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The total harmonic distortion (THD) and the power supply noise, qualified by the power supply rejection ratio (PSRR) and by the power supply induced intermodulation distortion (PS-IMD), are recognized to be potential drawbacks of class D amplifiers. In this paper, analytical expressions for the THD, PSRR, and PS-IMD of the bang-bang control class D amplifier (bang-bang amp) are derived; the bang-bang amp is arguably the most power-efficient class D amp for low-voltage power-critical applications including hearing aids. Based on the derived expressions, the effects of important parameters on the THD, PSRR, and PS-IMD are investigated, providing good insight to the design of the bang-bang amp to meet given design specifications. The analytical analyses are verified by comparing them against HSPICE simulations and hardware measurements. The bang-bang amp is also compared against the prevalent pulsewidth modulation class D amp, and in most cases, the former is shown to possess superior parameters, including lower power dissipation and hardware advantages for low-voltage power-critical applications.