This work presents the results of a study on electronically scanning antennas based on liquid crystals. In particular, the study aims at assessing the feasibility of a leaky wave antenna providing a continuous scanning at fixed frequency with a single voltage control. The radiating part is constituted by a parallel plate waveguide partially filled by liquid crystals with gradually modulated, electrically small slots etched on the upper wall. The feeding network is realized through a pillbox network. The concept is first validated through the realization and experimental characterization of a static antenna prototype. Preliminary experimental results on a reconfigurable antenna prototype are also presented.