This paper proposes a differential mode measurement and control system (DMCS) for differential MEMS resonant accelerometer (DMRA), which operates the differential resonators of the DMRA at different vibration modes. Unlike traditional DMRA, the first resonator of the differential resonator operates in the first-order mode (R1M1), and the second resonator operates in the second-order mode (R2M2). Within the measurement range of DMRA, the frequencies of the two resonators will not cross, so there will be no mutual interference. This ensures the structural symmetry of the DMRA while avoiding the measurement dead zone phenomenon caused by the coupling of the differential vibration beam at similar resonant frequencies. The structural symmetry of the differential resonator ensures good temperature consistency of the differential vibration beam, and the consistency of the temperature frequency coefficient matches well, which enables the differential resonator to strongly suppress the temperature-induced common-mode effects. During the temperature cycling process between -20 °C and 80 °C, the equivalent acceleration drift of R1M1 and R2M2 were 341.6 mg and 414.6 mg, respectively. After using the differential temperature compensation algorithm, the equivalent acceleration drift was reduced to 1.19 mg. The minimum Allan variance measured statically at room temperature decreased from 1.42 μ[email protected] s for R1M1 and 1.52 μ[email protected] s for R2M2 to 0.23 μ[email protected] s, indicating a significant improvement in the long-term stability of DMRA. In addition, the differential measuring method also eliminated common mode ambient noise in low frequency range, ultimately achieving a noise level of 220 @(0.2-0.8 Hz) for a prototype device with a measurement range exceeding ±5 g.
MEMS accelerometers are widely used as the core sensing components in miniaturized and portable Inertial Measurement Units (IMUs), have found broad applications in fields such as inertial navigation, energy exploration and mining, and consumer electronics due to their advantages of miniaturization, low power consumption, and high reliability. In high-precision navigation and gravimetry applications, the temperature drift characteristics of MEMS accelerometers play a crucial role in determining both short-term and long-term system accuracy, directly affecting the stability and measurement reliability of inertial navigation systems and high-precision gravimeters. For single resonant beam devices, methods such as optimizing device structure and materials to reduce temperature coefficient, temperature control to reduce temperature variation range, and numerical compensation to reduce output drift are commonly used. In recent years, differential MEMS resonant accelerometers (DMRAs) based on differential vibrating beams (DVBs) structures have become an essential technical route for achieving high-precision inertial measurement due to their common mode rejection characteristics. Unlike single resonant beam devices, the DMRA detects acceleration through the frequency difference of symmetrical resonators, which can effectively suppress environmental common mode interference (such as temperature fluctuations, electromagnetic noise, pressure fluctuations, etc.).
To achieve common-mode matching of symmetrical resonators and enhance the suppression of environmental common-mode interference, the resonators are designed with identical dimensions and, theoretically, exhibit identical resonant frequencies. However, this differential resonant accelerometer faces significant challenges in practical applications. Symmetric resonators are connected by proof mass, resulting in mechanical coupling between the two resonators. When the natural frequencies of two resonators tend to be consistent, mode localization occurs, resulting in abnormal transmission of vibration energy between the two resonators, forming a dead zone for acceleration measurement, as shown in Fig. 1. Researchers have proposed an isolation method that proof mass splitting in the middle, effectively eliminating coupling between DVBs and solving the measurement dead zone problem. However, this method reduces the scaling factor of accelerometers within the same device size and may result in mismatched responses to external acceleration inputs due to manufacturing errors, as the proof mass on both sides may not be completely symmetrical. The method of presetting frequency intervals through geometric mismatch can effectively avoid dead zones, however, it compromises the common-mode rejection capability of the DVBs. Inconsistent geometric dimensions lead to differences in thermal resistance and heat capacity, which in turn introduce temperature gradients. For DMRA with a large frequency offset range, a greater preset frequency difference is required. This increases the mismatch in resonator dimensions, making it difficult to suppress frequency drift induced by temperature gradients. Essentially, these methods have not resolved the deep-seated contradiction caused by mode coupling -- when the system attempts to maintain temperature stability through structural symmetry, it inevitably exacerbates the mechanical coupling between DVBs; Traditional methods of suppressing mechanical coupling can also disrupt the consistency of temperature characteristics. This mutually exclusive relationship of "symmetry anti coupling" has become a key bottleneck restricting the performance improvement of DMRA.
This paper presents a differential mode measurement and control system(DMCS) for DMRA. While maintaining identical geometric dimensions of the DVBs, the system drives the first resonator of DVBs at the first-order mode(R1M1) and the second resonator of DVBs at the second-order mode(R2M2), respectively, ensuring that their resonant frequencies do not coincide within the measurement range, thus avoiding the measurement dead zone. Furthermore, by preserving the symmetry of the structure, the system achieves a superior temperature drift suppression effect. In our previous work, we utilized a single resonator driven at both the first-order and second-order modes, taking advantage of the different acceleration scale factors and temperature coefficients of the two modes to decouple acceleration and temperature. However, since the first-order and second-order modes of the single resonator exhibit common-mode responses to both acceleration and temperature variations, the suppression of temperature drift also results in a reduction of the effective acceleration scale factor, thus weakening the temperature drift suppression effect. In contrast, the DMCS proposed in this paper ensures that the two modes exhibit common-mode responses to temperature drift, at the same time, due to the symmetry of the differential resonator along the sensitive axis, when external acceleration is input, the forces on the two resonators are opposite, so they exhibit differential-mode response to acceleration input (as described by Eq. 1 and Eq. 2, the sign of S and S is opposite). This differential mode response helps increase the effective acceleration scale factor when temperature drift is eliminated, thereby significantly enhancing the temperature drift suppression effect.
In the equations, T and T represents the temperature coefficients of R1M1 and R2M2, S and S denotes the acceleration scale factors of R1M1 and R2M2, f and f are the initial resonant frequencies (with external acceleration input of 0 g and temperature of 0 °C) of R1M1 and R2M2, respectively. By solving Eq. 1, the expression for acceleration is obtained as follows, k represents the ratio of the temperature coefficients of two modes (k=T/T).