# Microwave Liquid Crystal Technology
## 4 Use Cases for LC-based Microwave Devices
Researchers around the world develop new materials which can be used for tunable devices. Recent examples are e.g., phase change materials [31; 32] and electrochromic materials [33]. These have a great potential, and should be monitored consciously. Figure 10: Channel loss for different frequencies as sum of free space path loss (dashed lines) and the atmospheric attenuation according to ITU standard atmosphere (solid lines) for homogenous medium between transmitter and receiver. As reference the properties of a geostationary satellite for broadcasting at K\({}_{\mathrm{u}}\)-band (12 GHz) with 36,000 km transmission range with approximately 210 dB of insertion loss are highlighted. To describe the requirements and properties of LC-based array antennas in more detail, the use case of a \(\mathrm{K_{a}}\)-band LEO satellite system is discussed. As the satellite is non-stationary, the antennas must track the satellite all time. The orbit time of such a satellite is around 120 min, so the phase shifters have to provide tuning speed of more than roughly \(70^{\circ}/\mathrm{min}\)[34]. Hence, realization technology and material properties must match the requirements. The change in electrical length of the phase shifter is proportional to the dielectric contrast (anisotropy) of the used LC mixture. The phase shift of a transmission line phase shifter is defined by  
\[\varphi=\beta\cdot l\propto\sqrt{\epsilon}\cdot l, \tag{14}\]  
with the physical line length \(l\). The differential phase shift is defined as  
\[\Delta\varphi=\varphi_{\parallel}-\varphi_{\perp}=\left(\beta_{\parallel}- \beta_{\perp}\right)\cdot l\propto\left(\sqrt{\epsilon_{\parallel}}-\sqrt{ \epsilon_{\perp}}\right)\cdot l \tag{15}\]  
Hence, LC mixtures with high anisotropy, low dielectric loss but also high viscosity are targeted. Beside the material properties, the technological implementation is also challenging, as a hermetic liquid-proof must be realized to prevent the LC from leaking. One example for the realization of fully integrated planar LC-based array antennas has been published in [35]. Here, the phase shifters are implemented as meandered microstrip line phase shifters directly coupled to an array of patch antennas, see Figure 12. While planar implementations are well suited at the lower end of the frequency band, ohmic losses of the microstrip line topology increase with frequency. While the planar topology is meanwhile followed by the company Alcan Systems Darmstadt, Germany, research is focusing on other implementations such as high-performance rectangular waveguide based implementations. To compare different implementations the phase shifter Figure of Merit (FoM) is defined as  
\[\mathrm{FoM}=\frac{\Delta\Phi}{\max\mathrm{IL}} \tag{16}\]  
which is the ratio of the maximally achievable phase shift \(\Delta\Phi\) divided by the highest insertion loss for all tuning states \(\max\mathrm{IL}\). Figure 11: Possible implementation of the weighting functions \(w_{mn}\) for array antennas. The block diagrams are simplified in such a way that all components and stages not essential for signal weighting are neglected.