# Design Optimization of Reconfigurable Liquid Crystal Patch Antenna
## 3 Results and Discussion  
### Analysis of Optimal Liquid crystal Position on the Patch Surface  
As mentioned in the previous chapter, the operating frequency of the patch antenna is determined according to the patch length in the wave propagation direction, and radiation mainly occurs at both ends of the wave propagation direction. Therefore, considering the electric field distribution on the surface, the analysis is conducted through simulation to see how the frequency change rate changes while partially injecting a liquid crystal. In the nematic phase LC with directional ordering, the LC director can be controlled by the electric field, and dielectric constant change can be generated through the direction of LC director. In this simulation, the frequency change was confirmed by varying the dielectric constant in the electric field applied through the upper and lower patch antenna electrodes. In Figure 1a, glass substrates with a dielectric constant of 5.5 are used as the substrates with the patch antenna and the metal ground plane, and the patch antenna is placed on top of the upper glass substrate and the metal ground on the bottom of the lower glass substrate. The thickness of the upper and lower glass substrates is fixed at 100 \(\upmu\)m each. The liquid crystal substrate is inserted into the center between the two glass substrates as the part marked green in Figure 1a, and the thickness of the liquid crystal layer is also fixed at 100 \(\upmu\)m. The size of the patch antenna is designed to operate in the 3.5 GHz band with a size of 20 \(\times\) 20 mm\({}^{2}\), and the size of the metal ground plane is fixed at 30 \(\times\) 30 mm\({}^{2}\). In the first analysis process, the liquid crystal area is set as an independent variable, as shown in green in Figure 3a. The thickness of the liquid crystal is fixed at 100 \(\upmu\)m, and a square liquid crystal is placed in the center of the patch antenna, and the length of one side is gradually increased to calculate the rate of frequency change for the area \(a\times a\) mm\({}^{2}\). The frequency change rate of the patch antenna was calculated from the difference between the resonant frequency when the dielectric constant was 2.19 and the resonance frequency when the dielectric constant was changed to 2.43. In Figure 3b, the frequency change hardly occurs at the point where the area is less than about \((\lambda_{\rm e}/4)^{2}=100\) mm\({}^{2}\), whereas the frequency change rate increases in proportion to the area as the area of the liquid crystal increases through the \((\lambda_{\rm e}/4)^{2}\) point. As the area of the liquid crystal passes the 400 mm\({}^{2}\) corresponding to the patch antenna area, it can be seen that the increase is slowed and eventually converges to a constant value. Here, \(\lambda_{\rm e}\) means the effective wavelength considering the dielectric constant and corresponds to the length of about 40 mm. Figure 3: (**a**) Schematic diagram of the patch antenna that increases the liquid crystal area in a square shape, and (**b**) the amount of frequency change. Next, the size of the liquid crystal in the \(y\)-direction is fixed at 20 mm (\(\lambda_{\mathrm{e}}/2\)), and the rate of frequency change of the patch antenna is investigated by increasing the size in the \(x\)-direction only. Here, as shown in Figure 4, the results are confirmed by increasing the liquid crystal size in two opposite directions, direction 1 and direction 2, respectively. Similar results are obtained for both directions. While the size of \(a_{\mathrm{x}}\) increases from 0 at the beginning, the frequency change rate linearly increases according to the change in the dielectric constant of the liquid crystal. On the other hand, the frequency change rate stays at 50 MHz while changing from about 8 to 12 mm. As \(a_{\mathrm{x}}\) increases to 12 mm or more, the frequency change rate increases again, and when the size of the liquid crystal exceeds the patch size of 20 mm, the frequency change rate does not increase and converges to about 100 MHz.