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The fundamental effects of superstrate (cover) materials on printed circuits antennas are investigated. Substrate-superstrate resonance conditions are established which maximize antenna gain, radiation resistance, and radiation efficiency. Criteria are determined for material properties and dimensions for which surface waves are eliminated and a radiation efficiency due to substrate-superstrate effects of percent is obtained. Criteria for nearly omnidirectional -plane patterns and nearly omnidirctional -plane patterns are presented. Finally, a general criterion is given for choosing a superstrate to optimize efficiency for the important case of nonmagnetic layers with the antenna at the interface.