# Design Optimization of Reconfigurable Liquid Crystal Patch Antenna
## 3 Results and Discussion
### Analysis of Optimal Liquid Crystal Thickness in Patch Antenna Substrate  
Structurally, the spacing between the top metallic patch and the bottom ground plane has a dominant effect on the antenna radiation property. That is, as the substrate thickness increases, the frequency bandwidth of the patch antenna increases. Therefore, in this chapter, we analyze how the frequency change rate according to the vertical profile of the patch antenna substrate varies.  
The patch antenna is fabricated by patterning metal on a printed circuit board (PCB) substrate such as glass. At this time, the top substrate and the bottom substrate are separated to inject a liquid crystal between the substrates of the patch antenna. According to the ratio of the liquid crystal cell gap to the sum of the thickness of the glass substrate on which the top patch and the bottom ground plane are located, the frequency change rate is confirmed through simulation. The cell gap of the liquid crystal is set to \(d_{\mathrm{LC}}\), and the thickness of the glass substrate was set to \(d_{\mathrm{sub}}\). While changing the values of \(d_{\mathrm{LC}}\) and \(d_{\mathrm{sub}}\)  
Figure 8: (**a**) dB(S11) examples and (**b**) E-plane radiation patterns of the patch antenna when dielectric constant changes from \(\epsilon_{\parallel}\) to \(\epsilon_{\perp}\).  
the frequency change rate of the antenna according to the change of the dielectric constant of the liquid crystal is obtained, as shown in Figure 9b.  
The thickness (\(d_{\mathrm{LC}}\)) of the liquid crystal was changed to 30, 60, 100, 200, and 300 \(\upmu\)m, and the frequency change rate was confirmed while increasing the thickness of the upper and lower substrates to 1000 \(\upmu\)m, respectively. As the liquid crystal cell gap increases, the frequency change rate of the patch antenna increases. In addition, when the cell gap is fixed, the frequency change rate decreases as the thickness of the glass with a dielectric constant increases. In Figure 9c, the frequency change rate is redrawn as the ratio of the thickness of the entire substrate, not the absolute value of the thickness. Regardless of the absolute value of the liquid crystal cell gap, it can be seen that if the ratio of the liquid crystal layer to the total substrate thickness is constant, the frequency change rate is almost the same. For example, suppose the ratio of the thickness occupied by the liquid crystal layer compared to the total thickness of the antenna substrate is constant at 0.2. In that case, a frequency change rate of about 60 MHz can be secured regardless of whether the liquid crystal layer used is 100 \(\upmu\)m or 300 \(\upmu\)m. Therefore, in order to obtain a desired frequency change rate, it can be secured by appropriately adjusting the overall thickness rather than using an unconditionally thick expensive liquid crystal.  
Figure 9: (**a**) Patch antenna substrates to investigate liquid crystal effects and frequency change according to (**b**) the absolute value change in the thickness of liquid crystal and glass and (**c**) the change in the ratio of the liquid crystal cell gap to the total thickness.