WEBVTT 00:00:00.000 --> 00:00:01.968 align:middle line:90% [SQUEAKING] 00:00:01.968 --> 00:00:03.928 align:middle line:90% [RUSTLING] 00:00:03.928 --> 00:00:04.428 align:middle line:90% 00:00:04.428 --> 00:00:05.412 align:middle line:90% [CLICKING] 00:00:05.412 --> 00:00:09.347 align:middle line:90% 00:00:09.347 --> 00:00:09.930 align:middle line:90% PROFESSOR: OK. 00:00:09.930 --> 00:00:12.570 align:middle line:90% Why don't we get started? 00:00:12.570 --> 00:00:14.950 align:middle line:90% The end of the term approacheth. 00:00:14.950 --> 00:00:19.710 align:middle line:84% So please do get to work on the design projects 00:00:19.710 --> 00:00:21.400 align:middle line:84% if you're not already doing that. 00:00:21.400 --> 00:00:24.810 align:middle line:84% The homework lengths are being tapered down 00:00:24.810 --> 00:00:26.650 align:middle line:90% to open up room to do that. 00:00:26.650 --> 00:00:30.270 align:middle line:84% So please don't leave it to the last moment. 00:00:30.270 --> 00:00:32.460 align:middle line:84% And I know this is project season 00:00:32.460 --> 00:00:35.550 align:middle line:84% so I know many people have a lot of them going on. 00:00:35.550 --> 00:00:38.700 align:middle line:90% So try to start early. 00:00:38.700 --> 00:00:40.650 align:middle line:84% Everything I'm going to talk about today 00:00:40.650 --> 00:00:43.923 align:middle line:84% is in Principles of Power Electronics, chapter 26. 00:00:43.923 --> 00:00:49.990 align:middle line:90% 00:00:49.990 --> 00:00:53.380 align:middle line:84% Just as a review of what we talked about last time, 00:00:53.380 --> 00:00:58.720 align:middle line:84% we said if I thought about a power converter and its filter, 00:00:58.720 --> 00:01:10.300 align:middle line:84% if I have a filter like an Lc filter, I have some Cf and Lf, 00:01:10.300 --> 00:01:13.520 align:middle line:84% which I'm looking back into from the power converter. 00:01:13.520 --> 00:01:15.250 align:middle line:84% And the problem is if I'm driving current 00:01:15.250 --> 00:01:19.540 align:middle line:84% into this filter, if I don't worry about the voltage source 00:01:19.540 --> 00:01:22.150 align:middle line:84% but just think about maybe the source impedance is 00:01:22.150 --> 00:01:25.520 align:middle line:84% a short circuit, Cf and Lf are in parallel, 00:01:25.520 --> 00:01:27.890 align:middle line:84% so I'll get a real-- a peak and impedance and a lot 00:01:27.890 --> 00:01:31.580 align:middle line:84% of circulating current if I have any drive at the cutoff 00:01:31.580 --> 00:01:33.530 align:middle line:90% frequency of the filter. 00:01:33.530 --> 00:01:38.540 align:middle line:84% And we said both this very lightly damped system 00:01:38.540 --> 00:01:41.600 align:middle line:84% and the output impedance can be modified 00:01:41.600 --> 00:01:45.290 align:middle line:84% by adding a damping leg of one kind or another. 00:01:45.290 --> 00:01:51.350 align:middle line:84% So maybe what I do is I take an additional C damp and R damp 00:01:51.350 --> 00:01:54.230 align:middle line:84% so that, at the cutoff, C damp's a short circuit 00:01:54.230 --> 00:01:57.320 align:middle line:84% or close to it so R damp is in parallel with Lf and Cf. 00:01:57.320 --> 00:02:00.020 align:middle line:84% And I reduce the output impedance of the filter. 00:02:00.020 --> 00:02:00.720 align:middle line:90% So right. 00:02:00.720 --> 00:02:05.360 align:middle line:84% So maybe this z out looks something 00:02:05.360 --> 00:02:09.080 align:middle line:84% like this versus omega on a log scale. 00:02:09.080 --> 00:02:11.600 align:middle line:84% Maybe at low frequencies, it rises 00:02:11.600 --> 00:02:16.190 align:middle line:84% as omega L. At high frequency, it falls as 1 over omega C. 00:02:16.190 --> 00:02:19.610 align:middle line:84% And I'll get some peaking in here, which 00:02:19.610 --> 00:02:25.470 align:middle line:84% is limited by the magnitude of z out max 00:02:25.470 --> 00:02:28.218 align:middle line:84% is related to the damping resistor here. 00:02:28.218 --> 00:02:30.510 align:middle line:84% And if the damping resistors were actually in parallel, 00:02:30.510 --> 00:02:33.060 align:middle line:84% it would be exactly the damping resistance. 00:02:33.060 --> 00:02:36.450 align:middle line:84% Now the reason we care about that 00:02:36.450 --> 00:02:39.630 align:middle line:84% is both because we don't want a lot of peaking and undamped 00:02:39.630 --> 00:02:43.410 align:middle line:84% behavior in this filter, but it's also true 00:02:43.410 --> 00:02:45.690 align:middle line:84% that if I look in the other direction 00:02:45.690 --> 00:02:48.090 align:middle line:84% into the power converter and say what's 00:02:48.090 --> 00:02:50.430 align:middle line:84% the input impedance looking into the power converter 00:02:50.430 --> 00:02:56.500 align:middle line:84% incrementally, if I have some V in and then some 00:02:56.500 --> 00:03:01.750 align:middle line:84% I in to the converter and the converter is regulating, 00:03:01.750 --> 00:03:05.560 align:middle line:84% it's going to maintain a constant voltage across its load 00:03:05.560 --> 00:03:09.040 align:middle line:84% or, equivalently, it's going to draw ideally constant power 00:03:09.040 --> 00:03:10.520 align:middle line:90% to maintain its load. 00:03:10.520 --> 00:03:20.660 align:middle line:84% That means its IV characteristic V in I in looks like this 00:03:20.660 --> 00:03:25.840 align:middle line:84% because V in is proportional to 1 over I in. 00:03:25.840 --> 00:03:28.780 align:middle line:84% And so if we're sitting at some operating point, 00:03:28.780 --> 00:03:38.230 align:middle line:84% say this is I in and this is V in, 00:03:38.230 --> 00:03:53.490 align:middle line:84% incrementally, this slope is dV in dI in evaluated at V in I in 00:03:53.490 --> 00:03:58.350 align:middle line:84% is equal to a negative resistor because this slope is negative. 00:03:58.350 --> 00:04:05.700 align:middle line:84% So it turns out to be minus p out over I in squared. 00:04:05.700 --> 00:04:10.440 align:middle line:84% And so basically, if I'm looking into the converter 00:04:10.440 --> 00:04:17.579 align:middle line:84% from the filter, I'm effectively seeing a negative resistor here. 00:04:17.579 --> 00:04:21.390 align:middle line:84% And that negative resistor can make this whole thing oscillate. 00:04:21.390 --> 00:04:24.520 align:middle line:84% So we always want to make the output impedance 00:04:24.520 --> 00:04:27.810 align:middle line:84% of my filter very small compared to the magnitude 00:04:27.810 --> 00:04:30.900 align:middle line:84% of my negative input resistance here in order 00:04:30.900 --> 00:04:34.640 align:middle line:84% to make sure that this whole system won't oscillate. 00:04:34.640 --> 00:04:39.667 align:middle line:84% So that was what I hoped you took away from last class. 00:04:39.667 --> 00:04:41.125 align:middle line:84% Are there any questions about that? 00:04:41.125 --> 00:04:44.820 align:middle line:90% 00:04:44.820 --> 00:04:47.310 align:middle line:84% So today I want to talk about something 00:04:47.310 --> 00:04:48.500 align:middle line:90% a little bit different. 00:04:48.500 --> 00:04:52.170 align:middle line:84% We've kind of brushed lightly over one topic 00:04:52.170 --> 00:04:56.130 align:middle line:84% or neglected one kind of effect that you often 00:04:56.130 --> 00:04:58.830 align:middle line:84% have to contend with in EMI filter designs. 00:04:58.830 --> 00:05:03.250 align:middle line:84% And just to illustrate how important this general topic is, 00:05:03.250 --> 00:05:06.840 align:middle line:84% what this is is this is a power factor corrected laptop power 00:05:06.840 --> 00:05:08.880 align:middle line:90% supply which somebody gave me. 00:05:08.880 --> 00:05:13.020 align:middle line:84% And that's what happens to power supplies people give me. 00:05:13.020 --> 00:05:18.960 align:middle line:84% And if you look at this, here is the twice line frequency energy 00:05:18.960 --> 00:05:19.930 align:middle line:90% buffer over here. 00:05:19.930 --> 00:05:21.910 align:middle line:90% Here's the power stage. 00:05:21.910 --> 00:05:23.160 align:middle line:90% There's a rectifier up front. 00:05:23.160 --> 00:05:26.520 align:middle line:84% But a whole good chunk of this converter right over here 00:05:26.520 --> 00:05:30.090 align:middle line:84% is the EMI filter for plugging into the wall. 00:05:30.090 --> 00:05:34.230 align:middle line:84% And we're going to talk about how you would structure things 00:05:34.230 --> 00:05:37.380 align:middle line:84% in a line interface application but also in a bunch 00:05:37.380 --> 00:05:38.350 align:middle line:90% of other applications. 00:05:38.350 --> 00:05:41.700 align:middle line:84% And there's one kind of aspect we haven't really 00:05:41.700 --> 00:05:43.650 align:middle line:90% focused on yet. 00:05:43.650 --> 00:05:47.700 align:middle line:84% And to set that up, let me just give you 00:05:47.700 --> 00:05:49.170 align:middle line:84% instead of an AC application, let 00:05:49.170 --> 00:05:51.630 align:middle line:90% me talk about a DC application. 00:05:51.630 --> 00:05:56.520 align:middle line:84% So suppose I wanted to connect a power converter in a vehicle. 00:05:56.520 --> 00:05:58.500 align:middle line:84% And this could be a regular vehicle 00:05:58.500 --> 00:05:59.675 align:middle line:90% or an electrical vehicle. 00:05:59.675 --> 00:06:03.540 align:middle line:90% 00:06:03.540 --> 00:06:05.580 align:middle line:90% Here's my battery. 00:06:05.580 --> 00:06:08.860 align:middle line:84% And this is-- let me call this ground. 00:06:08.860 --> 00:06:11.370 align:middle line:84% This is like the chassis of the vehicle. 00:06:11.370 --> 00:06:15.510 align:middle line:84% And that's where the battery might be tied. 00:06:15.510 --> 00:06:17.560 align:middle line:84% I'm going to plug a power converter into this. 00:06:17.560 --> 00:06:20.670 align:middle line:84% I'm going to have some cabling to carry 00:06:20.670 --> 00:06:23.700 align:middle line:84% the ground and the battery voltage 00:06:23.700 --> 00:06:26.340 align:middle line:90% over to whatever I'm powering. 00:06:26.340 --> 00:06:27.300 align:middle line:90% OK. 00:06:27.300 --> 00:06:27.970 align:middle line:90% All right. 00:06:27.970 --> 00:06:29.333 align:middle line:90% So here's my cabling. 00:06:29.333 --> 00:06:30.750 align:middle line:84% And that cabling in the real world 00:06:30.750 --> 00:06:32.292 align:middle line:84% doesn't have zero impedance but let's 00:06:32.292 --> 00:06:33.850 align:middle line:90% not worry about that too much. 00:06:33.850 --> 00:06:37.360 align:middle line:84% Now I'm going to go dutifully put in my EMI filter. 00:06:37.360 --> 00:06:37.860 align:middle line:90% OK. 00:06:37.860 --> 00:06:47.080 align:middle line:84% So maybe I have Lf, Cf, and I'll be really smart. 00:06:47.080 --> 00:06:50.110 align:middle line:84% Maybe I'll say, OK, let me put in a damping resistor. 