VNA-Based Material Characterization in THz Domain without Classic Calibration and Time-Gating Alireza Kazemipour * , Johannes Hoffmann * , Michael Wollensack * , Djamel Allal † , Martin Hudlicka *† , Juerg Ruefenacht * , Daniel Stalder * and Markus Zeier * * Swiss Federal Institute of Metrology (METAS), Bern – Switzerland, alireza.kazemipour@metas.ch † Laboratoire National de Métrologie et d'Essais (LNE), France, *† Czech Metrology Institute, Czech Republic Abstract— A method is presented to measure materials and extract the complex permittivity without using classic VNA calibrations and time-gating. It is based on normalization to a "Thru" connection and analyzing error-terms and multiple- reflection phenomena. Measurement results (in free-space) are presented in 75-110 GHz and 500-750 GHz bands. Normalization technique can reduce the overall measurement uncertainties and simplify the material characterization process. Index Terms— Material characterization, parameter extraction, VNA time-gating, RF metrology, measurement uncertainty. I. INTRODUCTION Free-space calibration techniques are complicated in THz domain because of precise-positioning challenges and lack of reliable Short and Line standards. Actually, non-perfect calibration together with time-gating attribute more uncertainties to the final extracted material parameters. Here, we try to use a simple normalization process, analyze/correct the error-terms and then reduce the standing-waves effects. Fig. 1 shows VNA measurement error-terms and the relations between S(measured) and SDUT. Fig. 1. VNA measured S-parameters (Sij.M), error-terms (eij) and DUT S-parameters (Sij) (courtesy to IEEE-MTT Society). Ignoring the leakage-term and assuming for DUT (S21.DUT, S11=S22) and Thru-connection (S21=S12=1, S11=S22=0), yield:   21 () =  21. ()  21. (ℎ) × 1−  11  22 1+  11  22 ( 11 2 −  21  21 ) −  11 (  11 +  22 ) (1) we can analyze the error-terms of Eq. 1 by looking at the Fabry- Perot effects inside a material-slab (MUT). If the material is not very lossy, |S21|max. and |S11|min. occur simultaneously [1] at the frequency-points for which (S21) = n. Therefore, at |S11|min. (|S21|max. ≈ 1 & |S11|min.≈ 0, for low-loss materials):   21 () =  21. ()  21. (ℎ) 1−  11  22 1−  11  22 ( 21  21 ) (2) As deduced from Eq. 2, error-terms and system multiple- reflection on S21(MUT) all approximately vanish for |S21|max. & (S21)=n points. This is demonstrated for two low-loss materials (Fig. 2: Pyrex and Quartz, 500-750 GHz). Fig. 2. Normalized S21(MUT): Pyrex and Quartz, 500-750GHz.