Main content
Course: Electrical engineering > Unit 3
Lesson 1: Operational amplifierFeedback
Feedback is the design technique where a part of the amplifier output "feeds back" to the input of the amplifier. The overall effect creates a very stable gain determined by resistor ratios. Created by Willy McAllister.
Want to join the conversation?
3:33v+=v-=1v vin=v+-v-=0 so Vout=A(Vin)=A(0)=0?but Vout= 2v??(12 votes)
Akash, You caught me doing a little unstated rounding where I say there is 2V on the output when it looks like the opamp's input is 1 - 1 = 0V. Assume the gain A = 1 million. In truth, the voltage on the v- input is ever so slightly less than 1V, like 1V - 2uV. This is what gives us a small uV difference between v+ and v-. When multiplied by A, you get 2V on the output. I work out the exact algebra in the previous video called Non-inverting op-amp. https://www.khanacademy.org/science/electrical-engineering/ee-amplifiers/ee-opamp/v/ee-noninverting-opamp
The rounding of these little tiny uV voltages is common in opamp design.(13 votes)
If v+ = 1V and v- = 1V, the difference is 0. So doesn't an op-amp amplify the "difference"? The output should be 0...correct? Anything times 0 is 0...so I am lost how this even works if both the inputs are 1 V....(5 votes)
" If v+ = 1V and v- = 1V, the difference is 0."
The thing is that is never the case in the real world, v- is a little bit less then 1v and that makes the math work.
The example he is doing is to explain the feedback so the example is assuming an "ideal op amp" where v+ - v- =0
In the real world the answer is a very small number close to zero but not zero.(5 votes)
At2:31why does Vout equal 2 times Vin?(4 votes)- why there are diffrences between positive feedback and negative feedback?
why the op amp works as a schmitt trriger in the positive feedback and as an amplifier in the case of a negative feedback?(2 votes)- In negative feedback a small portion of the output is subtracted from the input. In positive feedback, a small portion of the output is added to the input.
Positive feedback makes the output go more in the direction of the input, it makes small changes of the input into bigger changes. A Schmitt Trigger uses positive feedback uses its gain to make its output snap rapidly in the same direction the input is moving.
Negative feedback is used for amplifiers. When you surround a high-gain amplifier (an opamp) with resistors in certain configurations like the ones discussed in this section, and then go through the circuit math, you can make circuits whose overall gain is controlled by the value of the resistors, and not dependent on the high gain of the opamp.(4 votes)
- Hi, thank you for this video, and I hope you're still responding to questions.
@4:38the concept of negative feedback is shown: The gain increase -> v_out increased -> v- increased -> v_out decreased. However, since v_out is continuously feeding back into v-, wouldn't it continuously oscillate between two values?
Hence, The gain increase -> v_out increased -> v- increased -> v_out decreased -> v_- decreased -> v_out increased -> ... so on.
Thank you.(2 votes)
You are correct that the output will wiggle around the desired (nominal) Vo value. When the input is unchanging, this wiggle is so small you can't see it on an oscilloscope.
Let's call the voltage input vin the "set point" for the circuit. The purpose of the opamp and resistors is to drive Vo to the value it needs to be to make v- match the input set point, v+.
Suppose Vout wanders off in some direction for any reason (gain flaw, temperature change). The negative feedback network (R1 and R2) is arranged to drive v- back in the direction of v+. The ideal magnitude of the correction (the size of the little arrow) is exactly the right size to perfectly correct the deviation. In an ideal circuit the correction would be perfect and the right Vo would be restored immediately.
In a real-world opamp circuit the correction might not be perfect (due to small internal voltage flaws, or time delays inside the opamp). In that case, the feedback network has a new "incorrect" Vo to work with, and it generates a new correction. This is the tiny wiggle you are asking about.
You hope each successive correction is smaller than the previous, so the output converges on the right value. This is a continuous process in an analog opamp, you don't see little discreet steps, just a continuous attempt to match the set point.
