>> Hello, this is Dr. Cynthia Furse at the University of Utah,

and today we're going to talk about designing op-amp systems.

Electrical engineering is about what can you do to a voltage.

A lot of times we like to add voltages together,

we like to add constants to them,

we like to multiply them by various values,

in order to make the circuit do what we want.

Let's suppose that we want our output to be

a linear combination of a constant and our input voltage like this.

This math might look like 2 times v_2

plus minus 2 times some voltage, something like this.

So, how do we design that system?

Whenever we are designing systems,

we like to break them down into individual components.

For example, we wouldn't really want to have to

consider the power plant, the breaker box,

and all the outlets in your house individually

every time we wanted to design a lamp or a fan.

We'll take that entire distribution system and we'll model that as

a single source voltage with its source resistance,

and then we might consider the lamp and the fan in

parallel like so and we design each of them independently.

In order to design individual blocks like this independently,

there's a very important concept,

that concept is input and output resistances.

Let's suppose that we have a circuit,

any circuit, that's this black box.

If we look in,

that's going to give us the input resistance and if we look into the output side,

that's going to give us the output resistance.

A lot of times in the book and elsewhere, you will see Z.

That is impedance as opposed to resistance,

it's a complex resistance,

so just consider that to be the same as resistance for this case.

If we are looking in to either side,

that's the same thing as using

the Thevenin resistances and you calculate it in the same way.

Now, let's consider the basics of input and output resistance.

Here is an example of an equivalent circuit that we would be very likely to build,

we would have a source right here with its input equivalent,

connected onto some amplifier circuit driving some load.

If we wanted to figure out how these we're working,

we would consider the input and output impedances of each of our blocks.

Here for example is our input circuit.

Now even though it's called an input circuit,

you notice it doesn't really have an input resistance,

it only has an output resistance.

The output resistance looking in,

resistance would be here.

We would short out our voltage source and the only resistance there would be Zs.

Now, let's consider the amplifier circuit.

Looking into the amplifier,

remember the fact that when we have a op-amp,

the input resistance is approximately infinity, it's very high.

So, when we look into an op-amp,

Zin is equal to infinity.

Let's consider the Zout,

remember that when we have an op-amp,

we have an output resistance Rout,

so our Zout is approximately zero.

Then let's look into our load,

Zin, is ZL like this.

So, we now have looked at our input and output resistances or

impedances for each one of the elements in our circuit,

and input impedance is looking into the input

and an output impedance is looking in to the output.

Now, let's go back to our circuit,

let's take a look again at the circuit and

decide what our input and output resistances are.

Just like in my previous case,

the output resistance of the source block is simply Zs.

Now, let's look at this fan block right here.

The input resistance right there would be

Rfan and the output resistance would also be Rfan.

Now, here's our last load right here, that's the lamp,

and looking into the lamp that gives me an input resistance of Rlamp.

Okay. Now, let's consider how we connect

circuits that have different input and output resistances.

If we wanted to connect circuit number one,

which has its input and output resistances right here

and we wanted to consider circuit two with its input and output resistances,

let's see what would happen if we hook them together.

Here's an example where I'll just be connecting a source impedance to a load.

So, if I look in here,

the output resistance is Zs,

and if I look in here,

the input resistance is ZL.

Now, imagine what would happen if I hook them together.

The output voltage that I might want like here would be Vout1,

and let's suppose that I wanted to drive this circuit with the source Vs,

and I'm going to drive this,

maybe a mixer input impedance or something,

and I connect them up like this.

What does that give me? That is a voltage divider,

we know something about voltage dividers.

We know that Vout1 is equal to

V_s times ZL over ZL plus Zs because that's the voltage divider.

Now, if ZL is small compared to Zs,

we're not going to get the voltage that we wanted at all.

The only time that we are going to get

the voltage that we want it to be deriving it with,

is if ZL is very large compared to the Zs.

So, ZL much greater than Zs will give us the result that Vout1 is equal to Vs.

So, this is a really important feature.

When we are designing circuits and I showed it graphically here,

if the input resistance of the second circuit is very large,

Zin2 is much greater than Zin1,

then we can consider these two circuits to be independent.

We can design them separately.

Any other case we can't do that and we'd have to analyze the entire circuit together.

So, we like it very much if the input impedance of a circuit is very high.

Now, in the event that doesn't happen,

what we're going to do is put something called a buffer in the circuit.

A buffer multiplies the incoming voltage by one,

but it has this magic thing that the input impedance of the buffer is always large,

and the output impedance of the buffer is always small.

That makes us so that we can always put a buffer in here,

we can always design our block separately.

So, the buffer allows us to design

our input equivalent circuit separate from our load equivalent circuit.

Now, another word that we often use for this is loading.

So, loading occurs when ZL is approximately equal to or less than Zs.

In this case, loading happens to make it so that

the output voltage that we want isn't the same as the output voltage that we input,

so loading is a bad thing.

Now, let's review again connecting input and output resistances.

If I have a large input resistance and I connect it to a small output resistance,

I can design my circuit without a buffer,

I can individually designed circuit one and circuit two as if they were not interrelated,

any other time I have to analyze the entire circuit.

In the event that I didn't have Zin2 much greater than Zout2,

what I would do is put a buffer in that case,

and that is going to make it so that I always have

a large input impedance and a small output impedance.

So, these are our two design criteria that allow us

to design individual elements of a more complex circuit.