# Design of a SIW Variable Phase Shifter for Beam Steering Antenna Systems
## 2 SIW Variable Phase Shifter
### SiW Variable Phase Shifter  
A reflection-type variable phase shifter is designed in this section, which consists of an SIW 3-dB coupler and the biasing circuit for the varactor diodes. Figure 3 shows the structure and parameters of the phase shifter. The phase shifter parameters including the coupler are designed based on the theoretical analysis introduced in [21]. The reader is referred to [21] for details. The waveguide width is designed based on the cutoff frequency [14], and the SIW width is defined by using the proposed  
Figure 1: Substrate integrated waveguide 3 dB coupler. Figure 2: Scattering parameters of the 3 dB coupler, (**a**) ideal, (**b**) \(\mathrm{S_{21}}=\mathrm{S_{31}}\) with dielectric and metal losses included compared to lossless analysis. formula in [22]. The _d/p_ ratio is chosen as 0.65 to have minimum wave leakage in the SIW circuit. Table 1 presents the phase shifter's dimensions. Before applying the varactor diodes to the coupler introduced in Section 2.1, two capacitors are applied to ports 3 and 4 (Figure 1) to analyze the phase variation that can be obtained by this circuit. As revealed in Figure 4, by changing the capacitor value from 0.1 pF to 5 pF, a phase variation of about 125\({}^{\circ}\) is obtained. After 5 pF, the value of the capacitor is so high that it resembles a short circuit (about 2 \(\Omega\) impedance), thus the phase variation saturates. For this design, the silicon hyper abrupt junction varactor diode SMV2201-040 LF [23] is chosen, which is specifically designed for wideband applications. For examining the performance of this diode, its equivalent circuit is modeled and analyzed in CST, which is demonstrated in Figure 5. A microstrip-to-SIW transition comprising a 50-\(\Omega\) microstrip line and a tapered microstrip section as well as two parasitic compensation stubs with width \(W_{1}\) and length \(L_{1}\) (Figure 3) are applied to ports 3 and 4 of the coupler for achieving the required capacitance for a 125\({}^{\circ}\) phase shift. An inductor is inserted between the DC voltage and the varactor diode to provide a quasi-open circuit for the RF  
Figure 4: Phase variation of the 3-dB coupler by applying different capacitance values at ports 3 and 4. Figure 3: SIW variable phase shifter structure and parameters. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Dimension (mm)** & **Parameter** & **Dimension (mm)** \\ \hline \(p\) & 1 & \(W_{1}\) & 6 \\ \(d\) & 0.65 & \(W_{2}\) & 3 \\ \(L_{1}\) & 1.5 & \(W_{3}\) & 18.6 \\ \(L_{2}\) & 29.46 & \(W_{4}\) & 6.508 \\ \(h\) & 0.508 & \(a_{SIW}\) & 7 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Dimensions of the SIW variable phase shifter. signal. Table 2 presents the relationship between the output phase of the phase shifter circuit and biasing voltage of the varactor diodes for a single-phase shifter. By increasing the biasing voltage from 0 to 20 V, a nonlinear variation of phase difference between 0\({}^{\circ}\) and 126\({}^{\circ}\) is achieved. Figures 6-8 demonstrate the performance of the variable phase shifter by applying 0 to 20 V biasing voltage to the circuit. While applying five different voltages, Figure 6 shows the reflection coefficient of the variable phase shifter which is better than -15 dB in all cases between 16 GHz and 18 GHz. The phase variation achieved by the equivalent circuit of the varactor diode is demonstrated in Figure 7 and verifies the 120\({}^{\circ}\) phase differences. Figure 8 presents the insertion loss of the proposed phase shifter, which improves from 11 dB to 3 dB by increasing the biasing voltage from 0 to 20 V. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Voltage (V)** & **Capacitor (pF)** & **Phase Shifter Angle (degree)** \\ \hline
0 & 2.10 & 0 \\
5 & 0.67 & 45.51 \\
10 & 0.33 & 75.92 \\
15 & 0.26 & 106.34 \\
20 & 0.23 & 126.02 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Phase shifter angle and capacitance as a function of biasing voltage.