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I'm designing a low noise variable power supply, while finding a low noise voltage regulator, I found this circuit which is called an opamp voltage regulator.

I don't really understand how does this work. My theory is that it works like a linear regulator like LM317 or LM7812 but I'm not sure. So can anyone explain to me how this circuit works.

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So can anyone explain to me how this circuit works.

It's a linear regulator; it uses negative feedback to adjust the BJT base voltage to just the right level to keep the output voltage at a defined value. The op-amp can be thought of as an ideal device with infinite gain and so, when operating correctly, its two inputs are, ostensibly, at the same voltage. I've slightly simplified your circuit and added some voltages and resistor values: -

enter image description here

Because the BJT is "within" the feedback loop it can be thought of as being inside the op-amp: -

enter image description here

Now, it's just an op-amp that can deliver an amp or two. No difference conceptually.

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That is more of a concept drawing than a real schematic, but it is a linear regulator. It is similar to the internal workings of a 7812-type regulator, except that 78xx regulators have only R1 and R3; there is no adjustability in the standard application.

Note that it differs significantly from the LM317 regulator type. Among other things, the ground current of a 7812 can vary with the output load current, while the current out of an LM317 "Adjustment" pin is almost perfectly constant.

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