## 3 Experimental Results and Validation
### Dielectric Characterization of Oil Samples  
The comparison of simulation and experimental results of the scattering parameters of the unloaded sensor is shown in Figure 2a. The simulated and measured S\({}_{21}\) showed the sensor resonating at 5.20 GHz and 5.25 GHz, respectively. The forward transmission coefficient was measured to check the resonant frequency, and as seen in Figure 2, the simulated and experimental results were close enough. The slight shift in resonance frequency was attributed to the fabrication tolerance. Before adulteration detection, the sensor was tested by measuring the permittivity values of some commonly available oils. Castor oil, mustard oil, flaxseed oil, and olive oil samples were used to experiment with dielectric characterization. The oils are commonly available and were bought from a supermarket. To calculate the complex permittivity of the different oil samples, a unique empirical formula is required [33]. Equations (2) and (3) were used to calculate the real part of the permittivity and loss tangent of the oil samples. Each oil sample had a different resonating frequency, and using the shift in resonating frequency compared with the unloaded sensor, characterization of the oil samples took place.  
\[\epsilon_{r}=\frac{-1}{0.19083}\ln\frac{\left(\Delta f\,-\,1.75477\right)}{-2.1 0315} \tag{2}\]  
\[\tan\delta\]  
\[=\frac{-1}{-0.2687-3.32877\epsilon_{r}+0.54996\left(\epsilon_{r}\right)^{2}} \ln\frac{\left(S_{21}\text{dB}+15.45006-0.01467\epsilon^{1.25886 cr}\right)}{-7.1 9478-0.03569\epsilon^{1.02166 cr}} \tag{3}\]  
Figure 3: (**a**) Front and back picture of the fabricated sensor. (**b**) Experimental set-up used for oil testing.  
where \(\Delta\)f is the difference between the sensor's unloaded resonant frequency and resonant frequency when the OUT was loaded.  
The resonating frequency of the sensor in the unloaded case was 5.25 GHz. Figure 4 shows that the frequency shifted to 4.83 GHz for castor oil, and 5.03 GHz for flaxseed oil. Moreover, the frequency shifted to 4.89 GHz for mustard oil, and 4.95 GHz for olive oil. These results illustrate that the sensor was sensitive enough to induce a reasonable change in the resonant frequency when loaded with the OUT sample.  
A comparison of the shift in resonant frequencies from the reference frequency of 5.25 GHz after the loading of the oil sample, is provided in Table 1. The shift in the frequency was proportional to the permittivity of the OUT.  
From the shift in resonance frequency, and using Equations (2) and (3), permittivity and loss tangent values of OUT were calculated as shown in Table 2. Table 2 shows the retrieved values of the dielectric constants of different oils. The actual values of dielectric constants of these oils could not be found in existing literature at 5.25 GHz. Therefore, at this point, we cannot comment on the accuracy of these values. Table 3 shows the quality factor and sensitivity values for different oil samples. The error column shows the variation of maximum error around the average value after taking multiple measurements for each oil.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Samples** & **Frequency (GHz)** & **\(\Delta\)f (GHz)** \\ \hline Castor oil sim. & 4.825 & 0.405 \\ Castor oil exp. & 4.832 & 0.398 \\ Mustard oil sim. & 4.860 & 0.370 \\ Mustard oil exp. & 4.890 & 0.340 \\ Olive oil sim. & 4.952 & 0.278 \\ Olive oil exp. & 4.953 & 0.277 \\ Flaxseed oil sim. & 5.045 & 0.185 \\ Flaxseed oil exp. & 5.030 & 0.200 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Comparison of shift in frequency for oil samples.  
Figure 4: Result of \(\mathbb{S}_{21}\) for: (**a**) castor and flaxseed oils; (**b**) mustard and olive oils.