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What is the purpose of the optional HxR regulators?

The HPR12/HNR12 are voltage regulators like the 7812/7912 IC’s. The difference is that they have a wider bandwidth, lower noise and lower output impedance. Additionally, they have kelvin-sense inputs so you can make a local regulator that doesn’t have to be physically close to the circuit being powered. Typical op-amp based circuits have a much greater sensitivity to power supply ripple and noise than the data sheet’s DC PSRR values would suggest.