The effect of contour concentricity on the acceleration sensitivity of quartz crystal resonators

Optimization of the acceleration sensitivity of quartz crystal resonators has been a challenging problem for resonator designers for decades. The structural symmetry of the resonator and mount combination has been shown in past work, both theoretical and practical, to have a strong influence on acceleration sensitivity, and specialized structures have been developed [1], [2], [3] that have greatly improved performance. However, with applications such as airborne radar systems, there is a persistent demand for further improvement. The design of many of the practical high-stability resonator products that have a need for good acceleration sensitivity is also constrained by other attributes, such as high quality factor, and these constraints typically result in a low-frequency overtone device with a fully contoured resonator element design. In this paper, the effect of the concentricity of the contour shape on the quartz disk in contoured resonators is considered, and results are presented that demonstrate a strong correlation between the contour offset from the blank center and the acceleration sensitivity of the resonator. Methods are also described for measurement of the contour position relative to the perimeter of the disk.