VA CUUM TUBES FOR R.4 DA R I.F. A MPLIFIERS 391 



2.33 X 10 '.1 [En + 



E,-'" 



^b = ; : . ,\3/2 ' — (6) 



<-r-i-T 



It is assumed that the electrons leave the cathode with zero initial velocities. 

 The failure to take into account the effects of initial velocities makes this 

 equation only a fair approximation for close-spaced tubes, but it is still 

 instructive to assume it is approximately correct for the purposes of the 

 present discussion. "-!'' is the active area of the structure, "o" is the 

 distance from the cathode to the plane of the grid, "6" is the distance from 

 the plane of the grid to the plate, Eb is the plate voltage, Ed is the effective 

 grid voltage (including the effect of contact potential) and /x is the amplifi- 

 cation constant. Dimensions are in cms. This stipulation is unnecessary 

 for equation (6) but is necessary for some of the later equations. For a 

 plane parallel tetrode or pentode, equation (6) is a good approximation if 

 Eb is replaced by the screen voltage Ec2 , m is replaced by the ''triode mu" 

 Hn {mil of control grid with respect to screen grid) and the coefficient M 

 introduced, where M is the ratio of the plate current to the cathode current. 

 The reason this approximation is good is that the field at the cathode, and 

 therefore the cathode current, is determined almost entirely by the poten- 

 tials of the first two grids. Because of the screening effect of these grids 

 the potential of the plate has little effect on the cathode current. We have 

 then 



2.33 X 10^' M^ (Eel + — ) 



^6 7 -. , ,\3/2 \') 



\ M12 CL / 



The distance "6" is now the distance from the plane of the grid to the plane 

 of the screen. This expression can be differentiated with respect to Ed to get 





"^""^ .'f. + l-L + if '' 



\ M12 a / 



It is assumed that /X12 and M are independent of Ed- If we let /o be the 

 cathode current densitv, then substitute MI^A for lb in (7), and eliminate 



/ ' E,\ 



the expression ( E^ + — ^ ) between (7) and (8), we have 

 \ M12/ 



3 {IM X 10^'')-'M.4/[" .^. 



^^ - 2 '' ~' ^"^^ ^^^ 



Yi + 1^ 



