Eliminating errors due to position uncertainty in coaxial airline based measurement of material parameters

The Nicolson-Ross-Weir (NRW) method is a classic technique for the measurement of complex permittivity and permeability of materials at RF and microwave frequencies. The method is based on the measurement of transmission and reflection coefficients of the material under test and subsequently, extracting the material parameters through a non-linear inversion process. The NRW method has a limitation on the thickness of the sample to be less than λ/2. The Stepwise NRW method that relies on seeking the correct branch in the inversion process, overcomes the limitation on the thickness on the sample. Both the methods rely on the reflection and transmission coefficients, which is obtained from two-port S-parameters measurements, by inserting the material under test inside a transmission line. In this work, a coaxial airline is used for the transmission line measurement. The de-embedding of the S-parameters, to obtain the reflection and transmission coefficients, requires the position/location of the sample inside the coaxial airline. This can potentially introduce errors due to position uncertainties. We propose a technique to estimate the position of the material under test inside the coaxial airline that eliminates inaccuracies due to positioning errors in the extraction process. The proposed technique relies on the symmetry of S-parameters to estimate the errors in the position of the material placed inside the coaxial airline. Subsequent de-embedding of S-parameters is performed taking into account the estimated error in the position of the material under test. Measurements and investigations are performed using both the NRW and stepwise NRW techniques illustrating the improvement in the accuracy of the measured material parameters.