900 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1957 



Subtracting (1.3) from (2.11), 



[P(/o') - P{to)] + [R{to') - Rm = -a,P(/o') - arPiUn. 



For small values of Op and ttr , such that 5„ = to' — /o is sufficiently small, 

 the same procedure as in Section 2.2 gives 



5„ = iPattp + rattr), (2.12) 



and 



V - ~^^^"^ r - -^^^'^ (2 13) 



For uncorrelated variations of rms amplitude g^ and Qr the correspond- 

 ing rms timing deviation is 



L = (Pa'ai + iVq;Y\ (2.14) 



Equations (2.12) and (2.14) give the timing deviations in regenerated 

 pulses resulting from amplitude variations in the pulses and in the 

 timing wave. 



2.4 Resultant Timing Deviations in Regenerated Pulses 



For small variations in the pulses and in the timing wave as considered 

 previousl}^ the resultant timing deviation in a particular regenerated 

 pulse is 



A - 5, + 5„. (2.15); 



Considering a large number of pulses, the resultant rms timing devia- 

 tion in terms of the rms deviation in the received pulses and in timing 

 wave is 



A = (5/ + 8jf\ (2.16) 



These expressions can also be written 



A = A;, + A. , (2.17) 



A = (A/ + ArY\ (2.18) 



^P = PrTp -\- Pattp , 

 Ap" = Pr'fp' + Pa'Qp', (2.19) 



Ar = IrTr + faar , 



A/ = rr'ir' + ra'Qr'. (2.20) 



