Determination of the Flat Coil Length in Wireless Charging Systems
DOI:
https://doi.org/10.24160/0013-5380-2026-2-84-89Keywords:
wireless energy transmission, spiral coil, Archimedean spiral, conductor length, resistance, numerical simulationAbstract
The application field of wireless charging systems is expanding from year to year. The most promising application areas are the charging of unmanned aerial vehicles, automated non-stationary robots, and electric vehicles. A key stage in the design of such systems is accurate calculation of the inductive coil parameters. An analysis of the literature sources has shown that there is lack of an explicit analytical dependence for determining the conductor length of a round flat spiral coil, although this parameter is critically important for calculating its resistance. The aim of the work is to derive an accurate formula for calculating the conductor length of a single-layer coil in the form of an Archimedean spiral with a uniform pitch and to simplify it for practical use. The validity of the derived formula has been confirmed by comparison with the results of electromagnetic field numerical simulation in the COMSOL Multiphysics environment: the discrepancy did not exceed 0.1 %. A comparative analysis is carried out with simplified calculation methods based on the average coil length and a model in the form of a set of concentric rings. It has been found that the first of the simplified methods provides an error of less than 0.1 %, while the second one leads to deviations of up to 4 %. The obtained dependences make it possible to effectively estimate the length and resistance of coils at the pre-design stage without the need to construct detailed 3D models.
References
1. Kim H. et al. Coil Design and Measurements of Automotive Magnetic Resonant Wireless Charging System for High-Efficiency and Low Magnetic Field Leakage. – IEEE Transactions on Microwave Theory and Techniques, 2016, vol. 64, No. 2, pp. 383–400, DOI: 10.1109/TMTT.2015.2513394.
2. Guo Y. et al. Rectifier Load Analysis for Electric Vehicle Wireless Charging System. – IEEE Transactions on Industrial Electronics, 2018, vol. 65, No. 9, pp. 6970–6982, DOI: 10.1109/TIE.2018.2793260.
3. Tiemann M. et al. Magnetic and Thermal Coupled Field Analysis of Wireless Charging Systems for Electric Vehicles. – IEEE Transactions on Magnetics, 2019, vol. 55, No. 6, DOI: 10.1109/TMAG.2019.2896780.
4. Nguyen M.Q. et al. Field Distribution Models of Spiral Coil for Misalignment Analysis in Wireless Power Transfer Systems. – IEEE Transactions on Microwave Theory and Techniques, 2014, vol. 62, No. 4, pp. 920–930, DOI: 10.1109/TMTT.2014.2302738.
5. Li Y. et al. Design and Optimization of Coupling Coils for Bidirectional Wireless Charging System of Unmanned Aerial Vehicle. – Electronics, 2020, vol. 9, No. 11, DOI: 10.3390/electronics9111964.
6. Hussain I., Woo D.K. Self-Inductance Calculation of the Archimedean Spiral Coil. – Energies, 2021, vol. 15, No. 1, DOI: 10.3390/en15010253.
7. Chen Q. et al. Winding Loss Analysis of Planar Spiral Coil and Its Structure Optimization Technique in Wireless Power Transfer System. – Scientific Reports, 2022, vol. 12, No. 1, DOI: 10.1038/s41598-022-24006-x.
8. Paese E. et al. Simplified Mathematical Modeling for an Electromagnetic Forming System with Flat Spiral Coil as Actuator. – Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2011, vol. 33, pp. 324–331, DOI: 10.1590/S1678-58782011000300008.
9. Krishnapriya S., Komaragiri R., Suja K.J. Fabrication, Characterization, and Modelling of a Novel Via-Less Single Metal Level Magnetic Microcoil Sensor for Biosensing Applications. – Sensors and Actuators A: Physical, 2019, vol. 290, pp. 190–197, DOI: 10.1016/j.sna.2019.02.025.
10. Aebischer H.A. Inductance Formula for Rectangular Planar Spiral Inductors with Rectangular Conductor Cross Section. – Advanced Electromagnetics, 2020, vol. 9, No. 1, DOI: 10.7716/aem.v9i1.1346.
11. Ben Fadhel Y. et al. Model-Based Optimization of Spiral Coils for Improving Wireless Power Transfer. – Energies, 2023, vol. 16, No. 19, DOI: 10.3390/en16196886
12. Jow U.M., Ghovanloo M. Design and Optimization of Printed Spiral Coils for Efficient Transcutaneous Inductive Power Transmission. – IEEE Transactions on Biomedical Circuits and Systems, 2008, vol. 1, No. 3, pp. 193–202, DOI: 10.1109/TBCAS.2007.913130.
13. Jow U.M., Ghovanloo M. Modeling and Optimization of Printed Spiral Coils in Air, Saline, and Muscle Tissue Environments. – IEEE Transactions on Biomedical Circuits and Systems, 2009, vol. 3, No. 5, pp. 339–347, DOI: 10.1109/TBCAS.2009.2025366.
