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

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Today, we're going to talk about Operational Amplifiers or Op Amps.

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Remember that electrical engineering is about what you can do to a voltage.

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For example, a resistor converts voltage to current, and current to voltage.

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A voltage divider divides the voltage, and a current divider divides the current.

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We can think of this as the operation of a voltage divider or a current divider.

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Here's the circuit that goes with that operation.

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Why do we need an Op Amp?

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Because there are many more operations that we would

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like to do than the devices that we have today.

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For example, an Op Amp circuit can amplify or multiply voltages.

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It can de-amplify or divide them.

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It can add, subtract, compare.

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It could switch voltages,

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and many more operations can be done with Op Amp circuits.

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So, what is an Op Amp?

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The Op Amps we use are going to come into the little chip like this.

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There are eight pins on this chip.

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This will fit into your protoboard and you can see chips one, two, three, four,

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and here, the pin numbers start with this little dot here at the top.

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On pin two, we have an input Vn,

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that's our negative input,

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and there's a Vp input on pin three,

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that's the positive input.

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Pin six has the V output.

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So, there are two voltage inputs and there's one voltage output.

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This triangle right here is the symbol that we use to represent the Op-Amp.

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The Op Amp is different than other devices that we have used in the past.

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A resistor, for example,

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always acts like a resistor even if we don't have it connected to power.

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But an Op Amp only acts like

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an operational amplifier if we connect it to its outside power supply,

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Vcc and minus Vcc.

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This is very important.

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Keep your eye on the Vcc as we go through this lecture.

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This is what's inside the amplifier.

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This is what's inside that triangle.

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Here is the negative input,

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the positive input, and the output.

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You can see there are a series of transistors that are hooked up in

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this fashion that make the operational amplifier do what we want it to do.

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However, these transistors only work if they are connected to Vcc and minus Vcc.

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This is why the amplifier is an active device.

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Without this power, it does not act like an operational amplifier.

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Okay. So, now that we know that we have

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this triangle that represents an operational amplifier,

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if we want to hook it up,

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we're going to hook it up this way with plus and minus Vcc.

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But that's complicated to draw,

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and we really just remember that we have Vcc and we normally draw it this way.

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Another thing to remember is all of those transistors in there,

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they divide the frontend and the backend of the amplifier in effect.

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So, even though we might have a positive current here and a negative current there,

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because there are all of those transistors and the power supply,

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sometimes current gets added and sometimes current gets subtracted.

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We don't really know in advance.

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So, all we can say is that i zero, the output current,

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is not equal to the sum of the two input currents.

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Now, let's talk about Op Amp Gain.

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Op Amp Gain is intrinsic to the amplifier.

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It's controlled by how the transistors are put together.

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It's sometimes also called Open Loop Gain.

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Op Amps have a very high voltage gain

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typically on the order of 10 to the fourth to 10 to the eighth.

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They also have a linear response.

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So, the gain tells us that the output is equal to the gain times the input.

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In this case, the input is considered to be

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the difference between the positive and negative inputs of the Op Amp.

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So, if we have a voltage gain of 10 to the fourth,

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it would be linear of something like this,

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a voltage gain of 10 to the eighth would be steeper.

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Because we have Vcc,

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remember I said follow Vcc,

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it limits the actual output of our operational amplifier.

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We cannot put out more power or

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more voltage than we were able to put in to our amplifier.

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So, our amplifier circuit always saturates at plus Vcc

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and minus Vcc because of the power supply limitations.

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Let's see how that saturation can help the operational amplifier acts like a switch.

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Here is a circuit where we hooked up our amplifier and we want to

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be able to control if a red or a green LED turns on.

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So, we've connected our negative input right here to ground along with our two LEDs.

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Remember that the LED only turns on if current

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goes through it in this direction because of its diode nature.

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So, let's see what happens if we put a voltage,

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let's say, two volts, on our positive input.

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In that case, remember that Vp minus Vn is the thing that we're interested in,

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and that's two minus zero in this case.

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So, it's two volts, two volts minus zero volts.

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Multiply that by a very large value, let's say, 10,000.

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So, our output voltage tries to go up to be 20,000.

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Well, the limitation of the power supply limits that,

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let's say, to 12 volts.

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So, the output voltage right here is 12.