00:06:50.110 --> 00:06:58.410 align:middle line:84% So here I have RD and CD So I've done my damping job here. 00:06:58.410 --> 00:07:00.360 align:middle line:90% That's my filter. 00:07:00.360 --> 00:07:01.890 align:middle line:84% Now I'll connect up my converter. 00:07:01.890 --> 00:07:04.060 align:middle line:84% And maybe my converter is a boost converter. 00:07:04.060 --> 00:07:07.290 align:middle line:90% So here's my boost converter. 00:07:07.290 --> 00:07:08.620 align:middle line:90% Has an inductor. 00:07:08.620 --> 00:07:15.910 align:middle line:84% Has a transistor, diode, output cap. 00:07:15.910 --> 00:07:17.470 align:middle line:90% And here's my load resistor. 00:07:17.470 --> 00:07:20.150 align:middle line:84% And I won't worry about the details of the load too much. 00:07:20.150 --> 00:07:22.750 align:middle line:84% And keep in mind, this whole thing 00:07:22.750 --> 00:07:26.060 align:middle line:84% is indeed referenced to ground, but there's some cabling. 00:07:26.060 --> 00:07:27.970 align:middle line:90% So let me just worry about this. 00:07:27.970 --> 00:07:35.350 align:middle line:84% I'll call this V source because the source of my transistor 00:07:35.350 --> 00:07:38.290 align:middle line:90% with reference to ground. 00:07:38.290 --> 00:07:39.070 align:middle line:90% OK. 00:07:39.070 --> 00:07:43.460 align:middle line:84% So what do I intend to happen in this converter? 00:07:43.460 --> 00:07:48.060 align:middle line:84% What I intend to happen is I draw a current from my battery. 00:07:48.060 --> 00:07:50.900 align:middle line:84% It goes through the cable, goes through the filter, 00:07:50.900 --> 00:07:53.900 align:middle line:84% enters the converter, and it might go down 00:07:53.900 --> 00:07:55.520 align:middle line:84% through the switch at some times or it 00:07:55.520 --> 00:07:59.150 align:middle line:84% might go down through the diode and the output sometimes. 00:07:59.150 --> 00:08:00.650 align:middle line:84% But basically, it goes through there 00:08:00.650 --> 00:08:03.440 align:middle line:84% and then it returns in this loop. 00:08:03.440 --> 00:08:05.750 align:middle line:90% So this is the current path. 00:08:05.750 --> 00:08:08.840 align:middle line:84% I'm really using to power this converter. 00:08:08.840 --> 00:08:10.950 align:middle line:84% And I filtered that current path. 00:08:10.950 --> 00:08:13.650 align:middle line:90% Here's my filter. 00:08:13.650 --> 00:08:14.790 align:middle line:90% OK. 00:08:14.790 --> 00:08:17.480 align:middle line:90% Well, that's good. 00:08:17.480 --> 00:08:22.810 align:middle line:84% But if I think about it, I've got a heat sink, 00:08:22.810 --> 00:08:24.200 align:middle line:90% the switch in the diode. 00:08:24.200 --> 00:08:26.710 align:middle line:84% So let's just think about the transistor. 00:08:26.710 --> 00:08:28.750 align:middle line:84% And let's remember how we do that. 00:08:28.750 --> 00:08:33.429 align:middle line:84% So maybe here I have my transistor. 00:08:33.429 --> 00:08:35.000 align:middle line:90% Here's my transistor. 00:08:35.000 --> 00:08:38.520 align:middle line:84% And then I'm going to put down a thermal pad. 00:08:38.520 --> 00:08:40.517 align:middle line:84% And then I'm going to connect that thermal pad. 00:08:40.517 --> 00:08:42.059 align:middle line:84% On the other side of that thermal pad 00:08:42.059 --> 00:08:45.530 align:middle line:84% will be whatever I'm heat sinking the device to. 00:08:45.530 --> 00:08:46.490 align:middle line:90% OK. 00:08:46.490 --> 00:08:49.010 align:middle line:84% What I'm often heat sinking the device to 00:08:49.010 --> 00:08:51.235 align:middle line:84% is either the case of the power supply 00:08:51.235 --> 00:08:52.610 align:middle line:84% and that case of the power supply 00:08:52.610 --> 00:08:56.150 align:middle line:84% is basically often connected back to ground. 00:08:56.150 --> 00:08:58.640 align:middle line:84% In fact, sometimes you'll use the case of the whole thing 00:08:58.640 --> 00:09:00.380 align:middle line:90% to be ground. 00:09:00.380 --> 00:09:03.530 align:middle line:84% And if I think about a transistor, 00:09:03.530 --> 00:09:06.680 align:middle line:84% in fact, what's the package of the transistor 00:09:06.680 --> 00:09:09.590 align:middle line:84% if you have a TO-247 or TO-220 or something, 00:09:09.590 --> 00:09:12.390 align:middle line:84% that's actually the drain node of this thing. 00:09:12.390 --> 00:09:14.930 align:middle line:84% So what I have is essentially a piece of metal 00:09:14.930 --> 00:09:19.280 align:middle line:84% here, a thin insulator for electrical insulation, and then 00:09:19.280 --> 00:09:20.660 align:middle line:90% a ground. 00:09:20.660 --> 00:09:21.480 align:middle line:90% So what is that? 00:09:21.480 --> 00:09:22.720 align:middle line:90% That's a capacitor. 00:09:22.720 --> 00:09:27.410 align:middle line:84% So it turns out that in most power supplies like this, 00:09:27.410 --> 00:09:30.110 align:middle line:84% there's going to be a significant parasitic 00:09:30.110 --> 00:09:32.270 align:middle line:90% capacitance-- 00:09:32.270 --> 00:09:35.930 align:middle line:84% I'll just call it Cp, parasitic capacitance-- that 00:09:35.930 --> 00:09:38.270 align:middle line:84% gets back to ground because ground 00:09:38.270 --> 00:09:39.800 align:middle line:90% is the chassis of the vehicle. 00:09:39.800 --> 00:09:42.038 align:middle line:84% Even if you didn't have a heatsink, 00:09:42.038 --> 00:09:43.580 align:middle line:84% you have a node flapping up and down. 00:09:43.580 --> 00:09:45.030 align:middle line:90% There's stuff around it. 00:09:45.030 --> 00:09:48.320 align:middle line:84% And so there is going to be some capacitance back to ground. 00:09:48.320 --> 00:09:49.270 align:middle line:90% Everybody buy that? 00:09:49.270 --> 00:09:51.930 align:middle line:90% 00:09:51.930 --> 00:09:59.550 align:middle line:84% And so you have this opportunity to have another current path 00:09:59.550 --> 00:10:03.280 align:middle line:90% that goes something like this. 00:10:03.280 --> 00:10:06.700 align:middle line:84% Current can flow through this lead. 00:10:06.700 --> 00:10:13.900 align:middle line:84% It could flow maybe even here up to here and back to ground, 00:10:13.900 --> 00:10:16.270 align:middle line:84% or it could flow up through this capacitor 00:10:16.270 --> 00:10:18.210 align:middle line:84% and through this inductor back to ground. 00:10:18.210 --> 00:10:21.280 align:middle line:84% But nonetheless, there is a path, at least 00:10:21.280 --> 00:10:25.540 align:middle line:84% one path, that's not going through a filter inductor. 00:10:25.540 --> 00:10:28.003 align:middle line:84% So I really, to the extent that this node is 00:10:28.003 --> 00:10:29.920 align:middle line:84% slapping up and down with respect to something 00:10:29.920 --> 00:10:33.940 align:middle line:84% very close to the ground, I'm going to get a bunch of current 00:10:33.940 --> 00:10:37.390 align:middle line:84% through this parasitic capacitance at high frequency, 00:10:37.390 --> 00:10:39.590 align:middle line:90% not DC current, just AC current. 00:10:39.590 --> 00:10:42.790 align:middle line:84% And if this lead is kind of long, 00:10:42.790 --> 00:10:44.360 align:middle line:90% that looks just like an antenna. 00:10:44.360 --> 00:10:44.860 align:middle line:90% Right? 00:10:44.860 --> 00:10:46.720 align:middle line:84% And I'm right next to my radio so I 00:10:46.720 --> 00:10:50.290 align:middle line:84% run into electromagnetic interference 00:10:50.290 --> 00:10:54.660 align:middle line:84% that I'm causing not necessarily through this lead 00:10:54.660 --> 00:10:58.710 align:middle line:84% but current coming through the other power lead. 00:10:58.710 --> 00:10:59.973 align:middle line:90% OK. 00:10:59.973 --> 00:11:04.240 align:middle line:90% And this is a problem. 00:11:04.240 --> 00:11:06.480 align:middle line:84% And in fact, I mentioned earlier in the class 00:11:06.480 --> 00:11:09.180 align:middle line:84% when we set up our line impedance stabilization network 00:11:09.180 --> 00:11:11.970 align:middle line:84% to measure everything, usually you actually 00:11:11.970 --> 00:11:14.730 align:middle line:84% have one LISN for measuring the noise 00:11:14.730 --> 00:11:18.720 align:middle line:84% on the hot line and another LISN for measuring 00:11:18.720 --> 00:11:21.330 align:middle line:90% the noise on the return line. 00:11:21.330 --> 00:11:24.750 align:middle line:84% So you really have to keep the EMI in both of these leads 00:11:24.750 --> 00:11:26.160 align:middle line:90% small. 00:11:26.160 --> 00:11:29.460 align:middle line:84% So what I want to do today is just 00:11:29.460 --> 00:11:35.130 align:middle line:84% talk about how we represent noise in these situations 00:11:35.130 --> 00:11:38.460 align:middle line:84% and then how do we design filters that deal with those 00:11:38.460 --> 00:11:39.610 align:middle line:90% that noise. 00:11:39.610 --> 00:11:43.890 align:middle line:84% So before I go on, are there any questions 00:11:43.890 --> 00:11:45.515 align:middle line:90% about what the issue is? 00:11:45.515 --> 00:11:49.410 align:middle line:90% 00:11:49.410 --> 00:11:49.910 align:middle line:90% OK. 00:11:49.910 --> 00:11:54.200 align:middle line:84% So let me think about maybe another example where 00:11:54.200 --> 00:11:55.850 align:middle line:90% this comes up. 00:11:55.850 --> 00:11:58.634 align:middle line:90% OK. 00:11:58.634 --> 00:12:03.510 align:middle line:84% And this would be something like that power supply that I'm 00:12:03.510 --> 00:12:05.770 align:middle line:84% passing around would be plugged into. 00:12:05.770 --> 00:12:08.650 align:middle line:84% So maybe what I have is at home, what do you have? 00:12:08.650 --> 00:12:11.860 align:middle line:90% You have an AC supply. 00:12:11.860 --> 00:12:16.900 align:middle line:84% So here's my AC supply and I have the hot terminal. 00:12:16.900 --> 00:12:19.420 align:middle line:84% That's the black wire running around your house. 00:12:19.420 --> 00:12:20.490 align:middle line:90% Black is for death. 00:12:20.490 --> 00:12:21.550 align:middle line:90% Don't get near that. 00:12:21.550 --> 00:12:24.540 align:middle line:84% You have the neutral wire, which is usually white. 00:12:24.540 --> 00:12:28.270 align:middle line:84% And you're going to carry some cabling inside your walls, 00:12:28.270 --> 00:12:29.520 align:middle line:90% hot and neutral. 00:12:29.520 --> 00:12:35.220 align:middle line:84% And I should say that neutral, back at the service entrance 00:12:35.220 --> 00:12:39.670 align:middle line:84% somewhere, is actually tends to be tied to ground. 00:12:39.670 --> 00:12:42.430 align:middle line:90% So the neutral. 00:12:42.430 --> 00:12:47.500 align:middle line:90% Is going to be near ground. 00:12:47.500 --> 00:12:50.385 align:middle line:84% But it doesn't actually have to be precisely at ground. 