662 BELL SYSTEM TECHNICAL JOURNAL 



4/3 obtained by Benham ^ in an analysis which considered effects 

 between cathode and grid only. Benham's value applies strictly to 

 the capacitance between cathode and the plane A in Fig. 1 while (99) 

 applies to the parallel combination of cathode-grid and grid-plate 

 capacitances. The constants of the individual capacitances may be 

 calculated from the fundamental equations (76)-(79) but are omitted 

 here because of space limitations. A series of experiments performed 

 several years ago by Mr. A. J. Rack and the writer and covering a 

 wide range of operating conditions with several vacuum tubes showed 

 values greater than unity for the dielectric constant of the cathode- 

 grid capacitance and less than unity for the grid-plate capacitance. 

 The parallel combination had a dielectric constant which was greater 

 than unity in the range investigated, being thus in accord with (99) 

 which always gives constants greater than unity for normal values of h. 



The input capacitance of detector- and voltmeter-tubes being thus 

 a somewhat complicated function, it is to be expected that the cal- 

 culation of the impedance at higher frequencies where transit times 

 are appreciable will be similarly complicated. To avoid undue length 

 only the first term contributing to the resistive component of the 

 active grid loss will be computed in detail. It must be pointed out, 

 however, that the series in powers of transit angle which represents 

 the input impedance converges slowly so that the first term is useful 

 only when the transit time is small. 



Keeping this in mind, we go to (96) and write the impedance in 

 series form, obtaining finally the following expression for the equivalent 

 shunting resistance between cathode and grid : 



1 ^ e,^ IXg 



Ra 180 /-p 



where 



y^A - yB + CI 



an 



(100) 



(y - h^f J 



Mo 



X 



Mo + |(l +y){\ +/0 -\{\-\-hY 



^ = 9 + 44/i + 45/^2, 



5 = 51/2^ -f 123/j'^ + 55/;.^ + ^h\ 



C = 45/;.* + 51h' + 24/;« + 11/;^ + 3h\ 



As in previous cases, this may be written in several ways, depending 

 on the mode of expression of 6c and rp. For example 



dc = IrcCoCc, 



