Impedance calculation of arbitrary-shaped thin-walled coils for eddy-current testing of planar media

•Eddy-current testing is used in a variety of fields, so it is important to analyze the coil impedance. At present, the calculation of the coil impedance is only for some specific shaped coils, such as circular, rectangular. However, to the best knowledge of the authors, the impedance calculation of arbitrary-shaped coil has not been reported in the literature. In this paper, a general method for calculating the impedance of an arbitrary-shaped coils is proposed, which enriches the research on ECT technology and provides an effective tool for ECT probe design and parameter optimization.•In this paper, a new single general formula is proposed, which can be used to calculate the impedance of arbitrary-shaped coil in free-space and the impedance change caused by the eddy-current within the conductive specimen. In the formula, the size and shape of coil is described by a new function, which is denoted as the coil function. The coil functions of common coils, such as circular, rectangular, triangular and trapezoidal coils were also derived in this paper.•A special experimental setup was set up, and several different shaped coils were wound. The impedance experiments of different shaped coils were carried out. Experimental results show that the proposed method is effective. Eddy-current testing is used in a variety of fields, so it is important to analyze the coil impedance. Previous studies on impedance calculation have mainly focused on circular and rectangular coils. This paper presents a general method to evaluate the impedance of an arbitrary-shaped thin-walled coil facing with a planar media. The impedance formulas are deduced by using second order vector potential (SOVP) method. In the formulas, the coil function, which is in double-integral form, is defined. The impedance calculation for arbitrary-shaped coils can be represented by the corresponding coil function. The coil functions for common coils such as circular, triangular, rectangular and trapezoidal coils are also derived in this paper. Finally, the impedance and impedance change of various shaped coils above an aluminum plate are measured, and compared with calculated values. The results indicated that they have a good agreement.