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All right.
Good morning.

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Good morning.
So, we have some fun stuff for

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today's lecture,
and as far as the final is

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concerned and so on,
I'd like you to forget about

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anything we do today,
absolutely.

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So, get your mind to become a
blank, and forget anything you

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hear in today's lecture.
So, what I'm going to show you

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today will hopefully completely
blow your minds.

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And I'm not talking about
controlled substances or

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anything.
So what I'm going to do is show

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you a few things that behave
completely and spectacularly

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differently than how you expect
them to.

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And, today's lecture is
appropriately called --

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OK.
So, we're going to violate the

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abstraction barrier here,
and do some fun things.

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And, the important thing to
realize is that in all of 6.002,

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we have, after all,
based on some assumptions we

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made at the beginning of the
course like lumped matter

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discipline and so on,
we have landed ourselves in

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this playground called the
playground of 6.002.

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And, within that playground,
certain ground rules apply.

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OK, and our entire course
depended on those assumptions

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being true.
So, for example,

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the first assumption we made
that brought us from Maxwell's

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equations to the lumped matter
discipline was,

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or rather the circuit
abstraction, was a lumped matter

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discipline.
And there were three tenets of

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the lumped matter discipline.
One is that the rate of change

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of flux was going to be zero
within our circuits,

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not inside elements,
but in the circuit itself,

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and second, the dq by dt was
going to be zero outside the

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elements, and third,
something we did not dwell upon

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in the course,
but it's certainly present in

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the course notes is that the
speeds of signals that we are

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going to consider are going to
be much slower than the speed of

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light.
OK, so we're going to be

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working in a realm where we are
going to be well slower than the

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speed of light.
OK, so starting with that,

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let me walk you through some
examples and some fun stuff.

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So, the first case is called
the Double Take.

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So, let me sketch out a small
little circuit for you,

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and take a look at the expected
behavior, and then show you what

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really happens in real life.
So, the first case,

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I have a voltage source,
and what I'm going to do is

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make a transition from a zero to
a one.

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Think of it as a step input,
and through a Thevenin like

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resistance, I want to feed it to
a circuit.

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The circuit will go to an
inverter.

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This node goes to an inverter,
and goes through some other

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circuits within our own design
here.

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So, again, remember,
a step input here,

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and this input goes through a
Thevenin like resistance,

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or is applied to some other
circuit elements.

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So, if I apply a step here,
what do you expect?

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You expect that,
so let me call that VI,

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and let me call that Vo.
So, if I plot VI as a function

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of time, and let's say this step
input happens at t=0.

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So let's say this is t=0 here,
and let's say this is a 5V

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step.
So, I expect that this input

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here is going to go to,
VI here, is going to go to 5V

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at t=0.
What do I expect at Vo?

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At Vo, based on our circuit
abstraction, I get a step input

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here.
I should get a step of some

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magnitude here,
depending on what's connected

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in this direction.
And let's simply say that

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what's connected here is an
inverter, and maybe other

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inverters at the other side.
So essentially,

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as far as this node is
concerned, it's got some wires

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connected to it.
And at the end of the wires,

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it has an open circuit,
an open circuit,

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for example,
like the gate input of this

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inverter.
So what do you expect at V

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nought?
A step input here,

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and at V nought I see an open
circuit.

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OK, so I expect the same step
at V nought: 5V.

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So, that's what we've prepared
you for, OK?

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But, the fun thing that we're
going to see,

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so this is what you expect,
and I'll show you a little demo

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that is going to show you
something very different.

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What you're going to see is not
this.

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OK, you're not going to be
seeing that.

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Rather, I'm going to show you
something that looks like this.

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So, at t=0, I do see Vo looking
like a step, and approximately

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halfway through,
decides, ah,

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well never mind,
and flattens out,

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OK, then says,
oh, OK, and zoom,

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it goes back up to 5V.
So, it sort of does a bit of a

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double take up there saying,
hey, what's going on here?

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And zoom, jumps up to 5V,
and then it's five as you

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expect.
OK, so this is some finite

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amount of time that looks like
that.

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OK, so try to understand what's
going on.

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So let me show you a quick
little demo.

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So that's the input VI.
OK, so that's the input VI that

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you expect, and I won't do
anything to my circuit at this

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point.
And, go ahead.

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So, let's see what happens now.
There you go.

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So now, I'm showing you the
output here at Vo.

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So at VI, there's a nice little
step, and at Vo,

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notice that I get something
that behaves like this.

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OK, and I promise you,
nothing we've taught you in

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6.002 prepares you for this.
OK, and as I mentioned at the

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beginning of this lecture,
it would behoove you to forget

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about everything you learn in
today's lecture for the next two

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weeks at least.
So what's going on here?

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Any ideas?
Anybody?

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Any thoughts?
So what's up with my circuit

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here?
It says, oh,

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OK, a step.
It starts off and says,

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oh, never mind,
and then meanders along at 2.5V

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and then says oh,
step, yes, I remember,

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and then boom,
it jumps up to 5V.

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So, any theories?
Any guesses?

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Any wild guesses?
OK, so let me draw you a little

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bit more of a detailed circuit,
and see if you can explain

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what's going on here.
So, the circuit that I've drawn

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there is not quite the circuit I
have at least in terms of my

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wires.
So, what I have is something

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that looks like this,
VI, and this is going to step

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to 5V.
I do have a resistance,

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R.
This is Vo, this does go to an

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inverter.
But what is also happening is

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that I have a long wire.
OK, you see this guy here?

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We had one of our union folks
stretch out along the floor

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here.
We have a really long wire that

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connects to the Vo node,
and there's also a long

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corresponding ground.
So, this wire is a coaxial

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cable that is used for Ethernet
and such like.

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It's got a core that carries a
signal, and around the core is

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shielding that is the ground.
OK, so that goes a long way,

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and at the end,
it is open.

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OK, it's an open circuit at the
end.

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I haven't connected anything
out there: open circuit.

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So, you know,
something's happening here

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that's making the circuit behave
like this.

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So, this is VI.
At Vo --

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So at Vo I'm getting this funny
behavior.

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OK, so does anybody want to
take the next piece of clues

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here, does anybody want to take
a stab at guessing what might be

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going on here?
Yes?

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Ah, we have a shill in the
audience here.

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So, the theory is that the step
here, think of it as an

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electromagnetic pulse that goes
from zero to five,

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and things in real life don't
travel instantaneously.

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So, there's something with a
wave that flies down,

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and the wave goes to the end,
flips, and then comes back,

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and then establishes the full
voltage here.

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So that is indeed at the root
of what's going on.

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And let me put it in layman's
terms and then describe the

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details of what's going on here.
OK, so the way to view what's

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going on is that I have this
long wire.

