A Microwave Sensor Based on Frequency-Locked Loop and Multiple Complementary Split-Ring Resonators for Retrieving Complex Permittivity of Liquid Samples

A novel microwave sensing system based on frequency-locked loop (FLL) and multiple complementary split-ring resonators (CSRRs) is proposed in this article. The microwave sensing system consists of two main parts: one is FLL-based sensor and another is demodulated circuit. The FLL-based sensor is composed of a voltage-controlled oscillator (VCO), power splitter, low noise amplifier (LNA), mixer, low-pass filter (LPF), phase shifter, and passive resonance unit. The passive resonance unit is evolved from a traditional 1CSRR-based sensor, and the transmission coefficient response of traditional one looks like high-pass filter. Then, a power splitter/combiner structure and four identical CSRRs are formed as 4CSRR-based sensor, which generates a transmission zero (TZ), so the quasi-dual-mode response is produced and mode 1 is utilized for measurement, and the quality factor of mode 1 is about 7.29. In simulation, the minimum volume of liquid sample (its real permittivity is assumed as 10) is <inline-formula> <tex-math notation="LaTeX">${1.1} \mu \text { L}$ </tex-math></inline-formula>, if the minimum relative resonant frequency shift of mode 1 is set as 3.3%. In the FLL-based sensor, VCO first transmits an initial oscillation frequency, and then, the magnitude and phase of RF signal are altered by through the resonance unit. The output dc voltage is correspondingly changed, and the changed dc voltage will alter the oscillation frequency of VCO. When liquid under tests (LUTs) with different complex permittivity are loaded on the resonance unit, the VCO will output different oscillation frequencies, and the different oscillation frequencies can be observed by the spectrum analyzer (SA). The demodulated circuit can decompose the oscillation signal into two dc voltages, i.e., <inline-formula> <tex-math notation="LaTeX">${V}_{I}$ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">${V}_{Q}$ </tex-math></inline-formula>. As different complex permittivity denotes various dc voltages for <inline-formula> <tex-math notation="LaTeX">${V}_{I}$ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">${V}_{Q}$ </tex-math></inline-formula>, <inline-formula> <tex-math notation="LaTeX">${V}_{I}$ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">${V}_{Q}$ </tex-math></inline-formula> can be adopted to retrieve the complex permittivity of liquid samples. In measurement, the proposed passive sensor has a compact structure with electrical size of <inline-formula> <tex-math notation="LaTeX">$0.1193 \lambda _{o}^{{2}}$ </tex-math></inline-formula>, where <inline-formula> <tex-math notation="LaTeX">$\lambda _{o}$ </tex-math></inline-formula> is the wavelength in free space. The average sensitivity of channel-I/Q for retrieving real permittivity is 0.36/1.86 mV/<inline-formula> <tex-math notation="LaTeX">$\Delta \varepsilon _{r}'$ </tex-math></inline-formula>, and the measured error for extracting real/imaginary parts of complex permittivity is about 8.3%/3.68%. The proposed microwave sensing system is a novel architecture of circuit system, and the presented detection method is a new attempt. Besides, samples with more parameters can be measured by utilization of the proposed microwave sensing system. All in all, the proposed microwave sensing system is a good candidate in the application of characterizing LUTs.