1 00:00:06,430 --> 00:00:07,260 PROFESSOR: Hi. 2 00:00:07,260 --> 00:00:10,050 Last time we talked about NVCC method and how to reduce the 3 00:00:10,050 --> 00:00:11,720 number of equations we had to deal with to solve a 4 00:00:11,720 --> 00:00:12,920 particular circuit. 5 00:00:12,920 --> 00:00:14,660 At this point, we're pretty well equipped to solve 6 00:00:14,660 --> 00:00:17,150 circuits in the general sense, but we really haven't talked 7 00:00:17,150 --> 00:00:19,570 about how to use that information or possibly use 8 00:00:19,570 --> 00:00:22,210 circuits in a particular way. 9 00:00:22,210 --> 00:00:27,040 Before we jump into both that and abstraction of circuits, 10 00:00:27,040 --> 00:00:28,820 we need to talk about op-amps. 11 00:00:28,820 --> 00:00:31,270 Op-amps is short for Operational Amplifier. 12 00:00:31,270 --> 00:00:33,840 And it's a tool that we can use in order to sample 13 00:00:33,840 --> 00:00:36,630 particular voltages from a subsection of the circuit 14 00:00:36,630 --> 00:00:38,300 without affecting it. 15 00:00:38,300 --> 00:00:39,870 Another thing we can use op-amps to do 16 00:00:39,870 --> 00:00:41,440 is modify our signal. 17 00:00:41,440 --> 00:00:44,000 Or if we're going to sample a voltage from a particular 18 00:00:44,000 --> 00:00:47,440 subsection of the circuit, we can then do stuff to that 19 00:00:47,440 --> 00:00:51,100 voltage without affecting the circuit, all within the op-amp 20 00:00:51,100 --> 00:00:53,760 or within the op-amp's special subset of circuitry. 21 00:00:58,530 --> 00:01:01,130 So first of all what is an operational amplifier? 22 00:01:01,130 --> 00:01:05,900 Well, an operational amplifier is a giant web of transistors. 23 00:01:05,900 --> 00:01:10,410 But what an operational amplifier does is act as a 24 00:01:10,410 --> 00:01:12,310 voltage-dependent voltage source. 25 00:01:12,310 --> 00:01:15,270 It can effectively sample voltages from an existing 26 00:01:15,270 --> 00:01:19,040 circuit and then use them to power some other object, for 27 00:01:19,040 --> 00:01:20,480 instance a light bulb. 28 00:01:20,480 --> 00:01:22,685 If you set up this kind of circuit, you will not actually 29 00:01:22,685 --> 00:01:24,880 be powering this light bulb with 5 Volts, because the 30 00:01:24,880 --> 00:01:27,240 light bulb itself acts as a resistor. 31 00:01:27,240 --> 00:01:30,270 And so the voltage drop across this part of the circuit is 32 00:01:30,270 --> 00:01:32,780 going to be different from just 5 Volts. 33 00:01:32,780 --> 00:01:36,660 If you want to enable a voltage drop of 5 Volts across 34 00:01:36,660 --> 00:01:42,140 this light bulb, then you have to stick up an op-amp. 35 00:01:42,140 --> 00:01:44,670 You have to use an op-amp to sample the voltage drop at 36 00:01:44,670 --> 00:01:48,540 this component and put it in between the light bulb and the 37 00:01:48,540 --> 00:01:51,395 rest of the circuit. 38 00:01:51,395 --> 00:01:54,040 When you see an op-amp on a schematic diagram, it'll 39 00:01:54,040 --> 00:01:56,880 frequently look like this. 40 00:01:56,880 --> 00:01:59,370 You'll have a positive input voltage, a negative input 41 00:01:59,370 --> 00:02:02,540 voltage, power rails, which are actually the thing that 42 00:02:02,540 --> 00:02:05,810 determine the range of expressivity that the op-amp 43 00:02:05,810 --> 00:02:10,419 has, and an output voltage. 44 00:02:10,419 --> 00:02:12,865 In reality, the relationship between the output voltage and 45 00:02:12,865 --> 00:02:27,910 then input voltages is something like this, where K 46 00:02:27,910 --> 00:02:31,120 is a very large number. 