# Design and Analysis of Pattern Reconfigurable Antenna Based on RF MEMS Switches
## 2 Antenna Structure Design
### Main Patch, Sub-Patches and Parasitic Patches Design  
The antenna's center frequency was 35 GHz and it used a high-resistivity silicon substrate that was 400 \(\upmu\)m thick and had a relative permittivity of 11.9. The design target was to have a length and width within 6 mm \(\times\) 5 mm. First, based on the microstrip rectangular patch structure, the main patch was analyzed. The top and side view structures of the rectangular patch are displayed in Figure 2 [8]. The patch's length L and width W of the rectangular patch can be determined using Formulas (1)-(4) [18], where \(\epsilon_{e}\) is the effective permittivity of high-resistivity silicon, \(\epsilon_{r}\) is the relative permittivity of high-resistivity silicon, \(\epsilon\) is the speed of light in vacuum, \(f\) is the center frequency of the antenna, \(h\) is the substrate thickness, \(W\) is the maximum value of the patch width that does not cause field distortion, and \(L\) is the patch length considering edge effects. \[W=\frac{c}{2f\sqrt{\frac{\upmu+1}{2}}}=1.701\ \text{mm} \tag{1}\]  
Figure 1: Surface current distribution of reconfigurable pattern antenna. \[\varepsilon_{e}=\frac{\varepsilon_{r}+1}{2}+\frac{\varepsilon_{r}-1}{2}\Big{(}1+ \frac{12h}{W}\Big{)}^{-\frac{1}{2}}=9.086 \tag{2}\]  
\[\Delta L=0.412h\frac{(\varepsilon_{r}+0.3)(W/h+0.264)}{(\varepsilon_{e}-0.258)( W/h+0.8)}=0.157\;\mathrm{mm} \tag{3}\]  
\[L=\frac{1}{2}\frac{c}{f\sqrt{\varepsilon_{e}}}-2\Delta L=1.108\;\mathrm{mm}. \tag{4}\]  
According to the above calculation, the dimensions of the 35 GHz microstrip rectangular patch antenna were about 1.7 mm \(\times\) 1.1 mm. In order to achieve reconfigurable antenna patterns, a sub-radiation patch was placed on each side of the rectangular patch, and the main and sub-patches were connected by switches, as shown in Figure 3. The reconfigurable antenna comprised a main patch, two sub-patches, two parasitic patches, two switches, a 50 \(\Omega\) microstrip line, and an impedance transformer. The switches S1 and S2 were responsible for controlling the connection between the main patch and the two sub-patches located on the left and right sides. The main patch can be connected to the two sub-patches on the left and right sides, respectively, by manipulating the on-off of the two switches. The antenna could then create three distinct functioning states and its pattern could be reconfigured in three directions. The specific working states of the antenna and the corresponding relationship between the working states of the switches are shown in Table 1. It should be noted that, since the antenna radiation pattern of both switches in the off state was consistent with the antenna radiation pattern of both switches in the on state, the situation in which both switches were in the off state was not considered here. Figure 2: Schematic diagram of the dimensions of the microstrip rectangular patch. (**a**) Vertical view; (**b**) Side view. After adding the sub-radiation patch, the antenna structure became irregular. Therefore, based on the original calculation of the regular rectangular patch size, the size of the main radiation patch and the sub-radiation patch were adjusted and simulated. The results of the simulation are presented in Figure 4. The findings indicate that the size \(L_{0}\) and \(W_{0}\) of the main radiation patch have little effect on the center frequency \(f_{0}\) of the antenna, while the size \(L_{1}\) of the sub-radiation patch has a great influence on the center frequency \(f_{0}\) of the antenna and \(f_{0}\) decreases as \(L_{1}\) increases. Therefore, the working frequency of the antenna can be changed by adjusting the size \(L_{1}\) of the sub-radiation patch, and then other parameters can be optimized. To ensure good performance of the antenna element, impedance matching must be achieved. Since it is difficult to know the exact impedance value after the antenna design is completed, a 1/4 wavelength impedance transformer was used to match the impedance of the 50 \(\Omega\) feed line at the input end.