PIEZOELECTRIC CRYSTALS IN OSCILLATOR CIRCUITS 



213 



where A = the area of the crystal in square centimeters. 

 / = the frequency in megacycles 

 Ct = circuit capacitance in mmf . 

 M = figure of merit of the crystal (assumed constant) 



Thus for crystals of a given area, the performance index should decrease as 

 the frequency increases. Figure (12.32) shows the theoretical variations of 

 PI as the function of the diameter of the electrodes of three frequencies and 



PI 



S 12 16 



ELECTRODE DIAMETER IN MM 



Fig, 12.32 — -Theoretical curves showing the relations of PI, electrode diameter, and 

 crystal frequency for BT crystals and a circuit capacitance of 50 n/xi 



for a circuit capacitance of 50 mmf. The activity of a 4-megacycle crystal 

 with 11-mm. diameter electrodes is about the same as a 10-megacycle 

 crystal with 18 mm. electrodes. It must be remembered in making this 

 comparison that it is assumed that the damping introduced by the mounting 

 is the same in both cases. Actually the damping is much greater for low- 

 frequency crystals of this type than for high-frequency ones and maximum 

 PI occurs at some intermediate frequency as shown by the curves of Fig. 

 12.33, These curves show that the damping caused by the particular 

 mounting used was small for frequencies above 6 megacycles but increases 

 rapidly below this value. 



