Wireless power transfer (WPT) via coupled magnetic resonances has been in development for over a decade. Frequency splitting occurs in the over-coupled region. In addition, the vibration of the receiver and relay coils is observed in the over-coupled region. The vibration mechanism of the relay coil is investigated in this study. First, the circuit model of a three-coil WPT system is established, and the transfer characteristics of the system are examined by applying circuit theories. Second, the transfer characteristics of the three-coil WPT system are analyzed using simulation software. Third, the energy equation of state of the three-coil WPT system is established with the introduction of entropy variable. Lastly, the experimental circuit of the three-coil WPT system is designed. The experimental results are consistent with the theoretical analysis. The vibration of the relay coil is clearly explained. The transfer characteristics of the three-coil WPT system, particularly the relay coil, may provide ideas to achieve the maximum output power and transmission efficiency under various operating conditions.
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