1 00:00:00 --> 00:00:02 All right. Good morning. 2 00:00:02 --> 00:00:08 Good morning. So, we have some fun stuff for 3 00:00:08 --> 00:00:13 today's lecture, and as far as the final is 4 00:00:13 --> 00:00:19 concerned and so on, I'd like you to forget about 5 00:00:19 --> 00:00:23 anything we do today, absolutely. 6 00:00:23 --> 00:00:31 So, get your mind to become a blank, and forget anything you 7 00:00:31 --> 00:00:38 hear in today's lecture. So, what I'm going to show you 8 00:00:38 --> 00:00:42 today will hopefully completely blow your minds. 9 00:00:42 --> 00:00:46 And I'm not talking about controlled substances or 10 00:00:46 --> 00:00:49 anything. So what I'm going to do is show 11 00:00:49 --> 00:00:54 you a few things that behave completely and spectacularly 12 00:00:54 --> 00:00:58 differently than how you expect them to. 13 00:00:58 --> 00:01:03 And, today's lecture is appropriately called -- 14 00:01:03 --> 00:01:17 15 00:01:17 --> 00:01:19 OK. So, we're going to violate the 16 00:01:19 --> 00:01:22 abstraction barrier here, and do some fun things. 17 00:01:22 --> 00:01:26 And, the important thing to realize is that in all of 6.002, 18 00:01:26 --> 00:01:29 we have, after all, based on some assumptions we 19 00:01:29 --> 00:01:33 made at the beginning of the course like lumped matter 20 00:01:33 --> 00:01:36 discipline and so on, we have landed ourselves in 21 00:01:36 --> 00:01:41 this playground called the playground of 6.002. 22 00:01:41 --> 00:01:44 And, within that playground, certain ground rules apply. 23 00:01:44 --> 00:01:47 OK, and our entire course depended on those assumptions 24 00:01:47 --> 00:01:49 being true. So, for example, 25 00:01:49 --> 00:01:53 the first assumption we made that brought us from Maxwell's 26 00:01:53 --> 00:01:56 equations to the lumped matter discipline was, 27 00:01:56 --> 00:01:59 or rather the circuit abstraction, was a lumped matter 28 00:01:59 --> 00:02:03 discipline. And there were three tenets of 29 00:02:03 --> 00:02:06 the lumped matter discipline. One is that the rate of change 30 00:02:06 --> 00:02:10 of flux was going to be zero within our circuits, 31 00:02:10 --> 00:02:13 not inside elements, but in the circuit itself, 32 00:02:13 --> 00:02:17 and second, the dq by dt was going to be zero outside the 33 00:02:17 --> 00:02:20 elements, and third, something we did not dwell upon 34 00:02:20 --> 00:02:23 in the course, but it's certainly present in 35 00:02:23 --> 00:02:27 the course notes is that the speeds of signals that we are 36 00:02:27 --> 00:02:31 going to consider are going to be much slower than the speed of 37 00:02:31 --> 00:02:36 light. OK, so we're going to be 38 00:02:36 --> 00:02:45 working in a realm where we are going to be well slower than the 39 00:02:45 --> 00:02:50 speed of light. OK, so starting with that, 40 00:02:50 --> 00:02:58 let me walk you through some examples and some fun stuff. 41 00:02:58 --> 00:03:06 So, the first case is called the Double Take. 42 00:03:06 --> 00:03:11 So, let me sketch out a small little circuit for you, 43 00:03:11 --> 00:03:17 and take a look at the expected behavior, and then show you what 44 00:03:17 --> 00:03:22 really happens in real life. So, the first case, 45 00:03:22 --> 00:03:28 I have a voltage source, and what I'm going to do is 46 00:03:28 --> 00:03:33 make a transition from a zero to a one. 47 00:03:33 --> 00:03:39 Think of it as a step input, and through a Thevenin like 48 00:03:39 --> 00:03:45 resistance, I want to feed it to a circuit. 49 00:03:45 --> 00:03:49 The circuit will go to an inverter. 50 00:03:49 --> 00:03:56 This node goes to an inverter, and goes through some other 51 00:03:56 --> 00:04:02 circuits within our own design here. 52 00:04:02 --> 00:04:05 So, again, remember, a step input here, 53 00:04:05 --> 00:04:11 and this input goes through a Thevenin like resistance, 54 00:04:11 --> 00:04:15 or is applied to some other circuit elements. 55 00:04:15 --> 00:04:20 So, if I apply a step here, what do you expect? 56 00:04:20 --> 00:04:24 You expect that, so let me call that VI, 57 00:04:24 --> 00:04:29 and let me call that Vo. So, if I plot VI as a function 58 00:04:29 --> 00:04:36 of time, and let's say this step input happens at t=0. 59 00:04:36 --> 00:04:44 So let's say this is t=0 here, and let's say this is a 5V 60 00:04:44 --> 00:04:49 step. So, I expect that this input 61 00:04:49 --> 00:04:57 here is going to go to, VI here, is going to go to 5V 62 00:04:57 --> 00:05:03 at t=0. What do I expect at Vo? 63 00:05:03 --> 00:05:07 At Vo, based on our circuit abstraction, I get a step input 64 00:05:07 --> 00:05:09 here. I should get a step of some 65 00:05:09 --> 00:05:12 magnitude here, depending on what's connected 66 00:05:12 --> 00:05:16 in this direction. And let's simply say that 67 00:05:16 --> 00:05:19 what's connected here is an inverter, and maybe other 68 00:05:19 --> 00:05:23 inverters at the other side. So essentially, 69 00:05:23 --> 00:05:26 as far as this node is concerned, it's got some wires 70 00:05:26 --> 00:05:30 connected to it. And at the end of the wires, 71 00:05:30 --> 00:05:32 it has an open circuit, an open circuit, 72 00:05:32 --> 00:05:35 for example, like the gate input of this 73 00:05:35 --> 00:05:41 inverter. So what do you expect at V 74 00:05:41 --> 00:05:44 nought? A step input here, 75 00:05:44 --> 00:05:49 and at V nought I see an open circuit. 76 00:05:49 --> 00:05:54 OK, so I expect the same step at V nought: 5V. 77 00:05:54 --> 00:06:01 So, that's what we've prepared you for, OK? 78 00:06:01 --> 00:06:04 But, the fun thing that we're going to see, 79 00:06:04 --> 00:06:09 so this is what you expect, and I'll show you a little demo 80 00:06:09 --> 00:06:13 that is going to show you something very different. 