Force-Frequency and Other Effects in Doubly Rotated Vibrators.

摘要

Precision frequency control requirements for future digital communication systems require improved crystal resonator performance in a number of aspects. Accordingly, the potential of doubly rotated quartz cuts has begun to be explored. In the neighborhood of the SC-cut (YX omega L) phi/theta, phi approximately equals 21.9 degrees, theta approximately equals +33.9 degrees, a variety of effects having their bases in nonlinear elasticity have been shown, or are predicted, to be improved with respect to corresponding AT-cut values. The static frequency-temperature behavior also shows improvement. This report concerns the force-frequency effect, thus far not investigated in any detail for doubly rotated quartz plate vibrators. It relates initial stress produced by mounting supports to resonance frequency changes; it contributes to long-term aging, and is related to the frequency excursions produced in shock and vibration environments. In-plane diametric forces applied to the periphery of vibrating plates produce frequency changes that depend upon the azimuth angle psi in the plane of the plate. For the IT-cut at phi = 19.1 degrees, the maximum value was found previously to be only about one-third that of the AT-cut. This points to a reduced coefficient at the SC-cut as well. Measurements of the force-frequency effect coefficients have now been extended to doubly rotated quartz plates. Also given are charts of the mode spectra in the region of the thickness modes, and the modal temperature coefficients.