[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.00,0:00:04.76,Default,,0000,0000,0000,,>> Now, let's do an example with our non-inverting operational amplifier.
Dialogue: 0,0:00:04.76,0:00:06.96,Default,,0000,0000,0000,,So, here comes an example.
Dialogue: 0,0:00:06.96,0:00:09.75,Default,,0000,0000,0000,,Let's start with our non-ideal model.
Dialogue: 0,0:00:09.75,0:00:12.12,Default,,0000,0000,0000,,This is the non-ideal model and let's connect it
Dialogue: 0,0:00:12.12,0:00:15.20,Default,,0000,0000,0000,,up in the non-inverting amplifier case that I showed you.
Dialogue: 0,0:00:15.20,0:00:18.12,Default,,0000,0000,0000,,So, we want to define our gain.
Dialogue: 0,0:00:18.12,0:00:20.34,Default,,0000,0000,0000,,This way we want to find the circuit gain of
Dialogue: 0,0:00:20.34,0:00:25.30,Default,,0000,0000,0000,,this amplifier circuit and the gain is defined as the output divided by the input.
Dialogue: 0,0:00:25.30,0:00:28.02,Default,,0000,0000,0000,,So, let's use some,
Dialogue: 0,0:00:28.02,0:00:29.34,Default,,0000,0000,0000,,the node-voltage method.
Dialogue: 0,0:00:29.34,0:00:32.10,Default,,0000,0000,0000,,Let's first consider this node A.
Dialogue: 0,0:00:32.10,0:00:35.50,Default,,0000,0000,0000,,So, let's consider our currents that are going out this way.
Dialogue: 0,0:00:35.50,0:00:38.52,Default,,0000,0000,0000,,We know sum of those must be equal to zero.
Dialogue: 0,0:00:38.52,0:00:40.95,Default,,0000,0000,0000,,So, what voltage do we have here?
Dialogue: 0,0:00:40.95,0:00:43.74,Default,,0000,0000,0000,,V out minus what voltages over here.
Dialogue: 0,0:00:43.74,0:00:51.56,Default,,0000,0000,0000,,That is A times Vp minus Vn and divide that by the resistor R0.
Dialogue: 0,0:00:51.56,0:00:54.54,Default,,0000,0000,0000,,Now, let's consider this value right here,
Dialogue: 0,0:00:54.54,0:00:59.53,Default,,0000,0000,0000,,V out minus this voltage is Vn.
Dialogue: 0,0:00:59.53,0:01:04.25,Default,,0000,0000,0000,,We're going to divide that by R1 and that is going to be equal to zero.
Dialogue: 0,0:01:04.25,0:01:08.16,Default,,0000,0000,0000,,Now, let's do our node at this point.
Dialogue: 0,0:01:08.16,0:01:18.24,Default,,0000,0000,0000,,We can say Vn minus V out divided by R1 plus Vn minus zero divided by R2,
Dialogue: 0,0:01:18.24,0:01:25.52,Default,,0000,0000,0000,,plus right here, Vn minus going all the way,
Dialogue: 0,0:01:25.52,0:01:28.44,Default,,0000,0000,0000,,keep going right there.
Dialogue: 0,0:01:28.44,0:01:34.32,Default,,0000,0000,0000,,Vn minus Vp divided by Ri and this all equals zero.
Dialogue: 0,0:01:34.32,0:01:36.00,Default,,0000,0000,0000,,Those are the two values.
Dialogue: 0,0:01:36.00,0:01:38.90,Default,,0000,0000,0000,,These are the two equations and we'd call them the A equation and
Dialogue: 0,0:01:38.90,0:01:42.32,Default,,0000,0000,0000,,the B equation that define the two nodes that we have.
Dialogue: 0,0:01:42.32,0:01:44.06,Default,,0000,0000,0000,,Let's also take a look at the circuit,
Dialogue: 0,0:01:44.06,0:01:45.68,Default,,0000,0000,0000,,see if there's anything else that we know.
Dialogue: 0,0:01:45.68,0:01:48.88,Default,,0000,0000,0000,,Because at the moment, we have three unknowns and only two equations.
Dialogue: 0,0:01:48.88,0:01:51.56,Default,,0000,0000,0000,,We don't know V out, Vn or Vp.
