WEBVTT 00:00:00.000 --> 00:00:01.976 align:middle line:90% [SQUEAKING] 00:00:01.976 --> 00:00:04.446 align:middle line:90% [RUSTLING] 00:00:04.446 --> 00:00:08.703 align:middle line:90% [CLICKING] 00:00:08.703 --> 00:00:10.370 align:middle line:84% DAVID PERREAULT: So you've gone through, 00:00:10.370 --> 00:00:11.990 align:middle line:84% and you've designed your converter, 00:00:11.990 --> 00:00:15.800 align:middle line:84% and you've worked out the magnetics and the controls 00:00:15.800 --> 00:00:18.720 align:middle line:84% and the circuit topology, all that stuff. 00:00:18.720 --> 00:00:22.670 align:middle line:84% And now it's time to put it on a board 00:00:22.670 --> 00:00:25.370 align:middle line:84% or put it in a package system and get 00:00:25.370 --> 00:00:27.140 align:middle line:90% the performance you want. 00:00:27.140 --> 00:00:30.110 align:middle line:84% And what you'll find is that depending 00:00:30.110 --> 00:00:32.750 align:middle line:84% upon how you do this, the details of how 00:00:32.750 --> 00:00:34.580 align:middle line:84% you put your circuit together, you 00:00:34.580 --> 00:00:38.540 align:middle line:84% can get great performance or terrible performance. 00:00:38.540 --> 00:00:42.410 align:middle line:84% And so what I'd like to do is spend a little bit 00:00:42.410 --> 00:00:46.640 align:middle line:84% of time today just talking about practical implementation issues. 00:00:46.640 --> 00:00:49.762 align:middle line:84% And this is something that I'm-- what I'm hoping is you'll keep 00:00:49.762 --> 00:00:52.220 align:middle line:84% this in the back of your mind until the day you're actually 00:00:52.220 --> 00:00:53.460 align:middle line:90% building one of these things. 00:00:53.460 --> 00:00:55.550 align:middle line:84% And maybe the first one you build 00:00:55.550 --> 00:00:58.783 align:middle line:84% might cause you some unhappiness. 00:00:58.783 --> 00:01:00.950 align:middle line:84% And then you'll remember this lecture and look at it 00:01:00.950 --> 00:01:02.970 align:middle line:84% and say, what can I do to fix that? 00:01:02.970 --> 00:01:05.990 align:middle line:84% Or you can remember it all now, and then you'll 00:01:05.990 --> 00:01:07.110 align:middle line:90% never have this problem. 00:01:07.110 --> 00:01:12.720 align:middle line:84% And I certainly found over time that the more attention you 00:01:12.720 --> 00:01:14.430 align:middle line:84% pay to this kind of thing I'm going 00:01:14.430 --> 00:01:17.820 align:middle line:84% to talk about right now in your first design, 00:01:17.820 --> 00:01:21.600 align:middle line:84% like, when you first build the system, 00:01:21.600 --> 00:01:23.740 align:middle line:84% the less trouble you'll have with it getting it 00:01:23.740 --> 00:01:26.030 align:middle line:90% across the finish line. 00:01:26.030 --> 00:01:30.490 align:middle line:84% OK, so let's talk about our friendly neighborhood buck 00:01:30.490 --> 00:01:31.870 align:middle line:90% converter. 00:01:31.870 --> 00:01:35.760 align:middle line:84% So suppose I have a buck converter. 00:01:35.760 --> 00:01:39.030 align:middle line:84% And let me assume I'm coming from some source impedance, 00:01:39.030 --> 00:01:40.620 align:middle line:84% that we don't have to worry about it. 00:01:40.620 --> 00:01:45.480 align:middle line:84% But I have a capacitor here to take the high-frequency input 00:01:45.480 --> 00:01:48.390 align:middle line:84% ripple current and hold the voltage steady. 00:01:48.390 --> 00:01:53.820 align:middle line:84% And I'll have a switch, and I'll have a diode, and my load 00:01:53.820 --> 00:01:54.630 align:middle line:90% inductor-- 00:01:54.630 --> 00:01:57.660 align:middle line:84% I mean, my output inductor and my load. 00:01:57.660 --> 00:02:03.970 align:middle line:84% As far as the switching of this circuit 00:02:03.970 --> 00:02:11.330 align:middle line:84% is concerned, when the diode is on, 00:02:11.330 --> 00:02:14.000 align:middle line:84% the path through the circuit's like this. 00:02:14.000 --> 00:02:18.200 align:middle line:84% When I turn the diode off and the switch turns on, 00:02:18.200 --> 00:02:22.850 align:middle line:84% essentially, I'm commutating to this branch. 00:02:22.850 --> 00:02:25.880 align:middle line:84% So I have a commutation between this branch 00:02:25.880 --> 00:02:27.920 align:middle line:84% and this branch of the circuit, and I'm 00:02:27.920 --> 00:02:30.170 align:middle line:84% assuming all the high-frequency current's going 00:02:30.170 --> 00:02:32.900 align:middle line:90% through the input capacitor. 00:02:32.900 --> 00:02:36.590 align:middle line:84% Likewise, when the switch is on, I'm carrying it this way. 00:02:36.590 --> 00:02:40.570 align:middle line:84% And when I turn the switch off, I essentially, 00:02:40.570 --> 00:02:44.130 align:middle line:84% from an AC perspective, I have a loop going this way. 00:02:44.130 --> 00:02:50.530 align:middle line:84% So essentially what dominates the high-frequency behavior 00:02:50.530 --> 00:02:55.690 align:middle line:84% in terms of high currents is this switching loop here. 00:02:55.690 --> 00:02:59.170 align:middle line:84% You can imagine that there's a large AC current running 00:02:59.170 --> 00:03:02.580 align:middle line:90% around this switching loop. 00:03:02.580 --> 00:03:05.610 align:middle line:84% This branch has almost constant current. 00:03:05.610 --> 00:03:07.440 align:middle line:84% If you've done a good job of filtering, 00:03:07.440 --> 00:03:11.850 align:middle line:84% this input will have an almost constant current. 00:03:11.850 --> 00:03:14.443 align:middle line:84% But this is where the big AC current is. 00:03:14.443 --> 00:03:16.860 align:middle line:84% So the first thing I think about when I'm putting together 00:03:16.860 --> 00:03:21.360 align:middle line:84% my circuit is how do I minimize that loop 00:03:21.360 --> 00:03:26.022 align:middle line:90% in terms of its inductance? 00:03:26.022 --> 00:03:30.960 align:middle line:84% And so one of the things we're going to talk about today 00:03:30.960 --> 00:03:34.480 align:middle line:90% is minimizing loop inductance. 00:03:34.480 --> 00:03:35.940 align:middle line:84% And you've got to-- the first thing 00:03:35.940 --> 00:03:38.340 align:middle line:84% you want to do when you look at any converter is, which loops do 00:03:38.340 --> 00:03:39.005 align:middle line:90% I care about? 00:03:39.005 --> 00:03:41.568 align:middle line:90% 00:03:41.568 --> 00:03:43.950 align:middle line:90% And this is the key loop. 00:03:43.950 --> 00:03:47.060 align:middle line:84% So the first thing I'm looking at when I'm laying out my power 00:03:47.060 --> 00:03:49.140 align:middle line:90% stage is, what's my diode? 00:03:49.140 --> 00:03:50.700 align:middle line:90% What's my capacitor? 00:03:50.700 --> 00:03:51.840 align:middle line:90% I'm sorry, what's my diode? 00:03:51.840 --> 00:03:52.860 align:middle line:90% What's my switch? 00:03:52.860 --> 00:03:53.850 align:middle line:90% Here's the capacitor. 00:03:53.850 --> 00:03:56.880 align:middle line:84% How am I going to close this loop to minimize that? 00:03:56.880 --> 00:03:59.510 align:middle line:84% And we've talked about how electromagnetic interference 00:03:59.510 --> 00:04:04.160 align:middle line:84% from that loop can couple into other systems. 00:04:04.160 --> 00:04:07.010 align:middle line:84% We'll talk about that in more detail. 00:04:07.010 --> 00:04:14.570 align:middle line:84% We should also recognize that where is the high switching 00:04:14.570 --> 00:04:17.990 align:middle line:90% node in this circuit? 00:04:17.990 --> 00:04:24.020 align:middle line:84% This node has a big square wave on it with respect to ground. 00:04:24.020 --> 00:04:27.128 align:middle line:90% 00:04:27.128 --> 00:04:32.960 align:middle line:84% So this node flying up and down can inject charge 00:04:32.960 --> 00:04:37.310 align:middle line:84% into other places in the circuit and cause noise. 00:04:37.310 --> 00:04:40.880 align:middle line:84% So making this node, this flying node, 00:04:40.880 --> 00:04:44.780 align:middle line:84% bigger than I need it to be is kind of a bad thing, 00:04:44.780 --> 00:04:47.780 align:middle line:84% because that can capacitively inject noise 00:04:47.780 --> 00:04:49.910 align:middle line:90% into other places in the system. 00:04:49.910 --> 00:04:52.850 align:middle line:84% So not only are going to think about how to make this tight. 00:04:52.850 --> 00:04:54.920 align:middle line:84% I also want to think about what's 00:04:54.920 --> 00:04:58.130 align:middle line:90% the size of this flying node. 00:04:58.130 --> 00:05:01.100 align:middle line:90% And if I imagine that I-- 00:05:01.100 --> 00:05:04.280 align:middle line:90% maybe I could place my-- 00:05:04.280 --> 00:05:06.560 align:middle line:84% maybe I could place my inductor over to the right 00:05:06.560 --> 00:05:09.860 align:middle line:84% and have a long lead going between the switching 00:05:09.860 --> 00:05:11.160 align:middle line:90% diode and the inductor. 00:05:11.160 --> 00:05:15.080 align:middle line:84% Or I could place, if this is my switching in diode node-- 00:05:15.080 --> 00:05:17.240 align:middle line:84% or I could put the inductor here and then 00:05:17.240 --> 00:05:21.900 align:middle line:84% have a long lead going to the output capacitor, 00:05:21.900 --> 00:05:25.445 align:middle line:84% these two things seem the same because the lead's either 00:05:25.445 --> 00:05:27.570 align:middle line:84% in series with the inductor on one side or another. 00:05:27.570 --> 00:05:30.720 align:middle line:84% But this node is flying up and down, 00:05:30.720 --> 00:05:33.150 align:middle line:90% and this node is about fixed. 00:05:33.150 --> 00:05:34.560 align:middle line:90% So, in voltage. 00:05:34.560 --> 00:05:38.010 align:middle line:84% So to the extent that this is forming a capacitor 00:05:38.010 --> 00:05:41.340 align:middle line:84% plate to other stuff, and this is forming a capacitor 00:05:41.340 --> 00:05:44.990 align:middle line:84% plate to other stuff, this is much worse than this one. 00:05:44.990 --> 00:05:50.210 align:middle line:84% So you've got to think about both this loop and this flying 00:05:50.210 --> 00:05:51.693 align:middle line:90% node in a buck converter. 00:05:51.693 --> 00:05:54.110 align:middle line:84% In a boost converter it would be a different looping node, 00:05:54.110 --> 00:05:56.070 align:middle line:84% or in some other converter would be different. 00:05:56.070 --> 00:05:58.400 align:middle line:84% But that's the first thing you want to think about. 00:05:58.400 --> 00:06:02.280 align:middle line:84% And it can really have a big impact on performance. 00:06:02.280 --> 00:06:06.590 align:middle line:84% And just to illustrate that, Rafa 00:06:06.590 --> 00:06:10.880 align:middle line:84% has actually set up a buck converter. 00:06:10.880 --> 00:06:18.640 align:middle line:84% And I'm going to let her show you four cases. 00:06:18.640 --> 00:06:19.140 align:middle line:90% OK. 00:06:19.140 --> 00:06:21.210 align:middle line:84% Why don't you tell me-- and since I have the mic, which 00:06:21.210 --> 00:06:22.650 align:middle line:90% case you're going to do first? 