So as we continue on with these Circuits 1 tutorials, I want to jump into op-amps
and we're actually going to do quite a few tutorials about operational amplifiers or
op-amps. And so that's why I have all of this set up, even though we're not going to be using
it in this tutorial specifically. Right now, we're just going to introduce the concept of
operational amplifiers and talk about the general way they operate, and two of the
most important things to remember in their usage that will make things a lot easier. Now,
operational amplifiers, or op-amps, I'm going to say, because that is quite the mouthful,
op-amps can be considered scary, but if you really just remember those two
basic things and ignore all of the real world complexities at first, then you'll be fine.
Once you get more comfortable with them, you can start throwing in some of the more
real aspects of op-amps and that's great, you will need to do that at some point. But at the
beginning, let's just keep it simple, make sure that you have a good foundational understanding
and then move forward with that. So first of all, let's look at what an op-amp looks like.
It's basically a triangle on its side. Let's see if I can do that ... Two inputs and an output,
and that's about it. We usually have one of these marked positive, one of these marked negative,
and then we just have output here, which we will call V out. So this can the V in negative,
this can be V in positive. And I do want to note that positive negative ... I just pointed
at the wrong ones. Positive or negative, it can be either way. It can be on the top or on the bottom.
There doesn't seem to be any rhyme or reason. So when you are looking at an op-amp, you need
to be careful, like where are they going in, make sure that it's properly labeled and you understand
what's going on. Now, an op-amp is simply that, it's an amplifier. And the way it works is you
just have an equation that drives this output. And that is your V out equals your amplifier with your
V in plus minus V in minus. And to make that simpler, you can just say V plus minus V minus.
So that a represents gain, which in an ideal operational amplifier is infinity. So thinking
about that kind of makes the math harder, so let's just say a rather large number. So as we look at
that, our equation is basically the voltage on the outside is the difference between our positive
or our input into the positive and our input into the negative times that gain.
So right there, you should know that any difference between V in plus V in minus is
going to yield an incredibly large output. And now we will get into that more in more depth later,
but right now that's good enough for us to go over the next two big portions of the op-amp, the next
two big rules for operational amplifiers. Now the first one is that this operational amplifier
will do whatever it can to make these two inputs match. As you look at it, if we were to take this
output and then go on over and connect it to the input, you can tell that of obviously in this
case, your output will drive your V negative over here. And let's look at this equation down here,
the way the output works and see how that makes sense and how these will come into equilibrium.
So let's just say that immediately, you put zero volts to V negative, five volts to V positive.
So you look at this equation and you have A, which let's say arbitrarily is a thousand,
even though it's going to be much, much greater than that, even in real life,
even though it's not going to be infinity, and then you have five volts minus zero.
And so V out is going to be 1000 times five. So your op-amp is going to be trying to drive V out
to 5,000 volts. And the thing is is on its way from zero to 5,000 volts, because obviously it's
not going to be instantaneous, it's going to pass five volts. And at that point, five minus five
is zero times a thousand or whatever is suddenly zero. So it stops driving and it just keeps that,
and as it goes a little bit higher, it'll change the output a little bit to correct. Oh, and then
it gets too high, input changes it to correct, and it'll just hit that spot that it's supposed to.
So that is the general principle by which the operational amplifier works,
and a lot of its configurations is some sort of variation of that. And that is the simplest,
but that's kind of the idea is that this output will do whatever it can to cause these two
inputs to match. And that is the first big rule of operational amplifiers, is that
this V negative and V positive should always have the same voltage. And that makes the math
so much easier. So if this is in a circuit and V positive is connected to ground.
In that circuit you know that V negative is going to be connected to ground. If you know
that V negative is connected to something and you know the voltage at one, you know the voltage at
the other one, and it makes the math so much easier. It really makes things great.
So that is one of the things that's really going to help you when you are solving circuits that
deal with operational amplifiers is that you can always assume that V in negative
and the V in positive, these two terminals will always have the exact same voltage. That's
principle number one. Now principle number two is pretty interesting, and that is that they is going
to be zero current into these inputs. So there is absolutely no input current into V in minus
or V in plus. And so that also really simplifies things because then you don't have to deal with
it as a third note of like, what's the current going in there? You just know it's going to be
zero. So if you have something coming in and something going out you know those two
parts of the circuit have to have the same current to them, and it really simplifies things.
Even if you're listening to me right now, thinking, how does that simplify things, trust me,
it does. If you know that there's no current going to either of these inputs and you know that
they're the same voltage, dealing with op-amps is going to become so much easier. Okay, so those
are the two most important things, and the way you can look at this, and it's nice and simple.
And if that's all you need great, that doesn't take into account a lot of real life issues that
we're going to discuss in just a moment. But if the next things I talk about confuse you and
you're like, wait, wait, how does that? Then don't even worry about them right now. Again,
later you need to. Right now, don't even worry about them. But I'm going to go over them just
so you have an idea of the things to expect. Now, one of the things with a real life
operational amplifier is you usually have inputs ... Well, basically your power right here,
and this will be some power source. I have another V plus and V minus right there. And
that, especially with old school amplifiers, you would get upwards of 15 volts and negative
15 volts. And I think they even got higher than that. But in today's world where everything's
zero to five volts or zero to 3.3 volts, you get a lot of operational amplifiers that can
work on a much lower voltage input than that. But not only is it you get out what you put in,
but there's another issue. So first what I mean by you get out what you put in,
if you have a voltage input of, on your power side of zero to five volts, and then you have voltages
coming in that's trying to get your voltage output to be seven volts or negative three volts.
