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All right.
Good morning all.

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Today we embark on another new
chapter in what we do.

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And the topic is going to be --

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We will talk about this thing
called an Operational Amplifier.

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Before I get into the lecture,
I want to point out a couple of

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things.
One is that you are going to

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hear about two big words in
today's lecture.

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Two big and incredibly
important words.

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And I want to mention those
words to you right now so that

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when I come to them in lecture
you can say OK,

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I better pay really close
attention, these are important

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words.
All right.

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One of them is abstraction.
The second one is feedback.

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Two incredibly important
concepts.

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Abstraction,
you have been seeing a couple

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times during this course,
once in the beginning where we

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abstracted out Maxwell's
equations by focusing on a

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smaller playground and simply
using KVL, KCL in place of those

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equations.
A big abstraction.

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It turns out that almost all of
EECS is based upon abstractions

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at various levels.
In the first lecture,

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I also showed you the layer
upon layer of abstraction that

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we built to be able to build
interesting systems.

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The second big thing is
feedback.

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And I am going to relate this
to anti-lock breaks in cars.

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And so, you can wait and see
how we do that.

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It's an incredibly important
concept.

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Before we dive into the
amplifier abstraction,

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let me first talk about
something that you know.

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Start with something that you
know and then lead up into the

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operational amplifier and its
circuits.

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You know about the MOSFET
amplifier.

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The MOSFET amplifier that you
know about looked like this.

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It was based on a MOSFET.

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There was a VS supply.
There was a vI input,

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a vO output and,
as I said, a VS supply.

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So, this was a MOSFET circuit
that you've seen before.

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One way of viewing this is that
this circuit has three major

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ports.
This here is the input port

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with voltage vI.
This here, between the drain

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terminal and the ground,
is the output port.

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I take the output between the
drain terminal and ground.

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And, finally,
we have a third port,

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which is this one.
It is called the power port.

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I apply VS between this
terminal here and the ground

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terminal.
And that gives us the power

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port.
This device here was a three

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port device.
Input port or control port,

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output port and a power port.
And so we looked at the circuit

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and did a whole bunch of
analyses of it.

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Then what I can do at this
point, now that you've seen

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this, it's often times
interesting to think about

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abstracting this out into some
kind of a building block.

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Much like in software,
you write a procedure and you

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abstract out the internal
details of the procedure in the

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procedure declaration and in the
call that you make.

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In the same way,
we can take this little device

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here and abstract that out into
the following abstraction.

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We could abstract that out as a
device that looks like this.

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I have my input port,
I have my output port and I

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have my power port.
So, I can apply VS here.

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Notice that I've taken these
six terminals here,

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one, two, three,
four, five and six,

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and put a box around it.
And just exposed the terminals

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to you.
And I need to tell you a little

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bit more about the internal
properties, but suffice it to

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say that you can begin working
with this little block.

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An even simpler version of this
for many applications might just

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look like this,
vI and vO where there is a

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ground that is shared among them
that is implicit in this

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picture.
And vI and vO can simply be the

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node voltages at these nodes.
This is a progressively more

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abstract representation of this
amplifier.

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What we can do is,
provided we know,

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we can abstract out the
relevant properties of this

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block and expose them outside.
And the relevant properties

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might well be that,
let's say here the properties

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may be that I in is always zero.
I can also express to you the

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gain of this amplifier.
I may also be able to tell you

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the Thevenin equivalent for the
output.

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There are some properties that
I can give you that will let you

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use this building block
abstractly.

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Today, what we will do is
introduce a powerful abstraction

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of a type of amplifier.
This is called the operational

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amplifier or "op amp" for short.
What I am going to do is give

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you a slightly more involved
building block than the one I

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have shown you there.
But suffice it to say that the

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idea is going to be the same.
This building block looks like

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this.
This building block has an

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input port.
This building block also has a

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port in which to connect power
or the power port.

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And the way I am going to
connect power,

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I am going to connect a plus VS
supply here.

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That is going to be my ground
node.

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And I am going to connect a
minus VS supply to this node

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here.
So, these voltages are both VS.

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I want to apply a plus VS here
and a negative VS out here.

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And I am going to take the
output between the ground node

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and the output node of the
operational amplifier and call

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that a vO.
This is the output port.

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So, input port and output port
and a power port.

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Think of this as a pattern
where I have an input port

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across which I connect the
input.

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I have a power port across
which I connect a plus VS,

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minus VS supply,
and then I take the output

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terminal and take a ground
terminal, which is defined by

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external components of my
circuitry, and use this as my

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reference node.
Remember ground is just a

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reference node.
I am going to use this as a

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reference node.
These two are equal in

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magnitude.
And take this as my output.

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And when I do something like
this, I can build an even

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simpler, so this is an abstract
differential input amplifier.

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In other words,
this amplifier is going to

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amplify whatever I apply at the
input.

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A slightly more abstract
representation of this looks

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like this.
vOUT and plus/minus vIN.

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This is a slightly more
abstract representation where,

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remember, we are going to draw
this again and again,

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maybe at least 38 or 39 times
in this course.

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And, remember,
each time you draw it,

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remember that there is an
implicit power port,

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a plus/minus supply that is
connected which we don't show.

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And I remember when I first
learned about it a long time ago

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there was a confusion in me
initially.

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How does this work?
Where is the power coming from?

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Just remember that power comes
from a plus/minus supply,

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and we just don't show that in
this abstraction.

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Now, the details,
a lot of details are in Chapter

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16 of your course notes.
That's the reading for that.

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The other thing is that there
are some other key properties of

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this amplifier.
And let me discuss those very

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quickly.
First of all,

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I can draw a circuit model for
the amplifier.

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Make some room for myself here.
And this is a circuit model for

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what we call the ideal
operational amplifier.

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And the circuit model is going
to look like this.

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This is an abstract device.
And, in terms of analyzing how

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this behaves in a circuit,
I am going to show you this

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abstract circuit that looks as
follows.

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Some input v is applied at
these two terminals here.

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And this terminal is called my
v plus terminal and this is

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called my v minus terminal,
so this corresponds to these

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two terminals.
I am telling you that the

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current going in is going to be
zero, so i plus is going to be

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zero and i minus is going to be
zero.

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i plus is the current in here
and i minus is the current into

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the v minus terminal,
and both these currents are

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going to be zero in this device
here.

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The output is going to look
like this.

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Let me just call it vOUT to be
consistent with this here.

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And taken with ground as my
reference.

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The output is simply Av.
In other words,

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what I am doing is I am going
to model this as a device that

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has a dependent source at its
output.

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And the dependent source here
is a voltage controlled voltage

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source.
It is a dependent source,

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it is a voltage controlled
voltage source such that the

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output voltage is A times the
voltage v across its input.

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This is actually very simple.
Think of these three terminals

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I have shown you here.
I applied input across these.

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And the output is going to be A
times whatever I applied.

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And A is going to tend towards
infinity.

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A is going to be huge.
And specific values for A might

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be a hundred thousand or a
million or things of that sort.

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Huge A in this abstract
amplifier.

