SHOT NOISE IN DIODES 615 



velocity, the term gives the equivalent noise generator, E. Thus 



E =^ iide-'^ + e~'^ - 1) (60) 



and the mean-square value of the noise emf. (at a frequency a;) is 

 given by : 



E' = ^^' \id-^' + e-^' - 1\\ (61) 



The problem is now reduced to finding the mean square value of 

 initial velocity fluctuation, /!„-, which corresponds to electrons cross- 

 ing the potential . minimum. This may be done by going to (55) 

 which gives the effective value of the instantaneous initial velocity 

 and separating all quantities, including the lower integration limits 

 into d-c. and a-c. components. Thus 



n{uc) = nojtic) + 8{uc) 



Uc = Uc + hUc' 

 u' = u' -\- bll' 



U = Ua -\- IJLa 



(62) 



The result may be expanded in series form and products of the 5's 

 may be disregarded inasmuch as the a-c. components are small in 

 comparison with the d-c. The indicated operations have as a result 



and 



e f"" 



IJ^a ^ Y \ ("' ~ Ua)b{Uc)dUc. (64) 



The Fourier analysis may be applied to this in the way outlined in 

 connection with (37) and (41) in Part I and gives the mean-square 

 value of velocity fluctuation corresponding to a frequency interval df 

 as follows : 



/^/ =j-^df \ (u' - Ua)-Uc{Uc)dUc = 7^^/( ^ ~ ^ ) • ^^^^ 



''uo 



This may be substituted in (62) giving for the effective noise emf. in 

 the frequency range df 



X '[^' + 2 - 2 (cos ^ + ^ sin ^)]. (66) 