The next interesting case is what happens when vin changes suddenly. You've caused an intentional change to the set point and the error signal (v+ - v-) can be very big. In this case, the feedback network flexes its muscles and drives this new big error back to zero as quick as it can. The speed an accuracy of the correction is the "dynamic" performance of the opamp circuit.(3 votes)
- If both the positive and the negative inputs are 1V, then won't the output be A(1-1V) = 0V?(2 votes)
- There are assumptions and simplifications happening here. We assume the gain of the opamp triangle is VERY high, like 1 million. We assume the current going into the + and - opamp inputs are ZERO.
Even with these ideal assumptions the gain expression I used at2:10is not exactly precise. It is very close, but not perfect. Remember in a previous video we developed an accurate gain expression that included a term like A/(A+1)? If the gain "A" is huge, then A/(A+1) is VERY close to 1. We then simplified the gain expression by allowing that A/(A+1) term to be exactly 1. It is a very good approximation.
So, voltages at the input to the opamp are super close, but not exactly identically equal. The difference may be perhaps 2 microvolt. This difference is represented exactly by A/(A+1). That 2 microvolt difference is enough to make the opamp generate the expected 2V output.
If you build this opamp circuit on your bench and try to measure v+ - v- your meter or scope will register 0v. The difference is too small for almost all instruments.
The essential skill for understanding opamps is to accept this sequence of assumptions and simplifications. Keep them in the back of your mind as you use the derived gain expressions for each opamp circuit configuration.(3 votes)
- Why inversion happens ? In what way does it help ?(1 vote)
- It is very common that the simplest transistor circuits perform an inversion of the input signal to get the output. It's just the nature of how transistors work that there is an inversion. As engineers, we quickly get used to this feature of simple circuits and figure out ways to take advantage of it. If the inverting feature is a problem, then you simply add a second inverting amplifier in series, and you get a right-side-up version of the input signal. It is usually the case that a non-inverting circuit takes a few more bits and pieces to assemble.(4 votes)
at3:35v- becomes 1v so what happens to vout then, will it decrease since there's an increase in v-(2 votes)- The discussion at3:35is figuring out the voltages at all nodes given the assumption that vin=1v. Everything is static at this point, so the voltages are not coming from somewhere else.
If we know v1 and we know the gain expression for the amplifier you can find the two other voltages, vout and v-. Again, at this point in the video everything is static and stable, so v- didn't "increase to" 1v, it became that value the moment we assumed vin=1v.
It is understood from previous videos that the opamp gain A is huge, and the difference between v+ and v- is way down in the microvolts, just enough to make the output of the opamp vout=2v.
From this point on in the video it talks about what happens if something changes in the circuit (gain A) and points out how negative feedback behaves and all the voltages wiggle a tiny bit.(2 votes)
- Are R1 and R2 values used in real world scenarios, or just examples? I mean, if we have an op-amp capable of amplifying by a factor or 10^5-10^6, why would we want to dumb it down to a factor of 2, by constructing this circuit?(2 votes)
- The genius of Feedback is to use a high but unpredictable/unstable gain of 10^5 to 10^6 and build a circuit with a VERY stable gain of 2, 10, or 100.
The gain of real-world opamps made with temperature-sensitive transistors is not very well controlled. But, precision resistors (accurate value, very little temperature sensitivity) give you very accurate overall gain values when combined in circuits with sloppy hi-gain opamps.(2 votes)
What does that "A goes up and likewise Vo , V(-) goes up " ? Does that means, A's value increases and consequently increasing the values of Vo and V(-) ? Or it has something to do with phase shift in the signal? I have read feedback is actually putting fraction of output energy back to input . Is that so ? How it would be with this context in the video?(1 vote)- You have it basically right. I'm trying to illustrate how feedback makes the overall circuit insensitive to a change in opamp gain (A). Suppose A goes up for some environmental reason (like it is warmer today than yesterday). That increase in A will try to cause a change in Vo, because Vo = A(v+ - v-). That's the little yellow arrow at4:05. Then you chase the changes around through the feedback path (the voltage divider) and back to the v- input on the opamp (the next two yellow arrows). The feedback perfectly accounts for the change of A and the output Vo actually holds steady.
