{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:39:54Z","timestamp":1760243994816,"version":"build-2065373602"},"reference-count":16,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2009,5,7]],"date-time":"2009-05-07T00:00:00Z","timestamp":1241654400000},"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>A new closed-loop drive scheme which decouples the phase and the gain of the closed-loop driving system was designed in a Silicon Micro-Gyroscope (SMG). We deduce the system model of closed-loop driving and use stochastic averaging to obtain an approximate \u201cslow\u201d system that clarifies the effect of thermal noise. The effects of mechanical-thermal noise on the driving performance of the SMG, including the noise spectral density of the driving amplitude and frequency, are derived. By calculating and comparing the noise amplitude due to thermal noise both in the opened-loop driving and in the closed-loop driving, we find that the closed-loop driving does not reduce the RMS noise amplitude. We observe that the RMS noise frequency can be reduced by increasing the quality factor and the drive amplitude in the closed-loop driving system. The experiment and simulation validate the feasibility of closed-loop driving and confirm the validity of the averaged equation and its stablility criterion. The experiment and simulation results indicate the electrical noise of closed-loop driving circuitry is bigger than the mechanical-thermal noise and as the driving mass decreases, the mechanical-thermal noise may get bigger than the electrical noise of the closed-loop driving circuitry.<\/jats:p>","DOI":"10.3390\/s90503357","type":"journal-article","created":{"date-parts":[[2009,5,7]],"date-time":"2009-05-07T11:31:22Z","timestamp":1241695882000},"page":"3357-3375","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Mechanical-Thermal Noise in Drive-Mode of a Silicon Micro-Gyroscope"],"prefix":"10.3390","volume":"9","author":[{"given":"Bo","family":"Yang","sequence":"first","affiliation":[{"name":"College of Instrument Science & Engineering, Southeast University, Nanjing 210096, China"}]},{"given":"Shourong","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Instrument Science & Engineering, Southeast University, Nanjing 210096, China"}]},{"given":"Hongsheng","family":"Li","sequence":"additional","affiliation":[{"name":"College of Instrument Science & Engineering, Southeast University, Nanjing 210096, China"}]},{"given":"Bailing","family":"Zhou","sequence":"additional","affiliation":[{"name":"College of Instrument Science & Engineering, Southeast University, Nanjing 210096, China"}]}],"member":"1968","published-online":{"date-parts":[[2009,5,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"055028","DOI":"10.1088\/0960-1317\/18\/5\/055028","article-title":"Development of a lateral velocity-controlled MEMS vibratory gyroscope and its performance test","volume":"18","author":"Sung","year":"2008","journal-title":"J. Micromech. Microeng."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1939","DOI":"10.1088\/0960-1317\/17\/10\/003","article-title":"Design and performance test of a MEMS vibratory gyroscope with a novel AGC force rebalance control","volume":"17","author":"Sung","year":"2007","journal-title":"J. Micromech. Microeng"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"299","DOI":"10.1016\/j.sna.2007.10.057","article-title":"Microgyroscope control system using a high-order band-pass continuous-time sigma-delta modulator","volume":"145-146","author":"Dong","year":"2008","journal-title":"Sens. Actuat. A"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"56","DOI":"10.1016\/j.sna.2007.12.033","article-title":"Dynamics and control of a MEMS angle measuring gyroscope","volume":"144","author":"Park","year":"2008","journal-title":"Sens. Actuat. A"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"52","DOI":"10.1016\/j.sna.2007.10.088","article-title":"Characterization of a novel micromachined gyroscope under varying ambient pressure conditions","volume":"145-146","author":"Kulygin","year":"2008","journal-title":"Sens. Actuat. A"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"520","DOI":"10.1109\/JMEMS.2005.844801","article-title":"An Approach for Increasing Drive-Mode Bandwidth of MEMS Vibratory Gyroscopes","volume":"14","author":"Cenk","year":"2005","journal-title":"J. Microelectromech. Syst."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"033008","DOI":"10.1117\/1.2778645","article-title":"Micro angular rate sensor design and nonlinear dynamics","volume":"6","author":"Tsai","year":"2007","journal-title":"J. Micro\/Nanolith. MEMS MOEMS"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1227","DOI":"10.1016\/S0026-2692(99)00046-4","article-title":"Mechanical\u2013thermal noise in micromachined gyros","volume":"30","author":"Merlo","year":"1999","journal-title":"Microelectron. J."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"903","DOI":"10.1109\/16.210197","article-title":"Mechanical-thermal noise in micromachined acoustic and vibration sensors","volume":"40","author":"Gabrielson","year":"1993","journal-title":"IEEE Trans. Electron Devices"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"493","DOI":"10.1109\/JSEN.2005.844538","article-title":"Mechanical-Thermal Noise in MEMS Gyroscopes","volume":"5","author":"Robert","year":"2005","journal-title":"IEEE Sens. J."},{"key":"ref_11","unstructured":"Robert, P.L. (2001). Mechanical-Thermal Noise in Vibrational Gyroscopes. Proc. Am. Control Conf., 3256\u20133261."},{"key":"ref_12","unstructured":"Reif, F. (1965). Fundamentals of Statistical and Thermal Physics., McGraw-Hill."},{"key":"ref_13","unstructured":"Ward, P. (1997). Electronics For Coriolis Force And Other Sensors. (U.S. Pat. 5600064)."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Sanders, J.A., and Verhulst, F. (1985). Averaging Methods in Nonlinear Dynamical Systems., Springer-Verlag.","DOI":"10.1007\/978-1-4757-4575-7"},{"key":"ref_15","unstructured":"Novozhilov, I.V. (1997). Fractional Analysis: Methods of Motion Decomposition., Birkh\u00e4user."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"599","DOI":"10.1115\/1.1514658","article-title":"Stability and Resolution Analysis of a Phase-Locked Loop Natural Frequency Tracking System for MEMS Fatigue Testing","volume":"124","author":"Sun","year":"2002","journal-title":"J. Dyn. Syst. Meas. Contr."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/9\/5\/3357\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T22:10:21Z","timestamp":1760220621000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/9\/5\/3357"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,5,7]]},"references-count":16,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2009,5]]}},"alternative-id":["s90503357"],"URL":"https:\/\/doi.org\/10.3390\/s90503357","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2009,5,7]]}}}