Approximate Simulation of Low Frequency Magnetic Shielding of a Rectangular Shielding Box with All Walls Perforated Periodical Holes

This article proposes an approximate analytical formulation to calculate the low-frequency magnetic shielding of a rectangular metallic box, with all walls perforated periodical holes. The solution is obtained by the combination of two submodels: the finite conductivity box with the holes covered and the perfect conductor box with the holes present. The first submodel represents the diffusion effect of magnetic field penetration through the conducting shell, and the second one denotes the aperture effect of magnetic field leakage through the holes. The total shielded magnetic field is the superposition of these from the two submodels. For the diffusion effect, an existing empirical formula based on the shape factor is used. To solve the second submodel, we employ two approximate methods: the method of images and the surface-impedance method. The method of images models each hole in the walls as an equivalent magnetic dipole and its images based on Bethe’s small aperture coupling theory. A PEC box is first considered. Comparisons with finite element simulations show that the method of images has better accuracy than the surface-impedance method. Then, a cubic aluminum box of 0.2 m in length is treated, which verifies that combining the two submodels can produce results in good agreement with finite element simulations for frequencies up to 10 MHz. In addition, the dependence of the shielding effectiveness on frequency is also analyzed. © 2023, Electromagnetics Academy. All rights reserved.