00:06:22.650 --> 00:06:24.340 align:middle line:84% RAFA ISLAM: We can start with the worst-case one. 00:06:24.340 --> 00:06:24.540 align:middle line:90% DAVID PERREAULT: OK. 00:06:24.540 --> 00:06:26.093 align:middle line:84% RAFA ISLAM: Have a big switch gap. 00:06:26.093 --> 00:06:26.880 align:middle line:90% And it'll be-- 00:06:26.880 --> 00:06:29.820 align:middle line:84% DAVID PERREAULT: Yeah, so suppose I did a bad thing 00:06:29.820 --> 00:06:30.970 align:middle line:90% in 2-dimensions. 00:06:30.970 --> 00:06:36.090 align:middle line:84% I made this loop terrible, and I had excess area 00:06:36.090 --> 00:06:38.030 align:middle line:90% on this switching node. 00:06:38.030 --> 00:06:40.750 align:middle line:84% So I'm just doing a bad job of laying out my circuit. 00:06:40.750 --> 00:06:43.380 align:middle line:84% What would that waveform look like? 00:06:43.380 --> 00:06:45.035 align:middle line:90% OK, so we can see the first one. 00:06:45.035 --> 00:06:51.730 align:middle line:90% 00:06:51.730 --> 00:06:56.710 align:middle line:84% And what you see is a whole pile of ringing in this circuit. 00:06:56.710 --> 00:06:58.603 align:middle line:84% So what she's looking at is you're 00:06:58.603 --> 00:07:00.770 align:middle line:84% looking at the voltage at the switching node, right? 00:07:00.770 --> 00:07:01.180 align:middle line:90% RAFA ISLAM: That's right. 00:07:01.180 --> 00:07:04.030 align:middle line:84% DAVID PERREAULT: Yeah, so it's this voltage we're looking at, 00:07:04.030 --> 00:07:05.960 align:middle line:90% this switching node voltage. 00:07:05.960 --> 00:07:09.140 align:middle line:84% And what you see is there's all kinds of excess ringing there. 00:07:09.140 --> 00:07:09.640 align:middle line:90% Why? 00:07:09.640 --> 00:07:11.530 align:middle line:84% Because there's this inductance in this loop which 00:07:11.530 --> 00:07:13.790 align:middle line:84% is ringing with things, and then it's settling down. 00:07:13.790 --> 00:07:18.940 align:middle line:84% And that's pretty bad because that can inject noise elsewhere 00:07:18.940 --> 00:07:19.790 align:middle line:90% in the circuit. 00:07:19.790 --> 00:07:21.800 align:middle line:84% It can even interfere with the circuit itself. 00:07:21.800 --> 00:07:24.910 align:middle line:84% So you'll see a lot of people have problems, 00:07:24.910 --> 00:07:27.100 align:middle line:84% that they build their circuit, and maybe it 00:07:27.100 --> 00:07:28.870 align:middle line:84% works at super-low voltage, the power. 00:07:28.870 --> 00:07:31.203 align:middle line:84% And they turn it up, and everything starts mis-operating 00:07:31.203 --> 00:07:32.330 align:middle line:90% and doing funny things. 00:07:32.330 --> 00:07:34.450 align:middle line:84% It's because you're having interference 00:07:34.450 --> 00:07:35.830 align:middle line:90% with your own circuit. 00:07:35.830 --> 00:07:37.720 align:middle line:84% So not only can you interfere with the world, 00:07:37.720 --> 00:07:39.620 align:middle line:90% you can interfere with yourself. 00:07:39.620 --> 00:07:43.245 align:middle line:84% Now that's the result of two bad things. 00:07:43.245 --> 00:07:44.870 align:middle line:84% Which one are we going to look at next? 00:07:44.870 --> 00:07:47.037 align:middle line:84% RAFA ISLAM: We're going to move the capacitor closer 00:07:47.037 --> 00:07:48.250 align:middle line:90% to the switch. 00:07:48.250 --> 00:07:50.690 align:middle line:84% DAVID PERREAULT: We're going to have a bad switching loop. 00:07:50.690 --> 00:07:51.715 align:middle line:84% RAFA ISLAM: Yes, smaller, smaller [INAUDIBLE]. 00:07:51.715 --> 00:07:52.540 align:middle line:90% DAVID PERREAULT: Yeah. 00:07:52.540 --> 00:07:53.040 align:middle line:90% Right. 00:07:53.040 --> 00:07:56.030 align:middle line:84% So we're going to reduce the capacitance here. 00:07:56.030 --> 00:07:59.010 align:middle line:84% We're going to improve one aspect of that. 00:07:59.010 --> 00:08:05.817 align:middle line:90% 00:08:05.817 --> 00:08:06.815 align:middle line:90% RAFA ISLAM: Sorry. 00:08:06.815 --> 00:08:08.811 align:middle line:90% [INAUDIBLE] 00:08:08.811 --> 00:08:10.807 align:middle line:90% OK, that should be good. 00:08:10.807 --> 00:08:17.795 align:middle line:90% 00:08:17.795 --> 00:08:20.345 align:middle line:84% DAVID PERREAULT: So that's much more pleasant in terms 00:08:20.345 --> 00:08:21.470 align:middle line:90% of the amount of switching. 00:08:21.470 --> 00:08:23.930 align:middle line:84% You can still-- you can see it's still noisy. 00:08:23.930 --> 00:08:26.660 align:middle line:84% Stuff's still going on, but not nearly as 00:08:26.660 --> 00:08:31.010 align:middle line:84% bad as when I was really sloppy about both the loop inductance 00:08:31.010 --> 00:08:32.900 align:middle line:90% and the node capacitance. 00:08:32.900 --> 00:08:36.500 align:middle line:84% Now we'll do the case where we have-- 00:08:36.500 --> 00:08:37.460 align:middle line:90% RAFA ISLAM: Small gap. 00:08:37.460 --> 00:08:42.470 align:middle line:84% DAVID PERREAULT: Yeah, the capacitor is bad, 00:08:42.470 --> 00:08:44.185 align:middle line:84% but I still have a big switching loop. 00:08:44.185 --> 00:08:48.840 align:middle line:90% 00:08:48.840 --> 00:08:51.510 align:middle line:84% And again-- yeah, you got some ringing. 00:08:51.510 --> 00:08:52.600 align:middle line:90% You might not like that. 00:08:52.600 --> 00:08:54.975 align:middle line:84% You might start thinking about putting snubbers in there. 00:08:54.975 --> 00:08:57.490 align:middle line:84% But it's not as bad as that first case. 00:08:57.490 --> 00:09:01.290 align:middle line:84% And then the last case is when perhaps better attention 00:09:01.290 --> 00:09:02.860 align:middle line:90% was paid to everything. 00:09:02.860 --> 00:09:05.880 align:middle line:90% And this is-- 00:09:05.880 --> 00:09:07.590 align:middle line:84% I don't want to say the ideal case, 00:09:07.590 --> 00:09:10.590 align:middle line:84% but this is when attention was paid 00:09:10.590 --> 00:09:12.220 align:middle line:90% to the layout of the circuit. 00:09:12.220 --> 00:09:14.430 align:middle line:84% So if you look at the two ends of that spectrum, 00:09:14.430 --> 00:09:16.620 align:middle line:84% you can see there's a pretty darn big difference 00:09:16.620 --> 00:09:19.812 align:middle line:84% between the actual performance of the converter. 00:09:19.812 --> 00:09:23.280 align:middle line:84% Now this is in a low-voltage kind of low-power thing 00:09:23.280 --> 00:09:25.900 align:middle line:90% that it's not that bad. 00:09:25.900 --> 00:09:27.900 align:middle line:84% But when you're operating at hundreds 00:09:27.900 --> 00:09:30.450 align:middle line:84% of volts and hundreds of amps, these things 00:09:30.450 --> 00:09:32.820 align:middle line:90% get really, really bad. 00:09:32.820 --> 00:09:35.650 align:middle line:84% So you really want to think about layout. 00:09:35.650 --> 00:09:36.740 align:middle line:90% So thanks very much. 00:09:36.740 --> 00:09:38.550 align:middle line:90% RAFA ISLAM: Sure. 00:09:38.550 --> 00:09:41.160 align:middle line:84% DAVID PERREAULT: So suppose I want 00:09:41.160 --> 00:09:48.670 align:middle line:84% to think about reducing the inductance of my loop? 00:09:48.670 --> 00:09:51.800 align:middle line:90% What does that mean in practice? 00:09:51.800 --> 00:09:53.950 align:middle line:84% Well, it means that I certainly want 00:09:53.950 --> 00:09:59.830 align:middle line:84% to place these three components close together 00:09:59.830 --> 00:10:02.710 align:middle line:84% such that if I think about the current flowing 00:10:02.710 --> 00:10:06.670 align:middle line:84% around in this loop, it forms a very tight area. 00:10:06.670 --> 00:10:09.700 align:middle line:84% So that's one way to think about it. 00:10:09.700 --> 00:10:11.742 align:middle line:84% If I imagine the current, AC current, circulating 00:10:11.742 --> 00:10:14.242 align:middle line:84% in this loop, how much flux is it throwing out in the world? 00:10:14.242 --> 00:10:15.910 align:middle line:84% And that relates to the inductance. 00:10:15.910 --> 00:10:22.362 align:middle line:84% Sometimes, of course, I have to put components at a distance. 00:10:22.362 --> 00:10:24.070 align:middle line:84% There's some interconnection between them 00:10:24.070 --> 00:10:25.912 align:middle line:90% that I have to live with. 00:10:25.912 --> 00:10:34.990 align:middle line:84% Why don't we think about what is the parasitic of a pair of wires 00:10:34.990 --> 00:10:38.530 align:middle line:84% or a pair of traces interconnecting something? 00:10:38.530 --> 00:10:41.440 align:middle line:84% So let's think about this example. 00:10:41.440 --> 00:10:43.153 align:middle line:90% Suppose I have two traces. 00:10:43.153 --> 00:10:47.330 align:middle line:90% 00:10:47.330 --> 00:10:50.420 align:middle line:90% Here's the first trace. 00:10:50.420 --> 00:10:54.760 align:middle line:84% And I'm going to carry current down it. 00:10:54.760 --> 00:10:57.200 align:middle line:84% And then I'm going to return the current somewhere else. 00:10:57.200 --> 00:11:00.680 align:middle line:84% So let me return it in a trace that's right underneath it, 00:11:00.680 --> 00:11:01.345 align:middle line:90% like this. 00:11:01.345 --> 00:11:06.780 align:middle line:90% 00:11:06.780 --> 00:11:11.050 align:middle line:90% And I will close off the end. 00:11:11.050 --> 00:11:13.730 align:middle line:84% I'm going to drive current in one and return it on the other. 00:11:13.730 --> 00:11:22.690 align:middle line:84% And let's say it's got a trace of a width W, of length L, 00:11:22.690 --> 00:11:25.260 align:middle line:84% and a spacing that I'm going to call delta. 00:11:25.260 --> 00:11:29.200 align:middle line:90% 00:11:29.200 --> 00:11:31.960 align:middle line:84% What would be the inductance of that loop, where 00:11:31.960 --> 00:11:35.320 align:middle line:84% I'm going to carry current down one side and back the other? 00:11:35.320 --> 00:11:44.320 align:middle line:84% And if I look at this end on, maybe I'm 00:11:44.320 --> 00:11:47.230 align:middle line:84% going to put current in one end, or maybe current 00:11:47.230 --> 00:11:48.160 align:middle line:90% will go in here. 00:11:48.160 --> 00:11:50.875 align:middle line:90% 00:11:50.875 --> 00:11:52.540 align:middle line:90% It goes down the conductor. 00:11:52.540 --> 00:11:55.605 align:middle line:84% Comes back the other side, coming out here. 00:11:55.605 --> 00:11:58.650 align:middle line:90% 00:11:58.650 --> 00:12:02.200 align:middle line:84% And from that, what I'm going to get is some magnetic fields. 00:12:02.200 --> 00:12:05.710 align:middle line:84% And they're going to be very concentrated 00:12:05.710 --> 00:12:07.190 align:middle line:90% in between the traces. 00:12:07.190 --> 00:12:11.611 align:middle line:84% I'm assuming these traces are quite close together. 00:12:11.611 --> 00:12:13.760 align:middle line:84% And it's going to look something like this. 00:12:13.760 --> 00:12:15.440 align:middle line:90% Here's the magnetic fields. 00:12:15.440 --> 00:12:18.800 align:middle line:90% Here's the H fields. 