EQUIVALENT CIRCUITS OF NETWORKS 



597 



It is well to note that this general low-frequency case is governed by the 

 two simultaneous equations 



(5) 



(6) 



(7) 



The network of Fig. 4 is thus a possible form of circuit interpretation of 

 (5) or (6). It may also be observed that (6) represents at least formally 

 the most general formulation of the Hnear active four-pole so that even at 

 very low frequencies the general four-pole point of view might be useful. 



Several observations may now be made. In the first place it should be 

 noted that these networks are not based on any study of the internal action 

 of the tube, but rather on the purely formal mathematical process of dif- 

 ferentiating the two functional relations which express the broad fact that 

 plate and grid currents are some unspecified linear continuous functions of 

 the grid and plate potentials in the neighborhood of the operating point. 



In the second place it may be observed that the network of Fig. 4 repre- 

 sents in a sense two separate networks interacting with each other by means 

 of voltage or current generators. This method of equivalent circuit repre- 

 sentation is the result of separate interpretation of the equivalent plate and 

 grid circuit theorems. As a corollary it follows that such a four-pole equiva- 

 lence involves at least two generators within the network in order to take the 

 effect of interaction into account. 



We may say that the networks discussed were satisfactory so long as the 

 frequency was low enough to allow displacement currents to be disregarded. 

 With the operation of circuits at higher frequencies (up to the order of 10® cps, 

 say) it became necessary to take the internal tube capacitances into account. 

 This was done by the superposition of a capacity network as shown in Fig. 

 5. It is interesting as well as instructive to formulate this network transi- 



