A Microwave Measurement System Based on High-Sensitivity Stepped-Impedance Resonators (SIRs) for Testing Permittivity of Dielectric Materials and Liquid Samples

A microwave measurement system based on a novel high-sensitivity multiple stepped-impedance transmission lines for testing permittivity of dielectric and liquid samples is put forward in this article. The developed microwave measurement system is constituted by a pair of multiple stepped-impedance transmission lines, radio-frequency (RF) oscillator, and frequency demodulation circuit. For the CSRR-based multiple stepped-transmission lines, the phase of transmission coefficient (<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">21</sub>) is utilized to characterize materials, and the maximum phase-variation of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">21</sub> can be obtained by solving the optimal solutions of the characteristic impedances of low- and high-impedance transmission lines with their electrical lengths of 90°. In pursuit of VNA-independent measurement and cost reduction, a reflective RF oscillator is synthesized. Then, the power divider, hybrid coupler, mixer, and low-pass filter (LPF) are integrated into the RF oscillator to form the measurement system. The monitoring system can output two DC voltages to retrieve the complex permittivity of liquid samples. In measurement, the maximum sensitivity for the CSRR-based second-order stepped-impedance transmission lines is about −47.95° /Δεʹ<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</i>. And the average sensitivities for the two channels of proposed microwave measurement system are about 0.44 mV/mV/Δεʹ<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</i> and 0.21 mV/Δεʹ<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</i> , respectively. In the realm of dielectric spectroscopy, the proposed microwave system shows significant promise for solid and liquid material analysis.