{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,14]],"date-time":"2026-05-14T14:52:01Z","timestamp":1778770321560,"version":"3.51.4"},"reference-count":28,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2020,4,6]],"date-time":"2020-04-06T00:00:00Z","timestamp":1586131200000},"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 this paper, the feasibility of applying a multi-branch equivalent model employing first- and second-order Cauer circuits for the analysis of electromagnetic transducers used in systems of wireless power transfer is discussed. A method of formulating an equivalent model (EqM) is presented, and an example is shown for a wireless power transfer system (WPTS) consisting of an air transformer with field concentrators. A method is proposed to synthesize the EqM of the considered transducer based on the time-harmonic field model, an optimization algorithm employing the evolution strategy (ES) and the equivalent Cauer circuits. A comparative analysis of the performance of the considered WPTS under high-frequency voltage supply calculated using the proposed EqM and a 3D field model in the time domain using the finite element method (FEM) was carried out. The selected results of the conducted analysis are presented and discussed.<\/jats:p>","DOI":"10.3390\/s20072052","type":"journal-article","created":{"date-parts":[[2020,4,7]],"date-time":"2020-04-07T03:58:39Z","timestamp":1586231919000},"page":"2052","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Application of Multi-Branch Cauer Circuits in the Analysis of Electromagnetic Transducers Used in Wireless Transfer Power Systems"],"prefix":"10.3390","volume":"20","author":[{"given":"Milena","family":"Kurzawa","sequence":"first","affiliation":[{"name":"Institute of Electrical Engineering and Electronics, Poznan University of Technology, 60-965 Poznan, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5427-059X","authenticated-orcid":false,"given":"Cezary","family":"J\u0119dryczka","sequence":"additional","affiliation":[{"name":"Institute of Electrical Engineering and Electronics, Poznan University of Technology, 60-965 Poznan, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4906-469X","authenticated-orcid":false,"given":"Rafa\u0142 M.","family":"Wojciechowski","sequence":"additional","affiliation":[{"name":"Institute of Electrical Engineering and Electronics, Poznan University of Technology, 60-965 Poznan, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,4,6]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Duncan, K.J. (2016, January 4\u20136). Laser based power transmission: Component selection and laser hazard analysis. Proceedings of the 2016 IEEE PELS Workshop on Emerging Technologies: Wireless Power Transfer (WoW), Knoxville, TN, USA.","DOI":"10.1109\/WoW.2016.7772073"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"389","DOI":"10.1109\/JSEN.2011.2161465","article-title":"One-to-Multipoint Laser Remote Power Supply System for Wireless Sensor Networks","volume":"12","author":"Wang","year":"2011","journal-title":"IEEE Sens. J."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Wagih, M., Komolafe, A., and Zaghari, B. (2020). Separation-Independent Wearable 6.78 MHz Near-Field Radiative Wireless Power Transfer using Electrically Small Embroidered Textile Coils. Energies, 13.","DOI":"10.3390\/en13030528"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"520","DOI":"10.1109\/TIE.2003.812472","article-title":"A contactless electrical energy transmission system for portable-telephone battery chargers","volume":"50","author":"Jang","year":"2003","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"140","DOI":"10.1109\/TIE.2003.822039","article-title":"Design and Implementation of Low-Profile Contactless Battery Charger Using Planar Printed Circuit Board Windings as Energy Transfer Device","volume":"51","author":"Choi","year":"2004","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_6","first-page":"20","article-title":"Resonant converter based contactless power supply for robots and manipulators","volume":"2","author":"Maradewicz","year":"2008","journal-title":"J. Autom. Mobile Robot. Intell. Syst."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"357","DOI":"10.1109\/TBCAS.2011.2126570","article-title":"A Low-Power Bidirectional Telemetry Device with a Near-Field Charging Feature for a Cardiac Microstimulator","volume":"5","author":"Lee","year":"2011","journal-title":"IEEE Trans. Biomed. Circuits Syst."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"2466","DOI":"10.1109\/TBME.2012.2203131","article-title":"An Inductively Powered Implantable Blood Flow Sensor Microsystem for Vascular Grafts","volume":"59","author":"Cheong","year":"2012","journal-title":"IEEE Trans. Biomed. Eng."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"10292","DOI":"10.3390\/s120810292","article-title":"A Wireless Magnetic Resonance Energy Transfer System for Micro Implantable Medical Sensors","volume":"12","author":"Li","year":"2012","journal-title":"Sensors"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Song, S., Zhang, Q., Zhu, C., and Wang, D. (2017, January 1\u20135). A practical static simulator for dynamic wireless charging of electric vehicle using receiver open circuit voltage equivalent. Proceedings of the 2017 IEEE Energy Conversion Congress and Exposition (ECCE), Cincinnati, OH, USA.","DOI":"10.1109\/ECCE.2017.8096825"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Alam Chowdhury, M.S., and Liang, X. (2019, January 5\u20138). Design of a Ferrite-Less Power Pad for Wireless Charging Systems of Electric Vehicles. Proceedings of the 2019 IEEE Canadian Conference of Electrical and Computer Engineering (CCECE), Edmonton, AB, Canada.","DOI":"10.1109\/CCECE.2019.8861908"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"2416","DOI":"10.1109\/20.390151","article-title":"Calculation of self and mutual impedances in planar magnetic structures","volume":"31","author":"Hurley","year":"1995","journal-title":"IEEE Trans. Magn."