Navigating Aspect Ratio Effects in Response Time Challenges of Liquid Crystal Coaxial Phase Shifters for Next-Generation mmW Communications

Millimeter-wave analog beam steering will play a major role in the current 5G and future 6G ecosystems. One material that may tip the balance is the liquid crystal (LC), a tunable dielectric that can be opto-electronically tuned to generate continuously variable phase (time) delays for passively feeding phased antenna arrays. However, a major barrier that prevents its implementation for expanded mission-critical applications or commercial success has long been its tuning speed, which is inversely related to the square of the LC layer's thickness. To this end, this work newly quantifies the geometry aspect ratio (AR) effects in our recently developed coaxial phase shifter filled with millimeter-wave-tailored LC of dielectric constant (Dk) between 2.5 and 3.3, to understand the interplay between the dielectric thickness, Dk of LC, and the device's response time (rise time) under the assumption that 50 Ω impedance matching is maintained. The semi-analytical and semi-empirical model predicts that a rise time of 2.48254 seconds is needed for our LC-filled coaxial phase shifter with an LC thickness of 0.34876 mm to switch from the 0 V bias (the isotropic state of LC with Dk of 2.754) to the saturated bias (Dk of 3.3). Limitations and discrepancies of the prediction are discussed for planar and non-planar implications of LC devices.