(cheery tone)
- Welcome.
And today we are going to talk about
the op-amp configuration of inverting
and non-inverting amplification.
So inverting and non-inverting amplifiers.
And so we've been talking about voltage followers
and the normal configuration of op-amps
but now we're gonna use them in probably one of the most
common ways they're used besides the voltage follower.
And that's where you have an input and then you say
I want it to be this much bigger
or sometimes smaller depending on how you want to do it.
So before we get into the configurations
of the inverting and non-inverting, I want to talk
about the inverting and non-inverting inputs to the op-amp.
And I'm sorry for that name confusion
but let's jump into that really quick.
So up until this point whenever I've talked about the inputs
to the op-amp.
I've just called 'em V plus V minus
the positive input, the negative input, stuff like that.
Another way to describe them that's probably
much more helpful and understanding intuitively
of what's going on is you have your non-inverting input
and your inverting input
which your positive is your non-inverting
and your negative is your inverting.
So what that means is that when you have a higher voltage
on your positive or your non-inverting input
then you have a high voltage coming out of your output.
Whereas if you have a higher voltage on your inverting
or your V negative to your op-amp
then you get a negative voltage on the outside.
And the reason it's doing this is because, again
your output is almost always attached to one
of the inputs and it's trying to drive those inputs
so that they have the same voltage.
So that's the behavior.
If you were to just use this and not connect the output
to the input and you were to put a higher voltage here
and instead of your non-inverting
then you'll have a very high voltage here.
And since op-amps technically have an infinite gain
if your positive non-inverting input is even
a little bit higher than your negative
then your output will be as high
as it can be in the positive range.
Whereas if you have the same thing where you're inverting
input has a higher voltage than your non-inverting input
then the output will be as negative
as your op-amp is capable of because it will want to
amplify that difference as much as possible.
Okay, let's see if that made sense.
I'm gonna go over that really quick once again.
So you're non-inverting or positive input.
If it is a higher voltage than you're inverting
or negative input, then your output is going to be positive.
If you are inverting or negative input is higher voltage
than your non-inverting or positive voltage
then your output is going to be negative.
Okay, are we good to go?
Hope so.
Awesome with that.
Now let's talk about how we can set this
up to work as an amplifier.
Now, strangely, well strangely at first you
get the inverting amplifier configuration much more often
than you get the non-inverting.
So we will start with that.
Okay, so here we have the inverting op-amp configuration
and we have our Vin going through Rin, Rf, for feedback.
And then the output, we have our non-inverting,
or positive input tied to ground.
And then we just have our output here.
Now if you don't need anything else, you can just look
at this and say, hey, other people have derived what my
in and out equation will be.
And it is simply that V-out over V-in,
which sometimes is just called 'a' for amplification factor
or something like that, equals negative RF over RN.
And that negative is where this is inverting.
So it will amplify the signal
and invert it to make it negative.
So let's take a moment and go
through it and see where this comes from.
It's very, very simple.
Again, most op-amp circuits are very easy to deal with.
So let's talk about that.
So hopefully by going through this process
you get a better intuitive feel
of what's going on with this inverting amplifier.
As always, we remember that these two have the same voltage
and there is no current into the inputs.
So we know that right here that is at zero volts
and that the current through R-in and RF is the same.
And using that, we can very quickly derive this formula.
Which I hate the word derive.
I've always hated derivations, so don't get scared by that.
If I'm okay with it, you're probably gonna be okay with it.
So let's just say we've got this current right
here that's the same as this current right here.
So we can say the current through R-in is simply
going to be V-in minus zero cause that's zero volts
over R-in.
And then we know that's the same as this.
So we can actually go here and we can do that is equal
to zero minus V-out
over RF, our feedback.
And again, we know those are the same because
this is just describing the current going through there
and this is describing the current going there.
Zero minus V-out gives us current flowing in that direction.
So we're already very straightforward.
We can get rid of those zeros because they're not needed.
