48 BELL SYSTEM TECHNICAL JOURNAL 



tions define transconductances, electrode resistances, and amplification 

 (or reflex) factors analogous to those just given. Since these quantities 

 are not used in this paper, they will not be given further consideration 

 here. The voltage applied to the control grid will be designated by Eg, 

 regardless of the grid employed for the purpose; and the trans- 

 conductance (or mutual conductance) and the amplification factor, 

 applying to the control grid and plate, will be designated by Sm and m. 

 respectively. 



If a load resistance, R, is inserted in the plate circuit of a multi- 

 electrode tube, and if the potentials of all of the elements other than the 

 control grid and plate are maintained constant, equation 3 reduces to 



dip = Sp-dEj, + S,n-dEg = -^ -dEp -\- -^ -dEg. (11) 



Kp Kp 



In this case, the only independent variable is Eg, and Ep varies by 

 reason of the changing potential drop across the external load resistance, 

 R, due to variations in the plate current, Ip, produced by the varying 

 grid potential. Consequently 



dEp = - dIp-R. (12) 



Substituting equation 12 in equation 11 and reducing. 



For vacuum tubes having curvilinear characteristics, equation 13 

 applies rigorously, of course, only to infinitesimal variations in Ip and 

 Eg. However, as in the case of the triode, the output from multi- 

 electrode tubes may be expressed by a power series in terms of finite 

 voltage variations applied to the elements, the coefficients in the series 

 being functions of the static characteristics. If these finite variations 

 in Ip and Eg are designated by ip and Cg, respectively, the output current 

 is expressed to the first order by 



Rr, + R' 



which is identical with the equation expressing the output current from 

 a triode. 



Letting Cp represent the variable voltage across the load resistance, 

 R, the voltage amplification is given by 



