TEM modes in parallel-line transmission structures

A transmission structure of many parallel conductors is capable of propagating many distinct quasi-TEM modes. A field theory of such modes is developed for a theoretically infinite number of very thin conductors. These possess infinitely many distinct propagation modes, which are the eigenfunctions of a pair of integral operators with Green's function kernels. The modes depend strongly on the structure cross-sectional shape and size, only slightly on the number and placement of individual conductors. The theory is illustrated by a structure comprising many thin parallel wires on a dielectric substrate backed by a ground plane, whose modal functions and velocity distributions are used to solve a simple crosstalk problem