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Although power-supply noise, qualified by power- supply rejection ratio (PSRR), has been recognized as a potential drawback of Class-D amplifiers (CDAs) compared to linear amplifiers, the mechanisms of PSRR for CDAs are not well established. It is also not well recognized that the power-supply noise can intermodulate with the input signal, manifesting into power-supply induced intermodulation distortion (PS-IMD), and that the PS-IMD can be significantly larger than the output distortion component at supply noise frequency. Furthermore, techniques to improve PSRR and PS-IMD are largely unreported in literature. In this brief, by means of a linear model, the PSRR and PS-IMD of single-feedback and double-feedback CDAs are analyzed and analytical expressions derived. A simple method is proposed to improve PSRR and PS-IMD with very low hardware overheads, and the improvement is ~ 26 dB. Analytical expressions for PSRR and PS-IMD of the improved design are derived and the pertinent parameters thereof are investigated. The model and analyses provide practical insight to the mechanisms of PSRR and PS-IMD, and how various parameters may be varied to meet a given specification.