# Influence of Dielectric Plate Parameters on the Reflection Coefficient of a Planar Aperture Antenna
## 3 Numerical Results
### The Influence of the Electromagnetic Parameters of the Dielectric on S\({}_{11}\)
Because the antenna is protected by dielectric materials (diamagnetic), all simulation calculations were performed for a material that has the complex permeability \(\upmu=\upmu^{\prime}-\upmu^{\prime\prime}=\upmu_{0}1-\upmu 0\) (relative permeability is equal to 1, and plate magnetic loss tangent \(\tan\delta_{\mu}=0\)). Simulation calculations were performed for changes in the real and the imaginary part of permeability (\(\upmu_{\pi}\) ranging from 0.9 to 1.1, and \(\tan\delta_{\mu}\) ranging from 0 to 2), and they showed that a deviation from the defined values \(\upmu_{\pi}=1\) and \(\tan\delta_{\mu}=0\) significantly degrades the value of the reflection coefficient S\({}_{11}\). Simulation Calculation of the Radiation Pattern of a Circular Aperture Antenna with a Dielectric Plate  
The effects of changes in the structural and electromagnetic parameters of the plate on the reflection coefficient of the aperture antenna with dielectric plate have been analyzed in previous subsections. It is necessary to determine whether changing the parameters of the dielectric plate while improving the reflection coefficient of the antenna distorts the radiation pattern of the antenna. Therefore, the simulation calculation results of the  
Figure 10: The simulated reflection coefficient S\({}_{11}\) for an aperture antenna with dielectric plate tan \(\delta\in[0.01,0.09]\). \begin{table}
\begin{tabular}{c c c} \hline \hline
**tg \(\delta\)** & **f, GHz** & **S\({}_{11}\), dB** \\ \hline
0.010 & 1.7887 & \(-\)41.48 \\
0.030 & 1.7887 & \(-\)41.48 \\
0.050 & 1.7887 & \(-\)34.41 \\
0.060 & 1.7820 & \(-\)35.19 \\
0.070 & 1.7820 & \(-\)39.01 \\
0.090 & 1.7820 & \(-\)43.43 \\
0.098 & 1.7820 & \(-\)41.48 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Calculated values of S\({}_{11}\) for different dielectric plate dielectric loss tg \(\delta\). influence of the change in the dielectric plate parameters on the radiation pattern of the aperture antenna are analyzed in this subsection. If we compare the radiation patterns of the aperture antenna with and without the dielectric plate (d = 0 and d = 11 mm for the same dimension of the dielectric material and the plane in Figure 11) with the previously defined best values of the dielectric plate parameters (i.e., the thickness d = 11 mm, \(\epsilon_{\rm r}\) = 2.5, \(\mu_{\rm r}\) = 1, \(\sigma\) = 0 S/m, tg \(\delta\) = 0.09, tg \(\delta_{\rm\mu}\) = 0, h\({}_{1}\)\(\times\) h\({}_{2}\) = 423 \(\times\) 450 mm\({}^{2}\), \(\rho\) = 1200 kg\(\cdot\)m\({}^{-3}\)), it can be concluded that there are some changes in the radiation diagram. The largest deviations of \(-\)2.5 dB at \(\pm\)25\({}^{\circ}\) (side lobes) and +5.0 dB at 158\({}^{\circ}\) (back lobe) can be seen in the \(H\) plane and +9.0 dB at 165\({}^{\circ}\) (back lobes) in the \(E\) plane, whereas deviations are negligible in the rest of the range of angles in both planes (\(E\) and \(H\) planes). Furthermore, a variation in the width and length of the dielectric plate, which ranges from \(\pm\)20% of the full size of the grounded plane (dimensions of the grounded plane are h\({}_{1}\)\(\times\) h\({}_{2}\) = 423 \(\times\) 450 mm\({}^{2}\)), does not result in significant changes in the radiation pattern compared to the dielectric plate with dimension h\({}_{1}\)\(\times\) h\({}_{2}\) = 423 \(\times\) 450 mm\({}^{2}\) (Figure 11). The largest deviations of +4.5 dB at \(\pm\)158\({}^{\circ}\) (back lobes) can be seen in the \(H\) plane, and +6.0 dB at 117 and 168\({}^{\circ}\) (back lobe) in the \(E\) plane, whereas deviations are negligible in the rest of the range of angles in both planes (\(E\) and \(H\) planes).