Solution of discrete modes for wave propagation along multiple conductor structures above a dissipative Earth

Abstract

The discrete propagating modes for an N-conductor transmission line located above a dissipative Earth are determined. The boundary-value problem is solved using a Fourier transform approach that results in a set of Sommerfeld-type integrals, whose accurate evaluation is shown to become imperative at higher frequencies. Because the integrand of one of the integrals exhibits a pair of first-order poles, a significantly different solution to the customary transmission line dispersion equations is obtained, and additional discrete modal solutions become mathematically feasible in the neighbourhood of the poles. An analytical expression is presented for the general evaluation of the multiple-conductor transmission line problem. A parametric study of the discrete propagating modes for typical single- and two-conductor systems is made and discussed. The validity of a simplified quasi-transverse-electromagnetic approach as well as a small-argument expansion are also presented.