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Dialogue: 0,0:00:00.00,0:00:03.63,Default,,0000,0000,0000,,>> Hello, this is Dr. Cynthia Furse at the University of Utah.
Dialogue: 0,0:00:03.63,0:00:07.76,Default,,0000,0000,0000,,Today, we're going to talk about Operational Amplifiers or Op Amps.
Dialogue: 0,0:00:07.76,0:00:11.84,Default,,0000,0000,0000,,Remember that electrical engineering is about what you can do to a voltage.
Dialogue: 0,0:00:11.84,0:00:16.66,Default,,0000,0000,0000,,For example, a resistor converts voltage to current, and current to voltage.
Dialogue: 0,0:00:16.66,0:00:21.34,Default,,0000,0000,0000,,A voltage divider divides the voltage, and a current divider divides the current.
Dialogue: 0,0:00:21.34,0:00:26.13,Default,,0000,0000,0000,,We can think of this as the operation of a voltage divider or a current divider.
Dialogue: 0,0:00:26.13,0:00:29.26,Default,,0000,0000,0000,,Here's the circuit that goes with that operation.
Dialogue: 0,0:00:29.26,0:00:31.38,Default,,0000,0000,0000,,Why do we need an Op Amp?
Dialogue: 0,0:00:31.38,0:00:33.78,Default,,0000,0000,0000,,Because there are many more operations that we would
Dialogue: 0,0:00:33.78,0:00:36.30,Default,,0000,0000,0000,,like to do than the devices that we have today.
Dialogue: 0,0:00:36.30,0:00:40.90,Default,,0000,0000,0000,,For example, an Op Amp circuit can amplify or multiply voltages.
Dialogue: 0,0:00:40.90,0:00:43.28,Default,,0000,0000,0000,,It can de-amplify or divide them.
Dialogue: 0,0:00:43.28,0:00:45.58,Default,,0000,0000,0000,,It can add, subtract, compare.
Dialogue: 0,0:00:45.58,0:00:46.100,Default,,0000,0000,0000,,It could switch voltages,
Dialogue: 0,0:00:46.100,0:00:50.56,Default,,0000,0000,0000,,and many more operations can be done with Op Amp circuits.
Dialogue: 0,0:00:50.56,0:00:52.42,Default,,0000,0000,0000,,So, what is an Op Amp?
Dialogue: 0,0:00:52.42,0:00:55.64,Default,,0000,0000,0000,,The Op Amps we use are going to come into the little chip like this.
Dialogue: 0,0:00:55.64,0:00:57.36,Default,,0000,0000,0000,,There are eight pins on this chip.
Dialogue: 0,0:00:57.36,0:01:01.37,Default,,0000,0000,0000,,This will fit into your protoboard and you can see chips one, two, three, four,
Dialogue: 0,0:01:01.37,0:01:06.56,Default,,0000,0000,0000,,and here, the pin numbers start with this little dot here at the top.
Dialogue: 0,0:01:06.56,0:01:09.60,Default,,0000,0000,0000,,On pin two, we have an input Vn,
Dialogue: 0,0:01:09.60,0:01:11.07,Default,,0000,0000,0000,,that's our negative input,
Dialogue: 0,0:01:11.07,0:01:13.50,Default,,0000,0000,0000,,and there's a Vp input on pin three,
Dialogue: 0,0:01:13.50,0:01:14.96,Default,,0000,0000,0000,,that's the positive input.
Dialogue: 0,0:01:14.96,0:01:17.13,Default,,0000,0000,0000,,Pin six has the V output.
Dialogue: 0,0:01:17.13,0:01:21.04,Default,,0000,0000,0000,,So, there are two voltage inputs and there's one voltage output.
Dialogue: 0,0:01:21.04,0:01:25.69,Default,,0000,0000,0000,,This triangle right here is the symbol that we use to represent the Op-Amp.
Dialogue: 0,0:01:25.69,0:01:29.56,Default,,0000,0000,0000,,The Op Amp is different than other devices that we have used in the past.
Dialogue: 0,0:01:29.56,0:01:31.04,Default,,0000,0000,0000,,A resistor, for example,
Dialogue: 0,0:01:31.04,0:01:34.88,Default,,0000,0000,0000,,always acts like a resistor even if we don't have it connected to power.
