The authors wish to acknowledge funding within the research project 18SIB09 TEMMT (Traceability for electrical measurement at millimeter-wave and terahertz frequencies for communications and electronics technologies). This project has received funding from the EMPIR programme co-financed by the Participating States and from the European Union's Horizon 2020 research and innovation programme. Material Parameter Extraction in THz Domain, Simplifications and Sensitivity Analysis Alireza Kazemipour Federal Institute of Metrology Bern, Switzerland alireza.kazemipour@metas.ch Juerg Rufenacht (METAS) Bern, Swizerland Michael Wollensack Federal Institute of Metrology (METAS) Bern, Switzerland Gregory Gaumann (METAS) Bern, Swizerland Johannes Hoffmann Federal Institute of Metrology (METAS) Bern, Switzerland Martin Hudlicka (CMI) Prague, Czech Republic See-Khee Yee Faculty of Electrical Eng. UThM University Johor, Malaysia Markus Zeier (METAS) Bern, Switzerland Abstract—Classic equations for material parameter extraction are reconsidered and slightly modified to achieve stable results at all frequencies. Meanwhile, closed-form solutions are developed to simplify the material parameter extraction process and uncertainty evaluation. The presented equations are independent of the material-slab thickness and therefore, can reduce the relevant systematic errors and uncertainties. Some representative results are reported in the frequency range 140-220 GHz together with the uncertainty analysis and sensitivity coefficients. Keywords—material characterization, extraction method, THz domain, sensitivity coefficient, measurement uncertainty I. INTRODUCTION Material parameter-extraction methods are based on reflection and transmission parameters (or only one of them) that often suffer from instability or complicated iterative process. The classic Nicolson-Ross-Weir (NRW) method [1] deals with  and T (see Eq.1 and Eq.2, for free-space propagation) to extract  and , simultaneously. The method gives unstable results for low-loss and high-refractive materials when S11~0 and |S21|~1 at specific frequencies. S11 = (1− 2 ) 1− 2  2 S21 = (1− 2 ) 1− 2  2 (1)   = X ± (√ 2 −1 ) and     = ( 1− 1+ ) 2 (2) with: X = (S 2 11 – S 2 21 + 1) / 2S11 = −    √     (3) Here, a simple comprehensive method is suggested to correct the instability first, and then classic equations (1 and 2) are simplified to closed-form formula. II. INSTABILITY CORRECTION In the NRW method [1], [2] the extraction ( and ) is established on Eq.1 together with Ln (T) -complex function- in Eq.3 and treating its phase ambiguity. Although the method has instability at some frequencies, but T and consequently √     are stable. The correction method here is based on the fact that in NRW method the unstable  and  are extracted in parallel, and their product is stable: (unstable) × (unstable) = (stable) × (stable) Therefore, in the case of non-magnetic materials for which r = 1 + j0, the correction factor is derived as simple as: r(stable) = r(unstable) × r(unstable) (4) In which r(unstable) and r(unstable) can be determined from the well-known algorithms based on the NRW method. Simply saying, the unstable '  j" (deviated from 1 + j0) is used as the correction factor. Fig. 1. 3mm Plexiglass slab (140-220 GHz): r Real (top) and Imaginary parts, stable results compared with unstable ones with "unstable '  j" as the correction factor (black curves, bottom).