Abstract
An analytical solution is presented for the interaction of an I-core coil with a metal tube of finite length. Using the Truncated Region Eigenfunction Expansion (TREE) method, the impedance variation of the I-core coil is expressed in a closed form. Notably, the 1D finite element method (1D FEM) is adopted to calculate the complex eigenvalues and eigenfunctions of the steel tube, by which the overflow issue of complex eigenfunctions has been surmounted. And the 1D FEM also simplifies the calculation in the ferrite core region immensely. A performant algorithm is obtained due to the matrix formalization and the high speed of the sparse eigenvalue solver. The tubes made of aluminum alloy and stainless steel are investigated by the proposed method and tested in the experiment. The high reliability and efficiency of the proposed method are proved, and the results are also validated by the comparison with simulation and measurement data.
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