SELF-TIMIXG REGENERATIVE REPEATERS 925 



(A„/Ai)^ ^ Q:J'\ (6-23) 



(6.24) 



The last expression gives the factor by which the rms timing devia- 

 tion at the output of repeater N is greater than at the output of the first 

 repeater. The rms deviation at the output of the first repeater is greater 

 than at the input by the factor a. The rms deviation at the output of 

 repeater .V is thus greater than at the input of the first repeater by the 

 factor, 



C\=a (~y \ (6.25) 



For this particular case {8r == 0) expressions equivalent to those 

 above have been derived in unpublished work by H. E. Rowe of Bell 

 Telephone Laboratories. 



In accordance with (6.22) and (6.24) the cumulation of random timing 

 deviations increases indefinitely with ^V when retiming is complete. The 

 icumulation factor as given by (6.24) is in fact the same as would be ob- 

 jtained if a timing wave were transmitted on a separate pair, with a 

 iresonant circuit at each repeater to limit noise and with amplification of 

 the timing wave at each repeater to obtain the same amplitude of the 

 timing wave as when it is derived from the pulse train. With partial 

 retiming cumulation is limited, for the reason that there is partial re- 

 generation of both the pulse train and the timing wave. 



Although with complete retiming the cumulation factor increases 

 indefinitely with N, this is of but little practical significance, because of 

 jthe slow rate of cumulation. At the output of a chain of .V repeaters an 

 rms deviation approximatelj^ equal to that at the input of the first re- 

 peater could be tolerated, in which case Ci = 1. On this basis the per- 

 missible number of repeaters would be 



(6.26) 



^ 800 when Q = 100. 



This assumes exact tuning of all resonant circuits. With mistuning of 

 the resonant circuits, the permissible number of repeaters in tandem 

 for a specified rms deviation at the output of the final repeater can be 



