In this paper, a wedge-shaped invisibility cloak whose diameter gradually increases along the arms of the wedge is introduced. The constitutive parameters of the cloak are obtained using a proper transformation. By considering two special cases for incident fields, (TEz and TMz), and paying attention that the wedge structure is invariant in axial and radial directions, the reduced set of cloaking parameters are obtained spatially invariant and larger than one, keeping the PML (perfectly matched layer) condition for perfect cloaking performance. Spatially invariant and isotropic constitutive parameters lead to the physically realizable cloak in a wide band of frequency for this specific type of incident fields. Manuscript profile