A Study on High-Resolution MEMS Quartz Resonant Accelerometer with a Low-Noise Oscillating Readout Circuit

Academic Background

Microelectromechanical system (MEMS) accelerometers have a wide range of applications in fields such as inertial navigation, seismic detection, wearable devices, and intelligent robots. Particularly in applications like satellite control and unmanned underwater vehicles, high-resolution and low-drift acceleration measurements are critical performance metrics. MEMS resonant accelerometers modulate the input acceleration signal to a carrier frequency and output the resonant frequency of the sensitive element as the measured value, offering lower noise levels compared to amplitude-output accelerometers (e.g., MEMS capacitive accelerometers). Additionally, resonant accelerometers have advantages such as high resolution, wide range, large dynamic range, and good environmental adaptability, making them a research hotspot for high-resolution MEMS accelerometers.

However, fluctuations in the acceleration output of MEMS resonant accelerometers under static input conditions (typically 0 g loading) are mainly caused by environmental factors such as temperature fluctuations or background noise. While temperature-induced trends can be compensated using methods like polynomial fitting, filtering techniques, and structural optimization, it is difficult to compensate for the white noise introduced by the Brownian motion of the resonator and electronic background using such methods, which becomes a key limitation on the accelerometer’s resolution. In recent years, high-resolution MEMS resonant accelerometers fabricated on silicon wafers have become a research focus due to their small size, low cost, and compatibility with semiconductor processes. However, silicon itself lacks an electromechanical conversion effect, requiring additional structures to drive and detect the resonator, which limits its linear range and resolution.

To address this issue, researchers have begun exploring the use of quartz material, which has a natural piezoelectric effect. Quartz resonators exhibit high Q-factor, wide linear operating range, and stable crystal structure, making them highly suitable for manufacturing high-resolution and long-term stability MEMS resonant accelerometers. However, the nonlinear effects of quartz resonators and the noise level of oscillating readout circuits remain key factors limiting their performance improvement. This paper proposes a novel oscillating readout circuit topology aimed at enhancing the stability and resolution of quartz resonant accelerometers.

Paper Source

This paper was co-authored by Kai Bu, Cun Li, Hong Xue, Bo Li, and Yulong Zhao from the School of Mechanical Engineering and the State Key Laboratory at Xi’an Jiaotong University. The paper was published in 2024 in the journal Microsystems & Nanoengineering under the title A 14 μHz/√Hz resolution and 32 μHz bias instability MEMS quartz resonant accelerometer with a low-noise oscillating readout circuit.

Research Process

1. Design of the Quartz Sensitive Element

The sensitive element of the MEMS quartz resonant accelerometer proposed in this paper consists of a proof mass connected to resonators via a leverage structure. When an acceleration signal is detected in the sensitive direction (y-axis), the proof mass exerts an axial force on the resonator under the influence of inertial force, and the leverage structure amplifies this force, thereby increasing the scale factor of the accelerometer. To suppress common-mode error interference, the sensitive element proposed in this paper adopts a differential resonator structure. When subjected to acceleration, the resonant frequency of one resonator increases while that of the other decreases, and the difference in the resonant frequency changes of the two resonators is used as the acceleration measurement value.

2. Design of the Oscillating Readout Circuit

This paper proposes a novel low-noise oscillating readout circuit (LNC), which consists of an operational amplifier (OPA)-based front-end, a phase shifter, an amplitude limiter, and a buffer. The front-end detects the motional charge of the quartz resonator’s operating mode and outputs a voltage proportional to its mode velocity. The phase shifter satisfies the oscillation condition, and the amplitude limiter feeds the oscillation back to the quartz resonator while setting the operating point to minimize flicker noise modulation. The outputs of the two oscillators are frequency-differenced by a multiplier to enable acceleration measurement.

3. Design of the Low-Noise Bandpass Front-End

The proposed bandpass front-end consists of two cascaded integrators and differentiators. The integrator integrates the charge generated by the quartz resonator’s surface during vibration through C1, outputting a voltage proportional to the resonator’s strain. The differentiator offsets the phase shift introduced by the integrator to meet the oscillation’s phase condition. This topology eliminates the trade-off between gain, bandwidth, and noise in traditional transimpedance amplifier front-ends, providing a gain of 14.5m and a phase drift of 0.04° at the oscillation frequency, with an input-referred current noise as low as 30.5 fA/√Hz.

