Abstract
AbstractThis paper describes a variational analysis, the frequency temperature characteristics and the electrical equivalent circuit constants of a face shear mode quartz crystal resonator with two supporting portions at the ends formed by an etching method. The object of this paper is to propose a new shape face shear mode quartz crystal resonator and to clarify its frequency temperature characteristics and its electrical equivalent circuit constants in the calculation and in the experiments. A vibration analysis is performed according to the following procedure.First, a frequency equation is derived by performing a vibration analysis of a face shear mode resonator being incorporated with a vibrational portion and supporting portions with an energy method. From the obtained frequency equation, a relationship of frequency temperature coefficients vs. a cut angle or a mass ratio is clarified.Second, some of the calculated results are compared with the experimental value. As a result, the calculated and experimental results show good agreement.Finally, various constants of an equivalent circuit for quartz crystal resonators are examined. It is shown that a face shear mode quartz crystal resonator with low series resistance and a high quality factor in the frequency range of 1.5 to 4.2 MHz is obtained, even if supporting portions are added and connected to the vibrational portion.
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