906 



THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1957 



With this change in phase, the factor cos \p of (3.2) is modified to 

 cos {\p + A\p) = cos \f/ cos A\{/ — sin i/' sin A\J/, 



= COS rp — — Tr Sin }{/ 



^vhere the approximation apphes for small values of \f/. The amplitude 

 variation resulting from the above change in phase is accordingly 



27r . , 



ar = —"^r-jT Sill S^- 



(3.15) 



Considering both the time deviation Xr and the corresponding ampli- 

 tude variation ar , the resultant time deviation in regenerated pulses is 

 in accordance with (2.20) 



Ar = r-rTr + TaQr ■ (3.16) 



The resultant equation can be written 



A, = /3r,. (3.17) 



-90 -75 -60 -45 -30 -15 15 30 45 60 75 90 



PHASE SHIFT ANGLE OF TIMING WAVE, ^, IN DEGREES 



Fig. 6 — Conversion of amplitude variations in received pulses and in timing 

 wave into timing deviations in regenerated pulses, for pulse shapes and timing 

 waves shown in Fig. 3. Timing deviations in regenerated pulses for amplitude 

 variations Op and ar in reeeived pulses and in timing wave is paQp + yaQr ■ 



