{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,24]],"date-time":"2026-03-24T05:19:43Z","timestamp":1774329583774,"version":"3.50.1"},"reference-count":20,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2020,3,25]],"date-time":"2020-03-25T00:00:00Z","timestamp":1585094400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001691","name":"Japan Society for the Promotion of Science","doi-asserted-by":"publisher","award":["19H0209B"],"award-info":[{"award-number":["19H0209B"]}],"id":[{"id":"10.13039\/501100001691","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Mass sensors based on the eigenmode shift of coupled cantilevers achieve much higher sensitivity than those based on the single cantilever\u2019s eigenfrequency shift. In the former sensors, two identical cantilevers and a weak coupling stiffness between them are required to achieve high sensitivity. However, conventional coupled cantilevers cannot satisfy these requirements because of machining accuracy. To satisfy both requirements, a virtual coupling between a real macrocantilever and a virtual cantilever, whose dynamics was calculated using a digital computer, was proposed in our previous research. The sensitive mass sensing of mg-order masses was achieved. In the present work, for minute mass sensing, we replace the real macrocantilever with a real microcantilever. The calculation speed of a digital computer is not fast enough to calculate the virtual cantilever\u2019s dynamics because the natural frequency of the microcantilver is much higher than that of the macrocantilever. Therefore, we use an analog circuit instead of a digital computer to achieve virtual coupling with the virtual cantilever. The proposed system enables us to tune the virtual cantilever\u2019s parameters to satisfy both requirements for high sensitivity by changing the analog circuit parameters. We verified experimentally that the proposed system achieved high sensitivity for mass sensing of the order of nanograms.<\/jats:p>","DOI":"10.3390\/s20071823","type":"journal-article","created":{"date-parts":[[2020,3,25]],"date-time":"2020-03-25T13:10:47Z","timestamp":1585141847000},"page":"1823","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Ultra-Sensitive Minute Mass Sensing Using a Microcantilever Virtually Coupled with a Virtual Cantilever"],"prefix":"10.3390","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1613-6730","authenticated-orcid":false,"given":"Yuki","family":"Kasai","sequence":"first","affiliation":[{"name":"Graduate School of System and Information Engineering, University of Tsukuba, Tsukuba, Ibaraki 305-8573, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8200-1597","authenticated-orcid":false,"given":"Hiroshi","family":"Yabuno","sequence":"additional","affiliation":[{"name":"Graduate School of System and Information Engineering, University of Tsukuba, Tsukuba, Ibaraki 305-8573, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9588-2522","authenticated-orcid":false,"given":"Yasuyuki","family":"Yamamoto","sequence":"additional","affiliation":[{"name":"Fluid Property Standards Group, Research Institute for Engineering Measurement, National Metrology Institute of Japan (NMIJ), National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba, Ibaraki 305-8563, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sohei","family":"Matsumoto","sequence":"additional","affiliation":[{"name":"Research Center for Ubiquitous MEMS and Micro Engineering, National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba, Ibaraki 305-8564, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,3,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"114102","DOI":"10.1063\/1.2899634","article-title":"Highly sensitive mass detection and identification using vibration localization in coupled microcantilever arrays","volume":"92","author":"Spletzer","year":"2008","journal-title":"Appl. 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