With the development of the designing and manufacturing level for micro-electromechanical system (MEMS) gyroscopes, the control circuit system has become a key point to determine their internal performance. Nevertheless, the phase delay of electronic components may result in some serious hazards. This study described a real-time circuit phase delay correction system for MEMS vibratory gyroscopes. A detailed theoretical analysis was provided to clarify the influence of circuit phase delay on the in-phase and quadrature (IQ) coupling characteristics and the zero-rate output (ZRO) utilizing a force-to-rebalance (FTR) closed-loop detection and quadrature correction system. By deducing the relationship between the amplitude-frequency, the phase-frequency of the MEMS gyroscope, and the phase relationship of the whole control loop, a real-time correction system was proposed to automatically adjust the phase reference value of the phase-locked loop (PLL) and thus compensate for the real-time circuit phase delay. The experimental results showed that the correction system can accurately measure and compensate the circuit phase delay in real time. Furthermore, the unwanted IQ coupling can be eliminated and the ZRO was decreased by 755% to 0.095°/s. This correction system realized a small angle random walk of 0.978°/√h and a low bias instability of 9.458°/h together with a scale factor nonlinearity of 255 ppm at room temperature. The thermal drift of the ZRO was reduced to 0.0034°/s/°C at a temperature range from −20 to 70 °C.

With the miniaturization of micro-electro-mechanical system (MEMS) gyroscopes, it is necessary to study their nonlinearity. The phase-frequency characteristics, which affect the start-up time, are crucial for guaranteeing the gyroscopes’ applicability. Nevertheless, although the amplitude-frequency (A-f) effect, one of the most obvious problems in nonlinearity, has been well studied, the phase response of nonlinear gyroscopes is rarely mentioned. In this work, an elaborate study on the characteristics and locking process of nonlinear MEMS gyroscopes is reported. We solved the dynamic equation using the harmonic balance method and simulated the phase-locked loop (PLL) actuation process with an iterative calculation method. It was shown that there existed an apparent overhanging and multi-valued phenomenon in both the amplitude–frequency and phase–frequency curves of nonlinear gyroscopes. Meanwhile, it was ascertained by our simulations that the locking time of PLL was retarded by the nonlinearity under certain conditions. Moreover, experiments demonstrating the effect of nonlinearity were aggravated by the high quality factor of the drive mode due to the instability of the vibration amplitude. A nonlinear PLL (NPLL) containing an integrator was designed to accelerate the locking process. The results show that the start-up time was reduced by an order of magnitude when the appropriate integral coefficient was used.

Tuning fork gyroscopes (TFGs) are promising for potential high-precision applications. This work proposes and experimentally demonstrates a novel high-Q dual-mass tuning fork microelectromechanical system (MEMS) gyroscope utilizing three-dimensional (3D) packaging techniques. Except for two symmetrically decoupled proof masses (PM) with synchronization structures, a symmetrically decoupled lever structure is designed to force the antiparallel, antiphase drive mode motion and eliminate low frequency spurious modes. Thermoelastic damping (TED) and anchor loss are greatly reduced by the linearly coupled, momentum- and torque-balanced antiphase sense mode. Moreover, a novel 3D packaging technique is used to realize high Q-factors. A composite substrate encapsulation cap, fabricated by through-silicon-via (TSV) and glass-in-silicon (GIS) reflow processes, is anodically bonded to the wafer-scale sensing structures. A self-developed control circuit is adopted to realize loop control and characterize gyroscope performances. It is shown that a high-reliability electrical connection, together with a high air impermeability package, can be fulfilled with this 3D packaging technique. Furthermore, the Q-factors of the drive and sense modes reach up to 51,947 and 49,249, respectively. This TFG realizes a wide measurement range of ±1800 °/s and a high resolution of 0.1°/s with a scale factor nonlinearity of 720 ppm after automatic mode matching. In addition, long-term zero-rate output (ZRO) drift can be effectively suppressed by temperature compensation, inducing a small angle random walk (ARW) of 0.923°/√h and a low bias instability (BI) of 9.270°/h.

