88 



Ro = 



BELL SYSTEM TECHNICAL JOURNAL 



2 . 



( 1 + cos 7] sin r; | (1 — cos f) 



12ro 



2 



sin r? cos v ) ({' — sin {') 



+ (2 cos 7] sin rj — 2) 



(57) 



Xo = rj^ H 1 + cos r; sin r; j (f - sin f ) 



/ 2 . 2 \ 



+ sin 77 cos ?7 (1 — cos t) 



\V V / 



+ 

 + 



y^ -^(1 - cosf) +2sinf 

 77 -\- -pV^ ~ 2 sin 77+77 cos 77 



(58) 



where 77 is the transit angle from cathode to grid, f is the transit angle 

 from grid to virtual cathode at the plate, and ro is the zero-frequency 

 resistance which would be present in a diode having the grid-plate 

 dimensions, and the same operating direct-current voltages and current 

 densities which occur in the grid-plate region of the triode under con- 

 sideration. 



Fig. 11 shows graphically the relation between Rq and Xo for a 

 wide frequency range, in terms of the reference resistance, ro. Curve A 

 is drawn for the hypothetical condition that 77 = ^, so that the tube is 

 exactly symmetrical about the grid. Actually such a condition could 

 not be attained, since the grid captures some of the electrons, leaving 

 fewer for producing space charge near the plate. The grid-plate 

 dimension would accordingly have to be increased in order to secure 

 the space charge, but this would cause the transit angle f to become 

 larger than 77. However, despite the fact that it does not correspond 

 to a physically realizable condition, curve A is nevertheless of use in 

 indicating the limit which is approached as the grid capture fraction is 

 made smaller and smaller. 



Curves B and C correspond to values of grid-plate transit angle 

 equal respectively to two and three times the cathode-grid transit 

 angle. Both these curves represent conditions which may readily be 

 obtained experimentally, and indeed, curves lying much closer to A 

 than does the curve B may be secured. For example, the general 

 relation for the ratio of the transit angles in terms of the direct currents 

 Ja and Jb in the cathode and in the plate region, respectively, when 



