MEMS resonant accelerometers are robust to electromagnetic interference and have higher sensitivity and resolution. However, they are susceptible to temperature variation, which may limit this type of sensor used in high-end applications. This paper proposes a TDS-PLL with MEMS VCO for MEMS resonant accelerometers to be immune to temperature drift. The theoretical analysis of TDS-PLL MRA demonstrates it can suppress the temperature drift, which is verified by simulation and measurement results. Measurement results of the TDS-PLL MRA show that the bias instability is 13.15 $\mu$ g and the noise level is 7.04 $\mu$ g/ $\surd $ Hz with 0.32g full scale at room temperature. The temperature coefficient of bias stability in TDS-PLL MRA achieves 2.21 mg/ $^{\circ}$ C in a temperature range of 300K to 360K, which is lower 5.5 times than that of the traditional PLL MRA with frequency shift.2022-0098

The development of mode-localized sensors based on amplitude output metrics has attracted increasing attention in recent years due to the potential of such sensors for high sensitivity and resolution. Mode-localization phenomena leverage the interaction between multiple coupled resonant modes to achieve enhanced performance, providing a promising solution to overcome the limitations of traditional sensing technologies. Amplitude noise plays a key role in determining the resolution of mode-localized sensors, as the output metric is derived from the measured AR (amplitude ratio) within the weakly coupled resonator system. However, the amplitude noise originating from the weakly coupled resonator’s closed-loop circuit has not yet been fully investigated. This paper presents a decouple-decomposition (DD) noise analysis model, which is applied to achieve high resolution in a mode-localized tilt sensor based on a weakly coupled resonator closed-loop circuit. The DD noise model separates the weakly coupled resonators using the decoupling method considering the nonlinearity of the resonators. By integrating the decoupled weakly coupled resonators, the model decomposes the weakly coupled resonator’s closed-loop circuit into distinct paths for amplitude and phase noise analyses. The DD noise model reveals noise effects at various circuit nodes and models the system noise in the closed-loop circuit of the weakly coupled resonators. MATLAB/Simulink simulations verify the model’s accuracy when compared to theoretical analysis. At the optimal operating point, the mode-localized tilt sensor achieves an input-referred instability of 3.91 × 10^-4°and an input-referred AR of PSD of 2.01 × 10^-4°⁄√Hz using the closed-loop noise model. This model is also applicable to other varieties of mode-localized sensors.

MEMS resonant accelerometers have attracted attention because of their high resolution and quasi-digital output, but their performances are seriously damaged by external temperature fluctuations. Our previous work proposed a Temperature-Drift Suppression Phase-Locked-Loop featuring a temperature-sensitive resonator (TSR) as a voltage-controlled oscillator to monitor the frequency variations of the accelerometer-sensitive resonator (ASR). To solve the problem of mismatched temperature coefficients between the TSR and ASR, the frequency synthesis unit is introduced in this paper. The temperature drift of the two resonators can offset each other by adjusting the division factor so that the acceleration drift caused by temperature can be mitigated. Additionally, the proposed SAFR algorithm automatically adjusts the locked range of the PLL, thereby expanding the full-scale range of the accelerometer. The effectiveness of the system is further validated through theoretical analysis and simulations. Experimental results indicate that the bias-instability is 3.7μg and the noise floor is 1.24μg/√Hz with ±2g full-scale range at room temperature. The temperature drift is 54mg within a temperature range of 10°C to 60°C which is reduced by 95% compared to the uncompressed MRA (1.23g).

This paper presents a scale factor calibration method based on virtual accelerations generated by electrostatic force. This method uses a series of voltage signals to simulate the inertial forces caused by the acceleration input, rather than frequent and laborious calibrations with high-precision instruments. The error transfer model of this method is systematically analyzed, and the geometrical parameters of this novel micromachined resonant accelerometer (MRA) are optimized. The experimental results demonstrate that, referring to the traditional earth’s gravitational field tumble calibration method, the error of the scale factor calibration is 0.46% within ±1 g by using our method. Moreover, the scale factor is compensated by virtual accelerations. After compensation, the maximum temperature drift of the scale factor decreases from 2.46 Hz/g to 1.02 Hz/g, with a temperature range from 40 °C to 80 °C.

This paper presents the theoretical analysis and experimental investigation of a weakly coupled resonant tilt sensor based on different output metrics, including mode frequency, amplitude ratio, amplitude difference, and eigenstate. Especially, we investigate the sensitivity, linear working range, stability, and noise analysis by theoretical analysis and evaluation of experimental results. The tilt sensor sensing element is the weakly coupled resonators, the output metrics of which shift is proportional to the effective stiffness perturbation caused by changes in input inertial force along the sensitive axis when any tilt angular is applied to the tilt sensor. Furthermore, it is demonstrated that there is an optimal operating point for amplitude difference output through theoretical analysis. The experimental results show that the minimum input-referred angle noise densities of the tilt sensor based on the amplitude ratio and amplitude difference are 1.03×10 ^-4 °/√Hz and 9.10×10 ^-5 °/√Hz, respectively. In addition, the weakly coupled resonant tilt sensor based on the amplitude ratio and amplitude difference outputs achieve resolutions of 9.79×10 ^-5 ° and 7.53×10 ^-5 ° with an integral time of 15s, and the mode frequency output achieves a resolution of 0.141×10 ^-5 ° with an integral time of 0.5s. The experimental results demonstrate that based on amplitude difference output has the best long-term stability and based on the mode frequency output has better short-term stability. Additionally, it is demonstrated that the output based on the amplitude ratio balances sensitivity, linear range, and long-term stability.

Mode-localized sensing paradigms applied to accelerometers have recently become popular research subjects. However, the output of mode-localized accelerometers is influenced by environment temperature due to the difference in the thermal properties of the coupling resonators and the temperature dependence of coupling stiffness. To improve the performance of mode-localized accelerometers against temperature, we proposed an in situ self-temperature compensation method by utilizing the resonant frequency besides of amplitude ratios, which can be implied online. Experimental results showed that there were nearly 79-times and 87-times improvement in zeros bias and scale factor, respectively.