Transform method for calculating low-frequency shieldingeffectiveness of planar linear multilayered shields

A two-dimensional analytical solution for quasistatic magnetic field shielding with planar infinite multilayered shields is presented. The magnetic field source is a system of long straight wires parallel to the shield, carrying sinusoidal currents. The analysis assumes that material media can be considered linear under the applied source fields. The spatial Fourier cosine and sine transforms are applied to the analytical expressions of the magnetic field intensity and flux density is obtained by solving the diffusion equation in each layer. Using transfer relations for every layer in terms of transformed variables allows one to obtain the shielded field, and thus the shielding effectiveness, with no need to determine the integration functions explicitly. The results obtained with both this approach and a finite-element computer code are in good agreement. The method seems to be also suited for the analysis of problems with more complex geometries and source distributions