Non-uniform voltage distribution across the electrode area results in inhomogeneous thin-film RF plasma deposition in large-area reactors. In this work, a two-dimensional analytic model for the calculation of the voltage distribution across the electrode area is presented. The results of this model are in good agreement with measurements performed without plasma at 13.56 MHz and 70 MHz in a large-area reactor. The principal voltage inhomogeneities are caused by logarithmic singularities in the vicinity of RF connections and not by standing waves. These singularities are only described by a two-dimensional model and cannot be intuitively predicted by analogy to a one-dimensional case. Plasma light emission measurements and thickness homogeneity studies of a-Si:H deposited films show that the plasma reproduces these voltage inhomogeneities. Improvement of the voltage uniformity is investigated by changing the number and position of the RF connections.