1 00:00:01,160 --> 00:00:03,360 >> Hi. In this next set of videos, 2 00:00:03,360 --> 00:00:05,580 we're going to take a look at little electronic devices known as 3 00:00:05,580 --> 00:00:07,860 operational amplifiers. My name is Lee Brinton. 4 00:00:07,860 --> 00:00:10,860 I'm an Electrical Engineering Instructor at Salt Lake Community College, 5 00:00:10,860 --> 00:00:14,115 and this is an Introduction to Electrical and Computer Engineering. 6 00:00:14,115 --> 00:00:19,215 Operational Amplifiers are little bugs, little silicon devices, 7 00:00:19,215 --> 00:00:22,050 and in these videos, 8 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. 9 00:00:24,820 --> 00:00:27,810 We'll introduce the ideal Op Amp approximations. 10 00:00:27,810 --> 00:00:31,425 We'll then look at a number of common Op Amp configurations, 11 00:00:31,425 --> 00:00:35,985 the applications that op-amps are frequently used in. 12 00:00:35,985 --> 00:00:37,935 So what is an Op Amp? 13 00:00:37,935 --> 00:00:40,840 An operational amplifier is, as I mentioned, 14 00:00:40,840 --> 00:00:43,610 a semiconductor circuit consisting of 15 00:00:43,610 --> 00:00:46,955 a bunch of transistors and some capacitors and resistors. 16 00:00:46,955 --> 00:00:54,395 But the main idea is that they have two input terminals and an output. 17 00:00:54,395 --> 00:00:58,380 The output terminal becomes a scaled version. 18 00:00:58,380 --> 00:01:03,650 By scaled, we mean a version of the input that is in some way changed. 19 00:01:03,650 --> 00:01:05,615 The output is a function of the input. 20 00:01:05,615 --> 00:01:11,215 It's either going to be amplified or have some other linear operation performed upon it. 21 00:01:11,215 --> 00:01:13,075 Now, at our level, 22 00:01:13,075 --> 00:01:17,540 we're not going to be concerned with all of these internal workings. 23 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, 24 00:01:24,290 --> 00:01:28,760 and we'll work with them in an ideal environment. 25 00:01:28,760 --> 00:01:32,810 So, first of all, op-amps are electronic devices. 26 00:01:32,810 --> 00:01:37,310 They come in silicon semiconductor packaging. 27 00:01:37,310 --> 00:01:40,975 Here's a picture of an eight pin chip. 28 00:01:40,975 --> 00:01:43,935 They come in eight-pin, 14-pin. 29 00:01:43,935 --> 00:01:47,330 Suffice to say that when you're working with operational amplifiers, 30 00:01:47,330 --> 00:01:49,310 you'll be taking a silicon chip and plugging 31 00:01:49,310 --> 00:01:51,815 it into a protoboard and working with it that way. 32 00:01:51,815 --> 00:01:56,249 Internally, functionally, the op-amp, 33 00:01:56,249 --> 00:01:58,130 as I mentioned, has two inputs. 34 00:01:58,130 --> 00:02:00,395 One we're going to designate with a minus sign. 35 00:02:00,395 --> 00:02:03,390 It's known as the inverting terminal. 36 00:02:08,590 --> 00:02:11,445 For the inverting input, 37 00:02:11,445 --> 00:02:14,830 one of them is designated with a positive sign that's known as 38 00:02:14,830 --> 00:02:22,805 the non-inverting terminal or input, 39 00:02:22,805 --> 00:02:26,600 and then there is the output. 40 00:02:26,600 --> 00:02:28,880 But these devices are electrical devices, 41 00:02:28,880 --> 00:02:30,405 and so they also need to be plugged in. 42 00:02:30,405 --> 00:02:32,215 They need to have power supplies. 43 00:02:32,215 --> 00:02:40,810 So, the op-amp will also have a positive voltage source and a negative voltage source. 44 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. 45 00:02:49,645 --> 00:02:55,895 First of all, pin one and pin five are not connected to anything. 46 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. 47 00:03:01,340 --> 00:03:06,190 You'll also notice that on the chip there's a marking. 