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 S₂₁ (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.

研究并简化了透射反射法和纯透射法的材料参数提取算法。通过分析简化的关系（在某些情况下为封闭形式）来确定不确定性灵敏度系数，从而弄清主要不确定性贡献并减少系统误差和随机误差。本文中呈现的简单闭合形式表达式显示了提取的介电常数对每个输入参数（例如S _21）的敏感性（相位和幅度），频率和材料厚度。使用太赫兹域中基于VNA的自由空间技术，给出了在75-110 GHz，140-220 GHz和500-750 GHz三个波导频率范围内的几种材料平板的结果。比较不同算法之间的结果（以及相关的不确定性）可以帮助选择适合于有损或低损耗材料以及较薄或较厚平板的最佳算法。这可以解释为什么同一套S参数数据通常使用不同的算法给出不同的最终结果（介电常数和磁导率），并验证校准和提取过程的可靠性。