Dialogue: 0,0:01:34.88,0:01:36.59,Default,,0000,0000,0000,,But an Op Amp only acts like
Dialogue: 0,0:01:36.59,0:01:41.00,Default,,0000,0000,0000,,an operational amplifier if we connect it to its outside power supply,
Dialogue: 0,0:01:41.00,0:01:43.52,Default,,0000,0000,0000,,Vcc and minus Vcc.
Dialogue: 0,0:01:43.52,0:01:44.98,Default,,0000,0000,0000,,This is very important.
Dialogue: 0,0:01:44.98,0:01:48.46,Default,,0000,0000,0000,,Keep your eye on the Vcc as we go through this lecture.
Dialogue: 0,0:01:48.46,0:01:51.24,Default,,0000,0000,0000,,This is what's inside the amplifier.
Dialogue: 0,0:01:51.24,0:01:52.98,Default,,0000,0000,0000,,This is what's inside that triangle.
Dialogue: 0,0:01:52.98,0:01:54.47,Default,,0000,0000,0000,,Here is the negative input,
Dialogue: 0,0:01:54.47,0:01:56.44,Default,,0000,0000,0000,,the positive input, and the output.
Dialogue: 0,0:01:56.44,0:01:59.24,Default,,0000,0000,0000,,You can see there are a series of transistors that are hooked up in
Dialogue: 0,0:01:59.24,0:02:03.35,Default,,0000,0000,0000,,this fashion that make the operational amplifier do what we want it to do.
Dialogue: 0,0:02:03.35,0:02:09.44,Default,,0000,0000,0000,,However, these transistors only work if they are connected to Vcc and minus Vcc.
Dialogue: 0,0:02:09.44,0:02:12.56,Default,,0000,0000,0000,,This is why the amplifier is an active device.
Dialogue: 0,0:02:12.56,0:02:16.96,Default,,0000,0000,0000,,Without this power, it does not act like an operational amplifier.
Dialogue: 0,0:02:16.96,0:02:19.19,Default,,0000,0000,0000,,Okay. So, now that we know that we have
Dialogue: 0,0:02:19.19,0:02:21.88,Default,,0000,0000,0000,,this triangle that represents an operational amplifier,
Dialogue: 0,0:02:21.88,0:02:23.22,Default,,0000,0000,0000,,if we want to hook it up,
Dialogue: 0,0:02:23.22,0:02:26.92,Default,,0000,0000,0000,,we're going to hook it up this way with plus and minus Vcc.
Dialogue: 0,0:02:26.92,0:02:28.79,Default,,0000,0000,0000,,But that's complicated to draw,
Dialogue: 0,0:02:28.79,0:02:33.41,Default,,0000,0000,0000,,and we really just remember that we have Vcc and we normally draw it this way.
Dialogue: 0,0:02:33.41,0:02:36.47,Default,,0000,0000,0000,,Another thing to remember is all of those transistors in there,
Dialogue: 0,0:02:36.47,0:02:40.44,Default,,0000,0000,0000,,they divide the frontend and the backend of the amplifier in effect.
Dialogue: 0,0:02:40.44,0:02:45.64,Default,,0000,0000,0000,,So, even though we might have a positive current here and a negative current there,
Dialogue: 0,0:02:45.64,0:02:48.94,Default,,0000,0000,0000,,because there are all of those transistors and the power supply,
Dialogue: 0,0:02:48.94,0:02:52.69,Default,,0000,0000,0000,,sometimes current gets added and sometimes current gets subtracted.
Dialogue: 0,0:02:52.69,0:02:54.72,Default,,0000,0000,0000,,We don't really know in advance.
Dialogue: 0,0:02:54.72,0:02:57.72,Default,,0000,0000,0000,,So, all we can say is that i zero, the output current,
Dialogue: 0,0:02:57.72,0:03:02.19,Default,,0000,0000,0000,,is not equal to the sum of the two input currents.
Dialogue: 0,0:03:02.93,0:03:05.80,Default,,0000,0000,0000,,Now, let's talk about Op Amp Gain.
Dialogue: 0,0:03:05.80,0:03:08.46,Default,,0000,0000,0000,,Op Amp Gain is intrinsic to the amplifier.
Dialogue: 0,0:03:08.46,0:03:11.09,Default,,0000,0000,0000,,It's controlled by how the transistors are put together.
Dialogue: 0,0:03:11.09,0:03:13.07,Default,,0000,0000,0000,,It's sometimes also called Open Loop Gain.
