Relationship between settling accuracy and resolution

Hello

what is the relationship between settling accuracy and resolution obtained from the output of the operational amplifier,

High accuracy demands high open loop DC gain as I read many papers, why considering only the DC gain?

How we can define the value of the gain for certain accuracy

Thank you

Sure an amplifier is defined by vin*gain=Vout. So in a unity gain follower example with Vout=1 and gain of 1 million Vin must be 1uV or specifically the input might be 1.000001V into the non-inverting input and 1V on the output and inverting input.

Do the math for your scenario. It works for AC too (the amplitudes would be AC amplitudes and the gain would be the open loop gain at that frequency).

There are two components to the settling accuracy of the amplifier. Once you use the word "settling", it already suggests that you also look at things dynamically.
So, first you have the DC settling - that is where the amplifier output ends at when you wait infinitely long time. This is defined by you loop gain T and that static error is about equal to 1/T.
Second, you have on top of that also dynamic settling - you give a step at the amplifier input and look how much the output has settled (with respect to the DC value defined by the static error) at given time. So here you don't wait infinitely long. The error from dynamic settling is exp(-t/tau) - this is assuming first order roll off of your frequency response and doesn't take into account any slewing.