An Efficient Mixed-signal Dielectric-partitioning Model of Liquid Crystals based Shielded Coplanar Waveguide for Electronically Reconfigurable Delay Lines Design

The optoelectronic proliferation of liquid crystals based passive microwave and millimetre-wave reconfigurable technology relies not only upon low-cost micro-fabrication techniques, but also on high-fidelity yet efficient device design and simulation methodologies based on an in-depth understanding of the complex coupling between waveguiding geometries and multi-material systems through multi-physics models. While closed-form analytical solutions are not possible for multi-volume complex geometries, numerically attempting the problem is of research and development interest, in particular for gaining fundamental insights on the coupling between liquid crystals optoelectronic response and millimetre-wave interactions, hence producing guidelines for in-house code development of specific optoelectronic device prototypes without resorting to commercial off the shelf software. To this end and by way of illustration, this work proposes a novel mixed-signal dielectric-partitioning model for local polarisation and tunability analysis into a liquid crystals based shielded coplanar waveguide tunable delay line targeting applications in the 57-66 GHz band. Due to the transverse electromagnetic nature of the fully enclosed coplanar waveguide structure, the traditional two-step approach (liquid crystals' quasi-electrostatic simulation in microscopic scale progressing to millimetre-wave simulation in macroscopic scale) could be rearranged into one single stage in terms of the molecular directors with respect to the identical electric vector field distributions. The proposed standalone and quasi-analytical model is verified by experimental measurements implemented on a 0-pi tunable true-time-delay phase shifter, with a 7.94% improvement in the predicting accuracy of the effective line length required, and a huge reduction in computational costs as compared with the traditional two-step method. The proposed efficient model is envisioned to inform the development of highly efficient in silico tools with high fidelity for liquid crystals based reconfigurable applications beyond displays.