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OK, in the very first lecture,
I started off by saying wires

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are ideal.
OK, ideal wires are such that I

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can transmit signals on them.
Wires are small so that the

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propagation time of signals is
inconsequential compared to the

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rise times and fall times of the
signals of interest.

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By having this really long
cable here, I have clearly

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violated that assumption,
which is the wires are really,

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really long here.
OK, and so I somehow need to

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model what the wire is doing to
my circuit when I don't have a

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small wire.
So what actually happens,

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the way to view it is the
following.

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So, although this is a wire,
to understand the mechanics of

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what's going on,
I really have to model it much

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more accurately,
OK?

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And, the way to model a wire
like this is that notice that

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every small element of a wire
has associated with it some

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inductance.
OK, so let's take a small

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segment of the coax cable here.
The coax cable is a small core

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surrounded by a metallic shield.
OK, that's a ground.

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And so, when I have a wire
surrounded by a metallic shield,

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that also has the capacitance,
OK, inductance and capacitance.

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So this small segment can be
modeled as a really small

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inductance, and a really tiny
capacitance.

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Similarly, the next segment can
be modeled as a tiny inductance

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and a capacitance.
There is also a resistance

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here, but let's assume that the
resistance is zero for our

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model, and also the parallel
resistance is also infinity.

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OK, so it's an inductor,
capacitor, and really the

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situation that I have is not a
pair of ideal wires,

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but really a really,
really small inductance,

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and a small capacitance in
parallel.

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So, it's more of a set of
distributed elements that I have

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here.
Notice that in my lump circuit

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abstraction, when we talked
about the RLC model for the wire

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between two inverters,
we lumped it.

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We lumped this thing into a
model that looked like this.

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OK, we lumped the resistance
into a source resistance.

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We lumped all the inductors
into a lumped inductor.

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We lumped all the capacitances
into a lumped capacitance.

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OK, but in this situation,
I can do this when the signal

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speeds of interest are much,
much, much slower than the

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speed of light than the
propagation speeds of

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electromagnetic signals.
In this case,

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that is not quite true.
And so, therefore,

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we have to model it much more
exactly.

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We need to see what's going on.
So, what's happening here is

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that at t=0, I get this step.
So, think of that as a pulse of

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energy, and the instant it comes
here, and instantaneously this

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guy looks like a voltage
divider, OK?

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I've chosen my resistance,
R, here to match the

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instantaneous impedance looking
in, which is also R.

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I've arranged it to be that
way.

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So, instantaneously,
the point at which the pulse

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appears at this point,
looking down here looks like

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another resistor to this pulse.
OK, therefore,

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when I start out,
I start out going up and

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pausing at 2.5 because
instantaneously,

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this looks like a resistance,
R.

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So instantaneously,
it's a voltage divider,

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R, and so it's 2.5 here,
instantaneously.

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OK, then what happens?
Then those little pulse

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propagates down.
What does it mean for a pulse

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of energy to propagate down?
Well, it begins sending a

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current through the inductor,
begins charging up the

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capacitor, current here,
so that's what I mean by saying

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that the pulse of energy goes
down.

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OK, it's a step that sends
current to the inductor and

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charges of the capacitors,
and that wave front moves out

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here and comes all the way here.
What happens there?

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Well, think about it.
Supposing you stand here,

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and you hold a long string in
your hand somehow,

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and just do this Gedanken
experiment.

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It's not easy to do.
And so, let's say you somehow

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have the long string that you're
holding onto,

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and the string on the other
side is not connected to

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anything.
OK, just imagine this

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experiment.
OK, and what you do is you

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00:16:50,000 --> 00:16:54,000
suddenly raise the string up at
your end by about a foot.

230
00:16:54,000 --> 00:16:56,000
What are you going to see
happen?

231
00:16:56,000 --> 00:16:59,000
So instantaneously,
the string is up here,

232
00:16:59,000 --> 00:17:04,000
but the rest of the string is
down a foot below.

233
00:17:04,000 --> 00:17:07,000
And then you see this wave
propagate down the string,

234
00:17:07,000 --> 00:17:09,000
right?
So here's a string.

235
00:17:09,000 --> 00:17:12,000
I lift this thing,
and you see this wave propagate

236
00:17:12,000 --> 00:17:15,000
all the way down,
the one foot wave propagate all

237
00:17:15,000 --> 00:17:17,000
the way down until you come
here.

238
00:17:17,000 --> 00:17:20,000
What happens here?
So, out here,

239
00:17:20,000 --> 00:17:23,000
the string is down here,
the wave propagates out here

240
00:17:23,000 --> 00:17:26,000
and pulls it up to one.
And then what?

241
00:17:26,000 --> 00:17:29,000
There's nothing connected
there, so the string is zipped

242
00:17:29,000 --> 00:17:34,000
up, but it's got the energy.
OK, where does energy go?

243
00:17:34,000 --> 00:17:37,000
Well, it continues going up,
and sends a wave back.

244
00:17:37,000 --> 00:17:40,000
OK, so just think of a string
that you pull up like this and

245
00:17:40,000 --> 00:17:43,000
propagates down,
boom, hits the other end,

246
00:17:43,000 --> 00:17:46,000
reverses, and comes back at me.
OK, you can look at a

247
00:17:46,000 --> 00:17:48,000
complementary situation,
not the same as this,

248
00:17:48,000 --> 00:17:51,000
but complementary by taking a
string, tying it to a door,

249
00:17:51,000 --> 00:17:54,000
and lifting it up.
It's not the same situation.

250
00:17:54,000 --> 00:17:57,000
It's a complementary situation
where it's tied down.

251
00:17:57,000 --> 00:18:00,000
Tying down a string is
tantamount to shorting the ends

252
00:18:00,000 --> 00:18:03,000
here.
OK, in that case what you'll

253
00:18:03,000 --> 00:18:07,000
see happen: as the wave goes
down, at the end the string

254
00:18:07,000 --> 00:18:11,000
can't move, so the wave goes and
flips around and comes back.

255
00:18:11,000 --> 00:18:13,000
Try it out at home.
Take a long piece of string,

256
00:18:13,000 --> 00:18:15,000
tie it up there,
do this, OK?

257
00:18:15,000 --> 00:18:19,000
And you'll see the wave go out,
flip, and then come back at

258
00:18:19,000 --> 00:18:21,000
you.
So, if your friends see you

259
00:18:21,000 --> 00:18:25,000
tying a long piece of string
doing this, hopefully they won't

260
00:18:25,000 --> 00:18:29,000
think you're nuts or something.
OK, so the same way here:

261
00:18:29,000 --> 00:18:33,000
this thing flies down,
OK, there's no way to dissipate

262
00:18:33,000 --> 00:18:35,000
the energy here,
so this thing continues up.

