# 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)  
To design a compact and effective array for UWB applications, at 3.1-10.6 GHz, the compact 2:1 NTL WPD [27] is chosen in this work as a feeding network to the 2 \(\times\) 1 VTSA array (Array 1). As a contribution and to demonstrate the performance of the NTL WPD despite the 33.31% compactness in its \(\lambda\)/4 transformers, the designed 2:1 UWB tapered transmission line (TTL) WPD based on the special TTL equation [30] is used here as a benchmark as shown in Figure 2. In this work, Rogers RO4003C substrate material (with a dielectric constant (\(\epsilon_{t}\)) = 3.55, height (h) = 0.813 mm, dielectric loss tangent of 0.0027, and copper thickness = 0.035 mm) is chosen due to (1) its excellent performance at high frequencies (low dielectric loss tolerance and loss), (2) excellent dimension stability, and (3) stable electrical properties versus frequency. Figure 2 illustrates the 33.31% size reduction of 2:1 NTL transformers (NTLTs) as compared to TTL transformers (TTLTs). According to the design equations of WPD in [31], isolation between ports requires an isolation resistor. As shown in Figure 2, three isolation resistors, R1 = 82 \(\Omega\) (TTL) and 130 \(\Omega\) (NTL), R2 = 620 \(\Omega\) (TTL) and 300 \(\Omega\) (NTL), and R3 = 470 \(\Omega\) (TTL) and 180 \(\Omega\) (NTL) are used to guarantee high isolation between the output ports (Port 2 and Port 3). These optimum values are determined based on detailed parametric studies in [27,30] that examine the effect of different resistor values on the divider's matching, transmission, and isolation. It should be noted that more resistors can enhance the isolation; however, only three are selected in this work to avoid the difficulties in soldering and integrating the surface mount resistors in the short distance between the two transformers (NTLTs or TTLTs). Detailed  
Figure 1: The major contributions in this work. parametric studies of 2:1 TTL and NTL WPDs can be found in [30] and [27], respectively. The comparison between their results (the values of S\({}_{11}\), S\({}_{22}\), S\({}_{33}\), S\({}_{23}\), S\({}_{12}\), S\({}_{13}\), S\({}_{12}\) group delay (GD), S\({}_{13}\) GD, S\({}_{12}\) phase and S\({}_{13}\) phase) are demonstrated in Figures 3 and 4 and Table 1.  
Figure 3a-f show that both dividers satisfy good input, output matching, and isolation between output ports through the UWB frequency band where the measured insertion losses S\({}_{12}\) and S\({}_{13}\) are close to the theoretical values, \(-\)1.76 dB and \(-\)4.77 dB, respectively. To reduce the effect of fabrication errors [32], the SMA connector is considered in the simulation of these dividers. The disturbance in the measured results shown in Figure 3d-f, especially at high frequencies beyond 8 GHz, is due to the worse impedance mismatch and the increased insertion loss (conductor and dielectric losses) for the non-pure TEM transmission line at higher frequencies [31]. In addition, the difference between the simulation and measurement environments contributes to this disturbance. To ensure that the radio signal is transmitted successfully in UWB applications, GD should be flat through the UWB frequency band [33]. As demonstrated in Figure 4a,b, the proposed dividers give a nearly flat GD, with an increase in measured findings owing to manufacturing and measurement tolerances, as well as the difference between the simulation and measurement environments. Finally, it is observed from Figure 4c,d that there is a slight phase difference between the NTL and TTL WPDs because of their transformers' different lengths. This slight phase difference and the acceptable values of return loss and isolation of NTL WPD indicate the effectiveness of applying NTL theory [27; 29] for compactness and performance improvement (wide BW) without the need for additional components. This makes the NTL WPD an excellent option for an antenna feeder.