The high-order mechanical resonances of the sensing element in a high-vacuum environment can significantly degrade the noise and distortion performance of seismic-grade sigma–delta MEMS capacitive accelerometers. However, the current modeling approach is unable to evaluate the effects of high-order mechanical resonances. This study proposes a novel multiple-degree-of-freedom (MDOF) model to evaluate the noise and distortion induced by high-order mechanical resonances. Firstly, the MDOF dynamic equations of the sensing element are derived using the principle of modal superposition and Lagrange’s equations. Secondly, a fifth-order electromechanical sigma–delta system of the MEMS accelerometer is established in Simulink based on the dynamic equations of the sensing element. Then, the mechanism through which the high-order mechanical resonances degrade the noise and distortion performances is discovered by analyzing the simulated result. Finally, a noise and distortion suppression method is proposed based on the appropriate improvement in high-order natural frequency. The results show that the low-frequency noise drastically decreases from about −120.5 dB to −175.3 dB after the high-order natural frequency increases from about 130 kHz to 455 kHz. The harmonic distortion also reduces significantly.

Harmonic distortion is one of the dominant factors limiting the overall signal-to-noise and distortion ratio of seismic-grade sigma-delta MEMS accelerometers. This study investigates harmonic distortion based on the multiple degree-of-freedom model (MDM) established in our previous study. The main advantage of using an MDM is that the effect of finger flexibility on harmonic distortion is considered. Initially, the nonlinear relationship between the input acceleration and output signal is derived using the MDM. Then, harmonic distortion is simulated and described in terms of the nonlinear input–output relationship. It is found that finger flexibility and parasitic capacitance mismatch both decrease harmonic distortion. Finally, the experimental testing of harmonic distortion is implemented. By reducing the finger length to realize a higher stiffness and compensating for the parasitic capacitance mismatch, the total harmonic distortion decreases from −66.8 dB to −86.9 dB.