Dialogue: 0,0:01:51.56,0:01:52.92,Default,,0000,0000,0000,,But if you look right here,
Dialogue: 0,0:01:52.92,0:01:57.70,Default,,0000,0000,0000,,you can see that Vp is equal to Vs. Because of the way the circuit is hooked up.
Dialogue: 0,0:01:57.70,0:02:01.29,Default,,0000,0000,0000,,So, let's just substitute that back in for
Dialogue: 0,0:02:01.29,0:02:06.14,Default,,0000,0000,0000,,Vp in each of those cases right there to make these equations a little bit simple.
Dialogue: 0,0:02:06.14,0:02:07.97,Default,,0000,0000,0000,,Now we have two unknowns,
Dialogue: 0,0:02:07.97,0:02:12.87,Default,,0000,0000,0000,,Vn and V out and we have two equations to solve them.
Dialogue: 0,0:02:13.15,0:02:20.26,Default,,0000,0000,0000,,So, in order to write those as a matrix equation and apply Cramer's rule,
Dialogue: 0,0:02:20.26,0:02:22.31,Default,,0000,0000,0000,,I've given you a little example here.
Dialogue: 0,0:02:22.31,0:02:24.47,Default,,0000,0000,0000,,You might want to just stop the video for a minute and
Dialogue: 0,0:02:24.47,0:02:26.72,Default,,0000,0000,0000,,take a look at the [inaudible] this example.
Dialogue: 0,0:02:26.72,0:02:29.63,Default,,0000,0000,0000,,I took the two equations right here and I converted
Dialogue: 0,0:02:29.63,0:02:32.63,Default,,0000,0000,0000,,them into matrix form for V out and Vn.
Dialogue: 0,0:02:32.63,0:02:34.20,Default,,0000,0000,0000,,Then I applied Cramer's rule.
Dialogue: 0,0:02:34.20,0:02:37.10,Default,,0000,0000,0000,,You may have to look that up online if you don't remember it from math.
Dialogue: 0,0:02:37.10,0:02:41.12,Default,,0000,0000,0000,,Let's stop the video right now and do a little bit of practice on
Dialogue: 0,0:02:41.12,0:02:46.91,Default,,0000,0000,0000,,this particular problem and see that you can get the answer for the gain of this Op Amp.
Dialogue: 0,0:02:47.63,0:02:50.66,Default,,0000,0000,0000,,Okay, I'm hoping that you spent a little bit of time
Dialogue: 0,0:02:50.66,0:02:53.12,Default,,0000,0000,0000,,with that example and did the non-ideal case.
Dialogue: 0,0:02:53.12,0:02:59.18,Default,,0000,0000,0000,,That's the last time you're going to have to do the non-ideal amplifier in this class.
Dialogue: 0,0:02:59.18,0:03:04.79,Default,,0000,0000,0000,,Now, let's rewrite our node a equation V out minus A times V
Dialogue: 0,0:03:04.79,0:03:12.98,Default,,0000,0000,0000,,n minus V p divided by R out plus V out minus Vn divided by R1 equals zero.
Dialogue: 0,0:03:12.98,0:03:16.51,Default,,0000,0000,0000,,Here's the KCL node that I had at node B.
Dialogue: 0,0:03:16.51,0:03:20.86,Default,,0000,0000,0000,,Now, let's apply our ideal Op Amp equations.
Dialogue: 0,0:03:20.86,0:03:23.58,Default,,0000,0000,0000,,Remember we know that Vs is equal to Vp.
Dialogue: 0,0:03:23.58,0:03:27.30,Default,,0000,0000,0000,,But we also know because its ideal that Vp equals Vn.
Dialogue: 0,0:03:27.30,0:03:29.95,Default,,0000,0000,0000,,So, if Vn equals Vp,
Dialogue: 0,0:03:29.95,0:03:31.44,Default,,0000,0000,0000,,then this is zero.
Dialogue: 0,0:03:31.44,0:03:35.10,Default,,0000,0000,0000,,Vn is Vs, Vn is Vs,
Dialogue: 0,0:03:35.10,0:03:40.23,Default,,0000,0000,0000,,Vn is Vs, and Vn minus Vp is equal to zero.
Dialogue: 0,0:03:40.23,0:03:43.20,Default,,0000,0000,0000,,Great, our A equation and our B equation,
Dialogue: 0,0:03:43.20,0:03:44.94,Default,,0000,0000,0000,,we've applied that simplification.
