618 



BELL SYSTEM TECHNICAL JOURNAL 



SO that (71) and (72) combine to give 



/i= - 



qn 



r 2 ,. 



1 + 



Zfiwi L *^ 



+ e- 



(73) 



The mean square shot noise current is thus given by 



/r = 



qa' 



H- 



Zfiwt 



-{it 



+ e-'" - 1) 



(74) 



The value of the mean square a-c. conduction current at the cathode 

 to be substituted in the above equation may be derived as follows : 

 The total current emitted from the filament was defined as 



n(uc)dUc = e | n[i{u,)duc + e \ b{ii^)duc. (75) 

 Jo Jo 



Hence 



h = e I 

 Jo 



8{Uc)dUc. 



(76) 



From (37) and (41), the contribution to the mean square of this 

 conduction current from the frequencies between / and f -\- df is 



qj — le'-df I n[){u,)diic = 2eludf. 

 Jo 



(77) 



With this result, the effect of transit time on the shot noise current is 

 given by 



//- = 



2ehdf 



1 + 



Z stOii. 



Al^ 



-^,[2 + Q'' - 2(cos + ^ si 



n0)]}. 



(78) 



where Z/ is the impedance of the external circuit at the frequency/ and 

 x/fcoe is the capacitive reactance of the diode at the same frequency. 

 Thus the shot noise current is modified by transit time in precisely the 

 same manner as the noise generator voltage for the thermal tube 

 noise. 



The effect of transit time upon the shot noise, as indicated in (78), 

 is identical with that obtained by Spenke for the same operating 

 condition of low space charge and high anode potential.^ Spenke 

 derives this result through a clever application of a Fourier Series in 

 which account was taken of the effect of transit time upon the wave 

 shape of the current induced in the anode by the electron moving from 



