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BELL SYSTEM TECHNICAL JOURNAL 



between the transconductance dl/dVg and the sum of Cgc and Cpc at this 

 point, we find from (30) 



M = (u/syndi + {di + ^2)/m]-^V(m + 1) m 



where / = el /me, e/m = 1.77 X 10" coulombs/kg. From (31), we find 

 on the other hand 



i/ = (47/3 d^yWip + 1) (34) 



0.05 0.10 0.15 20 0.25 0.30 0.35 40 0.45 0.50 

 DISTANCE ALONG CATHODE. 'Va 



Fig. 4 — Variation of current density in a triode. 



Both formulas indicate that for a cathode capable of supplying a given cur- 

 rent density the only means of improvement lies in decreasing the cathode- 

 grid spacing. The impro\-ement is extremely slow; doubling the figure of 

 merit requires an eight-fold decrease in spacing. 



We again emphasize that the calculated current densities and figures of 

 merit are functions of x, the distance along the cathode. The total current 

 between the two grid wires is found from (30) to be 



It = 2K (V„ -f VJnf^ dx/D" (35) 