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Aha! But that's very good because that gives us a twelve volt difference across

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our LED that drives the current in this direction and turns on our red LED.

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The green LED is trying to drive current in this direction,

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but the LED acts like an open circuit because of a diode and it doesn't turn on.

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Now, let's see what happens if we put a negative voltage on Vp instead.

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Then, Vp minus Vn is going to be minus two volts.

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Multiply that by a very large number and it tries to go to, say, minus 20,000.

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But it's limited by the power supply voltage,

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so it goes to minus 12.

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Well, if it's trying to drive current through here,

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the red LED acts like

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a diode and doesn't allow current to go through. It doesn't turn on.

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Oops! Sorry, I'm not trying to drive current in that direction.

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I'm actually trying to pull current in that direction.

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The green LED, however,

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does turn on because here goes the direction of the current for the green LED.

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So, if we make Vp positive,

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we can turn on the red LED,

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and if we make it negative,

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we can turn on the green LED.

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This allows us to have a circuit that acts like a switch for our two LEDs.

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Now, let's talk about Op Amp Gain versus Circuit Gain.

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The op-amp gain is always high and it's intrinsic to the inside of the op-amp.

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It's also called the open-loop gain or the voltage gain.

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Gain is typically defined as the output divided by the input, and in this case,

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the input is considered to be the difference of the two inputs.

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Circuit gain, on the other hand,

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we may have an op-amp in here and connect it up in this fashion.

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Connect the output right there.

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The circuit gain tells us about the op-amp that has

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its gain A for all of the other resistors around it also.

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Depending on how we connect up our op-amp circuit,

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gain can be large or small.

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If it's large, larger than one, that's amplification.

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Less than one is deamplification.

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If the gain is negative,

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we call it inverting,

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and if the gain is positive,

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we call it non-inverting.

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Here's a non-ideal op-amp equivalent circuit.

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Notice that right here is a dependent voltage source that depends on

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the gain and the difference between the two input voltages.

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So, for a non-ideal op-amp,

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we recognize that Ri is very large.

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It's typically on the order of 10 to six to the 10 to the 13th.

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A is very large, 10 to the fourth to 10 to the eighth.

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The output resistance is very small,

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one to a 100, and the supply voltage right here,

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Vcc and minus Vcc,

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and sometimes they draw it that way too,

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is five to 24 volts.

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Now, for an ideal op-amp, it's going to be different.

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For an ideal op-amp,

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we're going to assume that the input resistance is so large that it can be eliminated.

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In that case, it's like having an open circuit right there at the input.

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We can consider that the gain is so large that we can say Vp is equal to Vn,

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and we can say that the output resistance is so

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small that we can neglect it and consider it just as a wire.

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The implications of this are that for an ideal op-amp,

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we can say that Vp equal Vn,

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and we can say that no current goes into the either input of this op-amp.

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Sometimes it's also useful to remember,

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right here, that R out is equal to zero.

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You'll see why we need that in a minute.

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Okay. So, the circuit gain depends on the circuit.

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In this red box,

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I have an example of a non-inverting amplifier.

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Trust me for now that the output is going to be equal to

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R1 plus R2 over R2 times Vs for this particular op-amp circuit.

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In that case, we call this the gain,

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G, and we can see that it's always positive.

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That's because resistors are always positive.

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So, it's non-inverting, it's always positive.

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Now, let's see if this non-inverting amplifier can go to any value we want.

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No. Because we have this Vcc and minus Vcc,

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so we know that the gain has to be limited by Vcc.

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So, the op-amp gain is intrinsic to the amplifier,

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but the circuit gain depends on all of the resistors that we put around it.

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So, in summary, here are the important things to remember about an op-amp.

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Here is a model of a non-ideal op-amp.

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We're actually not going to use that very much in

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this class but I want you to remember these parameters.

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We are going to use the ideal op-amp model extensively.

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Remember that the important features of

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the non-ideal op-amp are that the negative and positive input are equal,

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that no current goes into either input,

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and that the output is not the sum of the two input currents.

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Remember also that we have Vcc and minus

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Vcc that limit the output voltage of our operational amplifier.

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Now, I hope you're wondering where the picture was on the front.

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That is the Wild Horse Corral on Antelope Island.