# Tunable RF Filters Based on Liquid Crystal for Space Applications
## 2 Materials and Methods  
### Liquid Crystal  
The filter is tuned by changes in the effective permittivity of a liquid crystal volume inside the resonator.  
Figure 2: Photograph of a practical realization of the resonator, as shown in Figure 1.  
Liquid Crystals (LC) are a functional material, which is well known for its application in LC displays (LCD). In display applications, the anisotropic material is used in a controllable light valve, which regulates the color filtered backlight of thousands of individual addressable pixels and therefore creates a visible image on the screen.  
In the nematic phase, LC shows both properties of a liquid as well as a crystal: The material is liquid, but the molecules show a certain orientation. This orientation can be influenced by special surface treatment or by an external electrical field. Due to their anisotropy, the LC molecules tend to align along electrical field lines.  
The anisotropic LC properties are also used at microwave frequencies, where two different permittivities along and perpendicular to the molecule axis can be observed. By changing the molecule orientation in an LC layer or volume, it can be used as a material with tunable effective permittivity. Figure 3 shows an example of a simple liquid crystal molecule.  
The liquid crystal mixture was specifically developed for this particular filter application. The properties of the LC mixture are listed in Table 1.  
The wide temperature range of the filter requires a high clearing point of the LC mixture. The clearing point represents an upper limit of the nematic phase range, and therefore, the maximum temperature where the LC has anisotropic properties and can be used as a functional material. The microwave permittivity anisotropy (\(\Delta\varepsilon=\varepsilon_{\parallel}-\varepsilon_{\perp}\)) determines the tuning range of the filter. The loss tangent, \(\tan\delta\), measures the dielectric absorption of the LC mixture in both molecule orientations and has an impact on the insertion loss of the filter. The low-frequency dielectric anisotropy is important in designing the static electrical field used for orienting the liquid crystal volume. The rotational viscosity has an impact on the tuning speed of the filter--a higher rotational viscosity means a slower tuning speed. Rotational viscosity of the presented mixture is relatively high compared to standard LC display mixtures; however, a fast tuning speed is not very important for the given filter application. Therefore, a trade-off was made in favor of good microwave properties.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Item** & **Parameter** & **Measured Value** \\ \hline
**Clearing Point** & & 119.7 \({}^{\circ}\)C \\ \hline  & \(\varepsilon_{\parallel}\) & 3.21 \\
**Microwave Properties at 19 GHz** & \(\varepsilon_{\perp}\) & 2.43 \\  & \(\tan\delta_{\parallel}\) & 0.0034 \\  & \(\tan\delta_{\perp}\) & 0.0111 \\ \hline  & \(\varepsilon_{\parallel}\) & 7.4 \\
**Dielectric Anisotropy at 1 kHz** & \(\varepsilon_{\perp}\) & 3.1 \\  & \(\Delta\varepsilon\) & 4.3 \\ \hline
**Rotational Viscosity** & \(\gamma_{1}\) & 726 mPas \\ \hline  & K\({}_{1}\) & 13.9 pN \\
**Elastic Constants** & K\({}_{3}\) & 24.5 pN \\  & V\({}_{0}\) & 1.91 V \\ \hline \hline \end{tabular}
\end{table}
Table 1: Measured characteristic data of liquid crystal used for the filter (all data taken at 20 \({}^{\circ}\)C).  
Figure 3: Liquid crystal molecule example.