SINGING ON TWO-WIRE CABLE CIRCUITS 



601 



Theoretical Distributions 



Circulating Current Margins 



A two-wire loaded cable circuit will be considered which consists of 



a number of repeater sections with 22-type repeaters. As shown on 



Fig. 1 there are various circulating paths in such a two-wire circuit 



WESTCMXl- 

 A 



2-WIRE REPEATERS 



CxO^^^ ^^^X 



B C 



^ 1 



Qa 



-oq- 



D 



-OO- 



E 



-CXh 

 F 



HXH3 EAST 

 G 



^ I ^ ; GD , Ge Gf Gg 



Qb gc go gE 9f g& 



END SINGING PATH 



Fig. 1 — Singing paths in a two-wire circuit. 



which might cause objectionable circulating currents at any given 

 frequency. Each repeater section consists of a large number of loading 

 sections which have approximately the same capacitance and the same 

 inductance per mile. Practically, however, there are deviations of the 

 capacitance and inductance in a given loading section from the 

 nominal average, each of which introduces an impedance irregularity 

 which prevents the balancing network from exactly balancing the line. 

 To determine the amount of current returned from each of these 

 irregularities in a given case and the phase at which it is returned is, 

 in general, impracticable. It is possible, however, to determine in 

 what percentage of circuits the circulating current at any given fre- 

 quency will exceed a certain percentage of the original current or, in 

 other words, the percentage of cases in which the loss in the circulating 

 current path will be less than a certain amount. The loss in the cir- 

 culating current path at a given frequency is called the circulating 

 current margin at that frequency. 



The distribution of return losses at any given frequency in a cable 

 section without repeater has been determined by G. Crisson in a paper 

 entitled " Irregularities in Loaded Telephone Circuits," Bell System 

 Technical Journal, October, 1925. This derives the distribution of 

 the return losses which would be measured at a given frequency on a 



