275 lines
6.9 KiB
Plaintext
275 lines
6.9 KiB
Plaintext
{
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"text": [
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null,
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"Let us summarize what we've\nlearned so far.",
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"So we started out with building\nthis playground, this",
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"EECS playground.",
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"And within this playground,\nwe've all decided that we will",
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"abide by the lumped matter\ndiscipline, the LMD.",
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"And these are simply constraints\nthat we impose",
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"upon ourselves to simplify\nour analysis.",
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"Notice that, you really\ndon't have to do that.",
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"You are welcome to hang out here\nand do whatever you want.",
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"But you might have a\nlot of fun as well.",
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"But, you will not be able to\nbuild things as simply as you",
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"would if you were inside\nthe EECS playground.",
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"But, Within this playground\nyou have promised that you",
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"will follow the lumped\nmatter discipline.",
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"Lumped matter discipline has\nthree components to it.",
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"One is that the elements will\nhave del phi b by del t equals",
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"zero, outside the elements.",
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"In other words, when you build\ncircuits, you want to make",
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"sure that the del phi b by del\nt is going to be zero.",
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"And inside the elements, we are\ngoing to make sure that",
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"when you define something--\ndescribe something as a lumped",
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"element, del q by del t,\nfor that element--",
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"the net del q by del t for\nthat element inside the",
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"element is going to be zero.",
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"And that's going to be true\nfor all your elements,",
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"registers, sources,\nwires, and so on.",
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"And the third element is that\nyou will only focus on signal",
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"speeds of interest that\nwill be way lower than",
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"the speed of light.",
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"Now one of the interesting facts\nof life is that as our",
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"microprocessors get faster and\nfaster, some of the chips",
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"inside your iPhones, and your\ndesktops, and so on, are",
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"clocking at speeds in excess\nof three to four gigahertz.",
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"When signal speeds are that\nfast, we are now getting to a",
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"point where the signal speeds\ninside our chips are",
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"approaching the speed\nof light.",
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"So they're not all\nthat far off.",
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"And so therefore, over the next\ndecade, as people try to",
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"push speeds to even higher\nvalues, various things are",
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"going to start breaking unless\nwe change things",
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"dramatically somehow.",
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"What this does is these\ndiscipline elements, the",
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"lumped matter discipline,\nenables us to create the",
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"lumped circuit abstraction.",
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"Look at our lumped elements.",
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"Lumped elements will\nbe described",
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"by their v-i relation.",
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"So each of these lumped elements\nof that sum i, that",
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"would be sum function of\nv, the v-i relation.",
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"The relation could be linear,\ncould be non-linear.",
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"Could be, in general, could be\nanything, just that they have",
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"some v-i relation.",
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"For the register you saw that\ni was v divided by R.",
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"For some other element, it could\nbe that i is 6.7 times v",
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"squared plus v divided by\n2 plus some constant 1.",
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"I mean, who knows.",
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"That could be some function of\nv. Could be linear, could be",
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"non-linear.",
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"And for this element, the power\nconsumed by the element",
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"is given by vi.",
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"Finally, we showed that when\nyou make the lumped matter",
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"discipline assumptions,\nMaxwell's equations simplify",
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"to extremely simple\nKVL and KCL.",
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"So, for example, KVL simply\nsays that the sum of the",
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"voltages around a\nloop is zero.",
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"While KCL says that the sum of\nthe current that go into a",
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"node is zero.",
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"You can also say the currents\ncoming out of a node are zero",
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"by the same principle.",
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"What is amazing about this is\nthat by making the lumped",
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"matter discipline, by abiding\nby the lumped matter",
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"discipline, we have been able\nto convert the use of",
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"Maxwell's equation into the use\nof very simple algebra.",
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"So we replaced our del phi's and\ndel t's, and all of that",
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"stuff, with extremely\nsimple algebra.",
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"And in the next set of segments\nI'm going to show you",
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"how we can simplify and analyze\ncircuits extremely",
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"easily using very, very\nsimple algebra.",
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"And, in fact, for the first half\nof this course, you are",
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"not going to see any\nsquigglies at all.",
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"It's going to be very,\nvery simple.",
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"And even later, we're not going\nto be seeing any partial",
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"differential equations.",
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"We will see some fairly simple\ndifferential equations, but by",
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"making the LMD assumptions, we\nhave really gotten rid of a",
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"lot of the complexity.",
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"And things are going to be\nreally, really, really simple.",
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null
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]
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} |