# A Sensor for Characterisation of Liquid Materials with High Permittivity and High Dielectric Loss
###### Abstract  
This paper reports on a sensor based on multi-element complementary split-ring resonator for the measurement of liquid materials. The resonator consists of three split rings for improved measurement sensitivity. A hole is fabricated at the centre of the rings to accommodate a hollow glass tube, through which the liquid sample can be injected. Electromagnetic simulations demonstrate that both the resonant frequency and quality factor of the sensor vary considerably with the dielectric constant and loss tangent of the liquid sample. The volume ratio between the liquid sample and glass tube is 0.36, yielding great sensitivity in the measured results for high loss liquids. Compared to the design based on rectangular split rings, the proposed ring structure offers 37% larger frequency shifts and 9.1% greater resonant dips. The relationship between dielectric constant, loss tangent, measured quality factor and resonant frequency is derived. Experimental verification is conducted using ethanol solution with different concentrations. The measurement accuracy is calculated to be within 2.8%, and this validates the proposed approach. dielectric sensor; high permittivity; high loss; liquid; complementary split ring resonator 20  
for low frequency measurements. The transmission line method requires that the material be placed in a part of the enclosed transmission line during measurements [9; 10]. It also requires precisely manufactured samples to fit the transmission line [11]. In addition, the injected liquid sample in an enclosed transmission line always faces the challenge of sealing the sample without leakage. The free space method uses free space as the transmission medium and is more suitable for dielectric measurement in the millimeter wave range [12]. The resonant cavity method is sensitive to low-loss and low-permittivity samples with high accuracy. The traditional resonant method usually creates a higher mode for high permittivity samples [13]. Moreover, high-loss samples usually degrade the quality factor, resulting in a considerable reduction of measurement accuracy [14]. In summary, new dielectric measurement techniques shall be developed for high-permittivity and high-loss liquid samples with sufficiently high sensitivity. In recent years, microwave sensors using the resonance method have become increasingly popular. Structures such as the split-ring resonator (SRR), complementary spiral resonator (CSR), and complementary split ring resonator (CSRR) are the most commonly used ones in the design of microwave liquid sensors [15; 16; 17; 18; 19; 20]. Examples of SRR structure can be found in Refs. [15; 16; 17; 18; 19; 20]. The sensor in Ref. [15] must maintain the fluidity of the liquid during measurement, which may cause a lot of loss of liquid samples. Sensors reported by [PERSON] et al. [16] can measure the dielectric constant of liquids, but not the loss tangent. This work was later further developed by the same group to realize dual-frequency operation [18]. [PERSON] et al. [17] developed a concentration sensor using the Q factor and the maximum \(S_{21}\) of the resonance as sensing magnitudes. [PERSON] et al. [19] modified this design using certified biocompatible material. The structure was fabricated by 3D printing, which provides stronger interaction between the electromagnetic fields and the sample. The microfluid sensor reported in Ref. [20] can measure both the real and imaginary parts by using both magnitude and phase of \(S_{21}\). However, the accuracy is not good enough, which may be attributed to the fact that that phase is more prone to measurement errors. Interestingly, [PERSON] et al. [21] made a systematic study on defect-ground-plane based resonators. This general method provides guidelines for the design of microstrip line resonators. Refs. [22; 23] reported on sensors based on CSR structures. The sensor reported by [PERSON] et al. [22] uses flexible materials but can only measure low-loss materials, while, the sensitivity of the sensor in Ref.