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In addition to that,
the other properties are that

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it is going to have infinite
input resistance.

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That means looking in this
looks like an open circuit.

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The fact that this is open here
implies the infinite input

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resistance across this port.
What about the output here?

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Remember, this is a voltage
source.

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And we have a zero output
resistance, which means that no

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matter how the load affects
this, as I apply a load this is

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going to behave like an ideal
voltage source and keep holding

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the voltage constant based on
whatever the function I

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establish here.
And A is virtually infinite.

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Let me pause there for a few
seconds and just dwell on this

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so you just understand what the
basic device is.

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Following this basic
definition, I am just going to

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build a whole bunch of fun
little circuits.

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The analysis will be pretty
straightforward,

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but this is a big conceptual
leap here where there is some

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circuitry inside.
Containing resistors,

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MOSFETs, a whole bunch of stuff
in there.

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I am not telling you what is
inside it.

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Much like I could build an
abstract amplifier,

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I could put an abstract box
around the amplifier you saw

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earlier, I want to put a box
around some circuitry.

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I am not telling you what the
circuitry is.

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And, if you are curious,
you should look at page 581 of

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your course notes.
There is an example solved.

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The example is for a
differential amplifier.

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This is the small signal
analysis chapter.

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That differential amplifier
that's solved in that example is

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usually the first stage in an
operational amplifier circuit.

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That differential amplifier is
the first stage at the input.

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And that differential
amplifier, as the name implies,

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amplifies not a single voltage
but amplifies a differential

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voltage.
Note that this guy amplifies

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the voltage difference between
these two terminals.

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That's v here.
And v is simply the same as v

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plus minus v minus.
It's the node voltage here

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minus the node voltage here.
That is what's amplified.

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It amplifies a difference.
Therefore, it is called a

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difference amplifier or a
differential amplifier.

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And so that input stage is what
is inside the op amp.

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It's got a bunch of other
circuitry like level shifters

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and so on.
And at the output it has got a

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buffer.
At at the output it has

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something that is reminiscent of
the source follower circuit that

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you learned about in
recitations, solved an example

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in the course notes and in your
homework as well.

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And you solved a variant of the
source follower on your quiz as

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well in problem two.
So, a circuit that looks like

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that appears at the output.
Remember, for the source

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follower, the resistance looking
in from the output was very,

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very small.
You have seen some of the

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pieces that go inside the
amplifier, but we will deal with

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this as a building block and
simply represent it using this

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abstract little circuit.
To dwell on this a little

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longer, this little device here
is the workhorse of the analog

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industry.
Much like your primitive gate

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abstraction, your inverter and
NAND gate and so on,

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much as your primitive inverter
or NAND gate was from the

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foundations of the digital
industry.

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Remember we learned how to
build this little abstract

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device called a NAND gate or an
inverter?

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We noticed that those form the
foundations of very complicated

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microprocessors.
Those were the building blocks

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of the digital industry.
In the same way,

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this little beast here is the
building block of the analog

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industry.
Just to give you an analogy

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from software,
think of this abstract little

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device as a library routine from
a library of functions when you

236
00:17:55,000 --> 00:18:01,000
program in C++ or whatever.
Can someone give me an example

237
00:18:01,000 --> 00:18:06,000
of an incredibly popular routine
that we use all the time that

238
00:18:06,000 --> 00:18:11,000
may be called the workhorse of
the software industry?

239
00:18:11,000 --> 00:18:13,000
Pardon?
An abstraction,

240
00:18:13,000 --> 00:18:17,000
an abstract procedure.
One example might be something

241
00:18:17,000 --> 00:18:21,000
like a printf.
Printf is an abstract name for

242
00:18:21,000 --> 00:18:25,000
a procedure that goes and does
something for you.

243
00:18:25,000 --> 00:18:31,000
It is amazing how we take the
lowly printf for granted.

244
00:18:31,000 --> 00:18:34,000
I stick my printf into my
program, it includes the

245
00:18:34,000 --> 00:18:37,000
standard IO library and it goes
and prints a value.

246
00:18:37,000 --> 00:18:40,000
You won't believe how
complicated the printf is.

247
00:18:40,000 --> 00:18:43,000
As you go into learning more
advanced software subjects,

248
00:18:43,000 --> 00:18:46,000
implementing the printf is a
nightmare.

249
00:18:46,000 --> 00:18:48,000
It is horrendously complicated.
Just imagine.

250
00:18:48,000 --> 00:18:52,000
You give it a string and it has
to go and print that on your

251
00:18:52,000 --> 00:18:55,000
terminal or on your Windows
system or whatever.

252
00:18:55,000 --> 00:19:00,000
Think of the complicated steps
it has to go through.

253
00:19:00,000 --> 00:19:02,000
But, as far as you're
concerned, it's simple.

254
00:19:02,000 --> 00:19:05,000
Just print out something and
you're done.

255
00:19:05,000 --> 00:19:08,000
The same way.
Think of this as the printf of

256
00:19:08,000 --> 00:19:10,000
the analog business.
It is really simple,

257
00:19:10,000 --> 00:19:13,000
and the analysis is going to be
incredibly simple,

258
00:19:13,000 --> 00:19:17,000
it will be mind-bogglingly
simple, but inside it,

259
00:19:17,000 --> 00:19:19,000
heavens forbid if you look
inside it.

260
00:19:19,000 --> 00:19:22,000
Tell you what,
go into to S-T-D-I-O dot in one

261
00:19:22,000 --> 00:19:25,000
of the library routines and just
pore through printf.

262
00:19:25,000 --> 00:19:30,000
The world's worst horrendous
macros are in there.

263
00:19:30,000 --> 00:19:33,000
I mean it is just nasty.
The same way inside the op amp,

264
00:19:33,000 --> 00:19:35,000
it is nasty.
You don't want to go there.

265
00:19:35,000 --> 00:19:38,000
Much like in your C programming
in your classes,

266
00:19:38,000 --> 00:19:42,000
you were able to use printf
without fully knowing how it was

267
00:19:42,000 --> 00:19:45,000
implemented.
Probably some MIT god or some

268
00:19:45,000 --> 00:19:48,000
key graduate implemented it,
but once it was implemented you

269
00:19:48,000 --> 00:19:52,000
just used it based on simple
abstract rules as to how it

270
00:19:52,000 --> 00:19:54,000
behaved.
You didn't have to know what

271
00:19:54,000 --> 00:19:57,000
was inside it to use it.
The same way with the

272
00:19:57,000 --> 00:20:02,000
operational amplifier.
So, just think of printf when

273
00:20:02,000 --> 00:20:06,000
you see this and just imagine
how simple it is going to be to

274
00:20:06,000 --> 00:20:09,000
use it.
You may think that I spend way

275
00:20:09,000 --> 00:20:12,000
too much time,
ten minutes dwelling on this

276
00:20:12,000 --> 00:20:15,000
abstract concept,
but I like to dwell on things

277
00:20:15,000 --> 00:20:18,000
that I think are incredibly
important.

278
00:20:18,000 --> 00:20:21,000
The concept of abstraction is
very important.

