Inverting and unity-gain op-amp with virtual ground

All right, so now I'm going to do the analysis of this op-amp configuration again, and I'm going to do it using the idea of a virtual ground. The idea of a virtual ground actually makes really short work of analyzing a circuit like this.

To review the virtual ground idea, it says if this voltage here, if V out, is in a reasonable range between the power supplies of its op-amp—remember, the power supplies are not shown here but they're connected up to the op-amp—then this is a number that's sort of like one hand of volts, you know, or two hands of volts between zero and plus or minus 10 volts, something like that.

The gain of this op-amp is huge; it's just gigantic. It's up in the hundreds of thousands or millions. 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.

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 going to 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 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. 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 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. In a real op-amp, there'll be a really tiny, tiny current there, but for our purposes right now, we can treat this as a 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 side, this is the relatively positive side, and this is the negative side. So I is zero minus V out divided by R2.

All right, 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.

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! 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. Now, 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 that 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. Again, what we want to do is find out what's V out in terms of V in. Now this circuit has no resistors in it. Okay, that's all right; we'll figure out what's going on here.

Okay, let's apply the idea of virtual ground. So I'm going to 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, or sorry, V in.

So boom! We just did it in one step. That's the answer. This configuration is called a 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 used the virtual ground idea to analyze it almost instantly.