81 00:06:13 --> 00:06:16 What you're going to see is not this. 82 00:06:16 --> 00:06:19 OK, you're not going to be seeing that. 83 00:06:19 --> 00:06:25 Rather, I'm going to show you something that looks like this. 84 00:06:25 --> 00:06:36 85 00:06:36 --> 00:06:40 So, at t=0, I do see Vo looking like a step, and approximately 86 00:06:40 --> 00:06:43 halfway through, decides, ah, 87 00:06:43 --> 00:06:45 well never mind, and flattens out, 88 00:06:45 --> 00:06:48 OK, then says, oh, OK, and zoom, 89 00:06:48 --> 00:06:52 it goes back up to 5V. So, it sort of does a bit of a 90 00:06:52 --> 00:06:57 double take up there saying, hey, what's going on here? 91 00:06:57 --> 00:07:01 And zoom, jumps up to 5V, and then it's five as you 92 00:07:01 --> 00:07:05 expect. OK, so this is some finite 93 00:07:05 --> 00:07:09 amount of time that looks like that. 94 00:07:09 --> 00:07:14 OK, so try to understand what's going on. 95 00:07:14 --> 00:07:18 So let me show you a quick little demo. 96 00:07:18 --> 00:07:24 So that's the input VI. OK, so that's the input VI that 97 00:07:24 --> 00:07:30 you expect, and I won't do anything to my circuit at this 98 00:07:30 --> 00:07:34 point. And, go ahead. 99 00:07:34 --> 00:07:37 So, let's see what happens now. There you go. 100 00:07:37 --> 00:07:41 So now, I'm showing you the output here at Vo. 101 00:07:41 --> 00:07:44 So at VI, there's a nice little step, and at Vo, 102 00:07:44 --> 00:07:48 notice that I get something that behaves like this. 103 00:07:48 --> 00:07:52 OK, and I promise you, nothing we've taught you in 104 00:07:52 --> 00:07:57 6.002 prepares you for this. OK, and as I mentioned at the 105 00:07:57 --> 00:08:01 beginning of this lecture, it would behoove you to forget 106 00:08:01 --> 00:08:06 about everything you learn in today's lecture for the next two 107 00:08:06 --> 00:08:11 weeks at least. So what's going on here? 108 00:08:11 --> 00:08:12 Any ideas? Anybody? 109 00:08:12 --> 00:08:16 Any thoughts? So what's up with my circuit 110 00:08:16 --> 00:08:17 here? It says, oh, 111 00:08:17 --> 00:08:20 OK, a step. It starts off and says, 112 00:08:20 --> 00:08:24 oh, never mind, and then meanders along at 2.5V 113 00:08:24 --> 00:08:28 and then says oh, step, yes, I remember, 114 00:08:28 --> 00:08:32 and then boom, it jumps up to 5V. 115 00:08:32 --> 00:08:35 So, any theories? Any guesses? 116 00:08:35 --> 00:08:40 Any wild guesses? OK, so let me draw you a little 117 00:08:40 --> 00:08:46 bit more of a detailed circuit, and see if you can explain 118 00:08:46 --> 00:08:52 what's going on here. So, the circuit that I've drawn 119 00:08:52 --> 00:08:58 there is not quite the circuit I have at least in terms of my 120 00:08:58 --> 00:09:02 wires. So, what I have is something 121 00:09:02 --> 00:09:07 that looks like this, VI, and this is going to step 122 00:09:07 --> 00:09:13 to 5V. I do have a resistance, 123 00:09:13 --> 00:09:18 R. This is Vo, this does go to an 124 00:09:18 --> 00:09:24 inverter. But what is also happening is 125 00:09:24 --> 00:09:34 that I have a long wire. OK, you see this guy here? 126 00:09:34 --> 00:09:39 We had one of our union folks stretch out along the floor 127 00:09:39 --> 00:09:42 here. We have a really long wire that 128 00:09:42 --> 00:09:46 connects to the Vo node, and there's also a long 129 00:09:46 --> 00:09:51 corresponding ground. So, this wire is a coaxial 130 00:09:51 --> 00:09:55 cable that is used for Ethernet and such like. 131 00:09:55 --> 00:10:01 It's got a core that carries a signal, and around the core is 132 00:10:01 --> 00:10:07 shielding that is the ground. OK, so that goes a long way, 133 00:10:07 --> 00:10:10 and at the end, it is open. 134 00:10:10 --> 00:10:14 OK, it's an open circuit at the end. 135 00:10:14 --> 00:10:19 I haven't connected anything out there: open circuit. 136 00:10:19 --> 00:10:23 So, you know, something's happening here 137 00:10:23 --> 00:10:28 that's making the circuit behave like this. 138 00:10:28 --> 00:10:32 So, this is VI. At Vo -- 139 00:10:32 --> 00:10:48 140 00:10:48 --> 00:10:51 So at Vo I'm getting this funny behavior. 141 00:10:51 --> 00:10:55 OK, so does anybody want to take the next piece of clues 142 00:10:55 --> 00:11:00 here, does anybody want to take a stab at guessing what might be 143 00:11:00 --> 00:11:02 going on here? Yes? 144 00:11:02 --> 00:11:06 Ah, we have a shill in the audience here. 145 00:11:06 --> 00:11:11 So, the theory is that the step here, think of it as an 146 00:11:11 --> 00:11:16 electromagnetic pulse that goes from zero to five, 147 00:11:16 --> 00:11:21 and things in real life don't travel instantaneously. 148 00:11:21 --> 00:11:26 So, there's something with a wave that flies down, 149 00:11:26 --> 00:11:32 and the wave goes to the end, flips, and then comes back, 150 00:11:32 --> 00:11:38 and then establishes the full voltage here. 151 00:11:38 --> 00:11:41 So that is indeed at the root of what's going on. 152 00:11:41 --> 00:11:46 And let me put it in layman's terms and then describe the 153 00:11:46 --> 00:11:51 details of what's going on here. OK, so the way to view what's 154 00:11:51 --> 00:11:54 going on is that I have this long wire. 155 00:11:54 --> 00:11:59 OK, in the very first lecture, I started off by saying wires 156 00:11:59 --> 00:12:03 are ideal. OK, ideal wires are such that I 157 00:12:03 --> 00:12:06 can transmit signals on them. Wires are small so that the 158 00:12:06 --> 00:12:11 propagation time of signals is inconsequential compared to the 159 00:12:11 --> 00:12:14 rise times and fall times of the signals of interest. 160 00:12:14 --> 00:12:18 By having this really long cable here, I have clearly 161 00:12:18 --> 00:12:21 violated that assumption, which is the wires are really, 162 00:12:21 --> 00:12:25 really long here. OK, and so I somehow need to 163 00:12:25 --> 00:12:29 model what the wire is doing to my circuit when I don't have a 164 00:12:29 --> 00:12:33 small wire. So what actually happens, 165 00:12:33 --> 00:12:37 the way to view it is the following. 166 00:12:37 --> 00:12:42 So, although this is a wire, to understand the mechanics of 167 00:12:42 --> 00:12:47 what's going on, I really have to model it much 168 00:12:47 --> 00:12:49 more accurately, OK? 169 00:12:49 --> 00:12:55 And, the way to model a wire like this is that notice that 170 00:12:55 --> 00:13:00 every small element of a wire has associated with it some 171 00:13:00 --> 00:13:04 inductance. OK, so let's take a small 172 00:13:04 --> 00:13:09 segment of the coax cable here. The coax cable is a small core 173 00:13:09 --> 00:13:14 surrounded by a metallic shield. OK, that's a ground. 