Don't get rid of that negative because that is needed.
And now all we have to do is put it
into the V-out over V-in format.
So let's take RF and multiply it on both sides,
and then take V and and divide it on both sides.
So we put RF up there, RF,
over R-in equals
- V-out over Vin.
And then we just multiply that
by negative to get that negative on the other side.
But just again, so you don't miss that step
I basically took our multiplied both sides
by RF and divided both sides by our V-in.
And so that moved up there and that moved down there.
And that just gives us V-out
over V-in equals -RF
over R-in.
See very, very simple derivation.
So that is, that's it.
But if you don't want to have to do this every single time
again, you can find this equation everywhere.
It's on our website, it's
on other people's websites, it's in books, it's everywhere.
Very, very common.
Now to give you an idea of what would happen.
So if we have this, so if you have V-in as one volt
you have RF as 10,000 ohms and you have RN as 1000 ohms
then your output is going to be negative 10 volts
because you have negative 10,000
over 1000 gives you negative 10.
So that multiplied by V-in
of one volt will give you your V-out of negative 10 volts.
And that's that's all it is.
That works both on DC and AC circuits.
So if you have a normal AC circuit or DC circuit in
if you put in one volt, you'll get 10 volts out.
If you have a square wave, especially one that's circling
or bouncing positive and negative
you're gonna get an inverse and an amplification.
So that'll be pretty exciting.
But that is it.
This is very, very common, very simple.
It's an easy way to get exactly what you want.
If you need a lot of precision
then you need just need a very precise resistors right here
for your RF and R-in to get exactly what you want.
But with that
I think that's everything we need to know about inverting.
Let's do the non-inverting and then do a really
quick practical example of a non-inverting circuit.
Now with non-inverting, you'll notice
that your input goes directly into the non-inverting input
and then your output uses a voltage divider
that is connected to your inverting output.
So on the other one, on the inverting, we had R-in
and our feedback, but since this is slightly different
it doesn't do feedback the same way the seems
like most people do.
R one and R two if you want to, honestly
it's all just a name
whatever keeps it straight in your brain.
But I'm using R one and R two
and I just wanted to point that
out just in case you're like, wait, why?
Why did you use R-in and RF last time?
It's just a standard.
Anyway.
So with this, our output is not going to be
a negative output.
It is going to be a positive output.
But it's gonna be a little bit more complicated
because instead of just having a direct amplification,
well RF over our RF over our R-in to get your amplification,
you have this one factor.
So this is again, the equation that describes
the output that you're going to get via over V-in
which again is, could be described as 'a',
your amplification factor equals one plus R two over R one.
So in this case, if you had R two
as 10,000 and R one as 1000,
your amplification factor would be 11 positive.
So if you put in one volt
you'd get 11 volts positive, 11 volts out.
So just like with the last one
let's go over how we get this.
And again, it's very, very simple
because we can make those same assumptions.
This and this are going to be the same voltage
and there is not gonna be any currency there.
So we know that the current
through R one and R two is the same.
Now with that, we can establish that this voltage is V-in
and then we can just write those two together.
So let's assume a direction.
We will assume that the current goes this way,
and which also means this way because that makes sense.
You typically have things going to ground
unless V out's negative, but we'll
we'll just make that assumption.
So here we have V-out, minus V-in,
over R two, equals this
current being V-in, minus zero,
over R one.
Okay?
And now it's just a matter of making it V-out
V-in to get us into this format.
So, let us multiply R two
over that side and divide it by V-in over here.
And then we will get V-out minus
V-in over V-in equals R two over R one.
Now since this is just subtraction, we can divide this.
So it's V-out over V-in minus V-in over V-in.
So let's write that down here.
I'm running outta space, so V-out
over V-in, minus V-in, over V-in.,
which obviously goes to one.
That will give us...
Okay, I'm gonna do a gives us instead of V-out over
V-in, minus one, which then makes it, man I'm
I'm doing more steps than is absolutely necessary here.
