To overcome the intra EMC problems in wireless communications, electromagnetic bandgap (EBG) structures can be used to effectively reduce power-bus noise. We previously proposed a vialess open-stub EBG structure. However, it still has the intrinsic disadvantage of a narrow stopband because it uses the open-stub's resonance. Thus, this paper aims to optimize the structural parameters of the vialess open-stub EBG structure to sufficiently suppress power-bus noise in a wider stopband. The structural parameters to determine the noise-reduction performance of the vialess open-stub EBG structure are the branch width Wb, the stub width Ws, and the unit-cell length a. Rectangular power buses were designed as test vehicles through the analytical approach and used to evaluate the stopband expansion and the noise suppression in the stopband in a full-wave simulation. The transmission characteristics showed that, after wb, Ws, and a are optimized, the stopband is expanded from 0.61 GHz (2.23-2.84 GHz) to 1.56 GHz (2.20-3.76 GHz). In addition, an optimized structure was made that reduced the amount of noise by approximately 10 dB.