PIEZOELECTRIC CRYSTALS IN OSCILLATOR CIRCUITS 



197 



The comparative stability of the crystal and tuned circuit is given by the 

 ratio 



FOQ 

 F{xy 



1 + 2 





(12.75) 



10,000 r 



100 

 Co 

 C| 



Fig. 12.25 — The stability coefficient of a crystal as compared to a coil and condenser 

 for variations of the ratio of capacitances 



X, 



Co 



This ratio is plotted in Fig. 12.25 for — = — 1 and with — the independent 



X, 



Ci 



Co 



function. It is apparent that the value of — of a crystal is the factor which 



determines its frequency stability for given operating conditions. For an 

 A T crystal in an air gap holder, the ratio of capacitances is of the order of 

 10 and its stability coefficient is therefore 2.6 X 10^ greater than for a simple 

 anti-resonant circuit. Since this is so much greater than the stability 

 coefficients for the other reactances which appear in the denominator of 

 equation (12.65) it represents the order of magnitude of improvement of the 

 frequency stabiUty of an oscillator obtained by the use of a crystal. 



