PIEZOELECTRIC CRYSTALS IN OSCILLATOR CIRCUITS 



167 



The frequency at which oscillations are maintained is determined by the 

 required phase relation of voltages applied to the tube. With crystal from 

 grid to plate, as in Fig. 12.4, the phase difiference of grid and plate voltages 

 is such that the circuit oscillates at only one of the normal modes, and with 

 crystal connected between grid and cathode, as in Fig. 12.5, it oscillates at 

 the other only. 



12.11 Crystal Between Grid and Plate 



With the crystal connected between the grid and plate of the tube, as in 

 Fig. 12.4, the coefficients of the general equation (12.1) are 



_ ^1 ^2 Ji_ 

 Li Lo Rp Cb 



1 



Pz = 



Pi = 



L\Ca 



+ ?4' + 



L\ Li 



LiCb R 



?p \Li Li) Cb 



Li Lo Ca L 



Li LiCaCb L1L2G; 



Ri J_ / 1 R1R2 _ 1 \ 



1 Lo Cb Rp \Li Ca Cb L\ Li Cb Li Cm Cm/ 



R2 / 1 _ 1 \ 



Rp \L1L2CaCb LiLiCmCmJ 



(12.4) 



where 



Ca 



Cb 



1^ 



Cb 



Ci Co 



cl 



c. 



C2 

 1 



cl 



fJiCx 



Cb C2 Cs 



v-'W 



c' 



C2C0 



Cm Co Ci 



_ 1 11 



Co C2 C3 



H = the amplification factor of the tube, 



dCp 

 Rp = TT- {Cg constant) 

 dtp 



The uncoupled damping factors, «„ and ab , the uncoupled undamped 

 angular frequencies, ^a and ^b , and the coupling coefficient r may be intro- 

 duced as follows: 



OCb = 



2Li' 



R^ 



2L2' 



0l = 



i = 



1 



L\Ca 

 1 



LiCb 



2 CaCb 



T = 



c 