174 00:13:14 --> 00:13:18 And so, when I have a wire surrounded by a metallic shield, 175 00:13:18 --> 00:13:23 that also has the capacitance, OK, inductance and capacitance. 176 00:13:23 --> 00:13:27 So this small segment can be modeled as a really small 177 00:13:27 --> 00:13:32 inductance, and a really tiny capacitance. 178 00:13:32 --> 00:13:36 Similarly, the next segment can be modeled as a tiny inductance 179 00:13:36 --> 00:13:40 and a capacitance. There is also a resistance 180 00:13:40 --> 00:13:44 here, but let's assume that the resistance is zero for our 181 00:13:44 --> 00:13:49 model, and also the parallel resistance is also infinity. 182 00:13:49 --> 00:13:52 OK, so it's an inductor, capacitor, and really the 183 00:13:52 --> 00:13:56 situation that I have is not a pair of ideal wires, 184 00:13:56 --> 00:14:00 but really a really, really small inductance, 185 00:14:00 --> 00:14:04 and a small capacitance in parallel. 186 00:14:04 --> 00:14:08 So, it's more of a set of distributed elements that I have 187 00:14:08 --> 00:14:11 here. Notice that in my lump circuit 188 00:14:11 --> 00:14:15 abstraction, when we talked about the RLC model for the wire 189 00:14:15 --> 00:14:18 between two inverters, we lumped it. 190 00:14:18 --> 00:14:22 We lumped this thing into a model that looked like this. 191 00:14:22 --> 00:14:27 OK, we lumped the resistance into a source resistance. 192 00:14:27 --> 00:14:32 We lumped all the inductors into a lumped inductor. 193 00:14:32 --> 00:14:36 We lumped all the capacitances into a lumped capacitance. 194 00:14:36 --> 00:14:40 OK, but in this situation, I can do this when the signal 195 00:14:40 --> 00:14:44 speeds of interest are much, much, much slower than the 196 00:14:44 --> 00:14:48 speed of light than the propagation speeds of 197 00:14:48 --> 00:14:50 electromagnetic signals. In this case, 198 00:14:50 --> 00:14:54 that is not quite true. And so, therefore, 199 00:14:54 --> 00:14:56 we have to model it much more exactly. 200 00:14:56 --> 00:15:01 We need to see what's going on. So, what's happening here is 201 00:15:01 --> 00:15:07 that at t=0, I get this step. So, think of that as a pulse of 202 00:15:07 --> 00:15:11 energy, and the instant it comes here, and instantaneously this 203 00:15:11 --> 00:15:14 guy looks like a voltage divider, OK? 204 00:15:14 --> 00:15:18 I've chosen my resistance, R, here to match the 205 00:15:18 --> 00:15:21 instantaneous impedance looking in, which is also R. 206 00:15:21 --> 00:15:24 I've arranged it to be that way. 207 00:15:24 --> 00:15:27 So, instantaneously, the point at which the pulse 208 00:15:27 --> 00:15:31 appears at this point, looking down here looks like 209 00:15:31 --> 00:15:35 another resistor to this pulse. OK, therefore, 210 00:15:35 --> 00:15:38 when I start out, I start out going up and 211 00:15:38 --> 00:15:41 pausing at 2.5 because instantaneously, 212 00:15:41 --> 00:15:43 this looks like a resistance, R. 213 00:15:43 --> 00:15:46 So instantaneously, it's a voltage divider, 214 00:15:46 --> 00:15:49 R, and so it's 2.5 here, instantaneously. 215 00:15:49 --> 00:15:52 OK, then what happens? Then those little pulse 216 00:15:52 --> 00:15:55 propagates down. What does it mean for a pulse 217 00:15:55 --> 00:15:58 of energy to propagate down? Well, it begins sending a 218 00:15:58 --> 00:16:02 current through the inductor, begins charging up the 219 00:16:02 --> 00:16:06 capacitor, current here, so that's what I mean by saying 220 00:16:06 --> 00:16:10 that the pulse of energy goes down. 221 00:16:10 --> 00:16:14 OK, it's a step that sends current to the inductor and 222 00:16:14 --> 00:16:19 charges of the capacitors, and that wave front moves out 223 00:16:19 --> 00:16:23 here and comes all the way here. What happens there? 224 00:16:23 --> 00:16:27 Well, think about it. Supposing you stand here, 225 00:16:27 --> 00:16:31 and you hold a long string in your hand somehow, 226 00:16:31 --> 00:16:35 and just do this Gedanken experiment. 227 00:16:35 --> 00:16:38 It's not easy to do. And so, let's say you somehow 228 00:16:38 --> 00:16:41 have the long string that you're holding onto, 229 00:16:41 --> 00:16:45 and the string on the other side is not connected to 230 00:16:45 --> 00:16:47 anything. OK, just imagine this 231 00:16:47 --> 00:16:50 experiment. OK, and what you do is you 232 00:16:50 --> 00:16:54 suddenly raise the string up at your end by about a foot. 233 00:16:54 --> 00:16:56 What are you going to see happen? 234 00:16:56 --> 00:16:59 So instantaneously, the string is up here, 235 00:16:59 --> 00:17:04 but the rest of the string is down a foot below. 236 00:17:04 --> 00:17:07 And then you see this wave propagate down the string, 237 00:17:07 --> 00:17:09 right? So here's a string. 238 00:17:09 --> 00:17:12 I lift this thing, and you see this wave propagate 239 00:17:12 --> 00:17:15 all the way down, the one foot wave propagate all 240 00:17:15 --> 00:17:17 the way down until you come here. 241 00:17:17 --> 00:17:20 What happens here? So, out here, 242 00:17:20 --> 00:17:23 the string is down here, the wave propagates out here 243 00:17:23 --> 00:17:26 and pulls it up to one. And then what? 244 00:17:26 --> 00:17:29 There's nothing connected there, so the string is zipped 245 00:17:29 --> 00:17:34 up, but it's got the energy. OK, where does energy go? 246 00:17:34 --> 00:17:37 Well, it continues going up, and sends a wave back. 247 00:17:37 --> 00:17:40 OK, so just think of a string that you pull up like this and 248 00:17:40 --> 00:17:43 propagates down, boom, hits the other end, 249 00:17:43 --> 00:17:46 reverses, and comes back at me. OK, you can look at a 250 00:17:46 --> 00:17:48 complementary situation, not the same as this, 251 00:17:48 --> 00:17:51 but complementary by taking a string, tying it to a door, 252 00:17:51 --> 00:17:54 and lifting it up. It's not the same situation. 