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BELL SYSTEM TECHNICAL JOURNAL 



where L and R represent the effective values of the crystal, 

 will be found to embody the relation 



(jiL 



PI = 



oiCtR 



= QiX, 



Equation (15.4) 



(15.8) 



where Xt is the reactance of Ct, the capacitance introduced by the circuit at 

 the operating frequency. If Ci is kept constant, Cc will at all times be 

 proportional to Qi. By insertion of an attenuator network, whose attenua- 

 tion varies with frequency in the same manner as does the reactance of Ct, 

 between terminals AB and the voltmeter, the meter indication will be 

 proportional to the product of these quantities or proportional to PI. With 



Cp=^ep (A) 



pc (B) 



Fig. 15.3 — Measuring circuits of the performance index meter. 



suitable calibrations, therefore, it should be possible to get indications of PI 

 as readily as is now done for Q. 



The circuit shown in Fig. 15.2 is now best redrawn as in Fig. 15.3A. The 

 crystal embodying elements Li , Ci , Ri , and Co of Fig. 15.2 is now repre- 

 sented in Fig. 15. 3A by the dotted rectangle and as having effective induct- 

 ance, L, and effective resistance, R, both of which are functions of frequency. 

 Capacitance, Ct, is simulated by capacitors d plus Cs and Ca- in series where 

 Cx represents the capacitance of the crystal socket. Zero internal impe- 

 dance of the generator is simulated by maintaining the driving voltage con- 

 stant at all times and at all frequencies. To facilitate explanation, the 

 measured voltage d at the place shown is considered to be the driving volt- 

 age from a zero internal impedance generator. 



Instead of using an ammeter to indicate current in the circuit, a voltmeter 

 is utilized to measure voltage across an element under such conditions as 



