Maximum power transfer theorem with arbitrary Efficiency for Wireless Power Transfer

Abstract Wireless power transfer (WPT) has been actively studied by many companies and research institutes for decades, and individual technologies have been highly developed. However, except for nearly contact WPT, it has not yet reached a standard adopted by multiple manufacturers. We believe that this is due to the lack of theory to evaluate the feasibility and validity of these proposals, while the market has high expectations for EV charging, which has led to unfeasible high specifications and many proposals for improvements. If non-physical proposals cannot be rejected, there is no way to set standard targets at a feasible level. The WPT consists of an electric circuit (Kirchhoff domain) that follows Kirchhoff’s law and a non-contact power transfer part (Maxwell domain) that follows Maxwell’s equations. Here, we show that by introducing the conduction wire electric field confinement by the free-electron model into the Axiomatic Maxwell’s equations (derived from the principle of relativity and the principle of action), the Kirchhoff and Maxwell domains can be integrated without contradiction. Furthermore, this study demonstrates the maximum power transfer theorem with arbitrary efficiency in the Kirchhoff domain, enabling the determination of all circuit constants necessary to meet specified requirements. Additionally, numerical analyses are presented to illustrate the application of this theorem in practical circuits, including switching power supplies and batteries.