00:12:18.800 --> 00:12:22.550 align:middle line:84% Looks like something like this, if I'm being schematic about it. 00:12:22.550 --> 00:12:26.120 align:middle line:84% Does that make sense to everybody? 00:12:26.120 --> 00:12:32.270 align:middle line:84% So the question is, if these are the H fields, 00:12:32.270 --> 00:12:34.080 align:middle line:90% how might I analyze this thing? 00:12:34.080 --> 00:12:37.790 align:middle line:84% And let me do an analysis, a very simple analysis, just 00:12:37.790 --> 00:12:41.600 align:middle line:84% to say what are the trade-offs in the interconnect? 00:12:41.600 --> 00:12:44.520 align:middle line:84% So we can say, OK, the integral of H 00:12:44.520 --> 00:12:52.600 align:middle line:84% dot dL is equal to the integral of a J dot dA, which is just 00:12:52.600 --> 00:12:54.580 align:middle line:90% the net current. 00:12:54.580 --> 00:12:58.090 align:middle line:84% I'm ignoring displacement current in this. 00:12:58.090 --> 00:13:01.900 align:middle line:84% So what I'm saying is that if I integrate the H 00:13:01.900 --> 00:13:06.710 align:middle line:84% field around any loop, I'm going to get the net current enclosed. 00:13:06.710 --> 00:13:12.190 align:middle line:84% So suppose this total current here is I. All right. 00:13:12.190 --> 00:13:15.280 align:middle line:90% Well, that's fine. 00:13:15.280 --> 00:13:17.680 align:middle line:84% The simplest thing for me to think about 00:13:17.680 --> 00:13:20.770 align:middle line:84% might be the fact that the fields are really concentrated 00:13:20.770 --> 00:13:22.930 align:middle line:84% in between the traces and they're 00:13:22.930 --> 00:13:25.100 align:middle line:90% kind of very diffuse out here. 00:13:25.100 --> 00:13:27.460 align:middle line:84% So maybe I can make the approximation-- 00:13:27.460 --> 00:13:30.280 align:middle line:84% and this is purely approximation that all the field that I'm 00:13:30.280 --> 00:13:32.980 align:middle line:90% interested in is in here. 00:13:32.980 --> 00:13:35.560 align:middle line:84% So then if I took this integral around this loop, 00:13:35.560 --> 00:13:40.060 align:middle line:84% I might say the integral of H dot dL is just H sub x-- 00:13:40.060 --> 00:13:42.310 align:middle line:84% let me call this the x direction. 00:13:42.310 --> 00:13:46.843 align:middle line:84% It's the H inside the inside between here times-- 00:13:46.843 --> 00:13:48.260 align:middle line:84% this is the width of the winding-- 00:13:48.260 --> 00:13:50.990 align:middle line:90% 00:13:50.990 --> 00:13:53.730 align:middle line:84% is equal to I. Or equivalently, I 00:13:53.730 --> 00:14:01.530 align:middle line:84% could approximate this H field as H sub x is equal to I over W. 00:14:01.530 --> 00:14:03.090 align:middle line:90% All right? 00:14:03.090 --> 00:14:06.690 align:middle line:84% Has the right units-- amperes per meter. 00:14:06.690 --> 00:14:09.387 align:middle line:84% How much energy am I storing in this thing? 00:14:09.387 --> 00:14:11.220 align:middle line:84% Well, again, I'm only going to pay attention 00:14:11.220 --> 00:14:13.053 align:middle line:84% to the-- really the energy I'm storing here. 00:14:13.053 --> 00:14:14.800 align:middle line:84% But that ought to be most of the energy. 00:14:14.800 --> 00:14:17.460 align:middle line:84% I'm going to ignore this sort of-- the fringing fields 00:14:17.460 --> 00:14:19.810 align:middle line:84% out here, even though I know they exist. 00:14:19.810 --> 00:14:22.960 align:middle line:84% So that means I get the integral-- 00:14:22.960 --> 00:14:28.790 align:middle line:84% the magnetic energy storage is equal to the integral of B dot H 00:14:28.790 --> 00:14:42.790 align:middle line:84% dV, which is going to give me 1/2 mu 0 H squared times 00:14:42.790 --> 00:14:49.450 align:middle line:84% the volume, which in this case is going to be equal to 1/2 mu 0 00:14:49.450 --> 00:14:53.920 align:middle line:84% I over I squared over W squared, times the volume, 00:14:53.920 --> 00:14:57.880 align:middle line:90% which is W times L times delta. 00:14:57.880 --> 00:15:01.870 align:middle line:84% So I'm finding all the energy stored in between the plates 00:15:01.870 --> 00:15:04.930 align:middle line:90% of this conductor in return. 00:15:04.930 --> 00:15:06.120 align:middle line:90% Any questions about that? 00:15:06.120 --> 00:15:08.910 align:middle line:90% 00:15:08.910 --> 00:15:17.070 align:middle line:84% So this is also equal to 1/2 Li squared. 00:15:17.070 --> 00:15:19.720 align:middle line:84% That's the energy I'm storing in the magnetic field. 00:15:19.720 --> 00:15:23.503 align:middle line:84% And if I work that out, this cancels. 00:15:23.503 --> 00:15:26.730 align:middle line:90% 00:15:26.730 --> 00:15:30.680 align:middle line:84% Then I get, if I just pattern match here, 00:15:30.680 --> 00:15:35.510 align:middle line:84% what I get is L is approximately equal to, 00:15:35.510 --> 00:15:43.440 align:middle line:84% with these simple simplifications, mu 0 L 00:15:43.440 --> 00:15:46.160 align:middle line:90% over W and delta. 00:15:46.160 --> 00:15:50.170 align:middle line:90% 00:15:50.170 --> 00:15:53.650 align:middle line:84% This is the equivalent of saying capacitance 00:15:53.650 --> 00:15:54.940 align:middle line:90% is epsilon 0 a over d. 00:15:54.940 --> 00:15:57.050 align:middle line:84% I'm ignoring fringing between two plates. 00:15:57.050 --> 00:15:59.840 align:middle line:84% This is the magnetic equivalent of that. 00:15:59.840 --> 00:16:06.730 align:middle line:84% So the inductance of this trace to carry a current up and back 00:16:06.730 --> 00:16:11.590 align:middle line:84% is going to be basically mu 0 l over w delta. 00:16:11.590 --> 00:16:15.880 align:middle line:84% So if I want a low-inductance loop, what do I want? 00:16:15.880 --> 00:16:17.890 align:middle line:84% Firstly, obviously, I mean, I'm assuming there's 00:16:17.890 --> 00:16:19.360 align:middle line:90% no magnetic material in here. 00:16:19.360 --> 00:16:21.318 align:middle line:84% Clearly I don't want magnetic material in there 00:16:21.318 --> 00:16:24.280 align:middle line:84% if I want it to be low inductance. 00:16:24.280 --> 00:16:26.230 align:middle line:90% I want it to be short. 00:16:26.230 --> 00:16:29.080 align:middle line:84% Put everything as close together in terms of the length 00:16:29.080 --> 00:16:31.870 align:middle line:84% I'm carrying the current over as possible. 00:16:31.870 --> 00:16:34.210 align:middle line:84% If I have to carry a current in a trace, 00:16:34.210 --> 00:16:36.760 align:middle line:84% I would like the trace to be wide. 00:16:36.760 --> 00:16:39.910 align:middle line:84% The wider the trace, the more the current and field 00:16:39.910 --> 00:16:43.570 align:middle line:84% spreads out, and the lower net energy stored. 00:16:43.570 --> 00:16:46.690 align:middle line:84% Because the width, the width helps 00:16:46.690 --> 00:16:48.170 align:middle line:90% me reduce the field magnitude. 00:16:48.170 --> 00:16:50.320 align:middle line:84% And even though I'm carrying it over a wider space, 00:16:50.320 --> 00:16:53.403 align:middle line:84% I have more volume, I get a lower inductance. 00:16:53.403 --> 00:16:54.820 align:middle line:84% And then the other thing I can see 00:16:54.820 --> 00:16:57.820 align:middle line:84% is here I want delta to be small. 00:16:57.820 --> 00:17:01.090 align:middle line:84% So if I'm going to carry current out and return it, 00:17:01.090 --> 00:17:06.369 align:middle line:84% I want the spacing between those traces to be really low. 00:17:06.369 --> 00:17:08.103 align:middle line:84% So the thing I'm thinking about when 00:17:08.103 --> 00:17:09.520 align:middle line:84% I'm thinking about what am I going 00:17:09.520 --> 00:17:12.103 align:middle line:84% to make this interconnect loop do, it's not only that I want-- 00:17:12.103 --> 00:17:14.829 align:middle line:84% I can think about, I can imagine this original thing I 00:17:14.829 --> 00:17:19.819 align:middle line:84% drew and say, yeah, I want this loop to be tight. 00:17:19.819 --> 00:17:23.599 align:middle line:84% But this might actually be in multiple dimensions 00:17:23.599 --> 00:17:24.960 align:middle line:90% that I have to think about. 00:17:24.960 --> 00:17:27.920 align:middle line:84% And if I have to carry current over some distance, 00:17:27.920 --> 00:17:31.250 align:middle line:84% carrying a wider trace and putting those traces closer 00:17:31.250 --> 00:17:35.630 align:middle line:84% together helps me make that inductance low. 00:17:35.630 --> 00:17:36.945 align:middle line:90% Any questions about that? 00:17:36.945 --> 00:17:43.530 align:middle line:90% 00:17:43.530 --> 00:17:48.390 align:middle line:84% So if I'm-- an example of this would be not only 00:17:48.390 --> 00:17:51.743 align:middle line:84% for the switching loop, but the gate drive. 00:17:51.743 --> 00:17:53.160 align:middle line:84% I got to put the gate drive, and I 00:17:53.160 --> 00:17:55.980 align:middle line:84% want to send current out and bring the current back. 00:17:55.980 --> 00:17:59.070 align:middle line:84% When I'm thinking about that, if you want the energy storage 00:17:59.070 --> 00:18:00.140 align:middle line:90% to be small-- 00:18:00.140 --> 00:18:02.400 align:middle line:84% at least the magnetic energy storage to be small-- 00:18:02.400 --> 00:18:03.700 align:middle line:90% use a wide trace. 00:18:03.700 --> 00:18:04.925 align:middle line:90% Put the return very close. 00:18:04.925 --> 00:18:12.520 align:middle line:90% 00:18:12.520 --> 00:18:16.900 align:middle line:84% Now, what would be the equivalent 00:18:16.900 --> 00:18:21.590 align:middle line:90% of that for this loop? 00:18:21.590 --> 00:18:26.730 align:middle line:84% What happens, the parasitic capacitance-- 00:18:26.730 --> 00:18:28.613 align:middle line:90% suppose I have some trace. 00:18:28.613 --> 00:18:32.140 align:middle line:90% 00:18:32.140 --> 00:18:34.630 align:middle line:84% This is my switching node, and this is, say, 00:18:34.630 --> 00:18:37.100 align:middle line:84% ground or something, or some other node. 00:18:37.100 --> 00:18:38.860 align:middle line:84% And I'm asking, what's the capacitance 00:18:38.860 --> 00:18:40.570 align:middle line:84% between these two pieces of metal 00:18:40.570 --> 00:18:42.190 align:middle line:84% that are very close to each other? 00:18:42.190 --> 00:18:48.880 align:middle line:84% That, I think is more familiar to people. 00:18:48.880 --> 00:18:54.220 align:middle line:84% People recall that the capacitance is equal to epsilon, 00:18:54.220 --> 00:18:57.610 align:middle line:84% is the dielectric between my two pieces of metal, 00:18:57.610 --> 00:19:01.300 align:middle line:84% times the area divided by the distance epsilon A 00:19:01.300 --> 00:19:04.810 align:middle line:84% over d, which in the way I've been writing this with these two 00:19:04.810 --> 00:19:09.560 align:middle line:84% plate sizes, would be epsilon times-- 00:19:09.560 --> 00:19:16.090 align:middle line:84% the area would be width times the length divided by delta. 00:19:16.090 --> 00:19:19.150 align:middle line:90% Does that make sense? 