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Robust wireless power transfer using a nonlinear parity–time-symmetric circuit

Nature volume 546, pages 387–390 (2017)Cite this article

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Abstract

Considerable progress in wireless power transfer has been made in the realm of non-radiative transfer, which employs magnetic-field coupling in the near field1,2,3,4. A combination of circuit resonance and impedance transformation is often used to help to achieve efficient transfer of power over a predetermined distance of about the size of the resonators3,4. The development of non-radiative wireless power transfer has paved the way towards real-world applications such as wireless powering of implantable medical devices and wireless charging of stationary electric vehicles1,2,5,6,7,8. However, it remains a fundamental challenge to create a wireless power transfer system in which the transfer efficiency is robust against the variation of operating conditions. Here we propose theoretically and demonstrate experimentally that a parity–time-symmetric circuit incorporating a nonlinear gain saturation element provides robust wireless power transfer. Our results show that the transfer efficiency remains near unity over a distance variation of approximately one metre, without the need for any tuning. This is in contrast with conventional methods where high transfer efficiency can only be maintained by constantly tuning the frequency or the internal coupling parameters as the transfer distance or the relative orientation of the source and receiver units is varied. The use of a nonlinear parity–time-symmetric circuit should enable robust wireless power transfer to moving devices or vehicles9,10.

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Figure 1: Comparison between conventional and PT-symmetry-based wireless power transfer schemes as the source–receiver resonant coupling rate κ varies as a function of transfer distance d.
Figure 2: Theory of operation.
Figure 3: Experimental verification of PT-symmetry-based wireless power transfer.

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Acknowledgements

Part of the work was supported by the TomKat Center for Sustainable Energy at Stanford. S.F. thanks R. Sassoon and A. Cerjan for discussions.

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Authors and Affiliations

  1. Department of Electrical Engineering, Ginzton Laboratory, Stanford University, Stanford, 94305, California, USA

    Sid Assawaworrarit, Xiaofang Yu & Shanhui Fan

Authors
  1. Sid Assawaworrarit
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  2. Xiaofang Yu
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  3. Shanhui Fan
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Contributions

S.A. performed the simulations and experiment. All authors contributed to formulating the analytical model, to analysing the data, and to writing the manuscript. S.F. initiated and supervised the project.

Corresponding author

Correspondence to Shanhui Fan.

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The authors declare no competing financial interests.

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Reviewer Information Nature thanks Y. Chong and G. Lerosey for their contribution to the peer review of this work.

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Extended data figures and tables

Extended Data Figure 1 Stability analysis for the steady-state solution with the lowest gain.

a, Lyapunov exponents are of the decaying type, showing that the steady-state solution with the lowest gain is stable for all transfer distances. At the PT transition point, the eigenmodes coalesce, resulting in marginal stability along with frequency bifurcation, which has no effect on the transfer efficiency. The coupling rates are extracted from our experimental setup and ω1 = ω2 = 1, γ10 = 5 × 10−4, γ2 = 0.013. b, Lyapunov exponents versus resonator detuning at the PT transition point. The marginal stability disappears with non-zero resonator detuning.

Extended Data Figure 2 Simulated transient response to sudden movements of the receiver.

Effect of sudden changes in the separation distance (top panels) on the mode amplitudes a1,2 (bottom panels). a, For a sudden shift in the separation distance between 75 cm and 65 cm, the nonlinear PT power transfer system settles into its steady state within 50 μs. The move across the PT phase transition point represents the worst case for the transient decay time. b, The transient response becomes shorter away from the PT phase transition. Here, a sudden shift in distance from 65 cm to 55 cm results in less than 25 μs of transient decay time. The inset (same axes as the main panel) shows a magnified transient response at around 250 μs. These transient response times are much shorter than the typical timescale of mechanical motions, demonstrating the viability of our proposed system for dynamic wireless power transfer. The simulations are performed by solving equation (6) in the time domain using the coupling rates extracted from the experimental setup and other pertinent parameters as follows: ω1 = ω2 = 2π × 2.50 MHz, γ10 = 2π × 1.25 kHz, γ2 = 2π × 32.5 kHz, and

Extended Data Figure 3 Tolerance to resonator detuning.

The transfer efficiency (equation (5)) is plotted as the receiver’s resonant frequency ω2 is detuned away from that of the source ω1. The range of acceptable detuning is limited to around the receiver’s linewidth γ2. The same limit also applies to other forms of resonant power transfer. The coupling rates are extracted from our experimental setup, ω1 = 1, γ10 = γ20 = 5 × 10−4 and γ2 = 0.013.

Extended Data Figure 4 Steady-state frequency as a function of unsaturated gain value.

The unsaturated gain rate is adjusted via resistor R1 in the circuit simulation with other circuit parameters fixed (Extended Data Table 1). The mode frequency remains largely unchanged as the source resonator’s unsaturated gain g1 is increased from near its required minimum value, g0, to 2g0. The only mode switching observed occurs at g1 = 2g0, near the transfer distance of 70 cm, where the system crosses the PT transition point. Since both frequency branches offer identical performance when the source’s and receiver’s resonances are tuned, the effect of mode switching to the other branch on the system performance here is minimal.

Extended Data Figure 5 Coupling rate as a function of separation distance.

a, Coil dimensions for the coupling rate calculation (equations (8)–(10)) are as follows: w = 0.25 mm, l = 2.54 cm and 2r = 58 cm. b, Comparison of the calculated and experimental values of the coupling rate as a function of the separation between the two coaxially aligned coils.

Extended Data Figure 6 Detailed coupled-mode model for a conventional wireless power transfer scheme.

Extended Data Table 1 Circuit parameters used in the simulations
Full size table

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Supplementary information

Demonstration of the PT symmetric scheme in a dynamic wireless power transfer scenario.

Robust power transfer is achieved by the virtue of PT symmetry in saturation as shown by the constant brightness of the LED bulb when the receiver is moved to and from the source. (MP4 23148 kb)

Demonstration of the conventional scheme in a dynamic wireless power transfer scenario.

The transferred power level is dependent on the source-to-receiver separation distance as shown by the variation of the LED brightness as the receiver is moved to and from the source. (MP4 22482 kb)

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Assawaworrarit, S., Yu, X. & Fan, S. Robust wireless power transfer using a nonlinear parity–time-symmetric circuit. Nature 546, 387–390 (2017). https://doi.org/10.1038/nature22404

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