SELF-TIMING REGENERATIVE REPEATERS 917 



In accordance with (2.21) the rms timing deviation at the output is 

 then : 



• 2 / 2 2 I 2 2\ I / 2 2 , 2 2\ /,- ^\ 



A = (Pr Tp + Pa flp ) + {Vr fr + r„ Qr ), (5.7) 



where in accordance with (4.13) and (4.16) 



ttr 



L2Q ^' - ''^'\ 



1/2 ^ 



(5.8) 



cos \p 



Tr = {^r + afj,") , (5.9) 



« = (i) . (5'«) 



When (5.9) is inserted in (5.7) 



.2 / 2 , 2 2x_ 2 I 2 2 I 2. 2 , 2 2 /t- , r>\ 



A = {Pr +Qcrr)Tp + PaQp + fr 6, + Ta tt^ . (5.12) 



This expression gives the rms timing deviation at the output in terms of 

 the rms deviation fp at the input and the various repeater parameters. 

 With timing from the output, rather than the input as assumed above, 

 Tp is replaced by A in (5.9), and the following relation is obtained: 



.2/, 2 2n 2_ 2 I 2 2 I 2-2 , 2 2 /- , r,\ 



A (1 - a fr ) = Pr Tp + Pa Qp + /> 5^ + r„ tt, . (5.13) 



In the above expressions p/ = 0.15, 7\' ^0.4 and a' = 0.03 {Q = 

 100) . The term a rj can thus be neglected in comparison with pi in 

 (5.12) and in comparison with 1 in (5.13). 



The following expression is thus obtained with timing from either the 

 input or the output: 



A = {pr fp" + PaQp') -j- (r/5r" + riqr') 



= A/ + A.-. 



5.4 Magnitude of Random. Timing Deviations 



The first two terms of (5.14) represents the rms timing deviations in 

 the regenerated pulses resvilting from timing deviations and ampUtude 

 variations in the received pulses. The last two terms represent the timing 

 deviations resulting from timing deviations and amplitude variations in 

 the timing wave. The conversion factors pr , Pa , 'V and ?•„ are discussed 

 in Section II and representative values given in Figs. 5 and 6. The values 

 of Qr and 8r are obtained from (5.8). 



