894 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1957 



be increased with the number of repeaters in tandem in the same way 

 as for ordinary repeaters. 



1 .2 Regeneration with Complete Retiming 



With complete retiming, the instants of pulse regeneration would 

 be controlled by a periodic retiming wave, R{t), with a fundamental 

 period eciual to the interval between pulses. The received pulse train 

 would be sampled at instants when the retiming wave had a certain 

 level Ls . The sampling instants ta would thus be given by 



R{t,) = L.. (1.2j 



E(io) would satisfy this equation for t^ — nT ± A7\ where T is the 

 nominal interval between pulses, n is an integer and AT" is a certain 

 tolerable deviation from the desired sampling instants. Pulses would be 

 regenerated provided P(^o) > L and would be omitted if P(/o) < L. 



With this method the timing deviations in regenerated pulses would 

 be limited to iAT, regardless of the timing deviations in received pulses. 

 There would be no cumulation of timing deviations in a repeater chain. 

 However, the tolerance of the repeaters to noise would be somewhat 

 reduced by the timing deviations dzAT. 



1.3 Regeneration with Partial Retiming 



Partial retiming is obtained by a combination of the above two 

 methods, by triggering regenerated pulses without sampling at instants 

 ta determined by 



P(/o) + R{i,) = L. (1.3) 



To permit regeneration without sampling and without a marked reduc- 

 tion in the tolerance of the repeaters to noise, the timing wave R(t) 

 must meet certain conditions illustrated in Fig. 1. One is that it must be 

 a nearly periodic function as for complete retiming. The second condi- 

 tion is that R{t) must be zero near the sampling points to obtain sub- 

 stantially the same tolerance to noise in the presence of a pulse as in 

 the absence of a pulse. A third condition is that R{t) must have sub- 

 stantial negative values between sampling points in order that the 

 repeater be rather insensitive to noise between sampling points, as ^xith 

 complete retiming. It will be recognized that, in general, the maximum 

 value of R{t) need not necessarily be zero, as in the above illustration. 

 It can be greater or smaller than zero, provided the triggering level i> 



