{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,8]],"date-time":"2026-02-08T11:04:19Z","timestamp":1770548659382,"version":"3.49.0"},"reference-count":23,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2019,12,22]],"date-time":"2019-12-22T00:00:00Z","timestamp":1576972800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"State Key Laboratory of Urban Water Resource and Environment (Harbin Institute of Technology)","award":["No. 3262016TS06"],"award-info":[{"award-number":["No. 3262016TS06"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The EM-    \u03a3 \u0394     (electromechanical sigma-delta) approach is a concise and efficient way to realize the digital interface for micro-electromechanical systems (MEMS) accelerometers. However, including a fixed MEMS element makes the synthesizing of the EM-    \u03a3 \u0394     loop an intricate problem. The loop parameters of EM-    \u03a3 \u0394     can not be directly mapped from existing electrical     \u03a3 \u0394     modulator, and the synthesizing problem relies an experience-dependent trail-and-error procedure. In this paper, we provide a new point of view to consider the EM-    \u03a3 \u0394     loop. The EM-    \u03a3 \u0394     loop is analyzed in detail from aspects of the signal loop, displacement modulation path and digital quantization loop. By taking a separate consideration of the signal loop and quantization noise loop, the design strategy is made clear and straightforward. On this basis, a discrete-time PID (proportional integral differential) loop compensator is introduced which enhances the in-band loop gain and suppresses the displacement modulation path, and hence, achieves better performance in system linearity and stability. A fifth-order EM-    \u03a3 \u0394     accelerometer system was designed and fabricated using 0.35     \u03bc m     CMOS-BCD technology. Based on proposed architecture and synthesizing procedure, the design effort was saved, and the in-band performance, linearity and stability were improved. A noise floor of 1     \u03bc g \/  Hz     , with a bandwidth 1 kHz and a dynamic range of 140 dB was achieved.<\/jats:p>","DOI":"10.3390\/s20010091","type":"journal-article","created":{"date-parts":[[2019,12,23]],"date-time":"2019-12-23T03:15:01Z","timestamp":1577070901000},"page":"91","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["A Straightforward Approach for Synthesizing Electromechanical Sigma-Delta MEMS Accelerometers"],"prefix":"10.3390","volume":"20","author":[{"given":"Dongliang","family":"Chen","sequence":"first","affiliation":[{"name":"MEMS Center, Harbin Institute of Technology, Harbin 150001, China"},{"name":"Key Laboratory of Micro-Systems and Micro-Structures Manufacturing, Harbin Institute of Technology, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Liang","family":"Yin","sequence":"additional","affiliation":[{"name":"MEMS Center, Harbin Institute of Technology, Harbin 150001, China"},{"name":"Key Laboratory of Micro-Systems and Micro-Structures Manufacturing, Harbin Institute of Technology, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qiang","family":"Fu","sequence":"additional","affiliation":[{"name":"MEMS Center, Harbin Institute of Technology, Harbin 150001, China"},{"name":"Key Laboratory of Micro-Systems and Micro-Structures Manufacturing, Harbin Institute of Technology, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wenbo","family":"Zhang","sequence":"additional","affiliation":[{"name":"MEMS Center, Harbin Institute of Technology, Harbin 150001, China"},{"name":"Key Laboratory of Micro-Systems and Micro-Structures Manufacturing, Harbin Institute of Technology, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yihang","family":"Wang","sequence":"additional","affiliation":[{"name":"MEMS Center, Harbin Institute of Technology, Harbin 150001, China"},{"name":"Key Laboratory of Micro-Systems and Micro-Structures Manufacturing, Harbin Institute of Technology, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guorui","family":"Zhang","sequence":"additional","affiliation":[{"name":"MEMS Center, Harbin Institute of Technology, Harbin 150001, China"},{"name":"Key Laboratory of Micro-Systems and Micro-Structures Manufacturing, Harbin Institute of Technology, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yufeng","family":"Zhang","sequence":"additional","affiliation":[{"name":"MEMS Center, Harbin Institute of Technology, Harbin 150001, China"},{"name":"Key Laboratory of Micro-Systems and Micro-Structures Manufacturing, Harbin Institute of Technology, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaowei","family":"Liu","sequence":"additional","affiliation":[{"name":"MEMS Center, Harbin Institute of Technology, Harbin 150001, China"},{"name":"Key Laboratory of Micro-Systems and Micro-Structures Manufacturing, Harbin Institute of Technology, Harbin 150001, China"},{"name":"State Key Laboratory of Urban Water Resource &amp; Environment, Harbin Institute of Technology, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,12,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Zheng, Q., Shi, B., Li, Z., and Wang, Z.L. 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