47 00:02:31,120 --> 00:02:35,550 The effect that this has is that Vout is going to be 48 00:02:35,550 --> 00:02:40,330 whatever Vout needs to be, such that 49 00:02:40,330 --> 00:02:41,610 Vplus is equal to Vminus. 50 00:02:45,060 --> 00:02:47,290 That's the basic rule you want to use when you're interacting 51 00:02:47,290 --> 00:02:48,700 with op-amps. 52 00:02:48,700 --> 00:02:52,760 So in this case, if we wanted to power this light bulb with 53 00:02:52,760 --> 00:02:55,750 5 Volts, we would do something like this. 54 00:03:31,760 --> 00:03:34,600 Excuse the sloppiness of the second diagram. 55 00:03:34,600 --> 00:03:36,710 We still have our 10 Volt voltage source. 56 00:03:36,710 --> 00:03:37,960 We still have our voltage divider. 57 00:03:40,400 --> 00:03:46,510 This point samples 5 Volts from this sub-circuit -- 58 00:03:46,510 --> 00:03:51,470 and isolates this part of the circuit from the light bulb. 59 00:03:57,150 --> 00:04:03,770 Vout has to be whatever value is necessary such that this 60 00:04:03,770 --> 00:04:07,630 sample point and this sample point are equal. 61 00:04:07,630 --> 00:04:11,380 Since this value is 5 Volts, this value will also be driven 62 00:04:11,380 --> 00:04:15,780 to 5 Volts by the op-amp, which means that 63 00:04:15,780 --> 00:04:17,959 this value is 5 Volts. 64 00:04:17,959 --> 00:04:20,260 And we've successfully managed to power a 65 00:04:20,260 --> 00:04:21,510 light bulb with 5 Volts. 66 00:04:23,700 --> 00:04:26,910 The other thing you might be asked to do is to take an 67 00:04:26,910 --> 00:04:31,580 existing schematic, an existing circuit diagram and 68 00:04:31,580 --> 00:04:34,400 figure out what the operational amplifier does to 69 00:04:34,400 --> 00:04:38,170 a given signal or possibly what Vout is or possibly what 70 00:04:38,170 --> 00:04:41,500 Vout is in terms of the input signal. 71 00:04:41,500 --> 00:04:45,860 So let's practice using this diagram. 72 00:04:54,970 --> 00:04:56,220 Here's what we're after. 73 00:04:58,720 --> 00:05:02,340 I'm going to figure out where Vplus is going to be. 74 00:05:02,340 --> 00:05:03,640 This is another voltage divider. 75 00:05:20,380 --> 00:05:25,280 I'm now interested in Vminus, in terms of Vout, which is 76 00:05:25,280 --> 00:05:26,530 another voltage divider. 77 00:05:44,870 --> 00:05:47,280 I can set these two equations equal to one another 78 00:05:47,280 --> 00:05:48,530 and solve for Vout. 79 00:06:41,160 --> 00:06:44,090 I found a new expression for Vout in the particular case 80 00:06:44,090 --> 00:06:45,530 where V is 10 Volts. 81 00:06:58,480 --> 00:07:03,410 If my input voltage were previously unspecified, or if 82 00:07:03,410 --> 00:07:13,650 this voltage source were not specified or just Vin, then I 83 00:07:13,650 --> 00:07:14,900 would be after this expression. 84 00:07:20,340 --> 00:07:22,150 Some things I'd like to mention, while we're talking 85 00:07:22,150 --> 00:07:27,420 about op-amps, all the operational amplifiers we've 86 00:07:27,420 --> 00:07:32,170 been working with so far deal with Vout in terms of Vin, 87 00:07:32,170 --> 00:07:35,140 where Vin is driven through the positive terminal, and the 88 00:07:35,140 --> 00:07:37,560 negative terminal is typically connected to ground. 89 00:07:37,560 --> 00:07:39,150 You can do the opposite and end up with 90 00:07:39,150 --> 00:07:40,670 some interesting effects. 91 00:07:40,670 --> 00:07:42,010 But it comes at a cost. 92 00:07:42,010 --> 00:07:46,190 It is entirely possible that you will end up driving your 93 00:07:46,190 --> 00:07:48,800 op-amp to an unstable equilibrium. 94 00:07:48,800 --> 00:07:50,505 What you need to look at is this relationship. 