438 BELL SYSTEM TECHNICAL JOURNAL 



In equalion (14), when the ampHfication factor, /x, is considered 

 constant, we have tlie well-known relation as given in Mr. Carson's 

 paper 



Experiments have shown, however, that when the resistance, Z, 

 is not small compared to rp the modulation resulting from variations 

 of M amounts to an appreciable part of the total. When the grid is 

 maintained at a negative potential with respect to the filament, (14) 

 may be simplified somewhat by the relation which then holds quite 

 closely', namely: 



9E/, 9£g 

 Equation (14) then becomes 



9m 







This equation is applicable to the calculation of the output current 

 when eg is known, and the grid takes no convection current, as is the 

 case in very many circuits met with in practice. 



It is instructive to investigate the relative magnitudes of the two 

 components of the second term of (16) in an actual experimental case. 

 For convenience, the contribution of the second component of this 

 term will be called, 'V modulation." A vacuum tube was measured 

 and found to have the following properties under operating conditions 



Yp = 6400 



r'^=-61.3 



M = 5.84 



The results of applying these to (16) are shown in the following 

 table : 



Z Total modulation /x modulation, % 



.03341/10^ e2 23.35 



rp .00515 lO'' e'-' 37.8 



2 rp .()()1S() 10^ e^ 46.6 



4 Yp .OOOSSU.'IO'^ e' 55.0 



^ See appendix I for proof of this. 



