WEBVTT 00:00:01.160 --> 00:00:03.360 >> Hi. In this next set of videos, 00:00:03.360 --> 00:00:05.580 we're going to take a look at little electronic devices known as 00:00:05.580 --> 00:00:07.860 operational amplifiers. My name is Lee Brinton. 00:00:07.860 --> 00:00:10.860 I'm an Electrical Engineering Instructor at Salt Lake Community College, 00:00:10.860 --> 00:00:14.115 and this is an Introduction to Electrical and Computer Engineering. 00:00:14.115 --> 00:00:19.215 Operational Amplifiers are little bugs, little silicon devices, 00:00:19.215 --> 00:00:22.050 and in these videos, 00:00:22.050 --> 00:00:24.820 we are going to be looking at what they are and what are they're good for. 00:00:24.820 --> 00:00:27.810 We'll introduce the ideal Op Amp approximations. 00:00:27.810 --> 00:00:31.425 We'll then look at a number of common Op Amp configurations, 00:00:31.425 --> 00:00:35.985 the applications that op-amps are frequently used in. 00:00:35.985 --> 00:00:37.935 So what is an Op Amp? 00:00:37.935 --> 00:00:40.840 An operational amplifier is, as I mentioned, 00:00:40.840 --> 00:00:43.610 a semiconductor circuit consisting of 00:00:43.610 --> 00:00:46.955 a bunch of transistors and some capacitors and resistors. 00:00:46.955 --> 00:00:54.395 But the main idea is that they have two input terminals and an output. 00:00:54.395 --> 00:00:58.380 The output terminal becomes a scaled version. 00:00:58.380 --> 00:01:03.650 By scaled, we mean a version of the input that is in some way changed. 00:01:03.650 --> 00:01:05.615 The output is a function of the input. 00:01:05.615 --> 00:01:11.215 It's either going to be amplified or have some other linear operation performed upon it. 00:01:11.215 --> 00:01:13.075 Now, at our level, 00:01:13.075 --> 00:01:17.540 we're not going to be concerned with all of these internal workings. 00:01:17.540 --> 00:01:24.290 We're going to be treating these as a black box device that has inputs and an output, 00:01:24.290 --> 00:01:28.760 and we'll work with them in an ideal environment. 00:01:28.760 --> 00:01:32.810 So, first of all, op-amps are electronic devices. 00:01:32.810 --> 00:01:37.310 They come in silicon semiconductor packaging. 00:01:37.310 --> 00:01:40.975 Here's a picture of an eight pin chip. 00:01:40.975 --> 00:01:43.935 They come in eight-pin, 14-pin. 00:01:43.935 --> 00:01:47.330 Suffice to say that when you're working with operational amplifiers, 00:01:47.330 --> 00:01:49.310 you'll be taking a silicon chip and plugging 00:01:49.310 --> 00:01:51.815 it into a protoboard and working with it that way. 00:01:51.815 --> 00:01:56.249 Internally, functionally, the op-amp, 00:01:56.249 --> 00:01:58.130 as I mentioned, has two inputs. 00:01:58.130 --> 00:02:00.395 One we're going to designate with a minus sign. 00:02:00.395 --> 00:02:03.390 It's known as the inverting terminal. 00:02:08.590 --> 00:02:11.445 For the inverting input, 00:02:11.445 --> 00:02:14.830 one of them is designated with a positive sign that's known as 00:02:14.830 --> 00:02:22.805 the non-inverting terminal or input, 00:02:22.805 --> 00:02:26.600 and then there is the output. 00:02:26.600 --> 00:02:28.880 But these devices are electrical devices, 00:02:28.880 --> 00:02:30.405 and so they also need to be plugged in. 00:02:30.405 --> 00:02:32.215 They need to have power supplies. 00:02:32.215 --> 00:02:40.810 So, the op-amp will also have a positive voltage source and a negative voltage source. 00:02:40.810 --> 00:02:49.645 This little diagram here is meant to show that inside this chip there is one op-amp. 00:02:49.645 --> 00:02:55.895 First of all, pin one and pin five are not connected to anything. 00:02:55.895 --> 00:03:01.340 This eight-pin chip had two pins that weren't needed and so there just to be ignored. 00:03:01.340 --> 00:03:06.190 You'll also notice that on the chip there's a marking. 