Two-conductor line model: Rapid inversion of eddy current data for foil thickness and conductivity determination

An eddy current method based on the theoretical model of a two-conductor line placed over a plane conductive medium is described. We show the performance of the method in determining thickness and electrical conductivity of foils. The expressions for the vector potential and the coil electrical impedance are obtained in the case when the coil is placed over a thin foil. This theoretical model was applied to measurements of a conductive foil using rectangular coils with finite length-to-width were manufactured. Copper and aluminum foils having thicknesses 15-216 mu m were studied experimentally in the frequency range 5-100 kHz. Theoretical values of the electrical impedance of the coils were compared to those measured. Agreement between theory and experiment was excellent. The method allows the determination of the thickness-conductivity product of a thin foil. Consequently, if the foil conductivity is known, we can find the thickness; and if the thickness is known the conductivity can be found. The inversion procedure, employing the Newton-Raphson method with two variables, namely the thickness-conductivity product and the coil lift-off, takes about 100 ms. Using a simplified formula for a very thin foil the inversion time can be further reduced. The formula gives an error in foil thickness determination of less than 2% when foils are thinner than 100 mu m. The agreement between measured conductivity and thickness and those obtained by other techniques is good. The uncertainty of the conductivity and thickness measurement is typically better than 2%, and often +/- 1% is obtained. The integral relations obtained allow the use of a fast inversion procedure that considerably reduces the time of development of eddy current methods and probes. The excellent agreement between theoretical and experimental results strongly suggests that the model can be used with success in numerous other eddy current applications. With a medium accuracy the model can be applied for eddy current measurements using rectangular coils with a length-to-width ratio as low as 5. (C) 1996 American Institute of Physics