ELECTRON TUBES FOR A COAXIAL SYSTEM 1127 



Substituting in (1), 



p ^ 2.64 X lO-'MAll"' ,^. 



a 



('+r-f>"H^'»""^(M^')] 



Collecting the constants and cancelling the A's, 



F = 4.74 X lO'Mll" ^2) 



\a b c/ \ n a / 



The expression for Ec2 can be found by substituting Ib = MIqA in assump- 

 tion III and solving for Ec2 . 



3/2 



2.33 X 10""^^ ' "^ 



MIqA = 



^ + £cl 





M 1.76 X 10-* 



£.. = M [5.68 X 10V»/S" (1+ ^ ^*) - £..] (3) 



The expression for fx can be found by applying assumption / and substitut 

 ing n = - in the Vogdes-Elder formula* for a plane structure. 



Or 



_ lirnb logio cosh (27rwr) 



^ ~ 2.303 log 



1 

 Substituting n = 



2.303 logio coth (iTrnr) logio coth (lirnr) 



1 

 a 



(10) 



2.73 - logio cosh f27r -j 



logio coth ( 27r - j logio coth ( 27r - j 



(4) 



Equation (11) can be derived by considering a particular structure and 

 introducing a small sinusoidal signal Eg cos pi added to the d-c. voltage 

 in the plate current expression, Assumption III. This can be written as 



Is + i =Gc (— + Eel + Eg cos ptj (12) 



* F. B. Vogdes and Frank R. Elder, Phys. Rev., 24, pp. 683-689, Dec, 1924. 



