• Paulo J. Abatti
  • Sérgio F. Pichorim
  • Caio M. de Miranda



Maximum power transfer, power transfer efficiency, relative power transfer, wireless power transfer


The condition for maximum power transfer of 2-coils wireless power transfer (WPT) system is derived from circuit analysis and discussed together with the respective WPT system efficiency (η). In the sequence, it is shown that a 4-coils WPT system (which can be divided in source, two communication and load circuits) without power losses at the two communication circuits (ideal 4-coils WPT system) presents, from maximum power transfer and efficiency point of view, a performance similar to those of a 2-coils WPT system. The exception is the influence of coupling coefficient (k): in 2-coils system η increases as k approaches one, while in ideal 4-coils WPT system η increases as k between the two communication coils approaches zero. In addition, realistic 4-coils WPT systems (with power losses at the two communication circuits) are also analyzed showing, for instance, that η presents a maximum as a function of k of the communication coils. In order to validate the presented theory, 4 coils were built, and a setup to perform 2- coils and 4-coils WPT systems has been carried out. Practical results show good agreement with the developed theory.


[1] S.Y.R. Hui, W.X. Zhong, and C.K. Lee, “A Critical Review of Recent Progress in Mid-Range Wireless Power
Transfer,” IEEE Trans. Power Electronics, vol. 29, no. 9, pp. 4500-4511, Sept. 2014.
[2] A. Kurs, A. Karalis, R. Moffatt, J. D. Joannopoulos, P. Fisher, and M. Soljacic, “Wireless power transfer via strongly
coupled magnetic resonances,” Science, vol. 317, no. 5834, pp. 83–86, Jul. 2007.
[3] A. L. Sample, D. A. Meyer, and J. R. Smith, “Analysis, Experimental Results, and Range Adaptation of Magnetically
Coupled Resonators for Wireless Power Transfer,” IEEE Trans.Ind. Electron. vol. 58, no. 2, pp. 544-554, Feb. 2011.
[4] A. K. RamRakhyani, S. Mirabbasi, and M. Chiao, “Design and optimization of resonance-based efficienct wireless
power delivery systems for biomedical implants,” IEEE Trans. Biomedical Circuits and Systems, vol. 5, no. 1, pp. 48-
63, Feb. 2011.
[5] M. Kim, K. Koo, S. Ahn, B. Bae, and J. Kim, “Analytical Expressions for Maximum Transferred Power in Wireless
Power Transfer Systems,” in Proc. EMC 2011, pp. 379-383.
[6] A. K. RamRakhyani and G. Lazzi, “On the Design of Efficient Multi-Coil Telemetry System for Biomedical Implants,”
IEEE Trans. Biomedical Circuits and Systems, vol. 7, no. 1, pp. 48-63, Feb. 2013.
[7] P. J. Abatti, S. F. Pichorim, and B. Schneider Junior, “A method to derive mutual inductance properties using electric
circuit analysis tools,” International Journal of Electrical Engineering Education, vol. 45, pp. 46-50, 2008.
[8] S. F. Pichorim and P. J. Abatti, “Design of Coils for Millimeter- and Submillimeter-Sized Biotelemetry,” IEEE Trans
Biomedical Engineering, vol. 51, no.8, pp. 1487-1489, Aug. 2004.




How to Cite

Paulo J. Abatti, Sérgio F. Pichorim, & Caio M. de Miranda. (2015). MAXIMUM POWER TRANSFER VERSUS EFFICIENCY IN MID-RANGE WIRELESS POWER TRANSFER SYSTEMS. Journal of Microwaves, Optoelectronics and Electromagnetic Applications (JMOe), 14(1), 97 109.



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