263
00:18:35,000 --> 00:18:39,000
And then, what I'm going to see
happen is the wave move back.

264
00:18:39,000 --> 00:18:43,000
OK, the wave begins to move
back, and that's another 2.5V,

265
00:18:43,000 --> 00:18:46,000
resulting in a net 5V at this
terminal.

266
00:18:46,000 --> 00:18:50,000
That wave begins to blast back,
OK, and then when it comes back

267
00:18:50,000 --> 00:18:53,000
here, after some amount of time,
it raises this to 5V,

268
00:18:53,000 --> 00:18:56,000
and that's what you see happen
here.

269
00:18:56,000 --> 00:18:59,000
So, this is a wave going down,
and then after a time,

270
00:18:59,000 --> 00:19:04,000
2t, it goes back up to 5V.
That's a return wave.

271
00:19:04,000 --> 00:19:07,000
It's 2t because to get down
here is t seconds,

272
00:19:07,000 --> 00:19:12,000
and then t seconds to come
back, which is why we have 2t.

273
00:19:12,000 --> 00:19:15,000
OK, that is why you see that
pulse at 2.5.

274
00:19:15,000 --> 00:19:19,000
OK, so I'd like to show you a
few more things here.

275
00:19:19,000 --> 00:19:22,000
Clearly we don't want that in
our circuits.

276
00:19:22,000 --> 00:19:27,000
Could someone tell me what
problem would happen if my

277
00:19:27,000 --> 00:19:32,000
signals looked like this in my
digital circuits?

278
00:19:32,000 --> 00:19:39,000
Instead of being nice little
steps, if there was a little

279
00:19:39,000 --> 00:19:46,000
thing in the middle and then a
step, what's the problem with

280
00:19:46,000 --> 00:19:51,000
signals like this?
In digital circuits,

281
00:19:51,000 --> 00:19:54,000
what did it violate?
Yeah?

282
00:19:54,000 --> 00:19:59,000
Exactly.
This little sucker here is

283
00:19:59,000 --> 00:20:05,000
meandering out in the forbidden
region for all of 2T.

284
00:20:05,000 --> 00:20:10,000
Can't do that.
OK, can't have that.

285
00:20:10,000 --> 00:20:17,000
Well, so we need to fix the
problem because this is real

286
00:20:17,000 --> 00:20:20,000
life.
OK, but what if you and your

287
00:20:20,000 --> 00:20:23,000
buddy were signaling each other
but using digital signals from

288
00:20:23,000 --> 00:20:24,000
one dorm room to another maybe a
few hundred feet down?

289
00:20:24,000 --> 00:20:26,000
Your circuit isn't going to
work because the signal's going

290
00:20:26,000 --> 00:20:28,000
to meander around in the
forbidden region for some time.

291
00:20:28,000 --> 00:20:29,000
So, any ideas what might you
do?

292
00:20:29,000 --> 00:20:30,000
Yeah?
Put a resistor on the end.

293
00:20:30,000 --> 00:20:32,000
OK, trick the circuit.
So, what you can do,

294
00:20:32,000 --> 00:20:33,000
and I'm going to show you a
little demo here,

295
00:20:33,000 --> 00:20:35,000
what you can do is the reason I
got this wave propagating back,

296
00:20:35,000 --> 00:20:38,000
was that there was nothing to
absorb the energy.

297
00:20:38,000 --> 00:20:41,000
So instead, what if I put
another resistor here,

298
00:20:41,000 --> 00:20:44,000
R?
So, as far as a burst of energy

299
00:20:44,000 --> 00:20:46,000
is concerned,
it says, oh,

300
00:20:46,000 --> 00:20:50,000
yeah, it just looks the same.
It's R, and goes and dissipates

301
00:20:50,000 --> 00:20:53,000
in this resistor,
R, and guess what?

302
00:20:53,000 --> 00:20:56,000
I don't have any wave going
back, and I'm done.

303
00:20:56,000 --> 00:21:00,000
So, what I'm going to find,
then, is that out here,

304
00:21:00,000 --> 00:21:03,000
this goes up to 5V,
but out here,

305
00:21:03,000 --> 00:21:07,000
I will have a signal that
starts out and goes up to 2.5,

306
00:21:07,000 --> 00:21:11,000
and that's it.
OK, I lift it up,

307
00:21:11,000 --> 00:21:14,000
it goes down,
it goes to 2.5 because in the

308
00:21:14,000 --> 00:21:17,000
lumped model that you've been
dealing with,

309
00:21:17,000 --> 00:21:20,000
it's a resistor R,
a resistor R to ground,

310
00:21:20,000 --> 00:21:23,000
and you're taking the
connection here or here.

311
00:21:23,000 --> 00:21:27,000
So, it's your standard lumped
model, your voltage resistive

312
00:21:27,000 --> 00:21:29,000
divider, and it just simply
works.

313
00:21:29,000 --> 00:21:34,000
Yeah, that's it.
So, this is the end of the

314
00:21:34,000 --> 00:21:37,000
cable.
OK, if somehow you could watch

315
00:21:37,000 --> 00:21:43,000
this and that at the same time,
so what I'm going to do,

316
00:21:43,000 --> 00:21:47,000
and this is a resistor,
R, I'm just going to plug it

317
00:21:47,000 --> 00:21:51,000
in.
OK, if the fates are smiling at

318
00:21:51,000 --> 00:21:56,000
me, what should you see there?
What should happen is that the

319
00:21:56,000 --> 00:22:01,000
second jump from 2.5 to 5 should
simply go away.

320
00:22:01,000 --> 00:22:06,000
It should just go to 2.5.
Let's try that.

321
00:22:06,000 --> 00:22:10,000
There you go.
I take it out,

322
00:22:10,000 --> 00:22:16,000
it jumps back up.
OK, so all I've done here is

323
00:22:16,000 --> 00:22:24,000
put in a resistor at the end,
and I'm still measuring the

324
00:22:24,000 --> 00:22:30,000
voltage here.
So, that's one solution.

325
00:22:30,000 --> 00:22:32,000
One solution is to put a
resistor here.

326
00:22:32,000 --> 00:22:36,000
So, I absorb the energy,
and the resistance has to be

327
00:22:36,000 --> 00:22:39,000
equal to the instantaneous
impedance looking in.

328
00:22:39,000 --> 00:22:42,000
And the instantaneous
impedance, for many of these

329
00:22:42,000 --> 00:22:45,000
cables is 50 ohms.
It's called a characteristic

330
00:22:45,000 --> 00:22:47,000
impedance.
OK, you'll learn a lot more

331
00:22:47,000 --> 00:22:51,000
about it if you take 6.014.
That course starts out with

332
00:22:51,000 --> 00:22:56,000
assuming that things are
distributed in that matter.

