## 2 Design of Antenna
### Antenna Design  
The progression of the antenna design process is clearly illustrated, as shown in Figure 3a. The antenna (Type 1) is the original symmetric Vivaldi antenna, utilising a rectangular and 50 \(\Omega\) feedline. For the antenna (Type 2), a small elliptical cut is employed in the feed-in position of the antenna. The antenna (Type 3) incorporates elliptical arc-shaped structures to cut the antenna (Type 2), while the antenna (Type 4) is composed of approximately 1/4 elliptical structures for cutting. Both antennas are proposed in this paper. Figure 3b shows a stacked plot comparison of the reflection coefficient during the Vivaldi evolution. The antenna (Type 1) is analysed using a rectangular shape. When the rectangular dimensions are 275 \(\times\) 210 \(\upmu\)m, from the analysis graph, it can be observed that at a frequency of 80.42 GHz, the return loss is below \(-10\) dB. The usable frequency range is 80.42-95.63 GHz. At a frequency of 88 GHz, the deepest point of the return loss is \(-26.144\) dB. The overall bandwidth where the return loss is below \(-10\) dB is 15.21 GHz. A small elliptical cut, with a radius of 125 \(\upmu\)m, is utilised from the feed-in point to enhance the antenna bandwidth (Type 2). Following this modification, the simulations are carried out.  
From the analysis graph of the simulation results, it can be observed that at a frequency of 81.61 GHz, the return loss is below \(-10\) dB. This represents an increase of 2.21 GHz compared to the rectangular shape. Furthermore, the maximum frequency value has increased from 95.63 to 98.69 GHz. The usable frequency range is from 82.63 to 98.69 GHz, which is an increase of 0.85 GHz in bandwidth compared to before the cut. At a frequency of 91 GHz, the deepest point of the return loss is \(-20.98\) dB. The overall bandwidth where the return loss is below \(-10\) dB is 16.06 GHz. The antenna (Type 3) involves cutting antenna (Type 2) with arc-shaped elliptical structures, followed by simulations. From the analysis  
Figure 2: S-parameters of the Vivaldi antenna.  
graph of the simulation results, it can be observed that at a frequency of 82.67 GHz, the return loss is below \(-10\) dB. This represents an increase of 1.03 GHz compared to the rectangular shape. Additionally, the maximum frequency value has increased from 98.69 to 100.36 GHz. The usable frequency range is from 83.67 to 100.36 GHz, which is an increase of 0.63 GHz in bandwidth compared to before the cut. At a frequency of 93 GHz, the deepest point of the return loss is \(-26.12\) dB. The overall bandwidth where the return loss is below \(-10\) dB is 16.69 GHz. The antenna (Type 4), which is the antenna structure proposed in this paper, is composed of approximately 1/4 elliptical structures with a radius of 325 \(\upmu\)m. After the cut, the simulations are conducted. From the analysis graph of the simulation results, it can be observed that at a frequency of 85.47 GHz, the return loss is below \(-10\) dB. The maximum frequency value has increased from 100.36 to 102.36 GHz, resulting in an additional bandwidth of 2 GHz compared to before the cut. The usable frequency range is from 85.47 to 102.36 GHz. The area is smaller than before the cut, and the bandwidth is wider. At a frequency of 95.5 GHz, the deepest point of the return loss is \(-23.60\) dB. The overall bandwidth where the return loss is below \(-10\) dB is 16.89 GHz.