Abstract
In this paper, a novel method is proposed to determine unique and stable relative complex permittivity of low-loss materials from the transmission/reflection (TR) measurements, though the positions of the materials under test are unknown. The proposed method systematically combines artificial neural network (ANN) models with the Nicolson-Ross-Weir (NRW) method. Firstly, an ANN model is established to estimate the position of the sample in the transmission line. Secondly, the NRW method is adapted to estimate the relative complex permittivity, and the unique solutions are selected with the help of dielectric properties. Thirdly, the noniterative technique in the literature is adapted to avoid the instabilities in the relative complex permittivity. Finally, the S-parameters of the amplitude-only or transmission-only measurements are used to accurately determine the relative complex permittivity. The proposed method is experimentally validated by two samples. The simulated data are used to further validate the accuracy of the proposed method. The results of the proposed method based on the transmission-only measurements are the most accurate.
Highlights
Precise knowledge on electromagnetic properties of materials is a fundamental requisite for engineering design of electrical systems
The methods based on the transmission/reflection (TR) measurements are widely adopted for determination of εr since they are broadband and easy to be carried out [3], [4]
The position of the sample can be shifted in the course of connecting or disconnecting the sample holder with the vector network analyzer (VNA) connectors [11]
Summary
Precise knowledge on electromagnetic properties of materials is a fundamental requisite for engineering design of electrical systems. Various techniques have been discussed to eliminate the drawback of multiple solutions, such as the group-delay technique [6], the multiple phase measurements approach [12], the amplitude-only method [13]–[15], the Kramers–Kronig relations method [8], [16], the stepwise. Two shorted-reflection and one transmission S-parameters are measured in the method that increases the uncertainty of the determined εr as the measured S-parameters are the main sources of errors in the extracted εr [28]. A simple method is proposed to eliminate the three drawbacks all at once.
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