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Robust and efficient wireless power transfer using a switch-mode implementation of a nonlinear parity–time symmetric circuit


Stationary wireless power transfer has been deployed commercially and can be used to charge a variety of devices, including mobile phones and parked electric vehicles. However, wireless power transfer set-ups typically suffer from an inherent sensitivity to the relative movement of the device with respect to the power source. Nonlinear parity–time symmetric circuits could be used to deliver robust wireless power transfer even while a device is moving rapidly, but previous implementations have relied on an inefficient gain element based on an operation-amplifier circuit, which has inherent loss, and hence have exhibited poor total system efficiency. Here we show that robust and efficient wireless power transfer can be achieved by using a power-efficient switch-mode amplifier with current-sensing feedback in a parity–time symmetric circuit. In this circuit, the parity–time symmetry guarantees that the effective load impedance on the switch-mode amplifier remains constant, and hence the amplifier maintains high efficiency despite variation of the transfer distance. We experimentally demonstrate a nonlinear parity–time symmetric radiofrequency circuit that can wirelessly transfer around 10 W of power to a moving device with a nearly constant total efficiency of 92% and over a distance from 0 to 65 cm.

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Fig. 1: Circuit design for efficient and robust wireless power transfer based on nonlinear PT symmetry.
Fig. 2: Power-efficient switch-mode amplifier operation.
Fig. 3: Efficient switch-mode amplifier as a resonator’s gain element.
Fig. 4: Experimental wireless power transfer system and measurements.

Data availability

The datasets generated and analysed during the current study are available at


  1. Kurs, A. et al. Wireless power transfer via strongly coupled magnetic resonances. Science 317, 83–86 (2007).

    Article  MathSciNet  Google Scholar 

  2. Karalis, A., Joannopoulos, J. D. & Soljačić, M. Efficient wireless non-radiative mid-range energy transfer. Ann. Phys. 323, 34–48 (2008).

    Article  Google Scholar 

  3. Assawaworrarit, S., Yu, X. & Fan, S. Robust wireless power transfer using a nonlinear parity–time-symmetric circuit. Nature 546, 387–390 (2017).

    Article  Google Scholar 

  4. Chabalko, M. J., Shahmohammadi, M. & Sample, A. P. Quasistatic cavity resonance for ubiquitous wireless power transfer. PLoS ONE 12, e0169045 (2017).

    Article  Google Scholar 

  5. Ra’Di, Y. et al. On-site wireless power generation. IEEE Trans. Antennas Propag. 66, 4260–4268 (2018).

    Article  Google Scholar 

  6. Hou, Y., Lin, M., Chen, W. & Yang, X. Parity–time-symmetric wireless power transfer system using switch-mode nonlinear gain element. In 2018 IEEE International Power Electronics and Application Conference and Exposition (PEAC) 1–5 (IEEE, 2018);

  7. Zhou, J., Zhang, B., Xiao, W., Qiu, D. & Chen, Y. Nonlinear parity–time-symmetric model for constant efficiency wireless power transfer: application to a drone-in-flight wireless charging platform. IEEE Trans. Ind. Electron. 66, 4097–4107 (2019).

    Article  Google Scholar 

  8. Donaldson, P. E. K. Power for neurological prostheses: a simple inductive RF link with improved performance. J. Biomed. Eng. 9, 194–197 (1987).

    Article  Google Scholar 

  9. Donaldson, P. E. K. Three separation-insensitive radiofrequency inductive links. J. Med. Eng. Technol. 11, 23–29 (1987).

    Article  Google Scholar 

  10. Zierhofer, C. M. & Hochmair, E. S. High-efficiency coupling-insensitive transcutaneous power and data transmission via an inductive link. IEEE Trans. Biomed. Eng. 37, 716–722 (1990).

    Article  Google Scholar 

  11. Kurs, A., Moffatt, R. & Soljačić, M. Simultaneous mid-range power transfer to multiple devices. Appl. Phys. Lett. 96, 044102 (2010).

    Article  Google Scholar 

  12. Sample, A. P., Meyer, D. A. & Smith, J. R. Analysis, experimental results and range adaptation of magnetically coupled resonators for wireless power transfer. IEEE Trans. Ind. Electron. 58, 544–554 (2011).

    Article  Google Scholar 

  13. Yu, X., Sandhu, S., Beiker, S., Sassoon, R. & Fan, S. Wireless energy transfer with the presence of metallic planes. Appl. Phys. Lett. 99, 214102 (2011).

    Article  Google Scholar 

  14. Yu, X. et al. Wireless power transfer in the presence of metallic plates: experimental results. AIP Adv. 3, 062102 (2013).

    Article  Google Scholar 

  15. Ho, J. S. et al. Wireless power transfer to deep-tissue microimplants. Proc. Natl Acad. Sci. USA 111, 7974–7979 (2014).

    Article  Google Scholar 

  16. Hui, S. Y. R., Zhong, W. & Lee, C. K. A critical review of recent progress in mid-range wireless power transfer. IEEE Trans. Power Electron. 29, 4500–4511 (2014).

    Article  Google Scholar 

  17. Li, S. & Mi, C. C. Wireless power transfer for electric vehicle applications. IEEE J. Emerg. Sel. Top. Power Electron. 3, 4–17 (2015).

    Article  Google Scholar 

  18. Wang, G., Liu, W., Sivaprakasam, M. & Kendir, G. A. Design and analysis of an adaptive transcutaneous power telemetry for biomedical implants. IEEE Trans. Circuits Syst. I 2, 2109–2117 (2005).