333
00:22:56,000 --> 00:22:59,000
OK, so if you want to design
multi-gigahertz chips,

334
00:22:59,000 --> 00:23:04,000
it turns out that if you have
signals that are traveling

335
00:23:04,000 --> 00:23:08,000
around at edge speeds in the
0.1-1 nanosecond range,

336
00:23:08,000 --> 00:23:12,000
remember, light travels roughly
one nanosecond a foot.

337
00:23:12,000 --> 00:23:16,000
And if the signals are roughly
of interest are 0.1 nanoseconds,

338
00:23:16,000 --> 00:23:20,000
then if the chips are one inch
in size, right there,

339
00:23:20,000 --> 00:23:24,000
the propagation speed of a
signal across a chip is 0.1

340
00:23:24,000 --> 00:23:26,000
nanoseconds.
OK, so today,

341
00:23:26,000 --> 00:23:30,000
we have to deal with these
issues and try to figure out

342
00:23:30,000 --> 00:23:36,000
what to do about them.
OK, so that's one solution that

343
00:23:36,000 --> 00:23:40,000
somebody pointed out.
There is a second solution.

344
00:23:40,000 --> 00:23:43,000
Anybody else have a second
solution for me?

345
00:23:43,000 --> 00:23:46,000
And then there's a third
solution, too.

346
00:23:46,000 --> 00:23:49,000
So it's OK.
You can give me either the

347
00:23:49,000 --> 00:23:53,000
second or the third solution.
It doesn't matter.

348
00:23:53,000 --> 00:23:56,000
Anybody?
You have two to choose from,

349
00:23:56,000 --> 00:23:57,000
come on.
Yeah?

350
00:23:57,000 --> 00:24:00,000
You can do that,
yeah.

351
00:24:00,000 --> 00:24:05,000
So we could define the problem
away by saying this transition

352
00:24:05,000 --> 00:00:02,500
is such that my high is below

353
00:24:07,000 --> 00:24:12,000
So, once it goes above 2.5,
who cares what it does?

354
00:24:12,000 --> 00:24:16,000
That's a good point.
That's solution number four,

355
00:24:16,000 --> 00:24:19,000
and that works.
OK, so I still need two and

356
00:24:19,000 --> 00:24:21,000
three.
Put a diode in there?

357
00:24:21,000 --> 00:24:26,000
Yeah, I guess you could.
If the diode had the same kind

358
00:24:26,000 --> 00:24:30,000
of impedance looking in,
it kind of may work.

359
00:24:30,000 --> 00:24:34,000
That's solution 4.2.
I'm still waiting for solution

360
00:24:34,000 --> 00:24:37,000
two and three.
Pardon?

361
00:24:37,000 --> 00:24:40,000
Cut off the cable?
Exactly.

362
00:24:40,000 --> 00:24:45,000
So, the solution says,
work on a different problem.

363
00:24:45,000 --> 00:24:49,000
And that is solution number
two.

364
00:24:49,000 --> 00:24:53,000
OK, so the idea is,
the root of all evil,

365
00:24:53,000 --> 00:24:58,000
this long wire,
which is why I had this thing

366
00:24:58,000 --> 00:25:02,000
here.
So instead, if I had short

367
00:25:02,000 --> 00:25:07,000
wires, then what will happen is
if it's a very small wire,

368
00:25:07,000 --> 00:25:12,000
it'll look like this.
And the wire's small enough.

369
00:25:12,000 --> 00:25:16,000
I will see an itty-bitty
thingamajig out there,

370
00:25:16,000 --> 00:25:20,000
but not a whole lot.
By the way, the fun thing is

371
00:25:20,000 --> 00:25:25,000
that you can actually calculate
the speed of light,

372
00:25:25,000 --> 00:25:28,000
the experiment I just showed
you.

373
00:25:28,000 --> 00:25:33,000
Can we put that up again?
No, the big one.

374
00:25:33,000 --> 00:25:37,000
So, in the experiment that I
showed you, this distance was

375
00:25:37,000 --> 00:25:39,000
about 500 nanoseconds,
OK?

376
00:25:39,000 --> 00:25:42,000
This distance was 500
nanoseconds this time interval.

377
00:25:42,000 --> 00:25:46,000
The length of this cable is
about 500 feet,

378
00:25:46,000 --> 00:25:50,000
somewhere around 500 feet.
So you can figure out the speed

379
00:25:50,000 --> 00:25:52,000
of light.
What's the speed of light?

380
00:25:52,000 --> 00:25:56,000
So, this is about 500
nanoseconds, and this cable is

381
00:25:56,000 --> 00:26:01,000
roughly 500 feet.
What's the speed of light?

382
00:26:01,000 --> 00:26:04,000
Roughly a foot per nanosecond.
So, would you believe that in

383
00:26:04,000 --> 00:26:08,000
6.002 we've figured out the
speed of light from a simple

384
00:26:08,000 --> 00:26:11,000
experiment?
All right, so let's do the next

385
00:26:11,000 --> 00:26:14,000
experiment now.
Let's take out the long cable,

386
00:26:14,000 --> 00:26:16,000
and connect a short cable
instead.

387
00:26:16,000 --> 00:26:20,000
So, what I'm going to do is
disconnect the long cable,

388
00:26:20,000 --> 00:26:22,000
and instead,
connect a small cable.

389
00:26:22,000 --> 00:26:26,000
It's still relatively long,
but much shorter than the 500

390
00:26:26,000 --> 00:26:28,000
foot cable.
So what you should see happen

391
00:26:28,000 --> 00:26:32,000
now is that the little step
should not be this big,

392
00:26:32,000 --> 00:26:37,000
but much, much smaller.
So, take a look up there.

393
00:26:37,000 --> 00:26:40,000
There you go.
OK, so with this thingamajig,

394
00:26:40,000 --> 00:26:43,000
the little blip there is very
small.

395
00:26:43,000 --> 00:26:47,000
And of course,
if I make it even smaller,

396
00:26:47,000 --> 00:26:52,000
then that can virtually vanish.
OK, so that is solution number

397
00:26:52,000 --> 00:26:54,000
two.
So, we've done one,

398
00:26:54,000 --> 00:26:58,000
two, four, 4.2.
So, what's solution number

399
00:26:58,000 --> 00:27:01,000
three?
One more solution.

400
00:27:01,000 --> 00:27:04,000
Pardon?
So, another solution we

401
00:27:04,000 --> 00:27:08,000
mentioned is we change this
resistance.

