## 2 Antenna Design and Optimization
### Parametric Analysis
#### 2.2.1 Dual-Band Response  
Two essential parameters were identified: the diameter of the centered circular cut (D) and the dimensions of the centered rectangular cut, namely its length (LH_cut) and width (WH_cut). Comprehensive simulation studies indicated that the optimal diameter for the centered circular cut (D) should be 9 mm, which is an improvement over the 8 mm used in Antenna 1 and the 10 mm in Antenna 2. Furthermore, the length of the centered rectangular cut (LH_cut) was optimized to 25.8 mm, compared to 24.8 mm in Antenna 1 and 26.8 mm in Antenna 2. The width of the centered rectangular cut (WH_cut) was refined to 3.5 mm, compared to 2.5 mm in Antenna 1 and 4.5 mm in Antenna 2. These adjustments collectively enhance the antenna's performance in achieving the desired response within the operating bands. Changing the Parameter Element D  
As illustrated in Figure 5, the design was simulated using various parametric values for (D), which denotes the diameter of the centered circular cut. It was noted that the response at 5 GHz varies significantly with alterations to this parameter. Specifically, when (D) is set to 9 mm, the response achieves optimal tuning. Further simulations indicated that reducing (D) to values below 9 mm resulted in a substantial leftward shift in the response. Conversely, increasing (D) beyond 9 mm caused the response to drop below 10 dB, adversely affecting the antenna's overall efficiency. These observations highlight the critical role of precisely adjusting the diameter of the centered circular cut during the design process, as it not only impacts the response but also influences the overall performance  
Figure 4: Axial ratio versus frequency of the three antennas given in Figure 1.  
of the antenna. By systematically optimizing (D) alongside other parameters, the design attains a robust configuration that effectively facilitates dual-band operation. Changing the Parameter Element LH_cut  
As depicted in Figure 6, the design was simulated using various parametric values for (LH_cut), which indicates the length of the centered rectangular cut. It was found that the response at 2.4 GHz varies significantly with changes to this parameter. Specifically, when (LH_cut) is set to 25.8 mm, the response achieves optimal tuning. Further simulations revealed that reducing (LH_cut) to values below 25.8 mm caused both bands to shift rightward, introducing a new response at 3.83 GHz. Similarly, increasing (LH_cut) beyond 25.8 mm resulted in a minor shift and the emergence of a new response in the middle, which negatively affected the antenna's overall efficiency. These results highlight the importance of meticulously adjusting the length of the centered rectangular cut during the design process, as it not only impacts the response but also has a cascading effect on the antenna's overall performance. By systematically optimizing (LH_cut) along with other parameters, the design achieves a robust configuration that effectively supports dual-band operation. Changing the Parameter Element WH_cut  
As depicted in Figure 7, the design was simulated with various values for (WH_cut), which denotes the width of the centered rectangular cut. It was found that the response at 2.4 GHz varies significantly with changes to this parameter. Specifically, when (WH_cut) is set to 3.5 mm, the response is optimally tuned. Further simulations indicated that reducing  
Figure 5: Return loss of the parameter D.  
Figure 6: Return loss of the parameter LH_cut. (WH_cut) to below 3.5 mm caused both bands to shift slightly to the right. On the other hand, increasing (WH_cut) beyond 3.5 mm negatively affected the response at 5 GHz, which in turn reduced the antenna's overall efficiency. These findings emphasize the necessity of carefully adjusting the width of the centered rectangular cut in the design process, as it influences the response and has a cascading effect on the antenna's performance.