## 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
To compensate for the decreasing tuning effectivity, the length of a line phase shifter could be extended in practice to maintain the desired differential phase shift; however, this is at the expense of a larger size and higher insertion losses. Another parameter that might affect the tuning effectivity is the rubbing direction of the polyimide film, since there are two different pre-orientations of the LC molecules possible: (1) along the cross-sectional plane and (2) along the propagation direction. This has been analyzed for an IMSL design with an effective LC layer height of \(h_{LC}=100~{}\upmu\)m and a width \(w\) of the signal electrode of 200 \(\upmu\)m to achieve a line impedance of 50 \(\Omega\)[74]. Figure 17 shows the simulation results with the in-house software tool _\"SimLCwg\"_ for the orientation effectivity \(\tau_{\varphi}(V_{b})\) of the IMSL filled with GT3 versus time in seconds after the switch-on and switch-off of the bias voltage for cross-sectional pre-orientation. The parameter is the biasing voltage \(V_{b}\) from 1 to 15 V. To stress the switch-on and switch-off processes, there are logarithmically scaled curves specifically for \(V_{b}=4\) V, corresponding with the upper horizontal time axis. Figure 16: Schematic of a tunable LC-filled inverted microstrip line (IMSL), using the hybrid biasing concept with polyimide films on top of the ground plane and strip line, both processed on a carrier substrate with \(\varepsilon_{r,s}\) (**left**). The cross-section illustrates its assembly: strip line (**top**) and ground plane (**bottom**) processed on glass carrier substrates with \(\varepsilon_{r,s}\), each covered by thin, rubbed polyimide films (thin blue lines) for the unbiased state \(V_{b}=0\) V and a fully biased state \(V_{b}>V_{sat}\) (**center**). Permittivity and loss tangent versus bias voltage \(V_{b}\) (**right**). The values are given for the LC TUD-566. Figure 17: Orientation effectivity \(\tau_{\varphi}\) versus time for \(\tau_{\text{on}}\) and \(\tau_{\text{off}}\) for the cross-sectional pre-orientation of an IMSL of \(h_{LC}=100~{}\upmu\)m filled with GT3. The parameter is the biasing voltage \(V_{b}\) from 1 to 15 V. In addition, there are logarithmically scaled curves for \(V_{b}=4\) V [74]. Reprinted from [2], Cambridge University Press, 2020. In the unbiased state \(V_{b}=0\), where only pre-alignment by means of surface anchoring is active, not all LC molecules are perpendicular to the RF field lines, i.e., the orientation effectivity \(\tau_{\varphi}(0)>0\), which is actually around 0.14. In the fully biased state beyond saturation (\(V_{b}>V_{sat}\)), not all LC molecules are in parallel to the RF field, leading to an orientation effectivity \(\tau_{\varphi}=\tau_{\varphi}(V_{sat})<1\), which is actually 0.86 for 15 V. Thus, the tuning effectivity is \(\Delta\tau_{\varphi}=\tau_{\varphi}(V_{sat})-\tau_{\varphi}(0)\approx 0.72\) for cross-sectional pre-orientation. For pre-orientation in the propagation direction, where only the short axis of the LC directors is effective for the RF field and the biasing field, \(\tau_{\varphi}(V_{sat})\) is less, but \(\tau_{\varphi}(0)=0\) is optimum, leading to a similar tuning effectivity \(\Delta\tau_{\varphi}\approx 0.72\). However, in this case, the tuning effectivity is equal to the orientation effectivity \(\Delta\tau_{\varphi}=\tau_{\varphi}\). To sum up the results in Figure 17, the higher the bias voltage \(V_{b}\), the higher the orientation effectivity \(\tau_{\varphi}(V_{b})\), having its maximum at the saturation voltage \(V_{sat}\). Note that the response times approach theoretically infinite for each curve, i.e., for each bias voltage. Therefore, in practice, it is often defined as the 10 to 90% rise \(T_{90}^{10}\) and the 90 to 10% decay \(T_{10}^{90}\) in the orientation effectivity \(\tau_{\varphi}(V_{b})\). While the rise time depends very much on the bias voltage, the decay time is nearly independent.