00:03:06.190 --> 00:03:10.800 Usually, there's a little dot closest to the number one pin. 00:03:10.800 --> 00:03:14.225 Sometimes you'll see a little notch taken out of the top. 00:03:14.225 --> 00:03:17.420 Whatever it is, there'll be something identifying pin one, 00:03:17.420 --> 00:03:19.560 and then they number the pins one, two, three, 00:03:19.560 --> 00:03:21.135 four coming down one side, 00:03:21.135 --> 00:03:23.340 and then going up the other side. 00:03:23.340 --> 00:03:27.620 So, what this diagram is telling us is that pin two, 00:03:27.620 --> 00:03:29.390 this pin right here, 00:03:29.390 --> 00:03:31.585 is connected to the inverting terminal, 00:03:31.585 --> 00:03:34.625 pin three is connected to the non-inverting terminal, 00:03:34.625 --> 00:03:39.080 pin six is where we'll be looking to get our output voltage, 00:03:39.080 --> 00:03:43.010 and pin four and pin seven will be 00:03:43.010 --> 00:03:47.920 tied to our negative and positive voltages respectively. 00:03:47.920 --> 00:03:55.430 Schematically, we have the op-amp showing wires coming to the input terminals, 00:03:55.430 --> 00:03:57.350 a wire going from the output terminal. 00:03:57.350 --> 00:04:02.570 This also shows the negative terminal reference to zero plus to minus, 00:04:02.570 --> 00:04:06.170 so it's dropping down to a negative voltage here for the power supply 00:04:06.170 --> 00:04:10.970 and from ground going up to a positive voltage. 00:04:10.970 --> 00:04:15.695 So, the op-amp does have both a positive and negative voltage powering it. 00:04:15.695 --> 00:04:19.310 Generally speaking, in a circuit schematic, 00:04:19.310 --> 00:04:22.625 we won't show the voltage sources, 00:04:22.625 --> 00:04:25.340 the pins where the power supplies are connected. 00:04:25.340 --> 00:04:29.930 We know that there's got to be a power source to them just like an amplifier in 00:04:29.930 --> 00:04:35.280 a guitar you plug it in and that's where it gets the power to do the amplification. 00:04:37.070 --> 00:04:41.220 These op-amps, again, let's just draw the symbol 00:04:41.220 --> 00:04:48.300 here with it's inverting and it's non-inverting terminal. 00:04:48.300 --> 00:04:51.270 The voltage at the non-inverting terminal, 00:04:51.270 --> 00:04:54.540 we're going to refer to as V sub n, and this, 00:04:54.540 --> 00:04:57.370 of course, will be referenced to a ground, 00:04:57.370 --> 00:04:58.460 so it's a node voltage. 00:04:58.460 --> 00:05:03.235 The voltage at the inverting terminal relative to ground we're going to call V sub n. 00:05:03.235 --> 00:05:09.020 The voltage at the non-inverting terminal we're going to refer to as V sub p. 00:05:09.020 --> 00:05:11.650 V sub n, it's not great nomenclature, 00:05:11.650 --> 00:05:13.180 but the n refers to the negative sign, 00:05:13.180 --> 00:05:16.020 the p refers to the positive sign. 00:05:16.020 --> 00:05:25.840 The op-amp is designed to perform the operation so that the output is equal to A, 00:05:25.840 --> 00:05:31.895 some constant, times the difference between those two voltages. 00:05:31.895 --> 00:05:37.090 So, A known as the open-loop gain of the amplifier times 00:05:37.090 --> 00:05:42.430 the voltage at the p or the non-inverting terminal minus 00:05:42.430 --> 00:05:48.220 the voltage at the n terminal will give you 00:05:48.220 --> 00:05:55.000 the output or the output is then this gain term multiplying that difference. 00:05:55.000 --> 00:06:03.160 This graph here shows the output V out as a function of that difference. 00:06:03.160 --> 00:06:05.770 The output is a linear. 00:06:05.770 --> 00:06:10.945 It's just a scaled version of that difference over 00:06:10.945 --> 00:06:16.790 quite a range of input values or range of Vp minus Vn values. 00:06:16.790 --> 00:06:26.200 But when the output gets to the positive source, the positive side, 00:06:26.200 --> 00:06:32.929 or when the output would exceed the negative source or power supply, 00:06:32.929 --> 00:06:35.845 the amplifier is set to saturate. 00:06:35.845 --> 00:06:38.070 It's impossible for, again, 00:06:38.070 --> 00:06:39.210 let's just draw those in here. 00:06:39.210 --> 00:06:41.950 This is positive Vcc, 00:06:41.950 --> 00:06:46.205 the positive power supply, and negative Vcc. 00:06:46.205 --> 00:06:51.440 These are the sources of the voltage and the output can't exceed those sources. 00:06:51.440 --> 00:06:56.870 So, if Vp minus V sub n were to get large enough that when it was multiplied by 00:06:56.870 --> 00:07:03.930 A the output would exceed positive Vcc or be less than negative Vcc, 00:07:03.930 --> 00:07:06.870 the amplifier then saturates. 