Intercomparison of dielectric reference materials available for the calibration of an open-ended probe at different temperatures

Abstract

The first half of the paper shows how a least-squares analysis may be applied to a bilinear model relating the uncorrected reflection coefficients observed with an open-ended probe to the complex permittivities of dielectric materials at the probe aperture. A large number of reference materials should be chosen, with dielectric data available from independent sources of varying accuracy in the literature, and the best-fit parameters derived for the bilinear model. The absolute residuals in epsilon ` and epsilon ``between the model and the reference data may then be obtained: they encompass errors in the data, in the measurements and in the model. Laboratory measurements on 17 different materials are intercompared in this way in the second half of the paper. The frequency range is from 20 MHz to 2 GHz and the residuals are compared at +25 degrees C and -20 degrees C using probe diameters of 7 and 22 mm. For the smaller probe and with a range of relative permittivities from 1 to 80, residuals rarely exceed +or-1 in epsilon ` or epsilon `` for any material from 100 MHz upwards; for the larger probe residuals are satisfactory down to 20 MHz though not up to 2 GHz. They are significantly reduced if the range of permittivities is more restricted (which is clearly a limitation of the model) and they are significantly reduced at -20 degrees C if a new calibration is adopted, rather than using the model parameters determined from measurements at +25 degrees C.