## 2 Design of Antenna
### Antenna Parameterisation Process
From the results in Figure 7, when the width of the radiating element W4 is 14 \(\upmu\)m, the bandwidth is the widest and the reflection coefficient has the lowest value. Therefore, the results of the S-parameter analysis for W4 = 14 \(\upmu\)m are adopted as the width of W4 for the antenna in this paper. Similarly, a parameter analysis is performed on the radiating elements of a \(1\times 2\) Vivaldi, as shown in Figure 9a. In Figure 9b, when W7 = 15 \(\upmu\)m, S11 is below \(-10\) dB at 89.81 GHz, the deepest point being \(-17.16\) dB, and the bandwidth is 89.81-103.49 GHz. When W7 = 10 \(\upmu\)m, S11 is below \(-10\) dB at 87.21 GHz, with the deepest point being \(-20.13\) dB, and the bandwidth is from 87.21 to 102.84 GHz. When W7 = 5 \(\upmu\)m, S11 is below \(-10\) dB at 86.12 GHz, with the deepest point being \(-21.34\) dB, and the bandwidth is 85.47-102.40 GHz. From the results in Figure 8, when the width of the radiating element  
Figure 6: (a) Diagram of W7’s location; (b) S-parameter simulation of W7 with S-parameters. Figure 7: (a) S-parameter simulation (S21) of W7; (b) S-parameter simulation (S31) of W7. \(\mathrm{W}_{7}\) is 5 \(\upmu\)m, the bandwidth is the widest and the return loss has the lowest value. Therefore, the results of the S-parameter analysis for \(\mathrm{W}_{7}\) = 5 \(\upmu\)m are adopted as the width of \(\mathrm{W}_{7}\) for the antenna in this paper. Next, a parameter analysis is conducted on the radiating elements of the 1 \(\times\) 4 Vivaldi antenna, as shown in Figure 10a. In Figure 10b, when \(\mathrm{W}_{5}\) = 22 \(\upmu\)m, S11 remains above \(-\)10 dB for all frequency bands. When \(\mathrm{W}_{5}\) = 18 \(\upmu\)m, S11 is below \(-\)10 dB at 109.85 GHz, with the deepest point \(-\)11.56 dB, and the bandwidth is 109.85-128.92 GHz. When \(\mathrm{W}_{5}\) = 14 \(\upmu\)m, S11 is below \(-\)10 dB at 108.47 GHz, with the deepest point being \(-\)12.51 dB, and the bandwidth is from 108.47 to 128.88 GHz. From the results in Figure 9, when the width of the radiating element \(\mathrm{W}_{5}\) is 14 \(\upmu\)m, the bandwidth is the widest and the return loss has the lowest value. Therefore, the results of the S-parameter analysis for \(\mathrm{W}_{5}\) = 14 \(\upmu\)m are adopted as the width of \(\mathrm{W}_{5}\) for the antenna in this article. Figure 8: (a) Diagram of \(\mathrm{W}_{4}\)’s location; (b) S-parameter simulation of \(\mathrm{W}_{4}\). Figure 9: (a) The diagram of \(\mathrm{W}_{7}\)’s location; (b) S-parameter simulation of \(\mathrm{W}_{7}\). Similarly, a parameter analysis is conducted on the radiating elements of the \(1\times 4\) Vivaldi, as shown in Figure 11a. In Figure 11b, when W\({}_{3}\) = 15 \(\upmu\)m, S11 remains above \(-\)10 dB for all frequency bands. When W\({}_{3}\) = 10 \(\upmu\)m, S11 remains above \(-\)10 dB for all frequency bands. When W\({}_{3}\) = 5 \(\upmu\)m, S11 is below \(-\)10 dB at 80.12 GHz, with the deepest point being \(-\)10.36 dB, and the bandwidth is 80.12-127.56 GHz. From the results in Figure 10, when the width of the radiating element W\({}_{3}\) is 5 \(\upmu\)m, the bandwidth is the widest and the reflection coefficient has the lowest value. Although, when W\({}_{3}\) is 18 \(\upmu\)m, the bandwidth is wider than at 14 \(\upmu\)m, it is not within the designed frequency band for this application. Therefore, the S-parameter of the analysis results for W\({}_{3}\) = 5 \(\upmu\)m are adopted as the width of W\({}_{7}\) for the antenna in this paper. Finally, the Vivaldi antenna array is configured in a 1 \(\times\) 4 format, and a parameter analysis is conducted on the radiating elements, Figure 12a, of the antenna. In Figure 12b, when W\({}_{5}\) = 22 \(\upmu\)m, S11 is below \(-\)10 dB at 88.64 GHz, the deepest point being \(-\)16.91 dB, and the bandwidth is 88.64-102.71 GHz. When W\({}_{5}\) = 18 \(\upmu\)m, S11 is below \(-\)10 dB at 87.02 GHz, the deepest point being \(-\)30.50 dB, and the bandwidth is 87.02-103.28 GHz.