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

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

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Refer to table four dash three in your book,

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

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Inverting summers, non-inverting summers,

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inverting and non-inverting amplifiers,

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subtracting amplifiers and voltage followers, or buffers.

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

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

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One side of the card is the system side,

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that tells us what operation is needed.

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In this case, we would have a multiplier.

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That's a non-inverting amplifier where

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

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to give us the output voltage, right here.

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

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This is the part that you would actually build.

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

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

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

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Here's the system side,

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here's the circuit side.

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

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

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

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resistances for these circuits.

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When I look into this circuit,

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I'm going to run up against

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

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

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But when I look into the inverting amplifier,

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I know it looks infinite in this direction,

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

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

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So, in this case,

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it's not equal to infinity.

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

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

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

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

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When I look into the inverting summer,

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

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Rin is not equal to infinity,

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

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When I look into the non-inverting summer however,

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that input resistance is close to

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

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Here's another system and circuit design card.

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This is a differencing amplifier,

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

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but then I will subtract them.

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Here's how I designed that system.

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

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

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

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

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

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

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

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

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

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That's the key idea.

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Here is the symbol we often use for a buffer.

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A buffer is a unity gain amplifier where we simply multiply

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

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This is the system design card,

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

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We simply connect the negative terminal,

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

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When I look into the input of a buffer,

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

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so, Rin for a buffer is always

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

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

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to do a linear combination of voltages.

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Perhaps these four voltages came from a series

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of sensors and some of them we really trust,

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we want to multiply them by a large number,

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and some we don't trust quite as much,

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we want to multiply them by a small number.

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

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There are many ways we could build this circuit.

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We could add things up first,

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we could subtract them first,

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we could multiply them.

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Many different combinations could give us the same output voltage.

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

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Here is an input resistance, sorry.

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

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

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the second voltage by four,

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the third voltage by five,

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and the fourth voltage by eight.

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

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

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

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

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

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So, basically, I'm doing this operation and

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

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On the other side,

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

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eight and put them into an inverting summer.

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

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

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

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

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in order to design the operations,

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the math, that I want my circuit to do.

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

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The non-inverting amplifier of course,

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has simply use two resistors and I design them so

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

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Whatever are my gains need to be.

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

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

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

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let's take a look at the input resistances in

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

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

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as long as the input resistance is near infinity.

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

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Rin is approximately equal to infinity.

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

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When I look at the inverting summer however,

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my input resistance is not close to

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

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

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either end of the inputs going into my inverting summer.

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So, what does that mean?

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

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

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separately from the inverting summer and so on,

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until I have designed my complete circuit

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

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

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

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through example four dash five in your book which is

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

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

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

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Here's the linear response that your sensor has,

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

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See if you can design that circuit.

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So, thank you very much for joining me today.

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

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This is White Canyon,

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a nice ride in American Fork.