Memristor Equivalent Model of an Inductive Wireless Power Transfer System Based on the Sigmoid Function

The bridge rectifier with filter circuit is a fundamental component of inductive wireless power transfer (IWPT) and other power electronic systems that accomplish ac–dc conversion. It belongs to the category of extended memristors. Circuits containing this component may exhibit unconventional dynamical characteristics, such as hidden attractors, coexistence of multiple attractors, multistability, and transient transitions. These characteristics increase system uncertainty. Focusing on IWPT systems with different compensation topologies, this article establishes memristor mathematical models for two types of bridge rectifier circuits, namely
C
-filtering and
LC
-filtering, based on the sigmoid function. Taking the S-S type IWPT system as an example, an equivalent memristor circuit model was developed, and the established model was verified through simulations and experiments. The results show that the established model accurately captures the static and dynamic characteristics of a system. The load characteristic of the IWPT system follows a pinched hysteresis loop, aligning with the three memristor features. The established model is concise in form and can uniformly describe the continuous conduction and discontinuous conduction modes. It perfectly models continuous and smooth instantaneous values and offers a suitable tool for analyzing system dynamics.