Quad Mass Resonator with Frequency Mismatch of 3 ppm Trimmed by Focused Ion Beam

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9 Citations (Scopus)


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.

Original languageEnglish
Article number9382848
Pages (from-to)392-400
Number of pages9
JournalJournal of Microelectromechanical Systems
Issue number3
Publication statusPublished - 2021 Jun


  • Quad mass resonator
  • focused ion beam
  • frequency trimming

ASJC Scopus subject areas

  • Mechanical Engineering
  • Electrical and Electronic Engineering


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