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Planar periodic metallic arrays behave as artificial magnetic conductor (AMC) surfaces when placed on a grounded dielectric substrate and they introduce a zero degrees reflection phase shift to incident waves. In this paper the AMC operation of single-layer arrays without vias is studied using a resonant cavity model and a new application to high-gain printed antennas is presented. A ray analysis is employed in order to give physical insight into the performance of AMCs and derive design guidelines. The bandwidth and center frequency of AMC surfaces are investigated using full-wave analysis and the qualitative predictions of the ray model are validated. Planar AMC surfaces are used for the first time as the ground plane in a high-gain microstrip patch antenna with a partially reflective surface as superstrate. A significant reduction of the antenna profile is achieved. A ray theory approach is employed in order to describe the functioning of the antenna and to predict the existence of quarter wavelength resonant cavities.