Electromagnetic bandgap (EBG) structures that prevent propagation of electromagnetic waves within a given frequency range are quite effective in suppressing simultaneous switching noise on parallel power planes. However, it is quite time consuming to compute the stopband frequencies of interest using full-wave electromagnetic simulation of the entire structure. In contrast, using dispersion-diagram analysis based on a unit-cell network of EBG structures is more efficient and less time consuming. This paper presents an approach for two-dimensional EBG structures by extending a well-known dispersion-diagram analysis of one-dimensional infinite periodic structures. The stopbands predicted with the proposed analysis were compared with good agreement to measured and simulated results. In addition, the concept was applied to test the stopband range of EBG structures formed on an actual printed circuit board with a test coupon of an EBG unit cell placed on the same board.