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2026-05-08
Design and Optimization of Four-Coil Magnetic Coupled Resonant Wireless Power Transfer
By
Progress In Electromagnetics Research C, Vol. 170, 78-88, 2026
Abstract
Magnetic Coupled Resonant (MCR) Wireless Power Transfer (WPT) is typically used for electrical charging, offering high tolerance to misalignment and wider transmission range. However, MCR-WPT is assumed to be a two-port circuit, including transmitter (Tx) and receiver (Rx), and exhibits lower efficiency than conventional inductive power transfer. Various studies have been proposed to increase the 4-coil MCR-WPT efficiency, but further challenges remain due to the turn technology complexity. A relevant and simple design solution is developed in the present paper that enables the optimization of Power Transfer Efficiency (PTE) by minimizing implementation cost. To achieve that goal, the transfer- and resonator-distances, TD and RD, respectively were optimized through theory, both circuit and 3-D electromagnetic (EM) simulations via 3-D modeling and experimentation. The validation PTE results obtained from analytic calculation, simulation and experimentation affirm that the maximum efficiencies of 94.10, 90.15% and 69.35% were obtained at optimal positions around RD = 7.5 mm and TD = 100 mm, respectively. The slight difference of the obtained PTE among theory and simulation with experiment is due to the setup instrument imperfection. The performed study is useful for the WPT charging systems, such as electronic sensors, wearable devices, and communication systems.
Citation
Sylcolin Rakotonandrasana, Bilal A. Khawaja, Habachi Bilal, Jeannot Velontsoa, Leonide Tongazara, Sébastien Lallechere, Glauco Fontgalland, Fayu Wan, and Blaise Ravelo, "Design and Optimization of Four-Coil Magnetic Coupled Resonant Wireless Power Transfer," Progress In Electromagnetics Research C, Vol. 170, 78-88, 2026.
doi:10.2528/PIERC26030202
References

1. Laha, Arpan, Abirami Kalathy, Majid Pahlevani, and Praveen Jain, "A comprehensive review on wireless power transfer systems for charging portable electronics," Eng, Vol. 4, No. 2, 1023-1057, 2023.
doi:10.3390/eng4020061        Google Scholar

2. Hui, S. Y., "Planar wireless charging technology for portable electronic products and Qi," Proceedings of the IEEE, Vol. 101, No. 6, 1290-1301, Jun. 2013.
doi:10.1109/jproc.2013.2246531        Google Scholar

3. Philips, Gavin R., Cecilia Clark, Jeffrey Wallace, Calvin Coopmans, Zeljko Pantic, and Cathy Bodine, "User-centred design, evaluation, and refinement of a wireless power wheelchair charging system," Disability and Rehabilitation: Assistive Technology, Vol. 17, No. 7, 815-827, 2022.
doi:10.1080/17483107.2020.1818135        Google Scholar

4. Zhang, Xiu, S. L. Ho, and W. N. Fu, "A hybrid optimal design strategy of wireless magnetic-resonant charger for deep brain stimulation devices," IEEE Transactions on Magnetics, Vol. 49, No. 5, 2145-2148, May 2013.
doi:10.1109/tmag.2013.2244585        Google Scholar

5. Degen, Christoph, "Inductive coupling for wireless power transfer and near-field communication," EURASIP Journal on Wireless Communications and Networking, Vol. 2021, No. 1, 121, May 2021.
doi:10.1186/s13638-021-01994-4        Google Scholar

6. Wang, Yijie, Zhan Sun, Yueshi Guan, and Dianguo Xu, "Overview of megahertz wireless power transfer," Proceedings of the IEEE, Vol. 111, No. 5, 528-554, May 2023.
doi:10.1109/jproc.2023.3265689        Google Scholar

7. Zhu, Jia-Qi, Yong-Ling Ban, Rui-Min Xu, and Chunting Chris Mi, "An NFC-connected coupler using IPT-CPT-combined wireless charging for metal-cover smartphone applications," IEEE Transactions on Power Electronics, Vol. 36, No. 6, 6323-6338, Jun. 2021.
doi:10.1109/tpel.2020.3036459        Google Scholar

8. Moon, SangCheol and Gun-Woo Moon, "Wireless power transfer system with an asymmetric four-coil resonator for electric vehicle battery chargers," IEEE Transactions on Power Electronics, Vol. 31, No. 10, 6844-6854, Oct. 2016.
doi:10.1109/tpel.2015.2506779        Google Scholar

9. Zhang, Lei, Wei Tian, Hao Ding, Kai Lu, Wei Hong, and Rongming Liu, "A hybrid magnetic couplers of wireless charging system for electric vehicles," Progress In Electromagnetics Research C, Vol. 101, 187-202, 2020.
doi:10.2528/pierc19122601        Google Scholar

