{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:11:34Z","timestamp":1760145094856,"version":"build-2065373602"},"reference-count":24,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2024,6,14]],"date-time":"2024-06-14T00:00:00Z","timestamp":1718323200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Key R&amp;D Program of China","award":["2020YFC2200604","181722KYSB20190040","2020YFC2200600","62301526"],"award-info":[{"award-number":["2020YFC2200604","181722KYSB20190040","2020YFC2200600","62301526"]}]},{"name":"Key Foreign Cooperation Projects of the Chinese Academy of Sciences","award":["2020YFC2200604","181722KYSB20190040","2020YFC2200600","62301526"],"award-info":[{"award-number":["2020YFC2200604","181722KYSB20190040","2020YFC2200600","62301526"]}]},{"DOI":"10.13039\/501100012166","name":"National Key R&amp;D Program of China","doi-asserted-by":"publisher","award":["2020YFC2200604","181722KYSB20190040","2020YFC2200600","62301526"],"award-info":[{"award-number":["2020YFC2200604","181722KYSB20190040","2020YFC2200600","62301526"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]},{"name":"the National Natural Science Foundation of China","award":["2020YFC2200604","181722KYSB20190040","2020YFC2200600","62301526"],"award-info":[{"award-number":["2020YFC2200604","181722KYSB20190040","2020YFC2200600","62301526"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The Taiji program is dedicated to the detection of middle and low-frequency gravitational waves, targeting the 0.1 mHz to 1 Hz frequency band. The project requires an acceleration residual sensitivity of 3 \u00d7 10\u221215 ms\u22122\/Hz1\/2, which necessitates a capacitance sensing resolution of 1 aF\/Hz1\/2 for the capacitive sensing system within the specified frequency range. The noise level of the resonant bridge significantly influences the resolution. Addressing the challenges in enhancing transformer performance parameters in existing resonant capacitance bridges and the constraints on improving the characteristics of resonant capacitance bridges, this study introduces a novel approach to reduce bridge thermal noise without optimizing existing parameters. The simulation results demonstrate that this scheme can reduce the noise to 0.7 times the original level and further reduce bridge thermal noise when other parameters affecting noise are optimized. This not only mitigates the demands for other performance parameters but also increases the range of maximum acceptable resonant frequency deviations and reduces its sensitivity to such variations. Experimental validation confirms that the proposed scheme effectively reduces noise by 0.7 times and improves the resolution of capacitance sensing to 0.6 aF\/Hz1\/2, thereby advancing the Taiji program gravitational wave detection capabilities.<\/jats:p>","DOI":"10.3390\/s24123844","type":"journal-article","created":{"date-parts":[[2024,6,14]],"date-time":"2024-06-14T08:02:26Z","timestamp":1718352146000},"page":"3844","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Research on High-Precision Resonant Capacitance Bridge Based on Multiple Transformers"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0009-0009-7729-5808","authenticated-orcid":false,"given":"Xin","family":"Liu","sequence":"first","affiliation":[{"name":"Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun 130033, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0001-9008-0045","authenticated-orcid":false,"given":"Yuzhu","family":"Chen","sequence":"additional","affiliation":[{"name":"Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun 130033, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4226-3186","authenticated-orcid":false,"given":"Longqi","family":"Wang","sequence":"additional","affiliation":[{"name":"Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun 130033, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5933-1814","authenticated-orcid":false,"given":"Tao","family":"Yu","sequence":"additional","affiliation":[{"name":"Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun 130033, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhi","family":"Wang","sequence":"additional","affiliation":[{"name":"Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun 130033, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7528-180X","authenticated-orcid":false,"given":"Ke","family":"Xue","sequence":"additional","affiliation":[{"name":"Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun 130033, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yanlin","family":"Sui","sequence":"additional","affiliation":[{"name":"Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun 130033, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yongkun","family":"Chen","sequence":"additional","affiliation":[{"name":"Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun 130033, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,6,14]]},"reference":[{"key":"ref_1","unstructured":"Mance, D. (2012). Development of Electronic System for Sensing and Actuation of Test Mass of the Inertial Sensor LISA. [Ph.D. Thesis, University of Split]."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"A247","DOI":"10.1088\/0264-9381\/13\/11A\/033","article-title":"LISA: Laser Interferometer Space Antenna for gravitational wave measurements","volume":"13","author":"Danzmann","year":"1996","journal-title":"Class. Quantum Gravity"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"S1","DOI":"10.1088\/0264-9381\/20\/10\/301","article-title":"LISA technology\u2014Concept, status, prospects","volume":"20","author":"Danzmann","year":"2003","journal-title":"Class. Quantum Gravity"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"153001","DOI":"10.1088\/0264-9381\/26\/15\/153001","article-title":"LISA technology and instrumentation","volume":"26","author":"Jennrich","year":"2009","journal-title":"Class. Quantum Gravity"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"035010","DOI":"10.1088\/0264-9381\/33\/3\/035010","article-title":"TianQin: A space-borne gravitational wave detector","volume":"33","author":"Luo","year":"2016","journal-title":"Class. Quantum Gravity"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"095008","DOI":"10.1088\/1361-6382\/aab52f","article-title":"Fundamentals of the orbit and response for TianQin","volume":"35","author":"Hu","year":"2018","journal-title":"Class. Quantum Gravity"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"05A107","DOI":"10.1093\/ptep\/ptaa114","article-title":"The TianQin project: Current progress on science and technology","volume":"2021","author":"Mei","year":"2021","journal-title":"Prog. Theor. Exp. Phys."