Comparison of Microwave Measurements and Theoretical Calculations of Dielectric Birefringence for a Liquid Crystal Loaded CPW-FE Phase Shifter

The effective permittivity and the variable phase shift of a microwave phase shifter using a liquid crystal loaded coplanar waveguide with floating electrode (CPW-FE), and the dielectric birefringence (Δϵ) of the liquid crystal layer in a liquid crystal microwave phase shifter are calculated, taking into account molecular orientations in a liquid crystal layer. The effective permittivity and the dielectric birefringence are determined from the liquid crystal molecular orientations and CPW-FE high-frequency electric field. Using liquid crystal continuum theory, we obtain a liquid crystal molecular orientation controlled by a bias voltage. Calculations of the dependence of the variable phase shift on the bias voltage and the dielectric birefringence qualitatively agree with measurements. Furthermore, the calculations confirm the mechanism of the change in permittivity.