Passive-active crosstalk beyond low-frequency breakdown in mathematical-physical models of liquid crystal phase shifters at low-frequency applications

While most of the liquid crystal-based configurable and reconfigurable devices nowadays were designed to operate at the high-frequency microwave, millimetre-wave and optical wavelengths, there is a scarce of discussion on their feasibility at transmitting the low-frequency (LF) spectrum (low-data-rate but featuring lower attenuation and longer-range communication or detection). This work identifies a crosstalk vulnerability between the LF transmission signal and the LC-driving bias field for the first time. Furthermore, we comparatively quantify diverse line length requirements spanning the spectrum from 1 Hz to 100 GHz for the same LC coaxial phase shifters but fabricated by two different strategies, one with the conventional alignment agent-rubbing process (technically demanding, time-consuming, and costly), the other one featuring rubbing-free at the cost of a reduced tuning range of permittivity per unit length (i.e., requesting a larger physical size for 360° shifting to feed a phased array antenna).