Size reduction of an electromagnetic bandgap (EBG) structure with large patches and small branches that connect adjacent patches for a power/ground plane pair is studied. To shrink the dimensions with a high isolation at the frequency of interest, this paper provides two approaches. One is a geometric approach which is to place two narrow slits on each patch. The increase of branch inductance with the long slit successfully decreases the on-set frequency of the stopband without increasing the patch size. The other approach is to use high-K material for a thin dielectric layer. In this case, the size reduction can be predicted according to a scaling law. These approaches are applied together to realize an EBG structure with the entire size of less than 20 mm on a side. It covers the GSM band with sufficient isolation. Through this study, the dispersion-diagram analysis is used to predict the stopband characteristics.