Free-space measurement using explicit, reference-plane and thickness-invariant method for permittivity determination of planar materials

In this paper, transmission phase-shift method was applied on free-space measurements for thin planar material characterization. The free-space measurement system consists of two pyramidal horn antennas, coaxial cables, network analyser, sliding guide, two antenna holders/stands, sample holder and two precision positioners. The free-space measurement system was operated in frequency range from 10 GHz to 15 GHz. The planar acrylic samples with different thicknesses were used for measurement validation. The relative permittivity of those samples were predicted from the measured reflection/transmission coefficients based on transmission phase shift concept. Before the actual measurement is done, systematic errors due to multiple reflections along the measurement distance between the horn antenna aperture and the planar sample surface were calibrated by using Thru-Reflect-Line (TRL) technique. In the free-space measurements, performance of the horn antenna and the distance between the two horn antennas played an important role in the measurement set-up. However, the mentioned measurement set-up factors were usually less discussed in previous literatures. Hence, in this study, these issues will be discussed in order to improve accuracy and reduce the multi-reflection in the measurement. Besides, the effect of thickness for the sample in permittivity prediction was also discussed and analysed in detail. Formerly, the thickness of the planar sample was not recommended to be more than a quarter of the wavelength in order to avoid phase-shift ambiguity problems and effects on the accuracy of the broadband relative permittivity prediction. Here, the phase-shift ambiguity issue due to the sample thickness was solved by the MATLAB command “unwrap” during the mathematical calculation of the permittivity value. In addition, this proposed method is sample position-invariant. Hence, the measurement errors due to the uncertainty of the sample position can be avoided.