478 BELL SYSTEM TECHNICAL JOURNAL 



high frequencies. In addition, the possibility of designing an electronic 

 negative capacitance is opened up and this is a highly desirable ob- 

 jective. 



However, it must be kept in mind that in the discussion, effects 

 such as velocity distributions, electron deflections and dispersion forces 

 have been neglected. Furthermore, in an actual tube the capacitance 

 Cg must also be considered. At the Kipp the capacitance C is equal 

 to — oc ; therefore, as the Kipp point is approached a positive capaci- 

 tance is expected. 



The capacitance and conductance both pass through zero when 



Jo^=l, (24) 



or when 



J" 2 



«02 = /o -y- • (25) 



But in general 



Wo2 = uoi + aoiTi + Jo-j- > (26) 



where Woi and aoi are the d-c. speed and acceleration in the plane of 

 grid Gi, Fig. 3. 



The relation between initial speed and acceleration for zero capaci- 

 tance and conductance is, therefore: 



woi + aoiTi = (27) 



and since both 7/01 and Ti are inherently positive, the initial acceleration 

 must be negative. For the capacitance to be negative the requirement 

 is obviously 



«oi + aoiTi < 0. (28) 



Necessary requirements for a negative capacitance are thus a finite 

 electron speed and a retarding field at the plane of injection. 



PART II 

 Experimental 



In this section some experimental results will be discussed. The 

 measurements all refer to the capacitance between control grid and 

 ground of some experimental tubes. The tubes were cylindrical in 

 structure and contained two positive grids close to the cathode followed 

 by a negative control grid. The first positive grid has the essential 

 function of controlling the magnitude of the current whereas the 



