PERFORMANCE INDEX OF QUARTZ PLATES 235 



(2) The measurement of the effective capacitance, Ct, of an oscillator as a 

 function of tuning, and 



(3) The variation of P.I. as a function of voltage across the crystal. 



The results presented are not to be considered as generalized data, but are 

 intended only to show a set of measurements obtained for a specific set of 

 operating conditions for each type of circuit. 



It has been pointed out that the frequency of oscillation is a function of 

 /?i , coi , 0)2 , Co and Ci , Since Ri , wi , co-) and Co are explicit parameters 

 of the crystal, the capacitor, Ct , becomes the only frequency determining 

 element in the P.I. meter. From analytical methods to be described in 



PI METER OSC. 



"7-~-^<_PIERCE OSC 



\ 



CALCULATED 



PERFORMANCE INDEX 



Fig. 15.6 — Frequency variations in oscillators as a function of Performance Index. 



Sections 15.80 and 15.92 the frequency difference between the P.I. meter 

 and the generalized oscillator (neglecting R^) is given as 



(C02 — CUi) / Co\ 



''bw^-a 



(U2 — Oil' 



(■ * I) 



(15.51) 



Since the magnitude of frequency change in the above equation is small 

 compared to the variations caused by changes in operating conditions, the 

 P.I. meter may be used as a frequency correlation medium. Fig. 15.6 is 

 an example of the correlation between the "Pierce" and "Tuned-Plate" 

 oscillator and the P.I. meter. The P.I. meter falls between these two 

 oscillators in frequency for any crystal activity. It must be recognized 

 that Fig. 15.6 is not conclusive to the extent of generalization; however, it is 

 indicative of possible correlation with these two popular oscillator circuits. 