253 00:17:54 --> 00:17:57 It's a complementary situation where it's tied down. 254 00:17:57 --> 00:18:00 Tying down a string is tantamount to shorting the ends 255 00:18:00 --> 00:18:03 here. OK, in that case what you'll 256 00:18:03 --> 00:18:07 see happen: as the wave goes down, at the end the string 257 00:18:07 --> 00:18:11 can't move, so the wave goes and flips around and comes back. 258 00:18:11 --> 00:18:13 Try it out at home. Take a long piece of string, 259 00:18:13 --> 00:18:15 tie it up there, do this, OK? 260 00:18:15 --> 00:18:19 And you'll see the wave go out, flip, and then come back at 261 00:18:19 --> 00:18:21 you. So, if your friends see you 262 00:18:21 --> 00:18:25 tying a long piece of string doing this, hopefully they won't 263 00:18:25 --> 00:18:29 think you're nuts or something. OK, so the same way here: 264 00:18:29 --> 00:18:33 this thing flies down, OK, there's no way to dissipate 265 00:18:33 --> 00:18:35 the energy here, so this thing continues up. 266 00:18:35 --> 00:18:39 And then, what I'm going to see happen is the wave move back. 267 00:18:39 --> 00:18:43 OK, the wave begins to move back, and that's another 2.5V, 268 00:18:43 --> 00:18:46 resulting in a net 5V at this terminal. 269 00:18:46 --> 00:18:50 That wave begins to blast back, OK, and then when it comes back 270 00:18:50 --> 00:18:53 here, after some amount of time, it raises this to 5V, 271 00:18:53 --> 00:18:56 and that's what you see happen here. 272 00:18:56 --> 00:18:59 So, this is a wave going down, and then after a time, 273 00:18:59 --> 00:19:04 2t, it goes back up to 5V. That's a return wave. 274 00:19:04 --> 00:19:07 It's 2t because to get down here is t seconds, 275 00:19:07 --> 00:19:12 and then t seconds to come back, which is why we have 2t. 276 00:19:12 --> 00:19:15 OK, that is why you see that pulse at 2.5. 277 00:19:15 --> 00:19:19 OK, so I'd like to show you a few more things here. 278 00:19:19 --> 00:19:22 Clearly we don't want that in our circuits. 279 00:19:22 --> 00:19:27 Could someone tell me what problem would happen if my 280 00:19:27 --> 00:19:32 signals looked like this in my digital circuits? 281 00:19:32 --> 00:19:39 Instead of being nice little steps, if there was a little 282 00:19:39 --> 00:19:46 thing in the middle and then a step, what's the problem with 283 00:19:46 --> 00:19:51 signals like this? In digital circuits, 284 00:19:51 --> 00:19:54 what did it violate? Yeah? 285 00:19:54 --> 00:19:59 Exactly. This little sucker here is 286 00:19:59 --> 00:20:05 meandering out in the forbidden region for all of 2T. 287 00:20:05 --> 00:20:10 Can't do that. OK, can't have that. 288 00:20:10 --> 00:20:17 Well, so we need to fix the problem because this is real 289 00:20:17 --> 00:20:20 life. OK, but what if you and your 290 00:20:20 --> 00:20:23 buddy were signaling each other but using digital signals from 291 00:20:23 --> 00:20:24 one dorm room to another maybe a few hundred feet down? 292 00:20:24 --> 00:20:26 Your circuit isn't going to work because the signal's going 293 00:20:26 --> 00:20:28 to meander around in the forbidden region for some time. 294 00:20:28 --> 00:20:29 So, any ideas what might you do? 295 00:20:29 --> 00:20:30 Yeah? Put a resistor on the end. 296 00:20:30 --> 00:20:32 OK, trick the circuit. So, what you can do, 297 00:20:32 --> 00:20:33 and I'm going to show you a little demo here, 298 00:20:33 --> 00:20:35 what you can do is the reason I got this wave propagating back, 299 00:20:35 --> 00:20:38 was that there was nothing to absorb the energy. 300 00:20:38 --> 00:20:41 So instead, what if I put another resistor here, 301 00:20:41 --> 00:20:44 R? So, as far as a burst of energy 302 00:20:44 --> 00:20:46 is concerned, it says, oh, 303 00:20:46 --> 00:20:50 yeah, it just looks the same. It's R, and goes and dissipates 304 00:20:50 --> 00:20:53 in this resistor, R, and guess what? 305 00:20:53 --> 00:20:56 I don't have any wave going back, and I'm done. 306 00:20:56 --> 00:21:00 So, what I'm going to find, then, is that out here, 307 00:21:00 --> 00:21:03 this goes up to 5V, but out here, 308 00:21:03 --> 00:21:07 I will have a signal that starts out and goes up to 2.5, 309 00:21:07 --> 00:21:11 and that's it. OK, I lift it up, 310 00:21:11 --> 00:21:14 it goes down, it goes to 2.5 because in the 311 00:21:14 --> 00:21:17 lumped model that you've been dealing with, 312 00:21:17 --> 00:21:20 it's a resistor R, a resistor R to ground, 313 00:21:20 --> 00:21:23 and you're taking the connection here or here. 314 00:21:23 --> 00:21:27 So, it's your standard lumped model, your voltage resistive 315 00:21:27 --> 00:21:29 divider, and it just simply works. 316 00:21:29 --> 00:21:34 Yeah, that's it. So, this is the end of the 317 00:21:34 --> 00:21:37 cable. OK, if somehow you could watch 318 00:21:37 --> 00:21:43 this and that at the same time, so what I'm going to do, 319 00:21:43 --> 00:21:47 and this is a resistor, R, I'm just going to plug it 320 00:21:47 --> 00:21:51 in. OK, if the fates are smiling at 321 00:21:51 --> 00:21:56 me, what should you see there? What should happen is that the 322 00:21:56 --> 00:22:01 second jump from 2.5 to 5 should simply go away. 323 00:22:01 --> 00:22:06 It should just go to 2.5. Let's try that. 324 00:22:06 --> 00:22:10 There you go. I take it out, 325 00:22:10 --> 00:22:16 it jumps back up. OK, so all I've done here is 326 00:22:16 --> 00:22:24 put in a resistor at the end, and I'm still measuring the 327 00:22:24 --> 00:22:30 voltage here. So, that's one solution. 328 00:22:30 --> 00:22:32 One solution is to put a resistor here. 329 00:22:32 --> 00:22:36 So, I absorb the energy, and the resistance has to be 330 00:22:36 --> 00:22:39 equal to the instantaneous impedance looking in. 331 00:22:39 --> 00:22:42 And the instantaneous impedance, for many of these 332 00:22:42 --> 00:22:45 cables is 50 ohms. It's called a characteristic 333 00:22:45 --> 00:22:47 impedance. OK, you'll learn a lot more 334 00:22:47 --> 00:22:51 about it if you take 6.014. That course starts out with 335 00:22:51 --> 00:22:56 assuming that things are distributed in that matter. 336 00:22:56 --> 00:22:59 OK, so if you want to design multi-gigahertz chips, 337 00:22:59 --> 00:23:04 it turns out that if you have signals that are traveling 338 00:23:04 --> 00:23:08 around at edge speeds in the 0.1-1 nanosecond range, 339 00:23:08 --> 00:23:12 remember, light travels roughly one nanosecond a foot. 340 00:23:12 --> 00:23:16 And if the signals are roughly of interest are 0.1 nanoseconds, 341 00:23:16 --> 00:23:20 then if the chips are one inch in size, right there, 342 00:23:20 --> 00:23:24 the propagation speed of a signal across a chip is 0.1 343 00:23:24 --> 00:23:26 nanoseconds. OK, so today, 344 00:23:26 --> 00:23:30 we have to deal with these issues and try to figure out 345 00:23:30 --> 00:23:36 what to do about them. OK, so that's one solution that 346 00:23:36 --> 00:23:40 somebody pointed out. There is a second solution. 