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Intrinsic noise sources and their correlation in gallium-nitride high electron-mobility transistors (HEMTs) are extracted and studied. Microwave noise measurements have been performed over the frequency range of 0.8-5.8 GHz. Using measured noise and scattering parameter data, the gate and drain noise sources and their correlation are determined using an equivalent-circuit representation. This model correctly predicts the frequency-dependent noise for two devices having different gate length. Three noise mechanisms are identified in these devices, namely, those due to velocity fluctuation, gate leakage, and traps.