Direct Permittivity Reconstruction From Power Measurements Using a Machine Learning Aided Method

Abstract

A machine learning aided (MLA) method is employed for the direct permittivity retrieval of dispersive and non-dispersive materials. The method requires low-cost measurements since it solely utilizes the amplitude of the transmission response ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$|S_{21}|$</tex-math> </inline-formula> ) to extract the complex permittivity. This precludes the need for a network analyzer, and therefore, the measurements can be performed using a power sensor. Unlike earlier works, however, the method introduced here does not require prior information about the dispersion model of the material under test (MUT), so it is applicable to a wider range of materials. The method is based on applying two artificial neural networks (ANNs) for the permittivity reconstruction of low and high-loss materials. The ANNs are trained using full-wave simulation results of a coaxial line loaded with different MUTs for the direct reconstruction of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\varepsilon^\prime$</tex-math> </inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\varepsilon^{\prime\prime}$</tex-math> </inline-formula> . As a proof of concept, several chemical liquids, their mixtures, and powdered samples were used to experimentally validate the technique within the 0.3–3 GHz band. The retrieved complex permittivities of samples were in good agreement with the reference data and those obtained by the well-known transmission/reflection Nicolson–Ross–Weir (NRW) method.