00:12:50.385 --> 00:12:54.370 align:middle line:90% 00:12:54.370 --> 00:12:56.980 align:middle line:90% And it'll be close somewhere. 00:12:56.980 --> 00:13:03.010 align:middle line:84% And very often, if I think about what wires are going out 00:13:03.010 --> 00:13:04.840 align:middle line:84% to the boxes, usually there will also 00:13:04.840 --> 00:13:07.640 align:middle line:84% be a ground wire that's connected to ground. 00:13:07.640 --> 00:13:12.490 align:middle line:84% And that's usually the green or the uninsulated wire. 00:13:12.490 --> 00:13:15.430 align:middle line:84% And if you have a three-terminal plug, one of those 00:13:15.430 --> 00:13:19.432 align:middle line:84% goes to the ground, one goes to neutral, one goes to hot. 00:13:19.432 --> 00:13:21.640 align:middle line:84% If you have a two-terminal plug, they get rid of this 00:13:21.640 --> 00:13:25.160 align:middle line:84% and they just don't have an explicit ground going. 00:13:25.160 --> 00:13:27.670 align:middle line:90% Make sense, everybody? 00:13:27.670 --> 00:13:31.300 align:middle line:90% So what happens again-- 00:13:31.300 --> 00:13:35.410 align:middle line:84% this is going to plug into whatever my device is. 00:13:35.410 --> 00:13:38.050 align:middle line:84% And I'll have terminal one, terminal two 00:13:38.050 --> 00:13:44.290 align:middle line:84% for hot and neutral, and then I may have some parasitic path. 00:13:44.290 --> 00:13:46.820 align:middle line:84% Why might I have a parasitic path? 00:13:46.820 --> 00:13:50.230 align:middle line:84% One reason is in a lot of equipment, 00:13:50.230 --> 00:13:52.610 align:middle line:84% we tend to ground the case of the equipment. 00:13:52.610 --> 00:13:55.370 align:middle line:84% So if it has a three-terminal plug, you plug it into the wall. 00:13:55.370 --> 00:13:58.480 align:middle line:84% That ground connection coming out of that third terminal 00:13:58.480 --> 00:14:00.590 align:middle line:84% is going to the case of the device. 00:14:00.590 --> 00:14:01.570 align:middle line:90% Why? 00:14:01.570 --> 00:14:03.850 align:middle line:84% Because suppose there's some fault 00:14:03.850 --> 00:14:07.150 align:middle line:84% inside the equipment and that fault 00:14:07.150 --> 00:14:10.430 align:middle line:84% shorts the hot terminal to the case. 00:14:10.430 --> 00:14:12.620 align:middle line:84% You don't want somebody walking up and touching 00:14:12.620 --> 00:14:14.200 align:middle line:84% the surface of that thing, getting electrocuted. 00:14:14.200 --> 00:14:14.700 align:middle line:90% Right? 00:14:14.700 --> 00:14:18.492 align:middle line:84% So if they ground the case, and some fault happens inside, 00:14:18.492 --> 00:14:20.450 align:middle line:84% huge current will flow, it'll blow the breaker, 00:14:20.450 --> 00:14:23.310 align:middle line:84% and then things will be disconnected and you'll be safe. 00:14:23.310 --> 00:14:26.930 align:middle line:84% So very often, there's an explicit connection 00:14:26.930 --> 00:14:30.200 align:middle line:84% between the case of the device and ground. 00:14:30.200 --> 00:14:34.100 align:middle line:84% And since the case happens to surround whatever the device is, 00:14:34.100 --> 00:14:38.220 align:middle line:84% like the power supply, it could be, in fact, if I had a boost 00:14:38.220 --> 00:14:41.660 align:middle line:84% PFC circuit, it looks exactly like the structure 00:14:41.660 --> 00:14:45.860 align:middle line:84% I just drew except that instead of being powered by DC, 00:14:45.860 --> 00:14:48.800 align:middle line:84% it's powered by AC and I essentially 00:14:48.800 --> 00:14:51.480 align:middle line:90% insert a rectifier here. 00:14:51.480 --> 00:14:53.300 align:middle line:84% That's what a boost rectifier looks 00:14:53.300 --> 00:14:56.430 align:middle line:84% like, the front end of a lot of power supplies. 00:14:56.430 --> 00:15:00.500 align:middle line:84% So this structure can very much represent 00:15:00.500 --> 00:15:01.970 align:middle line:84% what would happen in the AC case, 00:15:01.970 --> 00:15:04.580 align:middle line:84% too, except that somewhere I put a usually a full bridge 00:15:04.580 --> 00:15:07.940 align:middle line:84% to rectify an AC voltage, which I'd have over here to DC 00:15:07.940 --> 00:15:10.770 align:middle line:84% that my converter then processes. 00:15:10.770 --> 00:15:13.860 align:middle line:84% So the consequence of that is, is 00:15:13.860 --> 00:15:17.670 align:middle line:84% even though I don't intend it to be there, 00:15:17.670 --> 00:15:22.110 align:middle line:84% there's going to be some virtual third terminal which 00:15:22.110 --> 00:15:25.360 align:middle line:84% is connected by some parasitic capacitance 00:15:25.360 --> 00:15:27.095 align:middle line:90% again back to ground. 00:15:27.095 --> 00:15:29.910 align:middle line:90% 00:15:29.910 --> 00:15:30.930 align:middle line:90% OK. 00:15:30.930 --> 00:15:36.440 align:middle line:84% Even if the case isn't connected to ground, ground is around you. 00:15:36.440 --> 00:15:40.660 align:middle line:84% There's going to be some flow possibly through that. 00:15:40.660 --> 00:15:42.090 align:middle line:90% Any questions about that? 00:15:42.090 --> 00:15:47.030 align:middle line:90% 00:15:47.030 --> 00:15:50.040 align:middle line:84% I should have noted, by the way-- 00:15:50.040 --> 00:15:51.390 align:middle line:90% and I'll come back to this. 00:15:51.390 --> 00:15:55.230 align:middle line:84% It's a little bit easier to see in this case of the DC case. 00:15:55.230 --> 00:16:01.470 align:middle line:84% If I've done this and now I have very peaky currents coming 00:16:01.470 --> 00:16:06.660 align:middle line:84% through this parasitic capacitance, 00:16:06.660 --> 00:16:10.740 align:middle line:84% I have high frequency currents flowing on this lead, if this 00:16:10.740 --> 00:16:17.250 align:middle line:84% if this pathway has some parasitic resistance and maybe 00:16:17.250 --> 00:16:19.590 align:middle line:84% a little parasitic inductance from all the wiring, 00:16:19.590 --> 00:16:22.270 align:middle line:84% I can develop a voltage drop across here. 00:16:22.270 --> 00:16:25.090 align:middle line:90% And so this voltage is non-zero. 00:16:25.090 --> 00:16:26.650 align:middle line:84% I'll see what's called ground bounce. 00:16:26.650 --> 00:16:28.025 align:middle line:84% And maybe you've experienced this 00:16:28.025 --> 00:16:31.733 align:middle line:84% when you've tried to measure just ground on some circuit 00:16:31.733 --> 00:16:32.400 align:middle line:90% you're building. 00:16:32.400 --> 00:16:36.120 align:middle line:84% And it looks like it's got a bunch of high frequency junk 00:16:36.120 --> 00:16:37.500 align:middle line:90% on it. 00:16:37.500 --> 00:16:40.630 align:middle line:84% That's exactly due to this kind of phenomenon. 00:16:40.630 --> 00:16:44.670 align:middle line:84% So we can see, even though I intend 00:16:44.670 --> 00:16:46.530 align:middle line:84% this node to be-- in an ideal world, 00:16:46.530 --> 00:16:49.480 align:middle line:84% this would be a zero resistance, zero inductance wire 00:16:49.480 --> 00:16:51.600 align:middle line:84% and I intended there to be no voltage there, 00:16:51.600 --> 00:16:55.090 align:middle line:84% because it's not an ideal wire, it's a real one, 00:16:55.090 --> 00:17:00.430 align:middle line:84% there will be ground bounce here that I have to contend with. 00:17:00.430 --> 00:17:12.130 align:middle line:84% So when I go to think about this network, 00:17:12.130 --> 00:17:16.210 align:middle line:84% maybe I will think about a current into terminal one 00:17:16.210 --> 00:17:18.910 align:middle line:90% that I'm going to call i1. 00:17:18.910 --> 00:17:21.790 align:middle line:84% I'm going to think about a current into terminal two 00:17:21.790 --> 00:17:23.980 align:middle line:90% that I'm going to call i2. 00:17:23.980 --> 00:17:27.609 align:middle line:84% Again, I could talk about the voltage at terminal one 00:17:27.609 --> 00:17:28.940 align:middle line:90% with respect to ground. 00:17:28.940 --> 00:17:30.620 align:middle line:90% I'm going to call that v1. 00:17:30.620 --> 00:17:32.890 align:middle line:84% And I can think about the voltage at terminal two 00:17:32.890 --> 00:17:36.090 align:middle line:84% with respect to ground that I'm going to call that v2. 00:17:36.090 --> 00:17:38.860 align:middle line:84% And I will recognize that, yeah, v2 00:17:38.860 --> 00:17:41.250 align:middle line:84% should be close to ground because back 00:17:41.250 --> 00:17:43.250 align:middle line:84% through a bunch of wiring, it is tied to ground. 00:17:43.250 --> 00:17:44.800 align:middle line:90% But that's a DC. 00:17:44.800 --> 00:17:47.410 align:middle line:84% And even a DC there's some resistance there. 00:17:47.410 --> 00:17:51.730 align:middle line:84% So I can think about v1, v2, i1, and i2 00:17:51.730 --> 00:17:56.740 align:middle line:84% as being the net currents flowing into my device. 00:17:56.740 --> 00:17:57.915 align:middle line:90% Any questions about that? 00:17:57.915 --> 00:18:01.270 align:middle line:90% 00:18:01.270 --> 00:18:04.190 align:middle line:84% So what do I intend to happen in this device. 00:18:04.190 --> 00:18:06.737 align:middle line:84% I didn't really want this parasitic capacitance. 00:18:06.737 --> 00:18:07.570 align:middle line:90% I'm just getting it. 00:18:07.570 --> 00:18:08.070 align:middle line:90% Right. 00:18:08.070 --> 00:18:11.890 align:middle line:84% So the ideal path that, I'm thinking, OK, 00:18:11.890 --> 00:18:14.080 align:middle line:84% this is how my converter should work, 00:18:14.080 --> 00:18:16.870 align:middle line:84% is I should have current that's coming 00:18:16.870 --> 00:18:22.180 align:middle line:84% from the power, the voltage source, into terminal 1, 00:18:22.180 --> 00:18:27.130 align:middle line:84% coming back out terminal 2, and doing this kind of loop 00:18:27.130 --> 00:18:28.990 align:middle line:90% around like this. 00:18:28.990 --> 00:18:37.140 align:middle line:84% And that's fine but because of this parasitic, 00:18:37.140 --> 00:18:39.120 align:middle line:84% there can be some other path that I 00:18:39.120 --> 00:18:40.830 align:middle line:90% might want to think about. 00:18:40.830 --> 00:18:47.140 align:middle line:84% And if I didn't have this other path, what would I have? 00:18:47.140 --> 00:18:50.140 align:middle line:84% I'd have i1 is equal to minus i2. 00:18:50.140 --> 00:18:55.330 align:middle line:84% That's the ideal case when this other path doesn't exist. 00:18:55.330 --> 00:18:56.950 align:middle line:90% All right. 00:18:56.950 --> 00:19:01.420 align:middle line:84% If the other path does exist, we get 00:19:01.420 --> 00:19:04.750 align:middle line:84% what we would call a common mode signal 00:19:04.750 --> 00:19:06.393 align:middle line:90% that I'm going to call ICM. 00:19:06.393 --> 00:19:09.880 align:middle line:90% 00:19:09.880 --> 00:19:11.440 align:middle line:90% Common mode current. 