# Low-Profile Dual-Band Reflector Antenna for High-Frequency Applications
## 2 Antenna Configuration and Design  
### Main Reflector, SRA, and Higher-Band SR  
The configuration of the low-profile dual-band reflector antenna is shown in Figure 1. It consists of a main reflector, a composite feed, an SRA, and a higher-band SR. In detail, the main reflector, which is a ring-focus reflector, is shaped by rotating the curve along the ring-focus curve. The diameter of the main reflector is \(78.5\lambda_{h}\), where \(\lambda_{h}\) is the free-space wavelength at the higher frequency \(f_{h}\). Additionally, the composite feed, with the \(f_{h}/f_{l}\) ratio around 5, consists of a higher-band coaxial horn and a lower-band ring focus. Furthermore, the lower-band ring-focus SRA is a small reflectarray and designed by employing the rules mentioned in [28], while the higher-band SR is a metallic curving SR and formed by rotating the ellipse curve along the Z axis. Moreover, a metal clad layer serves as the SR in the higher band, which is attached to the top surface of the higher-band subreflector. The material of the substrates in the antenna is employed with a relative permittivity of 2.2 and a dielectric loss tangent of 0.01. The cross section of the geometry is illustrated in Figure 2. The point F\({}_{1}\) under SR is not only the phase center of the ring-focus main reflector but also one of the focal points for both lower-band and higher-band rays. The point F\({}_{2}\) is the phase center of the lower-band feed and the other focal point for lower-band rays. The phase center of the higher-band feed coincides with the other focus of the SR, as represented by the point F\({}_{3}\), which is located on the symmetry axis of the SR. Figure 2 shows the sketch of ray paths in both bands. Different SRs are designed separately to achieve dual-band operation ability and the SR designs, for both bands, are demonstrated as follows:  
1. According to the geometric optics (GO) theory, lower-band rays emerging from the point F\({}_{2}\) are first reflected by the SRA. Then, the rays reach the main reflector. Finally, the rays are reflected into the airspace along the Z axis. The dashed line in Figure 2 represents the virtual ray path from the SRA to the focal point F\({}_{1}\), which the ray does not actually pass through. The SR can provide the compensation phase for lower-band rays and, as a result, the virtual rays arriving at focal point F\({}_{1}\) are in phase. Based on the different lengths of lower-band ray paths, the desired compensation phase for SRA elements in various locations can be calculated. According to the GO theory analysis, the desired compensation phase for each element on the SRA aperture can be calculated by  
\[phase_{mn}^{desired}=kR_{1 mn}+kR_{2 mn} \tag{1}\]  
where \(k\) is the wavenumber in free space, and the spatial distance between the point F\({}_{2}\) and the \(mn\)th element of SRA is represented by \(R_{1 mm}\). Moreover, the distance between the point F\({}_{1}\) and the \(mn\)th element of SRA is represented by \(R_{2 mn}\). The SRA is a symmetric construction, and the distance between the center of the SRA and F\({}_{2}\) is 6.02\(\lambda_{h}\). The distance between F\({}_{1}\) and the surface of the SRA is 1.57\(\lambda_{h}\). Moreover, the diameter of the SRA is 15.7\(\lambda_{h}\), which is a compromise between the smaller blockage of the SRA and the reduced spillover loss of the lower-band feed. 2. Based on the GO theory, higher-band rays that emerge at point F\({}_{3}\) are first reflected by the SR. Then, these higher-band rays pass through point F\({}_{1}\) and reach the main reflector. Finally, the higher-band rays are reflected into the airspace. Here, \(D_{5}\) is the diameter of the SR. \(\theta_{m}\) is the semi-flare angle of the dielectric guide and \(F\) is the focal length of the main reflector. According to these three parameters and \(D\), the curve equations of the main reflector and SR are uniquely determined. Figure 1: Configuration of the low-profile dual-band reflector antenna.