The miniaturization of unit cells in planar electromagnetic bandgap (EBG) structures has been difficult because the stopband frequency depends on the unit-cell size. To solve this problem, we developed an EBG structure that uses two power planes (dual power plane: DPP) with the addition of a capacitive coupling element. This enables us to easily enlarge the capacitance formed in the unit cell and achieve miniaturization with a stopband frequency of interest. Using full-wave simulation, we tested a 2-mm-square (4-mm2) unit cell of the DPP-EBG structure and measured a stopband frequency around 2.4 GHz.