928 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1957 



interval as indicated in Fig. 3, and the peak amplitude of the timing 

 wave should be about equal to that of the received pulses. Under these 

 conditions the pulse repetition frequency will be present in the received 

 pulse train in sufficient amplitude to permit derivation of the timing 

 wave from the received pulse train, and to permit rapid self-starting in 

 the absence of a timing wave if it is derived from the regenerated pulse 

 train. 



A loss constant of the resonant circuit Q = 100 appears desirable. 

 This value is sufficiently low to be readily realized with simple resonant 

 circuits consisting of a coil and capacitor in series or parallel, without 

 unduly severe requirements on its frequency precision. It is also ade- 

 quately high from the standpoint of avoiding excessive random timing 

 deviations in regenerated pulses from amplitude and phase deviations 

 in the timing wave. 



The tolerable deviation in the resonant frequency from the pulse 

 repetition frequency with Q = 100 is about 0.2 per cent when the 

 timing wave is derived from the received pulse train, and about 0.06 

 per cent when it is derived from the regenerated pulse train. These 

 frequency precisions correspond to a maximum fixed phase shift of 15° 

 in the timing wave, and allow for the possibility that random timing 

 deviations resulting from amplitude variations in the timing wave maj- 

 cumulate directly along a repeater chain, rather than on a root -sum- 

 square basis. With root-sum-square cumulation of timing deviations 

 from all sources, the frequency deviations could be about twice as 

 great. 



"V^Tien the above requirements are met the reduction in the tolerance 

 to noise owing to timing deviations in a repeater chain is limited to 

 about 2 db. If the requirements on freriuency precision of the resonant 

 circuit are met, substantial degradation or improvement in performance 

 would not be expected as a result of moderate changes in the other 

 design parameters. 



VIII ACKNOWLEDGMENTS 



In this presentation the writer had the benefit of unpublished work, 

 referred to pre^'iously, b^' W. R. Bennett and .1. R. Pierce on the deriva- 

 tion of a timing wave from a pulse train with the aid of a resonant cii- 

 cuit, and by H. E. Rowe on the cumulation of timing deviations in a 

 chain of repeaters with complete retiming. Bennett, Pierce and Rowe are 

 at Bell Telephone Laboratories. He is also indebted to H. E. Rowe for 

 a critical review that resulted in several improvements in the analy.sis. 



