WEBVTT 00:00:00.000 --> 00:00:03.630 >> Hello, this is Dr. Cynthia Furse at the University of Utah. 00:00:03.630 --> 00:00:07.755 Today, we're going to talk about Operational Amplifiers or Op Amps. 00:00:07.755 --> 00:00:11.835 Remember that electrical engineering is about what you can do to a voltage. 00:00:11.835 --> 00:00:16.665 For example, a resistor converts voltage to current, and current to voltage. 00:00:16.665 --> 00:00:21.345 A voltage divider divides the voltage, and a current divider divides the current. 00:00:21.345 --> 00:00:26.130 We can think of this as the operation of a voltage divider or a current divider. 00:00:26.130 --> 00:00:29.265 Here's the circuit that goes with that operation. 00:00:29.265 --> 00:00:31.380 Why do we need an Op Amp? 00:00:31.380 --> 00:00:33.780 Because there are many more operations that we would 00:00:33.780 --> 00:00:36.300 like to do than the devices that we have today. 00:00:36.300 --> 00:00:40.905 For example, an Op Amp circuit can amplify or multiply voltages. 00:00:40.905 --> 00:00:43.275 It can de-amplify or divide them. 00:00:43.275 --> 00:00:45.575 It can add, subtract, compare. 00:00:45.575 --> 00:00:46.999 It could switch voltages, 00:00:46.999 --> 00:00:50.560 and many more operations can be done with Op Amp circuits. 00:00:50.560 --> 00:00:52.425 So, what is an Op Amp? 00:00:52.425 --> 00:00:55.640 The Op Amps we use are going to come into the little chip like this. 00:00:55.640 --> 00:00:57.365 There are eight pins on this chip. 00:00:57.365 --> 00:01:01.370 This will fit into your protoboard and you can see chips one, two, three, four, 00:01:01.370 --> 00:01:06.555 and here, the pin numbers start with this little dot here at the top. 00:01:06.555 --> 00:01:09.600 On pin two, we have an input Vn, 00:01:09.600 --> 00:01:11.070 that's our negative input, 00:01:11.070 --> 00:01:13.500 and there's a Vp input on pin three, 00:01:13.500 --> 00:01:14.955 that's the positive input. 00:01:14.955 --> 00:01:17.130 Pin six has the V output. 00:01:17.130 --> 00:01:21.035 So, there are two voltage inputs and there's one voltage output. 00:01:21.035 --> 00:01:25.690 This triangle right here is the symbol that we use to represent the Op-Amp. 00:01:25.690 --> 00:01:29.555 The Op Amp is different than other devices that we have used in the past. 00:01:29.555 --> 00:01:31.040 A resistor, for example, 00:01:31.040 --> 00:01:34.880 always acts like a resistor even if we don't have it connected to power. 00:01:34.880 --> 00:01:36.590 But an Op Amp only acts like 00:01:36.590 --> 00:01:41.000 an operational amplifier if we connect it to its outside power supply, 00:01:41.000 --> 00:01:43.520 Vcc and minus Vcc. 00:01:43.520 --> 00:01:44.975 This is very important. 00:01:44.975 --> 00:01:48.455 Keep your eye on the Vcc as we go through this lecture. 00:01:48.455 --> 00:01:51.245 This is what's inside the amplifier. 00:01:51.245 --> 00:01:52.985 This is what's inside that triangle. 00:01:52.985 --> 00:01:54.470 Here is the negative input, 00:01:54.470 --> 00:01:56.435 the positive input, and the output. 00:01:56.435 --> 00:01:59.240 You can see there are a series of transistors that are hooked up in 00:01:59.240 --> 00:02:03.350 this fashion that make the operational amplifier do what we want it to do. 00:02:03.350 --> 00:02:09.440 However, these transistors only work if they are connected to Vcc and minus Vcc. 00:02:09.440 --> 00:02:12.565 This is why the amplifier is an active device. 00:02:12.565 --> 00:02:16.955 Without this power, it does not act like an operational amplifier. 