72 BELL SYSTEM TECHNICAL JOURNAL 



and 



if n and cr are known, the maximum value of VgjVp may be calculated. 

 Fig- 7 shows that a value of 7 just greater than 2 will give the lowest 

 minimum value for (p {(p = 0.07) by intersection with curve a. In 

 this region ipjix <<C 1 so that 



y/- max. = - = 14. 



V p / «p 



For values of 7 only slightly less than 2 the minimum value of ip rises 

 abruptly, being given by the intersection with curve d, while for values 

 greater than 2 the rise in ^p is not so abrupt. 



It should be noted that for the usual cylindrical triode the departure 

 from the parallel plane case is not very marked in the grid-plate 

 region while it can be taken into account by the usual cylindrical 

 formulae for the cathode grid region. It therefore becomes possible 

 to extend this analysis in an approximate sort of way to cover the 

 cylindrical case. 



APPENDIX 



Definition of Symbols 



Vi = Potential of the first plane in volts, 

 V — Potential of a second plane in volts, 

 (p = Ratio of the potential at the second plane to the potential of the 



first plane, 

 / = Injected current in amperes per sq. cm., 

 X = Distance in centimeters, 

 d — Spacing between the two planes in centimeters (used when this 



distance is regarded as a fixed quantity), 

 5 = Distance between the two planes in centimeters (used when this 



distance is regarded as a variable), 

 a = Distance between the planes expressed in units Sq, 



So — 1.527 X 10""^ j.^j^ (centimeters), 



a = 1.527 X lO-^* = [10'»(2e/wc)i/V97rc2]i/2;'o 

 a^ = 2.33 X 10-«, 

 Z = Fraction of the injected current / which reaches the second 



plane, 

 / = Time in seconds, 

 T = Electron transit time between the planes in seconds, 



