SINGING ON TWO-WIRE CABLE CIRCUITS 615 



conditions in order to keep the percentage of circuits which will have 

 objectionable circulating currents and the percentage which will sing 

 occasionally low enough that serious service reactions will not be 

 obtained. 



Practical Considerations 

 Equipment and Terminating Effects 



When actual cable sections are investigated, the effect of the equip- 

 ment must be considered. The effect of adding, say, repeating coils 

 in the line and network sides of the repeater, is to introduce some 

 reflected current and to add a certain loss in the line which must be 

 made up by increasing the repeater gain. The cable return loss is 

 increased by twice the loss introduced, so that the only effect on cir- 

 culating current paths is due to the differences in the line and network 

 equipment. 



Appendix IV derives an expression for the distribution curve of an 

 active or passive single-frequency return loss of a line with equipment, 

 on certain assumptions. The complication of using this method to 

 determine circulating current margins or singing margins is large, 

 however, and an approximate method is illustrated below. 



Figure 7 shows an example of the combination of the equipment- 

 return loss with the return loss of a cable section without equipment. 

 It is assumed in this case that the equipment-return loss is 13 db higher 

 than the value of cable-return loss for which Sf = 0. For example, 

 the equipment return loss might be 40 db while the line return loss 

 was 27 -{- Sf db. A generally similar curve would be obtained from 

 the combination of the repeater section terminating effect with the 

 cable return losses. 



Since the principal interest in connection with these return losses 

 is with the lower values, it seems reasonable to say that the effect 

 may be approximated generally by shifting the Sf curve a certain 

 part of a decibel, depending upon the difference between Se and the 

 cable-return losses. Strictly speaking, of course, it not only shifts the 

 curve but also changes the standard deviation, but the complication 

 of taking account of this does not seem worth while with present lines 

 and equipment. 



Since we are interested in the singing margin which is exceeded 90 

 per cent of the time under average conditions, it would be possible to 

 select a value of cable return loss from the distribution curve which, 

 if it occurred in each repeater section of a particular circuit, would 

 give the indicated singing margin when the various intermediate 

 singing paths are combined together as the sum of their power ratios. 



