# A Sensor for Characterisation of Liquid Materials with High Permittivity and High Dielectric Loss
## 5 Measurements and Results  
Figure 12a,b shows photos of the sensor, which was fabricated using planar PCB technology. The sensor was made from RO3035 substrate with a thickness of 0.75 mm and a dielectric constant of 3.5 and loss tangent of 0.0015. The middle glass tube is made of fused quartz having a dielectric constant of 3.78. The tube has a diameter of 1.5 mm, a length of 75 mm, and an inner diameter of 0.3 mm. The bottom of the glass tube is sealed, and the upper end is open, which can be used to inject liquid samples into the tube. A pair of 50 \(\Omega\) SMA connectors are soldered onto both ends of the sensor. Measurement was conducted using a vector network analyzer (VNA) _Ceyear_ AV3672D. The VNA was calibrated using a standard short-load-open-thru (SLOT) method with a 3.5 mm calibration kit. The measurement frequency range was from 2.75 GHz to 3 GHz. After calibration, the \(S_{21}\) of unloaded situation was first measured. Then, the liquid samples were injected into the glass tube through syringes. In this study, the liquid sample was diluted ethanol solution with a mass concentration of 20%, 50%, 70% and 95%. These samples were injected into different glass tubes to avoid contamination. Placing the quartz glass tube filled with the measured sample to the CSRR center through the hole of the  
Figure 11: Nonlinear surface fitting for loss tangent and quality factor. Figure 12: Experimental verification. (**a**) Top view of the CSRR; (**b**) The sensor is fixed on a PTFE plate; (**c**) Experimental set up. sensor and recording the \(S_{21}\) for each sample. The measured data are plotted in Figure 13. From the measured data, the resonant frequency and the quality factor can be deduced. Therefore, the dielectric constant and loss tangent can be calculated by using the fitting Equations (5)-(7). The measured data are plotted to Figure 14 to better show the tendency of \(S_{21}\) with the concentration. With the increase in ethanol concentration, the resonant frequency shifts upwards, and the loss shows a decreasing tendency, which is consistent with simulations. The dielectric constant change due to the concentration of the liquid sample can be explained using mixture theory. The mixture of water and methanol shows concentration  
Figure 14: \(S_{21}\) of different concentration of ethanol. Figure 13: Comparison between measurement and simulation of \(S_{21}\) (**a**) unloaded; (**b**) 0% ethanol (water); (**c**) 20% ethanol; (**d**) 50% ethanol; (**e**) 70% ethanol; (**f**) 95% ethanol. dependent property. Water has larger permittivity and methanol has smaller permittivity. Therefore, with the increase in methanol concentration, the effective permittivity will decrease. Considering that the resonant frequency is inversely proportional to the square of the permittivity, it is seen that the resonant frequency moves towards a lower frequency side with the increase in concentration. The values are substituted into Equations (5)-(7) and the one that obtained the complex permittivity of the sample, as shown in Table 3. The measured results have a good agreement with values reported in Ref. [38]. The calculated accuracy in comparison to the cited values is as good as 2.8%, in contrast to the values in Ref. [38]. It is noted that the worst case is the imaginary part for pure water, as seen in Table 3. This figure (2.8%) is used to represent the accuracy. Table 4 shows the performance comparison between the proposed sensor of this work and other similar microwave dielectric sensors reported in the literature. For Refs. [24; 25], the main drawback is that only the real part can be measured. The accuracy of the sensor in Ref. [25] is 11%, which is even worse than a non-resonance method. For Refs. [26; 27; 28], samples are in direct contact with the sensor, making them unable to measure corrosive samples. It is observed that the resonance dip becomes worse when the loss tangent increases. In comparison, this design uses a partial-filled glass tube, which is helpful to increase the resonance dip for high loss media.