SELF-TIMIXG REGENERATIVE REPEATERS 919 



The probability that random phase deviations will exceed the above 

 rms values by a factor of more than 4 is small enough to be ignored. On 

 this basis the sum of the fixed and random dev'iations would be limited 

 to about 70°, if the fixed phase shift \p is less than ±30°. With this re- 

 quirement on the fixed phase shift for satisfactory performance, the 

 values of A/m^^x would be about half as great as previously gi\Tn in Sec- 

 tions 5.1 and 5.2, for a single repeater as considered here. 



VI REPEATER CHAINS 



6.0 General 



In the previous section, a single self-timed repeater was considered, 

 from the standpoint of fixed and random timing de\'iations, as deter- 

 mined by various repeater design parameters. In a repeater chain there 

 will be some cumulation of random timing deviations as the number of 

 repeaters in tandem is increased, and a resultant reduction in the 

 tolerance to noise of repeaters toward the end of the chain. Exact evalua- 

 tion of such cumulation is rendered difficult by the circumstance that 

 timing deviations from various sources may not follow the same law of 

 combination along the repeater chain. In the following, expressions are 

 given based both on root-sum-square and direct addition of random 

 timing deviations, which can be regarded as lower and upper limits. 



6.1 Combination of Randotn Timing Deviations 



To determine the rms \'alue of random timing de^'iations at the end 

 of a repeater chain, it is necessary to combine random deviations from 

 various repeaters. Random deviations from various sources at a repeater 

 do not necessarily follow the same law of cumulation along a repeater 

 chain. Since there is no correlation between timing deviations caused by 

 noise in A'arious repeater sections, these can be combined on a root-sum- 

 square basis. This, however, may not be appropriate as regards the 

 i combination of timing deviations resulting from imperfections in the 

 timing wave. Thus, with perfect tuning of all resonant circuits, the 

 timing waves at various repeaters would have ^•irtually identical ampli- 

 tude variations, but no phase deviations. While in this case there would 

 be complete correlation between the timing wa\e variations at the 

 repeaters, it does not follow that the resultant timing deviations should 

 be combined directly rather than on a root -sum-square basis along the 

 repeater chain. The timing deviations at the end of a chain of N re- 

 peaters resulting from amplitude variations in the timing wave of the 

 first repeater will be modified by .V int(M'mediate resonant circuits. Those 



