Hi,
There is a mistake:
top line: left of Q1 it says "Vin" - this is correct. But right of Q1, it also says "Vin" --> it should be "Vout"
Thus I doubt the circuit is from a reliable source. --> always look at reliable sources, as there are:
* Semiconductor manufacturers
* universities
* reputable electronics designers
(but not from random web sites)
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Functional description:
* Input capacitor C1,
* output capacitor C2
* power transistor Q1
* voltage reference VRef
* error amplifier OPAMP
* voltage divider R1, R2 as feedback to adjust the output voltage.
Basically it regulates VAdj to be the same as VRef.
If VAdj is too low, it increases the voltage on base_Q1, thus it increase VOut ... and vice versa.
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Would V-Ref be the same for both cases or not ?
If you use the same regulator: yes.
A different regulator may have a different VRef.
To me this is a too general question at all. It´s like asking: do all people have same shoe size when driving different cars? --> same people will have same shoe size, different people will have different shoe size.
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There are many different voltage regulators, with different internal and external circuit. Thus your schematic does not apply to all regulators.
As always:
Read the datasheet - it usually has a functional description.
Klaus