Mutual inductance model of double printed circuit board-based coplanar rectangular spiral coils for eddy-current testing

In the field of eddy-current testing (ECT), most studies on detection probes are primarily based on circular solenoid coils; related research on rectangular spiral coils is rare. In this study, an analytical model of the mutual inductance (MI) between two coplanar rectangular spiral coils was developed in which the two coplanar rectangular spiral coils were placed above a conductive plate. The MI calculation does not need to consider the thickness of the coils, which is consistent with the actual situation of the printed circuit boards (PCB)-based spiral coils, and simplifies the multi-turn rectangular spiral coil into a set of concentric single-turn coils. Two experimental setups were constructed to verify the analytical model and they were used to detect defects in the aluminium plate. The experimental results indicate that the analytical model can be used to evaluate the performance of ECT probes using PCB-based spiral coils, through the geometrical dimensions of the coils, centre distance and lift-off, and so forth. Compared with traditional methods, this method can still obtain satisfactory calculation accuracy after ignoring thickness parameters. The analytical model is also an effective tool to aid in the design of detection probes and optimisation of related parameters.