00:19:11.440 --> 00:19:14.320 align:middle line:84% Common mode because I think of it 00:19:14.320 --> 00:19:18.550 align:middle line:84% as coming through somehow the two leads together 00:19:18.550 --> 00:19:21.190 align:middle line:84% into the device and then out through the device 00:19:21.190 --> 00:19:23.830 align:middle line:90% through some third path. 00:19:23.830 --> 00:19:26.650 align:middle line:84% Does that make sense to everybody? 00:19:26.650 --> 00:19:32.250 align:middle line:84% And this common mode current maybe 00:19:32.250 --> 00:19:36.160 align:middle line:84% I would think of as flowing like this. 00:19:36.160 --> 00:19:39.100 align:middle line:84% Half of it's coming in this terminal so I'm going to call 00:19:39.100 --> 00:19:42.130 align:middle line:90% this 1/2 icm. 00:19:42.130 --> 00:19:45.150 align:middle line:84% Half of it's coming through this terminal. 00:19:45.150 --> 00:19:48.810 align:middle line:90% This is 1/2 ICM. 00:19:48.810 --> 00:19:52.590 align:middle line:84% And then it comes out the other side of the device 00:19:52.590 --> 00:19:55.410 align:middle line:90% and returns to ground like this. 00:19:55.410 --> 00:20:02.590 align:middle line:84% So this is what I'm thinking of as my common mode current. 00:20:02.590 --> 00:20:05.200 align:middle line:84% The current that I was thinking of flowing 00:20:05.200 --> 00:20:07.900 align:middle line:84% around the loop, which I'd have in the ideal case, 00:20:07.900 --> 00:20:10.545 align:middle line:84% we would call this the differential mode current. 00:20:10.545 --> 00:20:13.845 align:middle line:90% 00:20:13.845 --> 00:20:16.548 align:middle line:84% So how would I represent the common mode and differential 00:20:16.548 --> 00:20:17.090 align:middle line:90% mode current? 00:20:17.090 --> 00:20:19.400 align:middle line:84% Well, by definition, by what I've told you, 00:20:19.400 --> 00:20:26.600 align:middle line:84% icm is equal to I 1 plus I two right by. 00:20:26.600 --> 00:20:31.790 align:middle line:84% If I basically make this a supernode, icm is coming out, 00:20:31.790 --> 00:20:35.120 align:middle line:84% but I'm calling that icm, so it must be equal to I 1 plus I 00:20:35.120 --> 00:20:38.840 align:middle line:90% two everybody by that. 00:20:38.840 --> 00:20:43.550 align:middle line:84% Now I got to define what I think about this differential mode 00:20:43.550 --> 00:20:44.450 align:middle line:90% current. 00:20:44.450 --> 00:20:47.960 align:middle line:84% In the case when I didn't have icm, 00:20:47.960 --> 00:20:50.060 align:middle line:84% the differential mode current would be, 00:20:50.060 --> 00:20:55.400 align:middle line:84% you know, i1 would equal idm and i2 would be equal to minus idm. 00:20:55.400 --> 00:20:59.570 align:middle line:84% The way we tend to define the differential mode current, 00:20:59.570 --> 00:21:05.900 align:middle line:84% idm, is simply as being the average of the currents 00:21:05.900 --> 00:21:07.400 align:middle line:90% I thought I was going to get. 00:21:07.400 --> 00:21:13.670 align:middle line:84% So I would call it i1 minus i2 over 2. 00:21:13.670 --> 00:21:17.960 align:middle line:84% So this is sort of-- and the reason 00:21:17.960 --> 00:21:22.370 align:middle line:84% I'm emphasizing it this way is just because these 00:21:22.370 --> 00:21:25.190 align:middle line:84% are the definitions of the common mode and differential 00:21:25.190 --> 00:21:27.140 align:middle line:90% mode components. 00:21:27.140 --> 00:21:27.830 align:middle line:90% OK. 00:21:27.830 --> 00:21:33.380 align:middle line:84% If I went and said, OK, if I apply those two definitions, 00:21:33.380 --> 00:21:37.100 align:middle line:84% what I get for i1 and i2, if I recombine this, 00:21:37.100 --> 00:21:48.680 align:middle line:84% is I get i1 is equal to idm plus 1/2 icm. 00:21:48.680 --> 00:21:56.440 align:middle line:84% And i2 is equal to minus idm plus 1/2 icm. 00:21:56.440 --> 00:22:00.550 align:middle line:84% So by choosing things this way, what I'm really saying 00:22:00.550 --> 00:22:04.090 align:middle line:84% is, OK, if I had no common mode current, 00:22:04.090 --> 00:22:07.810 align:middle line:84% I'd have idm in terminal 1 and minus idm in terminal 2-- 00:22:07.810 --> 00:22:08.670 align:middle line:90% going to terminal 2. 00:22:08.670 --> 00:22:09.628 align:middle line:90% That's what I'd expect. 00:22:09.628 --> 00:22:13.150 align:middle line:84% And then I'm saying that each of these two terminals 00:22:13.150 --> 00:22:15.320 align:middle line:84% is carrying half the common mode current. 00:22:15.320 --> 00:22:19.720 align:middle line:84% That's essentially what the definition says. 00:22:19.720 --> 00:22:20.500 align:middle line:90% OK. 00:22:20.500 --> 00:22:21.980 align:middle line:84% Does that make sense to everybody? 00:22:21.980 --> 00:22:29.020 align:middle line:90% 00:22:29.020 --> 00:22:31.090 align:middle line:90% What about voltages? 00:22:31.090 --> 00:22:32.830 align:middle line:84% I focused on the currents here, but I 00:22:32.830 --> 00:22:34.630 align:middle line:84% said I have a voltage at terminal 1 00:22:34.630 --> 00:22:36.310 align:middle line:90% and a voltage at terminal 2. 00:22:36.310 --> 00:22:38.710 align:middle line:84% And I can assume that the voltage at terminal 2 00:22:38.710 --> 00:22:42.680 align:middle line:84% is ground because of this ground bounce kind of stuff going on 00:22:42.680 --> 00:22:44.800 align:middle line:84% and the fact that there's a bunch of cabling here, 00:22:44.800 --> 00:22:47.590 align:middle line:84% whether it's switching ground bounce or not. 00:22:47.590 --> 00:22:50.790 align:middle line:84% There's some difference between that and ground. 00:22:50.790 --> 00:22:55.810 align:middle line:84% So we can also come up with definitions of voltage. 00:22:55.810 --> 00:22:56.850 align:middle line:90% OK. 00:22:56.850 --> 00:23:00.120 align:middle line:84% The common mode voltage, if I'm going 00:23:00.120 --> 00:23:02.200 align:middle line:90% to look at the input point-- 00:23:02.200 --> 00:23:04.890 align:middle line:84% so I'm going to look at this point here. 00:23:04.890 --> 00:23:06.990 align:middle line:84% I could define the common mode voltage 00:23:06.990 --> 00:23:11.700 align:middle line:84% at the input of the device as being vcm 00:23:11.700 --> 00:23:15.810 align:middle line:90% is equal to v1 plus v2 over 2. 00:23:15.810 --> 00:23:19.050 align:middle line:84% So basically, the common mode voltage 00:23:19.050 --> 00:23:21.180 align:middle line:84% is the average of the two voltages 00:23:21.180 --> 00:23:26.160 align:middle line:90% driving node 1 and node 2. 00:23:26.160 --> 00:23:30.150 align:middle line:84% The differential mode voltage, vdm, 00:23:30.150 --> 00:23:33.900 align:middle line:90% is simply equal to v1 minus v2. 00:23:33.900 --> 00:23:34.440 align:middle line:90% OK. 00:23:34.440 --> 00:23:37.260 align:middle line:84% If I thought about it, v1 with respect 00:23:37.260 --> 00:23:42.930 align:middle line:84% to ground minus v2 with respect to ground is this voltage vdm. 00:23:42.930 --> 00:23:45.960 align:middle line:84% That's the voltage into which I was intending 00:23:45.960 --> 00:23:48.613 align:middle line:90% to apply to my device. 00:23:48.613 --> 00:23:50.530 align:middle line:84% It's the difference between the two terminals. 00:23:50.530 --> 00:23:52.530 align:middle line:90% It's my input of my device. 00:23:52.530 --> 00:23:55.290 align:middle line:84% So that is the differential mode voltage. 00:23:55.290 --> 00:23:58.640 align:middle line:84% The common mode voltage I'm just defining as the average. 00:23:58.640 --> 00:24:02.280 align:middle line:84% And if I put those two things together, 00:24:02.280 --> 00:24:13.560 align:middle line:84% what I get is that v1 is equal to vcm plus 1/2 vdm and v2 is 00:24:13.560 --> 00:24:19.110 align:middle line:90% equal to vcm minus 1/2 vdm. 00:24:19.110 --> 00:24:25.900 align:middle line:84% So I'm issuing a decomposition of voltage 1 00:24:25.900 --> 00:24:27.610 align:middle line:84% and voltage 2 with respect to ground 00:24:27.610 --> 00:24:31.780 align:middle line:84% and current 1 and current 2 into common mode and differential 00:24:31.780 --> 00:24:34.470 align:middle line:90% mode components. 00:24:34.470 --> 00:24:38.180 align:middle line:90% So this is just a decomposition. 00:24:38.180 --> 00:24:41.270 align:middle line:84% By the way, it's kind of funny because you 00:24:41.270 --> 00:24:44.360 align:middle line:84% notice that icm is i1 plus i2 and the vcm is the average. 00:24:44.360 --> 00:24:46.920 align:middle line:84% And the differential mode is defined the other way around. 00:24:46.920 --> 00:24:48.950 align:middle line:84% One of the reasons why you define it 00:24:48.950 --> 00:24:53.930 align:middle line:84% this way is because if I said what's the total power flowing 00:24:53.930 --> 00:24:57.500 align:middle line:84% here, I could say it was p I could write 00:24:57.500 --> 00:25:00.570 align:middle line:90% as being equal to v1 times i1. 00:25:00.570 --> 00:25:04.530 align:middle line:84% That's the power into this port with respect 00:25:04.530 --> 00:25:08.640 align:middle line:90% to ground plus v2 i2. 00:25:08.640 --> 00:25:10.830 align:middle line:84% And if I work that out, that works out 00:25:10.830 --> 00:25:19.290 align:middle line:84% to be precisely equal to vcm icm plus vdm idm. 00:25:19.290 --> 00:25:19.810 align:middle line:90% All right. 00:25:19.810 --> 00:25:22.020 align:middle line:90% So whether I decompose-- 00:25:22.020 --> 00:25:23.580 align:middle line:84% if I take my voltage and currents 00:25:23.580 --> 00:25:25.622 align:middle line:84% and I decompose it into common differential mode, 00:25:25.622 --> 00:25:29.220 align:middle line:84% it preserves the notion of power. 00:25:29.220 --> 00:25:29.720 align:middle line:90% OK. 00:25:29.720 --> 00:25:32.810 align:middle line:84% So that's just kind of a convenient, handy fact. 00:25:32.810 --> 00:25:35.480 align:middle line:84% It's not important from the perspective 00:25:35.480 --> 00:25:38.030 align:middle line:84% of we're trying to use common mode and differential 00:25:38.030 --> 00:25:39.200 align:middle line:90% mode to deliver power. 00:25:39.200 --> 00:25:41.690 align:middle line:84% I'm really trying to deliver my power into this thing 00:25:41.690 --> 00:25:42.840 align:middle line:90% through differential mode. 00:25:42.840 --> 00:25:45.270 align:middle line:84% That's the notion of how this thing is supposed to work. 00:25:45.270 --> 00:25:48.010 align:middle line:84% I really don't want any current flowing in my ground path. 00:25:48.010 --> 00:25:51.220 align:middle line:90% 00:25:51.220 --> 00:25:59.080 align:middle line:84% But the other reason why people think about this decomposition 00:25:59.080 --> 00:26:01.240 align:middle line:84% of voltages and currents is because I 00:26:01.240 --> 00:26:05.950 align:middle line:84% tend to use different techniques to fix common mode noise 00:26:05.950 --> 00:26:08.490 align:middle line:90% and differential mode noise. 