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The concept of a novel reactive impedance surface (RIS) as a substrate for planar antennas, that can miniaturize the size and significantly enhance both the bandwidth and the radiation characteristics of an antenna is introduced. Using the exact image formulation for the fields of elementary sources above impedance surfaces, it is shown that a purely reactive impedance plane with a specific surface reactance can minimize the interaction between the elementary source and its image in the RIS substrate. An RIS can be tuned anywhere between perfectly electric and magnetic conductor (PEC and PMC) surfaces offering a property to achieve the optimal bandwidth and miniaturization factor. It is demonstrated that RIS can provide performance superior to PMC when used as substrate for antennas. The RIS substrate is designed utilizing two-dimensional periodic printed metallic patches on a metal-backed high dielectric material. A simplified circuit model describing the physical phenomenon of the periodic surface is developed for simple analysis and design of the RIS substrate. Also a finite-difference time-domain (FDTD) full-wave analysis in conjunction with periodic boundary conditions and perfectly matched layer walls is applied to provide comprehensive study and analysis of complex antennas on such substrates. Examples of different planar antennas including dipole and patch antennas on RIS are considered, and their characteristics are compared with those obtained from the same antennas over PEC and PMC. The simulations compare very well with measured results obtained from a prototype λ/10 miniaturized patch antenna fabricated on an RIS substrate. This antenna shows measured relative bandwidth, gain, and radiation efficiency of BW=6.7, G=4.5 dBi, and er=90, respectively, which constitutes the highest bandwidth, gain, and efficiency for such a small size thin planar antenna.