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BELL SYSTEM TECHNICAL JOURNAL 



capacitor, Cr . After a crystal has been inserted in its proper place, oscilla- 

 tions will begin, but may be slightly above or below the resonant frequency 

 of the crystal plus Ct . By adjustment of Cr the frequency can be shifted 

 the slight amount necessary for resonance. This is observed by placing 

 switch 5 in the PI position and making the adjustment to give maximum 

 deflection of e„ . 



SWITCH "S" 



V.T.V.M. 



Fig. 15.4 — Diagram of Performance Index meter. 



15.20 Derivation of PI Circuit Equation 



The following circuit relations derived from Figure 15.3 show first, that 

 the ratio of Cp to Ci is a function of the Performance Index of the crystal, 

 and second, that the calibration circuit permits an absolute evaluation of 

 its magnitude. 



At resonance, the effective circuit Q, designated as Qo , is determined from 



Q2 = 



Cc + «0 



(-S 



(15.9) 



Since the circuit Q includes the capacitance of Cx as a part of the crystal, it is 

 necessary to express Q2 in terms of the crystal's properties (see Fig. 15.1). 



Since QA = -^ ) of the crystal is independent of Cx , the relationship between 



Qiand Q2 is readily obtained by equating the expressions for the anti-resonant 

 impedance first, when Cx is considered to be in shunt with the series capac- 

 itor, Ct, and second, when Cx is considered as part of the crystal. This re- 

 sults in 



Q2 =Qi 



Ct — Cx 

 Ct 



(15.10) 



