# Substrate-Integrated Waveguide Microwave Sensor for Water-in-Diesel Fuel Applications
## 3 Applicator Design
### Cross Slot SIW Applicator in Air  
The SIW applicator geometry is modified with the aim to improve the sensing performances. Two half geometries, allowing half mode behavior, of the previous applicator are placed in close position and coupled via a gap, named the horizontal slot. The further, horizontal, slot is designed to enhance the interaction between the EM field and the fuel samples. The new geometry, reporting the main parameters, is shown in Figure 9. The preliminary values of the geometric parameters are reported in Table 4. For this SIW applicator, asymmetric input and output microstrip lines are designed. This is justified by considering that it is similar to the composition of two half-mode structures. Figure 10 shows the equivalent circuit of the cross-slot SIW applicator [43; 44; 45]. The equivalent circuit is composed by two circuits similar to the previous one. Each of them refers to one of the two half-mode structures. The proximity coupling is modelled via the mutual inductance of \(M_{12}\), the effect of the cut on the half-mode structure is modeled by a properly high value load impedance \(Z_{L}\). Figure 7: Modulus of the electric field irradiated by the slot in the \(xy\) plane, single-slot SIW applicator in air. The SIW length is again set at \(L_{guide}=20\) mm. The optimization has regarded the parameters of slot width \(W_{slot}\), slot length \(L_{slot}\), and gap width \(W_{gap}\). \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Value** & **Description** \\ \hline \(L_{sub}\) & 35 mm & Substrate length \\ \(W_{sub}\) & 25 mm & Substrate width \\ \(L_{guide}\) & 20.3 mm & SIW length \\ \(W_{guide}\) & 6.9 mm & SIW width \\ \(W_{feat}\) & 4.7 mm & Microstrip line width \\ \(L_{feat}\) & 7.5 mm & Microstrip line length \\ \(W_{slot}\) & 0.3 mm & Slot width \\ \(L_{slot}\) & 4 mm & Slot length \\ \(W_{gap}\) & 0.3 mm & Gap width \\ \(s\) & 0.75 mm & Center–center distance of vias \\ \(d\) & 0.5 mm & Vias diameter \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Main geometric parameters of the designed cross-slot SIW applicator. Figure 8: Modulus of the scattering parameters \(S_{11}\) (solid curves) and \(S_{21}\) (dotted curves) as a function of frequency \(f\) for different values of the slot width \(W_{slot}\). Figure 9: Scheme of the designed cross-slot SIW applicator. For the slot width \(W_{slot}\), the parametric investigation is performed in the range \(W_{slot}=0.2-0.4\) mm. The modulus of the scattering parameters \(S_{11}\) and \(S_{21}\) as a function of the frequency \(f\) for different values of slot width \(W_{slot}\) is simulated. As the slot width \(W_{slot}\) decreases, the impedance matching increases. The best value is \(W_{slot}=0.2\) mm. This value is a trade-off. A narrower slot is not investigated, as previously discussed in Section 3.1. Moreover, good impedance matching with \(|S_{11}|=-22\) dB at the frequency of \(f=9.6\) GHz is reached. A further decrease in the length of \(W_{slot}\) is not interesting and could cause an interaction reduction with the background. The gap width \(W_{gap}\) is varied in the range of \(W_{gap}=0.2-0.4\) mm. Figure 11 shows the modulus of the simulated scattering parameters \(S_{11}\) (solid curves) and \(S_{21}\) (dotted curves) as a function of the frequency \(f\) for different values of gap width \(W_{gap}\). Additionally, the gap width modifies the applicator impedance matching. The best value is \(W_{gap}=0.2\) mm, ensuring the maximum transmission bandwidth and the minimum scattering parameter modulus \(|S_{11}|\). The impedance matching with \(|S_{11}|=-23\) dB at the frequency \(f=9.6\) GHz is obtained. The slot length \(L_{slot}\) is varied in the range of \(L_{slot}=4.9-5.3\) mm in order to ensure the maximum interaction between the fuel sample and the sensor. The modulus of the scattering parameters \(S_{11}\) and \(S_{21}\) as a function of the frequency \(f\) has been simulated for different values of \(L_{slot}\).