PERFORMANCE INDEX OF QUARTZ PLATES 219 



such a frequency that the total reactance is zero and at such an ampHtude 

 that the total resistance is zero. The performance of the crystal will 

 therefore not depend solely upon its figure of merit, but will involve the 

 impedance of the remainder of the oscillator. Up to the present time circuit 

 design engineers have not devised standards or units to express the quality 

 of their oscillator circuits without the crystal, so there are no corresponding 

 circuital units of quality with which to correlate figures of merit of crystals 

 to ascertain the suitability of one for the other. 



It was a practice for many years for manufacturers to test crystals in a 

 model of the oscillator in which the crystal was to be used. This required 

 manufacturers to keep on hand models of all oscillators for which they 

 expected to make crystals. To avoid the mounting number of such test 

 oscillators a special test set was developed which could be adjusted to simu- 

 late any oscillator. By correlating various oscillator circuits to a set of 

 adjustments on the test set, the actual model of the oscillator can be dis- 

 pensed with. This special test set usually referred to as the ' "D" spec, test 

 set', eliminated the "file" of oscillators, and substituted a file of adjustment 

 readings that would be their equivalent. However, the ' "D" spec.testset' is 

 still inadequate to the development engineer since it defines "activity" in 

 terms of oscillator grid current rather than in terms of the electrical equiva- 

 lent circuit of the crystal. The activity as expressed by grid current is a 

 purely arbitrary standard and serves only as a means of determining the 

 relative activity as against other crystals of the same frequency operated 

 under the same circuit conditions. 



The need for a system of measurement using units that are fundamental 

 and not empirical has led to the proposal of "Performance Index". An 

 instrument to make such measurements is to be described in this paper. 



Specifically the Performance Index is 



PI='^ (15.4) 



where Ct is the paralleling capacitance that is found in the oscillator circuit 

 to which the crystal is attached, and L and R represent the effective induc- 

 tance and resistance of the crystal as measured at the operating frequency 

 indicated in Fig. 15.1 C which is its equivalent at thai frequency. If the loss 

 in the holder is so low that the resistance, Rl, may be neglected, then PI 

 may be expressed in other relations that are more useful such as, 



_ M 1 



"^" V ^ Co j ^ (15.5) 



or PI = P'Ri 



