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PROFESSOR: Hi.

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Last time we talked about NVCC
method and how to reduce the

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number of equations we had
to deal with to solve a

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particular circuit.

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At this point, we're pretty
well equipped to solve

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circuits in the general sense,
but we really haven't talked

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about how to use that
information or possibly use

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circuits in a particular way.

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Before we jump into both that
and abstraction of circuits,

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we need to talk about op-amps.

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Op-amps is short for Operational
Amplifier.

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And it's a tool that we can
use in order to sample

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particular voltages from a
subsection of the circuit

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without affecting it.

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Another thing we can
use op-amps to do

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is modify our signal.

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Or if we're going to sample a
voltage from a particular

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subsection of the circuit, we
can then do stuff to that

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voltage without affecting the
circuit, all within the op-amp

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or within the op-amp's special
subset of circuitry.

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So first of all what is an
operational amplifier?

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Well, an operational amplifier
is a giant web of transistors.

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But what an operational
amplifier does is act as a

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voltage-dependent
voltage source.

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It can effectively sample
voltages from an existing

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circuit and then use them to
power some other object, for

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instance a light bulb.

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If you set up this kind of
circuit, you will not actually

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be powering this light bulb
with 5 Volts, because the

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light bulb itself acts
as a resistor.

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And so the voltage drop across
this part of the circuit is

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going to be different
from just 5 Volts.

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If you want to enable a voltage
drop of 5 Volts across

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this light bulb, then you have
to stick up an op-amp.

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You have to use an op-amp to
sample the voltage drop at

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this component and put it in
between the light bulb and the

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rest of the circuit.

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When you see an op-amp on a
schematic diagram, it'll

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frequently look like this.

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You'll have a positive input
voltage, a negative input

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voltage, power rails, which are
actually the thing that

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determine the range of
expressivity that the op-amp

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has, and an output voltage.

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In reality, the relationship
between the output voltage and

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then input voltages is something
like this, where K

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is a very large number.

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The effect that this has is
that Vout is going to be

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whatever Vout needs
to be, such that

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Vplus is equal to Vminus.

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That's the basic rule you want
to use when you're interacting

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with op-amps.

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So in this case, if we wanted to
power this light bulb with

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5 Volts, we would do something
like this.

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Excuse the sloppiness of
the second diagram.

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We still have our 10 Volt
voltage source.

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We still have our
voltage divider.

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This point samples 5 Volts
from this sub-circuit --

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and isolates this part of the
circuit from the light bulb.

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Vout has to be whatever value
is necessary such that this

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sample point and this sample
point are equal.

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Since this value is 5 Volts,
this value will also be driven

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to 5 Volts by the op-amp,
which means that

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this value is 5 Volts.

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And we've successfully
managed to power a

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light bulb with 5 Volts.

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The other thing you might be
asked to do is to take an

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existing schematic, an existing
circuit diagram and

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figure out what the operational
amplifier does to

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a given signal or possibly what
Vout is or possibly what

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Vout is in terms of
the input signal.

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So let's practice using
this diagram.

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Here's what we're after.

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I'm going to figure out where
Vplus is going to be.

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This is another voltage
divider.

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I'm now interested in Vminus,
in terms of Vout, which is

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another voltage divider.

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I can set these two equations
equal to one another

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and solve for Vout.

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I found a new expression for
Vout in the particular case

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where V is 10 Volts.

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If my input voltage were
previously unspecified, or if

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this voltage source were not
specified or just Vin, then I

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would be after this
expression.

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Some things I'd like to mention,
while we're talking

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about op-amps, all the
operational amplifiers we've

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been working with so far deal
with Vout in terms of Vin,

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where Vin is driven through the
positive terminal, and the

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negative terminal is typically
connected to ground.

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You can do the opposite
and end up with

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some interesting effects.

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But it comes at a cost.

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It is entirely possible that you
will end up driving your

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op-amp to an unstable
equilibrium.

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What you need to look at
is this relationship.

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There may be a particular point,
in which case your

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system is stable.

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But if you get any sort of minor
perturbations, you'll

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actually end up with
divergence.

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If this is the case, then
you'll probably

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burn out your op-amp.

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You can do this by hooking
it up in this way.

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This is expensive and could
possibly burn you.

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The other thing to note is that
the power rails on your

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op-amp limit its range
of expressivity.

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And I think I've said this
before, but it's worth

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mentioning again.

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If your op-amp is only powered
by 10 Volts, it cannot amplify

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your input signal to a final
value greater than 10 Volts.

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Likewise, if your input value
is a negative voltage, and

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you're working with a
non-inverting amplifier, if

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your ground is truly ground or
if your ground is higher

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relative than your input
voltage, you cannot actually

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express a negative voltage.

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The third thing I'd like to
quickly mention is that there

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are some terms associated with
op-amps that you might hear

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used by the staff or online,
that sort of thing.

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A buffer and a voltage follower
are the same thing.

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And that's explicitly when you
want to sample a signal or you

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want to sample a particular
voltage, and you don't want to

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multiply it or add it to
something or do any kind of

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LTI operations that we might be
able to do using op-amps in

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this course.

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You can work with amplifiers.

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And the thing we worked with
earlier was an amplifier for a

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value less than 1.

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You can also use op-amps
to some signals.

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And if you look for a voltage
summer amplifier on the

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internet, you should be able
to find some information.

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In any case, op-amps are
really powerful.

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They allow us to both isolate
a particular section of a

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circuit and sample a particular
voltage value from

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that circuit without affecting
that circuit, and also allow

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us to modify that particular
voltage value before using it

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in another part of our
overall circuit.

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Therefore, we're enabled to
design more complicated and

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powerful things.

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Next time, I'll talk about
superposition and Thevenin

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Norton equivalence, which will
further enable modularity and

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abstraction in our
circuit design.

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