1126 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 



_ 4.74 X WMIl'^ 



\a c/\ /x a / 

 £,, = ^ [5/8 X rn'o^'^ll" (1 + i ^) - £., 



2.73- - log,„cosh(27r-V 

 a \ a/ 



(3) 



logio coth 



(-0 



(4) 



Substitutions for Ci , C2 , and K in (1) are made from assumptions II 

 and V. Gn is found by differentiating the plate current expression (assump- 

 tion III) with respect to Ed , remembering that /x is independent of Ed 

 according to assumption IV. 



.1/2 

 ^ 2.33 X IQ-'MA 



^"^ = 2 ^ . _^ ? r\ 3/2 (5) 



(6) 



From assumption III we can write 



.1/32/3A , la + A^'^ 



(IP \l/2 Ib 0' I 1 T- I 



)u "^ '7 (2.33 X lo-'y'm^'^A'i' 



Substituting in (5) 



, (2.33 X 10-')M.1/!,'V" f 1 + 1 ''~±^) 

 ^ _ o ^ \ IX a / 



a'^ ( 1 + 1 e-±i ) (2.33 X 10-«)^^^M^^^^ 

 1.5(2.33 X 10-")'^^^'^'^'/^^^ 



Crm — 7 r 



\ yi a / 

 Since /« = M/(v4 by defmition, 



^ 2.64 X IQ-V^/J^' ,o^ 



t'w = ; r yfi) 



1/2 



(7) 



