# Design of a SIW Variable Phase Shifter for Beam Steering Antenna Systems
## 3 SIW Beam Steering Antenna System
### Beam Steering Antenna System  
Beam steering is accomplished by applying a progressive phase shift between neighboring elements in an array. The proposed beam steering antenna system includes two variable phase shifters, an antenna array consisting of two Vivaldi antennas, and a 90\({}^{\circ}\) phase transition. A microstrip-to-SIW transition is designed for feeding the antenna system by K-connectors at ports 1 and 2. First, a 50-\(\Omega\) microstrip line is designed based on principles explained in [26]. Then, it is tapered out for a better match. Figure 10 demonstrates the entire beam steering antenna system.  
Figure 10: Beam steering antenna system.  
Figure 9: SIW Vivaldi antenna, (**a**) reflection coefficient, (**b**) far-field radiation pattern at 17 GHz.  
A SIW 90\({}^{\circ}\) phase transition is applied between the 3-dB coupler and phase shifters. This transition causes 0\({}^{\circ}\) and 180\({}^{\circ}\) phase differences between the input ports of the right and left phase shifter when exciting port 1 and port 2, respectively [27]. Therefore, a 0\({}^{\circ}\) (sum) and 180\({}^{\circ}\) (difference) steering range is obtained by using this transition. Figure 11 displays the electric field distribution in the entire antenna system when port 1 is excited. As exhibited, minimum loss and no wave-leakage through the SIW transitions are accomplished.  
In order to calculate the beam steering range of the system by considering a phase shifter with a maximum of 125\({}^{\circ}\) phase variation, the following formula is used [28]:  
\[\psi=\frac{-360f}{c}\Big{(}[d_{x}+\Delta_{x}]\sin\theta\cos\phi+d_{y}\sin \theta\sin\phi\Big{)} \tag{1}\]  
where \(\psi\) is the phase shift between the elements, \(f\) is the frequency, \(c\) is the speed of light, \(d_{x}\) and \(d_{y}\) are \(x\)- and \(y\)-element spacing, \(\Delta_{x}\) is the row offset for a non-rectangular lattice, and \(\theta\) and \(\phi\) are the beam steering angles.  
As revealed in [23], by applying 0 to 20 V bias to the varactor diode, its capacitance changes between 0.23 pF and 2.1 pF. The gain pattern of the beam steering antenna system is presented in Figure 12 at mid-band frequency of 17 GHz, while port 1 is excited and port 2 is terminated. As expected by applying the same biasing voltage to both right and left phase shifters, a signal with a 180\({}^{\circ}\) phase difference feeds the Vivaldi antennas which consequently causes a deep null in the broad-sight direction of the antenna.  
Figure 11: Electric field distribution in SIW beam steering antenna system at 17 GHz when port 1 is excited.  
Figure 12: Simulated gain patterns of the beam steering antenna system at 17 GHz for 5 different loadings while port 1 is excited.  
Figure 13 presents the gain pattern of the antenna system for five different loadings when port 2 is excited and port 1 is terminated. Due to the 90\({}^{\circ}\) transition by exciting port 2, signals go through the SIW phase shifters with 180\({}^{\circ}\) phase differences. Therefore, by applying the same voltage to the right and left phase shifters, another 180\({}^{\circ}\) phase difference is added to the signal which causes a directive radiation pattern in the broad-sight direction of the system.  
By considering the progressive phase shift between the individual antennas by exciting port 1 and port 2, a beam steering range from \(-25^{\circ}\) to \(+25^{\circ}\) is obtained, which verifies the calculated value by using Equation (1).