Impedance of the eddy-current displacement probe: the transformer model

A new approach to calculation of the impedance of the eddy-current displacement probe is presented. It is based on the transformer model of the probe-to-target coupling. The usual method of calculating the impedance by solving for the electromagnetic field distribution in the probe and the conductive target involves solution of integral equations. Instead, a simpler approach is possible by modeling the probe-to-target coupling as a loaded transformer, involving only linear ac circuit analysis and elliptic integrals (readily available in MATHCAD, MATLAB, etc.). The model transformer has single primary and multiple secondary windings. The primary winding models the probe coil, while the distributed Eddy current's circulation paths are modeled by multiple secondary windings. The target active area (the eddy current's carrying area) is divided into concentric rings. Each ring is modeled as a single-turn secondary loaded with the ring impedance. Simulation shows that division of the target active area into a moderate number of rings (16) is sufficient for very good accuracy of the model. Accuracy was checked by comparison of the simulated transfer curve of the displacement transducer to the measured transfer curve of the actual transducer. The agreement between the model and the measurement is very good. The model can be used to investigate the influence of various coil shapes and target materials on linearity and sensitivity of the eddy-current displacement transducer.