Mutual impedance of air-cored coils above a conducting plate

The change in mutual impedance DeltaZ(12) due to eddy-current induction is considered for an arbitrary pair of air-cored coils located above a conducting plate. A general expression is derived for DeltaZ(12) and applied to the specific case of cylindrical coils with rectangular cross-section. A series of closed-form expressions for DeltaZ(12) is presented for the geometries that cover all of the possible coil configurations for which the orientation of the individual coils is either normal or tangential to the plate. Expressions are also obtained for DeltaZ(12) in the dipole limit and the results are compared with earlier work for dipole loops. The validity of the theory is tested against experimental measurements for representative high-symmetry coil systems above an aluminium-alloy plate. The theoretical calculations and experimental results are in excellent agreement over the experimental frequency range 100 Hz-50 kHz. The significance of the results for eddy-current non-destructive inspection using driver-pickup coils is discussed.