402
00:27:08,000 --> 00:27:11,000
and that will work,
if I make this very,

403
00:27:11,000 --> 00:27:16,000
very low, then I'll get much
closer to 5V here.

404
00:27:16,000 --> 00:27:21,000
Yeah, that's a possibility.
That's solution six I guess.

405
00:27:21,000 --> 00:27:24,000
So what was solution number
three?

406
00:27:24,000 --> 00:27:30,000
And you all should be able to
solve this.

407
00:27:30,000 --> 00:27:34,000
You guys know the answer.
OK, you folks should be able to

408
00:27:34,000 --> 00:27:35,000
solve this.
Yes?

409
00:27:35,000 --> 00:27:38,000
Ah, clock.
So, what I can do is just as

410
00:27:38,000 --> 00:27:42,000
was pointed out,
that I leveraged my abstraction

411
00:27:42,000 --> 00:27:45,000
by changing my VOH and VIH
thresholds.

412
00:27:45,000 --> 00:27:49,000
So that'll work.
The alternative thing is to use

413
00:27:49,000 --> 00:27:52,000
a clock.
A clock is a distinguished

414
00:27:52,000 --> 00:27:56,000
signal that I send around in my
digital circuit,

415
00:27:56,000 --> 00:28:00,000
OK?
So all I do is if I arrange it

416
00:28:00,000 --> 00:28:04,000
such that my clock doesn't
happen in this vicinity,

417
00:28:04,000 --> 00:28:10,000
but rather, my clock happens
late enough, then I'm going to

418
00:28:10,000 --> 00:28:15,000
sample and look at my signals
only on the rising and falling

419
00:28:15,000 --> 00:28:18,000
edges of the clock,
in which case I won't be

420
00:28:18,000 --> 00:28:23,000
looking at the signal,
but the signal is doing weird

421
00:28:23,000 --> 00:28:26,000
things.
OK, so a decent clock would

422
00:28:26,000 --> 00:28:30,000
also solve the problem.
OK, any last minute questions

423
00:28:30,000 --> 00:28:40,000
before we go onto the next one?
OK, the next problem that we're

424
00:28:40,000 --> 00:28:47,000
going to look at is titled the
Double Dip.

425
00:28:47,000 --> 00:28:56,000
OK, so what I'm going to do
here is our Vs power supply,

426
00:28:56,000 --> 00:29:06,000
and what I'm going to do is
feed the power supply to an

427
00:29:06,000 --> 00:29:12,000
inverter.
OK, so we've been doing this

428
00:29:12,000 --> 00:29:16,000
all along; Vs,
I feed the supply to an

429
00:29:16,000 --> 00:29:20,000
inverter.
And what I'm also going to do

430
00:29:20,000 --> 00:29:26,000
is, so this is ground,
and I'm going to feed it to,

431
00:29:26,000 --> 00:29:31,000
so feed the power supply
connection to a couple of

432
00:29:31,000 --> 00:29:39,000
inverters.
OK, and what I'm going to do is

433
00:29:39,000 --> 00:29:47,000
apply some sort of a signal to
this inverter,

434
00:29:47,000 --> 00:29:57,000
and I'm going to observe,
and I'm going to look at this

435
00:29:57,000 --> 00:30:03,000
signal here.
So, the abstraction should tell

436
00:30:03,000 --> 00:30:07,000
you that here's a power supply.
This is 5V, or whatever the

437
00:30:07,000 --> 00:30:10,000
supply voltage is to these two
inverters.

438
00:30:10,000 --> 00:30:14,000
That should be fine,
and feed some sort of input to

439
00:30:14,000 --> 00:30:18,000
this inverter,
OK, and the output here should

440
00:30:18,000 --> 00:30:20,000
be simply determined by this
input.

441
00:30:20,000 --> 00:30:25,000
This signal can have absolutely
no bearing on this output.

442
00:30:25,000 --> 00:30:30,000
OK, and let's look at that and
actually confirm it.

443
00:30:30,000 --> 00:30:35,000
So, I build a circuit like
this, and we look at this

444
00:30:35,000 --> 00:30:40,000
output, and initially there
should not be any,

445
00:30:40,000 --> 00:30:46,000
it should simply work fine.
OK, so it should work now,

446
00:30:46,000 --> 00:30:47,000
right?
OK.

447
00:30:47,000 --> 00:30:53,000
So what you have here,
this input here is the input

448
00:30:53,000 --> 00:30:56,000
that I'm feeding to this
inverter.

449
00:30:56,000 --> 00:31:02,000
That is a straight line.
Is that the power supply?

450
00:31:02,000 --> 00:31:06,000
It doesn't matter?
OK, so I believe this is the,

451
00:31:06,000 --> 00:31:10,000
we'll check in a few minutes,
but I suspect this is the power

452
00:31:10,000 --> 00:31:14,000
supply, and this guy here is the
output looking here.

453
00:31:14,000 --> 00:31:17,000
So, the green one is the look
here part.

454
00:31:17,000 --> 00:31:21,000
So, there must have been a
one-to-zero transition here,

455
00:31:21,000 --> 00:31:24,000
and that's all fine.
So, so far, so good.

456
00:31:24,000 --> 00:31:28,000
OK, no problem so far.
Now what I'm going to do is I'm

457
00:31:28,000 --> 00:31:32,000
going to do something to the
circuit that as far as

458
00:31:32,000 --> 00:31:35,000
abstraction is concerned,
it doesn't show up on the

459
00:31:35,000 --> 00:31:41,000
circuit.
OK, it's below the abstraction

460
00:31:41,000 --> 00:31:45,000
layer.
OK, I'm going to do something,

461
00:31:45,000 --> 00:31:48,000
and suddenly,
some things are going to

462
00:31:48,000 --> 00:31:51,000
happen.
Look up there.

463
00:31:51,000 --> 00:31:56,000
The circuit hasn't changed.
It's the same circuit.

464
00:31:56,000 --> 00:31:59,000
I've done nothing to the
circuit.

465
00:31:59,000 --> 00:32:05,000
OK, look at the green output.
I've done nothing to the

466
00:32:05,000 --> 00:32:09,000
circuit that is visible here.
OK, it's below the radar screen

467
00:32:09,000 --> 00:32:11,000
here.
It's below the abstraction

468
00:32:11,000 --> 00:32:14,000
barrier.
But, look at the disaster here.

469
00:32:14,000 --> 00:32:17,000
OK, in particular,
the spikes going up are not so

470
00:32:17,000 --> 00:32:20,000
much of a problem.
Because of the static

471
00:32:20,000 --> 00:32:23,000
discipline, if I am at five or
six or seven,

472
00:32:23,000 --> 00:32:27,000
it doesn't matter as long as I
am higher than VOH.

