Temperature coefficient of sensitivity dependence of the measurement error of quartz crystal resonators

This paper expounds the measurement error of Quartz Crystal Resonators (QXRs) vs. the temperature coefficient of force sensitivity. Based on the analysis of the differences between the temperature coefficient of frequency and the temperature coefficient of force sensitivity, the measurement error formula is deduced. According to the error formula, the physical signification of the temperature coefficient of force sensitivity is explained, and the method of selecting scale temperature is given. The measurement error formula has been verified recently by experimental results. To expand the selectable range of cut modes and to compare the performances of QXRs, the selecting principle of the best group of the angles (angles of cut of quartz crystal plate, θ, φ, and azimuth angle of applied force, φ) is given simultaneously. According to the measurement error formula and the selecting principle of the best group of the angles, the best azimuth angle of AT-cut used as force sensitive resonators is found through the analysis of the measurement error. This paper provides a theoretical basis on which the measurement accuracy of QXR force sensors is improved