QUARTZ CRYSTAL CIRCUIT ELEMENTS 459 



vibrations. Frequency discontinuities of the order of a kilocycle or 

 more which are a common occurrence with the F-cut plate have 

 disappeared and frequency-temperature curves that are linear over a 

 considerable temperature range can be obtained without much diffi- 

 culty. This is illustrated by Fig. 3 which shows frequency-tempera- 

 ture characteristics for both ^C-cut and F-cut plates of the same 

 frequency and area. The ^C-cut plate can be clamped to the same 

 extent as the F-cut plate. 



. There is still some coupling remaining to certain secondary fre- 

 quencies. These frequencies are difficult to identify but are thought 

 to be caused by overtones of fiexural vibrations set up by the x/ 

 shear itself and hence would be unaffected by the reduction of c^/. 

 These remaining frequencies do not cause much difficulty above 500 kc. 

 For the ^C-cut (-f 31°) plate the temperature coefficient of frequency 

 is + 20 cycles/million /C.°, while for the -BC-cut (— 60°) plate it is 

 — 20 cycles/million/C.°. 



In addition to these calculations for the Xy' vibration in plates 

 rotated about the X axis, a detailed study has been made of other 

 types of vibration and rotation about the other axes. For high 

 frequencies nothing has been found to compare with the reduction in 

 complexity of frequency spectrum obtainable with these two orienta- 

 tions. 



Temperature Coefficients 



This study has produced in the AC-cut a new type of plate 

 which has superior characteristics to the standard F-cut: i.e., a simpli- 

 fied frequency spectrum and a lower temperature coefficient. The 

 values of the temperature coefficients obtained for these new orienta- 

 tions are significant and suggest that perhaps other orientations can 

 be chosen for which the temperature coefficient will be zero. With 

 the measured values of the temperature coefficients for the different 

 orientations and the Cee equation (Appendix) it is possible to compute 

 the temperature coefficient for any angle. Figure 4 shows graphically 

 the results of such a computation for an Xy vibration as a function of 

 rotation about the X axis. It will be seen that at approximately 

 + 35° and — 49° the Xy vibration will have a zero temperature 

 coefficient of frequency. 



This curve has been checked experimentally, the check points being 

 indicated on the curve. Concentrating on a plate cut at -f- 35°, 

 which has been designated the ^7"-cut, it will be seen that this 

 type of plate offers considerable possibilities. Figure 5 shows the 

 frequency-temperature curves of a 2-megacycle AT-cxit plate and a 



