VACUUM TUBE ELECTRONICS 93 



if the plate fluctuates in potential by a very small amount, as it does 

 for incipient oscillations, and hence does not become positive during 

 the alternating-current alternation, then no direct-current plate cur- 

 rent can occur when the plate is biased negatively. After oscillations 

 have built up to an appreciable amplitude, the presence of plate cur- 

 rent is not only possible, but is in fact to be expected. 



We have at hand the mathematical tools with which to compute 

 our R — X diagram for the negative plate triode with complete space 

 charge near the cathode. Thus, instead of substituting (35) in (55) 

 we must substitute (53). Since complete space charge is still postu- 

 lated near the cathode, (26) and (25) are still applicable. The result is: 



R, = 



12ro 



2 



1 + cos 77 sin 77 If^ 



V 



/ 2 2 \ 



- ( sin 77 cos 77 j (f 2 coth f - ^) 



-f (2 cos 77+77 sin 77 — 2) 



(59) 



Xo 



12ro 



^4 



2 . 2 



sin 77 cos 77 1 t- 



77 77 



-(- I 1 + cos 77 sin 77 j {^~ coth i' — f ) 



+ iW - r- coth f + r) + (77 + k^ - 2 sin 77 + 77 cos 77) 



, (60) 



and the corresponding diagram is shown in Fig. 14. Here the curve A 

 shows oscillation possibilities for transit angles as small as 3/27r, while 

 a much greater amount of resistance would have to be added to the 

 circuit in order to eliminate the negative resistance and so stop the 

 oscillations. In all, then, this method appears to be a better way of 

 operating the system than with the positive plate, and this conclusion 

 is substantiated by experimental observations. 



As before, an increase in the grid capture fraction moves the oscilla- 

 tion region up to higher frequencies. 



In both of the examples cited above, and represented by Figs. 11 and 

 14, respectively, complete space charge was assumed near the cathode. 

 The effect of decreasing the cathode heating current so that this charge 

 becomes negligible may be computed by employing (37) in place of 

 (25), and (38) in place of (26). 



The resulting equations for a slightly positive plate are, 



