228 BELL SYSTEM TECHNICAL JOURNAL 



The quantity — is readily determined by the attenuator, A, when the 



switch, S, (Fig. 15.4) is operated between "M" and "P/" for the above 

 described conditions. The absolute calibration then depends upon A, Ra, 

 Ca and Cic. All four of these quantities may be determined within a few 

 per cent. 



15.30 Oscillator Correlation 



The equivalent crystal circuit has been discussed in so far as the measure- 

 ment of PI is concerned; however, for correlation with an oscillator, the 

 behavior of the crystal in that oscillator must be duplicated. Correlation 

 of the PI meter with an oscillator is a function of both amplitude and 

 frequency. It is obviously necessary from the derivation of (15.28) that 

 the frequency of operation be duplicated, but the necessity for ampli- 

 tude correlation can only be explained from the practical consideration that 

 the equivalent circuit components of Fig. 15.1 are parameters that may be 

 functions of amplitude. Crystals having nonlinear characteristics of the 

 type that necessitate amplitude correlation may in part be attributed to 

 either the method of mounting the crystal or couplings to other modes of 

 vibration whose coupling coefficients are functions of amplitude. 



In most oscillators the voltage across the terminals of a crystal is a func- 

 tion of many parameters such as plate voltage, vacuum tubes, etc. With 

 an average set of conditions, however, reasonable correlation is obtained 

 with the PI meter for a single adjustment of the generator voltage, ei , for 

 all crystals. The magnitude of Ci must, of course, be chosen to produce a 

 voltage across the crystal equal to the average value obtained in the oscil- 

 lator circuit for which the crystal is intended. 



Frequency correlation with an external oscillator is a function of the 

 effective capacitance, Ct, in shunt with the crystal. In order to duplicate 

 the oscillator frequency with the PI meter, the capacitance, Cs, (Fig. 15.4) 

 must be adjusted until the frequency of oscillation in the PI meter is the 

 same as that in the oscillator for a crystal having average activity. In 

 Fig. 15.4, the capacitance, d, is variable, and its dial is calibrated in terms 

 of both the total effective capacitance across the crystal, Ct, and the resulting 



R C C 



multiplying factor j-^ — ^ . The magnitude of Ct may be measured by 



means of a capacitance bridge connected across the crystal socket terminals 

 with the generator impedance shorted. 



The determination of the dynamic or effective capacitance, Ct, across the 

 crystal for an oscillator may similarly be obtained by adjusting the magni- 

 tude of Cs in the PI meter until the frequencies of oscillation in the PI 