473
00:32:27,000 --> 00:32:32,000
So as long as I'm higher than
VOH I don't have a problem.

474
00:32:32,000 --> 00:32:34,000
But the problems are these
repeated dips.

475
00:32:34,000 --> 00:32:38,000
OK, the dips are a problem
here, which is why I labeled

476
00:32:38,000 --> 00:32:42,000
this experiment the Double Dip.
OK, the dips are bad because if

477
00:32:42,000 --> 00:32:46,000
they are large enough,
they can then group the output

478
00:32:46,000 --> 00:32:49,000
down into the forbidden region,
or worse yet,

479
00:32:49,000 --> 00:32:53,000
make it look like a zero.
OK, so you're not prepared for

480
00:32:53,000 --> 00:32:55,000
this.
So what I'm going to do is tell

481
00:32:55,000 --> 00:32:59,000
you what I did to the circuit,
and then ask you to help me

482
00:32:59,000 --> 00:33:08,000
figure it out.
So all I did was applied a load

483
00:33:08,000 --> 00:33:17,000
resistance to this,
I think of 50 ohms or some RL.

484
00:33:17,000 --> 00:33:28,000
I just applied a load resistor.
And this inverter here,

485
00:33:28,000 --> 00:33:38,000
I believe, is a CMOS inverter
that looks, OK?

486
00:33:38,000 --> 00:33:41,000
So I have this input applied to
this inverter,

487
00:33:41,000 --> 00:33:43,000
and all I did is I applied an
RL load here.

488
00:33:43,000 --> 00:33:48,000
And notice that the load here
should not really change what's

489
00:33:48,000 --> 00:33:50,000
happening if this is an ideal
inverter, OK,

490
00:33:50,000 --> 00:33:54,000
the load here should simply
draw some current but really

491
00:33:54,000 --> 00:33:58,000
should not change any other
property.

492
00:33:58,000 --> 00:34:02,000
OK, so just remember,
what's the signal doing?

493
00:34:02,000 --> 00:34:05,000
The signal is high.
This guy turns on,

494
00:34:05,000 --> 00:34:10,000
and current flows like this.
So, let's say I had some sort

495
00:34:10,000 --> 00:34:14,000
of a capacitor here.
This charges like this,

496
00:34:14,000 --> 00:34:17,000
and when it's slow,
the PFET is on,

497
00:34:17,000 --> 00:34:20,000
and current flows through here
down here.

498
00:34:20,000 --> 00:34:25,000
And then when this goes high,
this guy goes off,

499
00:34:25,000 --> 00:34:29,000
and this guy turns on.
OK, so the current flows out

500
00:34:29,000 --> 00:34:35,000
this way and this charges
through this guy.

501
00:34:35,000 --> 00:34:39,000
When I turn it off,
the P fret turns on and draws

502
00:34:39,000 --> 00:34:44,000
current from the top.
OK, so do we have any theories

503
00:34:44,000 --> 00:34:50,000
as to why I'm getting that messy
stuff, the dips and the spikes,

504
00:34:50,000 --> 00:34:56,000
on the output of this inverter?
So why does this inverter care

505
00:34:56,000 --> 00:34:59,000
what the load of this inverter
is?

506
00:34:59,000 --> 00:35:04,000
I mean, who cares?
So, put your thinking caps on.

507
00:35:04,000 --> 00:35:08,000
Any theories?
You guys did pretty well with

508
00:35:08,000 --> 00:35:11,000
the previous one.
And this is much easier,

509
00:35:11,000 --> 00:35:15,000
actually.
Need a better power supply;

510
00:35:15,000 --> 00:35:20,000
OK, so what I'm going to do is
I'm going to replace the power

511
00:35:20,000 --> 00:35:24,000
supply, and instead,
use a much bigger power supply

512
00:35:24,000 --> 00:35:28,000
at 5V.
A big, mongo power supply that

513
00:35:28,000 --> 00:35:31,000
can supply 100 amps,
and guess what,

514
00:35:31,000 --> 00:35:34,000
I've made the changes,
but guess what,

515
00:35:34,000 --> 00:35:41,000
I still see the spikes.
Good try, but it didn't work

516
00:35:41,000 --> 00:35:43,000
out.
Good try, good try.

517
00:35:43,000 --> 00:35:46,000
What next?
Any other solutions?

518
00:35:46,000 --> 00:35:50,000
Yes?
So dips are because of the

519
00:35:50,000 --> 00:35:56,000
resistance, and the spikes are
because of the inductance?

520
00:35:56,000 --> 00:36:02,000
You're half correct.
So, which one is it?

521
00:36:02,000 --> 00:36:07,000
So, dips are because of
resistances, and spikes are

522
00:36:07,000 --> 00:36:11,000
because of inductances.
You're half correct.

523
00:36:11,000 --> 00:36:17,000
It turns out that both the dips
and the spikes are because of

524
00:36:17,000 --> 00:36:21,000
inductances.
OK, but be that as it may,

525
00:36:21,000 --> 00:36:27,000
let me give you the next clue
here, and then see if you can

526
00:36:27,000 --> 00:36:33,000
come closer to the answer.
So, what I've done here is I've

527
00:36:33,000 --> 00:36:38,000
made this wire really,
really long.

528
00:36:38,000 --> 00:36:41,000
OK, it's a really long wire,
OK, but it's a thick wire,

529
00:36:41,000 --> 00:36:44,000
so it's a long,
long, thick wire.

530
00:36:44,000 --> 00:36:46,000
So it's not the resistance.
It's really,

531
00:36:46,000 --> 00:36:50,000
really thick and mongo,
and it's a long wire,

532
00:36:50,000 --> 00:36:54,000
so a signal wire above a ground
plane behaves like an inductor.

533
00:36:54,000 --> 00:36:57,000
And so here,
it has the capacitance to,

534
00:36:57,000 --> 00:36:59,000
but in this case it's
inductance.

535
00:36:59,000 --> 00:37:04,000
It's inductance here.
So, I'll give you another ten

536
00:37:04,000 --> 00:37:10,000
seconds to think about it and
then tell you the answer.

537
00:37:10,000 --> 00:37:15,000
But despite the inductance
here, it turns out if I take out

538
00:37:15,000 --> 00:37:19,000
this resistor,
the problem goes away.

539
00:37:19,000 --> 00:37:24,000
Look, I take out the resistor,
the problem goes away.

540
00:37:24,000 --> 00:37:34,000
Yes, there is an inductor here.
OK, I take out this resistor,

541
00:37:34,000 --> 00:37:44,000
problem goes away.
I put the resistor back in,

542
00:37:44,000 --> 00:37:46,000
boom.
Yes?

