Two types of dual periodic circuits are introduced. The distributions of passbands and stopbands are generated from their dispersion relationships. Based on the study, Brillouin diagrams of three representative special cases are drawn; S parameters of these three cases are simulated by Aglient ADS; the S parameters of one of the three cases are verified by an experiment. The phase characteristics are compared with those generated from the dispersion relationship. The theoretical analysis and the experimental verification show that both types of the periodic structures can behave as electromagnetic band gap （EBG） structures, right-handed structures （RHS）, and left-handed structures （LHS）, when they operate at different frequency ranges. Thus, the possibility of a physical structure showing these three different characteristics at different frequency ranges is proven.