4. Design of the Anti-Aliasing Phase Shifter

To satisfy the oscillation’s phase condition, this paper proposes an anti-aliasing phase shifter, which consists of an analog phase shifter, an anti-aliasing filter, and an ADC. The analog phase shifter compensates for the phase drift introduced by the front-end, and the anti-aliasing filter limits the loop noise bandwidth to reduce aliasing noise introduced during ADC sampling. With a carefully designed hysteresis range, a 1-bit ADC outputs a square wave signal to drive the quartz resonator, ensuring fast and robust oscillation startup.

5. Design of the Amplitude Limiter

To limit the mode strain of the quartz resonator, this paper employs an amplitude-limiting strategy based on the digital signal output from the ADC. By using an amplifier with a gain of less than one, the amplitude of the drive signal is limited, thereby controlling the quartz resonator to operate in its weakly nonlinear region. This strategy reduces system power consumption without introducing excessive noise, and its effectiveness is verified through experiments.

Main Results

1. Front-End Test Results

The proposed bandpass front-end achieves a gain of 14.1m and a phase drift of 0.04° at the oscillation frequency, with an input-referred current noise as low as 30.5 fA/√Hz. Test results show that the output voltage noise of the front-end at 35 kHz is 430 nV/√Hz, slightly higher than the simulated value, likely due to unexpected parasitic effects in the actual circuit connections.

2. Noise Test Results

Compared to the traditional dual-inverter feedback topology (DIC), the proposed LNC significantly reduces the noise output of the accelerometer. At room temperature, the accelerometer output with the LNC varies within 0.9 mHz over 3 hours, with a standard deviation of 0.1 mHz, which is 5.5 times better than that of the DIC. In a 1-hour noise output test, the standard deviation of the LNC decreases from 2.6 mHz for the DIC to 0.3 mHz.

3. Accelerometer Test Results

The proposed MEMS quartz resonant accelerometer achieves a scale factor of 54.5 Hz/g under ±70 g input, with a maximum nonlinearity of 245 ppm. Allan variance tests show that the bias instability of the LNC is 32 μHz, significantly lower than the 0.31 mHz of the DIC. The accelerometer’s resolution and bias instability are 0.26 μg/√Hz and 0.59 μg, respectively, with a bandwidth of 552 Hz.

Conclusion

This paper implements a differential MEMS quartz resonant accelerometer with a novel oscillating readout circuit, thoroughly analyzes the phase noise modulation mechanism of MEMS quartz resonant accelerometers, and demonstrates that front-end performance is a key factor in determining the stability and resolution of accelerometers. The proposed low-noise bandpass front-end eliminates the trade-off between gain, bandwidth, and noise in traditional front-ends, and test results show that this topology provides a gain of 14.1m and a phase drift of 0.04° at the oscillation frequency, with an input-referred current noise as low as 30.5 fA/√Hz. Benefiting from excellent front-end performance, carefully designed phase compensation, and resonator operating points, the proposed MEMS quartz resonant accelerometer achieves a frequency resolution of 14 μHz/√Hz and frequency instability of 32 μHz, corresponding to an acceleration resolution of 0.26 μg/√Hz and bias instability of 0.59 μg, with a scale factor of 54.5 Hz/g, a bandwidth of 552 Hz, and a full scale of ±70 g, reaching international leading levels.

Research Highlights

1. High Resolution and Low Noise: The proposed MEMS quartz resonant accelerometer achieves a frequency resolution of 14 μHz/√Hz and frequency instability of 32 μHz, significantly outperforming traditional designs.
2. Novel Oscillating Readout Circuit: The proposed low-noise bandpass front-end eliminates the trade-off between gain, bandwidth, and noise in traditional front-ends, providing higher gain and lower noise.
3. Anti-Aliasing Phase Shifter: By using an anti-aliasing filter and a 1-bit ADC, aliasing noise is reduced, improving the stability and resolution of the oscillator.
4. Amplitude Limiting Strategy: A simple amplitude-limiting strategy controls the quartz resonator to operate in its weakly nonlinear region, reducing flicker noise modulation and enhancing the system’s long-term stability.

Research Value

This research provides new ideas and methods for the design of high-resolution MEMS quartz resonant accelerometers, offering significant scientific and application value. The accelerometer has broad application prospects in fields such as satellite control, unmanned underwater vehicles, and seismic detection.