00:19:19.150 --> 00:19:21.250 align:middle line:90% So what does this say? 00:19:21.250 --> 00:19:24.070 align:middle line:84% In this case, if I want to make capacitance small, 00:19:24.070 --> 00:19:27.555 align:middle line:84% I also want to make the length of this thing short. 00:19:27.555 --> 00:19:30.170 align:middle line:90% 00:19:30.170 --> 00:19:35.120 align:middle line:84% But notice that whereas inductance goes as-- 00:19:35.120 --> 00:19:37.460 align:middle line:84% let's see, where do I have it here? 00:19:37.460 --> 00:19:38.690 align:middle line:90% L over delta. 00:19:38.690 --> 00:19:48.590 align:middle line:84% So let me write C. C is equal to epsilon L times W over delta, 00:19:48.590 --> 00:19:50.270 align:middle line:90% right? 00:19:50.270 --> 00:19:54.590 align:middle line:84% If I thought about my inductance per unit length, 00:19:54.590 --> 00:20:01.295 align:middle line:90% is mu 0 over W delta. 00:20:01.295 --> 00:20:05.170 align:middle line:90% 00:20:05.170 --> 00:20:09.595 align:middle line:84% Capacitance-- what did I do here? 00:20:09.595 --> 00:20:11.845 align:middle line:84% AUDIENCE: I think [INAUDIBLE] top [INAUDIBLE] numbers. 00:20:11.845 --> 00:20:13.095 align:middle line:90% DAVID PERREAULT: It should be. 00:20:13.095 --> 00:20:14.320 align:middle line:90% Yes. 00:20:14.320 --> 00:20:15.820 align:middle line:90% That's completely wrong. 00:20:15.820 --> 00:20:19.590 align:middle line:84% That's what happens when I skip boards. 00:20:19.590 --> 00:20:23.170 align:middle line:90% The inductance needs to be mu 0. 00:20:23.170 --> 00:20:24.130 align:middle line:90% Yeah, all right. 00:20:24.130 --> 00:20:24.960 align:middle line:90% That's what I did. 00:20:24.960 --> 00:20:31.510 align:middle line:84% Delta over W. If I want the inductance [INAUDIBLE] low, 00:20:31.510 --> 00:20:37.674 align:middle line:90% make W big and delta small. 00:20:37.674 --> 00:20:42.300 align:middle line:90% This should be W over delta. 00:20:42.300 --> 00:20:43.620 align:middle line:90% It's the induct-- 00:20:43.620 --> 00:20:47.700 align:middle line:84% I'm sorry-- the capacitance [INAUDIBLE]. 00:20:47.700 --> 00:20:55.950 align:middle line:84% Inductance per unit length is then mu 0 delta over W. 00:20:55.950 --> 00:21:00.140 align:middle line:84% So L prime, because if I have to do it over some length, 00:21:00.140 --> 00:21:01.850 align:middle line:90% then I can say what this is. 00:21:01.850 --> 00:21:04.890 align:middle line:84% And I want delta to be small and W to be big. 00:21:04.890 --> 00:21:08.720 align:middle line:84% If I calculated the capacitance, the capacitance per unit length 00:21:08.720 --> 00:21:12.740 align:middle line:90% is epsilon times W over delta. 00:21:12.740 --> 00:21:16.340 align:middle line:84% So if I'm thinking about some trace in its return, 00:21:16.340 --> 00:21:19.850 align:middle line:84% or two pieces of metal close to each other, whatever 00:21:19.850 --> 00:21:24.980 align:middle line:84% I do to reduce the inductance increases the capacitance 00:21:24.980 --> 00:21:25.825 align:middle line:90% and vice versa. 00:21:25.825 --> 00:21:28.484 align:middle line:90% 00:21:28.484 --> 00:21:34.830 align:middle line:84% So in some cases, if I do the best thing I can do, 00:21:34.830 --> 00:21:37.170 align:middle line:84% I'm going to be trading capacitance for inductance, 00:21:37.170 --> 00:21:42.840 align:middle line:84% and I got to decide which I want, which I don't like less. 00:21:42.840 --> 00:21:44.910 align:middle line:84% Now, that doesn't mean you can't-- 00:21:44.910 --> 00:21:47.280 align:middle line:84% this trade off-- and I should say, by the way, 00:21:47.280 --> 00:21:53.870 align:middle line:84% 1 over L prime C prime ends up being 00:21:53.870 --> 00:21:55.910 align:middle line:90% the speed of light squared, OK? 00:21:55.910 --> 00:21:57.630 align:middle line:90% So it's a physical constant. 00:21:57.630 --> 00:21:59.930 align:middle line:90% It's mu 0 epsilon 0. 00:21:59.930 --> 00:22:04.370 align:middle line:84% But that doesn't mean I can't do anything 00:22:04.370 --> 00:22:06.560 align:middle line:90% bad here that doesn't help me. 00:22:06.560 --> 00:22:11.530 align:middle line:84% If I thought about, I'm going to carry some current 00:22:11.530 --> 00:22:12.643 align:middle line:90% over some distance. 00:22:12.643 --> 00:22:14.310 align:middle line:84% I'm going to carry current here and it's 00:22:14.310 --> 00:22:18.600 align:middle line:84% going to return underneath here, if I put some piece of metal 00:22:18.600 --> 00:22:20.970 align:middle line:84% out here that doesn't really carry any current, 00:22:20.970 --> 00:22:24.870 align:middle line:84% he can add capacitance without reducing inductance. 00:22:24.870 --> 00:22:27.930 align:middle line:84% So I can certainly do things to make both inductance 00:22:27.930 --> 00:22:30.090 align:middle line:84% and capacitance worse, or make one of them 00:22:30.090 --> 00:22:31.950 align:middle line:90% worse without helping the other. 00:22:31.950 --> 00:22:35.490 align:middle line:84% But when I get it down to the best interconnect strategy, 00:22:35.490 --> 00:22:38.730 align:middle line:84% at some point, if I put my trace and return close, 00:22:38.730 --> 00:22:41.790 align:middle line:84% I'm making the inductance low and the capacitance 00:22:41.790 --> 00:22:44.020 align:middle line:90% high and vice versa. 00:22:44.020 --> 00:22:46.920 align:middle line:84% And you just got to think about which piece of trace is it 00:22:46.920 --> 00:22:50.640 align:middle line:90% and what is it doing for you. 00:22:50.640 --> 00:22:51.830 align:middle line:90% Any question about that? 00:22:51.830 --> 00:22:59.220 align:middle line:90% 00:22:59.220 --> 00:23:03.885 align:middle line:84% Let's talk a little bit more about this switching node here. 00:23:03.885 --> 00:23:06.990 align:middle line:90% 00:23:06.990 --> 00:23:09.455 align:middle line:84% One thing it does, which we saw in the demo, 00:23:09.455 --> 00:23:10.830 align:middle line:84% is it'll cause a bunch of ringing 00:23:10.830 --> 00:23:12.917 align:middle line:84% because you have excess capacitance at this node 00:23:12.917 --> 00:23:13.750 align:middle line:90% that you don't like. 00:23:13.750 --> 00:23:15.690 align:middle line:84% But there are other capacitances that node, 00:23:15.690 --> 00:23:18.680 align:middle line:84% like the device capacitance and so forth. 00:23:18.680 --> 00:23:23.440 align:middle line:84% But what really often hurts you is the capacitance of that node 00:23:23.440 --> 00:23:27.340 align:middle line:84% not to ground, but to other stuff in your circuit. 00:23:27.340 --> 00:23:34.460 align:middle line:84% So let's just imagine this node is driven by the switching. 00:23:34.460 --> 00:23:37.750 align:middle line:84% So there's a volt-- there's a square-wave voltage here. 00:23:37.750 --> 00:23:42.790 align:middle line:84% So if I thought about modeling this, I might say, 00:23:42.790 --> 00:23:48.310 align:middle line:84% OK, here's my big square-wave voltage. 00:23:48.310 --> 00:23:52.444 align:middle line:84% This is going up and down like this. 00:23:52.444 --> 00:24:01.540 align:middle line:84% And this piece of metal here forms one plate of a capacitor. 00:24:01.540 --> 00:24:05.410 align:middle line:84% So maybe I think about that as being one plate. 00:24:05.410 --> 00:24:06.200 align:middle line:90% Here it is. 00:24:06.200 --> 00:24:10.490 align:middle line:90% He's one plate of a capacitor. 00:24:10.490 --> 00:24:11.390 align:middle line:90% All right. 00:24:11.390 --> 00:24:13.440 align:middle line:84% What's the other plate of my capacitor? 00:24:13.440 --> 00:24:15.380 align:middle line:84% Well, it depends what's around it. 00:24:15.380 --> 00:24:19.370 align:middle line:84% But imagine nearby, I have in my circuit, 00:24:19.370 --> 00:24:22.710 align:middle line:84% for example, suppose I have some control circuitry down here. 00:24:22.710 --> 00:24:25.010 align:middle line:90% It's ground referenced. 00:24:25.010 --> 00:24:28.590 align:middle line:84% I have drivers and sensors and comparators. 00:24:28.590 --> 00:24:32.185 align:middle line:84% They're going to do all the computation for me. 00:24:32.185 --> 00:24:36.830 align:middle line:84% And maybe within this there's some very sensitive node. 00:24:36.830 --> 00:24:42.470 align:middle line:84% Maybe that's the input of a comparator, or right 00:24:42.470 --> 00:24:44.780 align:middle line:84% where my error amplifier is, my op amp. 00:24:44.780 --> 00:24:48.350 align:middle line:84% And I can have some very high impedance nodes. 00:24:48.350 --> 00:24:52.520 align:middle line:90% So maybe I have a plate there. 00:24:52.520 --> 00:24:57.854 align:middle line:84% That plate is just the metal of that node. 00:24:57.854 --> 00:25:00.830 align:middle line:90% And it has some resistance too. 00:25:00.830 --> 00:25:04.620 align:middle line:84% So maybe my comparator has some resistance to ground. 00:25:04.620 --> 00:25:08.400 align:middle line:84% So this white could be inside this box. 00:25:08.400 --> 00:25:12.120 align:middle line:84% Maybe there's a comparator here, and he has a positive input. 00:25:12.120 --> 00:25:15.310 align:middle line:84% And there's some metal that I've got sitting right here. 00:25:15.310 --> 00:25:18.330 align:middle line:84% That's the other plate of this capacitor. 00:25:18.330 --> 00:25:20.300 align:middle line:90% Does that make sense? 00:25:20.300 --> 00:25:24.110 align:middle line:84% So if this voltage is here, what is this voltage? 00:25:24.110 --> 00:25:25.740 align:middle line:90% The induced voltage? 00:25:25.740 --> 00:25:29.700 align:middle line:84% Well, a simple RC divider, what does that tell me? 00:25:29.700 --> 00:25:31.650 align:middle line:84% It tells me I ought to be doing this. 00:25:31.650 --> 00:25:33.410 align:middle line:84% I ought to be seeing a voltage that 00:25:33.410 --> 00:25:41.630 align:middle line:84% spikes up and rings down, and then spikes down and rings up, 00:25:41.630 --> 00:25:43.905 align:middle line:90% and vice versa. 00:25:43.905 --> 00:25:46.560 align:middle line:84% So this is the voltage I'm going to see here. 00:25:46.560 --> 00:25:48.630 align:middle line:84% Does that make sense to everybody? 00:25:48.630 --> 00:25:51.373 align:middle line:84% And maybe the energy in these spikes isn't very big. 00:25:51.373 --> 00:25:53.040 align:middle line:84% But if that's the input to a comparator, 00:25:53.040 --> 00:25:56.340 align:middle line:84% maybe I'm very unhappy, because if that comparator is 00:25:56.340 --> 00:25:58.710 align:middle line:84% determining when the switch turns on and off, 00:25:58.710 --> 00:26:01.830 align:middle line:84% and I get a spike on that signal because 00:26:01.830 --> 00:26:05.285 align:middle line:84% of this capacitive injection, I could be really unhappy. 