SINGING ON TWO-WIRE CABLE CIRCUITS 613 



This may be written in more general fashion as 



Ms = (5i - F{Nu T) -Gc - 1.25) X (6 + £,) 



p 



+ (5i - F{N„ T) - gc- 1.25) X (6 + £2) + 5q(2.8) (15) 



V 



or still more generally, 



M, = {Sh + Su, - Sa - L + T + g_ - F{Ni, T -\- q) - 1.25) 



X (6 + £/ + 2Nrq) -^ (Sh + S^ - Sa - L + T + q 

 p 



- F(N2, T + q) - 1.25) X (6 + £/ + IN^q) + 5q(2.8). (16) 



p 



Criterion of Satisfactory Performance 



The above discussion derives methods of determining the circulating 

 current margin and the singing margin that will be obtained (on a 

 distributional basis) for a cable circuit under a given set of conditions. 

 As a practical matter, the overall net loss of the circuit will sometimes 

 vary, regulating repeaters will change in gain setting, temporary 

 troubles will occur and, in some instances, toll circuit terminations 

 will be removed while connections are being set up. Each of these 

 factors will reduce the singing margin that the circuit had under 

 average conditions. In the Bell System toll circuits are usually 

 designed so that a 10 db singing margin or more is obtained in 90 per 

 cent of the loaded two-wire cable circuits under average conditions. 

 This, of course, is the same thing as saying that 12 db singing margin 

 should be exceeded under average conditions in 71 per cent of the cases, 

 or 8 db in 97.7 per cent of the cases (see 5q(2.8) curve on Fig. 6). The 

 following table shows the percentages of circuits which will have 

 various lower singing margins under average conditions than the 

 indicated values, for various different assumptions as to the design 

 requirement (i.e., the singing margin which must be exceeded in 90 

 per cent of the cases). 



