{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,30]],"date-time":"2026-09-30T02:51:33Z","timestamp":1790736693975,"version":"4.1.0"},"reference-count":29,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2026,2,2]],"date-time":"2026-02-02T00:00:00Z","timestamp":1769990400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In order to satisfy the measurement of objects in compact settings, a miniaturized linear inductive encoder with a measurement range of 15 mm is investigated in this paper. The encoder structure integrates a movable part with conductive plates and a stationary part with planar excitation and inductive coils. When a high-frequency alternating current is applied to the excitation coils, a time-varying magnetic field will be generated. Meanwhile, the conductive plates on the movable element will produce an eddy current magnetic field to reduce or boost the magnetic field. As the movable part moves, two-channel amplitude-modulated electrical signals whose amplitudes vary with displacement are obtained. The CORDIC algorithm is utilized to calculate the displacement. The paper describes the structure and working principle of the encoder, presents corresponding finite element simulations of the magnetic field, and introduces a prototype fabricated by PCB technology. Experiments evaluating stability, resolution, and accuracy show that the encoder reaches the measurement accuracy of 12.8 \u03bcm within one pitch, and the resolution is 0.7 \u03bcm. Importantly, its minimal dimensions (20 mm \u00d7 10 mm \u00d7 1 mm) enable installation in highly constrained mechanisms.<\/jats:p>","DOI":"10.3390\/s26030973","type":"journal-article","created":{"date-parts":[[2026,2,3]],"date-time":"2026-02-03T12:46:11Z","timestamp":1770122771000},"page":"973","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A Miniature Inductive Encoder for Linear Displacement Measurement"],"prefix":"10.3390","volume":"26","author":[{"given":"Wei","family":"Xiong","sequence":"first","affiliation":[{"name":"Beijing Institute of Precise Mechanical and Electronic Control Equipment, Beijing 100076, China"},{"name":"Innovation Center for Control Actuators, Beijing 100076, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shouhao","family":"Wang","sequence":"additional","affiliation":[{"name":"Beijing Institute of Precise Mechanical and Electronic Control Equipment, Beijing 100076, China"},{"name":"Innovation Center for Control Actuators, Beijing 100076, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yajun","family":"Ma","sequence":"additional","affiliation":[{"name":"Beijing Institute of Precise Mechanical and Electronic Control Equipment, Beijing 100076, China"},{"name":"Innovation Center for Control Actuators, Beijing 100076, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Peng","family":"Chen","sequence":"additional","affiliation":[{"name":"Beijing Institute of Precise Mechanical and Electronic Control Equipment, Beijing 100076, China"},{"name":"Innovation Center for Control Actuators, Beijing 100076, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sijia","family":"Cao","sequence":"additional","affiliation":[{"name":"Beijing Institute of Precise Mechanical and Electronic Control Equipment, Beijing 100076, China"},{"name":"Innovation Center for Control Actuators, Beijing 100076, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jiajia","family":"Xu","sequence":"additional","affiliation":[{"name":"Beijing Institute of Precise Mechanical and Electronic Control Equipment, Beijing 100076, China"},{"name":"Innovation Center for Control Actuators, Beijing 100076, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yanxu","family":"Wang","sequence":"additional","affiliation":[{"name":"Beijing Institute of Precise Mechanical and Electronic Control Equipment, Beijing 100076, China"},{"name":"Innovation Center for Control Actuators, Beijing 100076, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,2,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"3232","DOI":"10.1063\/1.1499533","article-title":"High bandwidth nano-positioner: A robust control approach","volume":"73","author":"Salapaka","year":"2022","journal-title":"Rev. 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