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The effect of using composite material systems to create two-dimensionally periodic structures is analyzed. The structures utilize a two-dimensionally periodic material embedded within a host substrate to create multiple reflections, which inhibit propagation. Over the frequency region in which propagation is inhibited, the material is termed an electromagnetic bandgap (EBG) material. Through the fabrication techniques in the metamaterials program, namely free form fabrication and advanced ceramic manipulation, complex periodic systems are available. The effects that the availability of complex material systems has on the bandgap are numerous, including altered structure size, bandgap width, and attenuation per period. In this paper, the properties or the two-dimensional bandgap for several different material combinations are given.