# Low-Profile Dual-Band Reflector Antenna for High-Frequency Applications
## 2 Antenna Configuration and Design
### Element of Lower-Band SRA  
Due to the small diameter of the SRA, a subwavelength element is employed as the element of the SRA. It can more accurately achieve phase compensation than a half-wavelength element in such a small area. The SRA element consists of a cross patch and a rectangular loop [28], as shown in Figure 7. In addition, the size length of the square element is \(L=0.23\lambda_{l}\), where \(\lambda_{l}\) is the free-space wavelength at \(f_{l}\). The element is etched on a 0.077\(\lambda_{l}\) thick dielectric substrate with a relative permittivity of 2.2, and a dielectric loss tangent of 0.0009. The reflection phase curves consider different polarizations of the incident wave. The infinite periodic element model is built to simulate the reflection phase at \(f_{l}\). Moreover, another important consideration in the element analysis is the reflection phase under oblique incidences, as shown in Figure 7. Based on the relative position between the SRA and the lower-band feed, the maximum incident angle is about 50\({}^{\circ}\). Then, a max phase range over of 430\({}^{\circ}\) is obtained under different incident angles. It can be seen that the reflection phase of the SRA element varies with the incident angle, and the maximum phase change within the oblique incidence range of 0\({}^{\circ}\) to 50\({}^{\circ}\) is approximately 80\({}^{\circ}\). The range of the desired compensation phase is from 0\({}^{\circ}\) to 950\({}^{\circ}\) according to Formula (1). It is difficult for the SRA element to achieve such a wide compensation phase range from 0\({}^{\circ}\) to 950\({}^{\circ}\). Thus, a modified formula is proposed to calculate the desired compensation phase for each element on the SRA aperture:  
\[phase_{mn}^{desired}=mod(kR_{1 mn}+kR_{2 mn}+\Delta\Phi,430) \tag{2}\] \begin{table}
\begin{tabular}{c c} \hline \hline
**Factors** & **Gain (Efficiency)** \\ \hline Maximum directivity (dB) & 47.66 (100\%) \\ Feed mismatch loss (dB) & 0.066 (98.5\%) \\ Dielectric loss (dB) & 0.97 (78.8\%) \\ Spillover loss (dB) & 0.97 (63.0\%) \\ Taper loss (dB) & 1.10 (48.5\%) \\ Shade loss (dB) & 0.50 (43.2\%) \\ Calculated gain (dB) & 43.85 (43.2\%) \\ Simulated gain (dB) & 44.0 (42.9\%) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Loss budgets and aperture efficiency at \(f_{h}\). Figure 7: Reflection phase of the element under oblique incidences at \(f_{l}\). To reduce the zones of sharp phase variation, the desired compensation phase is divided by 430, as the maximum phase range over is over 430\({}^{\circ}\). Moreover, the \(\Delta\Phi\) is a constant reference phase that can optimize the desired compensation phase in the SRA. The desired compensation phase, as shown in Figure 8a and represented by Formula (2), occurs when \(\Delta\Phi\) is 170\({}^{\circ}\). A large phase variation from 400\({}^{\circ}\) to 50\({}^{\circ}\) is observed in the middle of the SRA, as illustrated in Figure 8a. This sharp phase variation, approximately 350\({}^{\circ}\) between adjacent elements in the middle of the SRA, results in a significant change in the geometrical parameters between adjacent elements. Due to this abrupt variation in the geometrical parameters of adjacent elements, the local periodicity assumption for the elements is not satisfied, which in turn affects the phase shift performance of the elements within the area of sharp variation. Even worse, the area of sharp variation is located in the middle of the SRA, where the energy illuminated from the composite feed is at its strongest. Most of the energy reflected by the SRA is not compensated for the desired phase. Thus, the sharp phase variation arising in the middle of the SRA will lead to a degenerated radiation performance. As shown in Figure 8b, the radiation patterns at \(f_{\rm{i}}\) show a gain lower than 26 dBi, corresponding to an antenna aperture efficiency lower than 17%. Additionally, the degenerate radiation patterns exhibit high sidelobes.