10. Cai, Jun, Yangyang Chen, Adrian David Cheok, Ying Yan, and Xin Zhang, "Overview of coupling coil design for magnetic coupled resonance wireless charging system of electric vehicles," IEEE Transactions on Transportation Electrification, Vol. 11, No. 4, 8903-8918, Aug. 2025.
doi:10.1109/tte.2025.3565803        Google Scholar

11. Li, Siqi and Chunting Chris Mi, "Wireless power transfer for electric vehicle applications," IEEE Journal of Emerging and Selected Topics in Power Electronics, Vol. 3, No. 1, 4-17, Mar. 2015.
doi:10.1109/jestpe.2014.2319453        Google Scholar

12. Zhang, Hua, Fei Lu, Heath Hofmann, Weiguo Liu, and Chunting Chris Mi, "A four-plate compact capacitive coupler design and LCL-compensated topology for capacitive power transfer in electric vehicle charging application," IEEE Transactions on Power Electronics, Vol. 31, No. 12, 8541-8551, Dec. 2016.
doi:10.1109/tpel.2016.2520963        Google Scholar

13. Dai, Jiejian and Daniel C. Ludois, "A survey of wireless power transfer and a critical comparison of inductive and capacitive coupling for small gap applications," IEEE Transactions on Power Electronics, Vol. 30, No. 11, 6017-6029, Nov. 2015.
doi:10.1109/tpel.2015.2415253        Google Scholar

14. Zhang, Yiming, Shuxin Chen, Xin Li, and Yi Tang, "Design methodology of free-positioning nonoverlapping wireless charging for consumer electronics based on antiparallel windings," IEEE Transactions on Industrial Electronics, Vol. 69, No. 1, 825-834, 2022.
doi:10.1109/tie.2020.3048322        Google Scholar

15. Zhong, W. X., Xun Liu, and S. Y. Ron Hui, "A novel single-layer winding array and receiver coil structure for contactless battery charging systems with free-positioning and localized charging features," IEEE Transactions on Industrial Electronics, Vol. 58, No. 9, 4136-4144, Sep. 2011.
doi:10.1109/tie.2010.2098379        Google Scholar

16. Covic, Grant Anthony and John Talbot Boys, "Modern trends in inductive power transfer for transportation applications," IEEE Journal of Emerging and Selected Topics in Power Electronics, Vol. 1, No. 1, 28-41, Mar. 2013.
doi:10.1109/jestpe.2013.2264473        Google Scholar

17. Adabi, Ramadhan Nur, Keigo Uehara, Naoto Shibata, and Mamiko Inamori, "Investigation of data transmission for wireless power transfer system in seawater," 2023 22nd International Symposium on Communications and Information Technologies (ISCIT), 399-402, Sydney, Australia, 2023.
doi:10.1109/ISCIT57293.2023.10376094

18. Sato, Naoki, Hiroyasu Kifune, and Shohei Komeda, "A coil layout of wireless power transfer systems based on multicoil arrangement for underwater vehicles," Electrical Engineering in Japan, Vol. 207, No. 2, 38-48, 2019.
doi:10.1002/eej.23205        Google Scholar

19. Yang, Canjun, Tianlei Wang, and Yanhu Chen, "Design and analysis of an omnidirectional and positioning tolerant AUV charging platform," IET Power Electronics, Vol. 12, No. 8, 2108-2117, 2019.
doi:10.1049/iet-pel.2018.5663        Google Scholar

20. Omata, Shogo, Kotaro Terada, and Atsushi Kurokawa, "Design and analysis of coil sensors for position recognition in wireless charging," 2025 15th International Conference on Power, Energy, and Electrical Engineering (CPEEE), 247-251, Fukuoka, Japan, 2025.
doi:10.1109/CPEEE64598.2025.10987249

21. Wang, Meng, Li Ren, Weina Liu, Yanyan Shi, and Youtian Niu, "Analysis and design of an efficient distance less-sensitive wireless power transfer system," Progress In Electromagnetics Research C, Vol. 106, 199-213, 2020.
doi:10.2528/pierc20091102        Google Scholar

22. Nakamura, Takuto, Takuya Hirata, Eko Setiawan, and Ichijo Hodaka, "A practical method for estimating mutual inductance in wireless power transmission system," International Journal of Circuits, Systems and Signal Processing, Vol. 16, 1027-1034, 2022.
doi:10.46300/9106.2022.16.125        Google Scholar

23. Kang, Seok Hyon and Chang Won Jung, "Magnetic resonant wireless power transfer with rearranged configurations," Journal of Electromagnetic Engineering and Science, Vol. 17, No. 2, 76-85, Apr. 2017.
doi:10.5515/jkiees.2017.17.2.76        Google Scholar

