# Antipodal Vivaldi Antenna Arrays Fed by Substrate Integrated Waveguide Right-Angled Power Dividers
## 3 Results
### SIW Two-Way Power Divider as Feed System  
The proposed array using an out-of-phase two-way power divider with 180-degree phase difference and its parameters are indicated in Figure 10. The entire structure is designed and fabricated on Rogers 6002 substrate. Substrate losses are included as tan \(\delta\) = 0.0012. The metallization thickness is \(t\) = 17.5 \(\upmu\)m with conductivity of \(\sigma\) = 5.8 \(\times\) 10\({}^{7}\) S/m. The microstrip-to-SIW transition is designed for connecting a 50 \(\Omega\) K-connector to the SIW and then optimized for the best match. All dimensions are presented in Figure 10.  
Figure 11 compares the measured and simulated reflection coefficient and gain of the antenna array. The reflection coefficient is better than \(-\)10 dB from 26.11 GHz to 28.33 GHz and a fairly high and uniform gain of about 8.5 dB in the entire operating frequency range is achieved. The measured results are in good agreement with simulations except for a small difference in the reflection coefficient in the middle frequency band which is mainly due to the K-connector which is shown in Figure 9. A regular coaxial connector is modeled in the simulation while in the measurement, an end launch connector has been used which causes the slight discrepancy between measurement and simulation. The radiation efficiency is calculated as a ratio between total co-polarized radiated power by the system to the input power accepted by the circuit. This parameter shows how efficient the system is in radiating or receiving the signal. The radiation efficiency for this system is 91.3% and 90.7% at 27 GHz and 28 GHz, respectively.  
Figure 10: Vivaldi antenna array with two-way out-of-phase SIW power divider as feed system. W\({}_{1}\) = 1.25 mm, W\({}_{2}\) = 1 mm, L\({}_{1}\) = 4.86 mm, a\({}_{\text{SIW}}\) = 5.4 mm, L\({}_{2}\) = 1 mm.  
Figure 9: Fabricated prototypes of H-plane SIW antenna arrays with two-way and three-way right-angled power dividers and size comparison with a Canadian two-dollar coin.  
Figure 12 shows the radiation pattern of the proposed circuit at three different frequencies. As a consequence of out-of-phase feeding, the far-field radiation pattern of this design has two main lobes with maxima at \(-20^{\circ}\) and \(20^{\circ}\), and a minimum at broadside that is 12 dB down from the maxima. Hence this antenna array is suitable for direction-finding applications where zooming in on the null of the pattern is faster than using a maximum.  
The second system is the combination of the two-way power divider with 120-degree phase difference (Figure 6a) and an antenna array which is displayed in Figure 13a. The proposed system provides a reflection coefficient better than \(-10\) dB between 25.7 GHz and 29 GHz (Figure 13b) and high gain of about 11 dB in the operating frequency range. The power divider's scattering parameters are also presented in Figure 13b which shows a reflection coefficient better than \(-15\) dB in the operating bandwidth. The radiation efficiency of this system is better than 90% over the entire bandwidth. This design affirms the phase control capability for direction finding applications since the new structure moves the null location from \(0^{\circ}\) to \(9^{\circ}\) which consequently shifts the radiated beam. Figure 14 demonstrates the far-field radiation pattern of this antenna array at 27 GHz.