[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.00,0:00:03.98,Default,,0000,0000,0000,,>> Hello, this is Dr. Cynthia Furse at the University of Utah,
Dialogue: 0,0:00:03.98,0:00:08.08,Default,,0000,0000,0000,,and today we're going to talk about designing op-amp systems.
Dialogue: 0,0:00:08.18,0:00:12.10,Default,,0000,0000,0000,,Electrical engineering is about what can you do to a voltage.
Dialogue: 0,0:00:12.10,0:00:14.55,Default,,0000,0000,0000,,A lot of times we like to add voltages together,
Dialogue: 0,0:00:14.55,0:00:16.08,Default,,0000,0000,0000,,we like to add constants to them,
Dialogue: 0,0:00:16.08,0:00:18.40,Default,,0000,0000,0000,,we like to multiply them by various values,
Dialogue: 0,0:00:18.40,0:00:20.58,Default,,0000,0000,0000,,in order to make the circuit do what we want.
Dialogue: 0,0:00:20.58,0:00:22.77,Default,,0000,0000,0000,,Let's suppose that we want our output to be
Dialogue: 0,0:00:22.77,0:00:26.90,Default,,0000,0000,0000,,a linear combination of a constant and our input voltage like this.
Dialogue: 0,0:00:26.90,0:00:30.76,Default,,0000,0000,0000,,This math might look like 2 times v_2
Dialogue: 0,0:00:30.76,0:00:36.44,Default,,0000,0000,0000,,plus minus 2 times some voltage, something like this.
Dialogue: 0,0:00:36.44,0:00:39.42,Default,,0000,0000,0000,,So, how do we design that system?
Dialogue: 0,0:00:39.42,0:00:41.28,Default,,0000,0000,0000,,Whenever we are designing systems,
Dialogue: 0,0:00:41.28,0:00:44.10,Default,,0000,0000,0000,,we like to break them down into individual components.
Dialogue: 0,0:00:44.10,0:00:46.19,Default,,0000,0000,0000,,For example, we wouldn't really want to have to
Dialogue: 0,0:00:46.19,0:00:48.23,Default,,0000,0000,0000,,consider the power plant, the breaker box,
Dialogue: 0,0:00:48.23,0:00:50.45,Default,,0000,0000,0000,,and all the outlets in your house individually
Dialogue: 0,0:00:50.45,0:00:52.96,Default,,0000,0000,0000,,every time we wanted to design a lamp or a fan.
Dialogue: 0,0:00:52.96,0:00:56.51,Default,,0000,0000,0000,,We'll take that entire distribution system and we'll model that as
Dialogue: 0,0:00:56.51,0:01:00.34,Default,,0000,0000,0000,,a single source voltage with its source resistance,
Dialogue: 0,0:01:00.34,0:01:03.44,Default,,0000,0000,0000,,and then we might consider the lamp and the fan in
Dialogue: 0,0:01:03.44,0:01:07.42,Default,,0000,0000,0000,,parallel like so and we design each of them independently.
Dialogue: 0,0:01:07.42,0:01:11.89,Default,,0000,0000,0000,,In order to design individual blocks like this independently,
Dialogue: 0,0:01:11.89,0:01:13.72,Default,,0000,0000,0000,,there's a very important concept,
Dialogue: 0,0:01:13.72,0:01:17.22,Default,,0000,0000,0000,,that concept is input and output resistances.
Dialogue: 0,0:01:17.22,0:01:19.03,Default,,0000,0000,0000,,Let's suppose that we have a circuit,
Dialogue: 0,0:01:19.03,0:01:20.96,Default,,0000,0000,0000,,any circuit, that's this black box.
Dialogue: 0,0:01:20.96,0:01:22.84,Default,,0000,0000,0000,,If we look in,
Dialogue: 0,0:01:22.84,0:01:26.82,Default,,0000,0000,0000,,that's going to give us the input resistance and if we look into the output side,
Dialogue: 0,0:01:26.82,0:01:29.04,Default,,0000,0000,0000,,that's going to give us the output resistance.
Dialogue: 0,0:01:29.04,0:01:32.54,Default,,0000,0000,0000,,A lot of times in the book and elsewhere, you will see Z.
Dialogue: 0,0:01:32.54,0:01:35.50,Default,,0000,0000,0000,,That is impedance as opposed to resistance,
Dialogue: 0,0:01:35.50,0:01:36.96,Default,,0000,0000,0000,,it's a complex resistance,
Dialogue: 0,0:01:36.96,0:01:41.02,Default,,0000,0000,0000,,so just consider that to be the same as resistance for this case.