24. Truong, Binh Duc, "Investigation on power optimization principles for series-configured resonant coupled wireless power transfer systems," AEU --- International Journal of Electronics and Communications, Vol. 106, 67-81, 2019.
doi:10.1016/j.aeue.2019.04.023        Google Scholar

25. Jabbari, Ali, Constantin Simovski, and Masoud Sharifian Mazraeh Mollaei, "Tunable dual-band high-impedance coil for wireless power transfer applications," IEEE Transactions on Antennas and Propagation, Vol. 71, No. 12, 9467-9476, 2023.
doi:10.1109/tap.2023.3318837        Google Scholar

26. De Miranda, Caio M., Sergio F. Pichorim, and Paulo J. Abatti, "On the impact of relay circuit losses in four-coil wireless power transfer systems," International Journal of Circuit Theory and Applications, Vol. 47, No. 12, 1922-1932, 2019.
doi:10.1002/cta.2685        Google Scholar

27. Chaimool, Sarawuth, Chawalit Rakluea, Prayoot Akkaraekthalin, and Yan Zhao, "Effect of losses in printed rectangular coils for compact wireless power transfer systems," Progress In Electromagnetics Research C, Vol. 97, 177-188, 2019.
doi:10.2528/pierc19092601        Google Scholar

28. Jabłoński, Paweł, Dariusz Kusiak, and Tomasz Szczegielniak, "Analytical-numerical approach to the skin and proximity effect in lines with round parallel wires," Energies, Vol. 13, No. 24, 6716, 2020.
doi:10.3390/en13246716        Google Scholar

29. Qiu, Hao, Xusheng Zhang, Junji Chen, Makoto Takamiya, and Yi Shi, "A 6.78-MHz coupling coefficient sensorless wireless power transfer system charging multiple receivers with efficiency maximization by adaptive magnetic field distributor IC," IEEE Transactions on Circuits and Systems I: Regular Papers, Vol. 71, No. 2, 974-983, 2024.
doi:10.1109/tcsi.2023.3340681        Google Scholar

30. Wang, Tianlei and Canjun Yang, "Magnetic field optimization for high-positioning-tolerant wireless charging platforms," Journal of Power Electronics, Vol. 20, No. 1, 22-33, 2020.
doi:10.1007/s43236-019-00018-1        Google Scholar

31. De Moraes, Vinícius T. M., Wassim Kabbara, Mohamed Bensetti, and Tanguy Phulpin, "Modeling and optimization of a new magnetic coupler topology for DIPT systems," IEEE Transactions on Magnetics, Vol. 59, No. 5, 1-4, May 2023.
doi:10.1109/tmag.2023.3246768        Google Scholar

32. Okamoto, Yoshifumi, Shinji Wakao, and Shuji Sato, "Topology optimization based on regularized level-set function for solving 3-D nonlinear magnetic field system with spatial symmetric condition," IEEE Transactions on Magnetics, Vol. 52, No. 3, 1-4, Mar. 2016.
doi:10.1109/tmag.2015.2492978        Google Scholar

33. Liu, Tianhao, Jens Voigt, Zhivin Sun, Allard Schnabel, Knappe-Grueneberg, Isaac Fan, and Liyi Li, "Two-step mirror model for the optimization of the magnetic field generated by coils inside magnetic shielding," 2018 Conference on Precision Electromagnetic Measurements (CPEM 2018), 1-2, Paris, France, 2018.
doi:10.1109/CPEM.2018.8500866

34. Matsumoto, Hirokazu, Wataru Yoneyama, Aozora Hata, and Yuki Sato, "Effective circuit configuration and control for coil-array wireless power transmitters," IEEE Open Journal of the Industrial Electronics Society, Vol. 4, 149-158, 2023.
doi:10.1109/ojies.2023.3272030        Google Scholar

35. Huh, Sungryul, Bumjin Park, Semin Choi, Yujun Shin, Haerim Kim, Jongwook Kim, Jaehyoung Park, Dongryul Park, and Seungyoung Ahn, "Transmitter coils selection method for wireless power transfer system with multiple transmitter coils and single receiver coil," IEEE Transactions on Power Electronics, Vol. 38, No. 3, 4092-4109, 2023.
doi:10.1109/tpel.2022.3216635        Google Scholar

36. Mirbozorgi, S. Abdollah, Esmaeel Maghsoudloo, Hadi Bahrami, Mohamad Sawan, and Benoit Gosselin, "Multi-resonator arrays for smart wireless power distribution: Comparison with experimental assessment," IET Power Electronics, Vol. 13, No. 18, 4183-4193, 2020.
doi:10.1049/iet-pel.2020.0562        Google Scholar

37. Cao, Yuan and Jaber A. Abu Qahouq, "Evaluation of input power splitting wireless power transfer system with multiple transmitters for efficiency maximisation," IET Power Electronics, Vol. 12, No. 10, 2485-2492, 2019.
doi:10.1049/iet-pel.2018.6228        Google Scholar

