# Influence of Dielectric Plate Parameters on the Reflection Coefficient of a Planar Aperture Antenna
## 3 Numerical Results
### The Influence of the Structural-Geometric Parameters of the Dielectric on \(S_{11}\)
#### 3.1.1 Influence of Dielectric Plate Thickness d on the Reflection Coefficient  
In this subsection, the focus is on the influence of the change in the thickness of the dielectric layer d on the reflection coefficient S\({}_{11}\) at the opening of the waveguide. The thickness d ranges from d = 0 mm to d = 13 mm, assuming all other parameters: \(\varepsilon_{\rm r}\) = 2.5, \(\mu_{\rm r}\) = 1, \(\sigma\) = 0 S/m, tg \(\delta\) = 0.09, tg \(\delta_{\rm\mu}\) = 0. Some values of these parameters were carefully selected according to [11; 17; 18].  
The simulation results show that the amplitude of the reflection coefficient S\({}_{11}\) decreases with increasing dielectric plate thickness d, namely from \(-\)12.57 dB (d = 0 mm) to \(-\)43.43 dB (d = 11 mm). After that, for dielectric plate thickness of 13 mm, the value of the reflection coefficient increases (\(-\)27.10 dB). This is consistent with the theoretical considerations in Section 2 and the minimum absolute value of the parameter S\({}_{11}\) (between 1 and 2 GHz) shown in Figure 2b. It can be seen that the resonant frequency increases (shifts to the right) with increasing dielectric plate thickness at the antenna aperture. After reaching dielectric plate thickness of about 11 mm (and the minimum value of parameter S\({}_{11}\)), the resonant frequency decreases with increasing dielectric plate thickness. The reason for this is that the reflected waves from the first (air-dielectric plate) and the second (dielectric plate-air) boundary at this thickness (about 11 mm) are in destructive interference, resulting in the minimum value of the reflection coefficient S\({}_{11}\). Figure 7 and Table 1 show the change in the reflection coefficient as a function of the change in the thickness of the dielectric d. The minimum values of the coefficient S\({}_{11}\) for certain values of d are listed in Table 1 together with the associated frequency f.  
\begin{table}
\begin{tabular}{c c c} \hline
**d, mm** & **f, GHz** & **S\({}_{11}\), dB** \\ \hline
0 & 1.7011 & \(-\)12.57 \\
1 & 1.7213 & \(-\)12.60 \\
3 & 1.7550 & \(-\)13.19 \\
5 & 1.7753 & \(-\)15.21 \\
7 & 1.7820 & \(-\)19.81 \\
9 & 1.7820 & \(-\)25.68 \\
11 (0.67 \(\lambda\)) & 1.7820 & \(-\)43.43 \\
13 & 1.7753 & \(-\)27.10 \\ \hline \end{tabular}
\end{table}
Table 1: Simulated values of S\({}_{11}\) for different dielectric plate thickness d.  
Figure 7: The simulated reflection coefficient S\({}_{11}\) for an aperture antenna with plate width in the range of d = 1–13 mm.  
3.1.2. Influence of the Dielectric Plate Dimension h\({}_{1}\times\) h\({}_{2}\) (Width \(\times\) Length) on the Reflection Coefficient and the Radiation Pattern of the Antenna Opening  
First, it is necessary to point out that simulation calculations of the reflection coefficient S\({}_{11}\) were performed to change the dimensions of the dielectric plate h\({}_{1}\times\) h\({}_{2}\) by \(\pm\)20%, which resulted in negligible changes in the reflection coefficient S\({}_{11}\).  
3.1.3. Influence of Dielectric Plate Density \(\rho\) on the Reflection Coefficient  
The structural parameters of the dielectric covering the antenna include, as already mentioned, the density of paper \(\rho\) in kg\(\cdot\)m\({}^{-3}\). The calculations showed a constant value of the reflection coefficient S\({}_{11}=-43.43\) dB (f = 1.7820 GHz) for \(\rho\in\) [500, 1800] kg\(\cdot\)m\({}^{-3}\). Therefore, for all further simulations of the reflection coefficient according to [19], it is assumed that \(\rho\) = 1200 kg\(\cdot\)m\({}^{-3}\).