00:26:08.490 --> 00:26:13.590 align:middle line:84% And so decomposing it that way tells you what techniques should 00:26:13.590 --> 00:26:16.920 align:middle line:90% I use to make a better filter. 00:26:16.920 --> 00:26:17.730 align:middle line:90% OK. 00:26:17.730 --> 00:26:19.670 align:middle line:84% So let's think about this for a second. 00:26:19.670 --> 00:26:22.860 align:middle line:90% 00:26:22.860 --> 00:26:27.750 align:middle line:84% What might I do in a filter design? 00:26:27.750 --> 00:26:31.330 align:middle line:84% Well, let's go design a filter for this thing now. 00:26:31.330 --> 00:26:33.540 align:middle line:84% And keep in mind, we're going to have 00:26:33.540 --> 00:26:35.880 align:middle line:84% to put some kind of filtering to deal with the fact 00:26:35.880 --> 00:26:38.940 align:middle line:84% that I can't allow lots of high frequency currents 00:26:38.940 --> 00:26:41.200 align:middle line:90% through this path. 00:26:41.200 --> 00:26:44.520 align:middle line:84% So I can't just say do what I did before 00:26:44.520 --> 00:26:47.130 align:middle line:84% and just have a single-ended kind of filter 00:26:47.130 --> 00:26:49.565 align:middle line:90% that filters one path. 00:26:49.565 --> 00:26:50.940 align:middle line:84% I'm going to have to do something 00:26:50.940 --> 00:26:54.790 align:middle line:84% that filters both leads going to my converter. 00:26:54.790 --> 00:26:55.290 align:middle line:90% OK. 00:26:55.290 --> 00:27:00.600 align:middle line:84% Now in some cases, you can get away with a single-ended filter. 00:27:00.600 --> 00:27:03.120 align:middle line:84% If this whole thing were built on top of a ground plane 00:27:03.120 --> 00:27:05.088 align:middle line:84% and there was no wires going anywhere, 00:27:05.088 --> 00:27:07.380 align:middle line:84% and there's just one big ground plane, well, then sure, 00:27:07.380 --> 00:27:09.838 align:middle line:84% you only need to filter one lead because everything else is 00:27:09.838 --> 00:27:11.320 align:middle line:84% traveling in the big ground plane. 00:27:11.320 --> 00:27:14.880 align:middle line:84% But if you have a device that's connected over some cabling, 00:27:14.880 --> 00:27:17.440 align:middle line:84% you better think twice because there could 00:27:17.440 --> 00:27:20.770 align:middle line:90% be some unintended path back. 00:27:20.770 --> 00:27:22.200 align:middle line:90% OK. 00:27:22.200 --> 00:27:22.800 align:middle line:90% All right. 00:27:22.800 --> 00:27:25.350 align:middle line:84% So let's go think about how I would design a filter 00:27:25.350 --> 00:27:28.350 align:middle line:90% to deal with this. 00:27:28.350 --> 00:27:29.590 align:middle line:90% So here I go. 00:27:29.590 --> 00:27:31.655 align:middle line:90% Here is my device again. 00:27:31.655 --> 00:27:34.800 align:middle line:90% 00:27:34.800 --> 00:27:41.690 align:middle line:84% And here's one, two, and my unintended terminal three. 00:27:41.690 --> 00:27:45.200 align:middle line:84% And if I thought of it-- let me just think about-- 00:27:45.200 --> 00:27:47.930 align:middle line:84% and it's not quite true, but let me just think about, 00:27:47.930 --> 00:27:54.395 align:middle line:84% for simplicity, as my converter being a source of drawing common 00:27:54.395 --> 00:27:56.870 align:middle line:90% and differential mode currents. 00:27:56.870 --> 00:27:59.660 align:middle line:90% So I might think of it this way. 00:27:59.660 --> 00:28:02.630 align:middle line:84% I might think of this coming in here 00:28:02.630 --> 00:28:09.000 align:middle line:84% and drawing a differential mode current IBM. 00:28:09.000 --> 00:28:12.140 align:middle line:84% And that would include the power current plus any switching noise 00:28:12.140 --> 00:28:15.360 align:middle line:84% or something coming between these two terminals. 00:28:15.360 --> 00:28:18.150 align:middle line:84% And then if I thought, well, I might 00:28:18.150 --> 00:28:21.400 align:middle line:84% be driving some common mode currents, what would that be? 00:28:21.400 --> 00:28:35.190 align:middle line:84% I'd have 1/2 icm being drawn this way out here and 1/2 icm 00:28:35.190 --> 00:28:37.000 align:middle line:84% being drawn this way to the output. 00:28:37.000 --> 00:28:40.830 align:middle line:84% And then this would be icm to ground 00:28:40.830 --> 00:28:44.340 align:middle line:84% through my parasitic capacitance back to ground. 00:28:44.340 --> 00:28:48.170 align:middle line:84% Does that make sense to everybody? 00:28:48.170 --> 00:28:54.130 align:middle line:84% So let's just-- let me pretend for a moment idm is zero. 00:28:54.130 --> 00:28:56.520 align:middle line:84% Let's just think I have a common mode currents that 00:28:56.520 --> 00:28:59.700 align:middle line:84% are being drawn together through pins and ones and twos 00:28:59.700 --> 00:29:02.030 align:middle line:90% and going back through ground. 00:29:02.030 --> 00:29:02.910 align:middle line:90% All right. 00:29:02.910 --> 00:29:04.320 align:middle line:90% What would I do to filter it? 00:29:04.320 --> 00:29:07.280 align:middle line:84% Well, they said the first thing I usually put in my filter 00:29:07.280 --> 00:29:10.620 align:middle line:84% is a capacitor between the two leads. 00:29:10.620 --> 00:29:13.470 align:middle line:84% And I'm going to call this-- for reasons we'll discuss, 00:29:13.470 --> 00:29:16.390 align:middle line:90% I'm going to call this c sub x. 00:29:16.390 --> 00:29:18.700 align:middle line:90% OK. 00:29:18.700 --> 00:29:22.860 align:middle line:84% Does this capacitor really do anything? 00:29:22.860 --> 00:29:26.610 align:middle line:84% If I thought about if the currents are 00:29:26.610 --> 00:29:32.130 align:middle line:84% kind of equally coming this way, this capacitor 00:29:32.130 --> 00:29:35.582 align:middle line:84% is like an open circuit to those currents. 00:29:35.582 --> 00:29:38.090 align:middle line:90% All right. 00:29:38.090 --> 00:29:42.120 align:middle line:84% Or if v1 and v2, the voltages, are going up and down together, 00:29:42.120 --> 00:29:44.780 align:middle line:84% it has a common mode component to the voltages, 00:29:44.780 --> 00:29:47.570 align:middle line:90% c sub x is drawing no current. 00:29:47.570 --> 00:29:52.430 align:middle line:84% So for the common mode case, I mean 00:29:52.430 --> 00:29:54.235 align:middle line:84% c sub x might as well not be there. 00:29:54.235 --> 00:29:57.752 align:middle line:90% 00:29:57.752 --> 00:30:02.270 align:middle line:84% So what could I do to deal with c sub x? 00:30:02.270 --> 00:30:05.240 align:middle line:84% Well, one thing I could do is put in what's 00:30:05.240 --> 00:30:08.570 align:middle line:90% known as a common mode choke. 00:30:08.570 --> 00:30:10.710 align:middle line:90% What is a common mode choke? 00:30:10.710 --> 00:30:16.310 align:middle line:84% A common mode choke is essentially a transformer 00:30:16.310 --> 00:30:18.980 align:middle line:90% that's wound like this. 00:30:18.980 --> 00:30:23.390 align:middle line:84% It has equal numbers of turns on each side. 00:30:23.390 --> 00:30:25.975 align:middle line:84% And it's wound with its dots like this. 00:30:25.975 --> 00:30:28.720 align:middle line:90% 00:30:28.720 --> 00:30:31.290 align:middle line:84% So if this were an ideal transformer 00:30:31.290 --> 00:30:37.770 align:middle line:84% and I said, OK, let's pretend that cx is an open circuit here, 00:30:37.770 --> 00:30:43.860 align:middle line:84% how much current can flow together through these two 00:30:43.860 --> 00:30:45.365 align:middle line:90% ideal transformer windings? 00:30:45.365 --> 00:30:49.600 align:middle line:90% 00:30:49.600 --> 00:30:51.400 align:middle line:84% Can I get a common mode component 00:30:51.400 --> 00:30:52.820 align:middle line:90% through an ideal transformer? 00:30:52.820 --> 00:30:55.580 align:middle line:90% 00:30:55.580 --> 00:30:57.320 align:middle line:90% Nobody's willing to bet on that? 00:30:57.320 --> 00:31:00.470 align:middle line:84% It's got to be zero because, in an ideal transformer, whatever 00:31:00.470 --> 00:31:02.750 align:middle line:84% comes into this dot comes out of that dot. 00:31:02.750 --> 00:31:06.180 align:middle line:84% It's an end to end transformer or a 1 to 1 transformer. 00:31:06.180 --> 00:31:10.100 align:middle line:84% So an ideal transformer only allows differential mode 00:31:10.100 --> 00:31:11.583 align:middle line:90% current. 00:31:11.583 --> 00:31:13.500 align:middle line:84% So that's why it's called a common mode choke. 00:31:13.500 --> 00:31:16.370 align:middle line:84% It chokes off the common mode current. 00:31:16.370 --> 00:31:17.090 align:middle line:90% OK. 00:31:17.090 --> 00:31:19.830 align:middle line:84% Well, what would I do in my filter design? 00:31:19.830 --> 00:31:24.530 align:middle line:84% This thing makes like a perfect inductor against common mode 00:31:24.530 --> 00:31:27.530 align:middle line:84% currents in some sense if I wanted to think about that, 00:31:27.530 --> 00:31:31.060 align:middle line:84% if I could go out and buy myself an ideal transformer. 00:31:31.060 --> 00:31:33.320 align:middle line:84% Now I can't go buy myself an ideal transformer. 00:31:33.320 --> 00:31:33.820 align:middle line:90% Why? 00:31:33.820 --> 00:31:37.760 align:middle line:84% Because they don't sell them at Digikey. 00:31:37.760 --> 00:31:40.420 align:middle line:84% What do I have to think of in terms of parasitics 00:31:40.420 --> 00:31:41.510 align:middle line:90% in my transformer? 00:31:41.510 --> 00:31:43.390 align:middle line:84% Well, one thing is I said I could 00:31:43.390 --> 00:31:48.850 align:middle line:84% put a magnetizing inductance L mu on one side of-- 00:31:48.850 --> 00:31:53.290 align:middle line:84% if this is the ideal transformer part, 00:31:53.290 --> 00:31:56.483 align:middle line:84% I can put a magnetizing L mu across one of the terminals. 00:31:56.483 --> 00:31:58.150 align:middle line:84% Now they have the same winding so they'd 00:31:58.150 --> 00:32:00.970 align:middle line:84% have the same inductance whichever place I put it right. 00:32:00.970 --> 00:32:06.140 align:middle line:84% But I could also represent L mu as 2L mu in parallel with 2L mu. 00:32:06.140 --> 00:32:10.210 align:middle line:84% So another way I could write this is I could put 2L mu 00:32:10.210 --> 00:32:12.790 align:middle line:84% on this side and, to make it symmetric, 00:32:12.790 --> 00:32:20.880 align:middle line:84% I could put 2L mu on the other side of the transformer. 00:32:20.880 --> 00:32:24.030 align:middle line:84% So I have some magnetizing on each side. 00:32:24.030 --> 00:32:26.646 align:middle line:90% And maybe I should have-- 00:32:26.646 --> 00:32:28.650 align:middle line:84% I'm intending to draw this in pink 00:32:28.650 --> 00:32:30.870 align:middle line:84% although I'm not sure you can see the difference just 00:32:30.870 --> 00:32:33.720 align:middle line:84% to illustrate that these are parasitic components. 