00:26:05.285 --> 00:26:07.950 align:middle line:90% 00:26:07.950 --> 00:26:09.140 align:middle line:90% Any questions about that? 00:26:09.140 --> 00:26:11.910 align:middle line:90% 00:26:11.910 --> 00:26:15.550 align:middle line:90% So what can I do about that? 00:26:15.550 --> 00:26:20.590 align:middle line:84% Well, one thing is we said the area, 00:26:20.590 --> 00:26:23.510 align:middle line:84% the capacitance is related to the area. 00:26:23.510 --> 00:26:25.880 align:middle line:84% I assume the two plate areas were the same here. 00:26:25.880 --> 00:26:28.730 align:middle line:84% This is some small area that's this node. 00:26:28.730 --> 00:26:31.390 align:middle line:84% This is some big area that's associated with carrying 00:26:31.390 --> 00:26:32.960 align:middle line:90% currents for my switching node. 00:26:32.960 --> 00:26:36.310 align:middle line:84% One thing I want to do is make that as small as possible. 00:26:36.310 --> 00:26:40.960 align:middle line:84% Also, keep the distance between this thing and this thing 00:26:40.960 --> 00:26:44.380 align:middle line:84% bigger so that the capacitance goes down. 00:26:44.380 --> 00:26:48.790 align:middle line:84% So I can put them far apart, as far as I can practically 00:26:48.790 --> 00:26:50.750 align:middle line:90% do it, and reduce the areas. 00:26:50.750 --> 00:26:55.090 align:middle line:84% And that will help me minimize that capacitance that's 00:26:55.090 --> 00:26:56.030 align:middle line:90% causing noise. 00:26:56.030 --> 00:26:59.960 align:middle line:84% Does that make sense to everybody? 00:26:59.960 --> 00:27:02.780 align:middle line:90% What else could I do about that? 00:27:02.780 --> 00:27:04.730 align:middle line:84% Well, another thing I could do about that 00:27:04.730 --> 00:27:07.910 align:middle line:84% is start to get smart about where those components are 00:27:07.910 --> 00:27:10.800 align:middle line:90% and what I put in between them. 00:27:10.800 --> 00:27:12.770 align:middle line:84% So one thing I could do is put in what's 00:27:12.770 --> 00:27:16.760 align:middle line:84% known as a Faraday shield, or lay out my circuit 00:27:16.760 --> 00:27:18.650 align:middle line:84% so I effectively get a Faraday shield. 00:27:18.650 --> 00:27:19.890 align:middle line:90% What's a Faraday shield? 00:27:19.890 --> 00:27:24.620 align:middle line:84% Let me just say, this is a model for what's going on. 00:27:24.620 --> 00:27:27.090 align:middle line:90% Suppose I did this instead. 00:27:27.090 --> 00:27:33.350 align:middle line:84% I said, OK, I have my switching node. 00:27:33.350 --> 00:27:35.570 align:middle line:90% It's switching up and down. 00:27:35.570 --> 00:27:37.310 align:middle line:90% And I still have this-- 00:27:37.310 --> 00:27:39.920 align:middle line:90% maybe this is still a-- 00:27:39.920 --> 00:27:43.430 align:middle line:84% I minimized it, but I've still got a certain plate area there. 00:27:43.430 --> 00:27:45.380 align:middle line:90% And I've still-- 00:27:45.380 --> 00:27:49.550 align:middle line:90% I need some area for my-- 00:27:49.550 --> 00:27:51.398 align:middle line:84% I need some area for my switching node, 00:27:51.398 --> 00:27:53.440 align:middle line:84% and he's still going to be a high-impedance node. 00:27:53.440 --> 00:27:54.982 align:middle line:84% The other thing I can do, by the way, 00:27:54.982 --> 00:27:56.930 align:middle line:84% is if I make this resistor smaller. 00:27:56.930 --> 00:28:00.580 align:middle line:84% That starts to become less nasty. 00:28:00.580 --> 00:28:03.145 align:middle line:84% But there's only so much I can do about that. 00:28:03.145 --> 00:28:04.270 align:middle line:90% Well, what else could I do? 00:28:04.270 --> 00:28:06.480 align:middle line:84% Maybe I could come in and say, OK, 00:28:06.480 --> 00:28:10.470 align:middle line:84% let me put some piece of metal that 00:28:10.470 --> 00:28:17.307 align:middle line:84% sits between the noisy node and the thing-- the sensitive node. 00:28:17.307 --> 00:28:19.140 align:middle line:84% And maybe I'll just take that piece of metal 00:28:19.140 --> 00:28:20.150 align:middle line:90% and I'll ground it. 00:28:20.150 --> 00:28:23.136 align:middle line:90% 00:28:23.136 --> 00:28:25.420 align:middle line:84% So what would be the circuit model for this? 00:28:25.420 --> 00:28:27.910 align:middle line:84% The circuit model for this would be the following. 00:28:27.910 --> 00:28:30.630 align:middle line:90% I have my-- 00:28:30.630 --> 00:28:32.670 align:middle line:84% I mean, this is sort of a circuit model already. 00:28:32.670 --> 00:28:38.880 align:middle line:84% But what I have is essentially one capacitor 00:28:38.880 --> 00:28:42.000 align:middle line:90% that's tied to ground. 00:28:42.000 --> 00:28:44.940 align:middle line:84% I have the capacitance between pink and green, 00:28:44.940 --> 00:28:47.250 align:middle line:90% and I'm grounding green. 00:28:47.250 --> 00:28:53.520 align:middle line:84% And then I have the capacitance between green and yellow. 00:28:53.520 --> 00:28:56.835 align:middle line:84% So here's my other capacitance, that goes to my sensitive node. 00:28:56.835 --> 00:28:59.340 align:middle line:90% 00:28:59.340 --> 00:29:02.650 align:middle line:84% And here's now the voltage I'm inducing on the sensitive node. 00:29:02.650 --> 00:29:05.280 align:middle line:84% What voltage would I be inducing due to this square wave 00:29:05.280 --> 00:29:05.975 align:middle line:90% in this case? 00:29:05.975 --> 00:29:10.700 align:middle line:90% 00:29:10.700 --> 00:29:12.950 align:middle line:84% Am I going to see a voltage over here in this circuit? 00:29:12.950 --> 00:29:15.690 align:middle line:90% 00:29:15.690 --> 00:29:16.360 align:middle line:90% No, right? 00:29:16.360 --> 00:29:20.175 align:middle line:84% I mean, he's got a grounded capacitor over here. 00:29:20.175 --> 00:29:22.530 align:middle line:84% So, essentially, this piece of metal 00:29:22.530 --> 00:29:24.810 align:middle line:90% acts as an electrostatic shield. 00:29:24.810 --> 00:29:28.470 align:middle line:84% If it was all the way around, you'd call it a Faraday cage. 00:29:28.470 --> 00:29:32.620 align:middle line:84% But it prevents this noisy signal from injecting onto this. 00:29:32.620 --> 00:29:33.940 align:middle line:90% Well, how would I do that? 00:29:33.940 --> 00:29:37.500 align:middle line:84% One way to do that is maybe I put this switching node 00:29:37.500 --> 00:29:39.590 align:middle line:90% on one side of my circuit board. 00:29:39.590 --> 00:29:41.790 align:middle line:84% I have a ground plane in between them, 00:29:41.790 --> 00:29:44.610 align:middle line:84% and I put my control circuitry on the other side of the circuit 00:29:44.610 --> 00:29:48.030 align:middle line:84% board that's sort of shielded or hidden from the high switching 00:29:48.030 --> 00:29:49.670 align:middle line:90% node. 00:29:49.670 --> 00:29:52.170 align:middle line:90% That makes sense to everybody? 00:29:52.170 --> 00:29:54.520 align:middle line:90% Now you can't always do that. 00:29:54.520 --> 00:29:55.730 align:middle line:90% What else could you do? 00:29:55.730 --> 00:29:57.550 align:middle line:84% If you have really sensitive stuff-- 00:29:57.550 --> 00:29:59.520 align:middle line:84% so suppose I had a radio receiver 00:29:59.520 --> 00:30:03.655 align:middle line:84% right next to my switching node circuit. 00:30:03.655 --> 00:30:04.910 align:middle line:90% Is that a good thing? 00:30:04.910 --> 00:30:07.780 align:middle line:84% No, but some days you don't get a choice, right? 00:30:07.780 --> 00:30:11.810 align:middle line:84% You can actually buy, for a printed circuit board mount, 00:30:11.810 --> 00:30:13.520 align:middle line:90% little shielding cans. 00:30:13.520 --> 00:30:15.310 align:middle line:84% So basically it's like it'll be-- 00:30:15.310 --> 00:30:18.310 align:middle line:84% it'll run around on the circuit board and provide a side edge, 00:30:18.310 --> 00:30:19.698 align:middle line:90% and then put a little cap on it. 00:30:19.698 --> 00:30:22.240 align:middle line:84% And you can put your whole-- your radio receiver or whatever, 00:30:22.240 --> 00:30:25.440 align:middle line:84% very sensitive noise, noise-sensitive element inside 00:30:25.440 --> 00:30:25.940 align:middle line:90% of there. 00:30:25.940 --> 00:30:28.990 align:middle line:84% So actually, if you take apart a Wi-Fi router or something 00:30:28.990 --> 00:30:33.100 align:middle line:84% like that, you'll often see these little kind of metal boxes 00:30:33.100 --> 00:30:35.740 align:middle line:84% at the top will pop off, and some of the RF stuff 00:30:35.740 --> 00:30:36.470 align:middle line:90% will be in there. 00:30:36.470 --> 00:30:38.560 align:middle line:84% That's both to keep the RF noise in 00:30:38.560 --> 00:30:40.388 align:middle line:84% and to keep the external stuff out. 00:30:40.388 --> 00:30:42.430 align:middle line:84% But you could do that with your control circuitry 00:30:42.430 --> 00:30:43.760 align:middle line:90% too, if you had to. 00:30:43.760 --> 00:30:45.337 align:middle line:90% But mostly what do you do? 00:30:45.337 --> 00:30:47.170 align:middle line:84% You try to be smart by not putting it close, 00:30:47.170 --> 00:30:49.420 align:middle line:84% or maybe putting it on the other side of the circuit board, 00:30:49.420 --> 00:30:51.840 align:middle line:84% and getting yourself an electrostatic shield in there. 00:30:51.840 --> 00:30:54.370 align:middle line:90% 00:30:54.370 --> 00:30:55.335 align:middle line:90% Questions about that? 00:30:55.335 --> 00:31:02.890 align:middle line:90% 00:31:02.890 --> 00:31:08.320 align:middle line:84% I should give you a little warning. 00:31:08.320 --> 00:31:11.470 align:middle line:84% When I did this approximation, and hopefully get 00:31:11.470 --> 00:31:14.350 align:middle line:84% the right actual equation here, to get 00:31:14.350 --> 00:31:17.740 align:middle line:84% the inductance and the capacitance, in both cases, 00:31:17.740 --> 00:31:20.240 align:middle line:84% I was neglecting fringing fields. 00:31:20.240 --> 00:31:25.120 align:middle line:84% So when does this inductance equation really work well? 00:31:25.120 --> 00:31:29.320 align:middle line:84% It works well when you have to really kind of wide conductors 00:31:29.320 --> 00:31:30.380 align:middle line:90% put close together. 00:31:30.380 --> 00:31:32.230 align:middle line:84% So maybe I send my gate drive signal out 00:31:32.230 --> 00:31:33.890 align:middle line:84% and I return it right underneath. 00:31:33.890 --> 00:31:37.090 align:middle line:84% That becomes a pretty good approximation to the loop 00:31:37.090 --> 00:31:38.650 align:middle line:90% inductance you're going to get. 00:31:38.650 --> 00:31:41.267 align:middle line:84% Or in a capacitance, if I have two pieces of metal that 00:31:41.267 --> 00:31:43.600 align:middle line:84% are of the same size, and they're really close together, 00:31:43.600 --> 00:31:45.370 align:middle line:84% that's a pretty good approximation. 00:31:45.370 --> 00:31:48.320 align:middle line:84% When I start to pull them apart, what happens? 00:31:48.320 --> 00:31:58.810 align:middle line:84% Well, in the capacitance case, for example, this approximation 00:31:58.810 --> 00:32:01.840 align:middle line:84% is really just capturing the fields that are directly 00:32:01.840 --> 00:32:03.210 align:middle line:90% between these plates. 00:32:03.210 --> 00:32:05.830 align:middle line:84% That's how you get to this equation. 