Tunable patch antenna printed on a biased nematic liquid crystal cell

A nematic liquid crystal (N-LC) cell is used as a substrate to a microstrip patch antenna in order to control its resonant frequency through the use of a DC or low-frequency AC bias voltage. The dielectric tensor properties of the liquid crystal (LC) are dependent on the orientation of the LC molecules, called the directors. The directors' tilt angle is controlled by the amplitude of an externally applied electric field. A finite-difference (FD) scheme with relaxation is formulated in order to solve the highly nonlinear partial differential equation (PDE) that models the directors' tilt angle in the LC. The problem of solving for the directors' field is coupled to an electrostatic boundary value problem (BVP) in a nonhomogeneous anisotropic medium. The orientation of the directors determines the constitutive parameters of the material. The HFSS is then utilized to obtain the radiation characteristics of the antenna under various bias conditions. Comparisons with measurements are provided in order to validate the proposed numerical approach and illustrate the potential use of LC's as tunable materials in microwave and millimeter-wave frequencies.