914 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1957 



V SELF-TIMED KEPEATEKS WITH PARTIAL RETIMING 



5.0 General 



As shown in the preceding section, timing for pulse regeneration can 

 be derived from the pulse trains, with certain random phase and ampli- 

 tude variations in the timing wave that can be reduced by increasing the 

 loss constant Q of the resonant circuit. This method of "self-timing" 

 can be combined with partial retiming, and the regeneration charac- 

 teristics of this type of repeater will be discussed in the following sections. 



For purposes of numerical illustration, the same type of pulse shape 

 and timing wave will be assumed as in the previous numerical illustration 

 in Section III. This pulse shape and timing wave closely approximates 

 those in experimental Wrathall repeaters, in which timing is derived 

 from the regenerated pulse train. In the following discussion timing 

 from the received pulse train will also be considered. 



5.1 Timing from Received Pulse Train 



It will be assumed that the timing wave is derived from the received 

 pulse train with the aid of a resonant circuit and that random timing 

 deviations are absent. The response of the resonant circuit is then a 

 sinusoidal wave as given by (4.1). From this wave it is possible to obtain 

 a retiming wave of the form 



R{t) = -cosiA 



1 — cos 



(5.1) 



This can be accomplished by holding the peaks of the timing wave from 

 the resonant circuit at zero potential with a diode. This is the form of 

 retiming wave previously considered in Section III, in conjunction with a 

 pulse shape given by (3.1). 



As shown in Section 3.7, the tolerance to noise will vary with the 

 phase shift \p of the resonant circuit, in accordance with (3.21). If a 

 reduction in the tolerance to noise of about 2 db is allowed, the maxi- 

 mum permissible phase shift would be about \J/ — 1 radian (57.6°). On 

 this basis the maximum permissible deviation A/max in the resonant fre- 

 cjuency from the pulse repetition frequency / as obtained from (4.2) 

 with \p = 1 radian becomes 



A/max ^ tan \J/ ^ L58- , -,v 



./■ 2Q 2Q • ^ ^^^ 



For various values of Q in the range that can he realized by simple 



