584 



BELL SYSTEM TECHNICAL JOURNAL 



It is obvious that a third equation is needed before the unknowns can 

 be found. But (4) and (5) express all the relationships that are 

 necessary for the equivalence of Figs. 8 and 9. It follows that we are 

 at liberty to impose arbitrarily a third restriction upon the currents 

 in Fig. 9. 



The choice of this restriction may be made in many ways, each 

 resulting in a different network, all equivalent however to Fig. 8 and 

 to the vacuum tube. For example, /i might be defined as consisting 

 of conduction current only. Such a choice might seem at first sight 

 to be a desirable one because it corresponds rather well with the 

 conception of the cathode-plate path as being determined by electron 

 movement at low frequencies. If it were adopted, however, the 

 generalized network resulting would be found to be quite awkward, 

 involving two or more internal generators and complex amplification 

 factors. 



The simplest network would be the one involving the fewest number 

 of internal generators, and the restriction adopted in the following 

 analysis for the currents in Fig. 9 is made with that object in view. 

 The result, as will be shown, corresponds at low frequencies with the 

 usual concept of the tube, and gives a high-frequency network where 

 neither the cathode-grid nor the grid-plate paths contain internal 

 generators. 



The restriction which accomplishes this result is obtained by placing 



Fp - F, = hZo 



(6) 



so that (4), (5) and (6) determine the internal currents, h, h and h, 

 in terms of the external currents Ip and Ig, and the, as yet, arbitrary 

 impedance Zq. 



The solution of (1) to (6) yields 



Fp + r, - 



v„ 



(7) 



(8) 



The choice of (6) eliminates the internal generator from the grid-plato 

 path, but still leaves the impedance Zo to be defined at will. From (8; 