Dialogue: 0,0:03:13.07,0:03:15.88,Default,,0000,0000,0000,,Op Amps have a very high voltage gain
Dialogue: 0,0:03:15.88,0:03:19.31,Default,,0000,0000,0000,,typically on the order of 10 to the fourth to 10 to the eighth.
Dialogue: 0,0:03:19.31,0:03:21.32,Default,,0000,0000,0000,,They also have a linear response.
Dialogue: 0,0:03:21.32,0:03:27.74,Default,,0000,0000,0000,,So, the gain tells us that the output is equal to the gain times the input.
Dialogue: 0,0:03:27.74,0:03:30.05,Default,,0000,0000,0000,,In this case, the input is considered to be
Dialogue: 0,0:03:30.05,0:03:33.44,Default,,0000,0000,0000,,the difference between the positive and negative inputs of the Op Amp.
Dialogue: 0,0:03:33.44,0:03:37.04,Default,,0000,0000,0000,,So, if we have a voltage gain of 10 to the fourth,
Dialogue: 0,0:03:37.04,0:03:38.79,Default,,0000,0000,0000,,it would be linear of something like this,
Dialogue: 0,0:03:38.79,0:03:41.99,Default,,0000,0000,0000,,a voltage gain of 10 to the eighth would be steeper.
Dialogue: 0,0:03:41.99,0:03:44.07,Default,,0000,0000,0000,,Because we have Vcc,
Dialogue: 0,0:03:44.07,0:03:46.08,Default,,0000,0000,0000,,remember I said follow Vcc,
Dialogue: 0,0:03:46.08,0:03:49.50,Default,,0000,0000,0000,,it limits the actual output of our operational amplifier.
Dialogue: 0,0:03:49.50,0:03:51.86,Default,,0000,0000,0000,,We cannot put out more power or
Dialogue: 0,0:03:51.86,0:03:54.99,Default,,0000,0000,0000,,more voltage than we were able to put in to our amplifier.
Dialogue: 0,0:03:54.99,0:03:59.02,Default,,0000,0000,0000,,So, our amplifier circuit always saturates at plus Vcc
Dialogue: 0,0:03:59.02,0:04:04.08,Default,,0000,0000,0000,,and minus Vcc because of the power supply limitations.
Dialogue: 0,0:04:04.70,0:04:10.38,Default,,0000,0000,0000,,Let's see how that saturation can help the operational amplifier acts like a switch.
Dialogue: 0,0:04:10.38,0:04:13.78,Default,,0000,0000,0000,,Here is a circuit where we hooked up our amplifier and we want to
Dialogue: 0,0:04:13.78,0:04:17.58,Default,,0000,0000,0000,,be able to control if a red or a green LED turns on.
Dialogue: 0,0:04:17.58,0:04:23.42,Default,,0000,0000,0000,,So, we've connected our negative input right here to ground along with our two LEDs.
Dialogue: 0,0:04:23.42,0:04:26.35,Default,,0000,0000,0000,,Remember that the LED only turns on if current
Dialogue: 0,0:04:26.35,0:04:29.69,Default,,0000,0000,0000,,goes through it in this direction because of its diode nature.
Dialogue: 0,0:04:29.69,0:04:32.80,Default,,0000,0000,0000,,So, let's see what happens if we put a voltage,
Dialogue: 0,0:04:32.80,0:04:35.38,Default,,0000,0000,0000,,let's say, two volts, on our positive input.
Dialogue: 0,0:04:35.38,0:04:41.20,Default,,0000,0000,0000,,In that case, remember that Vp minus Vn is the thing that we're interested in,
Dialogue: 0,0:04:41.20,0:04:43.84,Default,,0000,0000,0000,,and that's two minus zero in this case.
Dialogue: 0,0:04:43.84,0:04:46.48,Default,,0000,0000,0000,,So, it's two volts, two volts minus zero volts.
Dialogue: 0,0:04:46.48,0:04:49.94,Default,,0000,0000,0000,,Multiply that by a very large value, let's say, 10,000.
Dialogue: 0,0:04:49.94,0:04:54.34,Default,,0000,0000,0000,,So, our output voltage tries to go up to be 20,000.
Dialogue: 0,0:04:54.34,0:04:58.14,Default,,0000,0000,0000,,Well, the limitation of the power supply limits that,
Dialogue: 0,0:04:58.14,0:04:59.37,Default,,0000,0000,0000,,let's say, to 12 volts.
