# Design Optimization of Reconfigurable Liquid Crystal Patch Antenna
## 2 Materials and Methods  
### Modeling of Numerical Calculation  
A patch antenna is a planar shape that induces electromagnetic radiation through the gap between sandwiched metallic plates on top and bottom planes. As shown in Figure 1a, the total length of the patch length (\(L\)) and fringing field length (\(\Delta L\)) parallel to the wave propagation direction generates resonance at a frequency corresponding to the half wavelength, causing the radio waves to radiate into the air. If this is expressed more clearly as a formula [28], the resonance frequency (\(F_{\text{res}}\)) can be calculated as \(F_{\text{res}}=c/(2L_{\text{e}}\surd{\varepsilon_{\text{e}}})\), \(L_{\text{e}}=L+2L\). The \(c\) is the speed of light, and the \(\varepsilon_{\text{e}}\) is the effective permittivity of the substrate. The factors that determine the resonant frequency (\(F_{\text{res}}\)) are the patch antenna length and substrate thickness and the dielectric constant of the substrate material. By replacing the substrate with a liquid crystal, it is possible to implement a frequency tunable patch antenna by utilizing the dielectric anisotropy of the liquid crystal according to the voltage.  
In resonance mode, the electric field on the surface of the patch antenna is strongly coupled at both ends of the direction of the wave propagation as shown in Figure 1b, and null in the center region. Therefore, focusing on this electric-field distribution, we systematically analyze the effect of dielectric anisotropy of the liquid crystal on the operation of the patch antenna while controlling the injection location and the area of the liquid crystal. Additionally, in the case of ferrite, ferroelectric, and semiconductor devices, the dielectric loss increases as the frequency increases, whereas the dielectric loss of liquid crystal decreases as the frequency increases [29; 30; 31]. So, it is advantageous when used as a tunable device in the mm-wave frequencies. However, since liquid crystal is a costly material and cannot be used indefinitely, research to maximize tunability while using a minimum amount of liquid crystal is necessary. First, the position and the area of the liquid crystal on the surface of the patch, which significantly affects the amount of frequency change, are determined by considering the electric-field distribution over the antenna surface. Second, in terms of the substrate thickness, the effect of the thickness of the liquid crystal layer on the frequency change rate is analyzed, and finally, an idea for maximizing the frequency change rate and securing the radiation performance of the antenna is proposed. It is expected to provide a design rule for optimizing the performance of a patch antenna for variable frequency using a minimum amount of liquid crystal. In this paper, all the simulations are performed  
Figure 1: (**a**) Schematic diagram of a tunable liquid crystal patch antenna and (**b**) electric-field distribution on a patch antenna surface. Here, \(L\) and \(\Delta L\) refer to the patch length and fringing field length, respectively.  
by using an HFSS (high-frequency structure simulator, Ansys Inc.), which is a tool for analyzing electromagnetic wave propagation in the microwave frequencies.