PERFORMANCE INDEX OF QUARTZ PLATES 221 



gested method of measurement utilizes a suitable driving voltage at "X" 

 (Fig. 15.2) and a means to indicate the voltage at "X" as well as at points 

 AB. From these and other measured constants, the anti-resonant im- 

 pedance can be computed. 



This method of measurement has its own difficulties, but it is believed 

 corrections can be made to allow for errors introduced. Fundamentally, 

 the series resonant frequency and the anti-resonant frequency are the same 

 only when the resistances in the inductive and capacitive branches are equal. 

 When the resistance is practically all in the inductive branch, which is true 

 in this case, the impedance between terminals AB, at the series resonant 

 frequency will exhibit capacitive reactance, though the total impedance will 

 scarcely be different from that at the anti-resonant frequency. In the 

 Performance Index meter, although the voltage is introduced in series with 

 the circuit, the frequency is adjusted to the point of maximum voltage across 

 AB, which further minimizes this frequency difference. A second error is 

 inherently introduced by the loss in the crystal holder. This means 

 that the series resonant frequency is also altered by the presence of this loss. 

 Errors of any seriousness will result from the assumption that the series 

 resonant and anti-resonant frequencies are identical only when the resistance 

 in the inductive branch and loss in the crystal holder approach the effective 

 crystal reactance in magnitude. These errors will be discussed in greater 

 detail in a succeeding section. 



The development and operation of a satisfactory meter to measure PI 

 (Performance Index) depends upon a number of factors such as : 



1. A method to determine capacitance, Ct, of the circuit (Fig. 15.2). 



2. A generator "X" to produce the driving voltage ei having variability 

 in frequency and negligible internal impedance. 



3. A current indicator that introduces a minimum of reactance and 

 resistance. 



4. A circuit or method to indicate PI directly, or with a minimum of 

 calculations. 



5. A number of other factors associated with the above which will be 

 mentioned at the logical times. 



To construct a measuring circuit to determine the anti-resonant imped- 

 ance by means of a series circuit so as to avoid any unnecessary measure- 

 ments and computations involves the following basic principle. Excluding 

 p. Fig. 15.2 is essentially equivalent to the circuit used in Q meters. The 

 ratio of voltage Cc to the driving voltage d is the voltage stepup or the Q of 

 that part of the circuit containing the resistance. In this case, the resistance 

 is in the crystal which at the operating frequency has an effective Q of 



Qi = '^ (15.7) 