00:32:33.720 --> 00:32:34.530 align:middle line:90% OK. 00:32:34.530 --> 00:32:35.950 align:middle line:90% What else do I have? 00:32:35.950 --> 00:32:37.380 align:middle line:90% I also have leakage inductance. 00:32:37.380 --> 00:32:41.490 align:middle line:84% And if this is symmetrically wound, 00:32:41.490 --> 00:32:47.970 align:middle line:84% I would have L leakage here and an equal L leakage here. 00:32:47.970 --> 00:32:53.050 align:middle line:84% And that would represent a model for a real transformer. 00:32:53.050 --> 00:32:58.390 align:middle line:84% So in principle, if this is an ungapped transformer, 00:32:58.390 --> 00:33:02.950 align:middle line:84% common mode current could come, go through the 2L mu, 00:33:02.950 --> 00:33:05.830 align:middle line:84% the magnetizing inductance on each side through the leakage, 00:33:05.830 --> 00:33:06.670 align:middle line:90% and then in here. 00:33:06.670 --> 00:33:10.060 align:middle line:84% So it does pose a path for common mode current 00:33:10.060 --> 00:33:13.060 align:middle line:84% in the real world, but it's a very high impedance path 00:33:13.060 --> 00:33:15.100 align:middle line:84% because if this transformer is ungapped, 00:33:15.100 --> 00:33:18.210 align:middle line:90% L mu is a pretty big number. 00:33:18.210 --> 00:33:20.430 align:middle line:90% OK. 00:33:20.430 --> 00:33:22.330 align:middle line:90% That's inductive choking. 00:33:22.330 --> 00:33:26.088 align:middle line:84% What would I do to get rid of the-- 00:33:26.088 --> 00:33:28.343 align:middle line:84% what would I do to get rid of the-- 00:33:28.343 --> 00:33:32.400 align:middle line:90% 00:33:32.400 --> 00:33:34.740 align:middle line:84% help filter these common mode currents? 00:33:34.740 --> 00:33:37.140 align:middle line:84% Maybe what I would do is I would go in 00:33:37.140 --> 00:33:38.580 align:middle line:90% and I'd put in a capacitor. 00:33:38.580 --> 00:33:43.575 align:middle line:84% And I'm going to call this cy to ground here 00:33:43.575 --> 00:33:49.310 align:middle line:90% and another cy to ground here. 00:33:49.310 --> 00:33:55.100 align:middle line:84% So I hope what you'll see is half cm could come through here, 00:33:55.100 --> 00:33:57.960 align:middle line:84% come up through this capacitor, and happily circulate there. 00:33:57.960 --> 00:33:59.480 align:middle line:84% That's a low impedance capacitive 00:33:59.480 --> 00:34:00.750 align:middle line:90% path to high frequency. 00:34:00.750 --> 00:34:01.800 align:middle line:90% Same thing here. 00:34:01.800 --> 00:34:05.000 align:middle line:84% It can circulate this way because these guys 00:34:05.000 --> 00:34:06.650 align:middle line:90% are connected. 00:34:06.650 --> 00:34:11.139 align:middle line:84% And so the current at high frequency 00:34:11.139 --> 00:34:15.489 align:middle line:84% wants to go through the cy's but doesn't 00:34:15.489 --> 00:34:19.853 align:middle line:84% want to go this way because of the high magnetizing inductance. 00:34:19.853 --> 00:34:21.270 align:middle line:84% Does that make sense to everybody? 00:34:21.270 --> 00:34:25.300 align:middle line:90% 00:34:25.300 --> 00:34:32.130 align:middle line:84% This is actually very convenient because if we think about it, 00:34:32.130 --> 00:34:34.889 align:middle line:84% we have common mode currents, but we also 00:34:34.889 --> 00:34:36.400 align:middle line:90% have differential mode currents. 00:34:36.400 --> 00:34:40.590 align:middle line:84% If this is my differential mode current here, idm, 00:34:40.590 --> 00:34:43.949 align:middle line:84% idm is coming this way, where would the differential mode 00:34:43.949 --> 00:34:46.290 align:middle line:90% current flow? 00:34:46.290 --> 00:34:48.142 align:middle line:90% Let me ignore cx and cy. 00:34:48.142 --> 00:34:50.100 align:middle line:84% Let's pretend they're not there for the moment. 00:34:50.100 --> 00:34:52.120 align:middle line:84% Where would the differential mode current flow? 00:34:52.120 --> 00:34:54.222 align:middle line:90% Well, it could go through L mu. 00:34:54.222 --> 00:34:55.389 align:middle line:90% But think about it this way. 00:34:55.389 --> 00:34:56.764 align:middle line:84% Differential mode current doesn't 00:34:56.764 --> 00:34:59.800 align:middle line:84% mind going in this dot and out of this dot. 00:34:59.800 --> 00:35:02.350 align:middle line:90% This common mode choke. 00:35:02.350 --> 00:35:07.230 align:middle line:84% The ideal one is a perfect short for differential mode currents. 00:35:07.230 --> 00:35:08.700 align:middle line:84% So the differential mode currents 00:35:08.700 --> 00:35:10.630 align:middle line:84% don't go through the magnetizing inductance. 00:35:10.630 --> 00:35:13.700 align:middle line:84% They just go through the ideal portion of the transformer. 00:35:13.700 --> 00:35:15.920 align:middle line:84% And so you don't magnetize the core. 00:35:15.920 --> 00:35:18.620 align:middle line:84% And so even if you have high differential mode currents, 00:35:18.620 --> 00:35:21.140 align:middle line:84% because this is what you're delivering power to the device 00:35:21.140 --> 00:35:23.910 align:middle line:84% through, they don't magnetize the core. 00:35:23.910 --> 00:35:26.690 align:middle line:84% And so you don't need a big common mode choke 00:35:26.690 --> 00:35:31.550 align:middle line:84% to get a high effective common mode inductance 00:35:31.550 --> 00:35:33.390 align:middle line:84% because it doesn't store any energy, 00:35:33.390 --> 00:35:35.710 align:middle line:84% at least it doesn't store any differential mode energy. 00:35:35.710 --> 00:35:39.510 align:middle line:90% 00:35:39.510 --> 00:35:43.160 align:middle line:90% Any questions about that? 00:35:43.160 --> 00:35:47.840 align:middle line:84% So to the extent that the differential mode currents don't 00:35:47.840 --> 00:35:49.760 align:middle line:84% go through the magnetizing inductance, 00:35:49.760 --> 00:35:53.990 align:middle line:84% I can get very high magnetizing inductance with very few turns 00:35:53.990 --> 00:35:56.190 align:middle line:90% by using an ungapped core. 00:35:56.190 --> 00:35:58.780 align:middle line:84% And it's not going to be very large. 00:35:58.780 --> 00:36:01.650 align:middle line:84% And by the way, in the one I'm passing around here-- may 00:36:01.650 --> 00:36:02.470 align:middle line:90% I steal this back? 00:36:02.470 --> 00:36:02.870 align:middle line:90% I don't know. 00:36:02.870 --> 00:36:04.840 align:middle line:84% Did this make it over to the right hand side of the class? 00:36:04.840 --> 00:36:05.340 align:middle line:90% Yeah. 00:36:05.340 --> 00:36:07.400 align:middle line:90% So see these guys here? 00:36:07.400 --> 00:36:09.960 align:middle line:90% 00:36:09.960 --> 00:36:12.570 align:middle line:84% These are common mode chokes right here. 00:36:12.570 --> 00:36:15.900 align:middle line:84% And actually, what you'll see is the two sets 00:36:15.900 --> 00:36:17.100 align:middle line:90% of windings are identical. 00:36:17.100 --> 00:36:20.740 align:middle line:84% And they're split up on the core. 00:36:20.740 --> 00:36:23.160 align:middle line:84% They're split up on the core, actually, 00:36:23.160 --> 00:36:26.130 align:middle line:84% to help enhance the amount of leakage inductance 00:36:26.130 --> 00:36:27.790 align:middle line:90% that we have from those things. 00:36:27.790 --> 00:36:31.870 align:middle line:84% But it's symmetric in ungapped cores. 00:36:31.870 --> 00:36:33.110 align:middle line:90% And that's very convenient. 00:36:33.110 --> 00:36:34.420 align:middle line:90% Why? 00:36:34.420 --> 00:36:37.750 align:middle line:84% Well, I said if I wanted to kill the common mode 00:36:37.750 --> 00:36:44.980 align:middle line:84% component of current, I want it to cycle through cy. 00:36:44.980 --> 00:36:48.550 align:middle line:84% And my filter then, if I were to redraw this, 00:36:48.550 --> 00:36:51.910 align:middle line:84% let me just consider the common mode components. 00:36:51.910 --> 00:36:54.610 align:middle line:84% So if I just consider the common mode component-- so 00:36:54.610 --> 00:36:56.145 align:middle line:90% this is the cm only. 00:36:56.145 --> 00:36:59.350 align:middle line:90% 00:36:59.350 --> 00:37:09.795 align:middle line:84% I have half cm, 1/2 icm, 1/2 icm. 00:37:09.795 --> 00:37:14.910 align:middle line:90% 00:37:14.910 --> 00:37:18.330 align:middle line:90% Here I have cy. 00:37:18.330 --> 00:37:21.120 align:middle line:90% Here I have see cy. 00:37:21.120 --> 00:37:25.020 align:middle line:84% And then these are both going to ground, 00:37:25.020 --> 00:37:26.970 align:middle line:90% which is connected back here. 00:37:26.970 --> 00:37:35.610 align:middle line:84% Then I'm going through leakage on each side and 2L mu on each 00:37:35.610 --> 00:37:43.290 align:middle line:84% side because the ideal portion of the transformer is now gone. 00:37:43.290 --> 00:37:46.530 align:middle line:84% And then this is connected back to my input, which I'll just 00:37:46.530 --> 00:37:48.330 align:middle line:90% treat as a short circuit. 00:37:48.330 --> 00:37:54.510 align:middle line:84% So the currents here basically form-- 00:37:54.510 --> 00:37:58.280 align:middle line:84% and I'm acknowledging that I have ground connected back here, 00:37:58.280 --> 00:37:58.780 align:middle line:90% too. 00:37:58.780 --> 00:38:04.140 align:middle line:84% So basically, the currents form an lc filter 00:38:04.140 --> 00:38:07.080 align:middle line:84% that I could think of if I mirrored this, 00:38:07.080 --> 00:38:10.450 align:middle line:90% I could redraw this as this. 00:38:10.450 --> 00:38:12.190 align:middle line:84% So let me just mirror everything that 00:38:12.190 --> 00:38:15.200 align:middle line:84% looks like it's in parallel reflected across ground. 00:38:15.200 --> 00:38:16.810 align:middle line:90% And what I would get is this. 00:38:16.810 --> 00:38:32.830 align:middle line:84% L mu L leakage over 2 icm 2cy And then this is shorter this 00:38:32.830 --> 00:38:34.450 align:middle line:90% way. 00:38:34.450 --> 00:38:38.410 align:middle line:84% So putting aside damping, which I'm not talking about here, 00:38:38.410 --> 00:38:44.980 align:middle line:84% basically, I have a filter comprising 2cy is my capacitor 00:38:44.980 --> 00:38:49.730 align:middle line:84% and L mu plus half the leakage as my inductor. 00:38:49.730 --> 00:38:50.420 align:middle line:90% OK. 00:38:50.420 --> 00:38:53.200 align:middle line:90% Make sense to everybody? 00:38:53.200 --> 00:38:58.400 align:middle line:84% And that's handy because this c sub y, 00:38:58.400 --> 00:39:00.490 align:middle line:84% if I come back to my real system, 00:39:00.490 --> 00:39:03.280 align:middle line:84% it can be connected between the negative terminal 00:39:03.280 --> 00:39:05.360 align:middle line:84% and the positive terminal to ground. 