# Hypersentized Metamaterials Based on a Corona-Shaped Resonator for Efficient Detection of Glucose
## 3 Dielectric Measurement of the Glucose-Water and Glucose-Blood Samples  
The electrical properties of the samples were measured in the frequency range from 1 GHz to 8 GHz by using the open-ended coaxial probe with a 85070E dielectric measurement kit connecting to a vector network analyzer.  
A Vector Network Analyzer (VNA) KESIGHT brand PNA-L N5234A and dielectric probe were used to measure the values of dielectric constant and loss tangent of the glucose mixture with water at different concentrations (100 mg/dL to 500 mg/dL) in steps of 100 mg/dL and of the glucose mixture with blood under similar conditions. The experimental setup, shown in Figure 3, was used for electrical measurements of the prepared samples. The measurements were carried out at room temperature (25 \({}^{\circ}\)C). Before starting the measurements of selected samples, the apparatus calibration in the VNA should be completed. To perform calibration, the electrical property of pure water was given to the VNA, while making sure that the dielectric measurement was idle and air was being measured. The next step was to immerse the dielectric probe kit in water and calibrate the device accordingly. Then, the electrical characteristic of water was measured in order to ensure the correct calibration of the VNA. Consequently, it was able to detect the real and imaginary parts of the relative permittivity for various mixtures of the selected samples. The dielectric loss factor of each sample could be determined by dividing the imaginary part of the dielectric constant (\(\varepsilon\)\") by its real part (\(\varepsilon^{\prime}\)), \(\tan\delta=\varepsilon^{\prime\prime}/\varepsilon^{\prime}\).  
Figure 2: Metamaterial-based sensor with a corona-shaped resonator: (**a**) the boundary conditions and (**b**) equivalent circuit diagram whereas L denotes the inductance of the corona-shaped resonator, R is the resistance, and the capacitance between the outer ring and conductor is C\({}_{1}\), while C\({}_{2}\) is the capacitance between the inner conductor and copper ground plate.  
The theoretically extracted real part and imaginary part of the complex permittivity values are shown in Figure 4. The real part of the complex permittivity for the samples with 100, 200, 300, 400 and 500 mg/dL of glucose mixed with water was 80.5, 80.5, 80.5, 81 and 81, respectively, at the resonant frequency of 1 GHz. At the resonance frequency of 8 GHz, the values were 67.8, 68.2, 68.96, 69.53 and 70 for the same concentrations, respectively. The real and imaginary parts of the complex permittivity for different ratios of glucose-water showed a good agreement between the measured values and theoretically extracted ones from [PERSON]'s equation.  
To further validate the measured and theoretical results, we conducted an analysis of the real and imaginary parts of the complex permittivity of the glucose-blood samples, as shown in Figure 5. The measured and calculated results were in good agreement. The calculated curves of the real and imaginary permittivity versus frequency in the range of 1-8 GHz were derived theoretically from [PERSON]'s equation, Equations (4) and (5), after estimating the following parameters, Equations (6)-(8), upon the curve fitting of the experimental data.  
\[\varepsilon_{\infty}(\mathrm{x}) = -66.171\mathrm{x}^{3}+124.98\mathrm{x}^{2}-\ 65.129\mathrm{x}\ +\ 47.224 \tag{6}\] \[\varepsilon_{\mathrm{s}}(\mathrm{x}) = -136.39\mathrm{x}^{3}+225.95\mathrm{x}^{2}-\ 130.14\mathrm{x}\ +\ 20.669 \tag{7}\]  
Figure 4: The complex permittivity of glucose–water mixture: (**a**) measured real part, (**b**) calculated real part, (**c**) measured imaginary part and (**d**) calculated imaginary part.