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## Electrical engineering

### Course: Electrical engineering>Unit 3

Lesson 1: Operational amplifier

# Virtual ground - examples

Using the "virtual ground" idea, we reexamine the inverting op-amp and find a solution much quicker. We apply the virtual ground method to a unity-gain buffer (amplifier with gain = 1). Created by Willy McAllister.

## Video transcript

- [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.