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<p>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.</p>

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

  • 期刊论文

  • 发表日期：

    2026年2月28日

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  • Nian Li,
  • Chao Gao,
  • Feng Chen,
  • Zhenghua Qian,
  • I. Kuznetsova

摘要

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.