Bilinear calibration of coaxial transmission/reflection cells for permittivity measurement of low-loss liquids

Several parameters describing the quality of petrochemical products can be revealed from the permittivity spectrum of the product. This requires that the permittivity be measured with high sensitivity, so the calibration of measurement cells is of great importance. In this work calibration techniques for the transmission/reflection method for complex permittivity determination of low-loss liquids are studied. It is shown that a bilinear transformation can be used to determine the scattering parameters at the reference planes from the measured scattering parameters of a coaxial transmission/reflection cell. The permittivity of a sample in the cell can then be calculated with high precision from the reference plane parameters. The de-embedding procedure consists of determining three calibration coefficients by measuring three samples with known permittivities. Measurements on low-loss liquids and crude oils confirm the performance of the calibration procedure. The technique is compared to a simpler calibration method and the choice of calibration fluids to ensure broad-band measurements is discussed.