# Substrate-Integrated Waveguide Microwave Sensor for Water-in-Diesel Fuel Applications
## 3 Applicator Design
### Single Slot SIW Applicator in Air  
The first geometry, reporting the main parameters, is shown in Figure 5. The preliminary values of the geometric parameters are reported in Table 3. The geometry depicted in Figure 5 is obtained considering an SIW guide fed by a microstrip line. The strip line sizes  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Frequency (GHz)** & **Sensitivity**\(\frac{\Delta\epsilon_{r}}{\Delta\rho}\) (\(\times 10^{-3}\)/**ppm**) & \(R^{2}\) \\ \hline
9 & 0.399 & 0.79 \\
10 & 0.395 & 0.82 \\
11 & 0.376 & 0.86 \\
12 & 0.344 & 0.88 \\
13 & 0.304 & 0.91 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Sensitivities of the SPEAG DAK 3.5 probe-N9927A VNA as a water-in-fuel sensor for different frequencies.  
Figure 4: Real part \(\epsilon^{\prime}\) of the dielectric constant, measured with SPEAG DAK 3.5 probe-N9927A VNA, as a function of the water concentration \(\rho\) in diesel, for different frequencies.  
\(W_{feat}\) and \(L_{feed}\) are designed to ensure a characteristic impedance \(Z_{0}=50\)\(\Omega\)[42]. The vias diameter \(d\), the center-center distance \(s\), and the other preliminary geometrical values are chosen following [25; 26; 27; 28; 29]. The slot ensures the radiation of the EM field and its interaction with the fuel samples.  
Figure 6 shows the equivalent circuit of the single-slot SIW applicator [43; 44; 45]. The distributed-constants network, modelling the input and output microstrip transmission lines, includes the series impedance \(Z=R+j\omega L\) per unit length and the shunt admittance \(Y=G+j\omega C\) per unit length. The inductance \(L_{s}\) and the capacity \(C_{s}\) model the transverse slot [43; 44].  
Figure 5: Scheme of the designed single-slot SIW applicator in air.  
Figure 6: Equivalent circuit of the single-slot SIW applicator.  
Figure 7 shows the distribution of the modulus of the electric field irradiated by the slot in the \(xy\) plane, i.e., at the upper metal layer. The discontinuity between the feeding microstrip line and the SIW tends to confine the electric field near to the slot, as in a slotted resonant-like structure, improving the interaction with the fuel samples.  
The first optimization regards the SIW length \(L_{guide}\). Starting from the preliminary value reported in Table 3, \(L_{guide}=14\) mm, larger values have been simulated until \(L_{guide}=20\) mm, by considering a change step \(\Delta L_{guide}=2\) mm. The extreme of the range \(L_{guide}=20\) mm is arbitrarily fixed to guarantee a high compactness degree.  
The modulus of the scattering parameters \(S_{11}\) and \(S_{21}\) as a function of frequency \(f\) for different values of the SIW length \(L_{guide}\) has exhibited a bandwidth increase and an increased impedance matching at the fixed extreme value \(L_{guide}=20\) mm. The optimization of the radiating slot is performed with the aim of further improving the device operation. Figure 8 shows the 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 \(W_{slot}\). As the slot width becomes smaller, a better impedance matching can be observed. However, the extreme \(W_{slot}=0.2\) mm was arbitrarily fixed to allow a sufficient interaction between measurand background and EM field. Many other optimizations were performed by varying slot length \(L_{slot}\), center-center vias distance \(s\), and vias diameter \(d\), but the performances were worse.