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Novel microwave and millimeterwave (mm-wave) bandstop filters using artificial periodic substrate electromagnetic bandgap (EBG) are investigated in this paper. Three types of microstrip structures using periodically modified trace width, patterned dielectric substrate, and periodically modified ground plane are treated, respectively. By periodically modifying either the width of the conductor trace, the substrate height, or the dielectric constant of a standard microstrip transmission line, it has been possible to design microwave bandstop filter functions with wide stopband characteristics and reduced size, compared to conventional microwave/RF filter structures. Commercial electronic design automation (EDA) and computational electromagnetic tools such as Agilent's advanced design system (ADS) and CST Microwave Studio are used in the design and simulations of these filter structures. The effects of the physical parameters of the structures on the filter characteristic are studied. The design procedure and simulation results are described and possible applications of these filter structures are discussed in this paper. A particularly wide stopband is achieved by the circuits presented in this paper, which use only a few cell elements. A significant performance improvement of microstrip patch antenna has been observed by implementing one of the presented EBG periodic substrate structures.