volume | PIER Journals

Abstract

This paper proposes an analytical method for arbitrary spatial orientations that eliminates systematic errors arising from neglecting rounded corners in planar rectangular coils in wireless power transfer systems. The rounded rectangular coil is decomposed into straight and quarter-arc segments. Using Neumann's formula, mutual inductance expressions for straight-straight, straight-arc, and arc-arc interactions are derived. We establish a unified spatial model using Z-Y-X Euler angle transformations to describe arbitrary translations and rotations in 3D space. We obtain the total mutual inductance by superposition. Results show that neglecting rounded corners increases error as the corner radius grows. Under various conditions, including lateral and axial displacements and composite rotations, the method achieves average relative errors below 1.5% compared with finite element simulations (validated for corner radii up to 12 mm) and below 2.5% compared with experiments (validated for a corner radius of 5 mm), demonstrating high accuracy and robustness.

1. Wu, Jing, Bingnan Wang, William S. Yerazunis, and Koon Hoo Teo, "Wireless power transfer with artificial magnetic conductors," 2013 IEEE Wireless Power Transfer (WPT), 155-158, Perugia, Italy, 2013.
doi:10.1109/WPT.2013.6556906

2. Xia, C., J. Yan, G. Ren, et al. "Simultaneous wireless power and reverse signal transmission technology based on harmonic communication," Proceedings of the CSEE, Vol. 44, No. 13, 5297-5308, 2024.
doi:10.13334/j.0258-8013.pcsee.230780 Google Scholar

3. Chen, W., Y. Liu, X. Yan, et al. "Reactive shielding of four matching capacitors for resonant wireless power transfer in cardiac pacemakers," Transactions of China Electrotechnical Society, Vol. 40, No. 14, 4382-4394, Jul. 2025.
doi:10.19595/j.cnki.1000-6753.tces.241252 Google Scholar

4. Manos, Konstantinos, Yifan Rao, Tuo Zhao, Kevin Liu, Daniel Zhou, Calvin Nguyen, Eric Chen, Glaucio H. Paulino, and Minjie Chen, "Wireless actuation of magnetic robots with a modular 60 mT 3-D helmholtz coil system," 2025 IEEE Applied Power Electronics Conference and Exposition (APEC), 1274-1278, Atlanta, GA, USA, 2025.
doi:10.1109/APEC48143.2025.10977109

5. Hsieh, Yao-Ching, Zhong-Rong Lin, Ming-Cheng Chen, Hsin-Che Hsieh, Yu-Chen Liu, and Huang-Jen Chiu, "High-efficiency wireless power transfer system for electric vehicle applications," IEEE Transactions on Circuits and Systems II: Express Briefs, Vol. 64, No. 8, 942-946, Aug. 2017.
doi:10.1109/tcsii.2016.2624272 Google Scholar

6. Baua, Smit, Reza K. Amineh, and N. Sertac Artan, "Wireless power transfer with multi-layer planar spiral coils as secondary coils," 2018 IEEE Wireless Power Transfer Conference (WPTC), 1-4, Montreal, QC, Canada, 2018.
doi:10.1109/WPT.2018.8639247

7. Nottiani, Duccio Gallichi and Fabio Leccese, "A simple method for calculating lumped parameters of planar spiral coil for wireless energy transfer," 2012 11th International Conference on Environment and Electrical Engineering, 869-872, Venice, Italy, 2012.
doi:10.1109/EEEIC.2012.6221498

8. Luo, Zhichao and Xuezhe Wei, "Analysis of square and circular planar spiral coils in wireless power transfer system for electric vehicles," IEEE Transactions on Industrial Electronics, Vol. 65, No. 1, 331-341, Jan. 2018.
doi:10.1109/tie.2017.2723867 Google Scholar

9. Jiang, Yongbin, Yue Wu, Yaohua Li, Ziheng Xiao, Ning Wang, Min Wu, Xiaohua Wang, and Yi Tang, "Precise modeling for the inductance of rounded rectangular coils in wireless power transfer systems," IECON 2023 --- 49th Annual Conference of the IEEE Industrial Electronics Society, 1-7, Singapore, Singapore, 2023.
doi:10.1109/IECON51785.2023.10312669

10. Liu, X., Y. Cao, C. Xia, et al. "Optimization of hybrid compensation topology and anti-offset performance of wireless power transfer system based on QRQP coil," Transactions of China Electrotechnical Society, Vol. 40, No. 12, 3828-3841, Jun. 2025.
doi:10.19595/j.cnki.1000-6753.tces.242124 Google Scholar

