Microwave Dielectric Property Retrieval From Open-Ended Coaxial Probe Response With Deep Learning

Abstract

This work presents a technique for dielectric property retrieval through Debye parameter reconstruction from open-ended coaxial probe (OECP) response. Debye parameters were obtained with the application of a deep learning (DL) model to the reflection coefficient response of the OECP when terminated with a material under test. The OECP was modelled with the well-known admittance technique from 0.5 to 6 GHz with 20 MHz resolution. A dataset was generated using the admittance technique and obtained data was utilized to design the DL model. As part of the standard procedure, the dataset was separated to train, validate, and test parts by allocating the 80%, 10%, and 10% of the dataset to each section, respectively. Obtained percent relative error for Debye parameters were 1.86±3.01%, 3.33±9.52%, and 2.07±7.42% for <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\epsilon _{s}$ </tex-math></inline-formula> , <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\epsilon _\infty $ </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">$\tau $ </tex-math></inline-formula> , respectively. To further test the constructed DL model, OECP responses were measured at the same frequency band when it was terminated with five different standard liquids, four mixtures, and a gel-like material. Reconstructed Debye parameters from the DL model were used to retrieve the complex dielectric properties and obtained results were compared with the literature data. Obtained mean percent relative error was ranging from 1.21±0.06 to 10.89±0.08 within the frequency band of interest.