Multilayer planar rectangular coils for eddy current testing: Design considerations

Abstract Planar rectangular coils provide some interesting features different from those of pancake coils, such as good performance in conductivity measurement at high frequencies, high sensitivity to scratches and other shallow imperfections and the possibility of inspecting complex surfaces. The impedance of these coils has been modeled by different authors. A brief discussion of some analytical approaches in the literature is presented and calculations using the second-order vector potential approximation are introduced, aimed at the study of the influence of coil shape and size on the sensitivity to electrical conductivity of the substrate. Three cases were modeled, (A) coil in free space—inductance L 0 as a function of number of turns ( n ) and width of the spiral conductive lanes ( c ) for different coil inner shape factor ( rr i ); (B) coil on a conductive substrate (Zircaloy-4)—impedance change, Δ Z , as a function of f · σ , the product of the test frequency ( f ) and the substrate electrical conductivity ( σ ) for different rr i and (C) coil sensitivity to small changes in σ (Δ σ ). L 0 = L 0 ( c , n ) increased as expected with n and/or coil area and decreased with shape factor. Normalized Δ Z depends strongly on inner rr i , the curves (or surfaces) for smaller values of rr i enclosing those for larger values. Another shape factor, the outer shape factor ( rr o ), was introduced. Strong dependence of the sensitivity to Δ σ on n was observed, as well as the existence of an optimal theoretical frequency. Because the sensitivity to surface conditions also increases with coil size, it could be established that for conductivity assessment it is better to use coils with the smallest n and c , compatible with the particular application, and that the resolving power for this type of measurements is not greatly affected by the shape factor.