The Rigorous and Approximate Theories of Electrical Transmission Along Wires

HE theory of electrical transmission along straight parallel guiding conductors is of fundamental importance to the communication engineer. In its original, and largely in its present day form, it involves only relatively simple concepts which go back to the early work of Kelvin and Heaviside. In accordance with these concepts the transmission phenomena are completely determined by the self and mutual impedances of the conductors and the self and mutual capacities (together with the dielectric leakage). As a consequence, the phenomena are completely expressed in terms of the propagation constants and corresponding characteristic impedances of the possible modes of propagation deducible from these underlying concepts. The elementary theory sketched above is of beautiful simplicity and great value. It is, however, admittedly approximate, and in two respects is not altogether adequate. Its first defect is that it represents the transmission phenomena correctly only at some distance from the physical terminals of the system or at some distance from points of discontinuity. This defect is ordinarily of small practical significance when the conductors all consist of wires of small cross section. When, however, conductors of large cross sections, or the ground, form part of the transmission system, the elementary theory may be quite inadequate. The theoretical questions here involved were briefly discussed by the writer in a previous paper. 1 The mathematics involved in this problem are extremely complicated and the further work of the writer has not as yet been carried to a point which justifies publication.