Analytical Uncertainty Evaluation of Material Parameter Measurements at THz Frequencies
Alireza Kazemipour, Michael Wollensack, Johannes Hoffmann, Martin Hudlička, See Khee Yee, Jürg Rüfenacht, Daniel Stalder, Gregory Gäumann, M. Zeier
Abstract
Abstract Material parameter extraction algorithms are studied and simplified both for transmission-reflection and transmission-only methods. The simplified relations, which are closed-form in some cases, are analyzed to establish the uncertainty sensitivity coefficients and therefore, to clarify the main uncertainty contributions and reduce the systematic and random errors. Simple closed-form expressions presented in this paper show the sensitivity of the extracted permittivity to each input parameter such as S 21 (phase and amplitude), frequency, and the material thickness. Results are presented for several material slabs for three waveguide frequency ranges 75–110 GHz, 140–220 GHz, and 500–750 GHz using VNA-based free-space technique in the THz domain. Comparison of results (and the associated uncertainties) between different algorithms can help to choose the optimal one suitable for lossy or low-loss materials, and thin or thicker slabs. This can explain why the same set of S -parameters data usually gives different final results (permittivity and permeability) with different algorithms and verify the reliability of the calibration and extraction process.