A Compact Dual-Frequency Microwave Sensing System With Temperature Compensation for Liquid Permittivity Measurement

Ambient-temperature interference remains a major challenge in microwave sensing of liquid permittivity. This article presents a dual-frequency microwave sensing system that effectively compensates temperature-induced errors. The system comprises a microwave signal source, a dual-mode microstrip resonator, and a dual-band radio frequency (RF) rectifier. A modified split-ring resonator (MSRR) is employed as the passive sensing element and is read out by compact active circuitry, eliminating the need for a vector network analyzer as the core instrument. Two operating frequencies (1.325 and 2.893 GHz) are selected across the entire signal chain. Exploiting the complementary sensitivities of the two resonant modes to permittivity and temperature, the proposed voltage-domain readout achieves the liquid under test (LUT) permittivity extraction and suppresses temperature-induced errors without extra temperature sensing. A two-hidden-layer feedforward neural network is trained to map the voltage pair directly to the LUT permittivity. To quantify the voltage-domain responsiveness, a dual-frequency sensitivity metric is defined, yielding${S}_{V}({\varepsilon,T})\approx ~0.38$%–0.52% over representative temperatures. Experiments on ethanol–water solutions demonstrate a maximum relative error of 6.91%. The compact sensing system enables measurements with a small sample volume while maintaining low cost, compactness, and portability.