CONSTANT FREQUENCY OSCILLATORS 



85 



ings, the ratio of the voltage across the secondary to the voltage across 

 the primary depends upon the coil reactances only, and not at all upon 

 the attached impedances. In the circuit of Fig. 15 this ratio is given 

 by the expression : 



^' (20) 



Op 



In general, the voltage Cj, may be expressed in terms of the imped- 

 ance looking out of the plate-filament terminals of the tube. Thus 



C-T) 



Tp -\- Zjt 



(21) 



where Zp is the aforementioned impedance. 

 From (20) and (21) there results: 



1 



X, 



- 1 



(22) 



This equation completely expresses the operation of the oscillator in 

 so far as impedance relations for the fundamental current component 

 are concerned. From Fig. 15 ordinary circuit analysis shows that Zp 

 may be written 



^ = ^ + L 



so that (22) becomes: 



^)+^ + ^ 



X 1 / iXx Z5 



'+^/f; 



1 + 1/^ 



Z3 Z4 \ A 1 





'+^t 



A"! 



1 



(23) 



The next step is to separate this into its real and imaginary compo- 

 nents. We stipulate, as in the previous analyses, that the losses in the 

 external circuit elements are small compared with those occasioned by 

 the grid resistance of the tube. With this understanding, Z4 may be 

 separated into two parts, the one iX^, in parallel with the other which 

 constitutes the grid resistance Yg. Both Z3 and Z5 are taken as pure 

 reactances. Thus the last expression yields the two equations: 



k^km^k^k^^^^^y-^^ 



1 IXj. 

 X, 



1X2 



(24) 

 (25) 



