Being it's this time of the summer, it sounds a little more like Early Blight, which is a fungus. Early blight, caused by the fungus Alternaria solani, develops on the leaves in July and August as plants begin to mature. It shows up first on the lower leaves as dark circular spots with concentric rings that increase to about l/4 inch in diameter . The spots develop a target pattern. Similar spots may also develop on the stems later in the season. Spots may also develop on the tubers -- these spots are sunken or raised with a definite margin. The internal tuber tissues are brown to purple in color, often with a yellowish margin. The early blight fungus overwinters in potato tubers, on potato crop refuse and in the soil. The fungus produces spores which are carried by the wind. Infection occurs when spores land on leaves that remain wet for a few hours. Early blight is favored by warm, humid weather. Early infection reduces tuber yields by reducing the amount of leaves and the amount of food that will be stored in the tubers.
Control of early blight begins with a fall cleanup of all potato crop refuse and by using healthy seed tubers in the spring. Potatoes should be planted in a different part of the garden than last year. If early blight shows up on the lower leaves before or at flowering, spray the plants with fungicide to prevent new infections on healthy leaves. Early blight almost always occurs on the vines as they mature later in the season. This late infection does not reduce yield and control is not necessary. Chlorothalonil fungicides (Ortho Multi-Purpose fungicide) offer the best control of early blight while copper fungicides are less effective, providing only fair control. (With help from: Colorado State University ).
Best of luck!