In this paper, we analyzed the transmission characteristics of directional couplers in two parallel waveguides within a two-dimensional photonic crystal structure. Additionally, we analyzed the transmission characteristics of a resonator placed in waveguide. Next, we investigated the transmission characteristics of hexagonal resonator circuits situated in middle of the parallel waveguides. Considering effect of the resonator installed in a straight waveguide, propagation simulation with band-limited input signals were performed and compared for transmitted power at the output port. We found that only specific frequencies pass through the resonator in a straight waveguide. It can be applied to drop the desired channel by demultiplexing from wavelength division multiplexed (WDM) signals.