In this thesis, the methods of making photonic bandgap in microwave waveguide are proposed. For each structure, transmission and reflection characteristics are measured and analyzed. And, by enlarging the separation of central two cells in the photonic bandgap structures, the defect modes are introduced and analyzed. Moreover, new type of duplexers using photonic bandgap are proposed. The duplexers use two wide photonic bandgaps or defect modes to control the propagation of microwaves. In the structure using two different photonic bandgaps, an additional narrow reflection band appears in the transmission spectrum when the PBG structure is not properly located relative to the T-junction. By considering multiple reflections, it is proved that this additional reflection band in each PBG structure results from the interference between the input wave and the reflected wave from the other PBG structure. An effective way to prevent this interference effect is also discussed.