Accuracy enhancement of wideband complex permittivity measured by an open-ended coaxial probe

Abstract

When the wideband complex permittivity of a liquid solution was measured by an open-ended coaxial probe, its accuracy was inherently degraded due to an inexact conversion model compared with the uncertainty of the associated vector network analyzer. In this paper, the accuracy of the converted wideband complex permittivity is evaluated indirectly and then enhanced significantly. Firstly, the measured wideband complex permittivity is fitted by a dispersive permittivity profile in the Debye formula. Secondly, the new reflection coefficients are calculated numerically by applying the dispersive permittivity profile to a 2D finite-difference time-domain model of our probe. Thirdly, the inaccuracy of the fitted complex permittivity profile is quantified indirectly by the root mean square (RMS) error of the numerically calculated reflection coefficients in comparison with the originally measured reflection coefficients. Finally, four parameters of the Debye formula involved in the initially converted complex permittivity profile were calibrated iteratively until the RMS error of the repeatedly calculated reflection coefficients could be minimized. The validity of the above calibration procedure is assured numerically for a given wideband complex permittivity profile. In the case of our actual measurement of the fabricated cancer-equivalent solution, an unknown complex permittivity profile, the RMS error of the numerically calculated reflection coefficients could be reduced from 0.0416 to 0.0093. This calibration results in both relative dielectric constant and conductivity profiles being gradually enhanced as the frequency increases up to 5000 MHz.