SPEAKER 1: So before we wrap up on the SR and S models for
the MOSFET and switches, and building digital circuits
using these switches and MOSFETs, I would like to make
some observations.
Hopefully, these will convey some very interesting
insights, particularly those that relate to the connection
between the analog world and the digital world.
So first of all, notice that the switches that we've been
dealing with so far are non-linear.
When you build a circuit containing a switch, even the
very simple inverter that looked like this, VN versus
VR, notice that the transfer curve that you
got looked like this.
So this is clearly non-linear.
This is not a straight line.
It is piecewise linear.
In other words, it's linear in pieces.
But it is not a linear curve.
This is non-linear.
So when you build circuits using switches and MOSFETs and
so on, you end with non-linear behavior, and these are not
non-linear devices.
However, one of the interesting facts is, notice
that for a given setting of the switches--
so say for example, I pick a given set of values for A's,
B's, and C's.
Let's say I pick A equal to 1, B equal to 1, and I pick C
equal to 0, notice that what I get here is a set of switch
values that look like this.
For just above the switch, I get the on-state
resistance, B is 1.
So I get Ron here.
And this is 0, so I get an open connection up here.
OK, notice that for a given set of switch values, given
set control values---
A equal to 1, B equal to 1, and C equal to 0--
notice what we're left with is a linear subcircuit.
This is a remarkable result.
This is really nice.
What this says is that I can actually use my linear
techniques, my big bazookas, Superposition and Thevenin,
and so on, to analyze these subcircuits.
So if I generally take a digital circuit and pick a set
of values for the inputs, such as A's, B's, C's, and so on,
and then from that set of values, I replace the switches
with their either on states or off states, and the resulting
circuit is completely linear, and all my linear techniques
will apply.
This is a pretty nice [? insight. ?]
The second thing I want to talk about is something that
people commonly do with circuits, is look at the power
consumed by a circuit.
And power is becoming a really, really
big deal in our field.
And in fact, the consequences of power are driving the way
we are building our digital designs today.
And so, one of the things we'd like to do is analyze the
power consumed by our digital circuits.
Power is becoming extremely important in data centers and
other places, where almost a third to a half of the cost of
operating a large data center, such as those you might find
with Google, or Facebook, and so on that maintain all of
these computers when you go on Facebook and so on--
Facebook has these huge data centers that contain millions
of computers.
They're all burning power.
And it costs a lot of money.
And so, the amount of money can be extremely large.
And so, power is extremely important for that and many
other reasons.
So let's try to understand how to compute power for our
digital circuits.
So let's go to our example here, where I set A equal to
1, B equal to 1, and C is 0, and I get my subcircuit.
You should be able to directly write the power from here.
But if you really want to, you can go and simplify it a
little bit just to make it a little cleaner.
If you want, you can do something like this.
So this is Ron.
This is Ron.
And this RL.
And I get A equals 1, B equals 1,
controlling the two MOSFETs.
And then, since the other leg of the circuit is an open
circuit, I don't have to show it.
So what is the power consumed by this circuit?
And back to basics, the power here is simply given by the
voltage squared divided by the resistance.
So here the power is given by V squared divided
by 2Ron plus RL.
And this is simply, not surprisingly, VS
times the current i.
And if you have the current i flowing through
here, that is the power.
And i in turn is given by VS divided by 2Ron plus RL.
And so therefore, notice that this expression is the same as
this expression when you substitute for the current.
So notice here that the power, interestingly enough, relates
to VS squared.
So the power relates to the square of the
power supply voltage.
And this is pretty common in our digital circuits.
And so although for pedagogical reasons we
commonly use VS equals 5 volts in this course, because of
this huge power consumption and the power issue, modern
day circuits have kept reducing the voltage, VS, over
the past couple of decades.
And in fact, today, it is not uncommon to see a VS in the
order plus 0.7 volts or 0.8 volts.
We've come down substantially.
So notice that the power when VS was 5 volts, was
proportional to 5 squared, which is on the order of VS
squared at 25.
And then when I go to VS, which is almost 1/7 of 5
volts, I manage to reduce my power by a factor of 49.
So this is 1/7 the power supply voltage of the
[? past. ?]
And the square of that is 149.
And so therefore, by keeping on reducing the voltage, I
manage to reduce my power by close to a factor of 50.
Notice that when I reduce my voltage, VS, I have to modify
my devices to also reduce VT.
So commonly if VS is 5 volts, our VT that we used to use
used to be about 1 volt.
But in today's day and age, when power has gone down to
0.7 volts, the VTs may be on the order of 0.3 volts to
about 0.5 volts.
So VT is tending to become closer and closer to VS in
moder day circuits.
But for most of 6002x, for pedagogic reasons and to keep
our math simple, we will commonly used to be VS equals
5 volts, and commonly used VT equals 1 volt, unless
specified otherwise.
OK.
So before we wrap up on this, I'd like to show you a quick
little demo to show you that both analog and digital
signals and components are everywhere.
You will find the gates and digital circuits oftentimes
juxtaposed with analog circuits.
And these are called mixed signal designs because they
have both analog and digital stuff.
And so stand by, and let's have a little bit of fun.