Simplified analytical inductance model for a single turn eddy current sensor

摘要

Analytical solutions for the inductance can be easily obtained for coils with rectangular cross sections having multiple turns realizing a homogeneous current distribution. These models have at least six parameters and do not consider the self-capacitance of the coil. The inner magnetic field is partially included, so that the accuracy of the static impedance is limited especially at higher frequencies. Even at lower frequencies, reference measurements without target are generally needed for self-calibration. By direct evaluation of the magnetic vector potential at the contour of the coil wire, a coil inductance model with a simpler mathematical structure can be obtained, which allows a consideration of the self-capacitance and the inner inductance. This avoids the need for reference measurements and the influence of distance, conductivity and permeability can be easier quantified. Inductance calculation requires 250 ms on a standard personal computer for 100 frequencies resulting in a deviation of at most 5% for the static inductance. This is a good result with respect to the low impedances in the μΩ range, which are generally hard to measure. The proposed model represents a good basis for models of multiple turns with a precisely defined geometry including the self-capacitance effects.