The fringing-field broadening of a phase-step profile and its dependence on the thickness of a liquid-crystal (LC) cell were studied in a simple, three-electrode LC cell structure consisting of two lateral electrodes biased with a differential voltage and a third, grounded, electrode placed on the opposite substrate. The results were compared both with an approximate analytical model developed earlier for a fringe-field-broadening kernel and with computer simulations. Good agreement between the experiment and the theoretical as well as the simulation results is shown.