In this paper, the spatial impedance of the wireless power transfer (WPT) system is analyzed, and a resistance tunnel is found. First, the definitions of the spatial impedance in the near field are discussed, and one definition is chosen. By using this definition, the concept of the resistance and the reactance are extended from a scaler form into a vector form. Under this definition and this concept, the spatial impedance is analyzed, and a resistance tunnel is found. The tunnel possesses an obvious direction which is from the receive coil to the transmit coil, and possesses a concave phenomenon on the resistance's magnitude curves. The reason for the forming of the tunnel is also analyzed by discussing the x- and z-components of the resistance. Second, the influences on the resistance tunnel by four factors are discussed. Only the current phase difference determines the existence of the resistance tunnel. The other factors only influence the magnitude and the distribution of the resistance. The correctness of the theoretical calculation is verified by implementing an electromagnetic simulation via FEM. Since the WPT system is one of the typical coupling systems in the near field, one can infer that the resistance tunnel not only exists in the WPT system, but also exists in other coupling coil systems in the near field.
1. Khan, N., H. Matsumoto, and O. Trescases, "Wireless electric vehicle charger with electromagnetic coil-based position correction using impedance and resonant frequency detection," IEEE Trans. Power Electr., Vol. 35, No. 8, 7873-7883, 2020. doi:10.1109/TPEL.2020.2965476
2. Kadem, K., F. Benyoubi, M. Bensetti, Y. L. Bihan, E. Labour'e, and M. Debbou, "An efficient method for dimensioning magnetic shielding for an induction electric vehicle charging system," Progress In Electromagnetics Research, Vol. 170, 153-167, 2021. doi:10.2528/PIER21031903
3. Kim, Y. G. and S. Nam, "Determination of the impedance parameters of antennas and the maximum power transfer efficiency of wireless power transfer," IEEE Trans. Antenn. Propag., Vol. 67, No. 8, 5132-5144, 2019. doi:10.1109/TAP.2019.2912500
4. Arabsalmanabadi, B., H. Arab, V. H. G. Amador, S. Dufour, and K. Al-Haddad, "A three-dimensional discontinuous Galerkin time-domain finite element method for electromagnetic modeling of wireless power transfer coils," IEEE Open Journal of the Industrial Electronics Society, Vol. 2, 360-371, 2021. doi:10.1109/OJIES.2021.3077389
5. Zhang, K., L. Du, Z. Zhu, B. Song, and D. Xu, "A normalization method of delimiting the electromagnetic hazard region of a wireless power transfer system," IEEE Trans. Electromagn. C., Vol. 60, No. 4, 829-839, 2018. doi:10.1109/TEMC.2017.2752300
6. Chabalko, M., J. Besnoff, M. Laifenfeld, and D. S. Ricketts, "Resonantly coupled wireless power transfer for non-stationary loads with application in automotive environments," IEEE Trans. Ind. Electron., Vol. 64, No. 1, 91-103, 2017. doi:10.1109/TIE.2016.2609379
7. Li, W., Q. Wang, J. Kang, and Y. Wang, "Energy distribution characteristics of magnetically coupled resonant wireless power transfer systems considering four basic reactive power compensations," Progress In Electromagnetics Research M, Vol. 86, 1-16, 2019. doi:10.2528/PIERM19071608
8. Kang, J., Q. Wang, Y. Wang, and W. Li, "Polarization characteristic of the magnetic field in wireless power transfer systems," IEEE Trans. Antenn. Propag., Vol. 67, No. 11, 7114-7120, 2019. doi:10.1109/TAP.2019.2927840
9. Chu, S. Y., X. Zan, and A. Avestruz, "Electromagnetic model-based foreign object detection for wireless power transfer," IEEE Trans. Power Electr., Vol. 37, No. 1, 100-113, 2022. doi:10.1109/TPEL.2021.3100420
10. Shah, I. A. and H. Yoo, "Assessing human exposure with medical implants to electromagnetic fields from a wireless power transmission system in an electric vehicle," IEEE Trans. Electromagn. C., Vol. 62, No. 2, 338-345, 2020. doi:10.1109/TEMC.2019.2903844
11. Park, S., "Evaluation of electromagnetic exposure during 85 kHz wireless power transfer for electric vehicles," IEEE Trans. Magn., Vol. 54, No. 1, 1-8, 2018.
12. Lu, C., et al., "Investigation of negative and near-zero permeability metamaterials for increased efficiency and reduced electromagnetic field leakage in a wireless power transfer system," IEEE Trans. Electromagn. C., Vol. 61, No. 5, 1438-1446, 2019. doi:10.1109/TEMC.2018.2865520
13. Lee, S., et al., "Low leakage electromagnetic field level and high efficiency using a novel hybrid loop-array design for wireless high power transfer system," IEEE Trans. Ind. Electron., Vol. 66, No. 6, 4356-4367, 2019. doi:10.1109/TIE.2018.2851988
14. Bocan, K. N., M. H. Mickle, and E. Sejdic, "Multi-disciplinary challenges in tissue modeling for wireless electromagnetic powering: A review," IEEE Sens. J., Vol. 17, No. 20, 6498-6509, 2017. doi:10.1109/JSEN.2017.2748338
15. Wenngren, S., A. Clements, and T. Johnson, "Capacitively coupled resonator models for investigating spatial impedance variation in WPT systems," 2018 IEEE Wireless Power Transfer Conference (WPTC), 1-4, 2018.
