Steady-state and transient eddy current predictions using surface impedances in shell structures

Surface impedance techniques are useful means of predicting fields in eddy current problems since they circumvent the need to model the conducting regions themselves. Thus, with their use, two-and three-dimensional field predictions can be made using only scalar potentials. Their use is normally confined to (1) problems where the skin depth is small relative to the other dimensions of the problem and (2) steady-state problems where the skin depth itself is well defined. In this regard, the technique is approximate at best. Presented here is a formulation which can realize an exact prediction of the field, both in steady-state and transient problems. The technique is exact for those problems where knowledge is known as to the nature of the field variation tangential to the conductor shell interface; otherwise, an iterative numerical scheme must be employed to converge on the correct tangential variation. Surface impedances are determined generically and expressed in terms of transfer functions for shell-type structures in three different geometries. The surface impedances happen to be trigometric functions, Bessel functions, and spherical Bessel functions in planar, cylindrical, and spherical shell structures, respectively. Their use is easily implemented in finite difference, finite element, and boundary integral formulations; in this paper, the surface impedances are coupled into a boundary integral approach to verify their use in both two-dimensional cylindrical and a three-dimensional spherical problem. The results are compared to analytical expressions and are shown to disagree by no more than 0.01%