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## Electrical engineering

### Course: Electrical engineering>Unit 3

Lesson 1: Operational amplifier

# Virtual ground

The idea of a "virtual ground" makes some simplifying assumptions, giving us an elegant and simple way to look at op-amp circuits. Created by Willy McAllister.

## Want to join the conversation?

• at , what does he mean by the output voltage will be between +/- 12 volts , shouldn't it be 6 V ?
(5 votes)
• Hello Balraj,

The +/- 12 volts is an assumption. Here Willy assumed the op amp is powered by a dual power supply. The upper "rail" is 12 VDC and the lower "power rail" is -12 VDC. The op-amp can operate from many voltage (with stipulation) but +/- 12 is a common value seen in the literature.

The output of the op-amp may take on any value between the rails. In this example the output will be between +/- 12 volts.

The 6 VDC is the calculated voltage for a given assumption.

Regards,

APD
(6 votes)
• Everybody is getting confused because he explains that what we see in the real world is not exactly the same as the way we make calculations.
He constantly switches between the two without making it clear.

He should make a few videos about Ideal OP-AMPS without ever mentioning real world op amps, and after people understand that part he can go back to the real world explain how it really works.
That way people would understand why those problems were solved that way in the previous videos and appreciate it.

This way is just CONFUSING.
You go back and forth between the two.

And I see in every video people have the exact same question.
If Vin=v+ - v-
And Vout=A*Vin
Why isn't Vout=0 since Vin=0 since v+=v-
THE ANSWER IS YOU ARE USING ONE FORMULA FROM THE REAL WORLD AND ONE FORMULA THAT WE USE IN THE BOOK WORLD TO MAKE CALCULATIONS.
(2 votes)
• The op-amp is connected to a power supply. How can I know the exact rating (voltage and power?) that the power supply should have in order to operate the op-amp?
(3 votes)
• Hello Feneva,

The best place to look is the data sheet for the op amp. This document will give you the design maximum power supply voltage - never go higher than this. Most manufactures will also present a typical power supply voltage.

For traditional op-amps you will see +and - power supplies. Today you will also find many single supply op amps.

Regards,

APD
(3 votes)
• Sir, where is v+ = v- applicable and where it isn't ?
(3 votes)
• Good question. The answer may sound odd.

For any opamp circuit that does something useful, the assumption v+ = v- has to hold. That's because if it doesn't hold, the circuit is not working as intended and in fact is pretty much useless.

If the assumption is not true, and v+ - v- is some non-tiny voltage, the output of the opamp, A(v+ - v-), tries to become some huge number, like 100,000 volts. No opamp can actually do that. Instead, the output voltage becomes "pinned" to either the positive or negative power supply voltage. That is a useless circuit.

If you build an opamp circuit and you see the output voltage equals one of the power supplies, that's an indication something is wrong with the feedback connection.
(3 votes)
• This may be exactly what Eldi is talking about below, but at about he says that Vin=V+-V-; yet, regarding the very same circuit, he says at in the non-inverting op-amp video that Vin=V+. So... which is it? Similarly, he says that Vin=Vout/A, but I thought we proved that Vin=Vout*(R2/(R1+R2))....
(2 votes)
• Bob - I think your question is different than Eldi's question.
What you've noticed is inconsistency in how I used the variable name v_in various opamp videos. I inadvertently laid a trap for you to fall into. I apologize for that.
Let me try to explain the confusion.

In the introductory video "What is an operational amplifier?" at , the variable v_in refers to the voltage difference between the two input pins of the opamp,
v_in = v+ - v-

In the next video, “Non-inverting opamp”, at I change how I use the variable v_in. It refers to the name of the input signal coming from the voltage source on the left. The quantity ( v+ - v- ) comes up at , but it does not get its own special variable name.

In the next two videos on Feedback and Inverting Opamp v_in is used in the same way, as the name of the input signal.

The blunder comes in this Virtual Ground video. v_in goes back to being the name of
( v+ - v- ). All the info in the Virtual Ground video is correct, but I can totally see where the confusion comes from with v_in getting used differently in the sequence of videos.

Here’s what I would ask you to do… Please watch the first part of the Virtual Ground video again, and when I write v_in (two times) put your thumb over the top of it (two times). Ignore when I speak its name. Just focus on ( v+ - v- ). Does the virtual ground concept make more sense that way?

I may attempt to repair this video, but it will be hard to get released, since my fellowship at KA wrapped up in 2016. I’m continuing my teaching on my own web site, spinningnumbers.org. I'll post the repaired video there.

Thank you for pointing this out. - Willy
(3 votes)
• if Vin is zero how is it possible for there to be an output voltage, considering Vout=AVin .
(1 vote)
• Don't forget that opamps operate with both a positive and negative power supply. The output of the opamp can swing down below ground, all the way down to near the negative supply. An output value of 0 volts is just an ordinary value near the middle of the full output range.
(3 votes)
• awesome teaching skills.just one thing how does the power supply determines the range of Vo and ive seen many take I1 equal to I2 saying that input resistance is very high so no current flows between V+ and V- and all current from R1 i.e I1 goest to R2 i.e I2
(1 vote)
• The power supply voltages of an opamp limit on how high or low the output voltage, Vo, can go. If the power supplies are +12V and -12V, that's the total possible range of Vo. Inside the opamp there are two transistors connected to the Vo pin. One transistor pulls Vo up, the other pulls Vo down. The up-pulling transistor's other terminal is connected to +12, making +12 the highest possible voltage it can cause on Vo.
(2 votes)
• If the op amp saturates v+ is not equal to v-. why?
(1 vote)
• An opamp circuit has this aspect that "it works when it works". What I mean is that is that all these circuit theories like "virtual ground" work only if all assumptions are true. One of the assumptions is that the output of the opamp is capable of achieving a voltage that allows the virtual ground idea to work. If the output of the opamp is in saturation (stuck at either the high or low power supply) then the assumption is not true and all bets are off. The two inputs, v+ and v- will not be identical.
(2 votes)
• At how are we getting Vin = Vo/Va in terms of Vout? Saying in terms of Vout makes me think were solving for Vout, such as Vout = Vin/Va.. but where are we getting this equation in the first place?
(1 vote)
• This equation comes from the definition of the opamp symbol.
The opamp amplifies the difference between its two input pins.F
Give the voltage difference a name, like v+ - v- is called Vin. Then the opamp function is Vo = A Vin. (This is probably the equation you were expecting). All I did was solve for Vin. Vin = Vo/A.
(2 votes)
• By concept of virtual ground, if i assume my v+=0 and my v- =0. Would it mean that my vin = 0, then my v out would be 0 also?
(1 vote)
• That is correct. It's true because of how the opamp is defined: vout = A( v+ - v- ).
(2 votes)

## Video transcript

- [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.