Impedance Calculation of a Bobbin Coil in a Conductive Tube With Eccentric Walls

The complex impedance of an air-cored coil in a conductive tube with eccentric inner and outer cylindrical surfaces is calculated. The analytic expressions for the induced fields and the impedance variation due to the eddy-current flow inside the tube wall are derived using a second-order potential approach. The addition theorem of Bessel functions is employed to perform the transition between the local coordinate systems that conform to the boundaries of the structure. Although the model can be used for any coil shape and orientation, we focus our study on the configuration of a bobbin coil with axis parallel to the axes of the tube surfaces, but not necessarily coinciding with either of them. The results of the presented analysis are verified by a finite-element-method (FEM) solution.