00:32:05.830 --> 00:32:10.450 align:middle line:84% Once you start to have significant fringing fields, 00:32:10.450 --> 00:32:13.450 align:middle line:84% the distance between the plates is long 00:32:13.450 --> 00:32:18.190 align:middle line:84% compared to the areas or the lengths on the other dimensions 00:32:18.190 --> 00:32:20.350 align:middle line:84% of the plate, then these fringing fields 00:32:20.350 --> 00:32:22.420 align:middle line:90% start to become important. 00:32:22.420 --> 00:32:28.150 align:middle line:84% So you can't necessarily think of, oh, jeez, my capacitance 00:32:28.150 --> 00:32:30.580 align:middle line:84% is going to go exactly as the inverse 00:32:30.580 --> 00:32:33.500 align:middle line:84% of the distance between whatever things I'm going to have. 00:32:33.500 --> 00:32:36.760 align:middle line:84% That's true when they're really close together, but less true 00:32:36.760 --> 00:32:39.040 align:middle line:84% as you start to pull them far apart. 00:32:39.040 --> 00:32:44.890 align:middle line:84% So a classic analysis you might look at is like this. 00:32:44.890 --> 00:32:51.690 align:middle line:84% Suppose I took a sphere of radius r0. 00:32:51.690 --> 00:32:55.050 align:middle line:84% And I'm going to put a little charge on that sphere, 00:32:55.050 --> 00:33:01.680 align:middle line:84% plus Q. Total net charge on the sphere. 00:33:01.680 --> 00:33:06.540 align:middle line:84% And let me make the other plate of my capacitor a sphere that's 00:33:06.540 --> 00:33:13.560 align:middle line:84% around it at some big R. That itself 00:33:13.560 --> 00:33:18.110 align:middle line:84% forms a capacitance, where I have electric fields that are-- 00:33:18.110 --> 00:33:24.810 align:middle line:84% I'm going to have mirror charges distributed on my outer plate, 00:33:24.810 --> 00:33:28.140 align:middle line:84% on my outer sphere, and I'm going 00:33:28.140 --> 00:33:31.650 align:middle line:84% to have electric field pointing outward here like this. 00:33:31.650 --> 00:33:33.100 align:middle line:84% Does that make sense to everybody, 00:33:33.100 --> 00:33:34.100 align:middle line:90% the picture I'm drawing? 00:33:34.100 --> 00:33:36.720 align:middle line:84% I've got an inner sphere and an outer sphere. 00:33:36.720 --> 00:33:39.580 align:middle line:84% And I want to calculate the capacitance between them. 00:33:39.580 --> 00:33:40.900 align:middle line:90% And why am I doing spheres? 00:33:40.900 --> 00:33:43.290 align:middle line:84% Because I'm lazy and the math is easy. 00:33:43.290 --> 00:33:46.917 align:middle line:84% So think of whatever you got as being a little sphere. 00:33:46.917 --> 00:33:48.250 align:middle line:90% But here's what I'm going to do. 00:33:48.250 --> 00:33:51.510 align:middle line:84% Let me make the outer sphere go off to infinity. 00:33:51.510 --> 00:33:54.060 align:middle line:84% So I can say, what is the capacitance 00:33:54.060 --> 00:34:00.090 align:middle line:84% of this little sphere of metal to the rest of the universe? 00:34:00.090 --> 00:34:01.230 align:middle line:90% Well, what is that? 00:34:01.230 --> 00:34:02.565 align:middle line:90% Well, we can calculate that. 00:34:02.565 --> 00:34:05.460 align:middle line:90% 00:34:05.460 --> 00:34:08.384 align:middle line:84% If I take the integral of epsilon 0 A over-- 00:34:08.384 --> 00:34:11.900 align:middle line:90% 00:34:11.900 --> 00:34:16.159 align:middle line:84% the integral of epsilon E dot dA is 00:34:16.159 --> 00:34:18.690 align:middle line:84% equal to the net charge I'm enclosing. 00:34:18.690 --> 00:34:21.516 align:middle line:90% 00:34:21.516 --> 00:34:24.870 align:middle line:84% So if I then figured this out, suppose 00:34:24.870 --> 00:34:29.489 align:middle line:84% I took a sphere around my inner sphere, and I said, 00:34:29.489 --> 00:34:31.570 align:middle line:84% what's the radial electric field? 00:34:31.570 --> 00:34:36.270 align:middle line:84% What is the E sub r, the radial electric field, going to be? 00:34:36.270 --> 00:34:40.380 align:middle line:84% What is this electric field going to be at some distance r 00:34:40.380 --> 00:34:43.320 align:middle line:90% from the center? 00:34:43.320 --> 00:34:46.530 align:middle line:84% That's going to be equal to E sub r 00:34:46.530 --> 00:34:51.480 align:middle line:84% is just going to be equal to Q over epsilon times 00:34:51.480 --> 00:34:55.940 align:middle line:84% the area, which is 4 pi r squared. 00:34:55.940 --> 00:34:59.970 align:middle line:90% 00:34:59.970 --> 00:35:05.970 align:middle line:84% What's the voltage that's going to be between the outer sphere 00:35:05.970 --> 00:35:07.210 align:middle line:90% and the inner sphere? 00:35:07.210 --> 00:35:13.590 align:middle line:84% Well, the voltage is going to be equal to minus the integral of E 00:35:13.590 --> 00:35:19.950 align:middle line:84% sub r dr. Or I could write that, just to be easy, as 00:35:19.950 --> 00:35:22.560 align:middle line:90% infinity to r naught-- 00:35:22.560 --> 00:35:25.110 align:middle line:84% the integral from infinity out to the surface 00:35:25.110 --> 00:35:31.950 align:middle line:84% of my little piece of metal that's got charge on it, of Q 00:35:31.950 --> 00:35:36.990 align:middle line:84% over epsilon times 4 pi r squared, which 00:35:36.990 --> 00:35:47.310 align:middle line:84% is just going to be equal to Q divided by epsilon over 4 pi r. 00:35:47.310 --> 00:35:51.420 align:middle line:84% And that means that Q, if I write this, 00:35:51.420 --> 00:35:59.670 align:middle line:84% Q is just going to be equal to V times epsilon times 4 pi r-- 00:35:59.670 --> 00:36:00.840 align:middle line:90% r0. 00:36:00.840 --> 00:36:03.690 align:middle line:84% It's the radius of this little sphere, r0. 00:36:03.690 --> 00:36:07.890 align:middle line:84% But we know that Q is equal to CV. 00:36:07.890 --> 00:36:10.800 align:middle line:90% 00:36:10.800 --> 00:36:12.716 align:middle line:90% So this must be the capacitance. 00:36:12.716 --> 00:36:20.520 align:middle line:90% 00:36:20.520 --> 00:36:24.720 align:middle line:84% So I'm kind of taking the other case, where all of my field 00:36:24.720 --> 00:36:28.910 align:middle line:84% is fringing field out to the universe. 00:36:28.910 --> 00:36:32.920 align:middle line:84% And in this case, the capacitance to the universe, 00:36:32.920 --> 00:36:35.950 align:middle line:84% from some little sphere of metal that I've got sitting here, 00:36:35.950 --> 00:36:40.270 align:middle line:84% is exactly the dielectric, which presumably, if it's free space, 00:36:40.270 --> 00:36:44.120 align:middle line:84% is epsilon 0 times 4 pi times the radius of the sphere. 00:36:44.120 --> 00:36:48.940 align:middle line:84% So it's related to the square root of the area of the sphere. 00:36:48.940 --> 00:36:51.820 align:middle line:84% If I increase the area of this thing, 00:36:51.820 --> 00:36:54.740 align:middle line:84% the capacitance to the universe is not 0, 00:36:54.740 --> 00:36:57.310 align:middle line:84% even though the universe is infinitely far away. 00:36:57.310 --> 00:37:01.570 align:middle line:84% It's some finite amount related to the area or the radius 00:37:01.570 --> 00:37:03.940 align:middle line:90% of the thing I've got. 00:37:03.940 --> 00:37:07.300 align:middle line:84% So that's like-- this is basically a long way of saying, 00:37:07.300 --> 00:37:09.310 align:middle line:84% when I make things spaced far apart, 00:37:09.310 --> 00:37:11.650 align:middle line:84% fringing becomes very, very important, 00:37:11.650 --> 00:37:15.730 align:middle line:84% and I can get non-0 capacitances, 00:37:15.730 --> 00:37:18.200 align:middle line:90% or significant capacitances. 00:37:18.200 --> 00:37:20.830 align:middle line:84% And in that light, the only way you can really 00:37:20.830 --> 00:37:24.970 align:middle line:84% make that capacitance smaller is to basically make r not smaller, 00:37:24.970 --> 00:37:27.580 align:middle line:84% or basically make the area of the thing 00:37:27.580 --> 00:37:31.720 align:middle line:84% that you're worried about spraying field out smaller, 00:37:31.720 --> 00:37:34.605 align:middle line:84% so its capacitance to other stuff will be smaller. 00:37:34.605 --> 00:37:37.980 align:middle line:90% 00:37:37.980 --> 00:37:39.080 align:middle line:90% Questions about that? 00:37:39.080 --> 00:37:43.490 align:middle line:90% 00:37:43.490 --> 00:37:50.300 align:middle line:84% So this is just a case where Physics 101 leads you 00:37:50.300 --> 00:37:52.160 align:middle line:84% to some conclusions about how you should 00:37:52.160 --> 00:37:55.040 align:middle line:84% lay your circuits out, which comes back 00:37:55.040 --> 00:38:02.270 align:middle line:90% to make your loops very tight. 00:38:02.270 --> 00:38:03.310 align:middle line:90% And I could make this-- 00:38:03.310 --> 00:38:06.910 align:middle line:84% I could have done the same analysis for finding inductances 00:38:06.910 --> 00:38:08.330 align:middle line:90% of loops and so forth. 00:38:08.330 --> 00:38:10.060 align:middle line:90% You make your loop tight. 00:38:10.060 --> 00:38:11.920 align:middle line:90% You spread the area-- 00:38:11.920 --> 00:38:15.490 align:middle line:84% you spread the current out to get the inductance low, 00:38:15.490 --> 00:38:18.550 align:middle line:90% and make the loop very tight. 00:38:18.550 --> 00:38:20.890 align:middle line:90% Don't use excess loop. 00:38:20.890 --> 00:38:24.370 align:middle line:84% Don't use excess trace area, especially 00:38:24.370 --> 00:38:26.475 align:middle line:90% at this loop and this node. 00:38:26.475 --> 00:38:30.230 align:middle line:90% 00:38:30.230 --> 00:38:32.540 align:middle line:84% If you're going to go analyze a juke converter 00:38:32.540 --> 00:38:35.900 align:middle line:84% or some other kind of converter, which loop you care about 00:38:35.900 --> 00:38:37.190 align:middle line:90% is different. 00:38:37.190 --> 00:38:39.620 align:middle line:84% Which nodes you care about are different. 00:38:39.620 --> 00:38:42.110 align:middle line:84% But they're usually the ones with the square-wave currents 00:38:42.110 --> 00:38:45.260 align:middle line:84% in them and the square-wave voltages on them, 00:38:45.260 --> 00:38:49.400 align:middle line:84% or the high dv/dt or di/dt elements on them. 00:38:49.400 --> 00:38:53.470 align:middle line:84% And small changes can make a big difference. 00:38:53.470 --> 00:38:54.900 align:middle line:90% Questions about any of that? 00:38:54.900 --> 00:39:00.830 align:middle line:90% 00:39:00.830 --> 00:39:03.200 align:middle line:84% Let me just talk about a couple of other things 00:39:03.200 --> 00:39:05.972 align:middle line:84% that I've glossed over, or just not-- it's not 00:39:05.972 --> 00:39:06.930 align:middle line:90% that I've glossed over. 00:39:06.930 --> 00:39:10.220 align:middle line:84% I've just not worried about them. 00:39:10.220 --> 00:39:13.040 align:middle line:84% And these, again, are practical implementation issues 00:39:13.040 --> 00:39:14.960 align:middle line:84% which are important, but you've got 00:39:14.960 --> 00:39:17.270 align:middle line:84% to worry about them after you worry 00:39:17.270 --> 00:39:21.060 align:middle line:90% about the rest of your system. 