Hello, Peter,
About the two metrics that you mentioned here, I think both are useful. Of course the selection depends on applications. Most textbooks/papers use PSRR instead of PSR so that make many readers confused. For eg., when we characterize bandgap reference, we want to know the gain of the power supply 'disturbance' towards the output. That is
power supply rejection as you mentioned. Personally, I would like to use the term
power supply rejection here, but many textbooks/papers use the term PSRR, although it has different definition for bandgap from that for amplifiers.
When we characterize amplifiers, we need know the ratio of power supply rejection and the nominal signal-path gain. That is
power supply rejection ratio as you mentioned.
How much PSR or PSRR is OK depends on the applications.
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Best regards,
Yawei