## 2 Design of the Pattern Reconfigurable Antenna
### RF MEMS Switch Design  
The reconfigurations of the proposed antenna are realized by controlling the modes of RF MEMS switches; thus, the performance of RF MEMS switch is critical for the overall system. The thickness of the RF MEMS switch beam is 1 \(\upmu\)m, and the air gap between the beam and the signal line that connects the derived patch and assistant patch is 1.5 \(\upmu\)m. The other pivotal size is shown in Table 3. The top view and 3D view of the designed RF MEMS switch are illustrated in Figure 2. \begin{table}
\begin{tabular}{c c c c c} \hline
**Symbol** & **Value (\(\upmu\)m)** & **Symbol** & **Value (\(\upmu\)m)** & **Symbol** & **Value (\(\upmu\)m)** \\ \hline \(W_{du}\) & 2460 & \(W_{f}\) & 383 & \(W_{1}\) & 500 \\ \(L_{d}\) & 1000 & \(W_{au}\) & 400 & \(L_{1}\) & 300 \\ \(W_{db}\) & 2100 & \(W_{ab}\) & 580 & \(W_{2}\) & 600 \\ \(W_{dm}\) & 130 & \(L_{al}\) & 900 & \(L_{2}\) & 300 \\ \(L_{dm}\) & 1300 & \(L_{ar}\) & 518 & - & - \\ \hline \end{tabular}
\end{table} 
Table 1: The geometry configuration of the proposed antenna. \begin{table}
\begin{tabular}{c c c c} \hline
**Mode** & **Description** & **Main Lobe Direction (\(\upmu\) = 90\({}^{\circ}\))** & **Reconfigurable Radiating Pattern** \\ \hline (1,0) & Only left switch in the up state & \(\theta\) = \(-\)20.2 & left \\ (0,0) & Double switches in the up state & \(\theta\) = \(-\)0.2 & middle \\ (1,1) & Double switches in the down state & \(\theta\) = \(-\)0.2 & middle \\ (0,1) & Only right switch in the up state & \(\theta\) = 20.5 & right \\ \hline \end{tabular}
\end{table} 
Table 2: The reconfigurable radiating pattern main lobe direction and its associated radio frequency micro-electromechanical systems (RF MEMS) switches operating modes. Figure 2: Designed RF MEMS switch. (**a**) Top view. (**b**) 3D view. As shown in Figure 2, the RF MEMS switch is terminated by a \(\lambda_{g}/4\) sector open stub and a high resistivity bias line, which is used to apply the direct current. To alleviate the influences on return loss and resonant frequency, the \(\lambda_{g}/4\) sector open stub is employed, which has many advantages such as miniaturization of structure and the convenience of connection. The dielectric shown in Figure 2a,b is Si\({}_{3}\)N\({}_{4}\) with a thickness of 0.15 \(\upmu\)m, and it is used to separate the beam and the signal line when the air gap is 0 \(\upmu\)m. By actuating the RF MEMS switches using the direct current, the gap between the beam and the signal line varies from 0 to 1.5 \(\upmu\)m (i.e., down state to up state). The down or up state determinate whether the assistant patch is connected to the driven patch, i.e., when the switch is in the down state (the gap is 0 \(\upmu\)m), the assistant patch is detached from the driven patch, and vice versa. According to the simulated results, the isolation of the proposed RF MEMS switch reaches 20 dB, and the insertion loss is 0.35 dB at operating frequency 35 GHz, respectively. The performance of the antenna can therefore be guaranteed. When the position of the RF MEMS switch beam is pulled to the point \((2/3)g_{0}\), the increase of the restoring force is exceeded by the increase of the electrostatic force. This leads to a rapid drop-down of the RF MEMS beam, and the actuating voltage reaches a maximum. The actuating voltage can be calculated by  
\[V_{p}=\sqrt{\frac{2k_{e}}{\varepsilon_{0}W_{b}L_{d}}\frac{g_{0}}{3}\left(\frac {2g_{0}}{3}+\frac{t_{e}}{\varepsilon_{r}}\right)^{2}} \tag{1}\]  
where \(\varepsilon_{0}\) is the dielectric constant of free space, \(\varepsilon_{r}\) is the relative dielectric constant of dielectric Si\({}_{3}\)N\({}_{4}\), \(g_{0}\) is the gap between the RF MEMS switch beam and the signal line, \(k_{e}\) is the elastic coefficient of the beam, \(t_{e}\) is the thickness of the beam, and \(W_{b}\) and \(L_{d}\) are the width and length of the beam, respectively.