95 00:08:02,500 --> 00:08:06,430 There may be a particular point, in which case your 96 00:08:06,430 --> 00:08:07,550 system is stable. 97 00:08:07,550 --> 00:08:10,110 But if you get any sort of minor perturbations, you'll 98 00:08:10,110 --> 00:08:12,650 actually end up with divergence. 99 00:08:12,650 --> 00:08:14,880 If this is the case, then you'll probably 100 00:08:14,880 --> 00:08:16,380 burn out your op-amp. 101 00:08:16,380 --> 00:08:18,540 You can do this by hooking it up in this way. 102 00:08:38,000 --> 00:08:40,580 This is expensive and could possibly burn you. 103 00:08:43,460 --> 00:08:46,350 The other thing to note is that the power rails on your 104 00:08:46,350 --> 00:08:48,260 op-amp limit its range of expressivity. 105 00:08:48,260 --> 00:08:49,890 And I think I've said this before, but it's worth 106 00:08:49,890 --> 00:08:51,560 mentioning again. 107 00:08:51,560 --> 00:08:54,950 If your op-amp is only powered by 10 Volts, it cannot amplify 108 00:08:54,950 --> 00:08:58,790 your input signal to a final value greater than 10 Volts. 109 00:08:58,790 --> 00:09:01,660 Likewise, if your input value is a negative voltage, and 110 00:09:01,660 --> 00:09:05,890 you're working with a non-inverting amplifier, if 111 00:09:05,890 --> 00:09:08,350 your ground is truly ground or if your ground is higher 112 00:09:08,350 --> 00:09:12,880 relative than your input voltage, you cannot actually 113 00:09:12,880 --> 00:09:16,670 express a negative voltage. 114 00:09:16,670 --> 00:09:18,960 The third thing I'd like to quickly mention is that there 115 00:09:18,960 --> 00:09:21,420 are some terms associated with op-amps that you might hear 116 00:09:21,420 --> 00:09:24,582 used by the staff or online, that sort of thing. 117 00:09:24,582 --> 00:09:27,240 A buffer and a voltage follower are the same thing. 118 00:09:27,240 --> 00:09:30,680 And that's explicitly when you want to sample a signal or you 119 00:09:30,680 --> 00:09:32,690 want to sample a particular voltage, and you don't want to 120 00:09:32,690 --> 00:09:36,780 multiply it or add it to something or do any kind of 121 00:09:36,780 --> 00:09:39,500 LTI operations that we might be able to do using op-amps in 122 00:09:39,500 --> 00:09:42,290 this course. 123 00:09:42,290 --> 00:09:43,450 You can work with amplifiers. 124 00:09:43,450 --> 00:09:46,060 And the thing we worked with earlier was an amplifier for a 125 00:09:46,060 --> 00:09:48,060 value less than 1. 126 00:09:48,060 --> 00:09:51,040 You can also use op-amps to some signals. 127 00:09:51,040 --> 00:09:54,030 And if you look for a voltage summer amplifier on the 128 00:09:54,030 --> 00:09:56,830 internet, you should be able to find some information. 129 00:09:56,830 --> 00:09:58,740 In any case, op-amps are really powerful. 130 00:09:58,740 --> 00:10:02,070 They allow us to both isolate a particular section of a 131 00:10:02,070 --> 00:10:05,460 circuit and sample a particular voltage value from 132 00:10:05,460 --> 00:10:08,130 that circuit without affecting that circuit, and also allow 133 00:10:08,130 --> 00:10:11,640 us to modify that particular voltage value before using it 134 00:10:11,640 --> 00:10:16,220 in another part of our overall circuit. 135 00:10:16,220 --> 00:10:19,550 Therefore, we're enabled to design more complicated and 136 00:10:19,550 --> 00:10:21,240 powerful things. 137 00:10:21,240 --> 00:10:25,680 Next time, I'll talk about superposition and Thevenin 138 00:10:25,680 --> 00:10:29,010 Norton equivalence, which will further enable modularity and 139 00:10:29,010 --> 00:10:30,470 abstraction in our circuit design.