Circulating Currents and Singing on Two-Wire 

 Cable Circuits 



By LEONARD GLADSTONE ABRAHAM 



One of the important factors limiting the working net losses of two-wire 

 cable circuits is the possibility of excessive circulating currents or actual 

 singing. 



A theory is developed for the computation of the distribution of singing 

 margins on groups of two-wire circuits from the known gains and losses 

 and known functions of the deviations of loading coils, loading coil spacing, 

 cable capacitance and office equipment. The distribution functions of cir- 

 culating current margins, of active return losses and of active singing points 

 are also derived. 



The possible application of these methods to specific problems is discussed 

 and an example of the computations involved is given. 



The theory herein involves certain approximations and empiricisms in 

 determining the singing limitations but it is believed to give an answer 

 which approaches the exact answer rather closely. 



Introduction 



AMONG the considerations which limit the minimum working net 

 losses ^ of two-wire cable circuits, one of the most important is 

 the desirability of avoiding excessive circulating currents. These cir- 

 culating currents may manifest themselves as a quality impairment 

 due directly to frequency and phase distortion or as sustained oscilla- 

 tion (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 infor- 

 mation 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 prac- 

 tical considerations such as the effect of repeating coils and other 

 apparatus. In the second main division are discussed various consider- 

 ations 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. 



* "Certain Factors Limiting the Volume Efficiency of Repeatered Telephone Cir- 

 cuits," L. G. Abraham, Bell Sys. Tech. Jour., October, 1933. 



600 