00:02:16.955 --> 00:02:19.190 Okay. So, now that we know that we have 00:02:19.190 --> 00:02:21.875 this triangle that represents an operational amplifier, 00:02:21.875 --> 00:02:23.225 if we want to hook it up, 00:02:23.225 --> 00:02:26.915 we're going to hook it up this way with plus and minus Vcc. 00:02:26.915 --> 00:02:28.790 But that's complicated to draw, 00:02:28.790 --> 00:02:33.410 and we really just remember that we have Vcc and we normally draw it this way. 00:02:33.410 --> 00:02:36.470 Another thing to remember is all of those transistors in there, 00:02:36.470 --> 00:02:40.435 they divide the frontend and the backend of the amplifier in effect. 00:02:40.435 --> 00:02:45.635 So, even though we might have a positive current here and a negative current there, 00:02:45.635 --> 00:02:48.935 because there are all of those transistors and the power supply, 00:02:48.935 --> 00:02:52.690 sometimes current gets added and sometimes current gets subtracted. 00:02:52.690 --> 00:02:54.720 We don't really know in advance. 00:02:54.720 --> 00:02:57.715 So, all we can say is that i zero, the output current, 00:02:57.715 --> 00:03:02.190 is not equal to the sum of the two input currents. 00:03:02.930 --> 00:03:05.805 Now, let's talk about Op Amp Gain. 00:03:05.805 --> 00:03:08.465 Op Amp Gain is intrinsic to the amplifier. 00:03:08.465 --> 00:03:11.090 It's controlled by how the transistors are put together. 00:03:11.090 --> 00:03:13.070 It's sometimes also called Open Loop Gain. 00:03:13.070 --> 00:03:15.875 Op Amps have a very high voltage gain 00:03:15.875 --> 00:03:19.310 typically on the order of 10 to the fourth to 10 to the eighth. 00:03:19.310 --> 00:03:21.315 They also have a linear response. 00:03:21.315 --> 00:03:27.740 So, the gain tells us that the output is equal to the gain times the input. 00:03:27.740 --> 00:03:30.050 In this case, the input is considered to be 00:03:30.050 --> 00:03:33.440 the difference between the positive and negative inputs of the Op Amp. 00:03:33.440 --> 00:03:37.035 So, if we have a voltage gain of 10 to the fourth, 00:03:37.035 --> 00:03:38.790 it would be linear of something like this, 00:03:38.790 --> 00:03:41.990 a voltage gain of 10 to the eighth would be steeper. 00:03:41.990 --> 00:03:44.070 Because we have Vcc, 00:03:44.070 --> 00:03:46.080 remember I said follow Vcc, 00:03:46.080 --> 00:03:49.505 it limits the actual output of our operational amplifier. 00:03:49.505 --> 00:03:51.860 We cannot put out more power or 00:03:51.860 --> 00:03:54.990 more voltage than we were able to put in to our amplifier. 00:03:54.990 --> 00:03:59.015 So, our amplifier circuit always saturates at plus Vcc 00:03:59.015 --> 00:04:04.080 and minus Vcc because of the power supply limitations. 00:04:04.700 --> 00:04:10.375 Let's see how that saturation can help the operational amplifier acts like a switch. 00:04:10.375 --> 00:04:13.780 Here is a circuit where we hooked up our amplifier and we want to 00:04:13.780 --> 00:04:17.584 be able to control if a red or a green LED turns on. 00:04:17.584 --> 00:04:23.425 So, we've connected our negative input right here to ground along with our two LEDs. 00:04:23.425 --> 00:04:26.350 Remember that the LED only turns on if current 00:04:26.350 --> 00:04:29.690 goes through it in this direction because of its diode nature. 00:04:29.690 --> 00:04:32.800 So, let's see what happens if we put a voltage, 00:04:32.800 --> 00:04:35.380 let's say, two volts, on our positive input. 00:04:35.380 --> 00:04:41.200 In that case, remember that Vp minus Vn is the thing that we're interested in, 00:04:41.200 --> 00:04:43.840 and that's two minus zero in this case. 00:04:43.840 --> 00:04:46.485 So, it's two volts, two volts minus zero volts. 00:04:46.485 --> 00:04:49.935 Multiply that by a very large value, let's say, 10,000. 00:04:49.935 --> 00:04:54.335 So, our output voltage tries to go up to be 20,000. 