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This paper presents a novel two-dimensional (2-D) defected ground array (DGA) for planar circuits, which has horizontal and vertical periodicities of defect structure. The defected unit cell of DGA is composed of a Sierpinski carpet structure to improve the effective inductance. Measurements show that the proposed DGA provides steeper cutoff characteristics, lower cutoff frequency, and higher slow-wave factors than the conventional periodic defected ground structure in the same occupied surface.