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Mushroom-like electromagnetic band-gap (EBG) structures exhibit unique electromagnetic properties that have led to a wide range of electromagnetic device applications. This paper focuses on the reflection phase feature of EBG surfaces: when plane waves normally illuminate an EBG structure, the phase of the reflected field changes continuously from 180° to -180° versus frequency. One important application of this feature is that one can replace a conventional perfect electric conductor (PEC) ground plane with an EBG ground plane for a low profile wire antenna design. For this design, the operational frequency band of an EBG structure is defined as the frequency region within which a low profile wire antenna radiates efficiently, namely, having a good return loss and radiation patterns. The operational frequency band is the overlap of the input-match frequency band and the surface-wave frequency bandgap. It is revealed that the reflection phase curve can be used to identify the input-match frequency band inside of which a low profile wire antenna exhibits a good return loss. The surface-wave frequency bandgap of the EBG surface that helps improve radiation patterns is very close to its input-match frequency band, resulting in an effective operational frequency band. In contrast, a thin grounded slab cannot work efficiently as a ground plane for low profile wire antennas because its surface-wave frequency bandgap and input-match frequency band do not overlap. Parametric studies have been performed to obtain design guidelines for EBG ground planes. Two novel EBG ground planes with interesting electromagnetic features are also presented. The rectangular patch EBG ground plane has a polarization dependent reflection phase and the slotted patch EBG ground plane shows a compact size.