The effect of the fixed charge distribution on the performance of a disk-shaped membrane is discussed theoretically. The present analysis generalizes the problem studied in the literature to a two-dimensional case. A parameter M characterizing the distribution of the fixed charge in the membrane is proposed to predict its current efficiency, eta. Four types of fixed charge distribution, including linear, exponential, trigonometric, and piecewise continuous distributions, are examined. If M < 0, the fixed charges are more concentrated on the left-hand side of the membrane, and the reverse is true if it is positive. If M = 0, the fixed charges are uniformly distributed. We find that eta increases monotonically with M regardless of the level of the electrical potential applied across the membrane. This is different from the result for a one-dimensional case, where eta has a local maximum as M varies. If M > 0, eta increases with the applied potential across the membrane, and the reverse is true if M < 0. If M -->0, eta is insensitive to the applied potential.