524 



BELL SYSTEM TECHNICAL JOURNAL 



Theory 



Let us consider the circuit arrangement shown in Fig. 1, where 

 Zi, Z2 and Zz are linear impedances which may include interelectrode 

 admittances. The impressed variable electromotive forces whose 

 instantaneous values are denoted by Eg and Ep are in series with 

 the impedances Zg and Zp, respectively. In the absence of these 

 electromotive forces direct currents and voltages are established in 

 the circuit due to constant grid and plate electromotive forces. With 

 the variable electromotive forces impressed incremental currents and 

 voltages are produced. The instantaneous values of these incremental 

 voltages are indicated on Fig. 1 by g, e, v and p. The incremental 

 plate current is /. The positive directions of these quantities are 

 given by the directions of the arrows. 



Z3 



Ep(r\j 



Fig. 1 — Three-electrode vacuum tube and circuit. 



We will now make two restrictive assumptions: first that the grid 

 is never positive so that conductive grid current is absent, and second 

 that the amplification factor ix is constant. 



The basis for the analysis is given by the characteristic tube equa- 

 tion 



Er 



/ = /(£.+f) 



(I) 



where I is the total instantaneous current flowing from plate to 

 filament; Ec is the total instantaneous potential difference between 

 grid and filament and Eh the total instantaneous potential difference 

 between plate and filament, ix is the amplification factor. The 

 relation between the increments e, v and / is given by the following 

 equation : 



J = Piifxe + v) + P^ifxe + z;)2 + • • • + Pnifie + v)- + 



(2) 



