科研之友
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摘要
We derived an approximate formula for the quality factor (Q value or Q) of a quartz-crystal tuning fork by applying the approximate calculation method developed by Landau et al. and Lifshitz et al. to the thermoelastic coupling equations previously obtained from the viewpoint of the thermoelasticity for a cantilever beam. We found that our calculated Q obtained using the approximate formula is half of the measured Q for an etching-processed quartz-crystal tuning fork. Furthermore, we derived the equation of the size dependence of Q by further approximating the approximate formula for Q at a constant frequency and various frequencies. The predicted size dependence of Q from these obtained equations is confirmed by measuring the Q of seven commercially available quartz-crystal tuning forks. The equations, which show the size dependence of Q, and the approximate formula for Q obtained here are effective for explaining the decreases in Q of the miniaturized quartz-crystal tuning fork.
- 出版日期2011-8