48 00:03:06,190 --> 00:03:10,800 Usually, there's a little dot closest to the number one pin. 49 00:03:10,800 --> 00:03:14,225 Sometimes you'll see a little notch taken out of the top. 50 00:03:14,225 --> 00:03:17,420 Whatever it is, there'll be something identifying pin one, 51 00:03:17,420 --> 00:03:19,560 and then they number the pins one, two, three, 52 00:03:19,560 --> 00:03:21,135 four coming down one side, 53 00:03:21,135 --> 00:03:23,340 and then going up the other side. 54 00:03:23,340 --> 00:03:27,620 So, what this diagram is telling us is that pin two, 55 00:03:27,620 --> 00:03:29,390 this pin right here, 56 00:03:29,390 --> 00:03:31,585 is connected to the inverting terminal, 57 00:03:31,585 --> 00:03:34,625 pin three is connected to the non-inverting terminal, 58 00:03:34,625 --> 00:03:39,080 pin six is where we'll be looking to get our output voltage, 59 00:03:39,080 --> 00:03:43,010 and pin four and pin seven will be 60 00:03:43,010 --> 00:03:47,920 tied to our negative and positive voltages respectively. 61 00:03:47,920 --> 00:03:55,430 Schematically, we have the op-amp showing wires coming to the input terminals, 62 00:03:55,430 --> 00:03:57,350 a wire going from the output terminal. 63 00:03:57,350 --> 00:04:02,570 This also shows the negative terminal reference to zero plus to minus, 64 00:04:02,570 --> 00:04:06,170 so it's dropping down to a negative voltage here for the power supply 65 00:04:06,170 --> 00:04:10,970 and from ground going up to a positive voltage. 66 00:04:10,970 --> 00:04:15,695 So, the op-amp does have both a positive and negative voltage powering it. 67 00:04:15,695 --> 00:04:19,310 Generally speaking, in a circuit schematic, 68 00:04:19,310 --> 00:04:22,625 we won't show the voltage sources, 69 00:04:22,625 --> 00:04:25,340 the pins where the power supplies are connected. 70 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 71 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. 72 00:04:37,070 --> 00:04:41,220 These op-amps, again, let's just draw the symbol 73 00:04:41,220 --> 00:04:48,300 here with it's inverting and it's non-inverting terminal. 74 00:04:48,300 --> 00:04:51,270 The voltage at the non-inverting terminal, 75 00:04:51,270 --> 00:04:54,540 we're going to refer to as V sub n, and this, 76 00:04:54,540 --> 00:04:57,370 of course, will be referenced to a ground, 77 00:04:57,370 --> 00:04:58,460 so it's a node voltage. 78 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. 79 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. 80 00:05:09,020 --> 00:05:11,650 V sub n, it's not great nomenclature, 81 00:05:11,650 --> 00:05:13,180 but the n refers to the negative sign, 82 00:05:13,180 --> 00:05:16,020 the p refers to the positive sign. 83 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, 84 00:05:25,840 --> 00:05:31,895 some constant, times the difference between those two voltages. 85 00:05:31,895 --> 00:05:37,090 So, A known as the open-loop gain of the amplifier times 86 00:05:37,090 --> 00:05:42,430 the voltage at the p or the non-inverting terminal minus 87 00:05:42,430 --> 00:05:48,220 the voltage at the n terminal will give you 88 00:05:48,220 --> 00:05:55,000 the output or the output is then this gain term multiplying that difference. 89 00:05:55,000 --> 00:06:03,160 This graph here shows the output V out as a function of that difference. 90 00:06:03,160 --> 00:06:05,770 The output is a linear. 91 00:06:05,770 --> 00:06:10,945 It's just a scaled version of that difference over 92 00:06:10,945 --> 00:06:16,790 quite a range of input values or range of Vp minus Vn values. 93 00:06:16,790 --> 00:06:26,200 But when the output gets to the positive source, the positive side, 94 00:06:26,200 --> 00:06:32,929 or when the output would exceed the negative source or power supply, 95 00:06:32,929 --> 00:06:35,845 the amplifier is set to saturate. 96 00:06:35,845 --> 00:06:38,070 It's impossible for, again, 97 00:06:38,070 --> 00:06:39,210 let's just draw those in here. 98 00:06:39,210 --> 00:06:41,950 This is positive Vcc, 99 00:06:41,950 --> 00:06:46,205 the positive power supply, and negative Vcc. 100 00:06:46,205 --> 00:06:51,440 These are the sources of the voltage and the output can't exceed those sources. 101 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 102 00:06:56,870 --> 00:07:03,930 A the output would exceed positive Vcc or be less than negative Vcc, 103 00:07:03,930 --> 00:07:06,870 the amplifier then saturates. 104 00:07:06,870 --> 00:07:11,320 The output becomes simply the source voltage. 