Dialogue: 0,0:01:41.02,0:01:43.19,Default,,0000,0000,0000,,If we are looking in to either side,
Dialogue: 0,0:01:43.19,0:01:44.66,Default,,0000,0000,0000,,that's the same thing as using
Dialogue: 0,0:01:44.66,0:01:49.04,Default,,0000,0000,0000,,the Thevenin resistances and you calculate it in the same way.
Dialogue: 0,0:01:49.04,0:01:54.30,Default,,0000,0000,0000,,Now, let's consider the basics of input and output resistance.
Dialogue: 0,0:01:54.30,0:01:58.90,Default,,0000,0000,0000,,Here is an example of an equivalent circuit that we would be very likely to build,
Dialogue: 0,0:01:58.90,0:02:01.94,Default,,0000,0000,0000,,we would have a source right here with its input equivalent,
Dialogue: 0,0:02:01.94,0:02:06.10,Default,,0000,0000,0000,,connected onto some amplifier circuit driving some load.
Dialogue: 0,0:02:06.10,0:02:08.66,Default,,0000,0000,0000,,If we wanted to figure out how these we're working,
Dialogue: 0,0:02:08.66,0:02:12.54,Default,,0000,0000,0000,,we would consider the input and output impedances of each of our blocks.
Dialogue: 0,0:02:12.54,0:02:15.14,Default,,0000,0000,0000,,Here for example is our input circuit.
Dialogue: 0,0:02:15.14,0:02:16.76,Default,,0000,0000,0000,,Now even though it's called an input circuit,
Dialogue: 0,0:02:16.76,0:02:19.30,Default,,0000,0000,0000,,you notice it doesn't really have an input resistance,
Dialogue: 0,0:02:19.30,0:02:21.11,Default,,0000,0000,0000,,it only has an output resistance.
Dialogue: 0,0:02:21.11,0:02:23.10,Default,,0000,0000,0000,,The output resistance looking in,
Dialogue: 0,0:02:23.10,0:02:24.53,Default,,0000,0000,0000,,resistance would be here.
Dialogue: 0,0:02:24.53,0:02:29.65,Default,,0000,0000,0000,,We would short out our voltage source and the only resistance there would be Zs.
Dialogue: 0,0:02:29.65,0:02:32.22,Default,,0000,0000,0000,,Now, let's consider the amplifier circuit.
Dialogue: 0,0:02:32.22,0:02:33.93,Default,,0000,0000,0000,,Looking into the amplifier,
Dialogue: 0,0:02:33.93,0:02:39.88,Default,,0000,0000,0000,,remember the fact that when we have a op-amp,
Dialogue: 0,0:02:39.88,0:02:44.24,Default,,0000,0000,0000,,the input resistance is approximately infinity, it's very high.
Dialogue: 0,0:02:44.24,0:02:46.22,Default,,0000,0000,0000,,So, when we look into an op-amp,
Dialogue: 0,0:02:46.22,0:02:49.50,Default,,0000,0000,0000,,Zin is equal to infinity.
Dialogue: 0,0:02:49.50,0:02:51.30,Default,,0000,0000,0000,,Let's consider the Zout,
Dialogue: 0,0:02:51.30,0:02:53.18,Default,,0000,0000,0000,,remember that when we have an op-amp,
Dialogue: 0,0:02:53.18,0:02:55.67,Default,,0000,0000,0000,,we have an output resistance Rout,
Dialogue: 0,0:02:55.67,0:02:58.90,Default,,0000,0000,0000,,so our Zout is approximately zero.
Dialogue: 0,0:02:58.90,0:03:00.98,Default,,0000,0000,0000,,Then let's look into our load,
Dialogue: 0,0:03:00.98,0:03:04.60,Default,,0000,0000,0000,,Zin, is ZL like this.
Dialogue: 0,0:03:04.60,0:03:08.87,Default,,0000,0000,0000,,So, we now have looked at our input and output resistances or
Dialogue: 0,0:03:08.87,0:03:12.53,Default,,0000,0000,0000,,impedances for each one of the elements in our circuit,
Dialogue: 0,0:03:12.53,0:03:14.78,Default,,0000,0000,0000,,and input impedance is looking into the input
Dialogue: 0,0:03:14.78,0:03:18.30,Default,,0000,0000,0000,,and an output impedance is looking in to the output.
Dialogue: 0,0:03:18.32,0:03:20.70,Default,,0000,0000,0000,,Now, let's go back to our circuit,
Dialogue: 0,0:03:20.70,0:03:22.85,Default,,0000,0000,0000,,let's take a look again at the circuit and
Dialogue: 0,0:03:22.85,0:03:25.66,Default,,0000,0000,0000,,decide what our input and output resistances are.