Dialogue: 0,0:04:59.37,0:05:01.80,Default,,0000,0000,0000,,So, the output voltage right here is 12.
Dialogue: 0,0:05:01.80,0:05:06.20,Default,,0000,0000,0000,,Aha! But that's very good because that gives us a twelve volt difference across
Dialogue: 0,0:05:06.20,0:05:11.08,Default,,0000,0000,0000,,our LED that drives the current in this direction and turns on our red LED.
Dialogue: 0,0:05:11.08,0:05:14.45,Default,,0000,0000,0000,,The green LED is trying to drive current in this direction,
Dialogue: 0,0:05:14.45,0:05:19.14,Default,,0000,0000,0000,,but the LED acts like an open circuit because of a diode and it doesn't turn on.
Dialogue: 0,0:05:19.14,0:05:23.30,Default,,0000,0000,0000,,Now, let's see what happens if we put a negative voltage on Vp instead.
Dialogue: 0,0:05:23.30,0:05:27.11,Default,,0000,0000,0000,,Then, Vp minus Vn is going to be minus two volts.
Dialogue: 0,0:05:27.11,0:05:31.82,Default,,0000,0000,0000,,Multiply that by a very large number and it tries to go to, say, minus 20,000.
Dialogue: 0,0:05:31.82,0:05:34.44,Default,,0000,0000,0000,,But it's limited by the power supply voltage,
Dialogue: 0,0:05:34.44,0:05:36.29,Default,,0000,0000,0000,,so it goes to minus 12.
Dialogue: 0,0:05:36.29,0:05:39.47,Default,,0000,0000,0000,,Well, if it's trying to drive current through here,
Dialogue: 0,0:05:39.47,0:05:41.63,Default,,0000,0000,0000,,the red LED acts like
Dialogue: 0,0:05:41.63,0:05:45.30,Default,,0000,0000,0000,,a diode and doesn't allow current to go through. It doesn't turn on.
Dialogue: 0,0:05:45.30,0:05:48.26,Default,,0000,0000,0000,,Oops! Sorry, I'm not trying to drive current in that direction.
Dialogue: 0,0:05:48.26,0:05:50.27,Default,,0000,0000,0000,,I'm actually trying to pull current in that direction.
Dialogue: 0,0:05:50.27,0:05:52.16,Default,,0000,0000,0000,,The green LED, however,
Dialogue: 0,0:05:52.16,0:05:56.94,Default,,0000,0000,0000,,does turn on because here goes the direction of the current for the green LED.
Dialogue: 0,0:05:56.94,0:05:59.74,Default,,0000,0000,0000,,So, if we make Vp positive,
Dialogue: 0,0:05:59.74,0:06:01.76,Default,,0000,0000,0000,,we can turn on the red LED,
Dialogue: 0,0:06:01.76,0:06:03.17,Default,,0000,0000,0000,,and if we make it negative,
Dialogue: 0,0:06:03.17,0:06:05.08,Default,,0000,0000,0000,,we can turn on the green LED.
Dialogue: 0,0:06:05.08,0:06:10.14,Default,,0000,0000,0000,,This allows us to have a circuit that acts like a switch for our two LEDs.
Dialogue: 0,0:06:10.64,0:06:14.39,Default,,0000,0000,0000,,Now, let's talk about Op Amp Gain versus Circuit Gain.
Dialogue: 0,0:06:14.39,0:06:18.32,Default,,0000,0000,0000,,The op-amp gain is always high and it's intrinsic to the inside of the op-amp.
Dialogue: 0,0:06:18.32,0:06:21.06,Default,,0000,0000,0000,,It's also called the open-loop gain or the voltage gain.
Dialogue: 0,0:06:21.06,0:06:25.79,Default,,0000,0000,0000,,Gain is typically defined as the output divided by the input, and in this case,
Dialogue: 0,0:06:25.79,0:06:31.04,Default,,0000,0000,0000,,the input is considered to be the difference of the two inputs.
Dialogue: 0,0:06:31.04,0:06:32.86,Default,,0000,0000,0000,,Circuit gain, on the other hand,
Dialogue: 0,0:06:32.86,0:06:36.91,Default,,0000,0000,0000,,we may have an op-amp in here and connect it up in this fashion.
Dialogue: 0,0:06:36.91,0:06:38.60,Default,,0000,0000,0000,,Connect the output right there.
