Low-Frequency Magnetic Shielding Of Conductor Plate:Influence Of Loop Radius And Distance

In various practical applications such as electric vehicles,wireless power transfer,magnetic resonance imaging,and power transformers,low-frequency magnetic shielding is commonly employed to prevent electromagnetic interference between devices.Depending on specific requirements and working environments,different geometric shield structures are selected,including enclosures,solid plates,perforated plates,and metal meshes.The shielding effectiveness of a shield structure is quantified using shielding effectiveness.The measurement of shielding effectiveness in standards utilizes a magnetic shielding model with a circular antenna axially perpendicular to an infinite conductor plate,typically requiring specific loop radii and distances.However,due to equipment or spatial constraints,the actual measurements may involve various loop radii and distances,necessitating consideration of the impact of loop radii and distances.To meet ventilation requirements,reduce weight,and save costs,practical shield structures often involve finite-sized perforated plates with finite conductivity,considering three coupling paths:diffusion through the plate,edge effects around the plate,and transmission through small holes.Corresponding to these three coupling paths,this study sequentially conducts theoretical analyses and derivations for three models:infinite solid plate,solid perfect electric conductor(PEC)disk,and perforated PEC plate.The shielding characteristics under different loop radii and distances are analyzed,and the theoretical formulas are validated through finite element simulations and experiments.According to the superposition principle,the solution for the perforated conductor disk shielding model can also be obtained by combining the above three models,revealing that this model primarily relies on controlling the perforations or edge effects to enhance the shielding effectiveness in the highfrequency range,while improvements in conductor plate thickness,material,etc.,are required in the low-frequency range.If applied to rectangular shield plates with similar length and width,the analytical theory based on the disk model can also be utilized to estimate upper and lower bounds by considering the inscribed and circumscribed circles in the rectangular plate.Among the three sub-models,for the infinite conductor plate model,precise integral expressions are obtained through numerical solutions to investigate the influence of loop radii and loop spacing on shielding effectiveness.For the pure conducting plate and pure permeable plate,simplified and reliable approximations are respectively provided,offering clearer physical interpretations and significantly faster computational speed.The results indicate that when the loop spacing is smaller than the radius of the emitting loop,the effect of loop radii becomes prominent.Additionally,the conducting plate and permeable plate exhibit opposing and competing shielding mechanisms.For the PEC disk and perforated PEC plate models,a method is employed to transform the axisymmetric magnetic field problem into an electric field problem,resulting in exact analytical formulas for the magnetic field after shielding.Specifically,for the PEC disk,integral-based exact solutions for arbitrary field point vector magnetic potentials and exact analytical solutions for magnetic fields on the disk’s central axis are obtained.Moreover,when the radius of the emitting loop approaches zero,the magnetic field solution extends to the entire space.Regarding the perforated PEC plate model,analytical expressions for the shielded vector magnetic potentials and magnetic fields in the entire space are derived,including the z and p components.Finally,expressions for mutual inductance between loops and shielding effectiveness between loops are derived.These analytical theories not only serve as means to validate the accuracy of software simulations but also facilitate the analysis of influencing factors and the clarification of physical laws.Furthermore,the computational speed advantage of analytical solutions can be applied to optimization research,compensating for the high hardware requirements and time-consuming nature of simulations.