Temperature-induced frequency activity dips in AT-cut quartz crystal resonators

doi:10.1007/s10483-026-3360-9

Abstract

Abstract:

This study investigates the frequency-temperature behaviors in AT-cut quartz crystal resonators (QCRs). First, the dispersion relations of an infinite quartz plate are obtained through a semi-analytical finite element (SAFE) analysis, which explicitly reveals the intrinsic frequency-temperature dependence of different vibration modes. Subsequently, we address practical resonator configurations by examining finite quartz plates, where numerical simulations uncover critical interactions between the operational thickness-shear (TS) mode and coupling modes, i.e., the flexure (F), face-shear (FS), and extension (E) modes. Through the frequency spectra analysis, we demonstrate that both the plate aspect ratio and thermal variations affect mode-coupling behaviors. Unstable frequency-temperature variations (activity dips) are observed at critical resonator dimensions. Validation through the free-vibration eigen-frequency analysis and forced-vibration admittance characterization confirms the stable or unstable states predicted by the frequency spectra. The established framework not only reveals the origin of temperature-induced activity dips but also provides the crucial design criteria for suppressing the mode-coupling interference in high-stability resonators.

Key words: quartz crystal resonator (QCR), frequency spectrum, admittance, activity dip

2010 MSC Number:

O482.1

Nian LI, Chao GAO, Feng CHEN, Zhenghua QIAN, I. KUZNETSOVA. Temperature-induced frequency activity dips in AT-cut quartz crystal resonators. Applied Mathematics and Mechanics (English Edition), 2026, 47(3): 639-652.

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