Zero temperature coefficient characteristic of four-corner-truncated square quartz resonator supported at four nodal points in Lamé mode

This paper describes analytical and experimental study of a zero-temperature-coefficient square Lamé-mode quartz resonator supported at four nodal points. Comparison of vibration mode shapes of the resonators with and without four supporting beams in the modal analysis using finite element analysis indicated that several contour modes vibrating at large amplitude in the corners with frequency lower than that of the Lamé mode get a boost in frequency by the constraint at the corners and resulted in spurious modes to the Lamé mode by temperature shift. Comparison of mode shapes of these unwanted contour vibrating modes with and without truncation at the corners of the square quartz plate indicated another boost in frequency caused by the reduction in mass where the mode vibrates at large amplitude. Four-corner truncated square quartz resonators supported by four beams were designed and fabricated by wet etching process. Measured data of the fabricated resonators made of LQ1T and LQ2T cut quartz plates indicated a zero temperature coefficient and electrical equivalent circuit parameters comparable to those of a fundamental mode Lamé resonators with two point support.