But basically V-out over V-in equals adding one to
both sides one plus R two over R one.
Whew, okay, have all this space over here.
I, I did not use my space very wisely, but hopefully
that that shows you how this is related mathematically.
And again, it's pretty straightforward as long
as you remember that there's no current
into the inputs and you can make that assumption
that these are the same voltage.
It's very, very simple circuit analysis to derive these.
But you don't need to derive 'em all, all the time.
As long as you understand it, just go look it up
if you don't remember off the top of your head.
If it's been like three years
since you've done this, you're like, what was that again?
Just go look it up, you, it's fine.
You understand it, it intuitively.
But it is really important to understand this
so you can work with it.
Okay, now with this, I put together a non-inverting circuit
so we can just see it in action.
It's not gonna show anything surprising.
And I have used 2000 OHMS for my R two
1000 OHMS for my R one.
So with that I'm expecting my
my amplification factor to be one plus two over one.
So three.
So let me get that set up again really quick.
We will go over it and then we'll wrap this up.
Because you should now have a pretty good understanding
of how inverting and non-inverting op-amp circuits work.
All right, hopefully this is nice and visible,
but this is the same op-amp that we used
for the voltage follower example.
So this is a dual op-amp and so we don't really use anything
on this side cause that's the other op-amp in the circuit.
We have our negative power input
and our positive power input.
Basically VCC and ground, even though this is
at 14 volts and this is connected to ground.
Here we have our input.
And then on the next one
so this is our invert non-inverting input, excuse me
our V positive here.
And then up here we have our, excuse me
our inverting input, which we have
both these two resistors connected to.
One of them is going to the output right there.
And that that is the multimeters connected right here
to that output.
And then the other resistor is going to ground to
create that voltage divider that we just discussed.
So using our input
we should be seeing an amplification factor
of three on our output.
All right, so let's go look at our power supply
and our multimeter to see how this all works.
Okay, so here I have my power supply
and this is that power supply I was talking about.
So the zero to 14 volts, and then this is my voltage in
so the V-in to my non-inverting op amp circuit.
As you can see up here with two volts in
I am getting six, 6.2ish, six-ish volts out.
Which is exactly what we'd expect.
And then as we adjust this, there we go.
And now we see the three volts on the output.
That was a little bit of a delay, but again
you can see that amplification factor of three.
And then we can even go the other way up to three volts
and now we're at about nine.
So that's exactly how it works.
And again, this works with, with basically anything
both a DC and an AC circuit.
But whatever our voltage in our voltage out is simply three.
Now imagine we want to go up to five.
Let's see what happens.
Oh, hey, we can't go anymore because we're saturated.
And that is where the input changes.
So we can actually change this.
We can't go too much higher
before we start to damage the op-amp
but you can see that now we are being restricted
by our input to the op-amp, the power input.
So that's something where you need to take
into consideration when you're amplifying things.
You still have to worry about your input
to the op-amp itself because eventually you're gonna max
out and you're gonna start having problems and
and so that's it.
I, it's pretty straightforward.
You do still need to take into account, especially
with AC circuits, your slew rate, your response time
any sort of offset, any sort of other issues like that.
But as long as you're providing sufficient power
to your op-amp, and that's both positive and negative.
If you have an inverting op-amp
and you're not giving it a negative voltage
with a reference to ground so that it can go to both sides,
it's not gonna be able to do it.
Even though when we're doing our homework
and we're able to ignore the inputs a lot in real life
that's a very real consideration.
And for me in my practical, limited, but practical,
experience, that has been my biggest problem.
Oh, I need to make sure that my inputs
to my power supplies for my op amps are correct.
On paper, you don't need to worry about it.
It's much, much easier.
But in real life, those are things that
you need to consider.
Hopefully this was helpful with
both inverting and non-inverting amplifiers
and that you understand exactly again
how powerful and simple these op-amp circuits can be.
If you like the video, give it a like, subscribe
to our channel and we will catch you in the next one.
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