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An analysis is presented of the directivity and the design optimization of cylindrical electromagnetic band gap (CEBG) structures constituted of metallic wires and with defects. The directivity is studied for different transversal periods, radial periods and numbers of rings. In the proposed configuration, the defects are designed by removing multiple wires, such as to form a horn-shaped aperture inside the periodic structure. From numerical results, obtained with a home-made finite difference time domain (FDTD) code, it is shown that the structures with defects present a directive beam in the stop-bands of the corresponding structures without defects. The radiation characteristics of the CEBG material are compared with those of an equivalent-plane sectoral horn to explain the directivity mechanism. An optimization method is also proposed for minimizing the number of wires. To validate the analysis, an optimized directive antenna with a dipole as an excitation source was fabricated and measured.