## 2 Pattern Reconfigurable Antenna Structure and Design  
### Overall Structure and Design  
A strategy for a radiating pattern reconfigurable antenna is proposed, the structure is illustrated in Figure 1a, and the optimized geometry of the RF MEMS switch is shown in Figure 1b. The pattern reconfigurable antenna--fabricated on a high resistivity silicon substrate with a relative dielectric constant of 11.9 and thickness of 400 \(\upmu\)m--consists of one rectangular main patch radiator, two rectangular assistant patch radiators, one impedance transformer, and two RF MEMS switches. The RF MEMS switch is made of an anchor, a beam, and a \(\lambda_{g}/4\) sector open stub. All the conductor patches and RF MEMS beams are made of aluminum. The optimized configurations of the antenna and switches are shown in Table 1.  
In general, the microstrip antenna operates at a resonant state. Thus, the length of the radiator is selected to be approximately half the waveguide wavelength. The relationship between the length of the radiators and the resonant frequency can be summarized as follows [12].  
\[\left\{\begin{array}{l}L=\frac{1}{2}\frac{c}{f_{\mathrm{r}os}\sqrt{\varepsilon _{eff}}}\\ \\ \varepsilon_{eff}=\frac{\varepsilon_{f}+1}{2}+\frac{\varepsilon_{f}-1}{2} \left(1+\frac{10h}{W}\right)^{-\frac{1}{2}}\end{array}\right. \tag{1}\]  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Symbol** & **Description** & **Value** \\ \hline \(W_{0}\) & width of the main patch & 1500 \(\upmu\)m \\ \(L_{0}\) & length of the main patch & 900 \(\upmu\)m \\ \(W_{1}\) & width of the assistant patch & 960 \(\upmu\)m \\ \(L_{1}\) & length of the assistant patch & 970 \(\upmu\)m \\ \(W_{m}\) & width of the impedance transformer & 110 \(\upmu\)m \\ \(L_{m}\) & length of the impedance transformer & 1410 \(\upmu\)m \\ \(W_{b}\) & width of the switch beam & 90 \(\upmu\)m \\ \(L_{b}\) & length of the switch beam & 340 \(\upmu\)m \\ \(W_{h}\) & width of the hole & 54 \(\upmu\)m \\ \(L_{h}\) & length of the hole & 72 \(\upmu\)m \\ \(a\) & side length of releasing hole & 8 \(\upmu\)m \\ \(r\) & length of the sector stub & 575 \(\upmu\)m \\ \(\delta\) & angle of the sector stub & 25\({}^{\circ}\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Optimized configurations of the antenna and switches.  
where, \(c\) is the velocity of light in free space, \(f_{res}\) is the resonant frequency, \(h\) is the substrate thickness, \(W\) is the width of microstrip patch, and \(\varepsilon_{r}\) and \(\varepsilon_{\mathit{eff}}\) are the relative and effective dielectric constants, respectively.  
It is mentioned that the actual length of the radiator patch is optimized by simulation software and is not exactly equal to half of the waveguide wavelength, for the sake of gaining the best performance of overall structure. By controlling the states of different RF MEMS switches, the proposed antenna can switch among four operating states, and obtain three reconfigurable radiating patterns, as shown in Table 2.  
According to the above measurement results of the main lobe direction, the antenna can mainly achieve three reconfigurable radiating patterns--i.e., left (approximately \(-17^{\circ}\)), middle (approximately \(0^{\circ}\)), and right (approximately \(+17^{\circ}\)), respectively.