Dialogue: 0,0:06:38.60,0:06:41.51,Default,,0000,0000,0000,,The circuit gain tells us about the op-amp that has
Dialogue: 0,0:06:41.51,0:06:44.96,Default,,0000,0000,0000,,its gain A for all of the other resistors around it also.
Dialogue: 0,0:06:44.96,0:06:47.72,Default,,0000,0000,0000,,Depending on how we connect up our op-amp circuit,
Dialogue: 0,0:06:47.72,0:06:49.62,Default,,0000,0000,0000,,gain can be large or small.
Dialogue: 0,0:06:49.62,0:06:52.72,Default,,0000,0000,0000,,If it's large, larger than one, that's amplification.
Dialogue: 0,0:06:52.72,0:06:54.68,Default,,0000,0000,0000,,Less than one is deamplification.
Dialogue: 0,0:06:54.68,0:06:56.21,Default,,0000,0000,0000,,If the gain is negative,
Dialogue: 0,0:06:56.21,0:06:57.35,Default,,0000,0000,0000,,we call it inverting,
Dialogue: 0,0:06:57.35,0:06:58.54,Default,,0000,0000,0000,,and if the gain is positive,
Dialogue: 0,0:06:58.54,0:07:00.78,Default,,0000,0000,0000,,we call it non-inverting.
Dialogue: 0,0:07:01.16,0:07:04.78,Default,,0000,0000,0000,,Here's a non-ideal op-amp equivalent circuit.
Dialogue: 0,0:07:04.78,0:07:09.24,Default,,0000,0000,0000,,Notice that right here is a dependent voltage source that depends on
Dialogue: 0,0:07:09.24,0:07:14.00,Default,,0000,0000,0000,,the gain and the difference between the two input voltages.
Dialogue: 0,0:07:14.00,0:07:16.42,Default,,0000,0000,0000,,So, for a non-ideal op-amp,
Dialogue: 0,0:07:16.42,0:07:19.04,Default,,0000,0000,0000,,we recognize that Ri is very large.
Dialogue: 0,0:07:19.04,0:07:22.26,Default,,0000,0000,0000,,It's typically on the order of 10 to six to the 10 to the 13th.
Dialogue: 0,0:07:22.26,0:07:25.12,Default,,0000,0000,0000,,A is very large, 10 to the fourth to 10 to the eighth.
Dialogue: 0,0:07:25.12,0:07:27.22,Default,,0000,0000,0000,,The output resistance is very small,
Dialogue: 0,0:07:27.22,0:07:30.35,Default,,0000,0000,0000,,one to a 100, and the supply voltage right here,
Dialogue: 0,0:07:30.35,0:07:33.00,Default,,0000,0000,0000,,Vcc and minus Vcc,
Dialogue: 0,0:07:33.00,0:07:34.54,Default,,0000,0000,0000,,and sometimes they draw it that way too,
Dialogue: 0,0:07:34.54,0:07:36.58,Default,,0000,0000,0000,,is five to 24 volts.
Dialogue: 0,0:07:36.58,0:07:39.60,Default,,0000,0000,0000,,Now, for an ideal op-amp, it's going to be different.
Dialogue: 0,0:07:39.60,0:07:40.92,Default,,0000,0000,0000,,For an ideal op-amp,
Dialogue: 0,0:07:40.92,0:07:46.22,Default,,0000,0000,0000,,we're going to assume that the input resistance is so large that it can be eliminated.
Dialogue: 0,0:07:46.22,0:07:50.02,Default,,0000,0000,0000,,In that case, it's like having an open circuit right there at the input.
Dialogue: 0,0:07:50.02,0:07:56.59,Default,,0000,0000,0000,,We can consider that the gain is so large that we can say Vp is equal to Vn,
Dialogue: 0,0:07:56.59,0:07:59.04,Default,,0000,0000,0000,,and we can say that the output resistance is so
Dialogue: 0,0:07:59.04,0:08:02.50,Default,,0000,0000,0000,,small that we can neglect it and consider it just as a wire.
Dialogue: 0,0:08:02.50,0:08:06.00,Default,,0000,0000,0000,,The implications of this are that for an ideal op-amp,
Dialogue: 0,0:08:06.00,0:08:08.42,Default,,0000,0000,0000,,we can say that Vp equal Vn,
Dialogue: 0,0:08:08.42,0:08:13.38,Default,,0000,0000,0000,,and we can say that no current goes into the either input of this op-amp.
