The problem of a low-frequency shielding of a loop placed inside a coaxial torus shield is analyzed by the application of the Schelkunoff transmission theory of shielding. Copper and iron torus shields are considered. In the case of ferromagnetic material, the losses inside the medium are evaluated by new analytic formulations. One method reduces the full nonlinear diffusion problem to a linear problem through an optimization procedure. A second formulation attempts to approximate the differential magnetic permeability by a complete set of functions. The results of such a theory are adapted to the problem of measuring the shielding effectiveness of nonlinear shields. In particular, this measurement is reduced to the experimental characterization of the electric conductivity and of the B(H) dynamic hysteresis cycle of the shielding material. Direct shielding effectiveness measurements are obtained and compared with results obtained through the proposed procedure at different frequencies showing a substantially good agreement.

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