Circulating Currents and Singing on Two-Wire Cable Circuits

A MONG the considerations which limit the minimum working net losses 1 of tvvo-wire cable circuits, one of the most important is the desirability of avoiding excessive circulating currents. These circulating currents may manifest themselves as a quality impairment due directly to frequency and phase distortion or as sustained oscillation (singing). In a given two-wire cable circuit, if the exact location and nature of each irregularity were known, it would be possible to compute exactly whether sufficient singing margin is available. The practicable method, however, is to compute the singing margins which will be exceeded on various percentages of a large group of such circuits, from the information which is available about the irregularities on a distributional basis. This paper first derives theoretical distributions of circulating current margins and singing margins without regard to various practical considerations such as the effect of repeating coils and other apparatus. In the second main division are discussed various considerations which are involved in applying the theory. In the third main division detailed computation methods are illustrated. The attached appendices cover the mathematical derivation of certain quantities. 1 " C e r t a i n Factors Limiting the Volume Efficiency of Repeatered Telephone Circuits," L. G. Abraham, Bell Sys. Tech. Jour., October, 1933.