# Circularly Polarized Vivaldi Antennas Integrated with Septum-like Polarizer
## 2 Materials and Methods
### Performance Optimization Using Genetic Algorithm  
To easily optimize the performance of the proposed CP Vivaldi antenna, a genetic algorithm (GA) within the HFSS full-wave simulation is used. Figure 4 schematizes the entire process of GA optimization. Firstly, we designate the parameters that most affect its performance as variables. Ten variables are specified for the optimization: PS, PD\({}_{1}\), PW\({}_{1}\), PD\({}_{\text{add}}\), PW\({}_{\text{add}}\), SSP, SW\({}_{1}\), SW\({}_{2}\), \(\varphi_{1}\), and \(\varphi_{2}\). The center frequency of the proposed CP Vivaldi antenna is set to be 11 GHz, and the GA cost function is defined as follows with the AR values in the range 10.4-11.6 GHz at 300 MHz intervals:  
\[\begin{split}\text{Cost Function}&=\text{AR}(\text {at 10.4 GHz})^{2}+\text{AR}(\text{at 10.7 GHz})^{2}+\text{AR}(\text{at 11 GHz})^{2}\\ &\quad+\text{AR}(\text{at 11.3 GHz})^{2}\\ &\quad+\text{AR}(\text{at 11.6 GHz})^{2}.\end{split} \tag{4}\]  
And then, we create the initial population and evaluate the new cost function. Next, we evaluate the cost function by the population created through the process of selection, crossover, and mutation. If the new cost function is greater than the cost function by the previous population, repeat the GA loop. If the new cost function satisfies the termination condition (i.e., the cost function is close to 0), finish the GA optimization. The GA settings within HFSS are specified as follows: number of individuals = 30, number of survivors = 10, and Roulette selection pressure = 10. Because Vivaldi antennas already have secured broadband impedance matching, only ARs are included in the cost function. The optimal design corresponds to the case with the smallest cost function value. After performing approximately 2200 simulations, the lowest cost function value was obtained as 36, which is considered the optimal design. Table 1 lists the parameters of the optimized CP Vivaldi antenna.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameters** & **Dimension** & **Parameters** & **Dimension** \\ \hline PS & 9 mm & SSP & 85 mm \\ PD\({}_{1}\) & 1.29 mm & SW\({}_{1}\) & 1.9 mm \\ PW\({}_{1}\) & 2.34 mm & SW\({}_{2}\) & 2.09 mm \\ PD\({}_{\text{add}}\) & 0.11 mm & \(\varphi_{1}\) & 60\({}^{\circ}\) \\ PW\({}_{\text{add}}\) & 0.13 mm & \(\varphi_{2}\) & 68.9\({}^{\circ}\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Optimal parameters through using the genetic algorithm of the full-wave simulation tool, HFSS.  
Figure 4: Schematic of the GA optimization process.  
Figure 5 shows the reflection coefficient, AR, co- and cross-polarized gain of a CP Vivaldi with dual ports. The reflection coefficients S\({}_{11}\) and S\({}_{22}\) are maintained below \(-10\) dB over a wide bandwidth. The 3 dB AR bandwidth is 1.14 GHz (=10.3%) for RHCP and 1.03 GHz (=9.6%) for LHCP, the peak gain is 9.1 dB for RHCP and 8.7 dB for LHCP, and the \(-1\) dB gain bandwidth is 1.35 GHz (=12.3%) for RHCP and 1.1 GHz (=10.1%) for LHCP, respectively. In addition, flat gain characteristics are observed in a wide band. The stable directional radiation pattern for 10.4-11.6 GHz is also confirmed as shown in Figure 6. Therefore, the design concept of the proposed CP Vivaldi antenna with a pulse train-shaped polarizer is verified for operation in RHCP and LHCP modes in broadband.  
Figure 5: Performance of the proposed CP Vivaldi antenna with ideal two ports. (**a**) Reflection coefficient, (**b**) axial ratio, (**c**) boresight gain for RHCP, and (**d**) boresight gain for LHCP.  
Figure 6: Co-polarized radiation patterns of the proposed CP Vivaldi antenna with ideal two ports: (**a**) RHCP mode & \(xz\) plane, (**b**) RHCP mode & \(yz\) plane, (**c**) LHCP mode & \(xz\) plane, and (**d**) LHCP mode & \(yz\) plane.