High Sensitivity Detection Method for Liquid Concentrations Based on Coupled Microwave Resonators

This article presents a new measurement method for liquid concentrations based on two inductively coupled resonators with enhanced sensitivity compared with traditional methods in microwave frequency ranges. The equivalent circuit of the coupled resonators is proposed with its eigenequation having three eigenfrequencies derived. We demonstrate that, compared to a single resonator, the sensitivity of the center eigenfrequency shift to the changed capacitance increases by an order of magnitude if the product of the coupling coefficient and <inline-formula> <tex-math notation="LaTeX">$Q$ </tex-math></inline-formula>-factor of the second resonator is close to unity. In addition, that the reflection magnitude changes with the varied capacitance is also giant under impedance matching condition at the down and up eigenfrequencies. Based on the proposed method, a sensor composed of an open quarter-wavelength microstrip-line resonator (OQMR) and a split-ring resonator (SRR) for detecting concentrations of water–glucose solutions is designed. By adjusting the sample volume and the distance between two resonators, different coupling coefficients and <inline-formula> <tex-math notation="LaTeX">$Q$ </tex-math></inline-formula>-factors can be attained, enabling marked increases in the sensitivity. Experimental and simulated results show that the sensitivity of the center eigenfrequency shift and of the reflection magnitude change to the concentration are as high as 9.4 MHz/(mg/mL) and 5.41 dB/(mg/mL), respectively, both of which are excellent compared to other sensors.