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By means of area-transformation method, the material parameters of the invisible cloaks in elliptic-cylindrical and spherical coordinates were obtained. The material parameters of the invisible cloaks are nonsingular and the cloaks can operate in a wide bandwidth due to the area-transformation rather than the point-transformation. The invisible properties of the cloaks are nearly perfect when the original area is small enough compared with its counterpart in the transformed space. Full wave simulations based on finite element method verified the designed cloaks.