16. Karami, H. and K. Sheshyekani, "Harmonic impedance of grounding electrodes buried in a horizontally stratified multilayer ground: A full-wave approach," IEEE Trans. Electromagn. C., Vol. 60, No. 4, 899-906, 2018. doi:10.1109/TEMC.2017.2759259
17. Chen, Z., K. Solbach, D. Erni, and A. Rennings, "Electromagnetic field analysis of a dipole coil element with surface impedance characterized shielding plate for 7-T MRI," IEEE Trans. Microw. Theory, Vol. 64, No. 3, 972-981, 2016. doi:10.1109/TMTT.2016.2518168
18. Salarieh, B., H. M. J. De Silva, A. M. Gole, A. Ametani, and B. Kordi, "An electromagnetic model for the calculation of tower surge impedance based on thin wire approximation," IEEE Trans. Power Deliver., Vol. 36, No. 2, 1173-1182, 2021. doi:10.1109/TPWRD.2020.3003250
19. Jameson, N. J., M. H. Azarian, and M. Pecht, "Impedance-based condition monitoring for insulation systems used in low-voltage electromagnetic coils," IEEE Trans. Ind. Electron., Vol. 64, No. 5, 3748-3757, 2017. doi:10.1109/TIE.2017.2652359
20. Thiel, D. V. and R. Mittra, "Self-consistent impedance method for the solution of electromagnetic problems," 2000 Asia-Pacific Microwave Conference, Proceedings (Cat. No. 00TH8522), 281-285, 2000. doi:10.1109/APMC.2000.925788
21. Pao, H. and J. R. Wait, "Electromagnetic induction and surface impedance in a half-space from an overhead moving current system," IEEE Trans. Antenn. Propag., Vol. 48, No. 9, 1301-1305, 2000. doi:10.1109/8.898762
22. Tkachova, T. I., V. I. Shcherbinin, and V. I. Tkachenko, "Validity of surface impedance model for electromagnetic analysis of a corrugated gyrotron cavity," 2018 IEEE 17th International Conference on Mathematical Methods in Electromagnetic Theory (MMET), 238-241, 2018.
23. Chialina, S., M. Cicuttin, L. Codecasa, R. Specogna, and F. Trevisan, "Plane wave excitation for frequency domain electromagnetic problems by means of impedance boundary condition," IEEE Trans. Magn., Vol. 51, No. 3, 1-4, 2015. doi:10.1109/TMAG.2014.2358701
24. Hanson, G. W., "A common electromagnetic framework for carbon nanotubes and solid nanowires --- Spatially dispersive conductivity, generalized Ohm's law, distributed impedance, and transmission line model," IEEE Trans. Microw. Theory, Vol. 59, No. 1, 9-20, 2011. doi:10.1109/TMTT.2010.2090693
25. Chen, M., et al., "Experimental demonstration of invisible electromagnetic impedance matching cylindrical transformation optics cloak shell," J. Optics --- UK, Vol. 20, No. 4, 45608, 2018. doi:10.1088/2040-8986/aab25f
26. Yu, D., S. He, X. Chen, G. Zhu, and H. Yin, "Simulation of electromagnetic scattering for 3-D impedance surface using MoM-PO method," IEEE Trans. Antenn. Propag., Vol. 60, No. 8, 3988-3991, 2012. doi:10.1109/TAP.2012.2201087
27. Upton, M. E. G. and A. C. Marvin, "The fields due to a small loaded loop in free space," IEEE Trans. Electromagn. C., Vol. 36, No. 1, 7-13, 1994. doi:10.1109/15.265474
28. Amin, S., B. Ahmed, M. Amin, M. I. Abbasi, A. Elahi, and U. Aftab, "Establishment of boundaries for near-field, fresnel and Fraunhofer-field regions," 2017 IEEE Asia Pacific Microwave Conference (APMC), 57-60, 2017. doi:10.1109/APMC.2017.8251376
29. Brunett, J. D., V. V. Liepa, and D. L. Sengupta, "Extrapolating near-field emissions of low-frequency loop transmitters," IEEE Trans. Electromagn. C., Vol. 47, No. 3, 635-641, 2005. doi:10.1109/TEMC.2005.853168
31. Kang, J., Q. Wang, Y. Wang, and W. Li, "Optimization of the magnetic field computation in wireless power transfer system by two-dimensional feature selective validation and maximum value filtered method," IEEE Trans. Electromagn. C., Vol. 61, No. 4, 1061-1071, 2019. doi:10.1109/TEMC.2018.2858925
32. McLean, J. and R. Sutton, "The quasi-static near electric field of an inductive power transfer system," 2013 IEEE Symposium on Product Compliance Engineering (ISPCE), 1-6, 2013.
33. Papazov, S. P. and I. K. Daskalov, "Effect of contour shape of nervous system electromagnetic stimulation coils on the induced electrical field distribution," Biomed. Eng. Online, Vol. 1, No. 1, 2002. doi:10.1186/1475-925X-1-1