14. Biswal G., Dash S.K. Thermal Analysis of Constant Surface Area Tapered Helical Coils: Insights from Numerical Modelling. – Thermal Science and Engineering Progress, 2024, vol. 54, DOI: 10.1016/j.tsep.2024.102822.
15. Kadyrmjatov Y.R. et al. Application of COMSOL Multiphysics for Modeling Wireless Charging Systems. – 7th International Youth Conference on Radio Electronics, Electrical and Power Engineering (REEPE), 2025, DOI: 10.1109/REEPE63962.2025.10970942.
#
1. Kim H. et al. Coil Design and Measurements of Automotive Magnetic Resonant Wireless Charging System for High-Efficiency and Low Magnetic Field Leakage. – IEEE Transactions on Microwave Theory and Techniques, 2016, vol. 64, No. 2, pp. 383–400, DOI: 10.1109/TMTT.2015.2513394.
2. Guo Y. et al. Rectifier Load Analysis for Electric Vehicle Wireless Charging System. – IEEE Transactions on Industrial Electronics, 2018, vol. 65, No. 9, pp. 6970–6982, DOI: 10.1109/TIE.2018.2793260.
3. Tiemann M. et al. Magnetic and Thermal Coupled Field Analysis of Wireless Charging Systems for Electric Vehicles. – IEEE Transactions on Magnetics, 2019, vol. 55, No. 6, DOI: 10.1109/TMAG.2019.2896780.
4. Nguyen M.Q. et al. Field Distribution Models of Spiral Coil for Misalignment Analysis in Wireless Power Transfer Systems. – IEEE Transactions on Microwave Theory and Techniques, 2014, vol. 62, No. 4, pp. 920–930, DOI: 10.1109/TMTT.2014.2302738.
5. Li Y. et al. Design and Optimization of Coupling Coils for Bidirectional Wireless Charging System of Unmanned Aerial Vehicle. – Electronics, 2020, vol. 9, No. 11, DOI: 10.3390/electronics9111964.
6. Hussain I., Woo D.K. Self-Inductance Calculation of the Archimedean Spiral Coil. – Energies, 2021, vol. 15, No. 1, DOI: 10. 3390/en15010253.
7. Chen Q. et al. Winding Loss Analysis of Planar Spiral Coil and Its Structure Optimization Technique in Wireless Power Transfer System. – Scientific Reports, 2022, vol. 12, No. 1, DOI: 10.1038/s41598-022-24006-x.
8. Paese E. et al. Simplified Mathematical Modeling for an Electromagnetic Forming System with Flat Spiral Coil as Actuator. – Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2011, vol. 33, pp. 324–331, DOI: 10.1590/S1678-58782011 000300008.
9. Krishnapriya S., Komaragiri R., Suja K.J. Fabrication, Characterization, and Modelling of a Novel Via-Less Single Metal Level Magnetic Microcoil Sensor for Biosensing Applications. – Sensors and Actuators A: Physical, 2019, vol. 290, pp. 190–197, DOI: 10.1016/j.sna.2019.02.025.
10. Aebischer H.A. Inductance Formula for Rectangular Planar Spiral Inductors with Rectangular Conductor Cross Section. – Advanced Electromagnetics, 2020, vol. 9, No. 1, DOI: 10.7716/aem.v9i1.1346.
11. Ben Fadhel Y. et al. Model-Based Optimization of Spiral Coils for Improving Wireless Power Transfer. – Energies, 2023, vol. 16, No. 19, DOI: 10.3390/en16196886
12. Jow U.M., Ghovanloo M. Design and Optimization of Printed Spiral Coils for Efficient Transcutaneous Inductive Power Transmission. – IEEE Transactions on Biomedical Circuits and Systems, 2008, vol. 1, No. 3, pp. 193–202, DOI: 10.1109/TBCAS.2007.913130.
13. Jow U.M., Ghovanloo M. Modeling and Optimization of Printed Spiral Coils in Air, Saline, and Muscle Tissue Environments. – IEEE Transactions on Biomedical Circuits and Systems, 2009, vol. 3, No. 5, pp. 339–347, DOI: 10.1109/TBCAS.2009.2025366.
14. Biswal G., Dash S.K. Thermal Analysis of Constant Surface Area Tapered Helical Coils: Insights from Numerical Modelling. – Thermal Science and Engineering Progress, 2024, vol. 54, DOI: 10.1016/j.tsep.2024.102822.
15. Kadyrmjatov Y.R. et al. Application of COMSOL Multiphysics for Modeling Wireless Charging Systems. – 7th International Youth Conference on Radio Electronics, Electrical and Power Engineering (REEPE), 2025, DOI: 10.1109/REEPE63962.2025.10970942