Dialogue: 0,0:03:25.66,0:03:27.76,Default,,0000,0000,0000,,Just like in my previous case,
Dialogue: 0,0:03:27.76,0:03:31.99,Default,,0000,0000,0000,,the output resistance of the source block is simply Zs.
Dialogue: 0,0:03:31.99,0:03:35.11,Default,,0000,0000,0000,,Now, let's look at this fan block right here.
Dialogue: 0,0:03:35.11,0:03:38.63,Default,,0000,0000,0000,,The input resistance right there would be
Dialogue: 0,0:03:38.63,0:03:42.52,Default,,0000,0000,0000,,Rfan and the output resistance would also be Rfan.
Dialogue: 0,0:03:42.52,0:03:45.42,Default,,0000,0000,0000,,Now, here's our last load right here, that's the lamp,
Dialogue: 0,0:03:45.42,0:03:50.07,Default,,0000,0000,0000,,and looking into the lamp that gives me an input resistance of Rlamp.
Dialogue: 0,0:03:50.60,0:03:53.66,Default,,0000,0000,0000,,Okay. Now, let's consider how we connect
Dialogue: 0,0:03:53.66,0:03:56.40,Default,,0000,0000,0000,,circuits that have different input and output resistances.
Dialogue: 0,0:03:56.40,0:03:58.67,Default,,0000,0000,0000,,If we wanted to connect circuit number one,
Dialogue: 0,0:03:58.67,0:04:02.09,Default,,0000,0000,0000,,which has its input and output resistances right here
Dialogue: 0,0:04:02.09,0:04:06.70,Default,,0000,0000,0000,,and we wanted to consider circuit two with its input and output resistances,
Dialogue: 0,0:04:06.70,0:04:09.32,Default,,0000,0000,0000,,let's see what would happen if we hook them together.
Dialogue: 0,0:04:09.32,0:04:13.22,Default,,0000,0000,0000,,Here's an example where I'll just be connecting a source impedance to a load.
Dialogue: 0,0:04:13.22,0:04:14.60,Default,,0000,0000,0000,,So, if I look in here,
Dialogue: 0,0:04:14.60,0:04:16.95,Default,,0000,0000,0000,,the output resistance is Zs,
Dialogue: 0,0:04:16.95,0:04:18.28,Default,,0000,0000,0000,,and if I look in here,
Dialogue: 0,0:04:18.28,0:04:20.76,Default,,0000,0000,0000,,the input resistance is ZL.
Dialogue: 0,0:04:20.76,0:04:24.06,Default,,0000,0000,0000,,Now, imagine what would happen if I hook them together.
Dialogue: 0,0:04:24.06,0:04:28.34,Default,,0000,0000,0000,,The output voltage that I might want like here would be Vout1,
Dialogue: 0,0:04:28.34,0:04:33.02,Default,,0000,0000,0000,,and let's suppose that I wanted to drive this circuit with the source Vs,
Dialogue: 0,0:04:33.02,0:04:34.92,Default,,0000,0000,0000,,and I'm going to drive this,
Dialogue: 0,0:04:34.92,0:04:37.10,Default,,0000,0000,0000,,maybe a mixer input impedance or something,
Dialogue: 0,0:04:37.10,0:04:39.63,Default,,0000,0000,0000,,and I connect them up like this.
Dialogue: 0,0:04:39.82,0:04:43.82,Default,,0000,0000,0000,,What does that give me? That is a voltage divider,
Dialogue: 0,0:04:43.82,0:04:45.90,Default,,0000,0000,0000,,we know something about voltage dividers.
Dialogue: 0,0:04:45.90,0:04:51.84,Default,,0000,0000,0000,,We know that Vout1 is equal to
Dialogue: 0,0:04:51.84,0:04:58.86,Default,,0000,0000,0000,,V_s times ZL over ZL plus Zs because that's the voltage divider.
Dialogue: 0,0:04:58.86,0:05:04.76,Default,,0000,0000,0000,,Now, if ZL is small compared to Zs,
Dialogue: 0,0:05:04.76,0:05:07.79,Default,,0000,0000,0000,,we're not going to get the voltage that we wanted at all.
Dialogue: 0,0:05:07.79,0:05:09.29,Default,,0000,0000,0000,,The only time that we are going to get
Dialogue: 0,0:05:09.29,0:05:11.62,Default,,0000,0000,0000,,the voltage that we want it to be deriving it with,
Dialogue: 0,0:05:11.62,0:05:15.22,Default,,0000,0000,0000,,is if ZL is very large compared to the Zs.
Dialogue: 0,0:05:15.22,0:05:24.43,Default,,0000,0000,0000,,So, ZL much greater than Zs will give us the result that Vout1 is equal to Vs.