00:39:05.360 --> 00:39:09.880 align:middle line:84% It turns out I'm not allowed to use a very big y capacitor. 00:39:09.880 --> 00:39:13.150 align:middle line:84% I'm not allowed to connect a big capacitor between, say, 00:39:13.150 --> 00:39:18.460 align:middle line:84% hot, my AC voltage coming in, and ground, y, 00:39:18.460 --> 00:39:21.400 align:middle line:84% because, first of all, we're not supposed to carry currents 00:39:21.400 --> 00:39:22.120 align:middle line:90% in ground. 00:39:22.120 --> 00:39:24.880 align:middle line:84% This is actually allowing current to flow in the ground 00:39:24.880 --> 00:39:25.870 align:middle line:90% wire. 00:39:25.870 --> 00:39:31.715 align:middle line:84% Devices like GFI's-- you might have a GFI in your bathroom, 00:39:31.715 --> 00:39:34.090 align:middle line:84% a ground fault interrupter-- what they're really doing is 00:39:34.090 --> 00:39:37.490 align:middle line:84% they're looking at the difference between these two 00:39:37.490 --> 00:39:40.550 align:middle line:84% currents or, equivalently, they're looking for current 00:39:40.550 --> 00:39:41.480 align:middle line:90% going into the ground. 00:39:41.480 --> 00:39:43.313 align:middle line:84% And if they see current going to the ground, 00:39:43.313 --> 00:39:44.750 align:middle line:84% they think, ah, something's wrong, 00:39:44.750 --> 00:39:46.520 align:middle line:84% somebody is being electrocuted and the current's 00:39:46.520 --> 00:39:47.395 align:middle line:90% flowing through them. 00:39:47.395 --> 00:39:49.410 align:middle line:90% Shut everything off. 00:39:49.410 --> 00:39:54.060 align:middle line:84% So if you allowed your device to put a bunch of current 00:39:54.060 --> 00:39:56.730 align:middle line:84% into the ground, it's going to mess things like that up. 00:39:56.730 --> 00:39:59.702 align:middle line:84% So they put very strict limits on how much current you're 00:39:59.702 --> 00:40:00.910 align:middle line:90% allowed to put in the ground. 00:40:00.910 --> 00:40:03.930 align:middle line:84% And for 60 hertz currents, which is what they're really 00:40:03.930 --> 00:40:09.470 align:middle line:84% looking at, or 50 hertz in Europe, 00:40:09.470 --> 00:40:12.560 align:middle line:84% this y capacitor is very limited in value. 00:40:12.560 --> 00:40:14.450 align:middle line:84% Depending upon the application, you 00:40:14.450 --> 00:40:16.170 align:middle line:84% might be talking like 5 nanofarad. 00:40:16.170 --> 00:40:18.530 align:middle line:90% It's very small capacitors. 00:40:18.530 --> 00:40:22.280 align:middle line:84% So I don't get a very big capacitor value 00:40:22.280 --> 00:40:23.550 align:middle line:90% that I'm allowed to use. 00:40:23.550 --> 00:40:25.220 align:middle line:90% How do I get all my filtering? 00:40:25.220 --> 00:40:30.140 align:middle line:84% Well, I have the magnetizing inductance, which can be huge. 00:40:30.140 --> 00:40:34.310 align:middle line:84% So I have a tiny capacitor, but a really big inductor. 00:40:34.310 --> 00:40:36.980 align:middle line:90% And that gives me-- 00:40:36.980 --> 00:40:38.930 align:middle line:84% I can still get a low cutoff frequency 00:40:38.930 --> 00:40:43.540 align:middle line:84% and very good filtering for common mode signals. 00:40:43.540 --> 00:40:44.930 align:middle line:90% Does that make sense, everybody? 00:40:44.930 --> 00:40:49.000 align:middle line:90% 00:40:49.000 --> 00:40:50.800 align:middle line:84% And the reason I get away with that 00:40:50.800 --> 00:40:54.550 align:middle line:84% is because the high power currents, the differential mode 00:40:54.550 --> 00:40:59.080 align:middle line:84% currents, are not magnetizing the transformer core. 00:40:59.080 --> 00:41:00.080 align:middle line:90% That's common mode only. 00:41:00.080 --> 00:41:03.670 align:middle line:84% Let's think about differential mode only for a moment. 00:41:03.670 --> 00:41:06.280 align:middle line:84% And you notice when I drew the common mode filter, 00:41:06.280 --> 00:41:08.470 align:middle line:84% I completely ignored this x capacitor 00:41:08.470 --> 00:41:12.230 align:middle line:84% because he's not doing anything for the common mode component. 00:41:12.230 --> 00:41:15.175 align:middle line:84% Let's think about the differential mode only. 00:41:15.175 --> 00:41:17.880 align:middle line:90% 00:41:17.880 --> 00:41:22.590 align:middle line:90% So suppose here's my device. 00:41:22.590 --> 00:41:25.470 align:middle line:84% If I'm only thinking about the differential mode components, 00:41:25.470 --> 00:41:26.745 align:middle line:90% I have idm. 00:41:26.745 --> 00:41:35.700 align:middle line:90% 00:41:35.700 --> 00:41:37.800 align:middle line:84% I'm pretending common mode 0 now. 00:41:37.800 --> 00:41:44.160 align:middle line:84% I have an x capacitor, c sub x, which 00:41:44.160 --> 00:41:46.560 align:middle line:84% is sitting between terminal one and two. 00:41:46.560 --> 00:41:52.380 align:middle line:84% So this provides-- if I have a high frequency component to idm, 00:41:52.380 --> 00:41:54.330 align:middle line:84% it provides a low impedance path for it 00:41:54.330 --> 00:41:56.380 align:middle line:84% to flow through at high frequencies. 00:41:56.380 --> 00:41:59.110 align:middle line:90% 00:41:59.110 --> 00:42:01.870 align:middle line:90% If I look back into this-- 00:42:01.870 --> 00:42:06.230 align:middle line:84% for filter purposes, let me just ignore the source voltage. 00:42:06.230 --> 00:42:11.650 align:middle line:84% The ideal transformer portion of my transformer 00:42:11.650 --> 00:42:13.550 align:middle line:84% carries all the differential mode current 00:42:13.550 --> 00:42:15.270 align:middle line:90% so I don't magnetize the core. 00:42:15.270 --> 00:42:19.270 align:middle line:84% So basically, the differential mode, the magnetizing inductance 00:42:19.270 --> 00:42:22.150 align:middle line:90% is essentially shorted out. 00:42:22.150 --> 00:42:25.180 align:middle line:84% But the leakage inductance is not. 00:42:25.180 --> 00:42:31.810 align:middle line:84% So what I'm really going to see at differential mode 00:42:31.810 --> 00:42:33.310 align:middle line:90% is the following. 00:42:33.310 --> 00:42:34.840 align:middle line:90% I'm going to see-- 00:42:34.840 --> 00:42:37.450 align:middle line:84% I'm going to see the leakage inductance here 00:42:37.450 --> 00:42:39.610 align:middle line:84% and the leakage inductance on this side 00:42:39.610 --> 00:42:42.080 align:middle line:84% because there's two leakage inductance to the transformer. 00:42:42.080 --> 00:42:48.310 align:middle line:84% And then if I connect this at the bottom, that's fine. 00:42:48.310 --> 00:42:52.870 align:middle line:84% I should say we also have the y capacitors connected to ground. 00:42:52.870 --> 00:42:54.610 align:middle line:84% From a differential mode perspective, 00:42:54.610 --> 00:42:58.330 align:middle line:84% what that looks like is a y capacitor here 00:42:58.330 --> 00:43:00.490 align:middle line:90% and a y capacitor here. 00:43:00.490 --> 00:43:03.350 align:middle line:84% And the ground is like a virtual open. 00:43:03.350 --> 00:43:04.670 align:middle line:90% Nothing's flowing in ground. 00:43:04.670 --> 00:43:08.440 align:middle line:84% So these guys just look in series. 00:43:08.440 --> 00:43:11.590 align:middle line:84% So maybe what I could think of if I thought about 00:43:11.590 --> 00:43:16.340 align:middle line:84% this is net controlling the current flow around this loop. 00:43:16.340 --> 00:43:21.920 align:middle line:90% What I really have is idm. 00:43:21.920 --> 00:43:29.260 align:middle line:90% I have c sub x plus 1/2 c sub y. 00:43:29.260 --> 00:43:32.860 align:middle line:84% And c sub x, by the way, can be very big. 00:43:32.860 --> 00:43:34.278 align:middle line:90% There's no actual limit on it. 00:43:34.278 --> 00:43:36.820 align:middle line:84% I mean I don't want to carry too much 60 hertz current in it, 00:43:36.820 --> 00:43:39.670 align:middle line:84% but it's not going to be tiny like the y capacitor does 00:43:39.670 --> 00:43:41.920 align:middle line:84% because it's not connected to ground. 00:43:41.920 --> 00:43:44.590 align:middle line:90% And then I effectively have-- 00:43:44.590 --> 00:43:46.510 align:middle line:84% if I consider these two paths together, 00:43:46.510 --> 00:43:54.140 align:middle line:84% I have a net 2L leakage here and this forms my lc filter. 00:43:54.140 --> 00:43:57.590 align:middle line:84% Now c sub x can be pretty big so this capacitor can 00:43:57.590 --> 00:43:59.420 align:middle line:90% be relatively big. 00:43:59.420 --> 00:44:00.180 align:middle line:90% The leakage. 00:44:00.180 --> 00:44:01.110 align:middle line:90% Inductance is small. 00:44:01.110 --> 00:44:03.240 align:middle line:84% It's just the leakage inductance of my transformer. 00:44:03.240 --> 00:44:05.570 align:middle line:90% And that actually stores energy. 00:44:05.570 --> 00:44:08.360 align:middle line:84% If I'm passing differential mode currents to deliver power 00:44:08.360 --> 00:44:10.970 align:middle line:84% and those currents are amps or tens of amps, 00:44:10.970 --> 00:44:14.100 align:middle line:84% that's storing energy in the net leakage. 00:44:14.100 --> 00:44:17.870 align:middle line:84% But still, the leakage is relatively 00:44:17.870 --> 00:44:20.030 align:middle line:84% small compared to the magnetizing, a few percent 00:44:20.030 --> 00:44:20.850 align:middle line:90% maybe. 00:44:20.850 --> 00:44:25.050 align:middle line:84% So I can still keep my transformer pretty small. 00:44:25.050 --> 00:44:26.960 align:middle line:84% And now for differential mode, I get 00:44:26.960 --> 00:44:30.170 align:middle line:84% a big capacitor dominated by the x capacitor 00:44:30.170 --> 00:44:32.170 align:middle line:84% and then the leakage of my common mode choke. 00:44:32.170 --> 00:44:34.733 align:middle line:90% 00:44:34.733 --> 00:44:36.025 align:middle line:90% Are there questions about that? 00:44:36.025 --> 00:44:39.390 align:middle line:90% 00:44:39.390 --> 00:44:43.860 align:middle line:84% So what do I want to know when I'm designing a filter? 00:44:43.860 --> 00:44:45.210 align:middle line:90% Right. 00:44:45.210 --> 00:44:52.700 align:middle line:84% If my problem is common mode noise, 00:44:52.700 --> 00:44:58.940 align:middle line:84% beefing up the x capacitor here is 00:44:58.940 --> 00:45:01.980 align:middle line:84% going to do zippo because the common current doesn't even 00:45:01.980 --> 00:45:02.730 align:middle line:90% flow through that. 00:45:02.730 --> 00:45:05.960 align:middle line:90% It's a virtual open. 00:45:05.960 --> 00:45:08.485 align:middle line:84% Increasing my leakage inductance, 00:45:08.485 --> 00:45:09.860 align:middle line:84% well, I could, but it's not going 00:45:09.860 --> 00:45:12.680 align:middle line:84% to help much because at common mode, 00:45:12.680 --> 00:45:16.100 align:middle line:84% this guy is what's dominating the impedance, 00:45:16.100 --> 00:45:17.940 align:middle line:84% the magnetized dominating impedance. 