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A fully planar antenna design incorporating a high impedance surface (HIS) is presented. The HIS is composed by a periodic array of subwavelength dogbone-shaped conductors printed on top of a thin dielectric substrate and backed by a metallic ground plane. First, the characteristics of a dipole over PEC or PMC layers, a dielectric slab, and the HIS are compared and studied in detail, highlighting the advantages provided by the use of the HIS. Then, the design of a low profile folded dipole antenna working at 5.5 GHz on top of the HIS is described. The surface provides close to 6% antenna impedance bandwidth and increased gain up to 7 dBi, while shielding the lower half space from radiation. The antenna structure comprises three metal layers without any vias between them, and its overall thickness is 0.059λ0. The dipole is fed by a balanced twin lead line through a balun transformer integrated in the same antenna layer. A prototype has been built and measurements confirming simulation results are provided.