With the development of designing and manufacturing level for micro-electromechanical system (MEMS) gyroscopes, the control circuit system becomes a key point to determine their internal performances. Nevertheless, phase delay of electron components may result in some serious hazards. This paper describes a real-time circuit phase delay correction system for MEMS vibratory gyroscopes. A detailed theoretical analysis is provided to clarify the influences of circuit phase delay on the in-phase and quadrature (IQ) coupling characteristics and zero rate output (ZRO) utilizing force-to-rebalance (FTR) closed-loop detection and quadrature correction system. By deducing the relationship between amplitude-frequency, phase-frequency of MEMS gyroscope and the phase relationship of the whole control loop, a real-time correction system is proposed to automatically adjust the phase reference value of phase-locked loop (PLL) and thus compensate for the real-time circuit phase delay. The experimental results show that the correction system can accurately measure and compensate the circuit phase delay in real time. Furthermore, the unwanted IQ coupling can be eliminated and the ZRO is decreased by 755% to 0.095°/s. This correction system realizes a small angle random walk of 0.978°/√h, and a low bias instability of 9.458°/h together with a scale factor nonlinearity of 255 ppm at room temperature. Besides, the thermal drift of ZRO is reduced to 0.0034°/s/°C at a temperature range from -20°C to 70°C.

Tuning fork gyroscopes (TFGs) are promising for potential high-precision applications. This work proposes and experimentally demonstrates a novel high-Q dual mass tuning fork microelectro-mechanical system (MEMS) gyroscope utilizing three-dimensional (3D) packaging techniques. Except for two symmetrically-decoupled proof masses (PM) with synchronization structures, a symmetrically-decoupled lever structure is designed to force the antiparallel, antiphase drive-mode motion and basically eliminate the low-frequency spurious modes. The thermoelastic damping (TED) and anchor loss are greatly reduced by the linearly-coupled, momentum- and torque-balanced antiphase sense mode. Besides, a novel 3D packaging technique is used to realize high Q-factors. A composite substrate encapsulation cap, fabricated by through-silicon-via (TSV) and glass-in-silicon (GIS) reflow processes, is anodically bonded to the sensing structures at wafer scales. A self-developed control circuit is adopted to realize loop control and characterize gyro-scope performances. It is shown that a high-reliability electrical connection together with a high-air-impermeability package can be fulfilled with this 3D packaging technique. Furthermore, the Q-factors of the drive and sense modes reach up to 51947 and 49249, respectively. This TFG realizes a wide measurement range of ±1800° /s and a high resolution of 0.1° /s with a scale-factor nonlinearity 720 ppm after automatic mode-matching. Besides, the long-term zero-rate output (ZRO) drift can be effectively suppressed by temperature compensation, inducing a small angle random walk (ARW) of 0.923°/√h and a low bias instability (BI) of 9.270°/h.

Zero-rate output (ZRO) drift induces deteriorated micro-electromechanical system (MEMS) gyroscope performances, severely limiting its practical applications. Hence, it is vital to explore an effective method toward ZRO drift reduction. In this work, we conduct an elaborate investigation on the impacts of the internal and packaging stresses on the ZRO drift at the thermal start-up stage and propose a temperature-induced stress release method to reduce the duration and magnitude of ZRO drift. Self-developed high-Q dual-mass tuning fork gyroscopes (TFGs) are adopted to study the correlations between temperature, frequency, and ZRO drift. Furthermore, a rigorous finite element simulation model is built based on the actual device and packaging structure, revealing the temperature and stresses distribution inside TFGs. Meanwhile, the relationship between temperature and stresses are deeply explored. Moreover, we introduce a temperature-induced stress release process to generate thermal stresses and reduce the temperature-related device sensitivity. By this way, the ZRO drift duration is drastically reduced from ~2000 s to ~890 s, and the drift magnitude decreases from ~0.4 °/s to ~0.23 °/s. The optimized device achieves a small bias instability (BI) of 7.903 °/h and a low angle random walk (ARW) of 0.792 °/√ h, and its long-term bias performance is significantly improved.