- [Voiceover] I wanna take a look at our two op amp circuits
and make an interesting observation about
how this things are behaving when they are working properly.
When they're hooked up right,
there's something these things do
that is really helpful and makes life simple for us.
Let's let the gain of our op amp be 10 to the third,
or 10 to the sixth.
Really high gain, a million.
And we're gonna let the output voltage here,
V out,
let's say six volts.
And you remember, what's not shown here in this circuit
is the power supply
is going to both of these op amps.
Plus or minus, let's say it's plus or minus 12 volts.
Those power supplies are implicit.
They're not shown in the diagram but we know they're there.
Alright, now, if V out is six volts
and A is 10 to the sixth,
then what's V in?
V in is the difference between these two voltages here.
Let's call this the usual thing.
We'll call this V plus.
I'm gonna call this V minus.
And we know that V in,
we know that V in
equals V plus minus V minus.
And now what the question is
what is V in in terms of V out?
Well, V in
equals V out divided by A.
If we fill in the values we had,
it's six volts
divided by 10 to the sixth,
or six microvolts.
So this is six microvolts between here and here, okay?
So with six volts here,
there's six microvolts over here.
Okay, this is a really small voltage.
In order for this op amp
to have an output voltage
that stays between plus or minus 12 volts,
this voltage over here has to be really small.
It has to be down to the microvolts level.
So because I'm a practical engineer,
I'm just gonna say this is pretty much zero volts.
And if I say this is zero,
that's pretty much the same thing as saying
that V plus approximately equals V minus.
So that's a little observation we're gonna make right there.
So in this circuit, when it's working right,
these two voltages are pretty much the same.
So let's take this idea of V plus pretty much equals V minus
and apply it to this circuit over here.
Now this is our inverting configuration for an op amp.
So this is V plus.
And this is V minus in this circuit.
And let's do the same analysis that we did before.
If this is V out, and if V out is six volts,
that means that V plus minus V minus
divided by 10 to the sixth
equals six microvolts,
and that says that this
is six microvolts
in this direction.
When we did this over here,
because the signs of the inputs are flipped,
this was six microvolts this way.
So again, because of the enormous gain of this amplifier,
this is always gonna be a tiny, tiny number,
and so, heck, why not make it zero?
So if I treat this as zero, what it means is,
I'm gonna go right in here,
and I'm gonna change this to
zero volts.
So let's make a couple more observations, okay?
Right now, it says right here,
V plus equals zero
because it's grounded.
So what does that mean V minus is?
Well, V minus is also zero.
V minus is zero.
So that point right there
is at zero volts.
Okay, so that's pretty cool.
So, that point's at zero volts.
Now, is it connected to ground?
It's not connected to ground.
But at zero volts,
because of what this op amp is doing it for us,
this op amp is making sure, by this feedback path,
that this node is always next to this node
and that means it's always zero.
There's a really cool word that we use for this
and the word is virtual.
And what does the word virtual mean?
Well, virtual means that something is not there
but it seems like it is.
So in this case, this node is not connected to ground
but it seems like it is.
So this is referred to as a,
a virtual ground.
So these two ideas say the same thing.
V plus equals V minus is always the situation
around the input to an op amp,
when it's running properly,
and in the case particularly of this op amp configuration,
where the plus terminal is connected to ground,
we say that the other terminal, V minus,
is at a virtual ground, or is a virtual ground.
In the next video, I'm gonna go back
and do this inverting configuration of the op amp.
I'm gonna do the analysis again
with this idea of a virtual ground
and it's gonna be really easy
compared to doing all that algebra.