38. Tan, Shun Yao, Hui Jing Lee, Kuen Yao Lau, and Pin Jern Ker, "Simulation of 4-coils magnetic resonance coupling for multiple receivers wireless power transfer at various transmission distance," 2018 IEEE Student Conference on Research and Development (SCOReD), 1-5, Selangor, Malaysia, Nov. 2018.
doi:10.1109/SCORED.2018.8711181

39. Li, Zhongqi, Yixiong Lai, Jiliang Yi, and Junjun Li, "A method of tracking optimum efficiency for four-coil wireless power transfer system," Progress In Electromagnetics Research B, Vol. 76, 125-140, 2017.
doi:10.2528/pierb17040303        Google Scholar

40. Nair, Vijith Vijayakumaran and Jun Rim Choi, "An efficiency enhancement technique for a wireless power transmission system based on a multiple coil switching technique," Energies, Vol. 9, No. 3, 156, Mar. 2016.
doi:10.3390/en9030156        Google Scholar

41. Kiani, Mehdi, Uei-Ming Jow, and Maysam Ghovanloo, "Design and optimization of a 3-coil inductive link for efficient wireless power transmission," IEEE Transactions on Biomedical Circuits and Systems, Vol. 5, No. 6, 579-591, Dec. 2011.
doi:10.1109/tbcas.2011.2158431        Google Scholar

42. Tan, Shun Yao and Hui Jing Lee, "Critical review and simulation of mid-range wireless power transfer for electronic device," Journal of Physics: Conference Series, Vol. 1019, No. 1, 012002, 2018.
doi:10.1088/1742-6596/1019/1/012002

43. Abduljaleel, Hala, Saad Mutashar, and Sadik Gharghan, "Survey of near-field wireless communication and power transfer for biomedical implants," Engineering and Technology Journal, Vol. 42, No. 8, 1080-1103, 2024.
doi:10.30684/etj.2024.144480.1636        Google Scholar

44. Shevchenko, Viktor, Bohdan Pakhaliuk, Oleksandr Husev, Oleksandr Veligorskyi, Deniss Stepins, and Ryszard Strzelecki, "Feasibility study GaN transistors application in the novel split-coils inductive power transfer system with T-type inverter," Energies, Vol. 13, No. 17, 4535, Sep. 2020.
doi:10.3390/en13174535        Google Scholar

45. Xu, Jiale, Lei Gu, Zhechi Ye, Saleh Kargarrazi, and Juan Manuel Rivas-Davila, "Cascode GaN/SiC: A wide-bandgap heterogenous power device for high-frequency applications," IEEE Transactions on Power Electronics, Vol. 35, No. 6, 6340-6349, Jun. 2020.
doi:10.1109/tpel.2019.2954322        Google Scholar

46. Hussain, Iftikhar and Dong-Kyun Woo, "Inductance calculation of single-layer planar spiral coil," Electronics, Vol. 11, No. 5, 750, 2022.
doi:10.3390/electronics11050750        Google Scholar

47. Pacurar, Claudia, Vasile Topa, Claudia Constantinescu, Calin Munteanu, Marian Gliga, Sergiu Andreica, and Adina Giurgiuman, "Adapting the formula for planar spiral inductors’ inductance computation to the new oval geometric shape, ideal for designing wireless power transfer systems for smart devices," Mathematics, Vol. 13, No. 3, 348, Jan. 2025.
doi:10.3390/math13030348        Google Scholar

48. Liu, Xu, Chenyang Xia, and Xibo Yuan, "Study of the circular flat spiral coil structure effect on wireless power transfer system performance," Energies, Vol. 11, No. 11, 2875, Oct. 2018.
doi:10.3390/en11112875        Google Scholar

49. Cruciani, Silvano, Tommaso Campi, Francesca Maradei, and Mauro Feliziani, "Numerical modeling of Litz wires based on discrete transpositions of strands and 2-D finite element analysis," IEEE Transactions on Power Electronics, Vol. 38, No. 5, 6710-6719, May 2023.
doi:10.1109/tpel.2023.3240338        Google Scholar

50. Wu, Bin, Xiaodong Zhang, Xiucheng Liu, and Cunfu He, "An analytical model for predicting the self-capacitance of multi-layer circular-section induction coils," IEEE Transactions on Magnetics, Vol. 54, No. 5, 1-7, May 2018.
doi:10.1109/tmag.2018.2803771        Google Scholar

51. Özüpak, Yıldırım, "Analysis and experimental verification of efficiency parameters affecting inductively coupled wireless power transfer systems," Heliyon, Vol. 10, No. 5, e27420, 2024.
doi:10.1016/j.heliyon.2024.e27420        Google Scholar