# Substrate-Integrated Waveguide Microwave Sensor for Water-in-Diesel Fuel Applications
## 2 Water-Fuel Blend Characterization  
The SIW microwave applicator is designed to work in the frequency range \(f=9-11\) GHz with CST Studio Suite(r) software. This frequency range was chosen by observing the behavior of the complex dielectric permittivity of the fuel-water blend, on the basis of a wide-band investigation performed with a SPEAG DAK 3.5 probe [40] and a N9927A FieldFox Handheld Microwave Vector Analyzer by Keysight [41]. This preliminary investigation has highlighted changes in complex dielectric permittivity at the aforementioned frequencies, thus promising potential applications for sensing. Five fuel samples were prepared containing different concentrations of contaminant water. In particular, \(\rho=0\) ppm (pure diesel), \(\rho=50\) ppm, \(\rho=200\) ppm, \(\rho=500\) ppm, and \(\rho=1000\) ppm of water were prepared. Water concentrations higher than \(\rho=500\) ppm were not investigated because they are not interesting for practical applications, as they are over the acceptable limits regarding water contamination. The concentration \(\rho=1000\) ppm has been taken into account to verify the characteristics slope for extreme contaminations. Figure 1 shows the SPEAG DAK 3.5 probe-N9927A VNA characterization set-up. For each sample, the dielectric constant measurement was repeated seven times. These measurement results have been averaged to reduce measurement noise and fitted with a polynomial. Table 1 reports the order and the coefficient of determination \(R^{2}\) of the polynomial fitting the five measured dielectric constant curves. The fitting order has been chosen to maximize \(R^{2}\). The measured complex dielectric constants for the five samples as functions of the frequency are reported in Figure 2 (real part \(\varepsilon^{\prime}\)) and Figure 3 (imaginary part \(\varepsilon^{\prime\prime}\)). Figure 1: Characterization set-up with VNA Keysight N9927A FieldFox and DAK 3.5 probe. It is worth observing that the real part \(\epsilon^{\prime}\) increases as the water concentration increases in a wide frequency range, \(f=8-13\) GHz. To obtain reference values for the ad hoc-designed water-diesel fuel blend SIW applicator, we directly considered the SPEAG DAK 3.5 probe-N9927A VNA-measured characteristics. In particular, by choosing different frequencies, e.g., \(f=9,\ 10,\ 11,\ 12,\ 13\) GHz, different sensing characteristics, i.e., regression curves, can be drawn, as reported in Figure 4. At these frequencies, a direct proportionality between the water concentration \(\rho\) and the real part \(\epsilon^{\prime}\) occurs. Therefore, they are of interest for sensing applications. On the contrary, the frequencies \(f<7\) GHz or \(f>14\) GHz are not considered. The characteristics are quite similar, even if with a different coefficient of \(\rho\), the frequency \(f\) is higher than the frequency \(f\). \begin{table}
\begin{tabular}{c c c} \hline \hline
**Sample** & **Fitting Order** & \(R^{2}\) **of the Polynomial Fitting** \\ \hline \(\rho=0\) ppm & 8 & 0.95 \\ \(\rho=50\) ppm & 3 & 0.93 \\ \(\rho=200\) ppm & 3 & 0.97 \\ \(\rho=500\) ppm & 9 & 0.91 \\ \(\rho=1000\) ppm & 8 & 0.90 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Order and coefficient of determination \(R^{2}\) of the polynomial fitting the measured dielectric constant curves. Figure 3: Measured imaginary part \(\epsilon^{\prime}\) of the dielectric constant as a function of the frequency \(f\) for different water concentrations \(\rho\) in diesel. Figure 2: Measured real part \(\epsilon^{\prime}\) of the dielectric constant as a function of the frequency \(f\) for different water concentrations \(\rho\) in diesel. determination \(R^{2}\), indicating the proportionate amount of variation in the response variable explained by the independent variable in the linear regression model. We underline that this preliminary investigation has been performed to roughly identify a frequency range where the variation in the complex dielectric constant with water concentration promises potential applications to be investigated.