Analytical Modeling of a Coil Sensor With a Ferrite Shell Encircling a Conductive Tube for Nondestructive Evaluation

The interaction between an induction coil with a ferrite shell and a conductive tube of finite length is analyzed by the enhanced truncated region eigenfunction expansion (TREE) method. The eigenvalues and eigenfunctions are calculated using the 1-D finite element method (1D-FEM), which eliminates the numerical overflow inherent in conventional TREE. The analysis is simplified considerably by the eigenfunction normalization. At high frequencies, the Arnoldi shift accelerates eigenvalue computation, targeting large imaginary parts. The experimental data confirm the method’s reliability and potential for industrial applications.