# Rethinking Figure-of-Merits of Liquid Crystals Shielded Coplanar Waveguide Phase Shifters at 60 GHz
## 1 Introduction  
Mobile broadband terminals [1, 2, 3] are becoming a prime need and rely increasingly on a continuously tunable liquid crystals (LC)-based [4, 5, 6, 7] millimetre-wave (mmWave) beam steering flat-panel [8] antenna array, in lieu of rotating parabolic dishes [9]. The recent upsurge of high-bandwidth low-loss use cases places new demands on the selection of highly anisotropic LCs, which is as important for meeting the phase-tuning requirement as it is vital for low power dissipations in gigahertz (GHz) [10, 11, 12, 13] and towards terahertz (THz) [14, 15, 16, 17] regimes. Figure-of-merit (FoM) [18, 19] is hence introduced to balance the above two key performance characteristics. For the past two decades of development in the field of LC-based phase shifters (variable delay lines), FoM has received a considerable level of interest as a dominant framework for the interpretation of performance, which is particularly instrumental when different research groups report their devices with diverse achievable phase-shifting ranges (at the same frequency) but intend to compare the maximum insertion loss in a fair manner.  
The history and fundamental physics of LCs have well been studied [20, 21]. From the electronically tunable LC material to a reconfigurable device (e.g., a phase shifter) combined with LC, without loss of generality, it is tempting to ask whether the material's characterised FoM could directly inform the LC-based phase shifting device's FoM. Such a research topic has neither been raised nor been answered clearly in existing literature. In the early contexts where conventional tunable materials (e.g., ferroelectrics [22, 23]) areemployed, various integral parameters of FoM are defined, e.g., a commutation quality factor [24]. Recent review papers on state-of-the-art microwave LC technologies [8, 25] attempted to analytically link the phase shifter device's FoM with the LC material's FoM based on several loss-free assumptions that are impractical. The derived approximated equations have neither conveyed physical insights, nor been supported by highly resolved simulations or experimental validations. In other reviews [6, 26], the authors only briefly mentioned the LC device's FoM without involving the material's FoM in the investigation.  
To investigate this knowledge gap, this work intends to quantify the tunable LC materials' FoM (ratio of materials' tunability to maximum dissipation factor) and the device's FoM (ratio of differential phase shift to the maximum insertion loss) based on both numerical and experimental analysis performed on a state-of-the-art shielded coplanar waveguide (SCPW) [7]. The SCPW phase shifter is fabricated with nickel-free gold plating of an optimum thickness [27] (Figure 1) and edge-mounted with V connectors (1.85 mm). To probe the underlying behaviours, simulation is performed using an Ansys High-frequency Structure Simulator (HFSS, see top right of Figure 1) based on a bespoke mixed-signal quasi-analytical model (see the schematic view at the bottom left of Figure 1) that allows affordable yet reasonably reliable computation with a dielectric partitioning scheme [28] for local polarisation and tunability analysis of LC molecules interfacing the guided mmWave signals. Geometry details of Figure 1 are provided in the following section.