Changes in the impedance of a coil next to a one-dimensional layered conductor due to three-dimensional changes in the conductivity are studied. Eddy current probes are often used to inspect layered one-dimensional, nonmagnetic metal structures whose electrical conductivity varies primarily with depth beneath the surface. We present a perturbation method, the ‘‘layer approximation,’’ which yields simple and readily evaluated formulas for changes in the impedance of a small coil due to localized three-dimensional variations in the conductivity. The layer approximation is constructed to be accurate when the conductivity change due to the defect is small or the defect is nearly one-dimensional. The impedance is calculated and reported for a variety of defects in layered metal structures: voids, inclusions, interfacial roughness, and fasteners. We test the ‘‘robustness’’ of the layer approximation using an extreme case, a flat-bottom hole in an aluminum plate, as a ‘‘benchmark.’’ Both experimental measurements and more exact theoretical calculations are reported. Impedance measurements were made with a Hewlett–Packard 4194A impedance analyzer for a right-cylindrical flat-bottom hole in a 1-mm-thick 2024 aluminum alloy plate; the hole was on the side opposite to the coil. Frequencies were varied from 2.5 to 50 kHz. We also calculated the change in the impedance for this benchmark problem using the numerically exact volume integral method. For this benchmark problem, the layer approximation is in good agreement with experiment and more exact theory.
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