INTERCHANNEL INTERFERENCE DUE TO KLYSTRON PULLING 649 



power IS 



P/ _ Weif) 



Ps 



(12) 



We now obtain an expression for this ratio on the assumption that the 

 random noise signal S{t) (which is used to simulate the multichannel 

 signal) has the power spectrum 



>0 , < / < /6 



ws(f) = (13) 



[o, / > /. 



where Po is a constant. S(t) is measured in radians/sec and Poft is meas- 

 ured in (radians/sec) . Pofb is given by 



PoU = Sm = avg [<p'(t)Y = (27rcr)^ 



where a- is the rms frequency deviation of the signal measured in cycles/ 

 second. According to (5) this signal has the auto-correlation function 



Rs{t) = f Po cos 27r/r df = Po 

 Jo 



sin 27r/r 

 2irT 



fb 



= i'Zira) 



2 sm u 



u 



(14) 



where 



U = ZirfhT 



The interference power spectrum wdj) corresponding to the lOsiJ) of 

 (13) may be obtained by substituting (14) in (9) to get Rc{t) and then 

 using (8). The result is 



. . /i-N 1 \^T^^) —b I r/ 6m~1 sin u 7 — 1 



Wcif) = 4 ^ e J [{e - hu 



sm u 



1) 



(15) 



- (e 



-bu 1 sin u 



+ hu sin u — 1) cos 2j)T] 



cos au 

 ~%^b 



du 



where m is the same as in (14) and we have set 



a = f/fb b = {27raTf 



This integral may be expressed in terms of Lewin's integral which is 

 studied in Appendix III of Reference 1. Thus 



Wcif) 



(27rr) e 

 ~2^b 



2 -6 



[I{b, a) — I{ — h, a) cos 2pT] (radian/sec) '/cps (16) 



where I(b, a) and I{ — b, a) are tabulated for various values of a and b. 

 Since we began the problem by dealing directly with 6'{l) which is a 

 radian frequency, rather than d(t) which is a radian phase, wdf) has the 



