600 

 Whence, 



BELL SYSTEM TECHNICAL JOURNAL 



'yi 



/i 



' = y- j d(Ur)dUc — 7^ 



(27) 



This is the desired relation between rji' 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 



hni T 

 ee \ a 



h"- = F(y),') +/(r/o). 



(28) 



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

 values of F{r]Q) and/(i7o) 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 



r„ = 



F(r?oO +/(^o) I dFir,,') ^ dfivo) 



2 dr,o' drjo 



eIodf{r]o) 



BkT 1 



eh dfjrio) 

 drio 



(29) 



kT drjo 

 Since the noise generator voltage, 



E = hr, -f Fi, 

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



- I r {B - C - D)b[u,)du, 



2 n' r^ vy- + vHu,)durdv 



2 no n 



$(77) 



(30) 



By the additional symbols, 



H{Ue, vo, Vo') = 



G{uc, Vi Vo) = 



kT 



df(vo) 



(B - C - D) 



dr]o 



2 kT Vy + V 



^0—5 — 

 dr]o 



(31) 



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



E = Hb{u,)dti, + 1 G8{u,)du4v- (32) 