    Article  Google Scholar 

  19. Brecher, A. & Arthur, D. Review and Evaluation of Wireless Power Transfer (WPT) for Electric Transit Applications Report No. 0060 (FTA, 2014).

  20. Rüter, C. E. et al. Observation of parity–time symmetry in optics. Nat. Phys. 6, 192–195 (2010).

    Article  Google Scholar 

  21. El-Ganainy, R. et al. Non-Hermitian physics and PT symmetry. Nat. Phys. 14, 11–19 (2018).

    Article  Google Scholar 

  22. Feng, L., Wong, Z. J., Ma, R.-M., Wang, Y. & Zhang, X. Single-mode laser by parity-time symmetry breaking. Science 346, 972–975 (2014).

    Article  Google Scholar 

  23. Guo, A. et al. Observation of PT-symmetry breaking in complex optical potentials. Phys. Rev. Lett. 103, 093902 (2009).

    Article  Google Scholar 

  24. Lin, Z. et al. Unidirectional invisibility induced by PT-symmetric periodic structures. Phys. Rev. Lett. 106, 213901 (2011).

    Article  Google Scholar 

  25. Doppler, J. et al. Dynamically encircling an exceptional point for asymmetric mode switching. Nature 537, 76–79 (2016).

    Article  Google Scholar 

  26. Chen, P.-Y. et al. Generalized parity–time symmetry condition for enhanced sensor telemetry. Nat. Electron. 1, 297–304 (2018).

    Article  Google Scholar 

  27. Chen, W., Kaya Özdemir, Ş., Zhao, G., Wiersig, J. & Yang, L. Exceptional points enhance sensing in an optical microcavity. Nature 548, 192–196 (2017).

    Article  Google Scholar 

  28. Hodaei, H. et al. Enhanced sensitivity at higher-order exceptional points. Nature 548, 187–191 (2017).

    Article  Google Scholar 

  29. Sample, A. P., Waters, B. H., Wisdom, S. T. & Smith, J. R. Enabling seamless wireless power delivery in dynamic environments. Proc. IEEE 101, 1343–1358 (2013).

    Article  Google Scholar 

  30. Kim, N. Y., Kim, K. Y., Choi, J. & Kim, C.-W. Adaptive frequency with power-level tracking system for efficient magnetic resonance wireless power transfer. Electron. Lett. 48, 452–454 (2012).

    Google Scholar 

  31. Beh, T. C., Kato, M., Imura, T., Oh, S. & Hori, Y. Automated impedance matching system for robust wireless power transfer via magnetic resonance coupling. IEEE Trans. Ind. Electron. 60, 3689–3698 (2013).

    Article  Google Scholar 

  32. Larky, A. Negative-impedance converters. IRE Trans. Circuit Theory 4, 124–131 (1957).

    Article  Google Scholar 

  33. Schindler, J., Li, A., Zheng, M. C., Ellis, F. M. & Kottos, T. Experimental study of active LRC circuits with PT symmetries. Phys. Rev. A 84, 040101 (2011).

    Article  Google Scholar 

  34. Schindler, J. et al. PT-symmetric electronics. J. Phys. A 45, 444029 (2012).

    Article  Google Scholar 

  35. Lin, Z., Schindler, J., Ellis, F. M. & Kottos, T. Experimental observation of the dual behavior of PT-symmetric scattering. Phys. Rev. A 85, 050101 (2012).

    Article  Google Scholar 

  36. Kazimierczuk, M. K. RF Power Amplifiers (Wiley, 2008).

  37. Sedra, A. S. & Smith, K. C. Microelectronic Circuits (Oxford Univ. Press, 2010).

  38. Raab, F. Idealized operation of the class E tuned power amplifier. IEEE Trans. Circuits Syst. 24, 725–735 (1977).

    Article  Google Scholar 

  39. Raab, F. H. et al. Power amplifiers and transmitters for RF and microwave. IEEE Trans. Microw. Theory Tech. 50, 814–826 (2002).

    Article  Google Scholar 

  40. Li, H. et al. Design of a 10 kW GaN-based high power density three-phase inverter. In 2016 IEEE Energy Conversion Congress and Exposition (ECCE) 1–8 (IEEE, 2016);

  41. Choi, J., Tsukiyama, D., Tsuruda, Y. & Davila, J. M. R. High-frequency, high-power resonant inverter with eGaN FET for wireless power transfer. IEEE Trans. Power Electron. 33, 1890–1896 (2018).

    Article  Google Scholar 

  42. Haus, H. A. Waves and Fields in Optoelectronics (Prentice Hall, 1984).

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This work was supported by a Vannevar Bush Faculty Fellowship (grant no. N00014-17-1-3030) from the US Department of Defense.

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Authors and Affiliations



S.A. performed the simulations and measurements. S.F. supervised the project. Both authors contributed to writing the manuscript.

Corresponding author

Correspondence to Shanhui Fan.

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The authors declare no competing interests.

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Supplementary information

Supplementary Information

Supplementary Figs. 1–4 and discussion.

Source data

Source Data Fig. 1

Simulated total system efficiencies.

Source Data Fig. 2

Ideal amplifier waveforms.

Source Data Fig. 3

Calculated switching efficiency (Fig. 3a) and oscillation frequency and effective load impedance (Fig. 3b).

Source Data Fig. 4

Measured oscillation frequency, delivered power, total efficiency and the amplifier’s waveforms.

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Assawaworrarit, S., Fan, S. Robust and efficient wireless power transfer using a switch-mode implementation of a nonlinear parity–time symmetric circuit. Nat Electron 3, 273–279 (2020).

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