VOLUME EFFICIENCY OF REPEATEKED CIRCUITS 



525 



repeater is as follows: The active return loss '^ in one direction, say 

 east of the repeater under consideration, is first obtained (Fig. 2). 

 The passive return loss of the adjacent repeater section toward the 



2-WIRE 

 ^REPEATERS^ 



WESTC^^X^ CXh 



G' S', 



g' 



0' s;^ 



■C>0 



9" 



G'" P 

 -(XI— ^ EAST 



g,„ 



Fig. 2 — Singing paths in a 2-wire circuit. 



S' and S" are passive return losses of cable sections. 



P is the terminal return loss. 



C, G" and C" are west to east gains. 



g', g" and g'" are east to west gains. 



east {S') constitutes the first singing path and is determined as out- 

 lined above in considering echoes on two-wire circuits, except that the 

 4 db is not subtracted because singing occurs at only one frequency 

 and because approximately the worst frequency is selected for com- 

 putations. The passive return loss in the repeater section on the far 

 side of the next repeater to the east {S") is amplified and attenuated 

 through the intervening gains {G" + g") and losses (2L') to obtain 

 the second component, which is L' — G" + S" — g" + L' . Similar 

 components are determined for all other repeater sections to the east 

 of the one under consideration. (In the case of the circuit shown on 

 Fig. 2, there are no more such paths.) These paths are then combined 

 by adding the power ratios corresponding to these paths. The loss 

 of the resultant singing path is the active return loss from the repeater 

 under consideration with no currents returned from beyond the ter- 

 minal repeater (or from the circuit terminal if there is not a terminal 

 repeater). This active return loss is then combined wuth the path in- 

 cluding the terminal repeater, viz., (L' - G" + L" - G'" + P - g'" 

 + L" — g" + U), according to the sum of their current ratios to 

 obtain the active return loss (toward the east from the repeater in 

 question) of the circuit in normal operating condition. (The use of 

 current ratios rather than power ratios in this case is indicated by 

 theoretical considerations and confirmed by experimental data.) 



The active return loss toward the west from the repeater in question 



1^ An active return loss is a return loss with gain inserted in the paths of one or 

 more of the returned currents. The passive return loss is the return loss without 

 any currents returned from beyond the adjacent repeater (or other termination if 

 there is not a repeater there). 



