Preheat oven to 350 degrees F (175 degrees C). Lightly grease cookie sheets. Place popped popcorn into a food processor or blender; grind into small kernels.
In a large bowl, whip egg whites until frothy. Add baking powder, salt and cream of tartar; continue whipping to stiff peaks. Gradually mix in the sugar substitute. Fold in the popcorn pieces. Drop by teaspoonfuls onto the prepared cookie sheets.
Bake for 12 to 15 minutes in the preheated oven, or until lightly browned. Allow cookies to cool on cookie sheets before removing.