Lame-mode miniaturized quartz temperature sensors

Lame-mode is very useful for realization of a miniaturized quartz crystal resonator because its resonant frequency principally depends only on the contour dimensions. Because the heat capacitance for the miniaturized quartz crystal resonator is small and the frequency response versus temperature is very rapid, the quartz crystal resonator is useful for application in temperature sensors. In addition, because a Lame-mode quartz crystal resonator has zero temperature coefficients, designated LQ(1) cut and LQ(2) cut, and, particularly, the resonator for LQ(1) cut has a comparatively large value of the second-order temperature coefficient beta, a Lame-mode quartz crystal resonator can be obtained with the large first-order temperature coefficient alpha when beta = 0. In this paper, when cut angles phi = 45 degrees and theta = 45 degrees, alpha has a value of 44.6 x 10(-6)/degrees C in the calculation and 39.9 x 10(-6)/degrees C in the experiments with beta approximate to 0; when phi = 51.5 degrees and theta = 45 degrees, alpha = 68.1 x 10-(6)/degrees C in the calculation and 62.0 x 10(-6)/degrees C in the experiments with a value of beta larger than that of phi = 45 degrees and theta = 45 degrees. For both cut angles, the calculated frequency change vs. temperature is found to be sufficiently large and slightly larger than the measured one.