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Body area networks (BANs) are of importance for telemedicine and telehealth services, so they have caught many engineers' attention. A coordinator in a BAN plays a significant role to collect signals from sensors and interface with telecommunication networks. Since the wireless channel of BAN is very complicated and changeable, the modulation is not fixed. As a result, the coordinator must have different demodulators. In this paper, we propose a method to design a low-power circuit which can both demodulate BPSK and QPSK by using the technique of datapath merging. The results of the experiments show that the proposed demodulator implementation can reduce around 23% hardware area compared with the traditional implementation.