347 00:23:40 --> 00:23:43 Anybody else have a second solution for me? 348 00:23:43 --> 00:23:46 And then there's a third solution, too. 349 00:23:46 --> 00:23:49 So it's OK. You can give me either the 350 00:23:49 --> 00:23:53 second or the third solution. It doesn't matter. 351 00:23:53 --> 00:23:56 Anybody? You have two to choose from, 352 00:23:56 --> 00:23:57 come on. Yeah? 353 00:23:57 --> 00:24:00 You can do that, yeah. 354 00:24:00 --> 00:24:05 So we could define the problem away by saying this transition 355 00:24:05 --> 2.5. is such that my high is below 356 2.5. --> 00:24:07 357 00:24:07 --> 00:24:12 So, once it goes above 2.5, who cares what it does? 358 00:24:12 --> 00:24:16 That's a good point. That's solution number four, 359 00:24:16 --> 00:24:19 and that works. OK, so I still need two and 360 00:24:19 --> 00:24:21 three. Put a diode in there? 361 00:24:21 --> 00:24:26 Yeah, I guess you could. If the diode had the same kind 362 00:24:26 --> 00:24:30 of impedance looking in, it kind of may work. 363 00:24:30 --> 00:24:34 That's solution 4.2. I'm still waiting for solution 364 00:24:34 --> 00:24:37 two and three. Pardon? 365 00:24:37 --> 00:24:40 Cut off the cable? Exactly. 366 00:24:40 --> 00:24:45 So, the solution says, work on a different problem. 367 00:24:45 --> 00:24:49 And that is solution number two. 368 00:24:49 --> 00:24:53 OK, so the idea is, the root of all evil, 369 00:24:53 --> 00:24:58 this long wire, which is why I had this thing 370 00:24:58 --> 00:25:02 here. So instead, if I had short 371 00:25:02 --> 00:25:07 wires, then what will happen is if it's a very small wire, 372 00:25:07 --> 00:25:12 it'll look like this. And the wire's small enough. 373 00:25:12 --> 00:25:16 I will see an itty-bitty thingamajig out there, 374 00:25:16 --> 00:25:20 but not a whole lot. By the way, the fun thing is 375 00:25:20 --> 00:25:25 that you can actually calculate the speed of light, 376 00:25:25 --> 00:25:28 the experiment I just showed you. 377 00:25:28 --> 00:25:33 Can we put that up again? No, the big one. 378 00:25:33 --> 00:25:37 So, in the experiment that I showed you, this distance was 379 00:25:37 --> 00:25:39 about 500 nanoseconds, OK? 380 00:25:39 --> 00:25:42 This distance was 500 nanoseconds this time interval. 381 00:25:42 --> 00:25:46 The length of this cable is about 500 feet, 382 00:25:46 --> 00:25:50 somewhere around 500 feet. So you can figure out the speed 383 00:25:50 --> 00:25:52 of light. What's the speed of light? 384 00:25:52 --> 00:25:56 So, this is about 500 nanoseconds, and this cable is 385 00:25:56 --> 00:26:01 roughly 500 feet. What's the speed of light? 386 00:26:01 --> 00:26:04 Roughly a foot per nanosecond. So, would you believe that in 387 00:26:04 --> 00:26:08 6.002 we've figured out the speed of light from a simple 388 00:26:08 --> 00:26:11 experiment? All right, so let's do the next 389 00:26:11 --> 00:26:14 experiment now. Let's take out the long cable, 390 00:26:14 --> 00:26:16 and connect a short cable instead. 391 00:26:16 --> 00:26:20 So, what I'm going to do is disconnect the long cable, 392 00:26:20 --> 00:26:22 and instead, connect a small cable. 393 00:26:22 --> 00:26:26 It's still relatively long, but much shorter than the 500 394 00:26:26 --> 00:26:28 foot cable. So what you should see happen 395 00:26:28 --> 00:26:32 now is that the little step should not be this big, 396 00:26:32 --> 00:26:37 but much, much smaller. So, take a look up there. 397 00:26:37 --> 00:26:40 There you go. OK, so with this thingamajig, 398 00:26:40 --> 00:26:43 the little blip there is very small. 399 00:26:43 --> 00:26:47 And of course, if I make it even smaller, 400 00:26:47 --> 00:26:52 then that can virtually vanish. OK, so that is solution number 401 00:26:52 --> 00:26:54 two. So, we've done one, 402 00:26:54 --> 00:26:58 two, four, 4.2. So, what's solution number 403 00:26:58 --> 00:27:01 three? One more solution. 404 00:27:01 --> 00:27:04 Pardon? So, another solution we 405 00:27:04 --> 00:27:08 mentioned is we change this resistance. 406 00:27:08 --> 00:27:11 and that will work, if I make this very, 407 00:27:11 --> 00:27:16 very low, then I'll get much closer to 5V here. 408 00:27:16 --> 00:27:21 Yeah, that's a possibility. That's solution six I guess. 409 00:27:21 --> 00:27:24 So what was solution number three? 410 00:27:24 --> 00:27:30 And you all should be able to solve this. 411 00:27:30 --> 00:27:34 You guys know the answer. OK, you folks should be able to 412 00:27:34 --> 00:27:35 solve this. Yes? 413 00:27:35 --> 00:27:38 Ah, clock. So, what I can do is just as 414 00:27:38 --> 00:27:42 was pointed out, that I leveraged my abstraction 415 00:27:42 --> 00:27:45 by changing my VOH and VIH thresholds. 416 00:27:45 --> 00:27:49 So that'll work. The alternative thing is to use 417 00:27:49 --> 00:27:52 a clock. A clock is a distinguished 418 00:27:52 --> 00:27:56 signal that I send around in my digital circuit, 419 00:27:56 --> 00:28:00 OK? So all I do is if I arrange it 420 00:28:00 --> 00:28:04 such that my clock doesn't happen in this vicinity, 421 00:28:04 --> 00:28:10 but rather, my clock happens late enough, then I'm going to 422 00:28:10 --> 00:28:15 sample and look at my signals only on the rising and falling 423 00:28:15 --> 00:28:18 edges of the clock, in which case I won't be 424 00:28:18 --> 00:28:23 looking at the signal, but the signal is doing weird 425 00:28:23 --> 00:28:26 things. OK, so a decent clock would 426 00:28:26 --> 00:28:30 also solve the problem. OK, any last minute questions 427 00:28:30 --> 00:28:40 before we go onto the next one? OK, the next problem that we're 428 00:28:40 --> 00:28:47 going to look at is titled the Double Dip. 429 00:28:47 --> 00:28:56 OK, so what I'm going to do here is our Vs power supply, 430 00:28:56 --> 00:29:06 and what I'm going to do is feed the power supply to an 431 00:29:06 --> 00:29:12 inverter. OK, so we've been doing this 432 00:29:12 --> 00:29:16 all along; Vs, I feed the supply to an 433 00:29:16 --> 00:29:20 inverter. And what I'm also going to do 434 00:29:20 --> 00:29:26 is, so this is ground, and I'm going to feed it to, 435 00:29:26 --> 00:29:31 so feed the power supply connection to a couple of 436 00:29:31 --> 00:29:39 inverters. OK, and what I'm going to do is 437 00:29:39 --> 00:29:47 apply some sort of a signal to this inverter, 438 00:29:47 --> 00:29:57 and I'm going to observe, and I'm going to look at this 439 00:29:57 --> 00:30:03 signal here. So, the abstraction should tell 440 00:30:03 --> 00:30:07 you that here's a power supply. This is 5V, or whatever the 441 00:30:07 --> 00:30:10 supply voltage is to these two inverters. 