36 BELL SYSTEM TECHNICAL JOURNAL 



Substituting (8) in (7) we have 



r„ = ^'^'■-if^V' . (9) 



In order for Wq to be a maximum, 



Performing this operation on (9) and solving for /;, assuming K is con- 

 stant, we get 



"' no " r, ^'"^ 



since f'(Ip) is df(l;,)/dlp, which is obviously rp, the differential plate 

 resistance when Ip is flowing. 

 We may also write 



Ro=^^^/^' (11) 



Substituting (10) in (11) we obtain 



i?o = g (12) 



which gives the relation of Ro to rp for maximum power output. 



If we have the ip — Cp curves for any tube we may approximate 

 closely the point of maximum output at any peak grid voltage. This 

 can be accomplished by a process of cut and try in finding where the 

 quantity (Eb — epm)Ip becomes a maximum, since K remains fairly 

 constant, depending mostly on the bias voltage and grid excitation 

 voltage, as will be shown later. Also, for any given output impedance 

 and peak grid voltage, we may find the output from the ip — e.p curves 

 by cut and try by finding where 



17^ 



= KRq [from (11)] 



is satisfied. It wall be noticed from Figs. 4A and 5A that I\/Ip = 0.48. 

 In general, K will be near this value for well loaded conditions. The 

 actual value depends upon the exciting voltage and grid bias voltage, 

 and at low values of excitation it may differ considerably from the 

 value indicated above w^hich may render the cut and try methods 

 outlined subject to considerable error. 



In addition to finding the maximum output for a given set of con- 



