Triode Generator with Two Degrees of Freedom. 705 



Similarly the damping coefficient |^\, of the | j^^Jry 

 circuit is given by ^ 



«i = 



c^iv 



We call i a the variable part of the anode current and v a 

 the variable part of the anode potential. The application of 

 Kirchhoff's laws to the circuits then leads (with neglect of 

 the grid current) to : 



d*V a , 



" -\-a 2 ") 



d 3 iv, 



+ i«i 



' + a, 2 2 + (l- 



-*»)«, 



"*- } dt 



+(1 



-^(•, 



9 M 



«2 



+ 0) 2 2 « 



^ +X i 



— £ 2 )<w 



[ (02 Va 



= — 



1 VdH a 



+ <* 



•"(i- 



*ogK-» 



•'a-/, 



,, dial 



} dtX 



We further notice that 















V u 



T Si, 

 - Ll dt' 













Vg 



= -Mf', 







(1) 



where v g is the grid potential, so that a constant ratio exists 

 between the variable anode potential and grid potential, 

 namely, 



Vg = _M 

 v a L l ' 



Hence, though in general the anode current is a function of 

 both the anode and grid potentials, by means of this constant 

 ratio we are able to express the anode current as a function 

 of the variable anode potential alone. A method of deter- 

 mining experimentally this relation i a = ijr{v a ) has been 

 previously described *. For conditions for which free 

 oscillations are possible this characteristic has in general a 

 negative slope f for v a = 0. It is therefore appropriate to 

 develop the function i a = ty(v a ) as 



i a =-u'v + /3'v 2 i-v'v z , .... (la) 



where the index of v a has been dropped for simplicity as 

 will be done in the further treatment. 



* Appleton and Van der Pol, Phil. Mag. xlii. p. 201 (1921). 

 t When developed in this way the theory applies equally well to 

 ••dvnatron" circuits. 



Phil. Mag. S. 5. Vol. 43. No. 256. April 1922. 2 Z 



