An Extension of the Gain Criterion for Analyzing the Eigenmode Selection Mechanism of the Pseudo-Hermitian WPT System

Pseudo-Hermitian wireless power transfer (WPT) system relaxes the rigid limitations of the conventional parity-time (PT) WPT system, while its multimode characteristic needs to be clarified. To clarify the eigenmode selection mechanism, an accurate modeling of the gain element is usually required. Since it is unachievable to model all the existing gain elements accurately, a qualitative method would be more useful. Recently, the criterion of lowest gain is proposed, which claims that PT WPT and Pseudo-Hermitian WPT system will automatically stabilize at the eigenmode corresponding to a purely real eigenfrequency with the lowest gain. The criterion of lowest gain is a qualitative and empirical method without the requirement of the accurate modeling. However, this paper demonstrates that a stable eigenmode can still exist even if its corresponding gain is not the lowest, and found that the selected eigenmode can be determined by the initial operating condition. Therefore, an extension of the gain criterion is proposed, which claims that for all the eigenmodes with a purely real eigenfrequency in the system, the eigenmode with the lowest gain is always stable. The higher the gain of other eigenmode is, the lower the possibility of its stability is. Finally, experimental results have confirmed the correctness of our work.