Dielectric Spectrum Extraction of Liquids Using Noncontact Microwave Split Ring Resonator
Wendi Zhu, Masoud Baghelani, Ashwin K. Iyer
Abstract
This article presents a novel method for broadband dielectric spectroscopy of liquids utilizing a noncontact microwave split ring resonator (SRR). The proposed approach leverages the multiharmonic property of the microwave resonator to extract the permittivity of the liquid-under-test (LUT) at resonance frequencies. By fitting these extracted values using the Debye model, both the real and imaginary dielectric spectra of the LUT can be determined across a wide frequency range. The proposed method requires a one-time calibration process to ensure high accuracy. An experiment employing five calibration samples and five test samples was performed to validate the effectiveness of the proposed method. The results of the extracted permittivity spectrum using the proposed method are compared with those from a commercial dielectric probe. The proposed method exhibits high accuracy with a root mean square error of 0.59 for <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\epsilon'$</tex-math> </inline-formula> values at the resonance frequencies. For the extracted Debye model parameters, the proposed method achieves reasonable precision with percentage errors of 1.40% 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> , 12.68% for <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\epsilon_{\infty}$</tex-math> </inline-formula> , and 7.86% for <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> and is a cost-effective and accurate solution for dielectric spectroscopy. Due to its planar structure, the microwave SRR can be seamlessly integrated into various systems, holding potential for applying this method in microwave sensing, noninvasive biological sensing, oil and gas industries, and other fields requiring dielectric spectroscopy.