In this article, a technique based on artificial neural networks (ANNs) is proposed to extract stable complex permittivity and permeability of low-loss materials from transmission/reflection (T/R) measurements. The equations of attenuation constant $\alpha $ and phase constant $\beta $ of $a$ sample-filled transmission line are derived. The calculated $\alpha $ and $\beta $ are put into an ANN model. The outputs of the ANN model are stable complex permittivity and permeability over the whole measurement frequency range, while the values extracted by other techniques are resonant at the frequencies corresponding to integer multiples of one-half wavelength in the sample materials. Two low-loss materials with substantial thickness are measured in X-band to validate the proposed technique. Compared with the Nicolson–Ross–Weir (NRW) technique, the short-circuited technique, and an ANN technique without the derived equations, the proposed technique provides stable results for the two samples. In addition, the extracted values are compared with the “true values” measured from the thinner samples to further present the advantages of the proposed technique.

中文翻译：

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从透射/反射测量中提取低损耗材料的稳定复介电常数和渗透率

在本文中，提出了一种基于人工神经网络 (ANN) 的技术，从传输/反射 (T/R) 测量中提取低损耗材料的稳定复介电常数和磁导率。衰减常数方程 $\alpha $ 和相位常数 $\beta $ 的 $a$ 样品填充的传输线被推导出来。计算出的 $\alpha $ 和 $\beta $ 被放入一个 ANN 模型中。ANN 模型的输出是在整个测量频率范围内稳定的复介电常数和磁导率，而其他技术提取的值在对应于样品材料中二分之一波长整数倍的频率处谐振。在 X 波段测量了两种具有相当厚度的低损耗材料，以验证所提出的技术。与 Nicolson-Ross-Weir (NRW) 技术、短路技术和没有派生方程的 ANN 技术相比，所提出的技术为两个样本提供了稳定的结果。此外，将提取的值与从较薄样品测量的“真实值”进行比较，以进一步展示所提出技术的优势。