INTEKCHANNEL INTERFERENCE DUE TO KLYSTRON PULLING (347 



portional to the reactive component of the input impedance. More pre- 

 cisely, we assume that the ideal transmitter freciuency of p + ^'(0 I'adi- 

 ans/sec is changed by the pulUng effect to 



p + ip'ii) + 2wr sin [T{p + ip'{t))] radians/sec (2) 



where r is given by 



r = 2.5 I p I X (Pulling Figure in cycles/sec) 



POWER SPECTRUM OF INTERCHANNEL INTERFERENCE 



The distortion produced by the pulling effect is given by the third 

 term in (2). This distortion will be denoted b}^ ^'(0- 



d'{t) = 27rr sin [pT + T^'(t)] (3) 



Our problem is to compute the power spectrum of d'((). In particular, 

 we are interested in the case where the signal (p'{f) represents the compos- 

 ite signal wave from a group of carrier telephone channels in frequency 

 division multiplex. All of the channels except one are assumed to be busy. 

 Although the power spectrum of (p'{t) is zero for frequencies in the idle 

 channel, the same is not true for the power spectrum of d'(t). In fact, 

 the interchannel interference (as observed in the idle channel) is given 

 by that portion of the power spectrum of d'{t) which lies within the idle 

 channel. We shall denote the corresponding interchannel interference 

 power in the idle channel by wdf) df where the idle channel is assumed to 

 be of infinitesimal width and to extend from frequency / — df/2 to / -f 

 df/2. The function wdf) will now be computed by using the procedure 

 developed in Reference 1. 



The first step is to assume the signal ip'(f) to be a random noise current. 

 In order to avoid writing tp' a great many times we shall set (p'(t) = S(t), 

 where now S{t) stands for the signal. Then the autocorrelation function 

 for the distortion d'{t) is 



Re'(r) = avg [d'(t)9'{t + r)] 



= (27rr)- avg [sin (Tp + T<p'(t)) sin (Tp + T<p'(t + r))] 



= (27rr)' avg [sin (Tp -\- TS{t)) sin (Tp + rS(t + r))] 



= ^-^ avg [ cos (rSit) - rSit + r)) (4) 



- cos (2pT + TS(i) + TS(t + t))] 

 = U2irrf {exp [-T'RsiO) + T'R.ir)] 



- cos {2pT) exp [-r-Rs(0) - T'Rs(t)]\ 



