CONSTANT FREQUENCY OSCILLATORS 



87 



In practice, A^, A'.), and A'5 would usually be capacities, to corre- 

 spond to the circuit of Fig. 17. With this arrangement, and the rela- 

 tion given by (29) we have the frequency from (24) : 



1 



U 



C, + k^C, 



+ CA\+kJk^ 



(30) 



The value of C-2 is thus written from (28) and (29) as follows: 



Co = 







1 + k 



1 - k^ 



(31) 



This is the general value of C2 needed to stabilize the oscillator, and 

 applies to any grid-stabilized oscillator where the unity coupling con- 

 cept can be employed. In the case where C-, and C4 are small enough 

 to be neglected we have the equivalent circuit of the reversed feed-back 

 oscillator of Fig. 12, and for the value of the stabilizing capacity: 



C2 = 



Li Cs 



Lo 1 - k^ 



(32) 



When the notation of Fig. 17 is reconciled with that of Fig. 12, this is 

 in agreement with the conclusion reached for the reversed feed-back 

 oscillator by the former method of analysis. 



The present analysis has the twofold advantage of allowing the 

 interelectrode capacities to be included, which results in (31) instead 

 of (32) ; and of giving a more readily interpreted picture of the relation 

 required for stability, namely the "unity coupling" condition of equa- 

 tion (26). Equation (31) is moreover applicable to the tuned-plate, 

 tuned-grid type of oscillator, when there is magnetic coupling between 

 the input and output circuits. Thus, in the particular instance when 

 Li and Lo are equal, as also are C3 and C4, we have from (31) : 



C2 



Ca 



(1 + P) 

 (1 - k'-) 



+ Q 



(1 + ^) 

 (1 - k) 



(SS) 



Hence, if tuning is done by "ganging" C3 and d together and varying 

 them simultaneously, the stability may be maintained for all frequen- 

 cies by making Cg to consist of two parts: the one a fixed capacity 

 equal to 



a 



(1 - k) 



