Mutual Impedances of Parallel Wires*

Abstract

This is a theoretical paper relating to circuits of straight parallel wires traversed by alternating currents under such conditions (frequency of the alternating currents, diameter and spacing of the wires) that the resulting non-uniformity of the current distribution is sufficient to play an important part in determining the mutual and self impedances. The paper deals primarily with the mutual impedances; but incidentally the self impedances are dealt with almost as fully, except that no numerical calculations are made for them. Part I is mainly a discussion of the physical nature of the mutual and self impedances in the generalized manner necessitated by the non-uniformity of the current distribution. It deals with wires which are short enough compared with the wave-length so that the complicating effects of propagation are negligible and so that the current in each wire can be regarded as an aggregate of filamentary currents. Part II establishes, by recourse to electromagnetic wave theory, calculation formulas for the mutual and self impedances per unit length of a pair of long straight parallel transmission circuits forming a square array. Values of the mutual impedance are calculated over a frequency-range of 1 to 1000 kilocycles per second, for three cases of the circuits, and are compared with measured values.