105 00:07:11,320 --> 00:07:14,195 It can't go any further than the source voltage. 106 00:07:14,195 --> 00:07:20,340 Sometimes the source voltages are referred to as the rail voltages. 107 00:07:20,440 --> 00:07:27,715 You can think of them as something like two rails between which we must operate. 108 00:07:27,715 --> 00:07:31,120 We can't go beyond the rails. 109 00:07:32,360 --> 00:07:36,100 Operational amplifiers can function either 110 00:07:36,100 --> 00:07:39,430 in the saturation regions or in the linear regions. 111 00:07:39,430 --> 00:07:40,780 When it's in the linear region, 112 00:07:40,780 --> 00:07:44,940 the output again is just a scaled version of the input, 113 00:07:44,940 --> 00:07:46,655 and under those circumstances, 114 00:07:46,655 --> 00:07:48,760 we refer to them as amplifiers. 115 00:07:48,760 --> 00:07:53,950 You can also drive an amplifier into one saturation region or another saturation region, 116 00:07:53,950 --> 00:07:55,120 and under those circumstances, 117 00:07:55,120 --> 00:07:57,970 we sometimes think of them as switches. 118 00:07:57,970 --> 00:08:04,360 So, operational amplifier circuits or circuits containing op-amps will be designed 119 00:08:04,360 --> 00:08:07,285 to operate either within the linear region or designed 120 00:08:07,285 --> 00:08:10,750 to operate in the saturation regions. 121 00:08:10,750 --> 00:08:14,260 So, generally speaking, in a block diagram perspective, 122 00:08:14,260 --> 00:08:16,055 we're going to have some source. 123 00:08:16,055 --> 00:08:20,855 We're going to run it through our amplifier that has some gain term, 124 00:08:20,855 --> 00:08:24,830 and then the output voltage or the voltage delivered to 125 00:08:24,830 --> 00:08:29,210 the load will be some gain times the source. 126 00:08:29,210 --> 00:08:32,090 So, our gain might be 10 and if our gain was 10, 127 00:08:32,090 --> 00:08:36,440 then the output voltage would be 10 times what the input voltage would be. 128 00:08:36,440 --> 00:08:39,820 From a graphical perspective, 129 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, 130 00:08:46,040 --> 00:08:48,875 if V sub s had one volt peak, 131 00:08:48,875 --> 00:08:52,820 sinusoidal variation, the output then, 132 00:08:52,820 --> 00:08:56,070 let's see if we can draw this a little bit than I've started, 133 00:08:58,990 --> 00:09:03,000 would have the same form, 134 00:09:05,650 --> 00:09:08,365 but would be 10 times as big. 135 00:09:08,365 --> 00:09:13,270 The oscillations in the output would be 10 times as wide or it'd 136 00:09:13,270 --> 00:09:19,220 oscillate 10 times as great as the input did. 137 00:09:19,220 --> 00:09:22,650 All right. Because we're not interested, 138 00:09:22,650 --> 00:09:25,750 at least at this level, we're not concerned about what's going on inside, 139 00:09:25,750 --> 00:09:28,570 we're going to make some approximations that under 140 00:09:28,570 --> 00:09:32,390 normal circumstances are very, very good approximations. 141 00:09:32,390 --> 00:09:34,725 If these approximations are true, 142 00:09:34,725 --> 00:09:40,485 we'll find that the operational amplifier is operating within it's linear region. 143 00:09:40,485 --> 00:09:46,540 First of all, we're going to make the approximation that i sub p, 144 00:09:46,540 --> 00:09:48,380 the current going into 145 00:09:48,380 --> 00:09:50,960 the non-inverting terminal and the current 146 00:09:50,960 --> 00:09:53,825 going into the inverting terminal is very, very small. 147 00:09:53,825 --> 00:09:56,630 In fact, so small that under ideal circumstances, 148 00:09:56,630 --> 00:09:59,410 we're going to say that there is no current going in. 149 00:09:59,410 --> 00:10:02,450 Our output, as we've pointed out, 150 00:10:02,450 --> 00:10:05,585 is some gain term times the difference in voltages. 151 00:10:05,585 --> 00:10:06,860 Basically, we're saying, yes, 152 00:10:06,860 --> 00:10:09,440 there will be a small voltage, 153 00:10:09,440 --> 00:10:12,125 it turns out it's going to be a small voltage across here, 154 00:10:12,125 --> 00:10:16,030 but negligible current going in. 155 00:10:16,300 --> 00:10:23,045 The second approximation is that the voltage across here is going to be very small. 