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"102918","DOI":"10.1016\/j.rinp.2019.102918","article-title":"A brief analysis to Taiji: Science and technology","volume":"16","author":"Luo","year":"2020","journal-title":"Results Phys."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"05A108","DOI":"10.1093\/ptep\/ptaa083","article-title":"The Taiji program: A concise overview","volume":"2021","author":"Luo","year":"2021","journal-title":"Prog. Theor. Exp. Phys."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"685","DOI":"10.1093\/nsr\/nwx116","article-title":"The Taiji Program in Space for gravitational wave physics and the nature of gravity","volume":"4","author":"Hu","year":"2017","journal-title":"Natl. Sci. Rev."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"2050075","DOI":"10.1142\/S0217751X2050075X","article-title":"Taiji program: Gravitational-wave sources","volume":"35","author":"Ruan","year":"2020","journal-title":"Int. J. Mod. Phys. A"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"122003","DOI":"10.1103\/PhysRevD.84.122003","article-title":"Quantitative analysis of LISA pathfinder test-mass noise","volume":"84","author":"Ferraioli","year":"2011","journal-title":"Phys. Rev. D"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"395","DOI":"10.1007\/s00340-007-2923-0","article-title":"Subtraction of test mass angular noise in the LISA technology package interferometer","volume":"90","author":"Steier","year":"2008","journal-title":"Appl. Phys. B"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"112020","DOI":"10.1016\/j.sna.2020.112020","article-title":"Amplitude stability analysis and experimental investigation of an AC excitation signal for capacitive sensors","volume":"309","author":"Li","year":"2020","journal-title":"Sens. Actuators A Phys."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Chen, Y.Z., Liu, X., Wang, L.Q., Yu, T., Wang, Z., Xue, K., Sui, Y.L., and Chen, Y.K. (2024). Research and Optimization of High-Performance Front-End Circuit Noise for Inertial Sensors. Sensors, 24.","DOI":"10.3390\/s24030805"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Xue, K., Yu, T., Sui, Y.L., Chen, Y.K., Wang, L.Q., Wang, Z., Zhou, J., Chen, Y.Z., and Liu, X. (2023). Research and Implementation of a Demodulation Switch Signal Phase Alignment System in Dynamic Environments. Sensors, 23.","DOI":"10.3390\/s23229144"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"205010","DOI":"10.1088\/1361-6382\/acf8a8","article-title":"Development and experimental investigation of a high-precision capacitive displacement transducer of the inertial sensor for TianQin","volume":"40","author":"Wang","year":"2023","journal-title":"Class. Quantum Gravity"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Yu, J.B., Wang, C.R., Wang, Y., Bai, Y.Z., Hu, M., Li, K., Li, Z.X., Qu, S.B., Wu, S.C., and Zhou, Z.B. (2020). Investigation on stray-capacitance influences of coaxial cables in capacitive transducers for a space inertial sensor. Sensors, 20.","DOI":"10.3390\/s20113233"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Fang, Y.X., Lei, K.Z., Zhang, Q.F., Huang, Q., and Fan, Z.B. (2013, January 12). A high-precision temperature measurement system based on noise cancellation. Proceedings of the 2013 IEEE International Conference of IEEE Region 10, Hangzhou, China.","DOI":"10.1109\/TENCON.2013.6718505"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Xie, Y.F., Fan, J., Zhao, C., Yan, S.T., Hu, C.Y., and Tu, L.C. (2019). Modeling and analysis of the noise performance of the capacitive sensing circuit with a differential transformer. Micromachines, 10.","DOI":"10.3390\/mi10050325"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"034503","DOI":"10.1063\/5.0198159","article-title":"Noise and thermal performance of a sub-attofarad capacitance sensor for precision measurements, with applications in gravitational wave detectors","volume":"95","author":"Saraf","year":"2024","journal-title":"Rev. Sci. Instrum."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"055001","DOI":"10.1063\/1.4873334","article-title":"Resonant frequency detection and adjustment method for a capacitive transducer with differential transformer bridge","volume":"85","author":"Hu","year":"2014","journal-title":"Rev. Sci. Instrum."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Sui, Y.L., Yu, T., Wang, L.Q., Wang, Z., Xue, K., Chen, Y.K., Liu, X., and Chen, Y.Z. (2022). Analysis of a Capacitive Sensing Circuit and Sensitive Structure Based on a Low-Temperature-Drift Planar Transformer. Sensors, 22.","DOI":"10.3390\/s22239284"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1071","DOI":"10.1109\/JSEN.2011.2163389","article-title":"LTP is FEE sensing channel: Front-end modeling and symmetry adjustment method","volume":"12","author":"Gan","year":"2011","journal-title":"IEEE Sens. J."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/24\/12\/3844\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T14:58:35Z","timestamp":1760108315000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/24\/12\/3844"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,6,14]]},"references-count":24,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2024,6]]}},"alternative-id":["s24123844"],"URL":"https:\/\/doi.org\/10.3390\/s24123844","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2024,6,14]]}}}