00:07:06.870 --> 00:07:11.320 The output becomes simply the source voltage. 00:07:11.320 --> 00:07:14.195 It can't go any further than the source voltage. 00:07:14.195 --> 00:07:20.340 Sometimes the source voltages are referred to as the rail voltages. 00:07:20.440 --> 00:07:27.715 You can think of them as something like two rails between which we must operate. 00:07:27.715 --> 00:07:31.120 We can't go beyond the rails. 00:07:32.360 --> 00:07:36.100 Operational amplifiers can function either 00:07:36.100 --> 00:07:39.430 in the saturation regions or in the linear regions. 00:07:39.430 --> 00:07:40.780 When it's in the linear region, 00:07:40.780 --> 00:07:44.940 the output again is just a scaled version of the input, 00:07:44.940 --> 00:07:46.655 and under those circumstances, 00:07:46.655 --> 00:07:48.760 we refer to them as amplifiers. 00:07:48.760 --> 00:07:53.950 You can also drive an amplifier into one saturation region or another saturation region, 00:07:53.950 --> 00:07:55.120 and under those circumstances, 00:07:55.120 --> 00:07:57.970 we sometimes think of them as switches. 00:07:57.970 --> 00:08:04.360 So, operational amplifier circuits or circuits containing op-amps will be designed 00:08:04.360 --> 00:08:07.285 to operate either within the linear region or designed 00:08:07.285 --> 00:08:10.750 to operate in the saturation regions. 00:08:10.750 --> 00:08:14.260 So, generally speaking, in a block diagram perspective, 00:08:14.260 --> 00:08:16.055 we're going to have some source. 00:08:16.055 --> 00:08:20.855 We're going to run it through our amplifier that has some gain term, 00:08:20.855 --> 00:08:24.830 and then the output voltage or the voltage delivered to 00:08:24.830 --> 00:08:29.210 the load will be some gain times the source. 00:08:29.210 --> 00:08:32.090 So, our gain might be 10 and if our gain was 10, 00:08:32.090 --> 00:08:36.440 then the output voltage would be 10 times what the input voltage would be. 00:08:36.440 --> 00:08:39.820 From a graphical perspective, 00:08:39.820 --> 00:08:46.040 that means that if we were putting a sign wave in that had a one volt peak, 00:08:46.040 --> 00:08:48.875 if V sub s had one volt peak, 00:08:48.875 --> 00:08:52.820 sinusoidal variation, the output then, 00:08:52.820 --> 00:08:56.070 let's see if we can draw this a little bit than I've started, 00:08:58.990 --> 00:09:03.000 would have the same form, 00:09:05.650 --> 00:09:08.365 but would be 10 times as big. 00:09:08.365 --> 00:09:13.270 The oscillations in the output would be 10 times as wide or it'd 00:09:13.270 --> 00:09:19.220 oscillate 10 times as great as the input did. 00:09:19.220 --> 00:09:22.650 All right. Because we're not interested, 00:09:22.650 --> 00:09:25.750 at least at this level, we're not concerned about what's going on inside, 00:09:25.750 --> 00:09:28.570 we're going to make some approximations that under 00:09:28.570 --> 00:09:32.390 normal circumstances are very, very good approximations. 00:09:32.390 --> 00:09:34.725 If these approximations are true, 00:09:34.725 --> 00:09:40.485 we'll find that the operational amplifier is operating within it's linear region. 00:09:40.485 --> 00:09:46.540 First of all, we're going to make the approximation that i sub p, 00:09:46.540 --> 00:09:48.380 the current going into 00:09:48.380 --> 00:09:50.960 the non-inverting terminal and the current 00:09:50.960 --> 00:09:53.825 going into the inverting terminal is very, very small. 00:09:53.825 --> 00:09:56.630 In fact, so small that under ideal circumstances, 00:09:56.630 --> 00:09:59.410 we're going to say that there is no current going in. 00:09:59.410 --> 00:10:02.450 Our output, as we've pointed out, 00:10:02.450 --> 00:10:05.585 is some gain term times the difference in voltages. 00:10:05.585 --> 00:10:06.860 Basically, we're saying, yes, 00:10:06.860 --> 00:10:09.440 there will be a small voltage, 00:10:09.440 --> 00:10:12.125 it turns out it's going to be a small voltage across here, 00:10:12.125 --> 00:10:16.030 but negligible current going in. 00:10:16.300 --> 00:10:23.045 The second approximation is that the voltage across here is going to be very small. 