This paper reports a frequency trimming method for a resonator used in a quad-mass gyroscopes (QMG) by focused ion beam (FIB) etching. The effects of the suspension stiffness, coupling stiffness and mass perturbations on the anti-phase mode resonant frequency were studied theoretically and numerically, proving the effectiveness and merit of the suspension stiffness trimming. The asymmetry caused by the suspension stiffness mismatch was further considered and its effects on frequency and Q-factor were investigated. Then the relationship between the trimming geometry of the suspension springs and the resonant frequency was studied by finite element analysis (FEA). The proposed trimming was demonstrated by using a QMG device fabricated by a standard SOI process. The resonant frequency mismatch was initially about 2810 ppm. After the proposed FIB trimming on the suspension springs, the frequency mismatch decreased to be as small as 3 ppm and the uncertainties do not exceed 75 ppm in the variation of ambient temperature between ±2 K. A slight change of Q-factor was observed in the trimmed axis from 100,000 to 90,000.

中文翻译：

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通过聚焦离子束调整频率失配为 3 ppm 的四质量谐振器


本文报道了一种通过聚焦离子束（FIB）蚀刻对四质量陀螺仪（QMG）中使用的谐振器进行频率微调的方法。从理论上和数值上研究了悬架刚度、耦合刚度和质量摄动对反相模式谐振频率的影响，证明了悬架刚度微调的有效性和优点。进一步考虑了悬架刚度失配引起的不对称性，并研究了其对频率和 Q 因子的影响。然后通过有限元分析（FEA）研究了悬架弹簧的修整几何形状与谐振频率之间的关系。所提出的微调通过使用标准 SOI 工艺制造的 QMG 器件进行了演示。谐振频率失配最初约为 2810 ppm。在对悬架弹簧进行建议的 FIB 微调后，频率失配降至 3 ppm，环境温度在 ±2 K 范围内变化的不确定性不超过 75 ppm。修剪轴从 100,000 到 90,000。