Modeling and Optimized Design of the Free-Standing Magnetic Field Energy Harvester Based on Accurate Estimation of Effective Permeability

Free-standing magnetic field energy harvesters (FSMFEHs) offer a novel approach for powering sensors in the power IoT. A mathematical model is established in this article to provide a generalized design tool for the FSMFEH. An accurate estimation method for the effective permeability of the H-shaped core is proposed based on the effective permeability of the cylindrical core and flux continuity theorem, along with a correction term, to enhance the model's accuracy. Experimental results show that estimation errors are less than 8%. Based on this model, an effective performance optimization method for the FSMFEH is summarized. Especially, the differences in maximum power and maximum power density, and the impact of induced voltage on the power management circuit, are considered. In addition, utilizing the Steinmetz equation, it is found that the magnetic field generated by the coil current, rather than the external magnetic field, is the predominant factor leading to core losses. The optimized FSMFEH attains a power density of 2.28 mW/cm³ at an external magnetic field of 1 500 μT/50 Hz. Applying this performance optimization method to existing studies, the maximum power density is increased by more than 3.02 times compared to the original results with the same external magnetic field and dimensions.