Extraction of Stable Complex Permittivity and Permeability of Low-Loss Materials From Transmission/Reflection Measurements

Abstract

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.