00:04:54.335 --> 00:04:58.140 Well, the limitation of the power supply limits that, 00:04:58.140 --> 00:04:59.370 let's say, to 12 volts. 00:04:59.370 --> 00:05:01.795 So, the output voltage right here is 12. 00:05:01.795 --> 00:05:06.200 Aha! But that's very good because that gives us a twelve volt difference across 00:05:06.200 --> 00:05:11.075 our LED that drives the current in this direction and turns on our red LED. 00:05:11.075 --> 00:05:14.450 The green LED is trying to drive current in this direction, 00:05:14.450 --> 00:05:19.140 but the LED acts like an open circuit because of a diode and it doesn't turn on. 00:05:19.140 --> 00:05:23.300 Now, let's see what happens if we put a negative voltage on Vp instead. 00:05:23.300 --> 00:05:27.110 Then, Vp minus Vn is going to be minus two volts. 00:05:27.110 --> 00:05:31.820 Multiply that by a very large number and it tries to go to, say, minus 20,000. 00:05:31.820 --> 00:05:34.440 But it's limited by the power supply voltage, 00:05:34.440 --> 00:05:36.290 so it goes to minus 12. 00:05:36.290 --> 00:05:39.470 Well, if it's trying to drive current through here, 00:05:39.470 --> 00:05:41.630 the red LED acts like 00:05:41.630 --> 00:05:45.305 a diode and doesn't allow current to go through. It doesn't turn on. 00:05:45.305 --> 00:05:48.260 Oops! Sorry, I'm not trying to drive current in that direction. 00:05:48.260 --> 00:05:50.270 I'm actually trying to pull current in that direction. 00:05:50.270 --> 00:05:52.160 The green LED, however, 00:05:52.160 --> 00:05:56.935 does turn on because here goes the direction of the current for the green LED. 00:05:56.935 --> 00:05:59.740 So, if we make Vp positive, 00:05:59.740 --> 00:06:01.760 we can turn on the red LED, 00:06:01.760 --> 00:06:03.170 and if we make it negative, 00:06:03.170 --> 00:06:05.075 we can turn on the green LED. 00:06:05.075 --> 00:06:10.140 This allows us to have a circuit that acts like a switch for our two LEDs. 00:06:10.640 --> 00:06:14.390 Now, let's talk about Op Amp Gain versus Circuit Gain. 00:06:14.390 --> 00:06:18.320 The op-amp gain is always high and it's intrinsic to the inside of the op-amp. 00:06:18.320 --> 00:06:21.065 It's also called the open-loop gain or the voltage gain. 00:06:21.065 --> 00:06:25.790 Gain is typically defined as the output divided by the input, and in this case, 00:06:25.790 --> 00:06:31.035 the input is considered to be the difference of the two inputs. 00:06:31.035 --> 00:06:32.860 Circuit gain, on the other hand, 00:06:32.860 --> 00:06:36.910 we may have an op-amp in here and connect it up in this fashion. 00:06:36.910 --> 00:06:38.600 Connect the output right there. 00:06:38.600 --> 00:06:41.510 The circuit gain tells us about the op-amp that has 00:06:41.510 --> 00:06:44.960 its gain A for all of the other resistors around it also. 00:06:44.960 --> 00:06:47.720 Depending on how we connect up our op-amp circuit, 00:06:47.720 --> 00:06:49.625 gain can be large or small. 00:06:49.625 --> 00:06:52.715 If it's large, larger than one, that's amplification. 00:06:52.715 --> 00:06:54.680 Less than one is deamplification. 00:06:54.680 --> 00:06:56.210 If the gain is negative, 00:06:56.210 --> 00:06:57.350 we call it inverting, 00:06:57.350 --> 00:06:58.535 and if the gain is positive, 00:06:58.535 --> 00:07:00.780 we call it non-inverting. 00:07:01.160 --> 00:07:04.775 Here's a non-ideal op-amp equivalent circuit. 00:07:04.775 --> 00:07:09.245 Notice that right here is a dependent voltage source that depends on 00:07:09.245 --> 00:07:14.005 the gain and the difference between the two input voltages. 00:07:14.005 --> 00:07:16.420 So, for a non-ideal op-amp, 00:07:16.420 --> 00:07:19.040 we recognize that Ri is very large. 