A novel approach is proposed for miniaturizing the unit cell size of electromagnetic bandgap (EBG) structures that suppress power plane noise. In this approach, open stubs are introduced into the shunt circuits of these EBG structures. Since the stub length determines the resonant frequencies of the shunt circuit, the proposed structures can maintain the bandgaps at lower frequencies without increasing the unit cell size. The bandgap frequencies were estimated by dispersion analysis based on the Bloch theorem and full-wave simulations. Sample boards of the proposed EBG structures were fabricated with a unit cell size of 2.1mm. Highly suppressed noise propagation over the estimated frequency range of 1.9-3.6GHz including the 2.4-GHz wireless-LAN band was experimentally demonstrated.