924 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1957 



timing deviations is virtually completed in a chain of 3 to 6 repeaters, I 

 so that for experimental determinations of the degree of cumulation it I 

 suffices to operate a few repeaters in tandem. f 



^.4 Repeaters with Complete Retiming I 



In the particular case of complete retiming, pr = and Tt = 1 in , 

 (6.5) and (6.6) so that j 



7« = aia^s • • • On-i , (6.14) ' 



Pn = mm • ' • Qin ■ (6.15) i 



! 



For w » 1, approximation (4.16) can be employed, in which case ' 

 7. = s (— ) ' , Pn = f-Y . (6.16) ■ 



In this case (5.14) simplifies to 



^p + A.' = 5^ (6.17) 



since pa = 0, ?•„ = 0, pr = and fr = 1. 

 Hence (6.7) becomes 



A„ = 8r~yn' + fpapn'. (6.18) 



With approximations (6.16), 



A,;^ = i8j + f^h' (J^J'\ (6.19)1 



At the output of the first repeater, 



Ai' = 5; +«V- (6-20)1 



For n » 1 the sciuared propagation factor is accordingly 



An'/^r'-a \^:^'z (^T. (6.21) 



Qr" + Qc-Tp~ \Trn/ 



The squared rms cumulation factor for A^ » 2 repeaters becomes 



C'^ 1 





= 1 + a= ^' + ''' 



'■t.V\"= /8\"=' 



IT I VTT, 



In the particular case of perfect tuning of all resonant circuits 6^ = ' 

 and 



;_^i 



