# An L-Slot Frequency Reconfigurable Antenna Based on MEMS Technology
## 3 Simulation Result  
In this paper, we use CST STUDIO SUITE 2018 electromagnetic simulation software to build the base model of the antenna. Then, build the frequency reconfigurable antenna \begin{table}
\begin{tabular}{c c c} \hline \hline
**Dimension** & **Value (mm)** & **Comments** \\ \hline \(W\) & 5.27 & Width of antenna \\ \(L\) & 4.07 & Length of antenna \\ \(W_{1}\) & 2.68 & Width of radiation patch \\ \(L_{1}\) & 2.04 & Length of radiation patch \\ \(W_{2}\) & 0.10 & Width of L-slot \\ \(M_{1}\) & 0.50 & Length of L-slot along x-direction \\ \(M_{2}\) & 0.50 & Length of L-slot along y-direction \\ \(M_{3}\) & 0.15 & Length of L-slot folding back part \\ \(L_{2}\) & 1.31 & Distance of L-slot and radiation patch edges. \\ \(P\) & 0.30 & Distance of RF MEMS switch and radiation patch edges. \\ \(H\) & 0.254 & Thickness of substrate \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Structural Parameters of L-slot Frequency Reconfigurable Antenna. Figure 4: The current distribution on the antenna surface is shown in the figure, and the red arrows indicate the direction in which the currents converge. (**a**) The state without slot and switch; (**b**) The state with slot but no switch; (**c**) The state with slot and switch. model by optimizing the length and shape of the slot and the position of the RF MEMS switches. The excitation is applied to the antenna at the coaxial feed to simulate the shift of the reflection coefficient, orientation map, and gain of the antenna in the 40-60 GHz band in different states. Step 1: Establish a basic model of the antenna without slots and switches. The size of the patch is determined according to the relative permittivity (Rogers RT5880, \(\varepsilon_{r}\) = 2.2), thickness (\(H\) = 0.254 mm) and antenna operating frequency (\(\dot{V_{r}}\) > 40 GHz) of the selected dielectric substrate. Based on the following formula [21; 22], the width of the rectangular patch is:  
\[W=\frac{c}{2f_{r}}\left(\frac{\varepsilon_{r}+1}{2}\right)^{-1/2} \tag{3}\]  
When \(W/H\) is much greater than 1, the expression of the equivalent permittivity is  
\[\varepsilon_{e}=\frac{\varepsilon_{r}+1}{2}+\frac{\varepsilon_{r}-1}{2} \left(1+\frac{12H}{W}\right)^{-1/2} \tag{4}\]  
Due to the edge effect, each side of the patch is extended by \(\Delta l\) in the direction parallel to \(L\). \(L\) is modified by \(\varepsilon_{\rm e}\) and \(W/H\). Common expressions are  
\[\Delta l=0.412H\frac{(\varepsilon_{e}+0.3)(W/H+0.264)}{(\varepsilon_{e}-0.258 )(W/H+0.8)} \tag{5}\]  
The equivalent length of the patch is  
\[L=\frac{c}{2f_{r}\sqrt{\varepsilon_{e}}}-2\Delta l \tag{6}\]  
In Equations (3)-(6), \(W\) represents the patch width, \(L\) represents the patch length, c is the speed of light, \(\varepsilon_{r}\) and \(\varepsilon_{e}\) represent the relative permittivity and the equivalent permittivity of the dielectric substrate, and \(f_{r}\) represents the resonant frequency of the antenna. According to the formula above, the size of the proposed patch is as follows: \(W\) = 2.68 mm and \(L\) = 2.34 mm. The simulation results show that the resonant frequency of the antenna is 39.24 GHz, and the value of S11 is smaller, as shown in Figure 5a. After optimization, the operating frequency of the antenna is increased by reducing the length \(L\) of the patch, while the size of the substrate remains unchanged. The optimization process is shown in Figure 5b. As can be seen from Figure 5b, decreasing \(L\) causes the frequency to shift to the right, and the value of S11 to increase. Therefore, \(L\) is set to 2.04 mm in this paper, which is the choice when considering the operating frequency and the overall matching effect of the antenna. The operating frequency for this size is 43.47-46.21 GHz. Step 2: Build an antenna model with slots but no switches. Based on Step 1, add the L-slot on the left and right sides of the patch, respectively. At this point, the resonant frequency of the antenna is shifted from 44.8 GHz to 67.63 GHz, with an offset reaching 22.83 GHz. The S11 curve is shown in Figure 5c.