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

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

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

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A lot of times we like to add voltages together,

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we like to add constants to them,

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we like to multiply them by various values,

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in order to make the circuit do what we want.

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Let's suppose that we want our output to be

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

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This math might look like 2 times v_2

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plus minus 2 times some voltage, something like this.

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So, how do we design that system?

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Whenever we are designing systems,

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we like to break them down into individual components.

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

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consider the power plant, the breaker box,

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and all the outlets in your house individually

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

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

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a single source voltage with its source resistance,

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and then we might consider the lamp and the fan in

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parallel like so and we design each of them independently.

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In order to design individual blocks like this independently,

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there's a very important concept,

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that concept is input and output resistances.

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Let's suppose that we have a circuit,

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any circuit, that's this black box.

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If we look in,

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

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that's going to give us the output resistance.

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

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That is impedance as opposed to resistance,

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it's a complex resistance,

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

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If we are looking in to either side,

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that's the same thing as using

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

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

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

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

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connected onto some amplifier circuit driving some load.

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

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

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Here for example is our input circuit.

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Now even though it's called an input circuit,

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

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it only has an output resistance.

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The output resistance looking in,

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resistance would be here.

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

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Now, let's consider the amplifier circuit.

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Looking into the amplifier,

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

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

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So, when we look into an op-amp,

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Zin is equal to infinity.

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Let's consider the Zout,

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remember that when we have an op-amp,

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we have an output resistance Rout,

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so our Zout is approximately zero.

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Then let's look into our load,

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Zin, is ZL like this.

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

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impedances for each one of the elements in our circuit,

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and input impedance is looking into the input

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and an output impedance is looking in to the output.

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Now, let's go back to our circuit,

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let's take a look again at the circuit and

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decide what our input and output resistances are.

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Just like in my previous case,

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the output resistance of the source block is simply Zs.

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

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The input resistance right there would be

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Rfan and the output resistance would also be Rfan.

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

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

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Okay. Now, let's consider how we connect

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circuits that have different input and output resistances.

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If we wanted to connect circuit number one,

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which has its input and output resistances right here

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

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

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

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So, if I look in here,

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the output resistance is Zs,

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and if I look in here,

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the input resistance is ZL.

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

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

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

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and I'm going to drive this,

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maybe a mixer input impedance or something,

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and I connect them up like this.

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

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we know something about voltage dividers.

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We know that Vout1 is equal to

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

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Now, if ZL is small compared to Zs,

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

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The only time that we are going to get

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

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is if ZL is very large compared to the Zs.

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

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So, this is a really important feature.

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

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

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Zin2 is much greater than Zin1,

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then we can consider these two circuits to be independent.

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We can design them separately.

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

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

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Now, in the event that doesn't happen,

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

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A buffer multiplies the incoming voltage by one,

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

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and the output impedance of the buffer is always small.

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

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we can always design our block separately.

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So, the buffer allows us to design

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our input equivalent circuit separate from our load equivalent circuit.

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

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

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In this case, loading happens to make it so that

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

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so loading is a bad thing.

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

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

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I can design my circuit without a buffer,

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

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any other time I have to analyze the entire circuit.

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

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

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

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a large input impedance and a small output impedance.

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So, these are our two design criteria that allow us

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to design individual elements of a more complex circuit.