PIEZOELECTRIC CRYSTALS IN OSCILLATOR CIRCUITS 



201 



where Q is the Q of the crystal and r its ratio of capacitances. Thus the 

 figure of merit involves the dissipation in the crystal determined by Q 

 and the piezo-electric effect determined by r." 



It was pointed out in the preceding section that the frequency stability 

 increases as r is increased. The above equation shows that Q must increase 



Fig. 12.26 — The dependence of the quality function (^c of a crystal upon frequency 

 and figure of merit M 



proportionately if the same figure of merit is to be maintained. The fre- 

 quency stability obtainable in a particular oscillator is therefore limited 

 by the Q of the crystal and the frequency stability coefficients should be 

 compared on this basis. 



12.80 Activity of Crystals 



In deriving a figure of merit for crystals as oscillators, it was found that 

 the amplitude of oscillations in a given circuit not only depends upon M 

 but also it is a function of frequency relative to the resonant frequency 



