Lam/spl acute/e-mode miniaturized quartz temperature sensors

Lam/spl acute/e-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 Lam/spl acute/e-mode quartz crystal resonator has zero temperature coefficients, designated LQ/sub 1/ cut and LQ/sub 2/ cut, and, particularly, the resonator for LQ/sub 1/ cut has a comparatively large value of the second-order temperature coefficient /spl beta/, a Lam/spl acute/e-mode quartz crystal resonator can be obtained with the large first-order temperature coefficient or when /spl beta/=0. In this paper, when cut angles /spl phi/=45/spl deg/ and /spl theta/=45/spl deg/, /spl alpha/ has a value of 44.6/spl times/10/sup -6///spl deg/C in the calculation and 39.9/spl times/10/sup -6///spl deg/C in the experiments with /spl beta/=0; when /spl phi/=51.5/spl deg/ and /spl theta/=45/spl deg/, /spl alpha/=68.1/spl times/10/sup -6///spl deg/C in the calculation and 62.0/spl times/10/sup -6///spl deg/C in the experiments with a value of /spl beta/ larger than that of /spl phi/=45/spl deg/ and /spl theta/=45/spl deg/. For both cut angles, the calculated frequency change vs. temperature is found to be sufficiently large and slightly larger than the measured one.