442 00:30:10 --> 00:30:14 That should be fine, and feed some sort of input to 443 00:30:14 --> 00:30:18 this inverter, OK, and the output here should 444 00:30:18 --> 00:30:20 be simply determined by this input. 445 00:30:20 --> 00:30:25 This signal can have absolutely no bearing on this output. 446 00:30:25 --> 00:30:30 OK, and let's look at that and actually confirm it. 447 00:30:30 --> 00:30:35 So, I build a circuit like this, and we look at this 448 00:30:35 --> 00:30:40 output, and initially there should not be any, 449 00:30:40 --> 00:30:46 it should simply work fine. OK, so it should work now, 450 00:30:46 --> 00:30:47 right? OK. 451 00:30:47 --> 00:30:53 So what you have here, this input here is the input 452 00:30:53 --> 00:30:56 that I'm feeding to this inverter. 453 00:30:56 --> 00:31:02 That is a straight line. Is that the power supply? 454 00:31:02 --> 00:31:06 It doesn't matter? OK, so I believe this is the, 455 00:31:06 --> 00:31:10 we'll check in a few minutes, but I suspect this is the power 456 00:31:10 --> 00:31:14 supply, and this guy here is the output looking here. 457 00:31:14 --> 00:31:17 So, the green one is the look here part. 458 00:31:17 --> 00:31:21 So, there must have been a one-to-zero transition here, 459 00:31:21 --> 00:31:24 and that's all fine. So, so far, so good. 460 00:31:24 --> 00:31:28 OK, no problem so far. Now what I'm going to do is I'm 461 00:31:28 --> 00:31:32 going to do something to the circuit that as far as 462 00:31:32 --> 00:31:35 abstraction is concerned, it doesn't show up on the 463 00:31:35 --> 00:31:41 circuit. OK, it's below the abstraction 464 00:31:41 --> 00:31:45 layer. OK, I'm going to do something, 465 00:31:45 --> 00:31:48 and suddenly, some things are going to 466 00:31:48 --> 00:31:51 happen. Look up there. 467 00:31:51 --> 00:31:56 The circuit hasn't changed. It's the same circuit. 468 00:31:56 --> 00:31:59 I've done nothing to the circuit. 469 00:31:59 --> 00:32:05 OK, look at the green output. I've done nothing to the 470 00:32:05 --> 00:32:09 circuit that is visible here. OK, it's below the radar screen 471 00:32:09 --> 00:32:11 here. It's below the abstraction 472 00:32:11 --> 00:32:14 barrier. But, look at the disaster here. 473 00:32:14 --> 00:32:17 OK, in particular, the spikes going up are not so 474 00:32:17 --> 00:32:20 much of a problem. Because of the static 475 00:32:20 --> 00:32:23 discipline, if I am at five or six or seven, 476 00:32:23 --> 00:32:27 it doesn't matter as long as I am higher than VOH. 477 00:32:27 --> 00:32:32 So as long as I'm higher than VOH I don't have a problem. 478 00:32:32 --> 00:32:34 But the problems are these repeated dips. 479 00:32:34 --> 00:32:38 OK, the dips are a problem here, which is why I labeled 480 00:32:38 --> 00:32:42 this experiment the Double Dip. OK, the dips are bad because if 481 00:32:42 --> 00:32:46 they are large enough, they can then group the output 482 00:32:46 --> 00:32:49 down into the forbidden region, or worse yet, 483 00:32:49 --> 00:32:53 make it look like a zero. OK, so you're not prepared for 484 00:32:53 --> 00:32:55 this. So what I'm going to do is tell 485 00:32:55 --> 00:32:59 you what I did to the circuit, and then ask you to help me 486 00:32:59 --> 00:33:08 figure it out. So all I did was applied a load 487 00:33:08 --> 00:33:17 resistance to this, I think of 50 ohms or some RL. 488 00:33:17 --> 00:33:28 I just applied a load resistor. And this inverter here, 489 00:33:28 --> 00:33:38 I believe, is a CMOS inverter that looks, OK? 490 00:33:38 --> 00:33:41 So I have this input applied to this inverter, 491 00:33:41 --> 00:33:43 and all I did is I applied an RL load here. 492 00:33:43 --> 00:33:48 And notice that the load here should not really change what's 493 00:33:48 --> 00:33:50 happening if this is an ideal inverter, OK, 494 00:33:50 --> 00:33:54 the load here should simply draw some current but really 495 00:33:54 --> 00:33:58 should not change any other property. 496 00:33:58 --> 00:34:02 OK, so just remember, what's the signal doing? 497 00:34:02 --> 00:34:05 The signal is high. This guy turns on, 498 00:34:05 --> 00:34:10 and current flows like this. So, let's say I had some sort 499 00:34:10 --> 00:34:14 of a capacitor here. This charges like this, 500 00:34:14 --> 00:34:17 and when it's slow, the PFET is on, 501 00:34:17 --> 00:34:20 and current flows through here down here. 502 00:34:20 --> 00:34:25 And then when this goes high, this guy goes off, 503 00:34:25 --> 00:34:29 and this guy turns on. OK, so the current flows out 504 00:34:29 --> 00:34:35 this way and this charges through this guy. 505 00:34:35 --> 00:34:39 When I turn it off, the P fret turns on and draws 506 00:34:39 --> 00:34:44 current from the top. OK, so do we have any theories 507 00:34:44 --> 00:34:50 as to why I'm getting that messy stuff, the dips and the spikes, 508 00:34:50 --> 00:34:56 on the output of this inverter? So why does this inverter care 509 00:34:56 --> 00:34:59 what the load of this inverter is? 510 00:34:59 --> 00:35:04 I mean, who cares? So, put your thinking caps on. 511 00:35:04 --> 00:35:08 Any theories? You guys did pretty well with 512 00:35:08 --> 00:35:11 the previous one. And this is much easier, 513 00:35:11 --> 00:35:15 actually. Need a better power supply; 514 00:35:15 --> 00:35:20 OK, so what I'm going to do is I'm going to replace the power 515 00:35:20 --> 00:35:24 supply, and instead, use a much bigger power supply 516 00:35:24 --> 00:35:28 at 5V. A big, mongo power supply that 517 00:35:28 --> 00:35:31 can supply 100 amps, and guess what, 518 00:35:31 --> 00:35:34 I've made the changes, but guess what, 519 00:35:34 --> 00:35:41 I still see the spikes. Good try, but it didn't work 520 00:35:41 --> 00:35:43 out. Good try, good try. 521 00:35:43 --> 00:35:46 What next? Any other solutions? 