>> Hi. In this next set of videos,
we're going to take a look at little electronic devices known as
operational amplifiers. My name is Lee Brinton.
I'm an Electrical Engineering Instructor at Salt Lake Community College,
and this is an Introduction to Electrical and Computer Engineering.
Operational Amplifiers are little bugs, little silicon devices,
and in these videos,
we are going to be looking at what they are and what are they're good for.
We'll introduce the ideal Op Amp approximations.
We'll then look at a number of common Op Amp configurations,
the applications that op-amps are frequently used in.
So what is an Op Amp?
An operational amplifier is, as I mentioned,
a semiconductor circuit consisting of
a bunch of transistors and some capacitors and resistors.
But the main idea is that they have two input terminals and an output.
The output terminal becomes a scaled version.
By scaled, we mean a version of the input that is in some way changed.
The output is a function of the input.
It's either going to be amplified or have some other linear operation performed upon it.
Now, at our level,
we're not going to be concerned with all of these internal workings.
We're going to be treating these as a black box device that has inputs and an output,
and we'll work with them in an ideal environment.
So, first of all, op-amps are electronic devices.
They come in silicon semiconductor packaging.
Here's a picture of an eight pin chip.
They come in eight-pin, 14-pin.
Suffice to say that when you're working with operational amplifiers,
you'll be taking a silicon chip and plugging
it into a protoboard and working with it that way.
Internally, functionally, the op-amp,
as I mentioned, has two inputs.
One we're going to designate with a minus sign.
It's known as the inverting terminal.
For the inverting input,
one of them is designated with a positive sign that's known as
the non-inverting terminal or input,
and then there is the output.
But these devices are electrical devices,
and so they also need to be plugged in.
They need to have power supplies.
So, the op-amp will also have a positive voltage source and a negative voltage source.
This little diagram here is meant to show that inside this chip there is one op-amp.
First of all, pin one and pin five are not connected to anything.
This eight-pin chip had two pins that weren't needed and so there just to be ignored.
You'll also notice that on the chip there's a marking.
Usually, there's a little dot closest to the number one pin.
Sometimes you'll see a little notch taken out of the top.
Whatever it is, there'll be something identifying pin one,
and then they number the pins one, two, three,
four coming down one side,
and then going up the other side.
So, what this diagram is telling us is that pin two,
this pin right here,
is connected to the inverting terminal,
pin three is connected to the non-inverting terminal,
pin six is where we'll be looking to get our output voltage,
and pin four and pin seven will be
tied to our negative and positive voltages respectively.
Schematically, we have the op-amp showing wires coming to the input terminals,
a wire going from the output terminal.
This also shows the negative terminal reference to zero plus to minus,
so it's dropping down to a negative voltage here for the power supply
and from ground going up to a positive voltage.
So, the op-amp does have both a positive and negative voltage powering it.
Generally speaking, in a circuit schematic,
we won't show the voltage sources,
the pins where the power supplies are connected.
We know that there's got to be a power source to them just like an amplifier in
a guitar you plug it in and that's where it gets the power to do the amplification.
These op-amps, again, let's just draw the symbol
here with it's inverting and it's non-inverting terminal.
The voltage at the non-inverting terminal,
we're going to refer to as V sub n, and this,
of course, will be referenced to a ground,
so it's a node voltage.
The voltage at the inverting terminal relative to ground we're going to call V sub n.
The voltage at the non-inverting terminal we're going to refer to as V sub p.
V sub n, it's not great nomenclature,
but the n refers to the negative sign,
the p refers to the positive sign.
The op-amp is designed to perform the operation so that the output is equal to A,
some constant, times the difference between those two voltages.
So, A known as the open-loop gain of the amplifier times
the voltage at the p or the non-inverting terminal minus
the voltage at the n terminal will give you
the output or the output is then this gain term multiplying that difference.
This graph here shows the output V out as a function of that difference.
The output is a linear.
It's just a scaled version of that difference over
quite a range of input values or range of Vp minus Vn values.
But when the output gets to the positive source, the positive side,
or when the output would exceed the negative source or power supply,
the amplifier is set to saturate.
It's impossible for, again,
let's just draw those in here.
This is positive Vcc,
the positive power supply, and negative Vcc.
These are the sources of the voltage and the output can't exceed those sources.
