MODULATION IN VACUUM TUBES 459 



operating point. It is a simple matter to calculate these quantities 

 on the basis of Carson's and of van der Bijl's relations. 

 Thus the plate current is given by 



i = a{Ep + nEoY, 



the internal plate resistance to alternating currents is 



R,= l/2a(£p + M£.), 



and the internal plate resistance to direct current is 



Rdc = Ebla(Ep + fxEc)-. 



At the operating point for maximum power we have Eb "= — 2/xEc, 

 and when the alternating grid potential is equal in amplitude to the 

 grid bias, the above expressions may be manipulated to give 



(10) 



1. The d.c. power dissipation P = aEp^l4:, 



2. The a.c. power delivered W = aEp^/Sl, 



3. The 2d harmonic current Jo = aEp^l64, 



4. The fundamental current /i = a:£//4. 



From these we have for the ratio of d.c. to a.c. powers 



P/W =8, 



or the efihciency of power conversion at the maximum power condition 

 is 12| per cent. We find also 



W/J2 - 2Ep, 



or the relation of the fundamental power to the second harmonic 

 current depends upon just one parameter, the plate potential. Other 

 relations of interest are the two following: 



Rdc/Ro — 4, 

 /1//2 =16. 



These four relations are independent of tube structure (n, Ro) and we 

 know that they cannot be accurate in view of the assumptions made 

 in deriving them. In view, however, of the importance of general 

 relations of this type in the design of amplifiers, it is of interest to 

 compare these relations with the ones existing, as calculated by the 

 more accurate theory in which fj. variation enters. 



