{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,11]],"date-time":"2026-02-11T18:30:56Z","timestamp":1770834656124,"version":"3.50.1"},"reference-count":32,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2022,5,12]],"date-time":"2022-05-12T00:00:00Z","timestamp":1652313600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"King Mongkut\u2019s Institute of Technology Ladkrabang (KMITL)","award":["2564-02-01-022"],"award-info":[{"award-number":["2564-02-01-022"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In this paper, a circuit technique to extend the measuring range of a linear variable differential transformer (LVDT) is proposed. The transfer characteristic of the LVDT contains the odd function form of the cubic polynomial. Therefore, the measuring range of a commercial LVDT is linear in a narrow range compared to its physical dimensions. The wide measuring range of the LVDT requires a large structure of the LVDT, which increases the scale and the cost of the measurement system. The measuring range of the LVDT can be linearly extended to the maximum of the stroke range using the proposed technique. The realization of the proposed technique is based on the use of the hyperbolic sine (sinh) function of the electronic circuit building block, named the class AB bipolar amplifier. The class AB bipolar amplifier can be obtained by the current feedback operational amplifier (CFOA). The circuit of the proposed technique requires two CFOAs and an operational transconductance amplifier (OTA) as the active devices and all devices used in the proposed technique to synthesize the sinh function are commercially available. The proposed technique exhibits an ability to compensate for the nonlinear characteristic of the LVDT without digital components. The proposed technique is attractive in terms of its simple circuit configuration, small size, and low cost. The linear range extension of the LVDT used in this paper is significantly increased with a maximum error of about 18.3 \u03bcm of 6.2 mm at the full stroke range or the full-scale percentage error of about 0.295%. The results indicate that the proposed technique provides excellent performance to extend the measuring range of the LVDT without modifying the LVDT structure.<\/jats:p>","DOI":"10.3390\/s22103674","type":"journal-article","created":{"date-parts":[[2022,5,12]],"date-time":"2022-05-12T23:08:36Z","timestamp":1652396916000},"page":"3674","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["Linear-Range Extension for Linear Variable Differential Transformer Using Hyperbolic Sine Function"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2423-0102","authenticated-orcid":false,"given":"Apinai","family":"Rerkratn","sequence":"first","affiliation":[{"name":"School of Engineering, King Mongkut\u2019s Institute of Technology Ladkrabang, Ladkrabang, Bangkok 10520, Thailand"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jakkapun","family":"Tongcharoen","sequence":"additional","affiliation":[{"name":"School of Engineering, King Mongkut\u2019s Institute of Technology Ladkrabang, Ladkrabang, Bangkok 10520, Thailand"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0234-3475","authenticated-orcid":false,"given":"Wandee","family":"Petchmaneelumka","sequence":"additional","affiliation":[{"name":"School of Engineering, King Mongkut\u2019s Institute of Technology Ladkrabang, Ladkrabang, Bangkok 10520, Thailand"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4708-4665","authenticated-orcid":false,"given":"Vanchai","family":"Riewruja","sequence":"additional","affiliation":[{"name":"School of Engineering, King Mongkut\u2019s Institute of Technology Ladkrabang, Ladkrabang, Bangkok 10520, Thailand"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,5,12]]},"reference":[{"key":"ref_1","unstructured":"Pall\u00e1s-Areny, R., and Webster, J.G. (2001). Sensors and Signal Conditioning, John Wiley & Sons. [2nd ed.]."},{"key":"ref_2","unstructured":"Neubert, H.K.P. (1999). Instrument Transducers: An Introduction to Their Performance and Design, Clarendon."},{"key":"ref_3","unstructured":"Wilson, J.S. (2005). Sensor Technology Handbook, Elsevier."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"2248","DOI":"10.1109\/JSEN.2014.2364610","article-title":"An Adaptive Analog Circuit for LVDT\u2019s Nanometer Measurement Without Losing Sensitivity and Range","volume":"15","author":"Chen","year":"2015","journal-title":"IEEE Sens. J."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"5241","DOI":"10.1109\/TIA.2016.2587775","article-title":"Arc Flash Pressure Measurement System Design","volume":"52","author":"Zhang","year":"2016","journal-title":"IEEE Trans. Ind. Appl."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Kim, R.-W., Kim, C.-M., Hwang, K.-H., and Kim, S.-R. (2019). Embedded Based Real-Time Monitoring in the High-Pressure Resin Transfer Molding Process for CFRP. Appl. Sci., 9.","DOI":"10.3390\/app9091795"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Szewczyk, P., and Kudyba, P. (2022). Effectiveness of Selected Strain and Displacement Measurement Techniques in Civil Engineering. Buildings, 12.","DOI":"10.3390\/buildings12020172"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Gu, T., Qian, X., and Lou, P. (2021). Research on Temperature Compensation Method in Crankshaft Online Measurement System. Appl. Sci., 11.","DOI":"10.3390\/app11167558"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Jang, S., Nam, J., Lee, S., and Oh, J. (2019). A simple, reusable and low-cost LVDT-based in situ bolt preload monitoring system during fastening for a truck wheel assembly. Metals, 9.","DOI":"10.3390\/met9030336"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Di Rito, G., Luciano, B., Borgarelli, N., and Nardeschi, M. (2021). Model-Based Condition-Monitoring and Jamming-Tolerant Control of an Electro-Mechanical Flight Actuator with Differential Ball Screws. Actuators, 10.","DOI":"10.3390\/act10090230"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Blasi, L., Borrelli, M., D\u2019Amato, E., di Grazia, L.E., Mattei, M., and Notaro, I. (2021). Modeling and Control of a Modular Iron Bird. Aerospace, 8.","DOI":"10.3390\/aerospace8020039"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"153618","DOI":"10.1109\/ACCESS.2019.2948781","article-title":"Experimental Development of a Health Monitoring Method for Electro-Mechanical Actuators of Flight Control Primary Surfaces in More Electric Aircrafts","volume":"7","author":"Mazzoleni","year":"2019","journal-title":"IEEE Access"},{"key":"ref_13","unstructured":"Webster, J.G. (2010). Medical Instrumentation Application and Design, Wiley."