## 3 Passive Phased Arrays with Integrated Metallic and Dielectric Waveguide Phase Shifters
### High-Performance Metallic Waveguide Phase Shifter  
Since metallic waveguides have intrinsically lower metal losses than planar transmission lines, they will provide higher FoM for the same LC, particularly with higher frequencies. This can be decisive for applications where limited power is available or where generally high effectivity is required by handling high power and where its bulky appearance is not critical as for the horn-antenna array in Figure 14.  
The first experiments on an LC-tuned waveguide phase shifter at 30 GHz, using display LCs BL006 and E7, are presented in [257]. There, a center plane electrode, parallel to the broadside of a modified section of an WR28 rectangular waveguide applies a static field parallel to \(\overset{\rightarrow}{E}_{RF}\), and a pair of magnets on both small sides of the waveguide apply a static field perpendicular to \(\overset{\rightarrow}{E}_{RF}\), providing a phase shift of a bit more than \(100^{\circ}\) from 60 V to 200 V. The response times by the bias electric and magnetic fields was given as 0.1 s and typically 2 s, respectively. An innovative approach in [64] made also use of a WR28 rectangular waveguide, but it was only partially filled with LC in a Teflon or Rexolite container, which was centered in the waveguide as shown in Figure 15 (middle), and by tuning the LC phase shifter section with multiple pairs of electrodes on the top and bottom wall of the waveguide according to Figure 15. It exhibits snapshots for the two extreme tuning states, where the simulation was carried out with the in-house software tool _\"SimLCwg\"_[74; 229]. On the left, LC directors are mainly vertical oriented, i.e., in parallel to \(\overset{\rightarrow}{E}_{RF}\) experiencing \(\varepsilon_{r,h}\) and \(\tan\delta_{\parallel}\) (left), and on the right, LC directors are mainly horizontally oriented, i.e., in perpendicular to \(\overset{\rightarrow}{E}_{RF}\) of the TE\({}_{10}\) mode, which experiences \(\varepsilon_{r,\perp}\) and tan\(\delta_{\perp}\). This purely voltage-driven biasing concept is necessary to achieve high tuning effectivity and reasonable response times, despite large LC layer heights \(h_{LC}\) of several millimeters, since additional alignment layer forces have nearly no effect anymore. Large \(h_{LC}\) values require also high bias voltages \(V_{b}\). To improve the performance, the phase shifter section is built up by an LC-filled container in the center, since the field strength of the TE\({}_{10}\) fundamental mode is strongest there, providing high tuning effectivity. Since \(\varepsilon_{r,\parallel}>\varepsilon_{r,\perp}\), the RF field will be more concentrated in the center for LC orientation parallel to \(\overset{\rightarrow}{E}_{RF}\) (Figure 15 left) than for LC orientation perpendicular to \(\overset{\rightarrow}{E}_{RF}\) (Figure 15 right). At the same time, tan \(\delta_{\parallel}<\) tan\(\delta_{\perp}\); thus, losses can be nearly equal in both tuning states by the right design, mainly the width of the container, which was chosen to be 1/7 of the width \(a\) of the waveguide. This has a positive impact in terms of lower average losses and higher differential phase shift, i.e., on higher FoM. From measurements of a lab-scale demonstrator with a total length \(\ell=5\) cm and a phase shifter section of 3 cm filled with LC TUD-566 in [64], the FoM was more than 200\({}^{\circ}\)/dB at frequencies around 35 GHz for magnetically biasing and drops down to about 140\({}^{\circ}\)/dB for electrical biasing, due to the losses of the biasing electrodes processed on a 12 \(\upmu\)m thin Mylar foil and because the tuning effectivity could not fully be exploited as for magnetic biasing. To avoid reflections at the material edges, the LC container has a taper of 0.5 cm length at each side, while the metallic taper is integrated into the transition from the feed waveguide to the phase shifter section.