PERFORMANCE INDEX OF QUARTZ PLATES 231 



of the voltmeter calibration. The factor RaCa is a constant; therefore, the 

 P.I. equation (15.28) simplifies to 



P.I. = (A.OA'o (15.35) 



where 



AA = change in attenuator insertion loss between the "operate" and 



"calibrate" conditions in terms of output voltage ratio — ■ , given 



A 

 as ~. 



C i- Ra C .4 



Ki = T^ T7T2 where C< is the effective capacitance in series with the 



crystal, Ck is the fixed series capacitance and Cx is the crystal 

 socket capacitance. (See Fig. 15.3) 



15.60 P.I. Meter Applications 



The application of this instrument can be extended to determine other 

 properties of both crystal and oscillator. With the aid of a frequency 

 measuring means and a capacitance bridge, the P.I. meter may be used to 

 determine all the circuit constants designated in the electrical equivalent 

 circuit of Fig. 15.1. If the loss in the holder is negligible then the equations 

 are considerably simplified; however, in those instances where holder loss 

 must be considered, the approximation that Xt <^Ru which may be allowed 

 for most cases enables an evaluation of M and Qc that is readily computed. 



The dial controlling C^, that is calibrated in terms of the total capacitance, 

 Ct, makes possible the calculation of the magnitude of the input impedance 

 to the crystal circuit, i?, as well as Qi. 



X7 



^ = P.I. 



<2i 



p.i. 



x7 



(15.36) 



The magnitude of Qi may also be measured directly from equation (15.12) 

 where Qi was given as 



As may be seen from Fig. 15.4, eo/ei can be evaluated in terms of the 

 attenuator calibration by enabling switch, S, to select the "PI" and "M" 

 positions respectively and adjusting the attenuator such that the same 

 output meter indication is obtained in the two cases. 