00:07:19.040 --> 00:07:22.265 It's typically on the order of 10 to six to the 10 to the 13th. 00:07:22.265 --> 00:07:25.115 A is very large, 10 to the fourth to 10 to the eighth. 00:07:25.115 --> 00:07:27.215 The output resistance is very small, 00:07:27.215 --> 00:07:30.350 one to a 100, and the supply voltage right here, 00:07:30.350 --> 00:07:33.005 Vcc and minus Vcc, 00:07:33.005 --> 00:07:34.535 and sometimes they draw it that way too, 00:07:34.535 --> 00:07:36.580 is five to 24 volts. 00:07:36.580 --> 00:07:39.605 Now, for an ideal op-amp, it's going to be different. 00:07:39.605 --> 00:07:40.920 For an ideal op-amp, 00:07:40.920 --> 00:07:46.220 we're going to assume that the input resistance is so large that it can be eliminated. 00:07:46.220 --> 00:07:50.015 In that case, it's like having an open circuit right there at the input. 00:07:50.015 --> 00:07:56.589 We can consider that the gain is so large that we can say Vp is equal to Vn, 00:07:56.589 --> 00:07:59.045 and we can say that the output resistance is so 00:07:59.045 --> 00:08:02.495 small that we can neglect it and consider it just as a wire. 00:08:02.495 --> 00:08:06.005 The implications of this are that for an ideal op-amp, 00:08:06.005 --> 00:08:08.420 we can say that Vp equal Vn, 00:08:08.420 --> 00:08:13.385 and we can say that no current goes into the either input of this op-amp. 00:08:13.385 --> 00:08:16.280 Sometimes it's also useful to remember, 00:08:16.280 --> 00:08:19.415 right here, that R out is equal to zero. 00:08:19.415 --> 00:08:21.900 You'll see why we need that in a minute. 00:08:22.250 --> 00:08:25.730 Okay. So, the circuit gain depends on the circuit. 00:08:25.730 --> 00:08:26.960 In this red box, 00:08:26.960 --> 00:08:29.540 I have an example of a non-inverting amplifier. 00:08:29.540 --> 00:08:34.534 Trust me for now that the output is going to be equal to 00:08:34.534 --> 00:08:41.929 R1 plus R2 over R2 times Vs for this particular op-amp circuit. 00:08:41.929 --> 00:08:44.225 In that case, we call this the gain, 00:08:44.225 --> 00:08:47.330 G, and we can see that it's always positive. 00:08:47.330 --> 00:08:49.395 That's because resistors are always positive. 00:08:49.395 --> 00:08:52.750 So, it's non-inverting, it's always positive. 00:08:52.750 --> 00:08:58.760 Now, let's see if this non-inverting amplifier can go to any value we want. 00:08:58.760 --> 00:09:04.190 No. Because we have this Vcc and minus Vcc, 00:09:04.190 --> 00:09:07.745 so we know that the gain has to be limited by Vcc. 00:09:07.745 --> 00:09:11.200 So, the op-amp gain is intrinsic to the amplifier, 00:09:11.200 --> 00:09:16.230 but the circuit gain depends on all of the resistors that we put around it. 00:09:16.310 --> 00:09:21.430 So, in summary, here are the important things to remember about an op-amp. 00:09:21.430 --> 00:09:23.710 Here is a model of a non-ideal op-amp. 00:09:23.710 --> 00:09:25.510 We're actually not going to use that very much in 00:09:25.510 --> 00:09:28.060 this class but I want you to remember these parameters. 00:09:28.060 --> 00:09:31.945 We are going to use the ideal op-amp model extensively. 00:09:31.945 --> 00:09:33.790 Remember that the important features of 00:09:33.790 --> 00:09:37.390 the non-ideal op-amp are that the negative and positive input are equal, 00:09:37.390 --> 00:09:39.820 that no current goes into either input, 00:09:39.820 --> 00:09:43.765 and that the output is not the sum of the two input currents. 00:09:43.765 --> 00:09:47.540 Remember also that we have Vcc and minus 00:09:47.540 --> 00:09:52.715 Vcc that limit the output voltage of our operational amplifier. 00:09:52.715 --> 00:09:55.750 Now, I hope you're wondering where the picture was on the front. 00:09:55.750 --> 00:10:00.130 That is the Wild Horse Corral on Antelope Island.