916 



THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1957 



values of /3 are for phase shifts between and —60°. For t? = f , (3 ^ 0.7 

 and for r; = 1,8^ 0.9. 



For J? = f and rj = I the tolerable maximum phase shifts \p' in the 

 resonant circuit with timing from the regenerated pulse train, in rela- 

 tion to the maximum tolerable \{/ with timing from the input, are 



^P' ^ 0.3^p for 



V — 4, 



(5.6) 



and 



^' ^ 0.1x1/ for 7? = 1. 



Although greater phase shifts can be tolerated when 4/ is positive, and /?' 

 is smaller than above, the requirements on the resonant circuit must be 

 based on the worst condition that can be encountered, as above. 



From (5.6) it follows that for ?? = 1 the requirements on the per- 

 missible phase shift in the resonant circuit are much more severe than 

 for 17 = f . For this reason the latter value of rj is decidedly preferable 

 for the particular case in which the peak amplitudes of the pulse train 

 and the timing waves are equal, as assumed here. A value 77 = f is also 

 desirable from the standpoints of avoiding intersymbol interference 

 between adjacent pulses at the triggering instants, to permit the timing 

 wave to be derived from the pulse train and to permit self-starting of 

 the repeaters, as discussed later. 



In accordance with (5.6) the maximum tolerable frequency deviation 

 for 77 = f will be less than with timing from the received pulse train by 

 a factor of about 0.3. The maximum permissible frequency deviation for 

 a phase shift of about one radian in the timing wave and 0.3 radian in 

 the resonant circuit, will accordingly be about as follows: 



For a repeater with complete rather than partial retiming, the factor 

 |8 would be unity, and timing from the regenerated pulse train would 

 not be possible. 



5.3 Random Timing Deviations 



In combining random timing deviations from various sources at a 

 particular repeater, it will be assumed that there is no correlation be- j 

 tween the various deviations, so that they will combine on a root -sum- 

 square basis. 



