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link

In the above link, in the end it says

"If you replace the VOUT in the equation for V− by this value you'll find

V−=0V"

Does anyone understand what it means? If so, please explain it to me.

Community
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1p2r3k4t
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1 Answers1

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It's quite clear.

The equation for the inverting input voltage for that circuit is

$$ V_- = V_{IN}\left(\dfrac{R_F}{R_{IN}+R_F}\right) + V_{OUT}\left(\dfrac{R_{IN}}{R_{IN}+R_F}\right) $$

The equation for the output voltage for that circuit is

$$ V_{OUT} = -\dfrac{R_F}{R_{IN}} V_{IN} $$

So, the first equation above becomes

$$ V_- = V_{IN}\left(\dfrac{R_F}{R_{IN}+R_F}\right) -\dfrac{R_F}{R_{IN}} V_{IN} \left(\dfrac{R_{IN}}{R_{IN}+R_F}\right) = 0$$

But really, there's a far simpler way to "see" the result that the voltage at the inputs of an ideal op-amp must be equal when negative feedback is present.

(1) The output voltage of an ideal op-amp is \$A(V_+ - V_-)\$ in the limit as \$A \rightarrow \infty \$. Or as often said, the gain of an ideal op-amp is "infinite".

(2) Thus, for the output voltage to be finite, \$(V_+ - V_-) \$ must go to zero as \$A \rightarrow \infty \$, i.e., the input voltages must become exactly equal in the limit of infinite gain.

(1) and (2) establish that, for an ideal op-amp, the input voltages must be equal for the output voltage to be finite.

What is left to show is that negative feedback enforces this constraint while positive feed back opposes it which is not done in the linked answer.

Alfred Centauri
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  • I think that it will be more accurate to replace "for the output voltage to be finite" with "for the output voltage to be non-saturated" - I don't remember an infinite output swing to be a part of an ideal op-amp model. – Vasiliy Oct 02 '13 at 12:00
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    @Vasiliy, the output voltage of an *ideal* op-amp can be *any* value (infinity is *not* a value), i.e., an ideal op-amp does not saturate, so your statement wouldn't be accurate at all. – Alfred Centauri Oct 02 '13 at 12:20
  • I didn't know this. Thx – Vasiliy Oct 02 '13 at 12:25
  • Here's a link to Marshall Leach's notes on ideal op-amps: http://users.ece.gatech.edu/mleach/ece4435/chap01.pdf where he writes the following: "The voltage gain is very large, approaching infinity in the limit. If the output voltage is finite, this means that the difference voltage between the two inputs must approach zero". – Alfred Centauri Oct 02 '13 at 12:31
  • What I meant to say is that if the op-amp is saturated, then the input voltage can be higher than zero. Anyway, it is very minor semantic distinction which refers to open loop configuration, which is by itself is not that useful. Thx for the link, BTW – Vasiliy Oct 02 '13 at 12:46