The low frequency magnetic shielding of a rectangular metallic box, with all walls perforated periodical holes, is studied. The finite conductivity box with holes and the perfect conductivity box with holes are combined to solve the problem. The first sub model represents the diffusion effect, that is, the magnetic field penetrates the conductive shell, and the second sub model represents the aperture effect, that is, the magnetic field leaks through the hole. The total shielding magnetic field is obtained by superposition of the two submodels. For the diffusion effect, an existing empirical formula is used. For the aperture effect, an approximate simulation technique is proposed: each hole in the walls is modeled as a magnetic dipole. The corresponding dipole moment is obtained according to Bethe’s small aperture coupling theory. Then, the shielded magnetic field inside the box is obtained by superimposing the fields from the dipoles and their images. The full-wave simulations for a rectangular box with a finite conductivity wall are carried out, which shows our approximate technique has good agreement with the full-wave simulations.

The 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.

This letter proposes an approximate analytical formulation for the shielding problem of a perfectly electric conducting disk against the low-frequency magnetic field produced by a circular current loop placed coaxially with the disk. First, this problem is related to a complementarity problem: The leakage of the magnetic field through a circular hole on a perfectly magnetic conducting plane of infinite extension. Then, for the complementarity problem, we develop the accurate analytical solution if only the distribution of the normal component of the unshielded magnetic field along the surface of the hole can be expressed as a polynomial function of radial distance. The analytical formulation is verified with finite element simulations and measured results.

This letter proposes an accurate analytical formulation for the shielding problem of a perfectly electric conducting disk against the static magnetic field of a circular current loop placed coaxially with the disk. The key is to convert this problem into an electric field problem: the circular disk is grounded and is excited by nonuniform line charges distributed on the loop. The latter can be solved through the known Green function. Then, we obtain the accurate solution in integral form for magnetic vector potential at any field point and the accurate analytical solution for the magnetic field on the central axis of the disk. Also, the solution for the magnetic field is extended to the whole space when the loop radius is approaching zero.

This article focuses on the shielding effectiveness (SE) prediction of the periodic aperture array on an infinite PEC plate against the low frequency (≤1 MHz) magnetic field resulting from a current loop parallel to the plate. Two different models of the penetration field through the plate are presented. From the two models, the same simplified expression for the field on the central axis is derived. The SE of a 1000 mm × 1000 mm aluminum plate with 2500 apertures against the magnetic field from a current loop is measured. The results show that the theoretical results are in good agreement with the measurement if the frequency is higher than a critical frequency. Above the critical frequency, penetration from the apertures is primary factor for field leakage, and the SE is constant with the increasing frequency. When the frequency is lower than the critical frequency, penetration from the aluminum is primary channel for field leakage, and hence the SE reduces with the decreasing frequency. In this case, the upper limit of the SE does not exceed the SE of the corresponding solid plate without apertures.

This article focuses on wave impedance calculations employed in the transmission line analogy for the low-frequency magnetic shielding problem: a planar shield against a loop current source placed parallel to the shield. We present a unified formula for wave impedance calculations that is distinct from traditional definitions of the transverse E-field to H-field ratio, which is related to the ratio of the H-field components to its longitudinal derivative. The formula is relatively simple in terms of mathematical complexity when applied to derive a concrete wave impedance expression. For a circular loop, the formula produces the same wave impedance expression as the traditional definition for field points on the central axis of the loop. For field points off the axis, the formula more accurately predicts the shielding effectiveness relative to traditional definitions. Based on the proposed formula, we also obtain wave impedance expressions for rectangular, elliptical, and regular polygon loops under quasi-static assumptions. The effectiveness of these expressions is verified through comparisons with finite element simulations.

We propose an approximate analytical model for magnetic field penetration through a circular aperture on a perfectly conducting plate. The magnetic field source is a circular loop current placed parallel to the plate and coaxial with the aperture. It is shown that the aperture is equivalent to a magnetic quadrupole normal to the plate when the field point is far from the aperture. The model is validated using numerical simulations and a minor disagreement with experimental data is explained.

In this paper, an analytical model is presented to calculate the low frequency magnetic shielding effective (SE) of the spherical shell with a circular aperture and finite conductivity. This model is obtained by the combination of two submodels: the finite conductivity shell without the aperture, and the perfect conductor shell with the aperture. Both the submodels have existing analytical solutions. 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 aperture. The total magnetic field is the superposition of these from the two submodels. Calculation results are provided for an aluminum spherical shell of radius 0.1m for frequencies between 10Hz and 1MHz. The results are in good agreement with these form 2D axisymmetric finite element simulations. It is shown that there is a critical frequency. Below this frequency, the diffusion effect is dominant and the SE enhances with the increase of frequency. Above this frequency, the aperture effect is dominant and the SE keeps unchanged with the variation of frequency. In addition, the phase shift characteristics are also analyzed for the two effects respectively, and are employed to elucidate the mechanism of the resonance phenomenon of the SE around the critical frequency. Further, the effect of aperture depth is investigated numerically, which shows that increasing the depth has similar effect on SE like reducing aperture radius.

This study presents a double auxiliary resonant commutated pole (ARCP) inverter topology and modulation strategy. In the proposed inverter, the zero-voltage-switching (ZVS) turn-off of auxiliary switches influenced by parasitic circuit elements from the wiring process can be avoided. It is assured that the auxiliary switches achieve ZVS turn-off reliably. Hence, the reliability of the ARCP inverter is improved, especially in high-power application. According to the equivalent circuits in different operation modes under the proposed modulation strategy, the working principle, soft-switching implementation condition, and parameter design procedure of the proposed inverter are analysed successively in this study. Finally, a 10 kW, 16 kHz double ARCP inverter prototype is built. Experimental results are given to demonstrate the validity of the proposed inverter.