# Microwave Liquid Crystal Technology
## 5 Metallic Rectangular Waveguides  
A very common approach at K\({}_{\mathrm{a}}\)-band frequencies around 30 GHz for the realization of tunable LC-based high-performance RF components is the dielectrically filled metallic waveguide. The dielectric filling contains a cavity, in which the tunable LC material is filled. Hence, the cross section of the rectangular waveguide is (partially) filled with tunable LC, see Figure 13.  
By controlling its effective permittivity, the electrical length of the waveguide can be varied, resulting in a tunable delay line. In combination with the intrinsic low ohmic loss of the waveguide, this leads to an easy realization of phase shifters with a high figure-of-merit (FoM) of more than 120\({}^{\circ}\)/dB [36]. The LC orientation is controlled by means of six pairs of electrodes, which need to be included into the waveguide, due to its electrical boundaries. A high complexity of these biasing electrodes is required for avoiding the propagation of parasitic stripline modes between the electrodes and the waveguide's walls. An example for the parasitic modes as well as the biasing electrodes'  
Figure 12: Planar Antenna with LC enabled beam steering. (**Left**) early demonstrator of an \(2\times 2\) array published in [35] with (**top left**) the measured beam pattern at 17.5 GHz with a antenna gain of 6 dB realized by phase shifters with a FoM of 90\({}^{\circ}\)/dB. (**Right**) prototype of an \(8\times 8\) sub-array realized in thin film LC technology. The complete antenna consists of 16 panels and shows a gain of 30 dB with a steering range of \(\pm 55^{\circ}\). Figure 13: Schematic cross section of the metallic rectangular waveguide LC phase shifter with partial LC filling. complexity is given in Figure 14. The electrodes were processed on a thin Hostaphan film of 50 um thickness, being lead to the outside of the metallic waveguide for contacting to the voltage supply. Such phase shifters are used in lightweight horn antenna arrays for satellite communications. Although the LC's response time is comparatively high, it is already enough for specific applications, such as the tracking of a low earth orbit (LEO) satellite from a geostationary (GEO) satellite, where a steering speed of maximum 73\({}^{\circ}\)/min is required [11; 34; 37]. The concept of a dielectrically filled rectangular waveguide can also be adapted to W-band frequencies around 100 GHz [38; 39]. There, the waveguide was realized in split-block technology made of brass, where the bottom part has a u-shape, being sealed with a top lid, see Figure 15. The waveguide is tapered in width and height within the dielectrically filled section to still provide a single mode propagation. The tapering is done by means of \(\lambda/4\) transformer steps. The dielectric cavity is made of PTFE (\(\varepsilon_{r}=2.06\) and \(\tan\delta=0.000\,222\)[40]), being tapered in a triangular shape. The PTFE cavity is also designed in a u-shape, which is sealed by pressing the metallic lid on top. Figure 14: **(Left)** Field intensity of the guided modes within the dielectrically filled waveguide phase shifter for the case of straight biasing electrodes. Most power is confined in the TEM stripline mode, while nearly no power is in the fundamental TE\({}_{10}\) waveguide mode. **(Right)** Biasing electrodes with stepped-impedance structures and \(\lambda/4\)-stub lines for strip mode suppression. Figure 15: Split-block design of the magnetically biased W-band rectangular waveguide phase shifter based on LC. The dimensions of the split-block are \((l\times w\times h)=31.6\,\mathrm{mm}\times 30.0\,\mathrm{mm}\times 33.0\, \mathrm{mm}\). After sealing, the LC is filled into the dielectric cavity through filling holes on the top part of the split-block, see Figure 16. With the help of a syringe the LC is flushed through the cavity, by which the amount of air bubbles within the RF path can be significantly reduced.