Near-navigation Grade Quad Mass Gyroscope with Q-factor Limited by Thermo-elastic Damping

This paper presents experimental results on the noise performance of an ultra high quality factor (Q-factor) micromachined silicon Quad Mass Gyroscope (QMG). The device was vacuum sealed at below 0.1mTorr in an LCC package with activated getters, demonstrating the Q-factor better than 1.7 million, along the drive and sense modes, at the 1.6 kHz center frequency. A bias stability of 0.09 deg/hr and Angle Random Walk (ARW) of 0.015 deg/rt-hr were demonstrated, without any thermal compensation or post-processing of data. To the best of our knowledge, the result presented in this paper is the highest reported Q-factor for MEMS silicon gyroscopes, now demonstrating a true potential to achieve the navigation-grade performance. INTRODUCTION High Q-factor, isotropy of stiffness, and symmetry of damping along the drive and sense modes are the essential attributes of high precision Coriolis Vibratory Gyroscopes (CVGs). Q-factor maximization of the driveand sense-mode is a key to augment performance of the mode matched or nearly-matched CVGs. In our previous work, a QMG with as-fabricated frequency mismatch of 0.2 Hz and Q-factor of 1.17 million has been demonstrated with 0.88 deg/hr in-run bias stability and ARW of 0.06 deg/rt-hr, operating in force-rebalance (FRB) mode [1]. A vacuum sealed silicon Disk Resonator Gyroscope (DRG) has been reported with a Q-factor as high as 80,000 at 14 kHz center frequency, reporting in-run bias stability of 0.012 deg/hr and ARW of 0.002 deg/rt-hr with active temperature control and compensation [2]. A Q-factor of up to 1.38 million has been measured on bulk acoustic wave (m=3) degenerate modes at 2.745 MHz center frequency, in an actively controlled vacuum chamber [3]. A Q-factor as high as 2.7 million has been demonstrated on a vacuum sealed single-axis silicon resonator at 570 Hz resonant frequency [4]. In this work, we present the most recent characteristics of a vacuum sealed Quad Mass Gyroscope (QMG) packaged in a ceramic Leadless Chip Carrier (LCC) with getter activation. Device was operated in an open-loop rate mode, demonstrating a Q-factor of better than 1.7 million. Figure 1 demonstrates the ringdown results, showing the Q-factor of 1.7 million and 1.8 million along the Xand Y-axis, respectively. The open-loop rate mode characterization was performed in the lab conditions with phase-locked loop (PLL) and amplitude gain control (AGC) loops, without any additional calibration or compensation loops. RATE AND RATE-INTEGRATING GYROSCOPES In the rate operation mode, the scale factor is amplified by the quality factor of the sense mode, thus offering a higher ratesensitivity and a reduced Mechanical-Thermal Noise (MTN). The theoretical MTN angle random walk (ARW) for the gyroscope in operating in the open-loop mode is [5]: