# 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)
Now, the NTL UWB WPD (in the dashed box in Figure 2) [27] is integrated with two elements of compact UWB VTSAs [1] to obtain a compact 2 \(\times\) 1 UWB linear VTSA array as demonstrated in Figure 5, where \(\mathbf{r}\), \(W_{min}\), \(W_{max}\), \(L_{T}\), \(L_{up}\) (\(L_{T}\)/4), \(radsl\)(\(L_{T}\)/2), \(W_{a}\), \(W_{p}\) (50 \(\Omega\)), \(W_{ar}\), and \(L_{ar}\) are the tapering rate, aperture opening, the aperture width, the taper slot length, the quarter wavelength of both microstrip and slot lines in microstrip to slot (M/S) transition, the radius of the slot, the antenna feed line width, the width of three ports of NTL WPD, the width, and the length of the proposed antenna array, respectively. As illustrated in Figure 5, the exponential tapering profile was obtained using \(\pm A\)e\({}^{rx}\) where \(x\) is the position  
Figure 2: Configuration of compact UWB 2:1 unequal split TTL and NTL WPDs. along \(L_{T}\) and A = 0.5 \(\times\)\(W_{min}\). Based on the design equations explained in [1], at the UWB frequency band (3.1-10.6 GHz) with \(f_{\text{C}}\) = 6.85 GHz, the calculated \(L_{T}\) and \(W_{max}\) are selected to be 25 mm (>23.99 mm at \(f_{\text{C}}\) = 6.58 GHz) and 22 mm (20.88 mm < \(W_{max}\) < 23.07 mm), respectively. \(sp\) is the space between the two elements and can be calculated using  
\[sp\text{= }\lambda_{0}=\frac{C}{f_{0}\sqrt{\varepsilon_{r}}}\text{= }\frac{3\times 10^{8}}{3.1\times 10^{9}\sqrt{3.55}}=51.36\text{mm}, \tag{1}\]  
where \(c\) is the speed of light. Figure 3: Measured and simulated (a) S\({}_{11}\), (b) S\({}_{22}\), (c) S\({}_{33}\), (d) S\({}_{12}\), (e) S\({}_{13}\), (f) S\({}_{23}\) of compact UWB 2:1 NTL and TTL WPDs. \begin{table}
\begin{tabular}{c c c c c} \hline \multirow{2}{*}{**Parameters**} & \multicolumn{2}{c}{**Sim. **} & \multicolumn{2}{c}{**Meas. **} \\ \cline{2-5}  & **NTL** & **TTL** & **NTL** & **TTL** \\ \hline \multirow{2}{*}{S\({}_{11}\)} & \(<\)\(-\)10.62 dB at 3.46 to & \(<\)\(-\)11.84 dB at 1.4 to over & \(<\)\(-\)13.6 dB at below 1 to & \(<\)\(-\)10.55 dB at 2.27 to \\  & over 12 GHz & 12 GHz & 10.34 GHz & over 12 GHz \\ \hline \multirow{2}{*}{S\({}_{22}\)} & \(<\)\(-\)10.6 dB at below 1 to & \(<\)\(-\)11 dB at below 1 to & \(<\)\(-\)11.5 dB at below 1 to & \(<\)\(-\)11.8 dB at 2.5 to \\  & over 12 GHz & over 12 GHz & over 12 GHz & 11.56 GHz \\ \hline \multirow{2}{*}{S\({}_{33}\)} & \(<\)\(-\)14 dB at 2.21 to over & \(<\)\(-\)11.15 dB at 2.88 to & \(<\)\(-\)14.26 dB at 1.96 to & \(<\)\(-\)11.26 dB at 2.63 to \\  & 12 GHz & over 12 GHz & over 12 GHz & over 12 GHz \\ \hline \multirow{2}{*}{S\({}_{23}\)} & \(<\)\(-\)16.28 dB at 3.66 to & \(<\)\(-\)14.17 dB at 1.7 to over & \(<\)\(-\)10 dB at 3.22 to over & \(<\)\(-\)13.71 dB at 2.45 to \\  & over 12 GHz & 12 GHz & over 12 GHz & over 12 GHz \\ \hline \multirow{2}{*}{S\({}_{12}\)} & \(-\)1.76-1 dB & \(-\)1.76–1.5 dB & \(-\)1.76–1 dB & \(-\)1.76–1.5 dB \\  & \(-\)4.77 \(\pm\) 0.3 dB & \(-\)4.77 \(\pm\) 0.3 dB & \(-\)4.77 \(\pm\) 0.3 dB & \(-\)4.77 \(\pm\) 0.3 dB \\ \hline \multirow{2}{*}{S\({}_{12}\) GD} & around 0.22 ns & around 0.25 ns & around 0.5 ns & around 0.45 ns \\ \hline \multirow{2}{*}{S\({}_{13}\) GD} & around 0.25 ns & around 0.25 ns & around 0.45 ns & around 0.45 ns \\  & \multicolumn{3}{c}{\({}^{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{ \text  
Parametric Studies  
To address the array's mismatch caused by the integration of the antenna and power divider, different parametric analyses are conducted as illustrated in Figure 6. The selected parameters are within the red dashed box. Figure 6a shows that the matching at \(r=0.174\) (S\({}_{11}<-10.11\) dB at 2.507-10.414 GHz and maximum gain (MG) = 8.94 dBi) is better than the optimized value for the single element, i.e., \(r=0.17\) (S\({}_{11}<-9.69\) dB) and at other values (\(r=0.166\) (S\({}_{11}<-9.11\) dB) and \(r=0.178\) (S\({}_{11}<-9.6\) dB).