543
00:37:46,000 --> 00:37:54,000
OK, pretty good.
That's 86 points.

544
00:37:54,000 --> 00:38:03,000
So here's what's going on.
There's an inductor here,

545
00:38:03,000 --> 00:38:06,000
and when I put a 50 ohm
resistor here,

546
00:38:06,000 --> 00:38:10,000
I put this resistor.
When the PFET turns on,

547
00:38:10,000 --> 00:38:13,000
it draws a current.
OK, it's going to draw a

548
00:38:13,000 --> 00:38:15,000
current.
It draws a current;

549
00:38:15,000 --> 00:38:19,000
remember that across an
inductor, I have a drop.

550
00:38:19,000 --> 00:38:22,000
And the drop relates to the
di/dt.

551
00:38:22,000 --> 00:38:26,000
Remember, for a capacitor,
the current is Cdv/dt.

552
00:38:26,000 --> 00:38:29,000
For the inductor,
the voltage across the inductor

553
00:38:29,000 --> 00:38:33,000
is Ldi/dt.
So, if di/dt,

554
00:38:33,000 --> 00:38:37,000
from switching a large current
through the inductor every

555
00:38:37,000 --> 00:38:40,000
cycle, OK, big di/dt,
di/dt is large.

556
00:38:40,000 --> 00:38:44,000
I've made it large by having a
very small RL,

557
00:38:44,000 --> 00:38:47,000
so, you know,
pulling a big current through

558
00:38:47,000 --> 00:38:50,000
every few, whatever,
every cycle,

559
00:38:50,000 --> 00:38:53,000
and then stopping it.
And so therefore,

560
00:38:53,000 --> 00:38:58,000
I'm getting these big drops
across this inductor that relate

561
00:38:58,000 --> 00:39:00,000
to Ldi/dt.
In other words,

562
00:39:00,000 --> 00:39:05,000
the power supply here is fine.
While you guys were watching,

563
00:39:05,000 --> 00:39:08,000
I switched to the huge,
mongo power supply,

564
00:39:08,000 --> 00:39:12,000
and so this voltage is fine.
But then this voltage after the

565
00:39:12,000 --> 00:39:16,000
wire is the problem.
So, this voltage here doesn't

566
00:39:16,000 --> 00:39:19,000
look like this anymore.
Rather, it has spikes that go

567
00:39:19,000 --> 00:39:22,000
down, for example,
and when I switch the other

568
00:39:22,000 --> 00:39:24,000
way, they go up.
OK, so therefore,

569
00:39:24,000 --> 00:39:30,000
what I end up having here is
big spikes on this power supply.

570
00:39:30,000 --> 00:39:33,000
And when this guy's power
supply goes wacko,

571
00:39:33,000 --> 00:39:37,000
then I see the spikes on its
output as well.

572
00:39:37,000 --> 00:39:40,000
OK, so what are the solutions
for that?

573
00:39:40,000 --> 00:39:43,000
Any solutions here?
What can I do to fix the

574
00:39:43,000 --> 00:39:45,000
problem?
Pardon?

575
00:39:45,000 --> 00:39:46,000
Stop using the,
exactly.

576
00:39:46,000 --> 00:39:49,000
When in doubt,
do something else.

577
00:39:49,000 --> 00:39:54,000
Build a different design.
So what I could do is this is

578
00:39:54,000 --> 00:39:59,000
pretty dumb, using a long wire.
And so, no, but trust me,

579
00:39:59,000 --> 00:40:04,000
oftentimes you go to the store
room and they give you a big

580
00:40:04,000 --> 00:40:07,000
roll of wire,
and you're too lazy to cut a

581
00:40:07,000 --> 00:40:10,000
piece out.
Use the whole roll,

582
00:40:10,000 --> 00:40:13,000
and use the two ends,
and connect it in,

583
00:40:13,000 --> 00:40:15,000
OK?
So, if I had a much shorter

584
00:40:15,000 --> 00:40:18,000
piece of wire,
then that can solve my problem.

585
00:40:18,000 --> 00:40:22,000
But again, remember,
what's small to you may not be

586
00:40:22,000 --> 00:40:25,000
small to the circuit.
OK, so let's say,

587
00:40:25,000 --> 00:40:29,000
for example,
I'm Intel, and I'm building a

588
00:40:29,000 --> 00:40:33,000
10 GHz Pentium 6 processor.
OK, it's 0.1 nanosecond is my

589
00:40:33,000 --> 00:40:37,000
cycle time.
There, even a small,

590
00:40:37,000 --> 00:40:40,000
itty bitty wire can be a real
problem.

591
00:40:40,000 --> 00:40:44,000
OK, and so therefore,
distributing power throughout a

592
00:40:44,000 --> 00:40:47,000
one inch chip that's clocking at
10 GHz is a really,

593
00:40:47,000 --> 00:40:51,000
really hard problem.
And our own David Perreault,

594
00:40:51,000 --> 00:40:55,000
who is doing one of our
sections, is one of the world's

595
00:40:55,000 --> 00:40:58,000
experts in this field.
Distributing power,

596
00:40:58,000 --> 00:41:02,000
something as simple as,
how do I get 1V in a stable

597
00:41:02,000 --> 00:41:05,000
manner to every single device on
my chip?

598
00:41:05,000 --> 00:41:10,000
It's a hard problem.
OK, so now, you have to begin

599
00:41:10,000 --> 00:41:15,000
feeding your power supply
connections much like RC

600
00:41:15,000 --> 00:41:19,000
circuits, OK,
and you have to solve some hard

601
00:41:19,000 --> 00:41:25,000
problems to be able to simply
distribute power decently

602
00:41:25,000 --> 00:41:29,000
throughout your circuit.
So, what else can I do?

603
00:41:29,000 --> 00:41:32,000
Yeah?
Say it again?

604
00:41:32,000 --> 00:41:35,000
Ah, I can do that.
I could use different wires to

605
00:41:35,000 --> 00:41:39,000
connect each of the inverters.
That's a good point.

606
00:41:39,000 --> 00:41:44,000
So here, the coupling happens
because I connect the two

607
00:41:44,000 --> 00:41:48,000
inverters way out here.
So instead, I use a different

608
00:41:48,000 --> 00:41:50,000
cable.
I hadn't thought of that.

