This work analyses circuit phase delay for carrier-modulation MEMS capacitive gyroscopes. The temperature-dependent circuit phase delay is a major source of gyroscope output drift, which deteriorates the gyroscope bias instability (BI) and angle random walk (ARW). Effects of both drive-mode and sense-mode circuit phase delay on gyroscope performance when using different signal extraction architectures are analyzed in detail. The online suppression method which combines the so-called modified double sideband (MDSB) extraction architecture in the gyroscope drive mode and closed-loop force-rebalance loop in the sense mode can eliminate the impact of residual fluctuation error of circuit phase delay in real time. When drive-mode circuit phase delay equivalently varies from −20° to 20°, using MDSB decreases the fluctuation of the open-loop zero-rate output (ZRO) by 70% compared to using double sideband (DSB) and by 99.7% with respect to using single sideband (SSB). Meanwhile, improvement for the closed-loop ZRO using MDSB is 92.48% and 94% compared to cases using DSB and SSB, respectively. Furthermore, when the equivalent circuit phase delay of the sense-mode alters from −20° to 20°, ZRO variation for the gyroscope with force rebalanced sense loop and quadrature stiffness nulling loop decreases by 80% in contrast to the case with open loop, which demonstrates the effectiveness of online suppression for circuit phase delay of both the drive-mode and sense-mode. Using the online suppression method, the gyroscope has achieved a BI of 0.16° h ⁻¹ and ARW of 0.011° (√h) ⁻¹ . Furthermore, using the MDSB in the drive mode obtains the best stability compared to using the DSB and SSB as the temperature changes.

This paper presents the linear parametric resonance for MEMS vibratory gyroscopes using triangular area-varying capacitors. Compared to parametric resonance using gap-varying capacitors, the electrostatic stiffness using triangular capacitors is completely linear and independent of the motion displacement. A pump voltage in the square-rooted form consisting of both DC tuning voltage and AC signal with twice the drive resonance frequency is applied to the triangular capacitors in gyroscope sense mode for both mode matching and parametric amplification of Coriolis signal simultaneously. Parametric amplification or attenuation is realized by choosing specific phase and amplitude of the pump voltage. Experimental results show a maximum parametric gain of 13 times in gyroscope sense mode and the open-loop scale factor amplification of 4.8 times compared with the case where no pump voltage is applied. For one-hour zero-rate-output data, an improvement factor of 5.74 is achieved for angle random walk from 0.1745 ° √h ⁻¹ to 0.0304 ° √h ⁻¹ . Meanwhile, an improvement factor of 9.73 for bias instability is achieved from 3.609 ° h ⁻¹ (occurring at integration time 40 s) to 0.371 ° h ⁻¹ (at 52 s). The quadrature error due to stiffness coupling is reduced from 9 ° s ⁻¹ to 1 ° s ⁻¹ which agrees well with our analysis that Coriolis force is mechanically amplified while quadrature error is dampened.

We propose a MEMS gyroscope system working with a fixed resonance frequency which combines resonant constant-frequency (RCF) driving and real-time automatic mode-matching technique with the help of linear tuning triangular capacitors. The special tuning capacitors are implemented in both the gyroscope drive mode and sense mode as drive-mode frequency-tuning (DFT) and sense-mode frequency-tuning (SFT), respectively. RCF assures that the drive-mode equivalent resonance frequency after tuned can keep with the given constant excitation frequency, while real-time automatic mode-matching further eliminates mismatches between the drive-mode and sense-mode equivalent resonance frequencies. As a result, the gyroscope system achieves constancy and equality of the excitation frequency and two modal resonance frequencies. Performance evaluations show that the gyroscope with the sense mode quality factor of 26.7k reaches bias instability of 0.09°/h and angle random walk of 0.0087°/ $\surd \text{h}$ under room temperature without any compensation, and is capable of detecting an angular rate as low as 0.001°/s.

This paper presents for the first time an improved algorithm for vibration amplitude-phase information extraction of capacitive microelectromechanical systems (MEMS) gyroscopes. Amplitude and phase information resulting from the improved algorithm is insensitive to the phase variation of an interface capacitance-voltage (CV) circuit, thus both long time drift of the gyroscope and bias instability have been improved. Experimental results show that both the phase and amplitude information extracted using this improved algorithm is insensitive to phase variation of CV circuit which is in accordance with theory. Bias instability using this improved configuration is 0.64°/h, which is improved two times more than the configuration using traditional double-side-band (DSB) demodulation configuration, and 4.3 times more than the configuration using single-side-band (SSB) demodulation, respectively. Allan deviation analysis shows that the slow varying drift term using D&S configuration is effectively reduced due to its robustness to CV phase variation compared to test results using DSB or SSB configuration.

In this Letter, the authors theoretically and experimentally investigate the characteristics of phase delay in capacitive pick‐off circuits for micro‐electromechanical systems (MEMS) resonators for the first time in history. An analytical model considering the phase delay for capacitive pick‐off circuits is built up in theory. Only when they use their proposed novel modified double side‐band demodulation configuration for resonators to extract motional amplitude and phase, the phase delay of pick‐off circuits can be eliminated and extracted meanwhile in real time. Experiments show that the changing feature of phase delay primarily depends on temperature rather than drive frequency. Experimental results agree well with the theoretical model and reveal the relatively high correlation between the phase delay and temperature. This work provides a new indicator of temperature for resonators, using this phase delay of the pick‐off interface, to make temperature compensation.

This paper presents linear parametric amplification/attenuation for MEMS vibratory gyroscopes using triangular area-varying capacitors for the first time. A pump voltage containing both DC tuning voltage and AC parametric excitation voltage is added to triangular shaped capacitors, thus mode-matching, amplification of Coriolis force, and attenuation of quadrature error are realized simultaneously. Spring softening/hardening effect is totally cancelled out. Experimental results show that, ARW and BI are improved by 5.4 times and 8.3 times, respectively, for one MEMS gyroscope using linear parametric amplification, while the quadrature error is attenuated by 9 times compared to the non-amplification case.