## 4 Flat-Panel Beam-Steering Antennas with Low-Profile Phase Shifters with Fast Response
### Fast Tuning Low-Profile Planar Delay Line Phase Shifter
This time, a low-cost 700 \(\upmu\)m thick BF33 glass (\(\varepsilon_{r}=4.53,\ \tan\delta=0.008\)) is used as the top and bottom substrate, forming a LC cavity of about 4 \(\upmu\)m height filled with TUD-566. According to Figure 26, these varactors with a relatively large overlapping area of \(w\times L_{Overlap}\) are built up by metal  
Figure 24: Design schematic of a realized unit element. Cross-section of CPW Section A (**left**) and grounded CPW (varactor) section B (**middle**), both with the corresponding transmission line parameters of the proposed structure on the right side [185,227]. Figure 25: Measured S-parameters for the two extreme tuning states for \(V_{b}=0\) V and \(V_{b}=60\) V and the FoM versus frequency [185]. Reprinted from [2], Cambridge University Press, 2020.  
bridges and the signal line of the CPW. These bridges connect the two ground planes of the CPW on the bottom substrate by using gold via pillars, creating a small grounded coplanar waveguide (gCPW) segment with an additional ground plane on the top substrate. For both ends of the bridge, a trapezoidal geometry was chosen for implementing the vias over a large area to reduce their resistance. The geometrical parameters are set to \(w=50\)\(\mu\)m, \(g=150\)\(\mu\)m, \(L_{Vit}=240\)\(\mu\)m, \(L_{Overlap}=200\)\(\mu\)m, \(w_{Vit}=60\)\(\mu\)m, and \(w_{Trop}=60\)\(\mu\)m. The loaded-line phase shifter, which is built up by 38 identical unit elements, provides a differential phase shift of \(\Delta\varphi_{\text{max}}=360^{\circ}\) at the operating frequency of 20 GHz with a bias voltage of \(V_{b}\) of up to 30 V. By this, the LC can be tuned from the perpendicular pre-orientation to the parallel orientation, using the full anisotropy. The return loss was less than \(-20\) dB and the maximum insertion loss was about \(IL_{\text{max}}<5.5\) dB, thus yielding a FoM of \(65^{\circ}\)/dB. The response times to change the phase of \(360^{\circ}\) is \(\tau_{\text{on}}=40\) ms and \(\tau_{\text{off}}=260\) ms, respectively. It agrees well with \(\tau_{\text{off}}\) of the parallel-plate cell. The response times could further be reduced by using varactors with a thinner LC layer and/or a nematic LCs with lower rotational viscosity \(\gamma_{rot}\) as for Merck's third-generation LCs. Improved FoMs can be achieved by using a modified strip line arrangement on both layers according to Figure 27 (upper right) to reduce the shunt inductance of the loaded segments, but allowing a reduced input impedance. In this case, impedance matching sections are required at both ends for 50 \(\Omega\) input and output ports. Due to the reduced shunt inductances, this approach provides much better results than the structure in Figure 24.  
Figure 23.0 _Cont._  
Figure 23.1 Schematic of a LC varactor build up by a metal bridge on the top substrate (**left**), connecting the two ground planes of the CPW by vias and the signal line on the bottom substrate, filled with LC. Top view (**right**) [175]. As mentioned before, the slow-wave effect enables orientation effectivities \(\tau_{\varphi}\) greater than one, which refers to the tunability of a completely filled homogeneous gCPW or parallel plate waveguide. Here, the propagation constant is determined by the dielectric parameters of the LC. Using a loaded-line topology, the effective propagation constant can be increased by using proper \(L_{A}^{\prime}\) and \(C_{B}^{\prime}\) as independent design parameters. In order to achieve the same phase shift, the reduction in the required phase shifter length goes up to a factor of four for very thin layers and wide strip lines, as depicted in Figure 23.2 The plots show that the FoM is almost constant over the distance \(s\) between the conductors, which is slightly less than the effective LC layer height \(h_{LC}\), depending on the conductor thickness. Thus, for a width \(w=200\)\(\upmu\)m, FoMs of about 130 and 115\({}^{\circ}\)/dB can be achieved using TUD-566 and GT7 at 30 GHz, respectively, and 138\({}^{\circ}\)/dB with GT7 at 60 GHz.