156 00:10:23,045 --> 00:10:24,970 It's not going to be exactly zero, 157 00:10:24,970 --> 00:10:26,920 and it's important to notice that because, again, 158 00:10:26,920 --> 00:10:31,045 the output is some gain term times the difference. 159 00:10:31,045 --> 00:10:32,900 But it's going to be so small. 160 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 161 00:10:37,030 --> 00:10:41,735 the voltages in the circuit around it will be on the order of perhaps volts. 162 00:10:41,735 --> 00:10:43,970 So, if we're able to keep, 163 00:10:43,970 --> 00:10:46,810 and part of our circuitry will force 164 00:10:46,810 --> 00:10:51,880 the amplifier to operate in this range where Vp minus 165 00:10:51,880 --> 00:10:54,100 V sub n is approximately zero, 166 00:10:54,100 --> 00:11:00,850 or that Vp and V sub n are approximately equal to each other. 167 00:11:00,850 --> 00:11:04,450 We're going to design a circuitry to make that true so that in 168 00:11:04,450 --> 00:11:09,390 our analysis Vp minus V sub n is zero. 169 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 170 00:11:12,470 --> 00:11:14,900 the inverting terminal is 171 00:11:14,900 --> 00:11:18,590 approximately equal to the voltage at the non-inverting terminal. 172 00:11:18,590 --> 00:11:22,850 The next approximation is that this open-loop gain term, 173 00:11:22,850 --> 00:11:25,790 A, is really big. 174 00:11:25,790 --> 00:11:28,480 In fact, it approaches infinity. 175 00:11:28,480 --> 00:11:30,620 Now, it's not going to be infinite, 176 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, 177 00:11:36,845 --> 00:11:39,920 big enough that for the calculations that we'll be doing, 178 00:11:39,920 --> 00:11:49,205 we can consider it to be infinite which then makes for an interesting mathematical, 179 00:11:49,205 --> 00:11:52,070 not inconsistency, what's the word I'm talking about? 180 00:11:52,070 --> 00:11:55,160 Indeterminate form. If we have A, 181 00:11:55,160 --> 00:11:58,370 which is approximately infinite, multiplying a really, 182 00:11:58,370 --> 00:12:02,150 really small number, which is approximately zero, it is indeterminate, 183 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 184 00:12:07,400 --> 00:12:14,225 specify the gain of the amplifier via the circuitry that we wrap around the amplifier. 185 00:12:14,225 --> 00:12:18,860 Finally, the output resistance, 186 00:12:18,860 --> 00:12:25,165 the resistance seen driving at the output is very small. 187 00:12:25,165 --> 00:12:28,010 In fact, we're going to assume that it is zero so that 188 00:12:28,010 --> 00:12:32,390 our output voltage will not experience a drop across 189 00:12:32,390 --> 00:12:36,050 this resistance which means that we can think about the 190 00:12:36,050 --> 00:12:40,175 current here available within limits. 191 00:12:40,175 --> 00:12:43,310 We can get whatever current out of here we need without 192 00:12:43,310 --> 00:12:46,370 seeing appreciable voltage drop across here. 193 00:12:46,370 --> 00:12:48,770 So, for a reasonable range of currents, 194 00:12:48,770 --> 00:12:50,945 the output voltage will be unchanged. 195 00:12:50,945 --> 00:12:54,850 In that sense, it's something like an ideal current source. 196 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. 197 00:13:00,940 --> 00:13:04,415 That ties back into the input currents being zero. 198 00:13:04,415 --> 00:13:07,445 If you're driving a current into an infinite resistance, 199 00:13:07,445 --> 00:13:09,070 effectively an open circuit, 200 00:13:09,070 --> 00:13:11,980 the input currents are going to be zero. 201 00:13:12,590 --> 00:13:17,975 So, recapping, we had these little silicon devices called operational amplifiers. 202 00:13:17,975 --> 00:13:20,375 They draw almost no current at the inputs. 203 00:13:20,375 --> 00:13:25,125 The output is a scaled version of the input and we can use them. 204 00:13:25,125 --> 00:13:29,780 They're very utilitarian devices used in control systems, 205 00:13:29,780 --> 00:13:31,520 used in the circuit in the lab, 206 00:13:31,520 --> 00:13:35,070 and we'll get a lot of experience using these operational amplifiers.