{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,4]],"date-time":"2025-12-04T10:05:46Z","timestamp":1764842746391,"version":"build-2065373602"},"reference-count":35,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2023,6,7]],"date-time":"2023-06-07T00:00:00Z","timestamp":1686096000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>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\u2013delta 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\u2019s equations. Secondly, a fifth-order electromechanical sigma\u2013delta 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 \u2212120.5 dB to \u2212175.3 dB after the high-order natural frequency increases from about 130 kHz to 455 kHz. The harmonic distortion also reduces significantly.<\/jats:p>","DOI":"10.3390\/s23125394","type":"journal-article","created":{"date-parts":[[2023,6,8]],"date-time":"2023-06-08T02:02:28Z","timestamp":1686189748000},"page":"5394","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Multiple-Degree-of-Freedom Modeling and Simulation for Seismic-Grade Sigma\u2013Delta MEMS Capacitive Accelerometers"],"prefix":"10.3390","volume":"23","author":[{"given":"Xuefeng","family":"Wang","sequence":"first","affiliation":[{"name":"State Key Laboratory of ASIC and System, School of Microelectronics, Fudan University, Shanghai 200433, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Penghao","family":"Zhang","sequence":"additional","affiliation":[{"name":"State Key Laboratory of ASIC and System, School of Microelectronics, Fudan University, Shanghai 200433, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shijin","family":"Ding","sequence":"additional","affiliation":[{"name":"State Key Laboratory of ASIC and System, School of Microelectronics, Fudan University, Shanghai 200433, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,6,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"112498","DOI":"10.1016\/j.sna.2020.112498","article-title":"MEMS based geophones and seismometers","volume":"318","author":"Hou","year":"2021","journal-title":"Sens. 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