# 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\({}_{11}\)  
3.2.1. Influence of the Dielectric Plate Relative Permittivity \(\varepsilon_{\rm r}\) on the Reflection Coefficient  
In this study, simulations of the reflection coefficient S\({}_{11}\) for \(\varepsilon_{\rm r}\in\) [1.5, 10] were carried out under the condition that the thickness of the dielectric d is fixed at 11 mm (the best value from the previous subsection). The other dielectric parameters remain as given in Section 3.1.1. The simulation results are presented in Figure 8 and Table 2.  
It can be seen from the simulations that the value of the reflection coefficient S\({}_{11}\) is minimal at the dielectric constant \(\varepsilon_{\rm r}\) = 2.5, which, according to the literature cited above, proves that a material with such dielectric constant value is an excellent choice for the antenna radome. The frequency of the minimum value of the curve S\({}_{11}\)(f) and \(\varepsilon_{\rm r}\) = const, which also corresponds to the resonant frequency of the aperture antenna, increases (it moves to the right towards higher frequencies) with an increase in the permittivity constant. This increase in resonance occurs up to the value of the permittivity 2.5, at which the value of the reflection coefficient S\({}_{11}\) reaches the minimum value of \(-43.43\) dB at the frequency 1.7820 GHz. With a further increase in the permittivity, the value of the resonant frequency decreases, whereas the minimum value of the curve S\({}_{11}\)(f), \(\varepsilon_{\rm r}\) = const, increases. Figure 8: The simulated reflection coefficient S\({}_{11}\) for an aperture antenna with dielectric plate permittivity \(\varepsilon_{\rm r}\in\) [1.5, 3.1]. For those electrical conductivity values for which this condition is not met (from 1.0 \(\times\) 10\({}^{-1}\) to 10 S/m), the electrical conductivity component prevails, and the material is no longer considered a good dielectric. Therefore, the reflection coefficient increases significantly, as expected for a conductive material. Thus, due to moisture in the dielectric material, which causes a change in electrical conductivity of the material, and depending on moisture content, electrical conductivity can cause a significant change in the reflection coefficient S\({}_{11}\). .2.3 Influence of Dielectric Plate Dielectric Losses tan \(\delta\) on the Reflection Coefficient  
The imaginary part of the complex permittivity \(\varepsilon\) is a complex quantity that (Section 2.2) indicates the dissipation in the material. Because the material we analyze is a dielectric that is not perfect, this part of the permittivity over the dielectric and conductive components speaks of losses in the dielectric and conductive part of the material that is in the electric field. In this simulation calculation, the focus is on the dielectric part of the imaginary component of the permittivity. According to [19], the loss tangent ranges up to about 0.09 in the frequency range of 0.5-2.5 GHz. With this tan \(\delta\) range, simulations for S\({}_{11}\) were carried out, and the best value was achieved for tan \(\delta\) = 0.09--Figure 10 (i.e., S\({}_{11}\) = \(-\)43.43 dB). All dielectric parameters were set as in Section 3.1.1, and with the best values achieved in previous simulations. Note: A large number of tan \(\delta\) simulations were performed (very high resolution), but only the most relevant values are listed in Table 5.  
Figure 9: The simulated reflection coefficient S\({}_{11}\) for an aperture antenna with dielectric plate conductivity \(\sigma\in[0,10]\). 3.2.4. Influence of Dielectric Plate Relative Permeability \(\upmu_{\pi}\) and Magnetic Loss Tangent \(\delta_{\mu}\) on the Reflection Coefficient  
Because only dielectrics are used as protective shields for antennas, the analysis includes materials with a value of relative permeability of approximately 1.