522 00:35:46 --> 00:35:50 Yes? So dips are because of the 523 00:35:50 --> 00:35:56 resistance, and the spikes are because of the inductance? 524 00:35:56 --> 00:36:02 You're half correct. So, which one is it? 525 00:36:02 --> 00:36:07 So, dips are because of resistances, and spikes are 526 00:36:07 --> 00:36:11 because of inductances. You're half correct. 527 00:36:11 --> 00:36:17 It turns out that both the dips and the spikes are because of 528 00:36:17 --> 00:36:21 inductances. OK, but be that as it may, 529 00:36:21 --> 00:36:27 let me give you the next clue here, and then see if you can 530 00:36:27 --> 00:36:33 come closer to the answer. So, what I've done here is I've 531 00:36:33 --> 00:36:38 made this wire really, really long. 532 00:36:38 --> 00:36:41 OK, it's a really long wire, OK, but it's a thick wire, 533 00:36:41 --> 00:36:44 so it's a long, long, thick wire. 534 00:36:44 --> 00:36:46 So it's not the resistance. It's really, 535 00:36:46 --> 00:36:50 really thick and mongo, and it's a long wire, 536 00:36:50 --> 00:36:54 so a signal wire above a ground plane behaves like an inductor. 537 00:36:54 --> 00:36:57 And so here, it has the capacitance to, 538 00:36:57 --> 00:36:59 but in this case it's inductance. 539 00:36:59 --> 00:37:04 It's inductance here. So, I'll give you another ten 540 00:37:04 --> 00:37:10 seconds to think about it and then tell you the answer. 541 00:37:10 --> 00:37:15 But despite the inductance here, it turns out if I take out 542 00:37:15 --> 00:37:19 this resistor, the problem goes away. 543 00:37:19 --> 00:37:24 Look, I take out the resistor, the problem goes away. 544 00:37:24 --> 00:37:34 Yes, there is an inductor here. OK, I take out this resistor, 545 00:37:34 --> 00:37:44 problem goes away. I put the resistor back in, 546 00:37:44 --> 00:37:46 boom. Yes? 547 00:37:46 --> 00:37:54 OK, pretty good. That's 86 points. 548 00:37:54 --> 00:38:03 So here's what's going on. There's an inductor here, 549 00:38:03 --> 00:38:06 and when I put a 50 ohm resistor here, 550 00:38:06 --> 00:38:10 I put this resistor. When the PFET turns on, 551 00:38:10 --> 00:38:13 it draws a current. OK, it's going to draw a 552 00:38:13 --> 00:38:15 current. It draws a current; 553 00:38:15 --> 00:38:19 remember that across an inductor, I have a drop. 554 00:38:19 --> 00:38:22 And the drop relates to the di/dt. 555 00:38:22 --> 00:38:26 Remember, for a capacitor, the current is Cdv/dt. 556 00:38:26 --> 00:38:29 For the inductor, the voltage across the inductor 557 00:38:29 --> 00:38:33 is Ldi/dt. So, if di/dt, 558 00:38:33 --> 00:38:37 from switching a large current through the inductor every 559 00:38:37 --> 00:38:40 cycle, OK, big di/dt, di/dt is large. 560 00:38:40 --> 00:38:44 I've made it large by having a very small RL, 561 00:38:44 --> 00:38:47 so, you know, pulling a big current through 562 00:38:47 --> 00:38:50 every few, whatever, every cycle, 563 00:38:50 --> 00:38:53 and then stopping it. And so therefore, 564 00:38:53 --> 00:38:58 I'm getting these big drops across this inductor that relate 565 00:38:58 --> 00:39:00 to Ldi/dt. In other words, 566 00:39:00 --> 00:39:05 the power supply here is fine. While you guys were watching, 567 00:39:05 --> 00:39:08 I switched to the huge, mongo power supply, 568 00:39:08 --> 00:39:12 and so this voltage is fine. But then this voltage after the 569 00:39:12 --> 00:39:16 wire is the problem. So, this voltage here doesn't 570 00:39:16 --> 00:39:19 look like this anymore. Rather, it has spikes that go 571 00:39:19 --> 00:39:22 down, for example, and when I switch the other 572 00:39:22 --> 00:39:24 way, they go up. OK, so therefore, 573 00:39:24 --> 00:39:30 what I end up having here is big spikes on this power supply. 574 00:39:30 --> 00:39:33 And when this guy's power supply goes wacko, 575 00:39:33 --> 00:39:37 then I see the spikes on its output as well. 576 00:39:37 --> 00:39:40 OK, so what are the solutions for that? 577 00:39:40 --> 00:39:43 Any solutions here? What can I do to fix the 578 00:39:43 --> 00:39:45 problem? Pardon? 579 00:39:45 --> 00:39:46 Stop using the, exactly. 580 00:39:46 --> 00:39:49 When in doubt, do something else. 581 00:39:49 --> 00:39:54 Build a different design. So what I could do is this is 582 00:39:54 --> 00:39:59 pretty dumb, using a long wire. And so, no, but trust me, 583 00:39:59 --> 00:40:04 oftentimes you go to the store room and they give you a big 584 00:40:04 --> 00:40:07 roll of wire, and you're too lazy to cut a 585 00:40:07 --> 00:40:10 piece out. Use the whole roll, 586 00:40:10 --> 00:40:13 and use the two ends, and connect it in, 587 00:40:13 --> 00:40:15 OK? So, if I had a much shorter 588 00:40:15 --> 00:40:18 piece of wire, then that can solve my problem. 589 00:40:18 --> 00:40:22 But again, remember, what's small to you may not be 590 00:40:22 --> 00:40:25 small to the circuit. OK, so let's say, 591 00:40:25 --> 00:40:29 for example, I'm Intel, and I'm building a 592 00:40:29 --> 00:40:33 10 GHz Pentium 6 processor. OK, it's 0.1 nanosecond is my 593 00:40:33 --> 00:40:37 cycle time. There, even a small, 594 00:40:37 --> 00:40:40 itty bitty wire can be a real problem. 595 00:40:40 --> 00:40:44 OK, and so therefore, distributing power throughout a 596 00:40:44 --> 00:40:47 one inch chip that's clocking at 10 GHz is a really, 597 00:40:47 --> 00:40:51 really hard problem. And our own David Perreault, 598 00:40:51 --> 00:40:55 who is doing one of our sections, is one of the world's 599 00:40:55 --> 00:40:58 experts in this field. Distributing power, 600 00:40:58 --> 00:41:02 something as simple as, how do I get 1V in a stable 601 00:41:02 --> 00:41:05 manner to every single device on my chip? 602 00:41:05 --> 00:41:10 It's a hard problem. OK, so now, you have to begin 603 00:41:10 --> 00:41:15 feeding your power supply connections much like RC 604 00:41:15 --> 00:41:19 circuits, OK, and you have to solve some hard 605 00:41:19 --> 00:41:25 problems to be able to simply distribute power decently 606 00:41:25 --> 00:41:29 throughout your circuit. So, what else can I do? 607 00:41:29 --> 00:41:32 Yeah? Say it again? 