{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,13]],"date-time":"2025-10-13T15:23:08Z","timestamp":1760368988257,"version":"build-2065373602"},"reference-count":25,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2011,9,27]],"date-time":"2011-09-27T00:00:00Z","timestamp":1317081600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>This paper describes a novel design methodology using non-linear models for complex closed loop electro-mechanical sigma-delta modulators (EM\u03a3\u0394M) that is based on genetic algorithms and statistical variation analysis. The proposed methodology is capable of quickly and efficiently designing high performance, high order, closed loop, near-optimal systems that are robust to sensor fabrication tolerances and electronic component variation. The use of full non-linear system models allows significant higher order non-ideal effects to be taken into account, improving accuracy and confidence in the results. To demonstrate the effectiveness of the approach, two design examples are presented including a 5th order low-pass EM\u03a3\u0394M for a MEMS accelerometer, and a 6th order band-pass EM\u03a3\u0394M for the sense mode of a MEMS gyroscope. Each example was designed using the system in less than one day, with very little manual intervention. The strength of the approach is verified by SNR performances of 109.2 dB and 92.4 dB for the low-pass and band-pass system respectively, coupled with excellent immunities to fabrication tolerances and parameter mismatch.<\/jats:p>","DOI":"10.3390\/s111009217","type":"journal-article","created":{"date-parts":[[2011,9,27]],"date-time":"2011-09-27T20:09:10Z","timestamp":1317154150000},"page":"9217-9232","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":27,"title":["Genetic Algorithm for the Design of Electro-Mechanical Sigma Delta Modulator MEMS Sensors"],"prefix":"10.3390","volume":"11","author":[{"given":"Reuben","family":"Wilcock","sequence":"first","affiliation":[{"name":"School of Electronics and Computer Science, University of Southampton, Highfield, Southampton SO17 1BJ, UK"}]},{"given":"Michael","family":"Kraft","sequence":"additional","affiliation":[{"name":"School of Electronics and Computer Science, University of Southampton, Highfield, Southampton SO17 1BJ, UK"}]}],"member":"1968","published-online":{"date-parts":[[2011,9,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"456","DOI":"10.1109\/4.753678","article-title":"A three-axis micromachined accelerometer with a CMOS position-sense interface and digital offset-trim electronics","volume":"34","author":"Lemkin","year":"1999","journal-title":"IEEE J. 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