# High-Gain Waveguide-Fed Circularly Polarized Spidron Fractal Aperture Antenna
## 2 Antenna Design
### Design of the High-Gain Rectangular Waveguide-Fed CP Spidron Fractal Aperture Antenna  
In this section, we present the design of a rectangular waveguide-fed CP Spidron fractal aperture antenna incorporated with a superstrate to achieve high gain performance. The operating principle of the superstrate with regard to gain enhancement can be briefly explained by considering the multiple reflections between the superstrate and the ground plane with the source, as shown in Figure 4. Assume that electromagnetic waves are emitted from the source at an incident angle of \(\theta\); according to the ray tracking model [16; 17], the phase difference \(\Delta\phi\) between two adjacent transmitted rays can be calculated as  
\[\Delta\phi=\phi_{S}-\frac{2\pi\cdot 2S}{\lambda\cos(\theta)}+\phi_{GND}-(- \frac{2\pi}{\lambda}\cdot 2S\cdot\tan(\theta)\sin(\theta)) \tag{1}\]  
where \(\lambda\) is the wavelength in free space at the designed frequency; \(\phi_{S}\) and \(\phi_{GND}\) are the reflection phases of the superstrate and the ground plane, respectively; and \(S\) is the spacing between the superstrate and the ground plane.  
To realize high gain in the \(\theta\) direction, all transmitted rays should be in-phase, meaning that the phase difference \(\Delta\phi\) between two adjacent rays should be an integral multiple of \(2\pi\). For most practical applications, antennas are required to have maximum gain at \(\theta\) = 0\({}^{\circ}\). Therefore, the distance \(S\) should satisfy the following condition:  
\[S=\frac{\lambda}{4\pi}(\phi_{S}+\phi_{GND})+\frac{n\lambda}{2},n=0,1,2... \tag{2}\]  
where \(n\) is usually set to 0 to realize a low-profile antenna.  
Figure 3: Simulated magnetic current distributions of the Spidron fractal aperture at 11.1 GHz: (**a**) \(t\) = 0; (**b**) \(t\) = \(T/4\).  
The reflection phase \(\phi_{GND}\) of the ground plane is a constant of \(\pi\). The reflection phase \(\phi_{S}\) of the superstrate can be determined through the superstrate reflection model (SRM) [18]. The modeled unit cell of the superstrate is illustrated in Figure 5a, which is surrounded by four periodic boundaries (PBCs). Two ports are located above and below the unit cell. The reflection phase of the superstrate is extracted. As observed in Figure 5b, which plots the simulated reflection phase of the superstrate, the reflection phase \(\phi_{S}\) varies with the frequency, and its value at the designed frequency of 11.1 GHz is approximately 233\({}^{\circ}\). The distance \(S\) is then computed using Equation (2), with the resulting calculated value being approximately 15.5 mm.  
The effect of the superstrate on the antenna performance was investigated. Figure 6 shows a comparison of the reflection coefficients, AR values, and the realized gains of Antenna-3 (without a superstrate) and the proposed antenna (Antenna-3 with a superstrate). As observed from Figure 6a,b, CP operation is shifted toward the lower frequency range due to the presence of the superstrate above the antenna. The proposed antenna has a \(-10\) dB reflection bandwidth of 9.86-10.63 GHz and a 3 dB AR bandwidth of 10.74-11.08 GHz with a minimum AR value of 0.42 dB at 10.9 GHz. Within the 3 dB AR bandwidth, the RHCP gain of the proposed antenna varies from 9.06 to 9.85 dBic (see Figure 6c). Meanwhile, without the superstrate, Antenna-3 has relatively low RHCP gains that range from 3.66 to 3.84 dBic. A gain enhancement of more than 5.4 dBic is obtained when the superstrate is applied to the antenna.  
Figure 4: Multiple reflections between the superstrate and the ground plane.  
Figure 5: (**a**) Simulation model of the unit cell; (**b**) reflection phase of the superstrate.