents to generalize the formula to an arbitrary number of wires. The foundations of this approximate approach in standard perturbation theory are indicated, lending physical meaning to the approximations. A simple example involving a two-wire line is presented to establish the order of accuracy to be expected in using this formalism.