Frequency-Stable Robust Wireless Power Transfer Based on High-Order Pseudo-Hermitian Physics

Nonradiative wireless power transfer (WPT) technology has made considerable progress with the application of the parity-time (PT) symmetry concept. In this Letter, we extend the standard second-order PT-symmetric Hamiltonian to a high-order symmetric tridiagonal pseudo-Hermitian Hamiltonian, relaxing the limitation of multisource/multiload systems based on non-Hermitian physics. We propose a three-mode pseudo-Hermitian dual-transmitter-single-receiver circuit and demonstrate that robust efficiency and stable frequency WPT can be attained despite the absence of PT symmetry. In addition, no active tuning is required when the coupling coefficient between the intermediate transmitter and the receiver is changed. The application of pseudo-Hermitian theory to classical circuit systems opens up an avenue for expanding the application of coupled multicoil systems.

Figure 1

Schematics of (a) a standard PT-symmetric electronic dimer, (b) a three-mode pseudo-Hermitian system consisting of two gain (red) units and one loss (blue) unit, and (c) a conventional three-coil PT-symmetric system consisting of balanced gain and loss, as well as neutral (gray) electronic molecules. Here, $k$ or $k_0$ denotes the coupling coefficients between neighboring resonators; and the mutual coupling between the nonadjacent resonators [e.g., the transmitter I and receiver in (b)] is assumed to be negligible.

Figure 2

Evolution of the real (left panel) and imaginary (right panel) parts of the normalized eigenfrequencies $\tilde{\omega }=\omega /{\omega }_0$ as a function of the coupling coefficient $k$ for various non-Hermitian systems, i.e., (a),(b) three-mode pseudo-Hermitian system, (c),(d) three-coil PT-symmetric system, and (e),(f) standard PT-symmetric system. For all three systems, the loss parameter reads $\gamma =0.078$. Here, the blue curves denote the conjugate solution of $\omega$, while the red curves denote the additional solution of ${\omega }_1$ for three-mode systems. The ideal three-coil PT-symmetric WPT system always works in the state [red line in (c),(d)] where the frequency does not change with respect to the coupling coefficient $k$. The strong coupling regions are denoted by shading.

Figure 3

Evolution of the amplitude ratios (a) $|a_1/a_2|$ and (b) $|a_3/a_2|$, and the phase differences ${\varphi }_1-{\varphi }_2$ and (d) ${\varphi }_3-{\varphi }_2$ as functions of the coupling coefficient $k$ at steady state. In all the subfigures, the gray vertical reference line indicates $k=\gamma =0.078$.

Figure 4

(a) Steady-state frequency $f_s$, (b) voltage ratios $V_1/V_2$ (red for the left $y$ axis) and $V_3/V_2$ (blue for the right $y$ axis), and (c) power transmission efficiency ${\eta }_{\mathrm{PTE}}$ as functions of the coupling coefficient $k$. Theoretical (cal.), simulated (sim.) and experimental (exp.) results are illustrated by solid curves, dashed curves, and hollow markers, respectively. The shading regions indicate $k\ge \gamma =0.078$. The inset of (c) shows a photo of our experiment setup.