434 



BELL SYSTEM TECHNICAL JOURNAL 



grid is allowed to take convection current. The amplification factor, 

 H, is considered variable, and the effect of plate potential on grid 

 current is included. Under these conditions, the total plate current 

 of the tube can merely be said to be a function of the grid and plate 

 potentials; and the total grid current, likewise, is some other function 

 of the grid and plate potentials. The fundamental relations: 



Ip = Ip(Eg, Ep) 

 Ig = h{E.g, Ep) 



(1) 



(2) 



express, the operation of the device. They represent the static 

 characteristics of the tube. It is from these two relations alone that 

 the general theory must be built. 



In order to do this, the following notation will be employed : 



ip = Ipo~rip 



Ep = Epo + ep 



LLg = higo -(- Cg 



(3) 



It will be recognized that the lower case letters represent variations 

 in the normal values of the currents and voltages denoted by the zero 

 subscripts. It should be noted, moreover, that all voltages and 

 currents refer to the effect directly on the element of the tube, plate 

 or grid as the case may be. 



With the aid of (3), equations (1) and (2) may be written 



ip^Pieg-\-P2ep + \Pzeg--\-Piegep + \Piep''--{- . . . 

 ig^Tieg-\-T2ep + \Tzeg~-\-Tiegep-[-\Tiep''--\- . . . 

 where the P's and T's have the following significance : 



(4) 

 (5) 



Pi = 



Ti 



3lpo 

 dEg 



digo 

 dEg 



^'-Wp 



■j^ _ O-igo 



^'~dEp 



P,= 



T,= 



d-'i. 



po 



dEg' 

 dEg' 



P4 = 



T,= 



d'l. 



po 



dEgdEp 



d'Igo 



dEgdEp 



Pb = 



d% 



po 



rp _ d J-gO 



'~dEp' 



(6) 



Equations (4) and (5) are obtained directly from the extension of 

 Taylor's Theorem. The P's may be written in more useful form with 

 the aid of (1) and the well-known definitions of the amplification 