279
00:20:21,000 --> 00:20:25,000
And it's not just in software.
The concept of abstraction

280
00:20:25,000 --> 00:20:30,000
pervades all of EECS.
And if I were to give you a

281
00:20:30,000 --> 00:20:34,000
project to say go and ask every
professor what is the one word

282
00:20:34,000 --> 00:20:38,000
that you think best describes
all of EECS?

283
00:20:38,000 --> 00:20:41,000
Just pick one word.
Go ask every single professor

284
00:20:41,000 --> 00:20:44,000
you know.
What is a single word?

285
00:20:44,000 --> 00:20:48,000
If you were to characterize all
of EECS with just one word,

286
00:20:48,000 --> 00:20:52,000
what might that word be?
In my mind, it is the A word,

287
00:20:52,000 --> 00:20:54,000
abstraction.
It is all over.

288
00:20:54,000 --> 00:20:58,000
If you do a grep on all the
words used by all your

289
00:20:58,000 --> 00:21:03,000
professors in your four years
here, I promise you the first

290
00:21:03,000 --> 00:21:08,000
one will be know.
And the second one will be

291
00:21:08,000 --> 00:21:10,000
abstraction.
Check it out.

292
00:21:10,000 --> 00:21:13,000
See if what I am saying is true
or not.

293
00:21:13,000 --> 00:21:17,000
It is all over the place.
In 6.001, how many times do you

294
00:21:17,000 --> 00:21:21,000
think the word abstraction was
used in 6.001?

295
00:21:21,000 --> 00:21:25,000
It's all over the map.
It's the A word all over.

296
00:21:25,000 --> 00:21:30,000
Imagine your shock when you see
it being used in 002 because the

297
00:21:30,000 --> 00:21:35,000
same concept applies.
We build more complicated

298
00:21:35,000 --> 00:21:40,000
systems by abstracting out the
details of lesser objects,

299
00:21:40,000 --> 00:21:45,000
and then using those to build
the more complicated systems.

300
00:21:45,000 --> 00:21:50,000
Abstraction is a very powerful
mechanism of dealing with

301
00:21:50,000 --> 00:21:54,000
complexity.
Next step is how do I go about

302
00:21:54,000 --> 00:21:58,000
using the op amp?
Let me show you how it looks on

303
00:21:58,000 --> 00:22:03,000
a scope.
What I am going to do is apply

304
00:22:03,000 --> 00:22:09,000
input to the op amp,
I am going to look at the

305
00:22:09,000 --> 00:22:17,000
output, place the resistor RL to
ground and look at the output.

306
00:22:17,000 --> 00:22:25,000
And here I am going to apply a
plus VS and out here a minus VS.

307
00:22:25,000 --> 00:22:32,000
Again, remember that a plus VS
simply looks like this and a

308
00:22:32,000 --> 00:22:40,000
minus VS simply looks like this.
It's just an inverted VS

309
00:22:40,000 --> 00:22:45,000
applied here so I get a minus VS
at this input.

310
00:22:45,000 --> 00:22:50,000
First of all,
what I would like to do is as I

311
00:22:50,000 --> 00:22:57,000
change vIN, I am going to plot
for you how vOUT looks.

312
00:22:57,000 --> 00:23:03,000
vIN and this is vO.
I am going to plot vIN in terms

313
00:23:03,000 --> 00:23:08,000
of microvolts and vO in volts.
vIN is going to have a very

314
00:23:08,000 --> 00:23:14,000
very small, the scale is going
to be in microvolts because

315
00:23:14,000 --> 00:23:17,000
remember the gain of this is
huge.

316
00:23:17,000 --> 00:23:21,000
It's on the order of ten to the
sixth.

317
00:23:21,000 --> 00:23:25,000
It's huge.
Small changes in vIN are going

318
00:23:25,000 --> 00:23:32,000
to cause massive changes in vO.
I have a very fine scale on the

319
00:23:32,000 --> 00:23:36,000
X axis.
What is going to happen if I

320
00:23:36,000 --> 00:23:39,000
somehow magically make vIN
exactly zero?

321
00:23:39,000 --> 00:23:45,000
If I short these two terminals,
if this was a completely ideal

322
00:23:45,000 --> 00:23:50,000
op amp, which it never is,
if it's a completely ideal op

323
00:23:50,000 --> 00:23:53,000
amp, then my output should be
zero.

324
00:23:53,000 --> 00:24:00,000
As I increase my vIN the output
should be A times vIN.

325
00:24:00,000 --> 00:24:03,000
For some small value of vIN,
small v, let's say one

326
00:24:03,000 --> 00:24:06,000
microvolt, the output should be
one volt.

327
00:24:06,000 --> 00:24:10,000
A is a constant so this would
look like a straight line.

328
00:24:10,000 --> 00:24:14,000
And let's say my supply
voltages are 12 volts minus 12

329
00:24:14,000 --> 00:24:19,000
volts, if this were an ideal
amplifier and I didn't have to

330
00:24:19,000 --> 00:24:23,000
worry about the supply,
this would just go on extending

331
00:24:23,000 --> 00:24:25,000
forever.
But I have a plus 12 volt

332
00:24:25,000 --> 00:24:27,000
supply and a minus 12 volt
supply.

333
00:24:27,000 --> 00:24:32,000
My output cannot go past those
limits.

334
00:24:32,000 --> 00:24:35,000
And so, therefore,
my output kind of flattens out

335
00:24:35,000 --> 00:24:39,000
at these two points.
And it is called hitting the

336
00:24:39,000 --> 00:24:42,000
rails.
Output goes up and you hear a

337
00:24:42,000 --> 00:24:45,000
thunk sound and you hit the
rails.

338
00:24:45,000 --> 00:24:49,000
When you play with op amps in
your next lab,

339
00:24:49,000 --> 00:24:53,000
if you listen really,
really carefully you may hear

340
00:24:53,000 --> 00:24:55,000
it.
So, this saturates out.

341
00:24:55,000 --> 00:24:59,000
Not surprisingly,
this region where the output

342
00:24:59,000 --> 00:25:05,000
saturates at the supply is
called the saturation region.

343
00:25:05,000 --> 00:25:09,000
Remember, don't confuse it
with-- It's not the same as your

344
00:25:09,000 --> 00:25:13,000
saturation in the MOSFET.
It is a totally different

345
00:25:13,000 --> 00:25:16,000
thing.
It is just happenstance that we

346
00:25:16,000 --> 00:25:20,000
call this saturation.
And if you would like to think

347
00:25:20,000 --> 00:25:24,000
about it, you can think of it as
the thunk region.

348
00:25:24,000 --> 00:25:27,000
That's probably more
appropriate to distinguish it

349
00:25:27,000 --> 00:25:32,000
from the saturation region in
the MOSFET.

350
00:25:32,000 --> 00:25:36,000
And, not surprisingly,
this one is called the active

351
00:25:36,000 --> 00:25:39,000
region.
And it is in this region that

352
00:25:39,000 --> 00:25:43,000
we use the op amp.
Here it has hit the rails and

353
00:25:43,000 --> 00:25:48,000
is kind of dangling out there.
It's not much use to us.