00:10:23.045 --> 00:10:24.970 It's not going to be exactly zero, 00:10:24.970 --> 00:10:26.920 and it's important to notice that because, again, 00:10:26.920 --> 00:10:31.045 the output is some gain term times the difference. 00:10:31.045 --> 00:10:32.900 But it's going to be so small. 00:10:32.900 --> 00:10:37.030 In fact, it might be on the order of millivolts or tens of millivolts while all of 00:10:37.030 --> 00:10:41.735 the voltages in the circuit around it will be on the order of perhaps volts. 00:10:41.735 --> 00:10:43.970 So, if we're able to keep, 00:10:43.970 --> 00:10:46.810 and part of our circuitry will force 00:10:46.810 --> 00:10:51.880 the amplifier to operate in this range where Vp minus 00:10:51.880 --> 00:10:54.100 V sub n is approximately zero, 00:10:54.100 --> 00:11:00.850 or that Vp and V sub n are approximately equal to each other. 00:11:00.850 --> 00:11:04.450 We're going to design a circuitry to make that true so that in 00:11:04.450 --> 00:11:09.390 our analysis Vp minus V sub n is zero. 00:11:09.390 --> 00:11:12.470 The way we're going to work with that is that we're going to say that the voltage at 00:11:12.470 --> 00:11:14.900 the inverting terminal is 00:11:14.900 --> 00:11:18.590 approximately equal to the voltage at the non-inverting terminal. 00:11:18.590 --> 00:11:22.850 The next approximation is that this open-loop gain term, 00:11:22.850 --> 00:11:25.790 A, is really big. 00:11:25.790 --> 00:11:28.480 In fact, it approaches infinity. 00:11:28.480 --> 00:11:30.620 Now, it's not going to be infinite, 00:11:30.620 --> 00:11:36.845 but it's going to be on the order of maybe 50,000, 100,000, 200,000, 00:11:36.845 --> 00:11:39.920 big enough that for the calculations that we'll be doing, 00:11:39.920 --> 00:11:49.205 we can consider it to be infinite which then makes for an interesting mathematical, 00:11:49.205 --> 00:11:52.070 not inconsistency, what's the word I'm talking about? 00:11:52.070 --> 00:11:55.160 Indeterminate form. If we have A, 00:11:55.160 --> 00:11:58.370 which is approximately infinite, multiplying a really, 00:11:58.370 --> 00:12:02.150 really small number, which is approximately zero, it is indeterminate, 00:12:02.150 --> 00:12:07.400 and what we'll find is that we'll be able to determine the gain of the amplifier or 00:12:07.400 --> 00:12:14.225 specify the gain of the amplifier via the circuitry that we wrap around the amplifier. 00:12:14.225 --> 00:12:18.860 Finally, the output resistance, 00:12:18.860 --> 00:12:25.165 the resistance seen driving at the output is very small. 00:12:25.165 --> 00:12:28.010 In fact, we're going to assume that it is zero so that 00:12:28.010 --> 00:12:32.390 our output voltage will not experience a drop across 00:12:32.390 --> 00:12:36.050 this resistance which means that we can think about the 00:12:36.050 --> 00:12:40.175 current here available within limits. 00:12:40.175 --> 00:12:43.310 We can get whatever current out of here we need without 00:12:43.310 --> 00:12:46.370 seeing appreciable voltage drop across here. 00:12:46.370 --> 00:12:48.770 So, for a reasonable range of currents, 00:12:48.770 --> 00:12:50.945 the output voltage will be unchanged. 00:12:50.945 --> 00:12:54.850 In that sense, it's something like an ideal current source. 00:12:54.850 --> 00:13:00.940 At the input, the input resistance R sub i we're going to assume to be infinite. 00:13:00.940 --> 00:13:04.415 That ties back into the input currents being zero. 00:13:04.415 --> 00:13:07.445 If you're driving a current into an infinite resistance, 00:13:07.445 --> 00:13:09.070 effectively an open circuit, 00:13:09.070 --> 00:13:11.980 the input currents are going to be zero. 00:13:12.590 --> 00:13:17.975 So, recapping, we had these little silicon devices called operational amplifiers. 00:13:17.975 --> 00:13:20.375 They draw almost no current at the inputs. 00:13:20.375 --> 00:13:25.125 The output is a scaled version of the input and we can use them. 00:13:25.125 --> 00:13:29.780 They're very utilitarian devices used in control systems, 00:13:29.780 --> 00:13:31.520 used in the circuit in the lab, 00:13:31.520 --> 00:13:35.070 and we'll get a lot of experience using these operational amplifiers.