# Antipodal Vivaldi Antenna Arrays Fed by Substrate Integrated Waveguide Right-Angled Power Dividers
## 3 Results
### SiW Four-Way Power Divider as Feed System  
Based on the design procedure outlined above and the good agreement between measured and simulated results, an SIW four-way right-angled divider is designed and combined with four antipodal Vivaldi antennas. The locations and sizes of seven metallic vias are optimized for good port distribution and input match. Figure 19 shows the array structure and its parameters. The electric field division between the four output ports is presented in Figure 20. Note that the phases at the input ports to the antennas are neither in- nor out-of-phase with both ports 2, 3 and ports 4, 5 having similar phases, but there are approximately 90\({}^{\circ}\) between the two pairs of output ports (depending on frequency). \begin{table}
\begin{tabular}{c c} \hline \hline
**Frequency (GHz)** & **Measured Polarization Efficiency** \\ \hline
21 & 98.55\% \\
22 & 98.30\% \\
22.5 & 99.01\% \\
23 & 98.66\% \\
23.5 & 98.11\% \\
24 & 98.24\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Measured polarization efficiency vs. frequency. Figure 19: Vivaldi antenna array with four-way SIW power divider structure on Rogers RT6002 with \(h\) = 508 mm and \(\varepsilon_{r}\) = 2.94. The via positions are: \(x_{1}\) = 18.4 mm, \(x_{2}\) = 15.8 mm, \(x_{3}\) = 15.4 mm, \(x_{4}\) = 12.2 mm, \(x_{5}\) = 5.52 mm, \(x_{6}\) = 5.78 mm, \(x_{7}\) = 7.64 mm. Figure 18: Comparison between measured and simulated radiation efficiency of the three-way divider antenna system. The proposed structure provides a good performance at K-band frequencies with a reflection coefficient better than \(-10\) dB from 20 GHz to 24.12 GHz and a 6 dB power division with 1 dB deviation between 22.5 to 24 GHz as presented in Figure 21. This design achieves a gain of about 13 dB in its operating bandwidth which is low compared to that of 9.4 dB of the individual Vivaldi antenna (Section 2.3). The reason for this becomes obvious when we look at the 3D far-field radiation patterns in Figure 22. While the array shows single-beam performance between 23 GHz and 24.12 GHz, a dual beam is obtained in the lower frequency band from 20 GHz to 22 GHz. This is a consequence of the frequency-dependent input phases to the four Vivaldi antennas. The radiation efficiency of this antenna system is better than 80% between 21 to 24 GHz. 2D polar cuts of the radiation patterns are presented in Figure 23 to examine the E-plane (solid lines) and H-plane (dashed lines) behavior of this antenna array. Note that both planes agree in 0-degree and 180-degree directions. Figure 21: (**a**) Power levels of four port power divider; (**b**) reflection coefficient of Vivaldi antenna array with four-way SIW power divider. Figure 20: Electric field of four-way SIW power divider at 23 GHz. The co- and cross-polarization performances in the H-and E-planes of this array are depicted in Figure 24. It is observed that in the direction of the main beam, the cross-pol level is more than 30 dB down which reduces to about 20 dB at the half-power angles. This excellent cross-pol behavior is a consequence of the corrugations introduced in the individual Vivaldi elements (Figure 7). Therefore, good cross-polarization values are also obtained for the two- and three-element arrays in Sections 3.1 and 3.2 with 20 dB and 25 dB, respectively. Figure 23: 2D polar patterns of the Vivaldi antenna array with four-way SIW power divider at (**a**) 21 GHz, (**b**) 23 GHz, and (**c**) 24 GHz (E-plane—solid lines, H-plane—dashed lines). Figure 22: 3D far-field radiation patterns of Vivaldi antenna array with four-way SIW power divider at (**a**) (**a**) 21 GHz, (**b**) 23 GHz, and (**c**) 24 GHz. The performance of all four systems including directivity, maximum side lobe level, the 3 dB beamwidth, and half power beam width is summarized in Figure 19:0 In some cases, the side lobe level may be slightly higher than expected.