609
00:41:50,000 --> 00:41:54,000
That's a creative solution.
OK, so in fact,

610
00:41:54,000 --> 00:41:57,000
if you build a chip,
so we built this chip called

611
00:41:57,000 --> 00:42:01,000
RAW in our group,
and it has on the order of 10

612
00:42:01,000 --> 00:42:06,000
million gates.
And this chip we built with

613
00:42:06,000 --> 00:42:09,000
IBM's technology,
and it turns out that you don't

614
00:42:09,000 --> 00:42:14,000
send power supply in through a
pin and then connect that 1.5V

615
00:42:14,000 --> 00:42:18,000
supply to all your gates.
What you do is from that pin,

616
00:42:18,000 --> 00:42:22,000
you then build special power
supply buffering trees.

617
00:42:22,000 --> 00:42:25,000
And each tree,
each leaf of the tree drives a

618
00:42:25,000 --> 00:42:27,000
subcircuit.
In other words,

619
00:42:27,000 --> 00:42:31,000
if this is a chip,
you have lots and lots of gates

620
00:42:31,000 --> 00:42:36,000
throughout your chip.
What you do not do is bring in

621
00:42:36,000 --> 00:42:40,000
a power supply like this,
and then connect.

622
00:42:40,000 --> 00:42:45,000
You don't do that.
That's the worst possible thing

623
00:42:45,000 --> 00:42:49,000
you can do.
It's an absolute disaster for

624
00:42:49,000 --> 00:42:55,000
the reason just brought up.
OK, so instead what you do is

625
00:42:55,000 --> 00:42:59,000
divide up the chip into,
say, four quadrants.

626
00:42:59,000 --> 00:43:04,000
OK, in our case,
we have 16 quadrants.

627
00:43:04,000 --> 00:43:08,000
And then what you do is from
this point, you take one wire

628
00:43:08,000 --> 00:43:12,000
that goes to this quadrant,
one wire that comes here,

629
00:43:12,000 --> 00:43:15,000
one here, and one here,
so that you're getting the

630
00:43:15,000 --> 00:43:20,000
power supply very close to the
source, and you have different

631
00:43:20,000 --> 00:43:24,000
connections going to each
quadrant so that switching in

632
00:43:24,000 --> 00:43:27,000
this quadrant will not affect
this guy because of the

633
00:43:27,000 --> 00:43:33,000
inductance of this lead here.
OK, and if you hadn't taken

634
00:43:33,000 --> 00:43:37,000
6.002, you'd have been arguing
with IBM, I don't want 16 wires.

635
00:43:37,000 --> 00:43:40,000
I want just one wire.
OK, so there are other

636
00:43:40,000 --> 00:43:44,000
solutions, of course.
There's a couple more solution.

637
00:43:44,000 --> 00:43:49,000
One is that what you can do is
part of the problem here is that

638
00:43:49,000 --> 00:43:52,000
all my transitions are really,
really sharp.

639
00:43:52,000 --> 00:43:54,000
OK, so di/dt is very,
very large.

640
00:43:54,000 --> 00:43:58,000
So, there's a whole new
technique in design of digital

641
00:43:58,000 --> 00:44:01,000
and analog circuits,
which talks about,

642
00:44:01,000 --> 00:44:05,000
maybe I should call it waveform
engineering, OK,

643
00:44:05,000 --> 00:44:09,000
or edge engineering.
OK, it's also called edge

644
00:44:09,000 --> 00:44:12,000
smoothing.
The idea is that rather than

645
00:44:12,000 --> 00:44:16,000
have very sharp edges in your
circuit, you try to have

646
00:44:16,000 --> 00:44:19,000
smoother edges.
And when you have smoother

647
00:44:19,000 --> 00:44:22,000
edges, OK, then your di/dt is
now going to be less.

648
00:44:22,000 --> 00:44:25,000
It's not going to be very,
very high.

649
00:44:25,000 --> 00:44:29,000
Rather, your delta I is spread
out over a longer period of

650
00:44:29,000 --> 00:44:31,000
time.
Of course, that means the

651
00:44:31,000 --> 00:44:34,000
circuits may have to run a
little slower,

652
00:44:34,000 --> 00:44:38,000
but that can also solve the
problem.

653
00:44:38,000 --> 00:44:41,000
And in fact,
that same smoothing of the

654
00:44:41,000 --> 00:44:46,000
waveforms was also the solution
you saw in the capacitive

655
00:44:46,000 --> 00:44:49,000
coupling we saw a month and a
half ago.

656
00:44:49,000 --> 00:44:53,000
And let me show you the demo,
and then close up.

657
00:44:53,000 --> 00:44:55,000
Not working?
OK, that's OK.

658
00:44:55,000 --> 00:45:00,000
It doesn't matter.
So if you remember the demo

659
00:45:00,000 --> 00:45:05,000
from the lecture about a month
and a half ago in capacitors,

660
00:45:05,000 --> 00:45:10,000
I talked about a chip with two
pins, and there was this

661
00:45:10,000 --> 00:45:14,000
capacitive coupling between the
pins.

662
00:45:14,000 --> 00:45:18,000
And because of this,
if this waveform is switching,

663
00:45:18,000 --> 00:45:23,000
then because of this coupling,
you will end up getting,

664
00:45:23,000 --> 00:45:29,000
if this is the signal here,
you will end up getting spikes

665
00:45:29,000 --> 00:45:33,000
on this pin because of the
signaling of the other pin.

666
00:45:33,000 --> 00:45:39,000
And that's good old capacitive
coupling.

667
00:45:39,000 --> 00:45:42,000
OK, and to eliminate this,
what you can do is much like

668
00:45:42,000 --> 00:45:45,000
with the inductance system,
if you, rather than having

669
00:45:45,000 --> 00:45:49,000
sharp transitions on this pin,
if you have smooth transitions

670
00:45:49,000 --> 00:45:52,000
that look like this,
then what you can do is you'll

671
00:45:52,000 --> 00:45:56,000
now spread delta V from here to
here over a longer delta T.

672
00:45:56,000 --> 00:45:59,000
OK, delta T has become longer,
and because of that,

673
00:45:59,000 --> 00:46:03,000
you end up getting much better
behavior, and you don't end up

674
00:46:03,000 --> 00:46:06,000
getting these spikes.
So therefore,

675
00:46:06,000 --> 00:46:10,000
if you want to build really,
really fast circuits,

676
00:46:10,000 --> 00:46:13,000
you have to be really careful.
You can build fast circuits,

677
00:46:13,000 --> 00:46:15,000
but watch out for them fast
edges.

678
00:46:15,000 --> 00:46:18,000
OK, fast edges are nasty.
They kill you.

679
00:46:18,000 --> 00:46:22,000
That's something to remember as
you build the next generation of

680
00:46:22,000 --> 00:46:24,000
circuits.
Well, thank you all.

681
00:46:24,000 --> 00:46:27,000
I had a blast,
and I hope you guys had fun

682
00:46:27,000 --> 00:46:30,000
too.
Thank you.