## 4 Flat-Panel Beam-Steering Antennas with Low-Profile Phase Shifters with Fast Response
### Fast Tuning Low-Profile Planar Delay Line Phase Shifter
After having processed the 1 \(\upmu\)m thick gold structures (CPW and floating electrode) on both substrates by a standard lithography process, polyimide films are rubbed on both processed substrates in propagation direction with a thickness much lower than 100 nm to pre-orient the LC molecules. Hence, this device is fabricated in a fashion similar to LCDs. For its realization, fused silica with a height of \(h_{s}=700\)\(\upmu\)m, a relative permittivity of \(\varepsilon_{r,s}=3.82\), and a dielectric loss factor of \(\tan\delta_{s}=5\cdot 10^{-5}@16\) GHz were used as the top and bottom layer, which were separated by spacers with a diameter of about 5 \(\upmu\)m to determine the height of the LC cavity, which was filled afterwards with TUD-566. Although the whole structure was actually filled with the LC, Segments A without additional ground plane behave as a standard CPW line, since the thin LC layer is not affecting its properties significantly. The center conductor width was set to \(w=60\)\(\upmu\)m, while the gap between the center and adjacent conductors was set to \(g=195\)\(\upmu\)m. The total length \(\ell\) of the phase shifter was 12.7 mm. A bias voltage of \(V_{b}\) of up to 60 V is applied via the ITO biasing lines. By this, the LC can be tuned from the perpendicular pre-orientation to the parallel orientation, using the full anisotropy. The results of the S-parameter measurements versus frequency are shown in Figure 25. For a frequency of 20 GHz, more than a 130\({}^{\circ}\) differential phase shift has been achieved, accompanied with a \(IL_{\text{max}}\) of slightly more than 2 dB, thus obtaining a FoM better than 60\({}^{\circ}\)dB. Note that since a  
Figure 23: Schematic of a CPW periodically loaded with LC varactors (bridges between ground planes), where the LC is filled in between the bridge (grounded plane) and signal line of the CPW. length \(\ell\) of this loaded line phase shifter of 12.7 mm (\(\approx 0.85\lambda_{0}\)) provides \(\Delta\varphi_{\rm max}>130^{\circ}\) at 20 GHz, a 360\({}^{\circ}\)-phase shifter would be \(\ell\approx 3.3\lambda_{0}\). Due to its small LC layer height \(h_{LC}\) of 4.5 to 5 \(\upmu\)m, the measured response time \(\tau_{\rm on}\) is less than 110 ms from zero bias to a fully tuned state, and \(\tau_{\rm off}\) is now less than 340 ms from the fully tuned state back to zero, which is significantly faster than for the IMSL with the same LC above. This experimental value of \(\tau_{\rm off}\approx 340\) ms for the second-generation LC TUD-566 agrees well with the theoretical values of \(\tau_{\rm off}\approx 330\) to 410 ms for 4.5 to 5 \(\upmu\)m of the parallel-plate cell in Figure 8. It is somewhat slower than those measured for the single varactor of \(\tau_{\rm off}=92\) ms, using the first-generation LC GT3, because of its lower viscosity. Using the aforementioned analysis method with the transmission line parameters \(R^{\prime}\), \(L^{\prime}\), \(G^{\prime}\), and \(C^{\prime}\) for each Section A and B according to Figure 24, in order to calculate the effective line parameters for an input impedance around 50 Ohm, the differential phase shift obtained by using TUD-566 is about 124\({}^{\circ}\) at 20 GHz. The simulated switch-off response time is \(\tau_{\rm off}\approx 319\) ms, which agrees quite well with the experimental results. However, the resulting FoM of 108\({}^{\circ}\)/dB significantly overestimated the measured one above, because this analysis method does not deal with the low-pass filter like characteristic of the structure and the reduction of the \(Q\)-factor (reduction of more than 30% at 20 GHz [185]) due to cross currents and the resulting shunt inductance. Another practical approach with slightly different unit elements of the periodic structure is reported in [175] for a loaded-line phase shifter with a total length of \(\ell=27\) mm. It provided similar results.