# Bandwidth-Enhanced Circularly Polarized Crescent-Shaped Slot Antenna via Circular-Patch Loading
## 2 Antenna Design and Parametric Studies
### Parametric Studies  
Figure 2 presents a comparison of the reflection coefficients and AR performance capabilities of the antenna with circular patch loading (the proposed antenna) and an antenna without circular patch loading (reference antenna). Note that, for a fair comparison, a reference antenna identical in size to the proposed antenna was also optimized to attain good CP behavior. Thus, the geometrical parameters of the reference antenna are slightly different from those of the proposed antenna; they are as follows: \(g_{w}=50.8\) mm, \(R=24\) mm, \(r_{2}=10\) mm, \(r_{3}=10\) mm, \(w_{f}=1.12\) mm, \(l_{f}=2.36\) mm, \(l_{1}=1\) mm, \(l_{2}=4.3\) mm, \(l_{3}=15.5\) mm, \(w_{1}=6.12\), \(w_{2}=21.45\) mm, \(w_{3}=36.125\) mm, and \(w_{4}=8\) mm. As shown in Figure 2, the antenna without circular patch loading had a 3 dB AR bandwidth of 2.83-3.18 GHz (11.65%), which was enclosed within a \(-10\) dB reflection bandwidth of 2.61-4.90 GHz (60.99%). In contrast, by loading with the circular patch inside the crescent-shaped slot, both the reflection and 3 dB AR bandwidths were significantly broadened, resulting in a broad \(-10\) dB reflection bandwidth of 1.80-4.81 GHz (91.07%), and a broad 3 dB bandwidth of 1.80-4.52 GHz (86.08%). An increase of approximately 7.4 times in the 3 dB AR bandwidth was achieved by circular-patch loading. Figure 1: Proposed antenna configuration. Figure 2: Performance of the antennas with and without circular patch loading: (**a**) reflection coefficients; (**b**) Axial Ratios (ARs). The position of circular-patch loading \(O_{1}\) in the crescent-shaped slot was also investigated to find its effect on the reflection coefficient and AR performance outcomes. Simulated results are plotted in Figure 3. When the circular patch was located at the center (\(s_{x}=0\) mm, \(s_{y}=0\) mm), a 3 dB AR bandwidth of 1.92-3.24 GHz (51.16%) was attained. By moving the circular patch along the \(-x\)-axis (\(s_{x}=4\) mm, \(s_{y}=0\) mm), the 3 dB AR bandwidth was shifted toward the upper frequency range, and the \(-10\) dB reflection bandwidth was improved. When the circular patch was moved along the \(-y\)-axis (\(s_{x}=0\) mm, \(s_{y}=4\) mm), the \(-10\) dB reflection bandwidth was shifted downward in the lower frequency range, and the 3 dB AR bandwidth was enhanced. The optimal position of the circular patch is offset from the center along both the \(-x\)- and \(-y\)-axes (\(s_{x}=4\) mm, \(s_{y}=4\) mm), showing the widest 3 dB AR bandwidth entirely enclosed within the \(|S_{11}|<-10\) dB bandwidth. Figure 4 shows the impact of radius \(r_{1}\) of circular patch loading \(O_{1}\) on the reflection coefficients and AR performance capabilities. This figure shows that the \(-10\) dB reflection bandwidth tends to reduce with the decrease in \(r_{1}\). In contrast, 3 dB AR bandwidth is enhanced as \(r_{1}\) decreases. According to this analysis, the best value of \(r_{1}\) was finally set to 10.63 mm to achieve the widest overlapping bandwidth. Figure 4: Effect of radius \(r_{1}\) of circular patch loading \(O_{1}\) on antenna performance: (**a**) reflection coefficients; (**b**) ARs. Figure 3: Effect of the position of circular patch loading \(O_{1}\) on antenna performance: (**a**) reflection coefficients; (**b**) ARs. To visualize how CP radiation is realized, time-varying magnetic-current distribution concentrations in the slot were investigated. Figure 5 displays the magnetic-current distributions at 2.1 and 3.5 GHz, respectively, as observed from the \(+z\)-direction. Note that \(M\) indicates the vector sum of all component vectors. As shown in Figure 5a, at \(t=0\), vector \(M\) is oriented from the upper-right corner to the lower-left corner. At \(t=T/4\), vector \(M\) is directed from the lower-right corner to the upper-left corner. This vector is perpendicular to that at \(t=0\). In addition, these vectors revolve clockwise as time \(t\) changes.