>> Now, let's go back to our original problem and suppose that we want to design

our output voltage to a be a linear combination of our input voltage and a constant.

Refer to table four dash three in your book,

and this will show you various Op-amp circuits that you already know how to design.

Inverting summers, non-inverting summers,

inverting and non-inverting amplifiers,

subtracting amplifiers and voltage followers, or buffers.

Let's figure out how to use these to design the systems that we want to build.

To do this, I've developed a set of system and circuit design cards.

One side of the card is the system side,

that tells us what operation is needed.

In this case, we would have a multiplier.

That's a non-inverting amplifier where

our input voltage is multiplied by some number greater than one,

to give us the output voltage, right here.

On the other side of the card is the circuit side.

This is the part that you would actually build.

The part that is shown on the front is the area that's within

this blue dashed line here and that shows you the design for a non-inverting amplifier.

So, here are two other system and circuit design cards.

Here's the system side,

here's the circuit side.

There's the non-inverting amplifier that you're used to,

here's an inverting amplifier where we multiply by a negative number.

While we're at it, let's also take a look at the very important input,

resistances for these circuits.

When I look into this circuit,

I'm going to run up against

the input resistance of the Op-amp which we know is very high.

So, Rin for a non-inverting amplifier is approximately equal to infinity.

But when I look into the inverting amplifier,

I know it looks infinite in this direction,

but my current is able to follow this path right here,

which means that it is not going to have an infinite input resistance.

So, in this case,

it's not equal to infinity.

That means I probably don't need a buffer if I'm doing a non-inverting amplifier,

but I do need a buffer right here if I am doing an inverting amplifier.

Here are two summers, the system design card and the circuit design card.

Again, let's take a look at the input resistance.

When I look into the inverting summer,

is that input resistance infinity? No, it isn't.

Rin is not equal to infinity,

so plan to use a buffer if you're using an inverting summer.

When I look into the non-inverting summer however,

that input resistance is close to

infinity and so I won't be needing a buffer for that device.

Here's another system and circuit design card.

This is a differencing amplifier,

where I will multiply both of my voltages by a constant,

but then I will subtract them.

Here's how I designed that system.

Switches are other important things that Op-amps are able to do.

Remember we talked about a single-pole double-throw switch in an example

previously where my Op-amp railed out between Vcc and minus Vcc.

That's the equivalent of doing a single-pole double-throw switch.

Here's a single-pole single-throw switch where it goes between Vcc and ground.

Here's the system design card and here's how you build the circuit.

Now, a buffer of course is a very important part of many of

our circuits and that's because I'm able to buffer

the input and output resistances of various devices so that I can design them separately.

That's the key idea.

Here is the symbol we often use for a buffer.

A buffer is a unity gain amplifier where we simply multiply

our input value by one in order to get our output voltage.

This is the system design card,

here's the circuit design card that shows us how to build it.

We simply connect the negative terminal,

the negative input to the output terminal and that gives us a gain of one.

When I look into the input of a buffer,

I can see that I'm going up against the input resistance of the Op-amp,

so, Rin for a buffer is always

approximately equal to infinity and that's why we like them so well.

So, let's talk about an example where we might want

to do a linear combination of voltages.

Perhaps these four voltages came from a series

of sensors and some of them we really trust,

we want to multiply them by a large number,

and some we don't trust quite as much,

we want to multiply them by a small number.

So, here's the equation that we might like to have in order to get our output voltage.

There are many ways we could build this circuit.

We could add things up first,

we could subtract them first,

we could multiply them.

Many different combinations could give us the same output voltage.

Then here's an example of the way that I chose to do it.

Here is an input resistance, sorry.

Here is an input voltage V1 another input voltage V2, V3, and V4.

I'm going to use a non-inverting amplifier to multiply the first voltage by three,

the second voltage by four,

the third voltage by five,

and the fourth voltage by eight.

I can design a non-inverting amplifier that will do this and I know

that I will be able to do that when I get to the circuit design side of the card.

Well, now that I have multiplied each of my voltages by their appropriate value,

I'm going to take the ones that are positive, right here,

and I'm going to put them into a non-inverting summer and add them up.

So, basically, I'm doing this operation and

here's the output of this non-inverting summer.

On the other side,

I'm going to take the minus five and the minus

eight and put them into an inverting summer.

So, I'm basically doing this part of the math and it's going to show up here.

Finally, I'm simply going to add them up and that gives me

V out on the other side using a non-inverting summer.

So, this is how I use the system design side of my card,

in order to design the operations,

the math, that I want my circuit to do.

Then I flip the cards over to the circuit side and it shows me how to build them.

The non-inverting amplifier of course,

has simply use two resistors and I design them so

that the gain is three, four, five, eight.

Whatever are my gains need to be.

Sorry. Then, I put them into a non-inverting summer,

an inverting summer, and finally a non-inverting summer as shown here.

Now that we know what circuits we're going to do,

let's take a look at the input resistances in

order to decide if we need to put buffers in the circuit.

So, remember that I can design each of these elements independently

as long as the input resistance is near infinity.

Here's my non-inverting summer and sure when I look in here,

Rin is approximately equal to infinity.

So, I do not need buffers on the lines going into this circuit.

When I look at the inverting summer however,

my input resistance is not close to

infinity and so I'm going to need a couple of buffers here.

So, right there I'm going to put a buffer on

either end of the inputs going into my inverting summer.

So, what does that mean?

It means that I can design this card completely separately from this one.

I can design that separately from the non-inverting summer,

separately from the inverting summer and so on,

until I have designed my complete circuit

and then I can hook it up in the fashion shown here.

Sometimes we draw those buffers as black triangles and included that new here as well.

Now, I'd like you to take a chance to read

through example four dash five in your book which is

a practical application of this to the design of an elevation sensor.

I'll let you take the time to work through that example and see if you

understand how the various elements of the system can be put together.

Here's the linear response that your sensor has,

and here's the output that you would like to receive.

See if you can design that circuit.

So, thank you very much for joining me today.

I'm sure you're dying with curiosity about what the front picture was.

This is White Canyon,

a nice ride in American Fork.