578 BELL SYSTEM TE^CHNICAL JOURNAL 



realized that a change in electric intensity produces precisely the same 

 effect in a circuit as does an actual motion of charge. In Fig. 3 this 

 means that the current entering the branch between cathode and grid 

 for example consists not only of ordinary conduction current but also 

 of displacement current so that the current in the cathode-grid mesh 

 is the whole current flowing into the grid element. Likewise, the 

 current in the cathode-plate mesh is the whole current flowing into the 

 plate element of the tube. 



In Part II straightforward transformation of the equations repre- 

 senting Fig. 3 shows that it may be represented just as well by an 

 infinite number of other equivalent networks. Naturally our aim is 

 to choose the form of network which is easily adaptable to the greatest 

 number of practical applications, and the one that suggests itself 

 primarily for this purpose contains the fewest number of internal 

 generators. A second consideration in the choice of the best equivalent 

 network is that the network should resemble the familiar delta equiva- 

 lent of Fig. 2 as closely as may be, so that results based on that figure 

 may be interpreted readily in terms of the more general network. 



Fig. 2 is actually a modified form of a delta network. The most 

 general delta would be the one shown in Fig. 4 which consists of three 

 series branches, each containing an internal generator in series with 

 an impedance. When the mathematical transformations from Fig. 3 

 to Fig. 4 are carried through, it is found that a proper choice of defini- 

 tions for the various impedances reduces Fig. 4 to the network shown 

 in Fig. 5. Here only one internal generator remains, but that generator 

 acts in series with the internal plate impedance of the tube so that 

 Fig. 5 does not quite conform to the popular network where a capaci- 

 tance is assumed to shunt the internal generator by acting directly 

 between plate and cathode. However, again it can be shown that 

 Fig. 5 may be transformed to Fig. 6 and by a proper choice of the two 

 impedances Z' and Z", the internal generator reduces merely to our 

 familiar low-frequency amplification factor multiplied by the grid 

 potential variation. 



Thus Fig. 6 with the associated definitions of impedance represents 

 the generalized form of the equivalent network of negative-grid vacuum 

 tubes and is valid until the velocity of the electrons approaches that 

 of light or until the distance between elements of the vacuum tube 

 becomes comparable to the free-space wave-length of any ultra-high 

 frequency considered. The expressions for the various impedances in 

 Fig. 6 are naturally long and complicated. However, at frequencies 

 where the efi^ects of transit time of the electrons are only moderately 

 important, the complication reduces enormously and we have Fig. 7. 