608 00:41:32 --> 00:41:35 Ah, I can do that. I could use different wires to 609 00:41:35 --> 00:41:39 connect each of the inverters. That's a good point. 610 00:41:39 --> 00:41:44 So here, the coupling happens because I connect the two 611 00:41:44 --> 00:41:48 inverters way out here. So instead, I use a different 612 00:41:48 --> 00:41:50 cable. I hadn't thought of that. 613 00:41:50 --> 00:41:54 That's a creative solution. OK, so in fact, 614 00:41:54 --> 00:41:57 if you build a chip, so we built this chip called 615 00:41:57 --> 00:42:01 RAW in our group, and it has on the order of 10 616 00:42:01 --> 00:42:06 million gates. And this chip we built with 617 00:42:06 --> 00:42:09 IBM's technology, and it turns out that you don't 618 00:42:09 --> 00:42:14 send power supply in through a pin and then connect that 1.5V 619 00:42:14 --> 00:42:18 supply to all your gates. What you do is from that pin, 620 00:42:18 --> 00:42:22 you then build special power supply buffering trees. 621 00:42:22 --> 00:42:25 And each tree, each leaf of the tree drives a 622 00:42:25 --> 00:42:27 subcircuit. In other words, 623 00:42:27 --> 00:42:31 if this is a chip, you have lots and lots of gates 624 00:42:31 --> 00:42:36 throughout your chip. What you do not do is bring in 625 00:42:36 --> 00:42:40 a power supply like this, and then connect. 626 00:42:40 --> 00:42:45 You don't do that. That's the worst possible thing 627 00:42:45 --> 00:42:49 you can do. It's an absolute disaster for 628 00:42:49 --> 00:42:55 the reason just brought up. OK, so instead what you do is 629 00:42:55 --> 00:42:59 divide up the chip into, say, four quadrants. 630 00:42:59 --> 00:43:04 OK, in our case, we have 16 quadrants. 631 00:43:04 --> 00:43:08 And then what you do is from this point, you take one wire 632 00:43:08 --> 00:43:12 that goes to this quadrant, one wire that comes here, 633 00:43:12 --> 00:43:15 one here, and one here, so that you're getting the 634 00:43:15 --> 00:43:20 power supply very close to the source, and you have different 635 00:43:20 --> 00:43:24 connections going to each quadrant so that switching in 636 00:43:24 --> 00:43:27 this quadrant will not affect this guy because of the 637 00:43:27 --> 00:43:33 inductance of this lead here. OK, and if you hadn't taken 638 00:43:33 --> 00:43:37 6.002, you'd have been arguing with IBM, I don't want 16 wires. 639 00:43:37 --> 00:43:40 I want just one wire. OK, so there are other 640 00:43:40 --> 00:43:44 solutions, of course. There's a couple more solution. 641 00:43:44 --> 00:43:49 One is that what you can do is part of the problem here is that 642 00:43:49 --> 00:43:52 all my transitions are really, really sharp. 643 00:43:52 --> 00:43:54 OK, so di/dt is very, very large. 644 00:43:54 --> 00:43:58 So, there's a whole new technique in design of digital 645 00:43:58 --> 00:44:01 and analog circuits, which talks about, 646 00:44:01 --> 00:44:05 maybe I should call it waveform engineering, OK, 647 00:44:05 --> 00:44:09 or edge engineering. OK, it's also called edge 648 00:44:09 --> 00:44:12 smoothing. The idea is that rather than 649 00:44:12 --> 00:44:16 have very sharp edges in your circuit, you try to have 650 00:44:16 --> 00:44:19 smoother edges. And when you have smoother 651 00:44:19 --> 00:44:22 edges, OK, then your di/dt is now going to be less. 652 00:44:22 --> 00:44:25 It's not going to be very, very high. 653 00:44:25 --> 00:44:29 Rather, your delta I is spread out over a longer period of 654 00:44:29 --> 00:44:31 time. Of course, that means the 655 00:44:31 --> 00:44:34 circuits may have to run a little slower, 656 00:44:34 --> 00:44:38 but that can also solve the problem. 657 00:44:38 --> 00:44:41 And in fact, that same smoothing of the 658 00:44:41 --> 00:44:46 waveforms was also the solution you saw in the capacitive 659 00:44:46 --> 00:44:49 coupling we saw a month and a half ago. 660 00:44:49 --> 00:44:53 And let me show you the demo, and then close up. 661 00:44:53 --> 00:44:55 Not working? OK, that's OK. 662 00:44:55 --> 00:45:00 It doesn't matter. So if you remember the demo 663 00:45:00 --> 00:45:05 from the lecture about a month and a half ago in capacitors, 664 00:45:05 --> 00:45:10 I talked about a chip with two pins, and there was this 665 00:45:10 --> 00:45:14 capacitive coupling between the pins. 666 00:45:14 --> 00:45:18 And because of this, if this waveform is switching, 667 00:45:18 --> 00:45:23 then because of this coupling, you will end up getting, 668 00:45:23 --> 00:45:29 if this is the signal here, you will end up getting spikes 669 00:45:29 --> 00:45:33 on this pin because of the signaling of the other pin. 670 00:45:33 --> 00:45:39 And that's good old capacitive coupling. 671 00:45:39 --> 00:45:42 OK, and to eliminate this, what you can do is much like 672 00:45:42 --> 00:45:45 with the inductance system, if you, rather than having 673 00:45:45 --> 00:45:49 sharp transitions on this pin, if you have smooth transitions 674 00:45:49 --> 00:45:52 that look like this, then what you can do is you'll 675 00:45:52 --> 00:45:56 now spread delta V from here to here over a longer delta T. 676 00:45:56 --> 00:45:59 OK, delta T has become longer, and because of that, 677 00:45:59 --> 00:46:03 you end up getting much better behavior, and you don't end up 678 00:46:03 --> 00:46:06 getting these spikes. So therefore, 679 00:46:06 --> 00:46:10 if you want to build really, really fast circuits, 680 00:46:10 --> 00:46:13 you have to be really careful. You can build fast circuits, 681 00:46:13 --> 00:46:15 but watch out for them fast edges. 682 00:46:15 --> 00:46:18 OK, fast edges are nasty. They kill you. 683 00:46:18 --> 00:46:22 That's something to remember as you build the next generation of 684 00:46:22 --> 00:46:24 circuits. Well, thank you all. 685 00:46:24 --> 00:46:27 I had a blast, and I hope you guys had fun 686 00:46:27 --> 46:30 too. Thank you.