SHOT NOISE IN DIODES 

 deviation function may be shown to be: 



5(«,.) = Z E 



Tb,n{Uc) fg-''"^ - 1 



L 



T. e''" 



I_ — wcor 



(<-<m) 



603 



(37) 



where oi = 2ir/L, and /„ = wt. 



The mean square deviation may be found by squaring the above 

 expression and averaging the result over the long period of time L. 

 The result is 



5'(Mc) = 2I:E E j7,dju,)8,(u,) 



X 



^1 



r g+ iiaiT 1 



|_ + ilooT 



g~ilo)(tk-lm)^ 



Since the time-average of the instantaneous emission deviation 

 must be zero over the period, L, the contribution to the mean square 

 from the double summation with respect to k and m is zero, unless 

 m — k. 



Thus 



p 



8'{Uc) = 4E7T, fr^, E K'M. 



From (36), this equation reduces to 



-r:^7-^ 4 ^ r 1 - cos /cor ] , , 



(38) 



(39) 



The contribution to the mean square of the instantaneous deviation 

 in the electron emission, from the frequencies between / and f -\- df 

 is given by 



^l=lTrU+df)lo, 



8rM = J E 



1 — cos lo 



Wo (Mr). 



(40) 



The limit of this expression as the length of the periodicity, L, is 

 made infinite, may readily be shown to be 



8/{uc) = 2no(iic)df. 



(41) 



It is now possible to proceed to find the mean square value of the 

 noise generator voltage given in (32) with the aid of (37) and (41). 

 From (37), the noise generator voltage may be expressed as 



E= E E 7- ■; 



g ilu(l—tm) 



X] I II(tir)K(uc)duc + I I G8n,(uc)ducdr] } . (42) 



