Improving Reproducibility of Eddy-Current-Based Coating Thickness Estimation with Printed Circuit Board-Based Differential Coils

The accurate determination of the thickness of the metallic coating on steel substrates is essential in industrial quality control. Eddy current testing offers a non-destructive solution by evaluating the impedance or mutual impedance of one or multiple coils. Analytical models exist in the literature for selected sensor configurations. Building on these models, a model-based estimation approach can be applied to derive an estimate for coating thickness and other relevant material and geometry parameters. Conventional setups typically employ wire-wound coils. However, manufacturing tolerances introduce discrepancies between nominal and actual coil geometries, which lead to deviations in the coating thickness estimate. A printed circuit board (PCB)-based coil with lithographically defined geometry achieves substantially tighter fabrication tolerances and higher repeatability than wire-wound coils. In this work, an analytical mutual impedance model for a differential multi-layer PCB pancake coil is derived and validated against established models in the literature with respect to forward modeling accuracy and model-based parameter estimation performance. Furthermore, experimental measurements with two-layer and eight-layer PCB differential coil systems produce parameter estimates with significantly better reproducibility than wire-wound coils. The experimental results show that the two-layer PCB coil achieves close agreement between the absolute estimated parameters and the reference values without requiring additional calibration, while maintaining high sensitivity to coating thickness.