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Design and fabrication of a mode rectangular X-cut quartz resonator with zero temperature coefficient

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3 Author(s)
Yokoyama, Y. ; Appl. Electron., Tokyo Univ. of Sci. ; Kawashima, H. ; Kanie, H.

Rectangular X-cut quartz crystal resonators with cut angles thetas > 5.0deg and aspect ratios Rzy (= width 2z0/length 2y0) from 0.3 to 0.5 are investigated. The resonators oscillate mode is a length-extensional mode. A semiempirical frequency equation was derived from the stress expressed in terms of the trigonometric and the hyperbolic transcendental functions with constants estimated by the regression curve fit to the stress simulated by the finite-element method (FEM). Contours on which a point satisfies a zero first order temperature coefficient condition are shown in a cut angle thetas and Rzy diagram. We proved that a fabricated resonator with Rzy = 0.400 and thetas = 16.0deg, whose design parameter is located in the area of the contour, had a zero temperature coefficient

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Ultrasonics, Ferroelectrics, and Frequency Control, IEEE Transactions on  (Volume:53 ,  Issue: 5 )