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**Performance of a High Q-factor QMG in Open-loop and Closed-loop Instrumentations**

*Sina Askari, Mohammad H. Asadian, and Andrei M. Shkel, University of California Irvine*

**Location:** Pavilion Ballroom East

Alternate Number 2

In this paper, the characterization and analysis of a Silicon micromachined Quad Mass Gyroscope (QMG) in the rate mode of operation are presented. An ultra high-vacuum sealing with getter activation demonstrated the Q-factor as high as two million at 1.68 kHz of operational frequency, corresponding to the ringdown time constant as high as 380 seconds. The device shows an outstanding Q-factor among the Silicon MEMS Coriolis Vibratory Gyroscopes (CVGs). Allan Deviation (ADEV) and Power Spectral Density (PSD) analysis methods were used to evaluate the performance results.

The CVG control algorithm for this high Q-factor QMG was implemented based on the IEEE Std 1431. The device in this study was instrumented for the rate mode of operation, with the Open-Loop (OL) and Force-to-Rebalance (FRB) (also known as Closed-Loop (CL)) configurations of the sense mode. Four primary control loops were implemented for the rate mode characterization, including Phase-Locked Loop (PLL), Amplitude Gain Control (AGC), Quadrature Control Loop (QCL), and Rate Control Loop (RCL). These loops are essentially the individual PID controllers which track and stabilize the amplitude in the drive direction, phase of the drive oscillation frequency, the amplitude of the quadrature and rate parameters in the sense direction. Using these control loops, a gyroscope can be configured to operate in the open-loop or closed-loop rate modes. We are highlighting the challenges in the stabilization of the control loops corresponding to the Q-factor of the device in each mode.

As-fabricated, the frequency mismatch of 15 Hz was electrostatically tuned to 60mHz. Using ADEV method, we demonstrated bias instability of 0.096 deg/hr, Angle Random Walk (ARW) of 0.0107 deg/sqrt(hr), and Rate Random Walk (RRW) of 0.0043 deg/hr/sqrt(hr) in the OL mode of detection and bias instability of 0.0655 deg/hr, ARW of 0.0058 deg/sqrt(hr), and RRW of 0.0107 deg/hr/sqrt(hr) in the FRB mode of detection. These extracted parameters from ADEV were compared with the extracted parameters from the PSD method. The experimental high Q-factor data showed that the optimal size for bias estimation would reach 10% of its final value in 10 hrs for the ADEV method, and from the PSD method in 7 hrs. Similarly, for the ARW estimation, 10% of its final value was reached in 3.5 hrs using the ADEV method, and in 5 hrs using the PSD method. The total equivalent voltage noise of the front-end electronics simulated to be 5e-7V/sqrt(Hz), along with the measured scale-factor of the device this translates to ARW of 0.01 deg/sqrt(hr) for the circuit, which matches well with the experimental noise characterization. This suggested that the characterization reported is limited by the electronics noise sources of the readout circuit considered in the setup. The noise characterization of the FRB mode of detection showed an improvement in the bias by a ratio of 0.69 and an improvement in the ARW by a ratio of 0.54, this was explained by the forcer signal being applied along the sense axis which the frequency mismatch might be unintentionally tuned. The stability of the drive mode oscillation at the resonance is another critical parameter as it directly related to the scale factor of the device. Therefore, the variation in oscillations along the drive axis was analyzed experimentally and was used to support the experimentally obtained RRW noise parameter of the device.

We concluded that in a realistic MEMS gyroscope with imperfections (nearly matched, but non-zero frequency asymmetry), a high Q-factor would increase the frequency stability of the drive axis resulting in improved noise performance. A perfect frequency symmetry (zero frequency asymmetry) is required to exploit the ultimate influence of high Q-factor on the noise performance in both OL and FRB modes of operation.

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