SHOT NOISE IN DIODES 



599 



Let 



-V — y[a u' 



^ _ F(vo') +/(r?o) ^ dF(vo') ^ dfivo) 

 2 drjo' dr]o 



Z) 



Vx Jo ^('J) 



^7? 



(22) 



From the definition for -q, given in connection with (13) and (14), 

 it may be shown that 



Vl = Vl ~ Tf^ 1' 



(23) 



where V\ is the a-c. anode potential. With the definition given for 

 a(6) and |S(5) in (11) and (12), and from the above relations, (21) may 

 be rewritten as 



y]i'B - 



where 



eFi<i/(r7o) 1 \ r fr ^ n^u ^^ 



Jf-d^^NF^'l (C + D)5Mdu. 



'Vc ^Jy•2 -(- 7j 8(Ur)dU,dr] 



+ 



t TT Jo J- 



Hv) 



r 



(24) 



"^ = -'^^- 



V = 



2e_ 



hm 



Vo 



Before (24) can be used, the relation between 17/ and the a-c. anode 

 current, and also the expression for the a-c. plate impedance must be 

 obtained. From the general relation given in (1), the instantaneous 

 current per unit area is 



/»oo /»«5 r'j-- 



I ^ e i n(ue)duc = e tioMdu,. + e I 8{Uc)dUc 



J lie' «^«c' '^^c' 



= Nee-"' + e I d(uc)duc. 



Since the instantaneous voltage of the potential minimum may be 

 expressed as a sum of a d-c. component plus a small a-c. fluctuation, 

 the d-c. and first order fluctuation plate current are respectively 



Ii ^ - 't]i'Net-< + e 





8(uc)dUc 



(25) 

 (26) 



