46 BELL SYSTEM TECHNICAL JOURNAL 



two electrodes, which usually is maintained at a negative operating 

 potential, is connected to the input circuit and acts as a control 

 electrode. The second of these two electrodes, which is maintained at 

 a positive potential with respect to the cathode, acts as an anode or 

 collector of electrons and is connected in the output circuit. Just as 

 in the case of the triode, then, a study of the characteristics of multi- 

 electrode tubes is concerned with variations in the current collected by 

 the anode with variations in the potential applied to the control grid. 

 This anode or plate current may be expressed as a function of the 

 various electrode voltages by the following equation: 



7p = /(£;„ £„,, £„,, £„, etc.), (1) 



in which Ep is the operating voltage applied to the output anode or 

 plate, and Eg,, £„j, Eg^, etc., are the operating voltages applied to the 

 various grids numbered outward from the cathode. The variation in 

 the anode current, neglecting second and higher order terms, is given by 



dl, = %^ clE, + 11^ dEg, + 1^ dE,, + 1^ dEg, + etc. (2) 

 dtp dhg, dE,,^ dEy, 



The partial differential coefficients in equation 2 have the physical 

 dimensions of conductances and, if these conductances be designated 

 by the letter 5" with appropriate subscripts, the equation may be written 



dip = Spp-dEp + Spi-dEg, + Sp2-dE„„ + Sp3-dEg, + etc. (3) 



The plate or output anode conductance of a multi-electrode tube is 

 defined in the same manner as for the three-electrode tube. It is the 

 rate of change of plate current with plate voltage, that is, it is the 

 slope of the plate current-plate voltage characteristic at the selected 

 operating point, the potentials of all the other electrodes remaining 

 constant. Under this condition, from equations 2 and 3 



1 T 



Plate conductance = t-^ = Spp — Sp. (4) 



Obviously, the plate resistance also must be defined in the same 

 manner as in the triode, that is 



Plate resistance = Rp = -—jr- = ~^ • (5) 



dip Op 



dEp 

 In a similar manner, (he (ransconductance from the control grid to 



