448 BELL SYSTEM TECHNICAL JOURNAL 



Reference to the mathematical digression will make clear the forma- 

 tion of the impedances in this expression. (42) is an important rela- 

 tion since it shows that there is a possibility that the amplitude of the 

 detected current may be affected by the phase displacements of the 

 side bands of the original wave which occur during the detection. 

 For an ideal grid-leak detector, the magnitudes of the quantities 



T7^' Tir~i — ^7^ and 7T rp. are very small compared with Kg. Equa- 

 te {p-\-q)C {p-q)C 



tion (42) then becomes 



,■ - '■«' " ^« ^'^ cos at (43) 



In (43) we have the simplest possible form of the equation for a 

 grid leak detector. The next step is to show methods for evaluating 

 the quantities rg and r/. As may be seen from the relations given 

 in (7) and (8) 



1 _ digo / ^ dTg 



rg dEg' ' dEg' 



and, since the action of the grid-leak detector depends upon r/, it is 

 evident that fg is not a constant but varies with the value of Eg. 

 We may obtain rg by direct dynamical measurements or by drawing 

 tangents to the static grid-potential grid-current curve of the tube 

 under consideration. The value of rg thus obtained applies only 

 to a given value of Eg. Now Eg is a function of the voltage, e, as 

 will be shown : 



When e has the form given in (41), one of the resulting currents 

 in the plate circuit is a direct current given by 



. ^ 1 rg' t^Rg (A' r~B'~\ 



''' 2 rg{:rg+Rg){rp+R,)\2 ^ 2 J' 



This means that a constant voltage given by 

 1 r' R, FA^ . A^B 



[^.^^ 



^^" 2 rg (r,+i?,)L 2 



must have appeared on the grid in order to produce the constant 

 component of the plate current. This constant voltage is in addition 

 to that which we have denoted by Ego, since it is part of eg. More- 

 over, its intrinsic \alue is usually negative, since rg' is usually nega- 

 tive. This means that the "effective" Eg„ has been reduced by the 

 amount given in (44). However, rg is slightly different at this new 

 value of Ego and hence Cgd is not quite what a first calculation would 



