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For an ideal opamp the unity gain buffer has a voltage gain of exactly 1; so Vin = Vout:
But if we neglect all non-idealities except the DC open loop gain Aol, how can we mathematically/analytically demonstrate the effect of the Aol to the error between the input and the output voltage? I have read once that if Aol=infinity then Vin = Vout but if Aol=10000 then Vin is not exactly equal to Vout. But I cannot derive myself why neither I can find a source in internet for derivation of this.
But I cannot derive myself why neither I can find a source in internet for derivation of this.
Consider this: -
At the point marked with the red X we can say: -
$$(V_{IN}-V_{OUT})\cdot A_{OL} = V_{OUT}$$
$$A_{OL}\cdot V_{IN} = V_{OUT}\cdot(1 + A_{OL})$$
$$\dfrac{V_{OUT}}{V_{IN}} = \dfrac{A_{OL}}{1+A_{OL}}$$
Can you take it from here and plug some numbers in?