11. Wang, W., L. Wang, P. Zhang, et al. "Research on performance optimization of WPT system based on improved DSQP coil," Electronic Design Engineering, Vol. 33, No. 24, 36-41, Dec. 2025.
doi:10.14022/j.issn1674-6236.2025.24.007 Google Scholar

12. Liu, Shuo, Jianhui Su, Jidong Lai, Jian Zhang, and Haibo Xu, "Precise modeling of mutual inductance for planar spiral coils in wireless power transfer and its application," IEEE Transactions on Power Electronics, Vol. 36, No. 9, 9876-9885, Sep. 2021.
doi:10.1109/tpel.2021.3061667 Google Scholar

13. Altun, Hüseyin and Neslihan Pirinççi, "A novel analytical model for mutual inductance calculations between two nonidentical N-sided polygonal planar coils arbitrarily positioned in 3-D space for wireless power transfer," IEEE Transactions on Power Electronics, Vol. 38, No. 8, 10396-10411, Aug. 2023.
doi:10.1109/tpel.2023.3268336 Google Scholar

14. Li, Z., M. Bao, L. Kong, et al. "Calculation of mutual inductance between rectangular coils at arbitrary positions of porous magnetic media for wireless energy transmission systems," Transactions of China Electrotechnical Society, Vol. 40, No. 24, 7863-7878, 2025.
doi:10.19595/j.cnki.1000-6753.tces.242196 Google Scholar

15. Zheng, Muxin, Ziyun Luo, and Zongfeng Li, "Design of inductive magnetic sensor for space magnetic field measurement," 2024 4th International Conference on Electronics, Circuits and Information Engineering (ECIE), 91-97, Hangzhou, China, 2024.
doi:10.1109/ECIE61885.2024.10627226

16. Wu, Dehui and Hao Feng, "A novel method for calculating the mutual inductance between two perpendicular coils in wireless power transfer," International Journal of Circuit Theory and Applications, Vol. 51, No. 10, 4550-4564, 2023.
doi:10.1002/cta.3670 Google Scholar

17. Yu, Xipei, Junjie Feng, Liyan ZHu, and Qiang Li, "Modelling of a planar omnidirectional wireless power transfer system," 2024 IEEE Applied Power Electronics Conference and Exposition (APEC), 2609-2615, Long Beach, CA, USA, 2024.
doi:10.1109/APEC48139.2024.10509107

18. Pandey, Avanish, Suvendu Samanta, and Amarendra Edpuganti, "Accurate modeling approach of litz-wire based planar DD spiral coils for WPT applications," 2024 IEEE International Conference on Power Electronics, Drives and Energy Systems (PEDES), 1-6, Mangalore, India, 2024.
doi:10.1109/PEDES61459.2024.10961509

19. Qian, Libo, Mengfei Chen, Kexue Cui, Ge Shi, Jian Wang, and Yinshui Xia, "Modeling of mutual inductance between two misalignment planar coils in wireless power transfer," IEEE Microwave and Wireless Components Letters, Vol. 30, No. 8, 814-817, Aug. 2020.
doi:10.1109/lmwc.2020.3006211 Google Scholar

20. Zhang, K., "Calculation and analysis of plane magnetic field distribution and inductance of circular coil," Jiangsu Science & Technology Information, Vol. 39, No. 24, 45-49, Aug. 2022.
doi:10.3969/j.issn.1004-7530.2022.24.011 Google Scholar

21. Greenhouse, H., "Design of planar rectangular microelectronic inductors," IEEE Transactions on Parts, Hybrids, and Packaging, Vol. 10, No. 2, 101-109, Jun. 1974.
doi:10.1109/tphp.1974.1134841 Google Scholar

22. Acero, Jesús, Claudio Carretero, Ignacio Lope, Rafael Alonso, Óscar Lucia, and José M. Burdio, "Analysis of the mutual inductance of planar-lumped inductive power transfer systems," IEEE Transactions on Industrial Electronics, Vol. 60, No. 1, 410-420, Jan. 2013.
doi:10.1109/tie.2011.2164772 Google Scholar

23. Wu, Dehui, Qisheng Sun, Xiaohong Wang, and Fang Cheng, "Calculation of self-and mutual inductances of rounded rectangular coils with rectangular cross-sections and misalignments," IET Electric Power Applications, Vol. 12, No. 7, 1014-1019, 2018.
doi:10.1049/iet-epa.2017.0860 Google Scholar

Dr. Zhongjiu Zheng

Dr. Minghao Zhao

Prof. Zhuang Li

Dr. Xingfeng Cao

Dr. Anran Liu