A unified expression of magnetic susceptibility tensor is presented according to the magnetic-moment motion equation with Landau-Lifshitz damping term and Gilbert damping term. The application of equivalent magnetic permeability enables to transform the anisotropy problem to an isotropy one with the same electromagnetic solution in amorphous wire. By this transformation, the impedance of amorphous wire passing through an insulating or conducting magnetic ring are analyzed. Additionally, the magnetoimpedance effect in amorphous wire through a magnetic ring is simulated by the numerical analysis based on the finite element method. The results of theoretical analysis and numerical simulation, which agree with each other, indicate that the additional impedance caused by extra magnetic objects seriously reduces the magnetoimpedance change of amorphous wire and destroy the giant magnetoimpedance characteristic. Therefore, the return wire structure is proposed to diminish the additional impedance. The simulation results verified the effectiveness of this method.
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