Equivalent permeability calculation method based on peak flux for axially vertically stacked metamaterials

Purpose At low frequencies, energy no longer propagates in wave form, requiring distinct methodologies for studying metamaterials in the kHz band compared to high-frequency applications. To address the challenges in simulating low-frequency electromagnetic metamaterials, ANSYS Maxwell and Simplorer simulation software are used to model the proposed metamaterial core columns, which are stacked axially along the coordinate axes. Coupled simulations of transient magnetic fields and electrical circuits are conducted. This work aims to provide a theoretical foundation for using finite element numerical simulation methods to study low-frequency electromagnetic metamaterials. Design/methodology/approach In this paper, low-frequency electromagnetic metamaterials stacked axially and vertically are used as the research object, and the time domain finite element numerical simulation method is used to carry out the research. This work breaks through the research method of high-frequency electromagnetic metamaterials by calculating the S-parameter, T-parameter and R-parameter inversions of the equivalent permeability. Findings The process of model establishment and numerical simulation methods is detailed, and the reasons for the changes in the equivalent inductance of the electromagnetic metamaterial structure during the simulation are identified. A new method, called the flux peak method, is proposed for calculating the equivalent inductance of axially stacked electromagnetic metamaterial entities. The feasibility of this method is validated, and the impact of the simulation step size on the calculation results is analyzed. The results show that when the step size is set to 100 divisions per cycle, the error of the peak flux method is minimized to 0.4%. Originality/value This study systematically demonstrates the feasibility of using ANSYS Maxwell and Simplorer for numerical simulations of low-frequency electromagnetic metamaterials and breaks through the traditional methods used in high-frequency conditions. It further improves the theoretical foundation of finite element numerical simulations for low-frequency electromagnetic metamaterials.