Dialogue: 0,0:08:13.38,0:08:16.28,Default,,0000,0000,0000,,Sometimes it's also useful to remember,
Dialogue: 0,0:08:16.28,0:08:19.42,Default,,0000,0000,0000,,right here, that R out is equal to zero.
Dialogue: 0,0:08:19.42,0:08:21.90,Default,,0000,0000,0000,,You'll see why we need that in a minute.
Dialogue: 0,0:08:22.25,0:08:25.73,Default,,0000,0000,0000,,Okay. So, the circuit gain depends on the circuit.
Dialogue: 0,0:08:25.73,0:08:26.96,Default,,0000,0000,0000,,In this red box,
Dialogue: 0,0:08:26.96,0:08:29.54,Default,,0000,0000,0000,,I have an example of a non-inverting amplifier.
Dialogue: 0,0:08:29.54,0:08:34.53,Default,,0000,0000,0000,,Trust me for now that the output is going to be equal to
Dialogue: 0,0:08:34.53,0:08:41.93,Default,,0000,0000,0000,,R1 plus R2 over R2 times Vs for this particular op-amp circuit.
Dialogue: 0,0:08:41.93,0:08:44.22,Default,,0000,0000,0000,,In that case, we call this the gain,
Dialogue: 0,0:08:44.22,0:08:47.33,Default,,0000,0000,0000,,G, and we can see that it's always positive.
Dialogue: 0,0:08:47.33,0:08:49.40,Default,,0000,0000,0000,,That's because resistors are always positive.
Dialogue: 0,0:08:49.40,0:08:52.75,Default,,0000,0000,0000,,So, it's non-inverting, it's always positive.
Dialogue: 0,0:08:52.75,0:08:58.76,Default,,0000,0000,0000,,Now, let's see if this non-inverting amplifier can go to any value we want.
Dialogue: 0,0:08:58.76,0:09:04.19,Default,,0000,0000,0000,,No. Because we have this Vcc and minus Vcc,
Dialogue: 0,0:09:04.19,0:09:07.74,Default,,0000,0000,0000,,so we know that the gain has to be limited by Vcc.
Dialogue: 0,0:09:07.74,0:09:11.20,Default,,0000,0000,0000,,So, the op-amp gain is intrinsic to the amplifier,
Dialogue: 0,0:09:11.20,0:09:16.23,Default,,0000,0000,0000,,but the circuit gain depends on all of the resistors that we put around it.
Dialogue: 0,0:09:16.31,0:09:21.43,Default,,0000,0000,0000,,So, in summary, here are the important things to remember about an op-amp.
Dialogue: 0,0:09:21.43,0:09:23.71,Default,,0000,0000,0000,,Here is a model of a non-ideal op-amp.
Dialogue: 0,0:09:23.71,0:09:25.51,Default,,0000,0000,0000,,We're actually not going to use that very much in
Dialogue: 0,0:09:25.51,0:09:28.06,Default,,0000,0000,0000,,this class but I want you to remember these parameters.
Dialogue: 0,0:09:28.06,0:09:31.94,Default,,0000,0000,0000,,We are going to use the ideal op-amp model extensively.
Dialogue: 0,0:09:31.94,0:09:33.79,Default,,0000,0000,0000,,Remember that the important features of
Dialogue: 0,0:09:33.79,0:09:37.39,Default,,0000,0000,0000,,the non-ideal op-amp are that the negative and positive input are equal,
Dialogue: 0,0:09:37.39,0:09:39.82,Default,,0000,0000,0000,,that no current goes into either input,
Dialogue: 0,0:09:39.82,0:09:43.76,Default,,0000,0000,0000,,and that the output is not the sum of the two input currents.
Dialogue: 0,0:09:43.76,0:09:47.54,Default,,0000,0000,0000,,Remember also that we have Vcc and minus
Dialogue: 0,0:09:47.54,0:09:52.72,Default,,0000,0000,0000,,Vcc that limit the output voltage of our operational amplifier.
Dialogue: 0,0:09:52.72,0:09:55.75,Default,,0000,0000,0000,,Now, I hope you're wondering where the picture was on the front.
Dialogue: 0,0:09:55.75,0:10:00.13,Default,,0000,0000,0000,,That is the Wild Horse Corral on Antelope Island.