00:39:21.060 --> 00:39:27.360 align:middle line:84% Let's think about driving the gates of our converters, gates 00:39:27.360 --> 00:39:28.420 align:middle line:90% of our transistors. 00:39:28.420 --> 00:39:32.105 align:middle line:90% So if I think about my MOSFET-- 00:39:32.105 --> 00:39:33.480 align:middle line:84% so suppose, I don't know, suppose 00:39:33.480 --> 00:39:35.828 align:middle line:84% I make a boost converter, for example. 00:39:35.828 --> 00:39:37.620 align:middle line:84% So I've been talking about buck converters. 00:39:37.620 --> 00:39:39.702 align:middle line:84% Now I'll talk about boost converters. 00:39:39.702 --> 00:39:45.510 align:middle line:84% I'm going to have some circuit here, 00:39:45.510 --> 00:39:47.892 align:middle line:90% and I'm going to drive him. 00:39:47.892 --> 00:39:49.562 align:middle line:84% And usually what's going to be here 00:39:49.562 --> 00:39:51.270 align:middle line:84% is there's going to be some circuit which 00:39:51.270 --> 00:39:53.320 align:middle line:90% is making switching decisions. 00:39:53.320 --> 00:39:56.400 align:middle line:84% It's powered from some low-voltage supply. 00:39:56.400 --> 00:39:59.220 align:middle line:84% And it's got some input that's telling me 00:39:59.220 --> 00:40:00.596 align:middle line:90% when to switch this transistor. 00:40:00.596 --> 00:40:05.215 align:middle line:90% 00:40:05.215 --> 00:40:08.250 align:middle line:84% What is the input of that transistor look like? 00:40:08.250 --> 00:40:10.580 align:middle line:84% Well, you know, this thing in him, 00:40:10.580 --> 00:40:12.710 align:middle line:84% the last thing between me and my switch, 00:40:12.710 --> 00:40:16.430 align:middle line:84% is some of gate driver, which is going to be 00:40:16.430 --> 00:40:17.910 align:middle line:90% powered from some voltage. 00:40:17.910 --> 00:40:21.590 align:middle line:84% And he's got some signal coming in. 00:40:21.590 --> 00:40:26.066 align:middle line:84% And he's going to try to turn this transistor on and off. 00:40:26.066 --> 00:40:32.540 align:middle line:84% So if I thought about my transistor, here 00:40:32.540 --> 00:40:36.980 align:middle line:84% I'm going to drive this with some square-wave voltage. 00:40:36.980 --> 00:40:40.910 align:middle line:84% And I need to remember that this transistor is going 00:40:40.910 --> 00:40:45.560 align:middle line:84% to have some gate-source capacitance, 00:40:45.560 --> 00:40:49.130 align:middle line:84% he's going to have some drain-source capacitance, 00:40:49.130 --> 00:40:51.830 align:middle line:84% but he's also, importantly, going to have some gate 00:40:51.830 --> 00:40:53.196 align:middle line:90% to drain capacitance. 00:40:53.196 --> 00:40:56.985 align:middle line:90% 00:40:56.985 --> 00:41:00.610 align:middle line:84% And this gate to drain capacitance actually 00:41:00.610 --> 00:41:03.310 align:middle line:84% has a significant influence, especially in the case 00:41:03.310 --> 00:41:06.230 align:middle line:84% when, suppose I'm driving this between 0 00:41:06.230 --> 00:41:12.590 align:middle line:84% and 10 volts or something, or 0 and 5 volts if it's a lower, 00:41:12.590 --> 00:41:14.800 align:middle line:90% a logic-level kind of device. 00:41:14.800 --> 00:41:15.700 align:middle line:90% All right? 00:41:15.700 --> 00:41:19.490 align:middle line:84% But maybe this drain node is switching by hundreds of volts. 00:41:19.490 --> 00:41:23.410 align:middle line:84% So this capacitance is the so-called Miller feedback 00:41:23.410 --> 00:41:25.480 align:middle line:84% capacitance-- this guy right here. 00:41:25.480 --> 00:41:30.465 align:middle line:84% Can have a big impact on the switching characteristics here. 00:41:30.465 --> 00:41:33.150 align:middle line:90% 00:41:33.150 --> 00:41:34.290 align:middle line:90% Because what happens? 00:41:34.290 --> 00:41:38.730 align:middle line:84% If I look at the charge I'm sourcing in here, 00:41:38.730 --> 00:41:41.160 align:middle line:90% and the voltage Vgs I'm getting. 00:41:41.160 --> 00:41:44.430 align:middle line:84% And this voltage, if this is a N-channel MOSFET, 00:41:44.430 --> 00:41:47.640 align:middle line:84% it's this voltage that-- this Vgs voltage is what's 00:41:47.640 --> 00:41:50.280 align:middle line:90% controlling how he switches on. 00:41:50.280 --> 00:42:00.100 align:middle line:84% If I looked at Vgs versus Q sub g, 00:42:00.100 --> 00:42:03.480 align:middle line:84% the gate charge I'm putting in, what would happen? 00:42:03.480 --> 00:42:07.840 align:middle line:84% When this thing is off, Before he turns on, 00:42:07.840 --> 00:42:11.990 align:middle line:84% I'm going to start charging the gate. 00:42:11.990 --> 00:42:16.150 align:middle line:84% And this is the capacitance my gate driver is driving. 00:42:16.150 --> 00:42:18.460 align:middle line:90% dQ is C dV. 00:42:18.460 --> 00:42:19.510 align:middle line:90% All right? 00:42:19.510 --> 00:42:23.890 align:middle line:84% But what happens at some point is when Vgs gets bigger 00:42:23.890 --> 00:42:27.040 align:middle line:84% than the threshold voltage, I'm going 00:42:27.040 --> 00:42:29.770 align:middle line:90% to start turning on this FET. 00:42:29.770 --> 00:42:31.038 align:middle line:90% And what does that happen? 00:42:31.038 --> 00:42:33.080 align:middle line:84% This voltage, which was up at some high voltage-- 00:42:33.080 --> 00:42:35.850 align:middle line:84% this was the output voltage-- maybe that's 200 volts-- 00:42:35.850 --> 00:42:37.990 align:middle line:90% starts to swing down. 00:42:37.990 --> 00:42:39.730 align:middle line:84% And when it starts to swing down, 00:42:39.730 --> 00:42:43.180 align:middle line:84% I need to feed charge in from the gate 00:42:43.180 --> 00:42:48.496 align:middle line:90% to discharge this capacitor. 00:42:48.496 --> 00:42:51.160 align:middle line:84% And what that means is I'm going to be trying-- 00:42:51.160 --> 00:42:54.340 align:middle line:84% I'm going to be pumping charge in here. 00:42:54.340 --> 00:42:57.230 align:middle line:84% But the gate voltage isn't going to be going up appreciably. 00:42:57.230 --> 00:42:58.730 align:middle line:90% He's just going to sit flat. 00:42:58.730 --> 00:43:00.850 align:middle line:84% And all the charge I'm pumping in here 00:43:00.850 --> 00:43:06.650 align:middle line:84% is basically going to drive the drain down. 00:43:06.650 --> 00:43:09.620 align:middle line:84% So this capacitor basically suddenly makes 00:43:09.620 --> 00:43:13.340 align:middle line:84% the equivalent capacitance I'm driving at my gate very large. 00:43:13.340 --> 00:43:15.500 align:middle line:84% Eventually, once I've pumped enough in, 00:43:15.500 --> 00:43:17.960 align:middle line:84% this node comes down to close to ground, 00:43:17.960 --> 00:43:22.010 align:middle line:84% this voltage ceases changing, and then this goes up like this. 00:43:22.010 --> 00:43:26.840 align:middle line:84% So this happens somewhere near Vth, the threshold voltage 00:43:26.840 --> 00:43:28.713 align:middle line:90% of the FET. 00:43:28.713 --> 00:43:30.130 align:middle line:84% Does that make sense to everybody? 00:43:30.130 --> 00:43:32.720 align:middle line:90% 00:43:32.720 --> 00:43:35.090 align:middle line:90% Why am I pointing this out? 00:43:35.090 --> 00:43:36.820 align:middle line:90% Well, two reasons. 00:43:36.820 --> 00:43:42.960 align:middle line:84% Firstly, when I think about the amount of charge 00:43:42.960 --> 00:43:47.590 align:middle line:84% I need to put in, maybe this is my threshold voltage. 00:43:47.590 --> 00:43:49.080 align:middle line:90% I don't know, whatever that is. 00:43:49.080 --> 00:43:54.630 align:middle line:84% Maybe this is 10 volts and this is 50 nanocoulombs. 00:43:54.630 --> 00:44:01.650 align:middle line:84% So what I care about is I need to source this total charge 00:44:01.650 --> 00:44:04.330 align:middle line:90% to get to 10 volts. 00:44:04.330 --> 00:44:07.470 align:middle line:84% And if I only paid attention to what this capacitance was, 00:44:07.470 --> 00:44:11.380 align:middle line:84% I wouldn't really calculate the total charge I needed. 00:44:11.380 --> 00:44:13.380 align:middle line:90% And how much energy-- 00:44:13.380 --> 00:44:17.010 align:middle line:84% how much do I lose from this gate-drive power supply? 00:44:17.010 --> 00:44:18.450 align:middle line:84% Well, we talked about this when we 00:44:18.450 --> 00:44:20.242 align:middle line:84% talked about switched capacitor converters. 00:44:20.242 --> 00:44:26.560 align:middle line:84% If I'm supplying, here's some value Q sub G total, 00:44:26.560 --> 00:44:31.110 align:middle line:84% that supply is always coming from this gate-drive 00:44:31.110 --> 00:44:32.220 align:middle line:90% power-supply voltage-- 00:44:32.220 --> 00:44:33.810 align:middle line:90% 10 volts or something. 00:44:33.810 --> 00:44:37.470 align:middle line:84% So the amount of energy that comes in to charge up this gate 00:44:37.470 --> 00:44:47.790 align:middle line:84% is going to be equal to QG times Vgs max, or V supply, 00:44:47.790 --> 00:44:52.470 align:middle line:84% where this is my gate-drive power supply, V supply. 00:44:52.470 --> 00:44:54.360 align:middle line:84% If I wanted the power dissipation, 00:44:54.360 --> 00:44:55.950 align:middle line:90% that's how much I lose. 00:44:55.950 --> 00:44:58.690 align:middle line:84% Some of that energy goes to charging the gate. 00:44:58.690 --> 00:45:00.300 align:middle line:90% Some of it goes-- 00:45:00.300 --> 00:45:02.390 align:middle line:84% it gets dissipated in the resistors here. 00:45:02.390 --> 00:45:05.770 align:middle line:84% We talked about that when we talked about 00:45:05.770 --> 00:45:06.890 align:middle line:90% switch capacitor supplies. 00:45:06.890 --> 00:45:08.265 align:middle line:84% But then in the end, what happens 00:45:08.265 --> 00:45:10.360 align:middle line:84% is I dump all that energy anyways 00:45:10.360 --> 00:45:12.220 align:middle line:90% when I turn the switch off. 00:45:12.220 --> 00:45:16.510 align:middle line:84% And so each cycle I'm going to lose QG times V supply, where 00:45:16.510 --> 00:45:19.660 align:middle line:84% my power is going to be QG V supply times the switching 00:45:19.660 --> 00:45:21.180 align:middle line:90% frequency. 00:45:21.180 --> 00:45:23.030 align:middle line:84% Does that make sense to everybody? 00:45:23.030 --> 00:45:28.430 align:middle line:90% 00:45:28.430 --> 00:45:39.360 align:middle line:84% So P gate might be equal to Q sub G V supply times F switch-- 00:45:39.360 --> 00:45:41.120 align:middle line:84% the number of times I'm turning on and off 00:45:41.120 --> 00:45:42.037 align:middle line:90% the switch per second. 00:45:42.037 --> 00:45:44.840 align:middle line:84% Notice that it has nothing to do with the-- 00:45:44.840 --> 00:45:49.525 align:middle line:84% necessarily with the gate drive internal resistances 00:45:49.525 --> 00:45:51.900 align:middle line:84% for the same reasons we talked about when we talked about 00:45:51.900 --> 00:45:54.380 align:middle line:90% switch capacitor converters. 