354
00:25:48,000 --> 00:25:53,000
It's in this active region that
we use it because this is where

355
00:25:53,000 --> 00:25:58,000
the gain is seen.
Now, it turns out that this is

356
00:25:58,000 --> 00:26:01,000
a very high gain device.
It is very skittish.

357
00:26:01,000 --> 00:26:05,000
This gain is kind of a really
funny thing.

358
00:26:05,000 --> 00:26:08,000
It's dependent on a bunch of
factors.

359
00:26:08,000 --> 00:26:10,000
This could be temperature
dependent.

360
00:26:10,000 --> 00:26:15,000
This gain here and this curve
is just completely skittish.

361
00:26:15,000 --> 00:26:20,000
It could depend on temperature.
It could depend on time of day.

362
00:26:20,000 --> 00:26:24,000
It could depend on what
medication this amplifier is on.

363
00:26:24,000 --> 00:26:27,000
It could depend on its mood
swings.

364
00:26:27,000 --> 00:26:32,000
Who knows what?
This is kind of unstable.

365
00:26:32,000 --> 00:26:34,000
And A in particular is highly
unstable.

366
00:26:34,000 --> 00:26:36,000
It is going to be big,
that's for sure,

367
00:26:36,000 --> 00:26:40,000
but it could be ten to the six,
on a rainy day it might be two

368
00:26:40,000 --> 00:26:43,000
times ten to the six.
If it feeling sleepy it may be

369
00:26:43,000 --> 00:26:46,000
point five times ten to the
sixth.

370
00:26:46,000 --> 00:26:48,000
It is big but I cannot rely on
it.

371
00:26:48,000 --> 00:26:51,000
Let me show you an example.
I want to show you this curve

372
00:26:51,000 --> 00:26:54,000
for this MOSFET,
apply an input and plotting the

373
00:26:54,000 --> 00:26:56,000
output.
What I will do is take a look

374
00:26:56,000 --> 00:27:00,000
at this curve.
Then what I am going to do is

375
00:27:00,000 --> 00:27:04,000
use a heat gun to heat the op
amp and you are going to see

376
00:27:04,000 --> 00:27:07,000
this vary all over the map.
If you still remember last

377
00:27:07,000 --> 00:27:11,000
week, some of you may remember
that from some place in a

378
00:27:11,000 --> 00:27:15,000
similar situation where the gm
for the MOSFETs you were given

379
00:27:15,000 --> 00:27:18,000
was also dependent on
temperature and stuff like that.

380
00:27:18,000 --> 00:27:22,000
It is a very common occurrence.
And that is certainly the case

381
00:27:22,000 --> 00:27:24,000
for the MOSFET.

382
00:27:31,000 --> 00:27:34,000
Let's apply input.
Let's do this.

383
00:27:34,000 --> 00:27:38,000
This is vIN versus vOUT for the
amplifier.

384
00:27:38,000 --> 00:27:44,000
Notice that this is plus 12
volts, this is minus 12 volts.

385
00:27:44,000 --> 00:27:47,000
It is about two volts per
division.

386
00:27:47,000 --> 00:27:52,000
This axis here is in
microvolts, I believe.

387
00:27:52,000 --> 00:27:57,000
For a very small change,
for a few tens of microvolts,

388
00:27:57,000 --> 00:28:03,000
I have an incredibly high gain.
Notice that this has an

389
00:28:03,000 --> 00:28:07,000
incredibly high gain here.
The gain is the slope of this

390
00:28:07,000 --> 00:28:11,000
line, almost a vertical line.
What I am going to do next,

391
00:28:11,000 --> 00:28:14,000
is to have some fun,
is I am going to heat the op

392
00:28:14,000 --> 00:28:16,000
amp.
To show you that A is kind of

393
00:28:16,000 --> 00:28:20,000
really skittish and also the
fact that it doesn't quite hit

394
00:28:20,000 --> 00:28:24,000
zero, it does all kinds of weird
things, I am going to heat the

395
00:28:24,000 --> 00:28:27,000
op amp.
And then let's take a look at

396
00:28:27,000 --> 00:28:30,000
how that curve fluctuates.

397
00:29:00,000 --> 00:29:04,000
What you saw there was that the
op amp began to behave really

398
00:29:04,000 --> 00:29:07,000
weirdly as I heated it.
Instead of doing this it

399
00:29:07,000 --> 00:29:11,000
sometimes did this really
weirdly, like getting an offset

400
00:29:11,000 --> 00:29:15,000
from the center and so on.
And it does a bunch of other

401
00:29:15,000 --> 00:29:18,000
weird things,
but we won't go into those

402
00:29:18,000 --> 00:29:21,000
details.
It's not relevant for this

403
00:29:21,000 --> 00:29:23,000
course.
But the point is that the gain

404
00:29:23,000 --> 00:29:29,000
and the offset at the input are
dependent on temperature.

405
00:29:29,000 --> 00:29:33,000
And we look for ways to make it
less dependent on temperature.

406
00:29:33,000 --> 00:29:37,000
As the next step,
what I would like to do is

407
00:29:37,000 --> 00:29:40,000
build a circuit.
This is model equivalent of

408
00:29:40,000 --> 00:29:44,000
your Hello World program.
We are going to use the printf

409
00:29:44,000 --> 00:29:47,000
and build a small program on the
printf.

410
00:29:47,000 --> 00:29:51,000
You don't have to worry about
how printf is implemented,

411
00:29:51,000 --> 00:29:56,000
just that we can build very
highly interesting circuits with

412
00:29:56,000 --> 00:30:00,000
this horrendously complicated
function based on a simple

413
00:30:00,000 --> 00:30:08,000
abstraction of the device.
The circuit that we will build

414
00:30:08,000 --> 00:30:14,000
is called a noninverting
amplifier.

415
00:30:20,000 --> 00:30:22,000
From now on,
I am not going to show you the

416
00:30:22,000 --> 00:30:25,000
plus/minus VS.
I am not going to show the

417
00:30:25,000 --> 00:30:28,000
power port, but it is in there.
It's hidden under the

418
00:30:28,000 --> 00:30:31,000
abstraction layer.
This is my op amp.

419
00:30:31,000 --> 00:30:35,000
And I am going to build the
following circuit.

420
00:30:35,000 --> 00:30:38,000
This is my v plus and this is
my v minus.

421
00:30:38,000 --> 00:30:43,000
What I am going to do is for
the v plus I shall apply a vIN.

422
00:30:43,000 --> 00:30:47,000
Let me talk a little bit about
ground as well.

423
00:30:47,000 --> 00:30:52,000
Ground is commonly taken as the
point at which I connect my VS

424
00:30:52,000 --> 00:30:58,000
and minus VS supply.
It is kind of at the midpoint.

425
00:30:58,000 --> 00:31:03,000
And if VS and minus VS are very
carefully tuned then the output

426
00:31:03,000 --> 00:31:08,000
is also going to be at that same
ground reference when the input

427
00:31:08,000 --> 00:31:11,000
is zero.
So, the ground is defined as

428
00:31:11,000 --> 00:31:16,000
the point at which I connect my
plus/minus VS supplies.

