Study of the self-resonance frequency of a flat coil for an eddy-current position sensor

At present, a novel eddy-current position sensor is being developed with an aim to attain sub-nanometre resolution. The sensor contains a flat Archimedean coil that should have a high enough Self-Resonance Frequency (SRF). This paper studies the SRF of coils with various geometries. The SRFs increase in the vicinity of a conductive target, but are relatively constant at small standoff distances. For accurate results, a 3D finite element model must be used instead of a 2D model. Based on the finite element results, a relatively simple expression has been obtained that predicts the SRF for standoffs between 10 pm and 100 pm with a RMS deviation below 6 %.