The Gain of the Inverting Amplifier and Virtual Earth....

[Adam Ghannam]

This is an inverting amplifier incorporating an ideal op-amp with infinite open loop gain. I have a simple question concerning the derivation of its gain (-R2/R1). The point I circled is at 0V (Virtual Earth) but then, if V+=V-, Shouldn't Vout=0 regardless of what R2 and R1 are?? What's wrong in my understanding.

 

[Dale]

Shouldn't Vout=0 regardless of what R2 and R1 are?? What's wrong in my understanding.

If Vout=0 then either you would have Ohm’s law violated at R2 or you would have KCL violated at the - terminal.

 

[jim hardy]

but then, if V+=V-, Shouldn't Vout=0 regardless of what R2 and R1 are?? What's wrong in my understanding.

Nothing is wrong with your understanding.
Just you haven't yet 'bent' your thinking to wrap it around the "Operational Amplifier Circuit" .

If
open loop gain is infinite
and
input (V1 - V2) is zero
then $Output = Input X Gain = 0 X ∞ = indeterminate$

So we have to "bend" our thinking as follows
Output is some real number bounded by the amplifier's maximum output, usually near its supply voltage(s) typically less than 15 volts
So input is that modest real number divided by gain
and any real number divided by infinity is zero (remember your limits from first semester calculus)
That's 'bent thinking' , going from output to input, and it's counter intuitive because we usually go the other way..

Next replace gain of infinity by some large but real number like a million
if output is constrained to 15volts(or less)
input is constrained to 15 microvolts(or less)
and we just round that off to zero.

BIte the bullet and try it.

$Input = \frac{Output} {Gain} = \frac{15}{1,000,000} = 0.000015$ ,
which is zero to four decimal places
and in my day we used analog meters that couldn't even resolve a millivolt let alone measure microvolts.

Working op-amp circuits in your head will make that 'bent thinking' so intuitive you'll become barely able to remember struggling with it.
I have to reach back to 1965 to remember when it "clicked" for me.
Being a vacuum tube guy I resisted not the algebra but the notion of an infinite gain amplifier .
So consider it a thought experiment , nothing more than an exercise in arithmetic.
Modern op-amps are a lot closer to ideal than the old μA709s I learned on.

That simple 'bent thinking' will serve you well. .
old jim

 

[CWatters]

View attachment 237599
This is an inverting amplifier incorporating an ideal op-amp with infinite open loop gain. I have a simple question concerning the derivation of its gain (-R2/R1). The point I circled is at 0V (Virtual Earth) but then, if V+=V-, Shouldn't Vout=0 regardless of what R2 and R1 are?? What's wrong in my understanding.

They are only approximately equal. The difference between them is roughly Vout divided by the open loop gain which is huge.

 

[Lord Crc]

Rotate the image 90 degrees clockwise. If the voltage above R1 is positive, no current is flowing into V-, what must Vout be in order for V+ = V- = zero volts?

How about if the voltage above R1 is negative?