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BELL SYSTEM TECHNICAL JOURNAL 



Considering C as the critical repeater: 

 Path 



Toward A - 



Toward G 



1 27.35 



2 27.35 + 34 - 30 = 31.35 

 Total 25.90 Items 1 and 2 combined as the sum of their 



power ratios. 



1 27.37 



2 27.25 + 36 - 30.8 = 32.45 



3 27.25 + 38-31.8 + 30-27.8-35.65 



4 27.32 + 38 - 31.8 + 30 - 27.8 + 30 - 28.8 = 36.92 

 Total 25.42. Items 1, 2, 3 and 4 combined as the sum 



of their power ratios. 



The internal circulating current margin then is 25.90 + 25.42 

 — 33.7 = 17.62 db, or more in 72 per cent of the cases and the internal 

 singing margin is 25.90 + 25.42 - 2.5 - 33.7 = 15.12 db or more in 

 50 per cent of the cases, both under the average conditions specified. 



Now 10 db internal circulating current margin would be exceeded 

 under average conditions in the percentage of cases for which Sp is 

 10 — 17.62 = — 7.62 db or greater; i.e., in about 97.5 per cent of 

 the cases, reading from the Sp curve on Fig. 6. Or, similarly, 10 db 

 internal singing margin will be exceeded in about 97 per cent of the 

 cases, reading at 5q(2.8) = 10 - 15.12 = - 5.12 from the 5q(2.8) 

 curve on Fig. 6. 



The single-frequency loss in the end path toward A, before the 

 gain of repeater C is introduced is, for a net loss at the critical fre- 

 quency of 9 db, 34 + 34 - 30.0 - 14.4 + 7 + 5^ = 30.6 + Sf. In 

 the other direction the corresponding function is 36.1 + Sp. When 

 the net loss of the circuit is expressed as E rather than 9 db, these 

 functions become respectively 21.6 + -B + ^^ and 27.1 + £ + Sf- 

 The corresponding singing point distributions are 20.6 + £ + Sq{2) 

 and 26.1 + £ + Sq{2), respectively. 



The desired value of 10 db or more singing margin obtained in 90 

 per cent of the cases under average conditions will be obtained when 

 the following equation is satisfied: 



10 = (25.90 - 1.25) X (20.6 + E) 



+ (25.42 - 1.25) X (26.1 + £) - 33.7 + 5o(2.8), (17) 



V 



where Q = \^ per cent, 5^(2.8) = — 3.5 db. Substituting in the 



