# Design Optimization of Reconfigurable Liquid Crystal Patch Antenna
## 3 Results and Discussion
### Analysis of Optimal Liquid crystal Position on the Patch Surface
In the center of the patch antenna where the null electric field forms, even if liquid crystal is injected, it does not affect the frequency change rate much. The size of the liquid crystal in the \(x\)-direction is fixed at 20 mm, and the rate of frequency change is analyzed while increasing the size in the \(y\)-direction, as shown in Figure 5. Unlike the increase in the \(x\)-direction, as the size of \(a_{\mathrm{y}}\) increased, the tendency is monotonically increased. However, when the \(a_{\mathrm{y}}\) becomes more extensive than the patch antenna size of 20 mm, the frequency change rate becomes constant. Figure 4: (**a**) Schematic diagram of the patch antenna that increases the size of the liquid crystal in the \(x\)-axis, and (**b**) the amount of frequency change. Figure 5: (**a**) Schematic diagram of the patch antenna that increases the size of the liquid crystal in the \(y\)-axis, and (**b**) the amount of frequency change. In Figures 6 and 7, the liquid crystal area is fixed, and the frequency change rate is checked while moving the position where the liquid crystal is injected. One side of the liquid crystal is set to 20 mm, which is the length of one side of the patch antenna, and the other side is fixed at 6 mm so that a certain degree of frequency change can be seen without exceeding the size of \(\lambda_{e}/4\). First, a 6 \(\times\) 20 mm\({}^{2}\) liquid crystal is placed parallel to the \(y\)-axis in Figure 6a, and the frequency change rate is checked while moving on the \(x\)-axis, which is the wave propagation direction. In the graph of Figure 6b, when a 6 \(\times\) 20 mm\({}^{2}\) liquid crystal is located near the zero points, which is the center of the antenna, it shows a slight change of less than 5 MHz, and when the liquid crystal moves near \(\pm\)7 mm near both ends of the patch, it provides the maximum change rate of about 40 MHz. When the liquid crystal leaves both ends, the rate of frequency change decreases again. This simulation confirms that the change in the dielectric constant of the liquid crystal significantly affects the frequency change amount of the patch antenna when it is at both ends of the patch antenna. However, it has little effect when it is at the center. Figure 6: (**a**) Top view of the patch antenna showing the liquid crystal moving in the \(x\)-axis. (**b**) Frequency change rate according to the position of the liquid crystal in the \(x\)-direction. Figure 7: (**a**) Top view of the patch antenna showing the liquid crystal moving in the \(y\)-axis. (**b**) Frequency change rate according to the position of the liquid crystal in the \(y\)-direction. A 6 \(\times\) 20 mm\({}^{2}\) liquid crystal is placed parallel to the \(x\)-axis, and the frequency change rate of the patch antenna is checked while moving in the \(y\)-axis direction in Figure 7a. In this simulation, a constant frequency change rate of about 15 MHz is shown at most locations, except for \(\pm\)10 mm, where the liquid crystal deviates slightly from the area of the patch antenna. Since the electric field distribution is almost the same in the \(y\)-direction, when the liquid crystal with the same size is moved, the frequency change rate is uniformly displayed. As a result of confirming the horizontal distribution of the liquid crystal on the surface of the patch antenna, that is, the frequency variability according to the area and position of the liquid crystal, the larger the area where the liquid crystal is distributed, the higher the frequency variability. However, if the same amount of liquid crystal is injected, the frequency variability can be increased if the liquid crystal is injected near both ends of the patch in the \(x\)-direction rather than the central portion of the patch antenna. A liquid crystal having a volume of 6 mm in the \(x\)-direction, 20 mm in the \(y\)-direction, and 0.1 mm in thickness is placed at the end of the patch antenna parallel to the \(y\)-axis direction, and then a simulation is performed to predict the dB(S11) and gain patterns of the antenna.