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A High-Q Micromachined Quatrefoil Suspension Gyroscope



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Over the past three decades, advancements in the fabrication technology and the creation of new designs led to improvements in the performances of Coriolis vibratory micromachined gyroscopes. Micro-electromechanical systems (MEMS) Coriolis vibratory gyroscopes (CVGs) are an increasingly popular choice for a wide range of applications thanks to their compact size, low power consumption, and low cost. However, despite recent advancements, their accuracy remains lower than that of macroscopic mechanical and optical gyroscopes.

This thesis advances the design of a new MEMS gyroscope topology, termed as the quatrefoil suspension gyroscope (QSG). The QSG comprises of a centrally anchored axisymmetric design consisting of a freely suspended micromachined ring supported by spiral flexures winding outward from the anchor to the ring in both clockwise and anti-clockwise directions.

The QSG is fabricated on a (100) single-crystal silicon substrate with the device vacuum sealed at the wafer-level. The device operates on the basis of the modal coupling between two secondary elliptical modes of the ring via the Coriolis effect. These elliptical modes can be excited using a set of capacitive electrodes arranged proximal to the ring. The design provides good immunity to fabrication tolerances, achieving low frequency split between the secondary degenerate modes. The average frequency split between the modes of 17 devices, as fabricated, is 5.8 Hz (13.8 ppm). Such a low frequency split facilitates the implementation of mode-matching during the operation of the device.

The thesis also introduces a closed-loop method to apply electrostatic frequency tuning to efficiently implement mode-matching. The excellent results in terms of angle random walk (ARW), bias instability (BI), frequency split (as fabricated), and mechanical sensitivity obtained during the characterisation and testing phases of the new QSG are comparable to the best results documented in the literature on high performance MEMS CVGs.

In addition to the QSG, the mode-matched operation of an edge-anchored bulk acoustic wave (BAW) gyroscope is also reported in this work.

Gyroscopic operation in amplitude modulation (AM) is demonstrated in both the edge-anchored and the QSG gyroscope by driving one of the secondary degenerate elliptical modes while sensing the response on the other elliptical mode: for both devices, the quality factors achieved exceed 1 million at an operating frequency of ∼976 kHz for the edge-anchored and ∼ 426 kHz for the QSG. Key performance parameters of both devices are improved by implementing mode-matching using electrostatic frequency tuning to decrease the frequency split between the two secondary elliptical, near-degenerate, modes.

A 7.76 times improvement in sensitivity is recorded for the edge-anchored gyroscope operated in near mode-matched conditions with frequency tuning. The ARW and BI of the device are improved from 0.042 °/√hr to 0.037 °/√hr and 1.65 °/hr to 0.95 °/hr respectively, benchmarking favourably with respect to the state-of-the-art in BAW disk gyroscopes. \par In the case of the QSG, the mechanical sensitivity is improved by a factor of 25.4 for mode-matched operations in comparison to the untuned case. The ARW and BI improved to 0.01 °/√hr and 0.34 °/hr, i.e. by a factor of 7.7 and 8.24 respectively. The measured parameters are consistent with the specifications for high performance MEMS gyroscopes. Mode-matching by electrostatic frequency tuning is optimised by using the closed-loop method. The measured bandwidth and dynamic range are increased by operating the gyroscope using the force-to-rebalance (FTR) method. The QSG showed a linear response in the range ±400 °/s: above this range measurements were limited by the benchtop electronics employed for these measurements. \par Finally, this thesis also discusses gyroscopic operation using mechanical frequency modulation (FM) in the QSG. The gyroscope operates by tracking the resonance frequencies of the two high quality factor secondary degenerate elliptical modes. The frequency-based measurement of the input angular rate is realised using two digital phase-locked loops. Measured results demonstrate an ARW and BI of 0.917 °/√hr and 6.7 °/hr respectively, benchmarking favourably in comparison with other state-of-the-art FM gyroscopes.





Seshia, Ashwin


BAW Gyroscope, Electrostatic tuning, FM Gyroscope, Gyroscope, MEMS, Quatrefoil Suspension Gyroscope


Doctor of Philosophy (PhD)

Awarding Institution

University of Cambridge
Engineering and Physical Research Council UK; Silicon Microgravity; Innovate UK