PIEZOELECTRIC CRYSTALS IN OSCILLATOR CIRCUITS 



205 



This gives a relation between the performance index and the figure of merit 

 of the crystal. 



Another useful relation between M and PI is obtained from (12.89) and 

 (12.93). Equation (12.93) may be written 



M = 



Ri 



(12.95) 



This is of the same form as the Q oi a. coil when Xo is considered to be the 

 reactance of the coil and Ri its resistance. Like the Q of a coil M is essen- 



Fig. 12.28 — The change in PI and oscillating frequency of a crystal as the shunt 

 capacitance is increased 



tially constant over a wide frequency range. Now if we let Ct approach 

 zero in (12.89) it becomes 



1 



PI = 



xl 



RiJ'Cl Ri 



(12.96) 



This equation for PI is of the same form as the anti-resonant impedance of a 



coil and condenser in parallel, and like this impedance it changes rapidly 



with frequency. The maximum value of PI is therefore A^o times M and is 



obtained when Ct = 0. Figure 12.28 shows a curve of % PI plotted as a 



(J 

 function of — - . This curve represents the change in activity as capacitance 



Co 



is added across the crystals (increase in Ct). 