429
00:31:16,000 --> 00:31:20,000
I apply my vIN out here.
Then what I am going to do,

430
00:31:20,000 --> 00:31:24,000
here is my output vO.
I am going to have a resistive

431
00:31:24,000 --> 00:31:30,000
divider to ground here and label
these R1 and R2.

432
00:31:30,000 --> 00:31:36,000
And what I am going to do here
is feed this back to the input,

433
00:31:36,000 --> 00:31:40,000
to the v minus input.
I am going to sample the

434
00:31:40,000 --> 00:31:44,000
voltage here and feed that into
here.

435
00:31:44,000 --> 00:31:49,000
So, this is my abstract model
and this is my Hello World

436
00:31:49,000 --> 00:31:53,000
program.
What we are going to do is

437
00:31:53,000 --> 00:31:59,000
simply analyze how this little
program behaves.

438
00:31:59,000 --> 00:32:00,000
So, my equivalent circuit
model.

439
00:32:00,000 --> 00:32:03,000
The way to analyze these is
after one or two of these

440
00:32:03,000 --> 00:32:07,000
examples, you will be able to
directly analyze this just by

441
00:32:07,000 --> 00:32:09,000
looking at it,
by inspection.

442
00:32:09,000 --> 00:32:11,000
But, much as we did for the
other pieces,

443
00:32:11,000 --> 00:32:14,000
let me grunge through drawing
the equivalent circuit and

444
00:32:14,000 --> 00:32:18,000
grinding through the analysis,
and then show you the much

445
00:32:18,000 --> 00:32:20,000
simpler way of doing it.
And even here,

446
00:32:20,000 --> 00:32:23,000
even with this grinding
analysis, it is going to be

447
00:32:23,000 --> 00:32:26,000
pretty simple in any case.
So, I will replace the op amp

448
00:32:26,000 --> 00:32:30,000
with its equivalent circuit
model.

449
00:32:30,000 --> 00:32:33,000
Its equivalent circuit was v
plus, v minus.

450
00:32:44,000 --> 00:32:49,000
So, that was the equivalent
circuit model of the operational

451
00:32:49,000 --> 00:32:53,000
amplifier, just this piece.
I draw that for you.

452
00:32:53,000 --> 00:32:59,000
Then what I am going to do is I
connect my v in here.

453
00:32:59,000 --> 00:33:02,000
And, remember,
I have an R1,

454
00:33:02,000 --> 00:33:09,000
R2 resistive divider here.
And this one gets connected to

455
00:33:09,000 --> 00:33:14,000
this terminal there.
I also know that i plus is

456
00:33:14,000 --> 00:33:18,000
zero.
I also know that i minus is

457
00:33:18,000 --> 00:33:22,000
zero.
All I've done is simply

458
00:33:22,000 --> 00:33:30,000
replaced the amplifier with its
equivalent circuit.

459
00:33:30,000 --> 00:33:34,000
Let's go ahead and analyze that
circuit now.

460
00:33:34,000 --> 00:33:38,000
Let's go ahead and analyze that
circuit.

461
00:33:38,000 --> 00:33:42,000
And it's going to be pretty
simple, actually.

462
00:33:42,000 --> 00:33:48,000
What I am going to show you is
the hard way of doing it.

463
00:33:48,000 --> 00:33:54,000
I will show you a much easier
way, but the hard way itself is

464
00:33:54,000 --> 00:33:59,000
pathetically easy.
What I want to do is find vO in

465
00:33:59,000 --> 00:34:04,000
terms of vIN.
And there will be a bunch of

466
00:34:04,000 --> 00:34:08,000
other factors thrown in,
including things like R1 and

467
00:34:08,000 --> 00:34:12,000
R2, A and stuff like that.
Let's go and analyze it.

468
00:34:12,000 --> 00:34:16,000
vO, let's look at that circuit.
By the way, let me take 30

469
00:34:16,000 --> 00:34:20,000
seconds and make a little speech
at this point.

470
00:34:20,000 --> 00:34:24,000
When you see circuits like
this, and I saw this happen in

471
00:34:24,000 --> 00:34:27,000
quiz two as well,
for some reason,

472
00:34:27,000 --> 00:34:31,000
when you see a new kind of
circuit, don't completely go

473
00:34:31,000 --> 00:34:36,000
berserk or freeze or whatever.
There is just no reason to.

474
00:34:36,000 --> 00:34:39,000
You know the node method.
The node method is the

475
00:34:39,000 --> 00:34:43,000
workhorse of our business.
When in doubt apply the node

476
00:34:43,000 --> 00:34:45,000
method.
It will simply work.

477
00:34:45,000 --> 00:34:47,000
Don't freeze.
Don't think oh,

478
00:34:47,000 --> 00:34:50,000
man, I need to apply a pattern
that I know already.

479
00:34:50,000 --> 00:34:52,000
I must have seen this
somewhere.

480
00:34:52,000 --> 00:34:56,000
When in doubt boom,
apply the node method.

481
00:34:56,000 --> 00:35:00,000
This circuit here,
all I have here is one unknown

482
00:35:00,000 --> 00:35:03,000
node voltage.
I know the voltage of v plus,

483
00:35:03,000 --> 00:35:06,000
I need to compute the voltage
vO.

484
00:35:06,000 --> 00:35:10,000
There are two unknowns,
vO is an unknown and the

485
00:35:10,000 --> 00:35:14,000
voltage here at v minus is
another unknown.

486
00:35:14,000 --> 00:35:18,000
This is a very simple circuit
involving a dependent voltage

487
00:35:18,000 --> 00:35:23,000
controlled voltage source,
and you need to find out vO and

488
00:35:23,000 --> 00:35:27,000
v minus using the node method.
Just apply it.

489
00:35:27,000 --> 00:35:31,000
It's simple.
Don't freeze.

490
00:35:31,000 --> 00:35:36,000
Just look at it and say I can
do it and apply the node method.

491
00:35:36,000 --> 00:35:40,000
It will simply work.
So, let's do that.

492
00:35:40,000 --> 00:35:45,000
What I can do here is vO is A
times v plus minus v minus.

493
00:35:45,000 --> 00:35:50,000
This is actually really simple.
And then, if I take v plus

494
00:35:50,000 --> 00:35:55,000
here, I know v plus is simply
vIN so I will just make that

495
00:35:55,000 --> 00:36:01,000
substitution right away.
So, v plus is simply vIN.

496
00:36:01,000 --> 00:36:10,000
What is v minus?
v minus here is vO --

497
00:36:25,000 --> 00:36:27,000
What is v plus?
I'm sorry, v minus.

498
00:36:27,000 --> 00:36:33,000
v minus is simply the voltage
that is between R1 and R2.

499
00:36:33,000 --> 00:36:37,000
Notice that no current flows in
to the v minus node.