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Dai, W., Tang, W., Cai, C., Deng, L., and Zhang, X. (2018). Wireless Power Charger Based on Class E Amplifier with the Maximum Power Point Load Consideration. Energies, 11.","DOI":"10.3390\/en11092378"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Olukotun, B., Partridge, J., and Bucknall, R. (2019). Finite Element Modeling and Analysis of High Power, Low-loss Flux-Pipe Resonant Coils for Static Bidirectional Wireless Power Transfer. Energies, 12.","DOI":"10.3390\/en12183534"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"3692","DOI":"10.1109\/TMAG.2012.2196263","article-title":"Analysis of Wireless Power Transfer System Based on 3-D Finite-Element Method Including Displacement Current","volume":"48","author":"Zhang","year":"2012","journal-title":"IEEE Trans. Magn."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"897","DOI":"10.1109\/TMAG.2013.2282415","article-title":"2-D Versus 3-D Electromagnetic Field Modeling in Electromechanical Energy Converters","volume":"50","author":"Demenko","year":"2014","journal-title":"IEEE Trans. Magn."},{"key":"ref_17","first-page":"1","article-title":"Equivalent-Circuit Generation from Finite-Element Solution Using Proper Orthogonal Decomposition","volume":"52","author":"Shimotani","year":"2015","journal-title":"IEEE Trans. Magn."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Kurzawa, M., Jedryczka, C., and Wojciechowski, R.M. (2018, January 9\u201312). Analysis of Eddy Current System using Equivalent Multi-Branch Foster Circuit and Edge Element Method. Proceedings of the 19th International Conference Computational Problems of Electrical Engineering, Bansk\u00e1 \u0160tiavnica, Slovak Republic.","DOI":"10.1109\/CPEE.2018.8506899"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"714","DOI":"10.1109\/TMAG.2007.916391","article-title":"Network Representation of Conducting Regions in 3-D Finite-Element Description of Electrical Machines","volume":"44","author":"Demenko","year":"2008","journal-title":"IEEE Trans. Magn."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"581","DOI":"10.1108\/03321640610666736","article-title":"Magneto-electric network models in electromagnetism","volume":"25","author":"Demenko","year":"2006","journal-title":"COMPEL Int. J. Comput. Math. Electr. Electron. Eng."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"434","DOI":"10.1049\/iet-smt:20080068","article-title":"Calculation of inducted currents using edge elements and T\u2013T0 formulation","volume":"2","author":"Demenko","year":"2008","journal-title":"IET Sci. Meas. Technol."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"908","DOI":"10.1108\/03321641011044325","article-title":"Inducted currents analysis in multiply connected conductors using reluctance-resistance networks","volume":"29","author":"Wojciechowski","year":"2010","journal-title":"COMPEL Int. J. Comput. Math. Electr. Electron. Eng."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"279","DOI":"10.2528\/PIERB12061202","article-title":"Description of multiply connected regions with induced currents using T-T0 method","volume":"43","author":"Wojciechowski","year":"2012","journal-title":"Prog. Electromagn. Res. B"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"312","DOI":"10.1049\/iet-smt.2011.0114","article-title":"Comparative analysis of A\u2212V and A\u2212T\u2212T0 calculations of induced currents in multiply connected regions","volume":"6","author":"Wojciechowski","year":"2012","journal-title":"IET Sci. Meas. Technol."},{"key":"ref_25","unstructured":"Wojciechowski, R.M., Kurzawa, M., and J\u0119dryczka, C. (2018, January 26\u201329). Application of evolution strategy to determine the parameters of the multi-branch Foster and Cauer Circuit of Eddy current system. Proceedings of the Symposium on Electromagnetic Phenomena in Nonlinear Circuits 2018, Arras, France."},{"key":"ref_26","first-page":"301","article-title":"The system of wireless power transmission containing the serial-parallel resonant circuit in cooperation with the bridge voltage inverter","volume":"90","author":"Kurzawa","year":"2017","journal-title":"Poznan Univ. Technol. Acad. J. Electr. Eng."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"639","DOI":"10.1109\/43.384428","article-title":"Efficient linear circuit analysis by Pade approximation via the Lanczos process","volume":"14","author":"Feldmann","year":"1995","journal-title":"IEEE Trans. Comput. Des. Integr. Circuits Syst."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"2035","DOI":"10.1108\/COMPEL-03-2016-0088","article-title":"Direct synthesis of equivalent circuits from reduced FE models using proper orthogonal decomposition","volume":"35","author":"Shimotani","year":"2016","journal-title":"COMPEL Int. J. Comput. Math. Electr. Electron. Eng."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/7\/2052\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T09:15:52Z","timestamp":1760174152000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/7\/2052"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,4,6]]},"references-count":28,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2020,4]]}},"alternative-id":["s20072052"],"URL":"https:\/\/doi.org\/10.3390\/s20072052","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,4,6]]}}}