Dialogue: 0,0:05:25.40,0:05:29.07,Default,,0000,0000,0000,,So, this is a really important feature.
Dialogue: 0,0:05:29.07,0:05:34.40,Default,,0000,0000,0000,,When we are designing circuits and I showed it graphically here,
Dialogue: 0,0:05:34.40,0:05:39.68,Default,,0000,0000,0000,,if the input resistance of the second circuit is very large,
Dialogue: 0,0:05:39.68,0:05:42.44,Default,,0000,0000,0000,,Zin2 is much greater than Zin1,
Dialogue: 0,0:05:42.44,0:05:46.29,Default,,0000,0000,0000,,then we can consider these two circuits to be independent.
Dialogue: 0,0:05:46.29,0:05:47.93,Default,,0000,0000,0000,,We can design them separately.
Dialogue: 0,0:05:47.93,0:05:51.95,Default,,0000,0000,0000,,Any other case we can't do that and we'd have to analyze the entire circuit together.
Dialogue: 0,0:05:51.95,0:05:57.66,Default,,0000,0000,0000,,So, we like it very much if the input impedance of a circuit is very high.
Dialogue: 0,0:05:58.51,0:06:01.48,Default,,0000,0000,0000,,Now, in the event that doesn't happen,
Dialogue: 0,0:06:01.48,0:06:04.50,Default,,0000,0000,0000,,what we're going to do is put something called a buffer in the circuit.
Dialogue: 0,0:06:04.50,0:06:07.34,Default,,0000,0000,0000,,A buffer multiplies the incoming voltage by one,
Dialogue: 0,0:06:07.34,0:06:11.87,Default,,0000,0000,0000,,but it has this magic thing that the input impedance of the buffer is always large,
Dialogue: 0,0:06:11.87,0:06:14.88,Default,,0000,0000,0000,,and the output impedance of the buffer is always small.
Dialogue: 0,0:06:14.88,0:06:17.31,Default,,0000,0000,0000,,That makes us so that we can always put a buffer in here,
Dialogue: 0,0:06:17.31,0:06:19.67,Default,,0000,0000,0000,,we can always design our block separately.
Dialogue: 0,0:06:19.67,0:06:21.89,Default,,0000,0000,0000,,So, the buffer allows us to design
Dialogue: 0,0:06:21.89,0:06:26.50,Default,,0000,0000,0000,,our input equivalent circuit separate from our load equivalent circuit.
Dialogue: 0,0:06:26.50,0:06:31.38,Default,,0000,0000,0000,,Now, another word that we often use for this is loading.
Dialogue: 0,0:06:32.26,0:06:40.60,Default,,0000,0000,0000,,So, loading occurs when ZL is approximately equal to or less than Zs.
Dialogue: 0,0:06:40.60,0:06:44.49,Default,,0000,0000,0000,,In this case, loading happens to make it so that
Dialogue: 0,0:06:44.49,0:06:51.40,Default,,0000,0000,0000,,the output voltage that we want isn't the same as the output voltage that we input,
Dialogue: 0,0:06:51.40,0:06:54.48,Default,,0000,0000,0000,,so loading is a bad thing.
Dialogue: 0,0:06:54.89,0:06:59.62,Default,,0000,0000,0000,,Now, let's review again connecting input and output resistances.
Dialogue: 0,0:06:59.62,0:07:04.93,Default,,0000,0000,0000,,If I have a large input resistance and I connect it to a small output resistance,
Dialogue: 0,0:07:04.93,0:07:07.21,Default,,0000,0000,0000,,I can design my circuit without a buffer,
Dialogue: 0,0:07:07.21,0:07:13.06,Default,,0000,0000,0000,,I can individually designed circuit one and circuit two as if they were not interrelated,
Dialogue: 0,0:07:13.06,0:07:16.39,Default,,0000,0000,0000,,any other time I have to analyze the entire circuit.
Dialogue: 0,0:07:16.39,0:07:21.20,Default,,0000,0000,0000,,In the event that I didn't have Zin2 much greater than Zout2,
Dialogue: 0,0:07:21.20,0:07:24.27,Default,,0000,0000,0000,,what I would do is put a buffer in that case,
Dialogue: 0,0:07:24.27,0:07:26.56,Default,,0000,0000,0000,,and that is going to make it so that I always have
Dialogue: 0,0:07:26.56,0:07:30.01,Default,,0000,0000,0000,,a large input impedance and a small output impedance.
Dialogue: 0,0:07:30.01,0:07:33.40,Default,,0000,0000,0000,,So, these are our two design criteria that allow us
Dialogue: 0,0:07:33.40,0:07:37.82,Default,,0000,0000,0000,,to design individual elements of a more complex circuit.