Microwave Sensing System for Characterizing Liquid Samples Based on Self-Resonant Circuit and Phase-Locked Loop

This article proposes a novel microwave sensor based on a self-resonant circuit and a phase-locked loop for characterizing the complex dielectric constant of liquids. The sensor comprises a self-resonant circuit that includes a multi-coupled complementary split-ring resonator (MCCOLR), an RF amplifier, a power splitter, and a coaxial line, as well as both a frequency and a power demodulator. The MCCOLR designed at 2.47 GHz based on the traditional complementary split-ring resonator (CSRR), enhances the electric field through multiple coupled split rings, thereby improving sensitivity, while also acting as a frequency-selective component. When a test liquid is injected into the sensing region on the surface of the microwave resonator, the frequency and amplitude of the output signal are modified according to variations in the liquid’s complex dielectric constant. The frequency modulated (FM) and amplitude modulated (AM) signals are then converted into the corresponding voltage by the proposed frequency and power demodulator. For sensor calibration, a mathematical model is established using standard liquids with known complex dielectric constants to predict the complex dielectric constants of unknown samples. Experimental results demonstrate that the maximum error in extracting the real part of the dielectric constant is 3.96%, while the maximum error in the loss tangent is 3.48%. Furthermore, the maximum sensitivity achieved 3.35 mV/ε′. By eliminating the need for expensive laboratory equipment such as vector network analyzers (VNAs), RF signal generators, and spectrum analyzers, the proposed system reduces the overall cost. Moreover, this system can simultaneously characterize both the real part of the dielectric constant and the loss tangent, offering high sensitivity, high accuracy, and low cost.