500
00:36:37,000 --> 00:36:42,000
There is no current flowing in.
Voltage at v minus is simply

501
00:36:42,000 --> 00:36:46,000
the voltage given by the
resistive divider,

502
00:36:46,000 --> 00:36:50,000
which is vO times R2 divided by
R1 plus R2.

503
00:36:50,000 --> 00:36:52,000
Stare at that for another
second.

504
00:36:52,000 --> 00:36:58,000
The voltage at this node here
is simply given by the resistive

505
00:36:58,000 --> 00:37:02,000
divider.
Because no current is flowing

506
00:37:02,000 --> 00:37:06,000
in this direction.
And no current flows in because

507
00:37:06,000 --> 00:37:10,000
I am telling you there is no
current there based on my

508
00:37:10,000 --> 00:37:14,000
abstraction.
I am telling you i minus is

509
00:37:14,000 --> 00:37:16,000
zero.
That voltage is simply the

510
00:37:16,000 --> 00:37:19,000
voltage at this resistive
divider.

511
00:37:19,000 --> 00:37:23,000
And so I can simplify it
further and write this as vO.

512
00:37:23,000 --> 00:37:28,000
So I get, there is a one here.
And I move this thing over to

513
00:37:28,000 --> 00:37:35,000
this side so I get one plus A
times R2 divided by R1 plus R2.

514
00:37:35,000 --> 00:37:42,000
And that is equal to AvIN.
And simplifying it some more,

515
00:37:42,000 --> 00:37:51,000
I get vO is AvIN divided by one
plus AR2 divided by R1 plus R2.

516
00:37:51,000 --> 00:38:00,000
Notice how simple this is,
and this is the hard method.

517
00:38:00,000 --> 00:38:05,000
All I have done is analyze the
circuit using the basic circuit

518
00:38:05,000 --> 00:38:09,000
analysis principle that you
learned the first week of the

519
00:38:09,000 --> 00:38:12,000
course, and I have the output
for you.

520
00:38:12,000 --> 00:38:17,000
I just noted very carefully
what the relationships were

521
00:38:17,000 --> 00:38:20,000
between the various elements in
the abstraction.

522
00:38:20,000 --> 00:38:25,000
Notice here that I am told that
A is extremely large.

523
00:38:25,000 --> 00:38:30,000
A is on the order of ten to the
six and so on.

524
00:38:30,000 --> 00:38:36,000
And suppose it is the case
that, let me write that down

525
00:38:36,000 --> 00:38:40,000
again.
vO is AvIN, one plus AR2,

526
00:38:40,000 --> 00:38:44,000
R2.
Suppose R1 and R2 are more or

527
00:38:44,000 --> 00:38:52,000
less comparable and A is ten to
the six, it's a huge number,

528
00:38:52,000 --> 00:39:00,000
so this whole number is much,
much greater than one.

529
00:39:00,000 --> 00:39:06,000
If it is much huger than one,
what I can do is I can then

530
00:39:06,000 --> 00:39:13,000
write this as follows.
I can say that this is more or

531
00:39:13,000 --> 00:39:20,000
less equal to AvIN divided by
AR2 divided by R1 plus R2.

532
00:39:20,000 --> 00:39:26,000
I am ignoring the one here.
As soon as I do that,

533
00:39:26,000 --> 00:39:34,000
notice I can cancel out A and I
get vO to be approximately equal

534
00:39:34,000 --> 00:39:40,000
to vIN times R1 plus R2 divided
by R2.

535
00:39:40,000 --> 00:39:45,000
Notice now that when the gain
is very large the output is a

536
00:39:45,000 --> 00:39:49,000
function of the input multiplied
by some number.

537
00:39:49,000 --> 00:39:54,000
The beauty of this thing here
is that when A is very large,

538
00:39:54,000 --> 00:39:59,000
or this expression is very
large, A cancels out and there

539
00:39:59,000 --> 00:40:06,000
is no A in this relationship.
This means that even though the

540
00:40:06,000 --> 00:40:11,000
basic amplifier was very
skittish, the output here

541
00:40:11,000 --> 00:40:16,000
relates to the input based on
components that I have control

542
00:40:16,000 --> 00:40:20,000
over.
These are soldiers in my army.

543
00:40:20,000 --> 00:40:25,000
I control them.
So, to give you a sense of some

544
00:40:25,000 --> 00:40:29,000
numbers here,
suppose A was ten to the six.

545
00:40:29,000 --> 00:40:35,000
And I choose R1 to be 9R.
And R to be some R.

546
00:40:35,000 --> 00:40:44,000
Then vO is ten to the sixth vIN
divided by one plus ten to the

547
00:40:44,000 --> 00:40:52,000
six R divided by 9R plus R.
So, that is ten to the six vIN

548
00:40:52,000 --> 00:41:01,000
divided by one plus ten to the
six divided by ten.

549
00:41:01,000 --> 00:41:05,000
All right.
If I ignore the one here,

550
00:41:05,000 --> 00:41:11,000
the ten to the six and ten to
the six cancel out,

551
00:41:11,000 --> 00:41:17,000
this ends up giving me 10vIN.
So, I get a really nice

552
00:41:17,000 --> 00:41:23,000
amplifier whose output is simply
ten times the input and

553
00:41:23,000 --> 00:41:30,000
determined solely by some
resistor values.

554
00:41:30,000 --> 00:41:34,000
Let me show you another quick
demo this time and show you the

555
00:41:34,000 --> 00:41:37,000
amplifier again,
but with resistors connected

556
00:41:37,000 --> 00:41:41,000
like that.
And then I show you that I want

557
00:41:41,000 --> 00:41:45,000
to heat the amplifier to the
wazoo, the op amp to the wazoo,

558
00:41:45,000 --> 00:41:48,000
but vO is going to be
absolutely rock solid.

559
00:41:48,000 --> 00:41:51,000
Let's try that out.

560
00:42:00,000 --> 00:42:03,000
This time around,
this is the transfer function,

561
00:42:03,000 --> 00:42:07,000
the vO versus vIN.
And notice that this time

562
00:42:07,000 --> 00:42:11,000
around I have similar scales on
the X and Y axes,

563
00:42:11,000 --> 00:42:15,000
and this has a slope of 10.
This is the point where the

564
00:42:15,000 --> 00:42:20,000
amplifier saturates at plus 12
volts, and this is minus 12

565
00:42:20,000 --> 00:42:23,000
volts, and this point here is a
zero.

566
00:42:23,000 --> 00:42:25,000
So, this is vIN,
vOUT, plus 12,

567
00:42:25,000 --> 00:42:31,000
minus 12 and this slope is 10.
What I am going to do now is

568
00:42:31,000 --> 00:42:36,000
heat the op amp to the wazoo and
this ain't going to change

569
00:42:36,000 --> 00:42:40,000
because it's my external
resistors that control it

570
00:42:40,000 --> 00:42:45,000
independent of the value of A,
provided A continues to be very

571
00:42:45,000 --> 00:42:47,000
large.
I am just articulating the

572
00:42:47,000 --> 00:42:51,000
vOUT, vIN curve.
And let me start heating the op

573
00:42:51,000 --> 00:42:53,000
amp.