So, if Vp minus V sub n were to get large enough that when it was multiplied by
A the output would exceed positive Vcc or be less than negative Vcc,
the amplifier then saturates.
The output becomes simply the source voltage.
It can't go any further than the source voltage.
Sometimes the source voltages are referred to as the rail voltages.
You can think of them as something like two rails between which we must operate.
We can't go beyond the rails.
Operational amplifiers can function either
in the saturation regions or in the linear regions.
When it's in the linear region,
the output again is just a scaled version of the input,
and under those circumstances,
we refer to them as amplifiers.
You can also drive an amplifier into one saturation region or another saturation region,
and under those circumstances,
we sometimes think of them as switches.
So, operational amplifier circuits or circuits containing op-amps will be designed
to operate either within the linear region or designed
to operate in the saturation regions.
So, generally speaking, in a block diagram perspective,
we're going to have some source.
We're going to run it through our amplifier that has some gain term,
and then the output voltage or the voltage delivered to
the load will be some gain times the source.
So, our gain might be 10 and if our gain was 10,
then the output voltage would be 10 times what the input voltage would be.
From a graphical perspective,
that means that if we were putting a sign wave in that had a one volt peak,
if V sub s had one volt peak,
sinusoidal variation, the output then,
let's see if we can draw this a little bit than I've started,
would have the same form,
but would be 10 times as big.
The oscillations in the output would be 10 times as wide or it'd
oscillate 10 times as great as the input did.
All right. Because we're not interested,
at least at this level, we're not concerned about what's going on inside,
we're going to make some approximations that under
normal circumstances are very, very good approximations.
If these approximations are true,
we'll find that the operational amplifier is operating within it's linear region.
First of all, we're going to make the approximation that i sub p,
the current going into
the non-inverting terminal and the current
going into the inverting terminal is very, very small.
In fact, so small that under ideal circumstances,
we're going to say that there is no current going in.
Our output, as we've pointed out,
is some gain term times the difference in voltages.
Basically, we're saying, yes,
there will be a small voltage,
it turns out it's going to be a small voltage across here,
but negligible current going in.
The second approximation is that the voltage across here is going to be very small.
It's not going to be exactly zero,
and it's important to notice that because, again,
the output is some gain term times the difference.
But it's going to be so small.
In fact, it might be on the order of millivolts or tens of millivolts while all of
the voltages in the circuit around it will be on the order of perhaps volts.
So, if we're able to keep,
and part of our circuitry will force
the amplifier to operate in this range where Vp minus
V sub n is approximately zero,
or that Vp and V sub n are approximately equal to each other.
We're going to design a circuitry to make that true so that in
our analysis Vp minus V sub n is zero.
The way we're going to work with that is that we're going to say that the voltage at
the inverting terminal is
approximately equal to the voltage at the non-inverting terminal.
The next approximation is that this open-loop gain term,
A, is really big.
In fact, it approaches infinity.
Now, it's not going to be infinite,
but it's going to be on the order of maybe 50,000, 100,000, 200,000,
big enough that for the calculations that we'll be doing,
we can consider it to be infinite which then makes for an interesting mathematical,
not inconsistency, what's the word I'm talking about?
Indeterminate form. If we have A,
which is approximately infinite, multiplying a really,
really small number, which is approximately zero, it is indeterminate,
and what we'll find is that we'll be able to determine the gain of the amplifier or
specify the gain of the amplifier via the circuitry that we wrap around the amplifier.
Finally, the output resistance,
the resistance seen driving at the output is very small.
In fact, we're going to assume that it is zero so that
our output voltage will not experience a drop across
this resistance which means that we can think about the
current here available within limits.
We can get whatever current out of here we need without
seeing appreciable voltage drop across here.
So, for a reasonable range of currents,
the output voltage will be unchanged.
In that sense, it's something like an ideal current source.
At the input, the input resistance R sub i we're going to assume to be infinite.
That ties back into the input currents being zero.
If you're driving a current into an infinite resistance,
effectively an open circuit,
the input currents are going to be zero.
So, recapping, we had these little silicon devices called operational amplifiers.
They draw almost no current at the inputs.
The output is a scaled version of the input and we can use them.
They're very utilitarian devices used in control systems,
used in the circuit in the lab,
and we'll get a lot of experience using these operational amplifiers.