00:45:54.380 --> 00:45:55.525 align:middle line:90% Any questions about that? 00:45:55.525 --> 00:45:59.510 align:middle line:90% 00:45:59.510 --> 00:46:01.617 align:middle line:90% So let's think about-- 00:46:01.617 --> 00:46:03.950 align:middle line:84% so that's one thing I want you to pay attention about is 00:46:03.950 --> 00:46:06.440 align:middle line:84% you got to really look at these threshold curves 00:46:06.440 --> 00:46:08.750 align:middle line:90% to get your total loss. 00:46:08.750 --> 00:46:10.280 align:middle line:84% There's another thing you might want 00:46:10.280 --> 00:46:13.220 align:middle line:84% to think about when you think about the driver itself, 00:46:13.220 --> 00:46:15.380 align:middle line:90% and that's the following. 00:46:15.380 --> 00:46:20.490 align:middle line:84% What would this driver, this guy, look like inside? 00:46:20.490 --> 00:46:28.670 align:middle line:84% Inside this driver, you might model as one MOSFET 00:46:28.670 --> 00:46:29.843 align:middle line:90% and another MOSFET. 00:46:29.843 --> 00:46:32.450 align:middle line:90% 00:46:32.450 --> 00:46:37.020 align:middle line:84% And then he's connected to the gate that he's going to drive. 00:46:37.020 --> 00:46:38.990 align:middle line:84% So I'm going to either turn on the top. 00:46:38.990 --> 00:46:41.240 align:middle line:90% So this is my gate driver. 00:46:41.240 --> 00:46:45.260 align:middle line:84% I'm going to turn on-- this is V supply. 00:46:45.260 --> 00:46:47.390 align:middle line:84% So I'm going to turn on the top switch, 00:46:47.390 --> 00:46:49.602 align:middle line:84% and he's going to charge the gate, 00:46:49.602 --> 00:46:51.560 align:middle line:84% and then I'm going to turn on the bottom switch 00:46:51.560 --> 00:46:53.630 align:middle line:84% and he's going to discharge the gate and turn it off. 00:46:53.630 --> 00:46:55.050 align:middle line:84% Does that make sense to everybody? 00:46:55.050 --> 00:46:58.020 align:middle line:90% 00:46:58.020 --> 00:47:03.060 align:middle line:84% Let's think about-- and by the way, sometimes-- 00:47:03.060 --> 00:47:04.330 align:middle line:90% let me just think about this. 00:47:04.330 --> 00:47:06.622 align:middle line:84% I'm going to simplify this as just being a capacitance, 00:47:06.622 --> 00:47:07.930 align:middle line:90% a simple linear capacitance. 00:47:07.930 --> 00:47:10.020 align:middle line:84% But what we know is it's anything 00:47:10.020 --> 00:47:12.000 align:middle line:90% but a simple linear capacitance. 00:47:12.000 --> 00:47:15.030 align:middle line:84% Maybe I'm thinking about this equivalent capacitance 00:47:15.030 --> 00:47:17.386 align:middle line:84% now for simplicity, this chordal capacitance. 00:47:17.386 --> 00:47:22.180 align:middle line:90% 00:47:22.180 --> 00:47:25.640 align:middle line:84% Let's think about charging this up and discharging it. 00:47:25.640 --> 00:47:28.260 align:middle line:90% 00:47:28.260 --> 00:47:33.360 align:middle line:84% If I turn on, one of my tendencies 00:47:33.360 --> 00:47:38.380 align:middle line:84% might be to turn this on as fast as possible. 00:47:38.380 --> 00:47:42.900 align:middle line:84% But maybe-- let me just imagine I have some resistance here. 00:47:42.900 --> 00:47:45.450 align:middle line:84% Sometimes I have resistance in the driver, 00:47:45.450 --> 00:47:47.370 align:middle line:84% sometimes I have resistance in the gate, 00:47:47.370 --> 00:47:50.450 align:middle line:84% and sometimes I actually add external resistor. 00:47:50.450 --> 00:47:52.800 align:middle line:84% Why would I add external resistor? 00:47:52.800 --> 00:47:55.260 align:middle line:90% We talked about EMI before. 00:47:55.260 --> 00:47:58.500 align:middle line:84% When I turn this transistor on, I 00:47:58.500 --> 00:48:02.070 align:middle line:90% am discharging this capacitance. 00:48:02.070 --> 00:48:03.930 align:middle line:84% So I have some capacitance here, and I'm 00:48:03.930 --> 00:48:06.130 align:middle line:90% discharging it into the switch. 00:48:06.130 --> 00:48:07.620 align:middle line:90% Capacitance on my diode. 00:48:07.620 --> 00:48:10.540 align:middle line:84% I'm discharging it, or I'm charging it into the switch. 00:48:10.540 --> 00:48:12.630 align:middle line:84% That causes a huge pulse of current 00:48:12.630 --> 00:48:19.346 align:middle line:84% in this loop which could cause a lot of noise if it rings a lot. 00:48:19.346 --> 00:48:23.940 align:middle line:84% And yet, the amount I lose, at least in the capacitive portion, 00:48:23.940 --> 00:48:26.740 align:middle line:84% doesn't depend on how fast I turn it on, right? 00:48:26.740 --> 00:48:30.000 align:middle line:84% So at some level, maybe I'm motivated 00:48:30.000 --> 00:48:36.600 align:middle line:84% to turn on my switch somewhat slowly so that I don't discharge 00:48:36.600 --> 00:48:39.960 align:middle line:84% this capacitance really, really fast and cause a lot of noise. 00:48:39.960 --> 00:48:42.840 align:middle line:84% So a lot of the time, we actually 00:48:42.840 --> 00:48:45.270 align:middle line:84% put additional resistance in here 00:48:45.270 --> 00:48:51.450 align:middle line:84% to slow up how fast I turn on the device. 00:48:51.450 --> 00:48:54.580 align:middle line:84% And some gate drivers will tell you what that is. 00:48:54.580 --> 00:48:59.640 align:middle line:84% Sometimes you put in a discrete resistor to do that. 00:48:59.640 --> 00:49:02.350 align:middle line:84% What about turning off the device? 00:49:02.350 --> 00:49:06.700 align:middle line:84% When I turn off the device, well, he was on, 00:49:06.700 --> 00:49:08.440 align:middle line:90% so this already has 0 voltage. 00:49:08.440 --> 00:49:10.690 align:middle line:84% When I turn them off, this device 00:49:10.690 --> 00:49:12.080 align:middle line:84% isn't going to turn on instantly. 00:49:12.080 --> 00:49:14.247 align:middle line:84% It's not going to turn on until the inductor charges 00:49:14.247 --> 00:49:15.885 align:middle line:90% up this capacitance again. 00:49:15.885 --> 00:49:18.040 align:middle line:84% So in some sense, this capacitance, 00:49:18.040 --> 00:49:20.860 align:middle line:84% it hurt me when I turned it on, but now that I'm turning him 00:49:20.860 --> 00:49:23.560 align:middle line:84% off, he's actually acting like a little bit like a snubber 00:49:23.560 --> 00:49:27.612 align:middle line:84% and slowing down the rate of rise of this thing. 00:49:27.612 --> 00:49:34.420 align:middle line:84% But the longer I take to turn him off, the more overlap I get. 00:49:34.420 --> 00:49:38.140 align:middle line:84% If the longer his current takes to fall, the more voltage 00:49:38.140 --> 00:49:43.000 align:middle line:84% I'm building up across this transistor and dissipating them. 00:49:43.000 --> 00:49:47.170 align:middle line:84% So it doesn't cost me anything to turn them off fast, 00:49:47.170 --> 00:49:49.060 align:middle line:84% whereas it cost me something to turn them 00:49:49.060 --> 00:49:51.260 align:middle line:90% on fast, in terms of noise. 00:49:51.260 --> 00:49:55.810 align:middle line:84% So very often we would like to turn on the transistor 00:49:55.810 --> 00:50:01.352 align:middle line:84% somewhat slowly, and turn them off really fast. 00:50:01.352 --> 00:50:03.880 align:middle line:90% So you don't want-- 00:50:03.880 --> 00:50:06.970 align:middle line:84% this resistor, if I load it all onto this resistor, 00:50:06.970 --> 00:50:08.680 align:middle line:84% I don't want this resistor to be the same 00:50:08.680 --> 00:50:10.200 align:middle line:90% for turning on and turning off. 00:50:10.200 --> 00:50:13.600 align:middle line:84% And what you'll see in a lot of drivers is that what they'll do 00:50:13.600 --> 00:50:17.320 align:middle line:84% is, for turn on, this resistance, or equivalently 00:50:17.320 --> 00:50:22.460 align:middle line:84% the positive sourcing capability will be a bigger resistance. 00:50:22.460 --> 00:50:24.610 align:middle line:84% And the resistance for turning off 00:50:24.610 --> 00:50:26.480 align:middle line:84% will be a much smaller resistance. 00:50:26.480 --> 00:50:29.080 align:middle line:84% So you can turn the transistor off fast, 00:50:29.080 --> 00:50:30.880 align:middle line:84% but turn them on only slightly slow. 00:50:30.880 --> 00:50:34.630 align:middle line:84% And that will help reduce your noise. 00:50:34.630 --> 00:50:38.740 align:middle line:84% If you don't like what that looks like, 00:50:38.740 --> 00:50:42.460 align:middle line:84% you can add your own resistor that will slow down the turn on. 00:50:42.460 --> 00:50:44.960 align:middle line:84% Maybe you don't want to slow down the turn off as much. 00:50:44.960 --> 00:50:47.600 align:middle line:84% So for the turn off, maybe what you do 00:50:47.600 --> 00:50:51.090 align:middle line:84% is you put a diode and a smaller resistor, or no resistor here. 00:50:51.090 --> 00:50:53.630 align:middle line:84% So he charges slowly through the yellow resistor 00:50:53.630 --> 00:50:57.080 align:middle line:84% and he discharges quickly through the green diode. 00:50:57.080 --> 00:51:00.920 align:middle line:84% So you can control rate of turn on and turn off 00:51:00.920 --> 00:51:04.400 align:middle line:84% to control that switching and the noise injection 00:51:04.400 --> 00:51:06.080 align:middle line:90% elsewhere in your circuit. 00:51:06.080 --> 00:51:08.870 align:middle line:84% And you think about that when you buy your driver, 00:51:08.870 --> 00:51:12.055 align:middle line:84% and how you drive-- you connect your driver to your switch. 00:51:12.055 --> 00:51:14.680 align:middle line:90% 00:51:14.680 --> 00:51:15.585 align:middle line:90% Questions about that? 00:51:15.585 --> 00:51:18.340 align:middle line:90% 00:51:18.340 --> 00:51:21.550 align:middle line:84% So I'm of out of time to talk about these practical 00:51:21.550 --> 00:51:22.540 align:middle line:90% implementation issues. 00:51:22.540 --> 00:51:25.780 align:middle line:84% This is like, you could spend a whole course on this. 00:51:25.780 --> 00:51:28.900 align:middle line:84% But at least I hope you get a bit 00:51:28.900 --> 00:51:32.560 align:middle line:84% of a sense of how you might do some of these things 00:51:32.560 --> 00:51:34.040 align:middle line:90% in laying out your circuit. 00:51:34.040 --> 00:51:36.310 align:middle line:84% And so at least I've attempted this term 00:51:36.310 --> 00:51:39.730 align:middle line:84% to take you from what's the basic operation of a switching 00:51:39.730 --> 00:51:42.320 align:middle line:84% circuit, how do you design all the components, 00:51:42.320 --> 00:51:46.030 align:middle line:84% how do you control it, how do you deal with the filters, 00:51:46.030 --> 00:51:47.570 align:middle line:90% how do you lay it out? 00:51:47.570 --> 00:51:49.760 align:middle line:84% And I'm afraid that's all we have time for. 00:51:49.760 --> 00:51:52.960 align:middle line:84% I wish you the best in finishing your projects, and a really nice 00:51:52.960 --> 00:51:53.500 align:middle line:90% summer. 00:51:53.500 --> 00:51:55.120 align:middle line:90% So have a great day. 00:51:55.120 --> 00:51:58.770 align:middle line:90% [APPLAUSE] 00:51:58.770 --> 00:52:07.000 align:middle line:90%