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"290","DOI":"10.1590\/S1678-58782007000300009","article-title":"Development of an automated and dedicated measuring system for straightness evaluation","volume":"29","author":"Paziani","year":"2007","journal-title":"J. Braz. Soc. Mech. Sci. Eng."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1637","DOI":"10.1088\/0957-0233\/16\/8\/014","article-title":"Differential synchronous demodulator for modulating sensors and impedance measurements","volume":"16","author":"Casanella","year":"2005","journal-title":"Meas. Sci. Technol."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"926","DOI":"10.1109\/19.252529","article-title":"Differential Synchronous Demodulation for Small-signal Amplitude Estimation","volume":"42","author":"Koukourlis","year":"1993","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1109\/TIM.2019.2895481","article-title":"A Fully Differential Synchronous Demodulator for AC Signals","volume":"69","author":"Sifuentes","year":"2020","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"340","DOI":"10.15866\/iree.v11i3.8906","article-title":"Accurate LVDT Signal Converter","volume":"11","author":"Petchmaneelumka","year":"2016","journal-title":"Int. Rev. Electr. Eng. (IREE)"},{"key":"ref_19","first-page":"2171","article-title":"Linear Variable Differential Transformer Temperature Compensation Technique","volume":"30","author":"Petchmaneelumka","year":"2018","journal-title":"Sens. Mater."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Tongcharoen, J., Petchmaneelumka, W., and Riewruja, V. (2015, January 13\u201316). Low-Cost Resolver-to-DC Converter. Proceedings of the 15th International Conference on Control, Automation and Systems, Busan, Korea.","DOI":"10.1109\/ICCAS.2015.7364630"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"9501","DOI":"10.1109\/JSEN.2018.2872510","article-title":"Study of a Modified LVDT Type Displacement Transducer with Unlimited Range","volume":"18","author":"Mandal","year":"2018","journal-title":"IEEE Sens. J."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"5045","DOI":"10.1109\/JSEN.2019.2902879","article-title":"Simple Technique for Linear-Range Extension of Linear Variable Differential Transformer","volume":"19","author":"Petchmaneelumka","year":"2019","journal-title":"IEEE Sens. J."},{"key":"ref_23","first-page":"475","article-title":"Linear-range Extension for Linear Variable Differential Transformer Using Binomial Series","volume":"32","author":"Petchmaneelumka","year":"2020","journal-title":"Sens. Mater."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Polyanin, A.D., and Manzhirov, A.V. (2007). Handbook of Mathematics for Engineers and Scientists, Taylor & Francis Group.","DOI":"10.1201\/9781420010510"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1016\/j.aeue.2017.05.037","article-title":"Fractional Order Linear Variable Differential Transformer: Design and analysis","volume":"79","author":"Veeraian","year":"2017","journal-title":"AEU-Int. J. Electron. Commun."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"947","DOI":"10.1109\/TIM.2009.2031385","article-title":"A Novel Method of Extending the Linearity Range of Linear Variable Differential Transformer Using Artificial Neural Network","volume":"59","author":"Mishra","year":"2010","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Das, S., Das, D.P., and Behera, S.K. (2013, January 19\u201321). Enhancing the linearity of LVDT by two-stage functional link artificial neural network with high accuracy and precision. Proceedings of the 2013 IEEE 8th Conference on Industrial Electronics and Applications (ICIEA), Melbourne, Australia.","DOI":"10.1109\/ICIEA.2013.6566578"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"3316","DOI":"10.1109\/JSEN.2022.3142195","article-title":"Low-Cost Linearity Range Enhancement for Linear Variable Differential Transformer","volume":"22","author":"Prommee","year":"2022","journal-title":"IEEE Sens. J."},{"key":"ref_29","unstructured":"(2022, February 01). Available online: https:\/\/www.analog.com\/media\/en\/technical-documentation\/data-sheets\/AD844.pdf."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Petchmaneelumka, W., Riewruja, V., Songsuwankit, K., and Rerkratn, A. (2021). A Temperature-Compensation Technique for Improving Resolver Accuracy. Sensors, 21.","DOI":"10.3390\/s21186069"},{"key":"ref_31","unstructured":"Boylestad, R.L., and Nashelsky, L. (2014). Electronic Devices and Circuit Theory, Pearson Education Ltd.. [11th ed.]. ISBN 13: 978-1-292-02563-6."},{"key":"ref_32","unstructured":"(2022, February 01). Available online: https:\/\/datasheetspdf.com\/pdf\/538693\/IntersilCorporation\/CA3280A\/1."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/10\/3674\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T23:09:34Z","timestamp":1760137774000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/10\/3674"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,5,12]]},"references-count":32,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2022,5]]}},"alternative-id":["s22103674"],"URL":"https:\/\/doi.org\/10.3390\/s22103674","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,5,12]]}}}