600 

 Whence, 



BELL SYSTEM TECHNICAL JOURNAL 



rn 





)duc — 



h 



(27) 



This is the desired relation between t// and the a-c. anode current. 



To find the other desired relation, it is first observed that by (20) 

 and (25), the d-c. voltage-current relation is 



ex 

 If 



[hm It 

 ee \a 



1/2 



h'" = F(W) +/(r7o 



(28) 



This is identical with that obtained by Fry and Langmuir. The 

 values of F{r]o') and/(?7o) have been tabulated by Langmuir.'^ 



From this d-c. relation, it may readily be shown that the a-c. plate 

 impedance of the planar diode is 



FJVo') -\-f(vo) _^ dF(r,o') ^ dfivo) 



r,, = 



dr,o' 



drio 



BkT 1 



elo dfivo) 



eh df(rio) 



(29) 



IrjG 



kT dr]o 

 Since the noise generator voltage, 



E = I,r^ + Vu 

 the substitution of (27) and (29) reduces (24) to the following relations: 





eE dfivo) 

 kT dr]o 



J I r (B - C - D)8(n,)dih 

 2 r""' [""= yjf^^^8(u,)du4ri 



2 H" n 



$(7?) 



(30) 



By the additional symbols, 



H{Uc, VO, T/o') = 



kT 



df(vo) 



(B - C - D) 



h 



GiUc, r?, Vo) = — 



dr]o 



2 kT Vy + 7? 

 V^ J dfivo) Hv) 

 dr]o 



(31) 



the noise generator voltage may be expressed in the condensed form, 



H8{uc)du, -f I Gb{n,)dudn- (32) 