00:45:17.940 --> 00:45:21.140 align:middle line:84% So if I have common mode noise, what I really need to do 00:45:21.140 --> 00:45:26.250 align:middle line:84% is increase the magnetizing inductance component. 00:45:26.250 --> 00:45:28.160 align:middle line:84% That's what would help me or maybe 00:45:28.160 --> 00:45:30.620 align:middle line:84% have another pair of y capacitors over here 00:45:30.620 --> 00:45:32.600 align:middle line:90% and make a higher order filter. 00:45:32.600 --> 00:45:36.980 align:middle line:84% But I want to focus on the elements, the magnetizing 00:45:36.980 --> 00:45:40.640 align:middle line:84% inductance, and the y capacitors that dominate 00:45:40.640 --> 00:45:43.180 align:middle line:90% my common mode filtering. 00:45:43.180 --> 00:45:46.990 align:middle line:84% If the thing that's killing me is differential mode noise, 00:45:46.990 --> 00:45:52.450 align:middle line:84% then I might as well not worry about the magnetizing inductance 00:45:52.450 --> 00:45:55.780 align:middle line:90% because it's not helping me. 00:45:55.780 --> 00:45:59.020 align:middle line:84% And I ought to focus on the x capacitor 00:45:59.020 --> 00:46:02.140 align:middle line:84% and the leakage components or adding in another filter stage 00:46:02.140 --> 00:46:04.820 align:middle line:84% and worrying about the leakage components. 00:46:04.820 --> 00:46:08.660 align:middle line:84% So we can really think about the strategy used 00:46:08.660 --> 00:46:11.165 align:middle line:84% to design these filters in terms of the common mode 00:46:11.165 --> 00:46:12.540 align:middle line:84% and differential mode components. 00:46:12.540 --> 00:46:16.280 align:middle line:84% And I'm using different elements to help me build the filter 00:46:16.280 --> 00:46:19.180 align:middle line:90% and pass the specifications. 00:46:19.180 --> 00:46:22.510 align:middle line:84% Now in the final analysis when I go to measure this stuff 00:46:22.510 --> 00:46:29.080 align:middle line:84% and I'm doing my EMI testing, what I'm really 00:46:29.080 --> 00:46:36.820 align:middle line:84% coming back and doing is setting up a LISN on this lead 00:46:36.820 --> 00:46:39.340 align:middle line:84% and looking, from the source's perspective, 00:46:39.340 --> 00:46:42.820 align:middle line:84% looking in the ripple in i2 and looking in the ripple in i1 00:46:42.820 --> 00:46:45.790 align:middle line:84% or, equivalently, the voltage on the LISN for this lead 00:46:45.790 --> 00:46:47.540 align:middle line:84% and the voltage on the LISN for this lead. 00:46:47.540 --> 00:46:49.270 align:middle line:84% So my EMI measurements aren't done 00:46:49.270 --> 00:46:51.220 align:middle line:84% in terms of common mode and differential mode, 00:46:51.220 --> 00:46:53.980 align:middle line:84% but there will be common mode and differential modes 00:46:53.980 --> 00:46:56.690 align:middle line:84% components to those that I can go think about. 00:46:56.690 --> 00:47:01.102 align:middle line:84% And we often figure out ways to separate those 00:47:01.102 --> 00:47:03.310 align:middle line:84% because I'm going to do different things in my filter 00:47:03.310 --> 00:47:04.780 align:middle line:90% to fix them. 00:47:04.780 --> 00:47:05.500 align:middle line:90% OK. 00:47:05.500 --> 00:47:09.730 align:middle line:84% What might I do if I wanted-- like if I just had this device 00:47:09.730 --> 00:47:13.690 align:middle line:84% and I wanted to go figure out the common mode current going 00:47:13.690 --> 00:47:15.735 align:middle line:84% into it, how do you think I'd do that? 00:47:15.735 --> 00:47:20.430 align:middle line:90% 00:47:20.430 --> 00:47:26.220 align:middle line:84% I could go get a current probe and grab both of this lead 00:47:26.220 --> 00:47:28.990 align:middle line:84% and this lead together through the current probe. 00:47:28.990 --> 00:47:31.095 align:middle line:84% So only the sum of the currents is 00:47:31.095 --> 00:47:33.220 align:middle line:84% what I measured, which is precisely the common mode 00:47:33.220 --> 00:47:35.010 align:middle line:90% current. 00:47:35.010 --> 00:47:38.250 align:middle line:84% So I could grab a current probe and say, oh, 00:47:38.250 --> 00:47:39.500 align:middle line:90% do I have common mode current? 00:47:39.500 --> 00:47:40.000 align:middle line:90% Oh, I do. 00:47:40.000 --> 00:47:42.330 align:middle line:84% I better think about fixing the common mode. 00:47:42.330 --> 00:47:47.220 align:middle line:84% Or if I grab this lead through the probe in one direction 00:47:47.220 --> 00:47:53.250 align:middle line:84% and I flipped i2 and I measured i1 plus minus i2, 00:47:53.250 --> 00:47:58.830 align:middle line:84% i1 plus minus i2 is precisely twice the differential mode 00:47:58.830 --> 00:48:00.600 align:middle line:90% current. 00:48:00.600 --> 00:48:03.480 align:middle line:84% So I can separate out common mode and differential mode 00:48:03.480 --> 00:48:04.030 align:middle line:90% currents. 00:48:04.030 --> 00:48:05.650 align:middle line:84% I can do the same thing with voltages. 00:48:05.650 --> 00:48:08.910 align:middle line:84% If I look at the average of the voltages at terminal 1 and 2, 00:48:08.910 --> 00:48:11.340 align:middle line:84% if they're bouncing up together and down together, 00:48:11.340 --> 00:48:12.810 align:middle line:90% that's common mode. 00:48:12.810 --> 00:48:16.500 align:middle line:84% If they're doing this, that's differential mode. 00:48:16.500 --> 00:48:20.517 align:middle line:84% So I can use differential probes or sometimes 00:48:20.517 --> 00:48:23.100 align:middle line:84% what you can do is you look at how much your ground's bouncing 00:48:23.100 --> 00:48:25.680 align:middle line:84% and say, yeah, that's related to my common mode. 00:48:25.680 --> 00:48:31.832 align:middle line:84% But I'll think differently about how I will deal with those. 00:48:31.832 --> 00:48:33.540 align:middle line:84% And even when you're making measurements, 00:48:33.540 --> 00:48:34.450 align:middle line:90% you tend to do this. 00:48:34.450 --> 00:48:37.050 align:middle line:84% Actually, if you look at this cord, 00:48:37.050 --> 00:48:39.930 align:middle line:84% you see this kind of cylinder on this cord? 00:48:39.930 --> 00:48:42.840 align:middle line:84% All that cylinder is is basically 00:48:42.840 --> 00:48:45.960 align:middle line:84% a ring, a toroidal ring of ferrite through which 00:48:45.960 --> 00:48:47.440 align:middle line:90% both leads are slipped. 00:48:47.440 --> 00:48:50.860 align:middle line:84% So this is just a one-turn common mode choke. 00:48:50.860 --> 00:48:53.530 align:middle line:84% It's helping keep common mode noise out. 00:48:53.530 --> 00:48:55.840 align:middle line:84% And it's very high impedance to common mode. 00:48:55.840 --> 00:48:59.650 align:middle line:84% Gives you almost no impedance to differential mode. 00:48:59.650 --> 00:49:02.020 align:middle line:84% And that's why you can get a lot of filtering 00:49:02.020 --> 00:49:04.680 align:middle line:90% with a very small core. 00:49:04.680 --> 00:49:08.820 align:middle line:84% So that's just a notion that everything I've 00:49:08.820 --> 00:49:10.215 align:middle line:90% said about filtering is true. 00:49:10.215 --> 00:49:12.340 align:middle line:84% And sometimes you only need differential filtering. 00:49:12.340 --> 00:49:13.980 align:middle line:84% If you're building something over a ground plane 00:49:13.980 --> 00:49:16.860 align:middle line:84% and currents can return wherever they may in the ground plane, 00:49:16.860 --> 00:49:17.890 align:middle line:90% that's not a problem. 00:49:17.890 --> 00:49:19.650 align:middle line:84% But if you're going to build something 00:49:19.650 --> 00:49:23.070 align:middle line:84% with some pair of wires going out to the wall, 00:49:23.070 --> 00:49:25.620 align:middle line:84% or to your car battery, or to something else, 00:49:25.620 --> 00:49:27.180 align:middle line:84% you better start thinking in terms 00:49:27.180 --> 00:49:30.870 align:middle line:84% of common mode and differential mode, voltages and currents 00:49:30.870 --> 00:49:31.430 align:middle line:90% for noise. 00:49:31.430 --> 00:49:34.370 align:middle line:90% 00:49:34.370 --> 00:49:37.120 align:middle line:90% Any questions? 00:49:37.120 --> 00:49:37.810 align:middle line:90% Yeah. 00:49:37.810 --> 00:49:39.850 align:middle line:84% AUDIENCE: So common mode and differential mode, 00:49:39.850 --> 00:49:44.470 align:middle line:84% do they both occur simultaneously or do they just-- 00:49:44.470 --> 00:49:48.760 align:middle line:84% are they situations that occur separately? 00:49:48.760 --> 00:49:51.360 align:middle line:84% PROFESSOR: Well, different things might drive common mode 00:49:51.360 --> 00:49:53.890 align:middle line:84% and differential mode noise, but, typically, they're 00:49:53.890 --> 00:49:54.920 align:middle line:90% occurring together. 00:49:54.920 --> 00:49:57.945 align:middle line:84% And it's just a question of what you're seeing on pin one 00:49:57.945 --> 00:49:59.320 align:middle line:84% and what you're seeing on pin two 00:49:59.320 --> 00:50:00.653 align:middle line:90% in terms of voltage and current. 00:50:00.653 --> 00:50:02.140 align:middle line:84% So they occur together but what's 00:50:02.140 --> 00:50:07.250 align:middle line:84% dominant may depend upon the situation. 00:50:07.250 --> 00:50:11.620 align:middle line:84% So if I suddenly increase the parasitic capacitance 00:50:11.620 --> 00:50:15.070 align:middle line:84% of my transistor to ground, suddenly I'd 00:50:15.070 --> 00:50:16.870 align:middle line:84% probably see a bunch of common mode noise 00:50:16.870 --> 00:50:20.510 align:middle line:84% there too, even if I have a differential mode component. 00:50:20.510 --> 00:50:21.010 align:middle line:90% OK. 00:50:21.010 --> 00:50:25.900 align:middle line:84% So if I'm making this third terminal current path easier, 00:50:25.900 --> 00:50:30.100 align:middle line:84% that's probably going to lead to common mode noise, for example. 00:50:30.100 --> 00:50:31.870 align:middle line:90% But no, they occur together. 00:50:31.870 --> 00:50:36.130 align:middle line:84% You've got to filter both at the same time. 00:50:36.130 --> 00:50:37.190 align:middle line:90% Other questions? 00:50:37.190 --> 00:50:40.750 align:middle line:90% 00:50:40.750 --> 00:50:41.410 align:middle line:90% OK. 00:50:41.410 --> 00:50:42.850 align:middle line:84% Next class, we're going to take up 00:50:42.850 --> 00:50:44.620 align:middle line:84% an entirely new class of converter 00:50:44.620 --> 00:50:47.000 align:middle line:90% but we will do that tomorrow. 00:50:47.000 --> 00:50:48.900 align:middle line:90% Have a great day. 00:50:48.900 --> 00:50:52.000 align:middle line:90%