## 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  
An early example of a 4 cm long inverted microstrip line (IMSL) delay line phase shifter filled with K15 can be found in [259]. It exhibits a FoM \(<\) 20\({}^{\circ}\)/dB for the X-band and a response time of about one second for a LC layer height of \(h_{LC}\) = 50 \(\upmu\)m and width of the strip line of \(w\) = 100 \(\upmu\)m. A similar FoM \(<\) 20\({}^{\circ}\)/dB at 20 GHz was achieved in [260] by using a display LC BL-008 filled in an IMSL phase shifter on a glass substrate, yielding a phase shift of 370\({}^{\circ}\), accompanied by an insertion loss of about 20 dB. The width of the strip line was \(w\) = 100 \(\upmu\)m and the LC layer height \(h_{LC}\) = 50 \(\upmu\)m. In [261], two-phase shifter configurations have been studied, using inverted microstrip lines with two coplanar waveguide accesses, where the active parts are 3 cm and 1.1 cm long, respectively, and both are 100 \(\upmu\)m thick filled with K15. The phase shift at 20 GHz was 61\({}^{\circ}\) with a bias voltage of up to 20 V, accompanied with an insertion loss roughly between 4 and 5 dB, i.e., an FoM in between 12\({}^{\circ}\)/dB and 15\({}^{\circ}\)/dB. With the emergence and progress of newly developed LC mixtures, the FoM could be improved significantly. Thus, with Merck's first-generation LCs, an FoM of about 110\({}^{\circ}\)/dB at 24 GHz was already achieved in 2003 with an IMSL phase shifter [45; 46; 47]. Since then, various IMSL phase shifters at different frequencies are presented, e.g., in [65; 70; 74; 128; 166; 173; 175; 185]. Figure 16 (left) illustrates its assembly: the strip or signal line (top) and ground plane (bottom) are processed on separated glass carrier substrates with \(\varepsilon_{r,s}\). The inner sides of these carrier substrates with the strip line and ground plane, respectively, are covered by thin, rubbed polyimide films (thin blue lines in Figure 16 center) for pre-alignment of the LC director \(\overrightarrow{n}\). Then, the substrate carrying the signal electrode is flip-chipped, introducing a cavity in between both substrates with a height \(h_{LC}\) fixed by spacers. Then, this cavity is sealed to prevent a leakage of LC afterwards, when the LC is filled inside this cavity. This LC has a dielectric constant \(\varepsilon_{r,LC}\), which varies in between \(\varepsilon_{r,\perp}\) and \(\varepsilon_{r,\parallel}\), depending on the bias voltage \(V_{b}\) according to Figure 16 (right), where a few values of \(\varepsilon_{r,LC}\) and \(\tan\delta_{LC}\) for TUD-566 are indicated for different bias voltages. For electrical tuning, the strip line and the ground plane are used as biasing electrodes according to the hybrid biasing scheme, as explained before. With the change of \(\varepsilon(V)\) due to the bias voltage \(V\), the propagation constant \(\gamma(V)\sim\sqrt{\mu\cdot\varepsilon(V)}\) changes, and hence, the differential phase shift \(\Delta\varphi(V)\sim\frac{2\uppi}{\lambda_{0}}\Big{\{}\sqrt{\varepsilon(0)}- \sqrt{\varepsilon(V)}\Big{\}}\cdot\ell\) for a certain physical length \(\ell\). A major objective in designing an IMSL phase shifter is to maximize the material's tunability, to achieve a high tuning effectivity \(\Delta\tau_{\varphi}\), and hence, a high differential phase shift \(\Delta\varphi\) and FoM. For example, if a carrier substrate with a significantly higher permittivity compared to the LC is chosen (\(\varepsilon_{r,s}>>\varepsilon_{r,LC}\)), the RF field will propagate partially in this substrate instead in the LC section, reducing the tuning effectivity \(\Delta\tau_{\varphi}\), and hence, the FoM. E.g., for \(\varepsilon_{r,s}=2.2\), 3.82, 7, and 10, the FoM is about 92, 87, 82, and 78\({}^{\circ}\)/dB at 30 GHz and 110, 106, 93, and 62\({}^{\circ}\)/dB at 100 GHz for an IMSL with \(w=200~{}\upmu\)m, \(s\approx h_{LC}=100~{}\upmu\)m and \(h_{s}=300~{}\upmu\)m filled with GT3-23001 [74].