A shunt pulsation trap for a cyclic positive displacement (PD) compressor reduces gas pulsation and NVH, and improves off-design efficiency, without using a traditional serial pulsation dampener and a variable geometry. A shunt pulsation trap for a cyclic PD compressor is configured to trap and attenuate gas pulsations before discharge and includes a housing having a flow suction port, a flow discharge port, a compressor cavity, and a pulsation trap chamber adjacent to the PD compressor cavity. The pulsation trap chamber includes at least one pulsation dampening device, at least one injection port (trap inlet) branching off from the PD compressor cavity into the pulsation trap chamber and a feedback region (trap outlet) communicating with the PD compressor outlet. The associated methods of reducing pulsations are included as another aspect of the invention.