# Substrate-Integrated Waveguide Microwave Sensor for Water-in-Diesel Fuel Applications
## 6 Cross-Slot SIW Applicator Characterization, Water-in-Diesel Background  
The same fuel samples, characterized in Section 2 and simulated in Section 4, were used for testing the cross-slot SIW applicator as a water-in-fuel sensor. The bag containing  
Figure 14: Constructed cross-slot SIW applicator. Figure 15: Cross-slot SIW. Modulus of the scattering parameters \(S_{11}\) and \(S_{21}\) as a function of the frequency \(f\) for measured (solid curves) and simulated (dotted curves). the fuel samples is constituted by polyethylene. Figure 16 shows measurements proving that it can be considered transparent, allowing complete radiating field transmission, and does not affect the water-in-diesel characterization. The complete measurement set-up is shown in Figure 17a. It is composed by the VNA Keysight FieldFox, connected to the constructed cross-slot SIW applicator. Figure 17b shows the plastic bag as transparent at microwave frequencies and placed on the applicator. Its stability is ensured by an appropriate support. Figure 18a shows the measured modulus and Figure 18b the measured phase of the scattering parameter \(S_{11}\) as a function of the frequency, for the five different water  
Figure 16: Cross-slot SIW. Modulus of the scattering parameters \(S_{11}\) (solid curves) and \(S_{21}\) (dotted curves) as a function of the frequency \(f\) measured in air (blue curves), measured with polyethylene (red curve), and simulated (black curves). Figure 17: (**a**) Measurement set-up using the Keysight VNA N9927A FieldFox and the constructed cross-slot SIW applicator as a water-in-fuel sensor; (**b**) magnified view of one of the measured fuel samples. concentrations \(\rho\). These curves do not allow us to easily obtain a sensing characteristic since no change proportional with the water concentration is observed. Figure 19a shows the measured modulus and Figure 19b the measured phase of the scattering parameter \(S_{21}\) as a function of the frequency \(f\) for the five different water concentrations \(\rho\). As expected, no \(S_{21}\) phase shift can be observed with variations in water concentration. On the contrary, the measured modulus varies quite linearly, as predicted by simulations. It is affected by the radiated power interacting with the sample, which allows the sensor operation. As for the simulated parameters of Figure 15, the modulus of the scattering parameter \(S_{21}\) decreases as the water concentration increases, showing an inverse proportionality. Table 7 reports the values of the measured modulus of the scattering parameter \(S_{21}\) for the different concentrations at a frequency of \(f=9.76\) GHz, where the \(|S_{21}|\) is maximized for all the five curves. Figure 18: (**a**) Measured modulus of the scattering parameter \(S_{11}\) as a function of the frequency and (**b**) measured phase of the scattering parameter \(S_{11}\) as a function of the frequency for the five different water concentrations \(\rho\). Figure 19: (a) Measured modulus of the scattering parameter \(S_{21}\) as a function of the frequency and (b) measured phase of the scattering parameter \(S_{21}\) as a function of the frequency for the five different water concentrations \(\rho\). \begin{table}
\begin{tabular}{c c} \hline \hline
**Water Concentration \(\rho\) (ppm)** & \(1S_{21}\)**@9.76 GHz (dB)** \\ \hline
0 & \(-6.17\) \\
50 & \(-6.48\) \\
200 & \(-7.21\) \\
500 & \(-7.68\) \\
1000 & \(-8.49\) \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Measured modulus of the scattering parameter \(S_{21}\) for the five water concentrations at a frequency of \(f=9.76\) GHz. Figure 20 shows the measured modulus of the scattering parameter \(S_{21}\) as a function of the water concentration. The proportionality is quite linear, so it is possible to calculate the sensitivity as  
\[\frac{\Delta|S_{21}|}{\Delta\rho}=1.42\;\mathrm{mdB/ppm}\;\mathrm{\char 37}\]  
The coefficient of determination is \(R^{2}=0.94\), which is in excellent agreement with the simulation illustrated in Section 4.