# Microwave Liquid Crystal Technology
## 5 Metallic Rectangular Waveguides
The LC section within the dielectric cavity has a width of \(1.0\,\mathrm{mm}\) a height of \(0.6\,\mathrm{mm}\) and a length of \(14.6\,\mathrm{mm}\), providing a differential phase shift of more than \(360^{\circ}\) according to the simulation carried out with CST Studio Suite. This demonstrator can only be biased magnetically, since no biasing electrodes can be included to this design. Hence, rare-earth magnets were placed outside the split-block during the measurements, see Figure 16. They are generating a magnetic field of around \(0.7\,\mathrm{T}\). The measurements were carried out using an Aritsu 37397C vector network analyzer (VNA) combined with two 3740A-EW extensions for frequencies in the extended W-band. These first proof-of-concept measurements revealed a good matching of \(-10\,\mathrm{dB}\) over an \(8\,\mathrm{\char 37}\) bandwidth. This limitation in bandwidth is due to the narrow-banded quarter-wave transformer steps. A differential phase shift between \(300^{\circ}\) to \(330^{\circ}\) was achieved, being \(60^{\circ}\) to \(100^{\circ}\) less than simulated. This is due to the flexible PTFE material which makes an exact processing of the LC cavity difficult. Further, the press-fit sealing causes a narrowing of the LC section. Accompanied with an insertion loss of less than \(3\,\mathrm{dB}\), this results in a phase shifter FoM between \(105^{\circ}/\mathrm{dB}\) to \(148^{\circ}/\mathrm{dB}\) from \(90\,\mathrm{GHz}\) to \(107\,\mathrm{GHz}\), as can be seen from Figure 17. The deviation of the insertion loss has its origin in the interruption of the current walls, due to a non-perfectly closed split-block. However, it is very challenging to implement an electrical biasing system due to the limited space as well as the electrical boundary conditions. Within the limited space of \(1.6\,\mathrm{mm}\) in width for the dielectrically filled section, several pairs of electrodes need to be placed on the substrate material, including stepped impedance structures for stripline mode suppression. Simulations with the in-house director dynamics simulation tool SimLCwg [8] proved, that two pairs of electrodes are sufficient but not ideal for a proper LC alignment, as shown in Figure 18[41]. There it can be seen, that a small region with a perpendicular LC alignment will still be left in the center of the waveguide when the LC is supposed to be aligned parallel. However, an odd number of pairs of electrodes is not possible, since the centered filling system of the split-block in combination with the press-fit sealed PTFE container should be kept in the design. Also, the limited space in combination with lithography challenges are limiting the realization of more than three pairs of electrodes. Figure 12:0 (**Left**) Cross section and (**Right**) measurement setup for the magnetically biased W-band rectangular waveguide phase shifter. The substrate material on which the electrodes were processed had to be as thin as possible. By this, the impedance of the parasitic microstrip line consisting of the biasing electrodes and the waveguide walls is decreased. Hence, the excitation of the unintended stripline modes is suppressed. For a first proof, a 20 \(\upmu\)m thin PET film was used. As metallization, chromium was evaporated on the PET film. After this, the electrodes including their stepped impedance structures are processed on the substrate by means of lithography steps. Further, the split-block design was changed in the way that the electrodes can be guided to the outside. There, the voltage source can be connected to the biasing lines with the help of spring-probe-pins. The design of the PTFE container was changed as well. Due to the mounting of the electrodes, the taper was chosen as discrete taper instead of a triangular taper. The processed biasing electrodes, the re-designed split-block as well as PTFE container are given in Figure 12:1  
Figure 12:2 Measured (solid) and simulated (dashed) results of the magnetically biased W-band rectangular waveguide phase shifter based on LC.