Dialogue: 0,0:03:44.94,0:03:46.88,Default,,0000,0000,0000,,Do we need to apply anything for the currents?
Dialogue: 0,0:03:46.88,0:03:49.10,Default,,0000,0000,0000,,No, so we don't need to use that information.
Dialogue: 0,0:03:49.10,0:03:50.60,Default,,0000,0000,0000,,But keep your eye on this one.
Dialogue: 0,0:03:50.60,0:03:53.100,Default,,0000,0000,0000,,Remember that the output resistance is zero. We're going to need that.
Dialogue: 0,0:03:53.100,0:03:58.22,Default,,0000,0000,0000,,Right here this equation gives us the idea that we could solve for V out
Dialogue: 0,0:03:58.22,0:04:02.51,Default,,0000,0000,0000,,very easily because the only values we have are V out and Vs.
Dialogue: 0,0:04:02.51,0:04:05.27,Default,,0000,0000,0000,,But remember that this value is zero.
Dialogue: 0,0:04:05.27,0:04:07.22,Default,,0000,0000,0000,,So, it's like we're dividing by zero.
Dialogue: 0,0:04:07.22,0:04:09.65,Default,,0000,0000,0000,,This is not a good equation for us to use.
Dialogue: 0,0:04:09.65,0:04:11.93,Default,,0000,0000,0000,,Let's use the B equation instead.
Dialogue: 0,0:04:11.93,0:04:13.37,Default,,0000,0000,0000,,So, for the V equation,
Dialogue: 0,0:04:13.37,0:04:18.71,Default,,0000,0000,0000,,I want to solve for V out and I can say right here there's my V out.
Dialogue: 0,0:04:18.71,0:04:25.100,Default,,0000,0000,0000,,So, I can say that V out is equal to Vs times one divided by R2,
Dialogue: 0,0:04:25.100,0:04:31.42,Default,,0000,0000,0000,,plus one divided by R1 and then I have a V out over R1 on the other side.
Dialogue: 0,0:04:31.42,0:04:36.20,Default,,0000,0000,0000,,So, if I solve this, I can say that V out over Vs and happens to be
Dialogue: 0,0:04:36.20,0:04:43.76,Default,,0000,0000,0000,,my gain is going to multiply this thing out R1 plus R2 over R1 R2.
Dialogue: 0,0:04:43.76,0:04:46.34,Default,,0000,0000,0000,,Then I'm going to bring this R1 over to the other side,
Dialogue: 0,0:04:46.34,0:04:48.10,Default,,0000,0000,0000,,see this R1 came over here.
Dialogue: 0,0:04:48.10,0:04:52.16,Default,,0000,0000,0000,,So, now my R1 cancel out and my gain which is my output
Dialogue: 0,0:04:52.16,0:04:56.21,Default,,0000,0000,0000,,divided by my input is R1 plus R2 over R2.
Dialogue: 0,0:04:56.21,0:05:00.32,Default,,0000,0000,0000,,Awesome. If we actually calculate that for the numbers that we have here,
Dialogue: 0,0:05:00.32,0:05:01.52,Default,,0000,0000,0000,,the value is five.
Dialogue: 0,0:05:01.52,0:05:06.86,Default,,0000,0000,0000,,If we had calculated it using the non-ideal case, it was 4.99975.
Dialogue: 0,0:05:06.86,0:05:11.33,Default,,0000,0000,0000,,So, this is a very good approximation for an ideal Op Amp.
Dialogue: 0,0:05:11.33,0:05:15.24,Default,,0000,0000,0000,,This is how we are going to do our problems in the future.
Dialogue: 0,0:05:15.74,0:05:19.78,Default,,0000,0000,0000,,So remember, that the circuit gain depends on a circuit.
Dialogue: 0,0:05:19.78,0:05:21.66,Default,,0000,0000,0000,,Here's the gain we just derived it.
Dialogue: 0,0:05:21.66,0:05:23.92,Default,,0000,0000,0000,,Remember saturation is going to take over too.
Dialogue: 0,0:05:23.92,0:05:26.02,Default,,0000,0000,0000,,We can't make this gain just as large as we want.
Dialogue: 0,0:05:26.02,0:05:30.94,Default,,0000,0000,0000,,It's controlled by the power supplies that we put on this Op Amp.
Dialogue: 0,0:05:30.94,0:05:34.45,Default,,0000,0000,0000,,Again, back to our Wild Horse Corral.