# Simple Compact UWB Vivaldi Antenna Arrays for Breast Cancer Detection
## 2 The Proposed Antenna Design
### Simple Compact 2 \(\times\) 1 UWB Linear VTSA Array (Array 1)
Figure 6b illustrates that the best obtained S\({}_{11}\) is at \(L_{T}=26.3\) mm (S\({}_{11}<-10.11\) dB at 2.507-10.414 GHz and MG = 8.94 dBi), which is better than at the optimized value for the single element, \(L_{T}=25\) mm (S\({}_{11}<-8.98\) dB at 2.62-10.483 GHz MG = 8.4 dBi). Since \(r\) and \(L_{T}\) in the array are higher than that of the single element, the value of \(W_{max}\) is increased to 27.46 mm, which also will enhance the antenna gain [34]. As shown in Figure 6c, the best impedance matching is achieved at \(L_{quv}=5.5\) mm (S\({}_{11}<-10.11\) dB at 2.507-10.414 GHz and MG = 8.94 dBi), which is better than that at the optimized value for the single element, \(L_{quv}=5.7\) mm (S\({}_{11}<-9.84\) dB). As illustrated in Figure 6d, \(W_{min}=0.34\) mm (S\({}_{11}<-10.11\) dB at 2.507-10.414 GHz and MG = 8.94 dBi) gives the best impedance matching and highest gain (related to \(W_{max}\)), which is better than that at the optimized value for the single element, \(W_{min}=0.3\) mm (S\({}_{11}<-9.57\) dB at 2.62-10.38 GHz and MG = 8.72 dBi). Figure 6e shows that as _radsl_ increases, the BW decreases, and the gain increases. However, the best S\({}_{11}\) is obtained at _radsl_ = 2.35 mm (S\({}_{11}<-10.11\) dB at 2.507-10.414 GHz and MG = 8.94 dBi), which is better than that at the optimized value for the single element, i.e., at _radsl_ = 1.89 mm (S\({}_{11}<-7.96\) dB). Although at _radsl_ = 2.58 mm (S\({}_{11}<-10\) dB at 3.03-10.419 GHz and MG = 8.96 dBi), the gain is 0.78% higher, _radsl_ = 2.35 mm is selected because of its improved impedance matching and broader BW. Since _dis_ is related to the antenna width of a single element, \(W_{ant}=dis+L_{quv}\), it affects the BW. As _dis_ increases, the BW enhances as shown in Figure 6f. The best impedance matching is obtained at _dis_ = 45 mm (S\({}_{11}<-10.11\) dB at 2.507-10.414 GHz and MG = 8.94 dBi), which is better than at the optimized value for the single element, _dis_ = 37.2 mm (S\({}_{11}<-8.85\) dB). Figure 5: Layout of Array 1. The best impedance matching is found, as shown in Figure 6g at \(W_{a}\) = 0.96 mm (S\({}_{11}\)\(<\) -10.11 dB at 2.507-10.414 GHz and MG = 8.94 dBi), which is better than at the optimized value for the single element, \(W_{a}\) = 1.2 mm (S\({}_{11}\)\(<\) -8.81 dB). As shown in Figure 6h, the obtained impedance matching is not satisfactory at the calculated \(sp\) = 51.36 mm (S\({}_{11}\)\(<\) -7.12 dB at 3.11-10.43 GHz and MG = 8.6 dBi); however, as \(sp\) increases (>51.36 mm), the impedance matching and gain improve, and the best matching is achieved at \(sp\) = 83.8 mm (S\({}_{11}\)\(<\) -10.11 dB at 2.507-10.414 GHz and MG = 8.94 dBi). Finally, the optimum impedance matching level is reached, as seen in Figure 6i at \(W_{p}\) = \(W_{P1}\) (for port 1) = \(W_{P2}\) (for port 2) = \(W_{P3}\) (for port 3) = 1.85 mm (S\({}_{11}\)\(<\) -10.11 dB at 2.507-10.414 GHz and MG = 8.94 dBi), which outperforms the calculated one at \(W_{p}\) = 1.819 mm (S\({}_{11}\)\(<\) -9.16 dB). The optimized values for Array 1 with its single element (VTSA) are illustrated in Table 2.  
Figure 6: Parametric study of the proposed UWB Array 1 in terms of S\({}_{11}\) and gain on (**a**) \(r\), (**b**) \(L_{T}\), (**c**) \(L_{qp}\), (**d**) \(W_{min}\), (**e**) _radsl_, (**f**) _dis_, (**g**) \(W_{a}\), (**h**) \(s_{p}\), and (i) \(W_{p}\).