ELECTROSTATIC FIELD IN VACUUM TUBES ill 



Equation (24) may be interpreted in a number of different ways of which 

 we shall mention the following two: 



1. The "equivalent voltage" Vg + VJn does not act at the grid but at a 

 distance D from the cathode, where 



D = di+ {d, + d^la (28) 



Roth the equivalent voltage and distance vary along the cathode surface. 



2. The "equivalent voltage" 



V, = (V, + Fp/m)/[1 + (1 + dMW] (29) 



acts in the grid plane and varies with distance along the cathode surface. 

 As far as the cold tube is concerned the two formulas are equivalent at 

 the cathode, but not at the grid. When the tube is heated and complete 

 space charge is present, the two formulas also differ at the cathode. The 

 current density in the presence of space charge is, according to (28) and 

 Child's law: 



/ = K(V, + VM^'^/D' (30) 



while, from (29), 



/ = KVl^'/dl (31) 



In both, K"^ = 32 e^e/Sl m, where e/m is the ratio of electronic charge to mass. 

 The value of current given by (31) is [1 + (1 + c?2M)/m]''^ times as large 

 as that given by (30). li ti >> 1 + d^/di the two values are nearly the 

 same. In tubes with close grid-to-cathode spacing the inequality may not 

 be fulfilled. As to which viewpoint is more accurate, we note that Ferris 

 and North in their papers "■ ^^ on input loading adopted the latter, and that 

 at high frequencies where electron transit time must be considered the second 

 viewpoint is preferable because of the more accurate representation of 

 effects at the grid. For a more complete discussion see Reference 19. 

 Figure 4 shows curves of relative current density as a function of distance 

 along the cathode as computed from Eq. (31). The transconductance for 

 unit area of cathode surface as computed from the same equation is given by: 



= 3.512(F, + Vp/ixY'^idi/Dy^ micromhos. (32) 



The resulting variation with distance along the cathode is shown in Fig. 5. 

 Defining the figure of merit If at a point x along the cathode as the ratio 



