# Influence of Dielectric Plate Parameters on the Reflection Coefficient of a Planar Aperture Antenna
## 2 Analysis of the Parameters of the Dielectric Plate on the Antenna Aperture
### The Thickness and Width \(\times\) Length of the Antenna Aperture Dielectric Plate
#### 2.1.1 Propagation and Reflection of a Plane Wave at the Boundary of Two Mediums
are:  
\[\mathrm{S}_{11}=\frac{E_{\mathrm{r}}}{E_{\mathrm{i}}}=\frac{Z_{\mathrm{c2}}-Z _{\mathrm{c1}}}{Z_{\mathrm{c2}}+Z_{\mathrm{c1}}}=\frac{Z_{\mathrm{c2}}-Z_{ \mathrm{0}}}{Z_{\mathrm{c2}}+Z_{\mathrm{0}}}, \tag{1}\]1  
\[\mathrm{S}_{11}=\frac{E_{\mathrm{r}}}{E_{\mathrm{i}}}=\frac{Z_{\mathrm{c2}}-Z _{\mathrm{c1}}}{Z_{\mathrm{c2}}+Z_{\mathrm{c1}}}=\frac{Z_{\mathrm{c2}}-Z_{ \mathrm{0}}}{Z_{\mathrm{c2}}+Z_{\mathrm{0}}}, \tag{1}\]2  
and for \(z=0\), we have the tangential component of the TE\({}_{11}\) mode electric field at the waveguide aperture (antenna aperture) [15]:  
\[\mathrm{S}_{11}=\frac{E_{\mathrm{r}}}{E_{\mathrm{i}}}=\frac{Z_{\mathrm{c2}}-Z _{\mathrm{c1}}}{Z_{\mathrm{c2}}+Z_{\mathrm{c1}}}=\frac{Z_{\mathrm{c2}}-Z_{ \mathrm{0}}}{Z_{\mathrm{c2}}+Z_{\mathrm{0}}}, \tag{1}\]3  
\[\mathrm{S}_{11}=\frac{E_{\mathrm{r}}}{E_{\mathrm{i}}}=\frac{Z_{\mathrm{c2}}-Z _{\mathrm{c1}}}{Z_{\mathrm{c2}}+Z_{\mathrm{c1}}}=\frac{Z_{\mathrm{c2}}-Z_{ \mathrm{0}}}{Z_{\mathrm{c2}}+Z_{\mathrm{0}}}, \tag{1}\]4  
where \(\mathrm{E}_{0}\) is the amplitude of the electric field; \(\mathrm{J}_{1}\) and \(\mathrm{J}_{1}^{\prime}\) are the Bessel function of the first order and its derivative, respectively; \(x_{11}^{\prime}=1.841\) is the zero point of the derivative of the Bessel function of the first order; \(\rho^{\prime}\leq a\) is a waveguide radius variable; \(\varphi\prime\) is the variable of the azimuthal angle of the waveguide; \(\beta_{w}=\sqrt{\omega^{2}\mu\epsilon-\left(\frac{1841}{a}\right)^{2}}\) is the propagation constant in a circular waveguide; and the label \(\prime=\frac{\partial}{\partial\rho^{\prime}}\) is a partial derivative by the radius variable. The opening of the antenna is usually protected by a dielectric shield (radome), which has the primary role of protecting the antenna from atmospheric influences and damage. Nevertheless, this radome can significantly improve the radiation properties of the antenna by choosing a dielectric that allows for less reflection and better adjustment of the antenna impedance. Mounting radomes on the antenna opening leads to the problem of EM wave propagation through a layered medium. This article has examined a total of three mediums through which an electromagnetic wave is propagated. The first medium refers to the space inside the waveguide of the circular aperture antenna. The second medium is the dielectric plate, and the third medium has the properties of free space. This scenario is illustrated in \[\mathrm{S}_{11}=\frac{E_{\mathrm{r}}}{E_{\mathrm{i}}}=\frac{Z_{\mathrm{c2}}-Z _{\mathrm{c1}}}{Z_{\mathrm{c2}}+Z_{\mathrm{c1}}}=\frac{Z_{\mathrm{c2}}-Z_{ \mathrm{0}}}{Z_{\mathrm{c2}}+Z_{\mathrm{0}}}, \tag{1}\]5 The first and the third medium have the same dielectric properties. Due to the geometry of the problem, in the case of excitation of the antenna aperture with a waveguide, the incident wave arrives at the first boundary at an angle of \(\Theta_{\mathrm{i}}=0^{\circ}\). It can be easily concluded that the other two angles are \(\Theta_{\mathrm{r}}=0^{\circ}\)and \(\Theta_{\mathrm{t}}=0^{\circ}\). In addition to the electromagnetic parameters of the dielectric plate, the analysis will include two aspects related to the dimensions of the dielectric plate itself. These are the thickness of the dielectric plate and the width/length in relation to the grounded plane. The thickness has a significant influence on the values of the S\({}_{11}\) parameter, whereas the width/length of the dielectric plate is about the connection between the majority of the grounded plane and possible diffraction problems. In the remainder of the article, simulation analysis using the HFSS application routine will solve the problems of reflection and transmission, and the emphasis will be placed on determining the minimum of the reflection coefficient S\({}_{11}\) with different parameters of the protective shield (radome).