SELF-TIMING REGENERATIVE REPEATERS 921 



tion resulting from the effect on the timing wave of unit rms deviation 

 in the received pulse train at the second repeater. 



At the output of the third repeater, the squared rms de\'iation is 

 smaller than at the output of the first repeater by the factor 



2 /2| 22x2. 222, 22 2 2 /n c,\ 



73 = KPt + Ql l-r )Pr + pT «1 I'r + «! /V ^2 'V (b.2) 



= p/ + 'Zai'pr'rr' + Qi'a-irr^. (6.3) 



As indicated in Fig. 8, the first term in (6.2) represents the reduction 

 owing to partial retiming of the received pulse train at the third repeater. 

 The second term, {pr(xirr)\ is the additional rms deviation resulting from 

 the effect on the timing wave at the third repeater of an rms deviation 

 Pr in the received pulse train. The third term (airr-a2rr)" is the additional 

 deviation caused by the effect on the timing wave of an rms deviation 

 QiVr in the received pulse train. The factor a2rr represents the modifica- 

 tion in the rms deviation ai/\ by a second resonant circuit, with ao de- 

 fined as in Section 4.3. 



At the output of the fourth repeater, the rms timing deviation is 

 reduced by the following factor, obtained in the same manner: 



2 6 I ., 2 4 2 I o 2 2_ 2 4 I 2 2 2^, 6 /,. a \ 



74 = Pr + 3ai Pt Vt + 3gi ^2 Pr Vj + Si ^2 «:i 'V • yoA) 



At the output of repeater n, the squared rms timing deviation is 

 smaller than at the output of the first repeater by the propagation 

 factor 



(6.5) 



. , ^ 2(n-l) 2 2 2 2 



where pr and /v are defined as in Section 2.2, and ai , 0:2 • • • a« as in 

 Section 4.3. 



In the above formulation the rms deviation at the output of the first 

 repeater was assumed given by (5.14), which is an approximation of 

 (5.12) in which the term a'r/r/ was neglected. This term will have a 

 different propagation factor p„ , the expression for which differs from 

 that for 7„ as given by (6.5) in that the subscripts of the factors «_,- are 

 raised by one unit. Thus, 



