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An infinitesimally thin spiral antenna, sandwiched by bottom and top dielectric layers having the same relative permittivity, is analyzed under the condition that the dielectric layers are of finite extent and the antenna is backed by an infinite conducting plane. As the thickness of the top dielectric layer increases, the input impedance and axial ratio (AR) vary in an oscillatory fashion, with a period slightly larger than one-half of the guided wavelength of a wave propagating in an unbounded dielectric material. These oscillatory variations are reduced by adding a layer, called the "anti-reflection layer (ARL)," to the top dielectric layer. A representative spiral antenna with an ARL shows a frequency bandwidth of approximately 11% for a 3-dB AR criterion, having a gain of approximately 13 dBi (6 dBi higher than a printed spiral antenna without the top dielectric and ARL) and a voltage standing wave ratio of less than 1.2.