PROFESSOR: Hi.
Last time we talked about NVCC
method and how to reduce the
number of equations we had
to deal with to solve a
particular circuit.
At this point, we're pretty
well equipped to solve
circuits in the general sense,
but we really haven't talked
about how to use that
information or possibly use
circuits in a particular way.
Before we jump into both that
and abstraction of circuits,
we need to talk about op-amps.
Op-amps is short for Operational
Amplifier.
And it's a tool that we can
use in order to sample
particular voltages from a
subsection of the circuit
without affecting it.
Another thing we can
use op-amps to do
is modify our signal.
Or if we're going to sample a
voltage from a particular
subsection of the circuit, we
can then do stuff to that
voltage without affecting the
circuit, all within the op-amp
or within the op-amp's special
subset of circuitry.
So first of all what is an
operational amplifier?
Well, an operational amplifier
is a giant web of transistors.
But what an operational
amplifier does is act as a
voltage-dependent
voltage source.
It can effectively sample
voltages from an existing
circuit and then use them to
power some other object, for
instance a light bulb.
If you set up this kind of
circuit, you will not actually
be powering this light bulb
with 5 Volts, because the
light bulb itself acts
as a resistor.
And so the voltage drop across
this part of the circuit is
going to be different
from just 5 Volts.
If you want to enable a voltage
drop of 5 Volts across
this light bulb, then you have
to stick up an op-amp.
You have to use an op-amp to
sample the voltage drop at
this component and put it in
between the light bulb and the
rest of the circuit.
When you see an op-amp on a
schematic diagram, it'll
frequently look like this.
You'll have a positive input
voltage, a negative input
voltage, power rails, which are
actually the thing that
determine the range of
expressivity that the op-amp
has, and an output voltage.
In reality, the relationship
between the output voltage and
then input voltages is something
like this, where K
is a very large number.
The effect that this has is
that Vout is going to be
whatever Vout needs
to be, such that
Vplus is equal to Vminus.
That's the basic rule you want
to use when you're interacting
with op-amps.
So in this case, if we wanted to
power this light bulb with
5 Volts, we would do something
like this.
Excuse the sloppiness of
the second diagram.
We still have our 10 Volt
voltage source.
We still have our
voltage divider.
This point samples 5 Volts
from this sub-circuit --
and isolates this part of the
circuit from the light bulb.
Vout has to be whatever value
is necessary such that this
sample point and this sample
point are equal.
Since this value is 5 Volts,
this value will also be driven
to 5 Volts by the op-amp,
which means that
this value is 5 Volts.
And we've successfully
managed to power a
light bulb with 5 Volts.
The other thing you might be
asked to do is to take an
existing schematic, an existing
circuit diagram and
figure out what the operational
amplifier does to
a given signal or possibly what
Vout is or possibly what
Vout is in terms of
the input signal.
So let's practice using
this diagram.
Here's what we're after.
I'm going to figure out where
Vplus is going to be.
This is another voltage
divider.
I'm now interested in Vminus,
in terms of Vout, which is
another voltage divider.
I can set these two equations
equal to one another
and solve for Vout.
I found a new expression for
Vout in the particular case
where V is 10 Volts.
If my input voltage were
previously unspecified, or if
this voltage source were not
specified or just Vin, then I
would be after this
expression.
Some things I'd like to mention,
while we're talking
about op-amps, all the
operational amplifiers we've
been working with so far deal
with Vout in terms of Vin,
where Vin is driven through the
positive terminal, and the
negative terminal is typically
connected to ground.
You can do the opposite
and end up with
some interesting effects.
But it comes at a cost.
It is entirely possible that you
will end up driving your
op-amp to an unstable
equilibrium.
What you need to look at
is this relationship.
There may be a particular point,
in which case your
system is stable.
But if you get any sort of minor
perturbations, you'll
actually end up with
divergence.
If this is the case, then
you'll probably
burn out your op-amp.
You can do this by hooking
it up in this way.
This is expensive and could
possibly burn you.
The other thing to note is that
the power rails on your
op-amp limit its range
of expressivity.
And I think I've said this
before, but it's worth
mentioning again.
If your op-amp is only powered
by 10 Volts, it cannot amplify
your input signal to a final
value greater than 10 Volts.
Likewise, if your input value
is a negative voltage, and
you're working with a
non-inverting amplifier, if
your ground is truly ground or
if your ground is higher
relative than your input
voltage, you cannot actually
express a negative voltage.
The third thing I'd like to
quickly mention is that there
are some terms associated with
op-amps that you might hear
used by the staff or online,
that sort of thing.
A buffer and a voltage follower
are the same thing.
And that's explicitly when you
want to sample a signal or you
want to sample a particular
voltage, and you don't want to
multiply it or add it to
something or do any kind of
LTI operations that we might be
able to do using op-amps in
this course.
You can work with amplifiers.
And the thing we worked with
earlier was an amplifier for a
value less than 1.
You can also use op-amps
to some signals.
And if you look for a voltage
summer amplifier on the
internet, you should be able
to find some information.
In any case, op-amps are
really powerful.
They allow us to both isolate
a particular section of a
circuit and sample a particular
voltage value from
that circuit without affecting
that circuit, and also allow
us to modify that particular
voltage value before using it
in another part of our
overall circuit.
Therefore, we're enabled to
design more complicated and
powerful things.
Next time, I'll talk about
superposition and Thevenin
Norton equivalence, which will
further enable modularity and
abstraction in our
circuit design.