There is speed limit on how quickly the feedback path can adapt to changes. That's the phase shift idea you mentioned. But that is a more advanced topic I'm not covering in this video.
When we say, "a portion of the output energy is fed back to the input", that's the wording we use when 1/2 of Vo is connected back to the v- input of the opamp.(2 votes)
3:33Video transcript
- [Voiceover] So now I wanna
talk a little bit about the concept of Feedback. This is a, this is a
really important concept. It was developed in the 1920s,
the idea of using Feedback, and it was done at, at Bell Labs, Bell Telephone Laboratories. Remember we talked about
this on the op amp, this being the, the non-inverting input, so if this voltage went
up, this voltage went up, and the negative sign
is the inverting input, so these, these voltage here and here, move in opposite directions. And the key to understanding
what Feedback is, is to pay attention to
this inversion path, and these non-inverting paths. We're gonna start over
here with just isolating the voltage divider part of our circuit, so that's copied over here. And when you think about,
let's look at what happens if V out goes up. And what happens to V minus in this case? Well V minus goes in what
direction in a voltage divider? It goes up. So this is a, this is a
non-inverting structure. If V out goes up, then the
thing we care about V minus, goes up as well. And likewise if V out goes
down, then V minus goes down. So that's isolating
just on this part of it, we have no inversion
happening around here. So we go around here now, and let's look at what happens on this path here, if we go up in V in, then
we know V out goes up. If we then change colors
to, let's try this. If V minus goes up, then V out goes down. That's the inverting path. So there's, so there's one
inversion in this circuit, and it happens right here
where V minus goes to V out, so that's where the inversion is. So now let me set up
just an example circuit. We'll set R1 equal to R2. And from the last video, we
developed a gain expression, and we said that V out
equals R1 plus R2, over R2, times V in, and with these,
with these resistor values, V out equals two times V in. Alright, so this is
equal to, two times V in. And what does that make this point here? V minus, this is V minus, and from our voltage divider,
we know a voltage divider says that V minus equals V out times R2, which is just R, over R plus R, or V minus equals one-half, V out. So, we have let's put a, let's put a voltage on here. Let's put a real voltage on here. Let's say this is at one volt, alright? And going through our amplifier, we know that V out equals two volts, and that means that V minus
equals one-half of V out, so V minus is one volt. So this is one volt here. So let's say for the moment, that something happens to the circuit, like we heated up or something like that, and let's say the gain
goes up a little bit. Now what that means is, that this amplifier, which is amplifying this voltage difference right here, is gonna be a little higher, so the voltage here is
gonna go up a little bit. Let's use this color. It goes up a little bit, and that means that this output voltage is gonna go up a little bit. And we already decided from
looking at this voltage divider, that if this point goes up,
that this point will go up. It goes up half as much, but it, it goes in the up direction. When this voltage goes up, that means this voltage goes up, and
now we find ourselves, we're at the inverting input. We're at the inverting
input to the amplifier, and that means what? When a change at the
inverting input goes up, that means the output goes down. And that's in the opposite direction of the original change. So this is the mechanism of Feedback. A went up a little bit. We thought that V out would go up a bit, which meant this point goes up, which meant it gets fed back to the input, to the inverting input, and then it goes back down, and this balancing act
that's going on right here, that is the mechanism, that
is what we call Feedback. You get this Feedback effect, when this connection is made right here, back to the inverting
input, to the op amp. And in particular, because
it's the inverting input, this is called Negative Feedback. So this is the mechanism of Feedback, in particular, Negative Feedback and, what it does for us is, it provides us a way
to exploit and to use, this enormous gain that
these amplifiers have, to create really stable, really
nicely controlled circuits, that are controlled by the
values of the components we attached to the, to the amplifier. So that's the idea of Feedback, a really powerful idea, and really at the heart
of analog electronics.