VOLUME EFFICIENCY OF REPEATERED CIRCUITS 521 



power ratios (less than unity for a loss greater than zero) of the indi- 

 vidual weighted losses together and finding the equivalent weighted 

 echo path corresponding to this sum. When this equivalent path 

 becomes zero db (a power ratio of 1.0), the circuit (without variations) 

 is considered to be just satisfactory from an echo standpoint. 



The distribution of gains between the different repeaters in a two- 

 wire circuit usually has an appreciable effect upon the minimum net 

 loss which may be obtained for a giv^en circuit. If the gain in each 

 direction of transmission of each repeater is equal to the loss of the 

 preceding repeater section (or is less than it by a fixed amount called 

 the taper), it may be shown that the echo limitations computed as 

 above are completely determined by the delays involved, the taper, 

 the terminal return loss and by the differences between the return 

 loss, S, and attenuation loss, L, of the repeater sections, i.e., the 

 values of S-L."^ The minimum echo net loss of any given two-wire 

 circuit (for given terminal conditions), therefore, is determined by the 

 delays, S-L, the taper and the number of repeater sections. The 

 value of S-L which is of the greatest importance is usually that in the 

 important echo range, i.e., about 500 to 1,500 cycles. 



While the terminal return loss is taken as a fixed value (6 db) in 

 these computations, the return loss at intermediate repeater points 

 varies according to the structure of the line. The statistical distribu- 

 tion of the return losses of loaded cable circuits may be computed 

 as outlined by Crisson.^ It is customary to compute the return loss, 

 Sl, at 1,000 cycles, using the distribution function ^f = in Crisson's 

 formulas. To determine the echo limitations, the value Sm = Sl — ^ 

 is used, principally to take into account the fact that the computed 

 values of Sl are at a single frequency. 



In addition to the return loss of the bare cable facilities, the return 

 loss of the repeating coils and other office equipment and the effect 

 of the termination at the far end of the repeater section must be con- 

 sidered. These components are: 



Si = Sc, 



Ss = St -\- 2L -\- 2C, 



where Si, S2 and S3 are the return losses (attenuated to the repeater), 



' In the following, this is assumed the same for each repeater section. It may be 

 seen that the use of S-L instead of 5 and L separately effectively removes one variable 

 from computations. 



*" Irregularities in Loaded Telephone Circuits," by George Crisson, B. S. T. J., 

 Vol. IV, and Elec. Comm., Vol. 4, October, 1925. Specific values of the deviations 

 from which Sh may be computed are given in a paper entitled "Long Distance Tele- 

 phone Circuits in Cable," by A. B. Clark and H. S. Osborne. 



