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It make work with (-) input grounded, but that violates the input voltage limits.
1715693061
When the device is regulating the output, both inputs are at (nearly) the same voltage.
At the output, since the small amount of switching noise injected into the signal by the switch, will be X100 times less in relation to the signal amplitude.
It's not "poor".
Because that's all it needs to have for normal operation.
The 5V reference voltage is normally connected to a divide-by-two resistor pair to give a 2.5V reference at one input.
The other input then has a divider from the output to generate 2.5V at the desired regulated voltage...
The TL431 is a programmable shunt regulator (rather like a programmable Zener).
It starts to conduct current, cathode-to-anode, when the voltage at it REF pin (junction of R2 and R3 in your circuit) goes above 2.5V.
When it conducts, then it sinks current from R1, thus reducing to base current...
A low-cost (<U$2), rail-rail I/O general-purpose CMOS op amp with very good specs is the TLV915x, where x is 1 (single), 2(dual), or 4(quad).
It has an offset voltage of 125µV, 4.5MHz GBW, 10.5nV/√Hz noise, and 20V/µs slew-rate.
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