574
00:43:01,000 --> 00:43:06,000
Notice that it's pretty stable.
It doesn't change because it is

575
00:43:06,000 --> 00:43:09,000
independent of the amplifier
values.

576
00:43:09,000 --> 00:43:14,000
What I have done now is by
connecting these resistors in

577
00:43:14,000 --> 00:43:18,000
this way, I have a nice
amplifier with a gain of ten.

578
00:43:18,000 --> 00:43:22,000
The question you may ask
yourselves is why?

579
00:43:22,000 --> 00:43:27,000
There is this little sucker in
there that wants to shoot things

580
00:43:27,000 --> 00:43:32,000
up by ten to the sixth.
Wants to knock things off the

581
00:43:32,000 --> 00:43:36,000
one rail or the negative rail.
Why is it that it's behaving

582
00:43:36,000 --> 00:43:39,000
like a docile lamb here and
giving us a nice little factor

583
00:43:39,000 --> 00:43:41,000
of ten gain no matter what I do
to it?

584
00:43:41,000 --> 00:43:44,000
Why is it doing that?
What is the intuition behind

585
00:43:44,000 --> 00:43:46,000
it?
I will draw something on the

586
00:43:46,000 --> 00:43:50,000
board, but for the next ten
seconds I want you think about

587
00:43:50,000 --> 00:43:51,000
it.
See if you can come up with

588
00:43:51,000 --> 00:43:54,000
some insight as to why is it
doing that.

589
00:43:54,000 --> 00:43:57,000
Why is it exactly ten?
Why isn't the ten to the sixth

590
00:43:57,000 --> 00:44:01,000
kind of killing me somehow?
Why am I getting exactly ten no

591
00:44:01,000 --> 00:44:04,000
matter what happens?
See if you can come up with

592
00:44:04,000 --> 00:44:07,000
some intuition and then I will
show you how it works.

593
00:44:07,000 --> 00:44:10,000
I will redraw the circuit in
the meantime.

594
00:44:28,000 --> 00:44:30,000
Let me see if I can give you
some intuition.

595
00:44:30,000 --> 00:44:34,000
This is my circuit,
and let's say this is R and

596
00:44:34,000 --> 00:44:36,000
this is R.
As an example,

597
00:44:36,000 --> 00:44:42,000
let's assume that the input is
5 volts, vIN is 5 volts.

598
00:44:42,000 --> 00:44:46,000
If R and R are equal,
what should the output be?

599
00:44:46,000 --> 00:44:50,000
It's R and R,
so it's R1 plus R2 divided by

600
00:44:50,000 --> 00:44:53,000
R2, right?
It's 2R divided by R,

601
00:44:53,000 --> 00:44:59,000
so it has a gain of two.
My amplifier has a gain of two

602
00:44:59,000 --> 00:45:03,000
because R1 plus R2 divided by
R2, which is my gain,

603
00:45:03,000 --> 00:45:09,000
is R plus R divided by R equals
two.

604
00:45:09,000 --> 00:45:13,000
So, this will be 10 volts.
If that is 10 volts this is

605
00:45:13,000 --> 00:45:16,000
going to be 5 volts,
correct?

606
00:45:16,000 --> 00:45:18,000
This R and R,
voltage divider,

607
00:45:18,000 --> 00:45:22,000
this is five,
so I get 5 volts here.

608
00:45:22,000 --> 00:45:24,000
This is v plus.
This is v minus.

609
00:45:24,000 --> 00:45:27,000
I get R and R,
5 volts here,

610
00:45:27,000 --> 00:45:32,000
that's how the circuit looks.
Now let's understand what is

611
00:45:32,000 --> 00:45:34,000
going on.
And listen very carefully.

612
00:45:34,000 --> 00:45:37,000
This is going to be a key
insight that I hope you will

613
00:45:37,000 --> 00:45:40,000
carry with you for the rest of
your lives.

614
00:45:40,000 --> 00:45:41,000
This is really,
really key.

615
00:45:41,000 --> 00:45:45,000
What you are going to see is,
I think, the third big ah-ha

616
00:45:45,000 --> 00:45:47,000
moment in 6.002.
Like small signal analysis,

617
00:45:47,000 --> 00:45:51,000
like the frequency domain stuff
we saw, I think this is the

618
00:45:51,000 --> 00:45:54,000
third big one in the next 30 or
40 seconds, things that are

619
00:45:54,000 --> 00:45:57,000
completely either not
necessarily intuitive but are

620
00:45:57,000 --> 00:46:02,000
just spectacular in terms of
what they can do for you.

621
00:46:02,000 --> 00:46:04,000
Let's see.
Let's suppose that because I am

622
00:46:04,000 --> 00:46:08,000
heating it, let's suppose that A
suddenly tends to increase.

623
00:46:08,000 --> 00:46:11,000
It wants to increase because I
have heated it.

624
00:46:11,000 --> 00:46:15,000
A is saying I want to get out
this mold here and starts to

625
00:46:15,000 --> 00:46:19,000
break through its shackles here.
Let's say, as a Gedanken

626
00:46:19,000 --> 00:46:22,000
experiment, that it tries to
shoot up this to 12 volts.

627
00:46:22,000 --> 00:46:26,000
It tries to push it up higher.
This is just a Gedanken

628
00:46:26,000 --> 00:46:30,000
experiment.
The up arrow says that the

629
00:46:30,000 --> 00:46:34,000
increase in A is trying to push
up vO momentarily.

630
00:46:34,000 --> 00:46:38,000
Let's see what happens.
It is trying to push up vO

631
00:46:38,000 --> 00:46:43,000
momentarily, so let's say this
goes to 12 hypothetically.

632
00:46:43,000 --> 00:46:47,000
If that goes to 12,
what should this volt node go

633
00:46:47,000 --> 00:46:49,000
to?
Six, exactly.

634
00:46:49,000 --> 00:46:52,000
This goes to 6 volts.
If that goes to six,

635
00:46:52,000 --> 00:46:56,000
what does v minus go to?
6 volts again.

636
00:46:56,000 --> 00:47:02,000
So, v minus goes to 6 volts.
Now at the input I have 5 volts

637
00:47:02,000 --> 00:47:06,000
at v plus and 6 volts at v
minus, so where should the

638
00:47:06,000 --> 00:47:09,000
output go?
The output should go down

639
00:47:09,000 --> 00:47:13,000
because the voltage of the
negative terminal is higher.

640
00:47:13,000 --> 00:47:17,000
And so the output is A times v
plus minus v minus.

641
00:47:17,000 --> 00:47:22,000
And because this has gone down,
this has gone up here it is

642
00:47:22,000 --> 00:47:25,000
going to try to pull the output
down.

