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Thickness Modes in Circular AT-Cut Quartz Plates with Circular Electrodes,
COMTEC ECONOMATION INC FLAGSTAFF AZ
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Over the past years, several papers have been presented which contain theoretical analyses of the coupled thickness-shear and thickness-twist mode resonances in rectangular and circular quartz plates. These studies involved the solution of the differential equations with certain assumed boundary conditions and the determination of the eigenfrequencies related to the thickness modes using computers. However, to this date, the complexities of the mathematics have prevented a similar analysis of the commonly manufactured resonator consisting of a circular AT-cut quartz blank with circular electrode on its major surfaces. The purpose of this study was to derive useful equations which can be employed in designing such AT-cut quartz resonators. This paper describes the results of an empirical analysis to determine how the frequency and the relative activity of the thickness modes in AT-cut quartz resonators depends on the diameter of the circular electrodes and the mass loading.
APPROVED FOR PUBLIC RELEASE