A Novel Broadband Measurement Method for Electromagnetic Parameters of Liquids Based on Resonance and Transmission-Reflection of Striplines

In this article, a novel broadband measurement method for electromagnetic (EM) parameters of liquids employing a stripline test kit (STK) is proposed. In this method, the inherent resonance and transmission-reflection characteristics of the stripline structure are used to extract the EM parameters of liquids. The permittivity (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\boldsymbol {\varepsilon }\mathbf {'}$ </tex-math></inline-formula>) of a liquid can be derived from the resonant frequency of the stripline immersed in the STK filled with the liquid. The S-parameters of the stripline test structure immersed in air and in a liquid are utilized to calculate the loss tangent (tan<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\delta $ </tex-math></inline-formula>) of the liquid. The calculation formulas for the liquid loss tangent are derived. The research indicates that the permittivity measurement error of liquids is bounded by that of air, and the liquid’s loss tangent measurement error is primarily determined by the liquid’s permittivity measurement error and the transmission coefficient measurement error of the vector network analyzer (VNA). In this work, an STK was devised and built to measure the EM parameters of air and five liquids, including three fluorochemicals and two synthetic oils, across a temperature range from <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$25~^{\circ }$ </tex-math></inline-formula>C to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$55~^{\circ }$ </tex-math></inline-formula>C. EM parameters of these liquids are obtained up to 30 GHz, covering more than 55 resonant frequency points. Meanwhile, cyclohexane and silicone oil were tested to evaluate the uncertainty of this method. The results show a permittivity measurement error of less than 3% across the wide frequency and temperature ranges tested. Additionally, the proposed STK method is more convenient and efficient than existing industry methods.