643
00:47:25,000 --> 00:47:29,000
That is going to pull the
output down let's say to 9 volts

644
00:47:29,000 --> 00:47:34,000
or something.
Cachunk, there is a big battle

645
00:47:34,000 --> 00:47:35,000
going on here.
A has gone up,

646
00:47:35,000 --> 00:47:39,000
it has boosted it up to 12,
but the moment that goes to 12,

647
00:47:39,000 --> 00:47:41,000
this goes to 6,
this goes to 6,

648
00:47:41,000 --> 00:47:45,000
and the op amp output has to go
down to 9 volts now because this

649
00:47:45,000 --> 00:47:48,000
input is higher here.
If this goes to 9,

650
00:47:48,000 --> 00:47:51,000
this goes to 4.5.
If that goes to 4.5,

651
00:47:51,000 --> 00:47:53,000
this goes to 4.5.
What happens now?

652
00:47:53,000 --> 00:47:55,000
If this goes to 4.5,
what happens?

653
00:47:55,000 --> 00:48:00,000
It wants to go back up.
Can't it make up its mind?

654
00:48:00,000 --> 00:48:04,000
This guy wants to go back up
now because v plus is higher

655
00:48:04,000 --> 00:48:07,000
than v minus.
What am I seeing here?

656
00:48:07,000 --> 00:48:11,000
This whole circuit here behaves
like my little son,

657
00:48:11,000 --> 00:48:14,000
my 9-year-old.
If say do this,

658
00:48:14,000 --> 00:48:17,000
he wants to do the exact
opposite.

659
00:48:17,000 --> 00:48:21,000
So, there is a trick in how you
make them do things for you.

660
00:48:21,000 --> 00:48:25,000
Look at this.
Because of this arrangement of

661
00:48:25,000 --> 00:48:29,000
the circuit when A tries to push
the output up,

662
00:48:29,000 --> 00:48:34,000
the rest of the circuit tries
to pull it back down to where it

663
00:48:34,000 --> 00:48:39,000
used to be.
If the circuit tries not to

664
00:48:39,000 --> 00:48:43,000
follow the true path,
the rest of the circuit tries

665
00:48:43,000 --> 00:48:48,000
to whack it into shape so it
follows a true path.

666
00:48:48,000 --> 00:48:52,000
And what's happening is
because, in this arrangement,

667
00:48:52,000 --> 00:48:57,000
I have fed back a portion of
the output to the negative

668
00:48:57,000 --> 00:49:01,000
input.
I have fed back some of the

669
00:49:01,000 --> 00:49:06,000
output to the negative input.
And by providing this feedback

670
00:49:06,000 --> 00:49:09,000
of a portion of the output to
the negative input,

671
00:49:09,000 --> 00:49:14,000
I have arranged it in a way
that I have something called

672
00:49:14,000 --> 00:49:18,000
negative feedback.
What negative feedback does is

673
00:49:18,000 --> 00:49:23,000
that if this wanted to go wild
and crazy, the circuit provides

674
00:49:23,000 --> 00:49:27,000
it with some negative feedback
like you just saw.

675
00:49:27,000 --> 00:49:32,000
Feedback, a big word.
If you take a poll of all the

676
00:49:32,000 --> 00:49:35,000
EECS faculty,
I suspect that feedback would

677
00:49:35,000 --> 00:49:39,000
rank at least as the ninth or
tenth most important word in the

678
00:49:39,000 --> 00:49:41,000
EECS.
If abstract is number one,

679
00:49:41,000 --> 00:49:46,000
I think this would rank like a
nine or a ten or something.

680
00:49:46,000 --> 00:49:48,000
So, that's the reason why it
worked.

681
00:49:48,000 --> 00:49:53,000
In the last couple of minutes,
let me give you some insight,

682
00:49:53,000 --> 00:49:57,000
based on something that you
know, on how feedback works.

683
00:49:57,000 --> 00:50:02,000
This is a road here.
Let's look at anti lock breaks.

684
00:50:02,000 --> 00:50:05,000
This is my tire.
And let's say I have a set of

685
00:50:05,000 --> 00:50:09,000
disk brakes here.
As the car is moving forward,

686
00:50:09,000 --> 00:50:13,000
if I apply the brakes the tire
stops rolling,

687
00:50:13,000 --> 00:50:18,000
but if I apply the breaks too
hard it can lock up the tire and

688
00:50:18,000 --> 00:50:22,000
the whole car can skid.
The way anti lock breaks work

689
00:50:22,000 --> 00:50:26,000
is as follows.
There is a controller that sits

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00:50:26,000 --> 00:50:30,000
here.
And there is a little person

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looking at the wheel and seeing
is it turning.

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00:50:34,000 --> 00:50:39,000
So, this is a feedback.
And it is saying is it turning?

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Yes.
Or, is it not turning?

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00:50:42,000 --> 00:50:45,000
No.
All this person watching the

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00:50:45,000 --> 00:50:50,000
tire is doing is saying is it
turning or is it not turning.

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That is it.
That is a negative feedback.

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00:50:54,000 --> 00:50:59,000
And so, if it is no and if it
is yes.

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00:50:59,000 --> 00:51:03,000
If it is yes then what this
does is it applies the brakes

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00:51:03,000 --> 00:51:06,000
even more strongly.
It is turning so I can apply

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00:51:06,000 --> 00:51:08,000
more brakes.
But if it says oops,

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it stopped turning,
what it does is it simply

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00:51:11,000 --> 00:51:15,000
releases, the controller
releases the brakes.

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00:51:15,000 --> 00:51:18,000
And when the controller
releases the brakes this one

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00:51:18,000 --> 00:51:23,000
tends to loosen up a little bit
and the tire starts turning

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00:51:23,000 --> 00:51:25,000
again.
So, this way you are constantly

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00:51:25,000 --> 00:51:30,000
keeping the tire in its region
of critical friction so that it

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00:51:30,000 --> 00:51:34,000
is constantly moving.
And static friction applies to

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00:51:34,000 --> 00:51:37,000
how hard you can brake and it
doesn't start skidding.

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00:51:37,000 --> 00:51:41,000
In fact, if you take your car
out, and I don't say you do

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00:51:41,000 --> 00:51:42,000
this.
Let's say go onto the Charles

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00:51:42,000 --> 00:51:46,000
River in the dead of winter and
you drive on the lake and you

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00:51:46,000 --> 00:51:49,000
slam your anti lock brakes on,
on an icy patch,

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00:51:49,000 --> 00:51:52,000
you will notice that there is a
constant sound that looks like

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00:51:52,000 --> 00:51:55,000
something is vibrating in there.
That is exactly what is

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00:51:55,000 --> 00:51:57,000
happening.
Oops, the tire is locked.

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00:51:57,000 --> 00:52:01,000
Release the brakes.
The wheel is turning.

717
00:52:01,000 --> 00:52:03,000
Jam the brakes on.
That is exactly what is

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00:52:03,000 --> 00:52:05,000
happening.
The same way as out there,

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00:52:05,000 --> 00:52:08,000
you notice that oops,
the output is going up,

720
00:52:08,000 --> 00:52:10,000
pull it down,
oops, it's going down,

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00:52:10,000 --> 00:52:12,000
pull it up.
So, there is constant negative

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00:52:12,000 --> 00:52:15,000
feedback that is keeping the
output stable.

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00:52:15,000 --> 00:52:18,000
A very important concept.
And I will ask your recitation

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instructors to cover the very
simple method that is on page 9.