Your operational amplifier can't do that. Its outputs are constrained by the power inputs.
So if you do plus 15, negative 15, then it can output something in that 30 volt range,
unless it can't. Now, if the output can go all the way up to 15 and all the way down to
negative 15 in this case, it's what's called a rail to rail amplifier. And that means it can go
all the way to the voltage rails. It's more common now to have those rail to rail amplifiers,
but sometimes you still don't have those. And what happens is you have a little bit of head
space in there that you're losing some voltage on the inside of the amplifier because of voltage
drops over p–n junctions and stuff like that. So if you do not have a rail to rail amplifier,
you need to know, is it taking off two volts on each side, so this 15 and negative 15 actually
has an output that can only go from positive 13 to negative 13? Don't know. That's something
you're going to need to look into. So rail to rail, power supply rail to rail is much
more necessary when you're only going from zero to five volts. But when you have a pretty wide
swing like this, then it's more common to see where it's not a rail to rail
amplifier. And the reason you wouldn't have rail to rail amplifiers is because you're
always going to have a trade off somewhere in some performance. It just depends on your
application and what you need. But now you're familiar with the term and let's move on.
The next thing to think about when you're looking at a real operational amplifier, as I said,
that these voltages are always the exact same, of course in real life they're not going to be the
exact same. There's going to be some little minute difference. And that's called the offset voltage.
Now the offset voltage is usually a very, very small number. And again, normally you can ignore
it, but depending on the precision required, that might be something you need to take into account.
However, again, if you're first getting into this and you are doing your basic circuit analysis with
an operational amplifier, don't worry about that. Make the assumption that V minus and V plus are
the exact same, or else it's going to get much, much more complicated. But again, in real life,
you do need to worry about that. And another thing to worry about with those is in real life,
even though we say that there's no current into those inputs, there is a small current.
That current is actually called the input bias current. And again, it's going to be incredibly
small and most of the time you're going to be able to ignore it. But again, depending on your
application, you may need to consider that, and it may be something that your teacher or your
professor says, "Oh yes, calculate this," assuming that there's a difference in the bias current. And
if that's the case, I'm sorry, because that does make things a lot more complicated. As I mentioned
earlier, the output, as it's driving things, it's not instantaneous. It can't go from zero to
infinity instantaneously, or zero to anything instantaneously. But we assume that it can,
when we're doing these calculations. Now the reality is you can calculate how quickly the
voltage will rise or drop, and that's called the slew rate. And so, as I was mentioning, as it's
trying to make it go from zero to five, it kind of goes up and it passes through five and then
it's oh, hey, it matches, and goes like that. That's because it is moving and it has that slew
rate. If it were instantaneous, it would just jump up and kind of jump down and kind of do this weird
balancing thing, which fortunately it doesn't do. But that slew rate is the inability of the
output to produce an infinite amount of current, thereby instantaneously changing the voltage.
Did that make sense? So the slew rate is the fact that your output has to change voltage
in a non-instantaneous way. So when we're go going over these circuits,
particularly with the voltage follower, I set up an example, you'll see that output, it's trying
to go from zero to five volts. It goes kind of like this and does a little bit of a bouncing and
stuff as it settles in because it can't just zero five instantaneously. So that's the slew rate.
And sometimes that's your friend; most of the time, it's not.
All right, and that leaves us with one final thing that's related to the slew rate,
and that is bandwidth. As I've been talking about this, I've been envisioning and you probably have
been as well, DC circuits. But this also works with AC circuits, and so when you're doing an
AC circuit, that's where you're going to see more of that slew rate. And you're also going to have
problems with the bandwidth, which once you get up to a certain frequency, basically your
operational amplifier, your op is not going to be able to keep up. It's not going to be able to
recreate or create a signal quickly enough to have any sort of integrity. You get to this point
where it just doesn't work anymore and you're outside of the bandwidth of the op-amp. And that
is a case of if you're having something that's changing very, very quickly in the slew rate,
just simply can't keep up, you're not going to be reproducing the signal accurately.
So that's where you say forget it, this operational amplifier isn't going to work,
let's find another op-amp, or we need to find a completely different solution
altogether. Okay, and that is it. We are going to go into a lot of the most common configurations
because these are all over the place in circuits. And once you get that foundational understanding,
they are not only easy, but they are so incredibly helpful. So again, those first two rules are the
first one is that these two inputs have a matching voltage, always. Just remember that
when you're doing anything and you're looking at a circuit like, how am I supposed to do
this? Remember that if one's tied to ground or if one's tied to five volts or whatever,
you know what the other voltage is immediately. And then the second thing is there is no current
into those inputs. So any current that is flowing past has to keep on flowing past.
So in the feedback loop, you're going to have the same current there as you do on the input.
Those are the two things. They're very, very important. Other than that, op-amps
are pretty straightforward. They do get more complicated with the realistic aspects thrown in,
but still, that's nothing to worry about right now. It's really not that bad once
you have a good grasp of how they work. Okay, I'm really excited to do the next couple
of op-amp videos. They are going to be a lot of fun because they are so incredibly powerful. And
I'm really glad for the equipment I have here that can show the way it actually works. So I'm
very excited, I hope you'll join us with those videos, I hope you enjoyed this video and it has
helped you understand operational amplifiers a little bit more. I'm realizing right now,
right at the very end, that I have not slowed my speech down. I apologize for that. If this
was too fast, please slow it down in the YouTube settings. Thanks. If you liked it, give it a like,
subscribe to our channel, all that good jazz. We'll catch you on the next one.