## 4 Flat-Panel Beam-Steering Antennas with Low-Profile Phase Shifters with Fast Response
### Low-Profile Planar Inverted Microstrip Line and Grounded Coplanar Waveguide Phase Shifter
Hence, \(T_{90}^{10}\) and \(T_{10}^{90}\) correspond to the switch-on and switch-off response times in Equations (5) and (6), respectively, and related to that, to the 10 to 90% rise and 90 to 10% decay in the measured capacitance for LC varactors or differential phase shift for LC phase shifters. at 60 GHz, the FoM increases, while the response time remains the same. This is mainly because the electrical losses decrease (despite the \(\sqrt{f}\)-law), since electrically, the dimensions increase by a factor of 2, and in addition, dielectric losses due to the LCs slightly decrease. Hence, these topologies are well suited for higher frequencies. Figure 18: Plots for designing an IMSL phase shifter filled with first-generation LC GT3-23001 (**above**), with second-generation LC TUD-566 (**middle**) and third-generation LC GT7-29001 (**below**) for 30 GHz (**left**) and 60 GHz (**right**), respectively. As the top substrate, use is made of fused silica with a height \(h_{\mathrm{s}}=300\)\(\upmu\)m, a relative permittivity of \(\varepsilon_{r,s}=3.82\), and a dielectric loss factor of \(\tan\delta_{\mathrm{s}}=5\)\(\cdot\)10\({}^{-5}\). The electrical conductivity of the metal parts is set to \(\sigma=4\cdot\)10\({}^{7}\) S/m. A pre-orientation of the LC in the propagation direction was chosen. These plots exhibit the curves of a constant phase shifter figure-of-merit (FoM) (full red lines), orientation effectivity \(\tau_{\varphi}\) (dashed blue lines), and line impedance \(Z_{line}\) (dotted gray lines), depending on the strip line width \(w\) (vertical axis), the thickness \(s\approx h_{LC}\) (lower horizontal axis), and the 90 to 10% decay time \(T_{10}^{90}\), which corresponds to the switch-off response time (upper horizontal axis). Another planar topology often used in the literature for LC-tunable phase shifters are grounded CPWs [66; 74; 262; 263], where the schematic is shown in Figure 19 together with the calculated parameter plots for GT3 at 30 GHz by using the in-house software tool _\"SimLCwg\"_ again. Comparing it with Figure 18 (upper left) indicates that the orientation effective \(\tau_{\psi}\) (dashed blue lines) and the phase shifter figure-of-merit FoM (full red lines) are significantly less than for an IMSL. Therefore, IMSL is the preferred planar line topology. Beside this analysis, some lab-scale demonstrators have been implemented to investigate the feasibility. In [45; 46; 47; 186], two inverted microstrip line-based phase shifters were realized with similar geometry, i.e., with a physical length of about 50 mm and LC layer heights of \(h_{LC}\) = 230 \(\upmu\)m and 254 \(\upmu\)m, respectively, as well as a line width of \(w\) = 600 \(\upmu\)m, using a polyimide film PI-2555. Both result in a FoM of 110\({}^{\circ}\)/dB at 24 GHz with a Merck's first-generation LC, MDA-03-2838, having a material's figure-of-merit \(\eta_{LC}\approx\) 11.8. The phase shifters were tuned by a bias voltage of up to 40 V, where 90% of the maximal differential phase shift was achieved by less than 20 V. A schematic and the realized phase shifter are shown in Figure 20. As substrate material, IMM3 from Rogers Corp. was chosen, which has a permittivity of \(\varepsilon_{\mathrm{r}}=3.27\) and a dielectric loss of \(\tan\delta=2\cdot 10^{-3}\). The ground electrode and the carrier substrate on the top side are separated by a spacer made of RT/Duroid5880 from Rogers Corp. with \(\varepsilon_{\mathrm{r}}=2.2\) and \(\tan\delta=9\cdot 10^{-4}\), forming the LC cavity. Thin polyimide films of about 200 to 300 nm thickness was spin coated on both inner surfaces to pre-align the LC molecules. Figure 19: Plots for designing a grounded CPW phase shifter filled with LC GT3-23001 for 30 GHz (**right**). As substrate, use is made of fused silica. The electrical conductivity of the metal parts is set to \(\sigma=4\cdot 10^{7}\) S/m.