- [Voiceover] Alright, so now I'm gonna do the analysis
of this op-amp configuration again,
and I'm gonna do it using the idea of virtual ground.
And the idea of a virtual ground actually,
it makes really short work of analyzing a circuit like this.
To review the virtual ground idea,
it says if this voltage here, V out,
is in a reasonable range between the power supplies
of its op-amp, and remember the power supplies are
not shown here but they're connected up to the op-amp,
so this is a number that's sort of like one hand of volts,
or two hands of volts, between zero and plus or minus
10 volts, something like that.
And the gain of this op-amp is huge, it's just gigantic.
It's up in the 100s of thousands or millions.
And so, whenever there's a normal, finite size voltage here,
it means the voltage here is about zero,
it's very close to zero,
it's down in the very small microvolts.
And, the idea of a virtual ground,
says that if this node here is at zero volts,
which we've drawn it grounded, so it's at zero volts,
that means that this minus terminal is gonna be
also held at zero volts, very close to zero volts.
And that makes this virtually a ground,
or a virtual ground.
Another way to write this is to say that the V plus
is approximately equal to V minus.
Now, my professor who taught me this,
had a little symbol for it, what he did was he
drew it like this, so you can sketch that on your
schematics, just a little symbol there,
and that symbol will help remind you that those two nodes
are at the same voltage.
Okay, so let's do the analysis again,
we had, this was R1, and this is R2,
and we have a current flowing here, called i.
And we can write an expression for i,
so the voltage on this side...
The voltage on this side of the resistor is V in,
and the voltage on this side of the resistor is,
it's zero volts, it's zero volts,
because we have a virtual ground here,
so we know the voltage on both sides.
So I can say right away, i equals the voltage difference
V in minus zero, so just V in, divided by R1.
So we have an expression for i.
Now, as you remember, the thing we also know about op-amps
is that this current is zero here,
there's no current going into the input of an ideal op-amp.
A real op-amp there'll be a really tiny current there.
For our purposes right now we can treat this as zero
current going in here,
so what does that mean?
That means that i goes through R2.
So let's write an expression for i going through R2,
and we need to know the voltage on each side of R2,
well this side, this is V naught, or V out.
This side is V out, and this side, again,
we get to use the zero,
so i through R2 equals, let's get the sign right,
so the current's going in this way,
so this is the positive, this is the relatively positive
side and this is the negative side,
so i is zero minus V out, divided by R2.
Now, let's set these two currents equal to each other,
so that means that V in over R1 equals minus V out over R2,
and what we want is an expression that tells us what V out
is in terms of V in, so V out equals V in times,
let's see, R2 goes on top, R1 goes on the bottom,
and there's a minus sign.
And we did it, and that's the expression for V out
in terms of V in, for the inverting op-amp configuration.
Now, by using the virtual ground idea,
the analysis became really simple,
it's basically one two three steps to get to the answer.
Compare that to the algebra that we did in the previous
video when we did this from first principles.
So that's an example of applying the virtual ground idea
to analyze an op-amp circuit.
I'll do one more real quick.
So here's a different op-amp configuration,
we haven't seen this one before.
First thing to notice, first thing to notice is
now plus is on top.
Always take a peek at your op-amp to see which terminal
is on top.
We have V in here, as usual, and here's V out,
and again, what we wanna do is find out what's V out
in terms of V in.
Now this circuit has no resistors in it,
okay, that's alright, we'll figure out what's going on here.
Okay, let's apply the idea of a virtual ground,
so I'm gonna make my little virtual ground symbol here,
like that, that reminds me that these two terminals
are the same voltage if we're doing the right thing,
so let's figure out what V out is.
V out equals this terminal here, and this one
is pretty much equal to this one,
and what's this one?
This is V out, sorry V in.
So, boom.
We just did it, in one step, that's the answer.
This configuration is called the buffer.
Or it's also called a unity-gain buffer.
This is just a long way to say the gain is one.
So that's an example of a unity-gain buffer,
and we use the virtual ground idea to analyze it
almost instantly.