WEBVTT 00:00:00.000 --> 00:00:09.590 align:middle line:84% [SQUEAKING] [RUSTLING] [CLICKING] 00:00:09.590 --> 00:00:11.180 align:middle line:84% DAVID PERREAULT: OK, good afternoon. 00:00:11.180 --> 00:00:18.410 align:middle line:84% So we now have magnetic components, like transformers, 00:00:18.410 --> 00:00:19.800 align:middle line:90% at our disposal. 00:00:19.800 --> 00:00:21.650 align:middle line:84% And once we have transformers, there's 00:00:21.650 --> 00:00:24.830 align:middle line:84% a lot of interesting things we can do in power converter design 00:00:24.830 --> 00:00:27.860 align:middle line:84% that we couldn't just do with inductors or capacitors. 00:00:27.860 --> 00:00:30.230 align:middle line:84% And the material I'm going to talk about today, 00:00:30.230 --> 00:00:33.620 align:middle line:84% which are nominally called isolated converters, 00:00:33.620 --> 00:00:39.050 align:middle line:84% is the topic of Principles of Power Electronics chapter 7. 00:00:39.050 --> 00:00:45.870 align:middle line:84% And The notion here is, how do we design isolated power 00:00:45.870 --> 00:00:46.370 align:middle line:90% converters? 00:00:46.370 --> 00:00:48.650 align:middle line:84% When I say isolated power converters, what do I mean? 00:00:48.650 --> 00:00:53.593 align:middle line:84% Well, there's three motivations for an isolated kind of topology 00:00:53.593 --> 00:00:56.010 align:middle line:84% or the kind of topologies we're going to talk about today. 00:00:56.010 --> 00:00:58.066 align:middle line:90% The first is galvanic isolation. 00:00:58.066 --> 00:01:03.770 align:middle line:90% 00:01:03.770 --> 00:01:05.930 align:middle line:84% If I'm going to build something that's 00:01:05.930 --> 00:01:09.140 align:middle line:84% going to plug into the wall and power my laptop, 00:01:09.140 --> 00:01:12.200 align:middle line:84% I would really like it that if lightning strikes outside, 00:01:12.200 --> 00:01:13.650 align:middle line:90% I don't get electrocuted. 00:01:13.650 --> 00:01:16.610 align:middle line:84% So what you would really like is some kind 00:01:16.610 --> 00:01:19.610 align:middle line:84% of saturating isolation barrier between you 00:01:19.610 --> 00:01:22.560 align:middle line:84% and the actual stuff that's connected to the wall. 00:01:22.560 --> 00:01:28.340 align:middle line:84% And so if you take any laptop adapter or computer adapter, 00:01:28.340 --> 00:01:31.490 align:middle line:84% the transformer in that basically 00:01:31.490 --> 00:01:34.482 align:middle line:84% has thousands of volts of isolation 00:01:34.482 --> 00:01:36.690 align:middle line:84% to protect against something like a lightning strike. 00:01:36.690 --> 00:01:38.600 align:middle line:84% And in fact, it has at least three layers 00:01:38.600 --> 00:01:42.710 align:middle line:84% of isolation built into it, such that if any one of them fails, 00:01:42.710 --> 00:01:44.600 align:middle line:90% you have enough. 00:01:44.600 --> 00:01:48.270 align:middle line:84% So that's one important reason why 00:01:48.270 --> 00:01:51.090 align:middle line:84% you might want physical, galvanic isolation for safety 00:01:51.090 --> 00:01:52.800 align:middle line:90% reasons. 00:01:52.800 --> 00:01:56.970 align:middle line:84% The second reason that we often use transformers, 00:01:56.970 --> 00:01:59.520 align:middle line:84% and whether or not you have galvanic isolation, 00:01:59.520 --> 00:02:01.363 align:middle line:90% is for large conversion ratios. 00:02:01.363 --> 00:02:07.620 align:middle line:90% 00:02:07.620 --> 00:02:12.120 align:middle line:84% So if I want to step down or up 20 to 1, something like that, 00:02:12.120 --> 00:02:14.562 align:middle line:84% yeah, I can do that with a straight-up buck converter 00:02:14.562 --> 00:02:15.520 align:middle line:90% or something like that. 00:02:15.520 --> 00:02:17.970 align:middle line:84% But it turns out we can do a lot better if we 00:02:17.970 --> 00:02:20.340 align:middle line:84% have some voltage and current scaling, which 00:02:20.340 --> 00:02:22.740 align:middle line:90% we can do with a transformer. 00:02:22.740 --> 00:02:25.380 align:middle line:84% The third reason that's very common 00:02:25.380 --> 00:02:28.123 align:middle line:84% is that we can do multiple outputs. 00:02:28.123 --> 00:02:31.830 align:middle line:90% 00:02:31.830 --> 00:02:37.260 align:middle line:84% So a typical power supply for your computer or something, 00:02:37.260 --> 00:02:41.350 align:middle line:84% maybe you want plus 12 plus 5 minus 5, 00:02:41.350 --> 00:02:43.840 align:middle line:84% so you can supply a whole bunch of different stuff at once. 00:02:43.840 --> 00:02:45.450 align:middle line:84% And yeah, you could build separate power converters 00:02:45.450 --> 00:02:46.065 align:middle line:90% to do that. 00:02:46.065 --> 00:02:48.190 align:middle line:84% But wouldn't it be nice to build one converter that 00:02:48.190 --> 00:02:51.340 align:middle line:84% does it all in a more compact form factor? 00:02:51.340 --> 00:02:54.890 align:middle line:84% And having transformers at our disposal lets us do that. 00:02:54.890 --> 00:02:56.890 align:middle line:84% And lastly, which I don't put up here, 00:02:56.890 --> 00:02:58.900 align:middle line:84% it turns out it's just transformers 00:02:58.900 --> 00:03:01.780 align:middle line:84% open up the range of topologies and structures 00:03:01.780 --> 00:03:04.480 align:middle line:84% you can put into a converter and thereby help you 00:03:04.480 --> 00:03:08.110 align:middle line:90% design some interesting things. 00:03:08.110 --> 00:03:11.620 align:middle line:84% So let's take a look at an example-- 00:03:11.620 --> 00:03:13.810 align:middle line:84% or we'll take a look at two examples today 00:03:13.810 --> 00:03:16.180 align:middle line:84% of the kind of things you do with a transformer 00:03:16.180 --> 00:03:17.090 align:middle line:90% and a converter. 00:03:17.090 --> 00:03:20.860 align:middle line:84% So if we thought about it, a basic converter 00:03:20.860 --> 00:03:26.440 align:middle line:84% that we've analyzed before, if I have Vin, 00:03:26.440 --> 00:03:34.570 align:middle line:84% I might have my switch here, and then I'll call this Vout. 00:03:34.570 --> 00:03:40.030 align:middle line:90% 00:03:40.030 --> 00:03:42.640 align:middle line:84% And our main energy storage element 00:03:42.640 --> 00:03:44.800 align:middle line:84% in this converter for transferring 00:03:44.800 --> 00:03:47.870 align:middle line:90% energy is this inductor L. 00:03:47.870 --> 00:03:51.310 align:middle line:84% And we said, if I analyze this converter, the voltage 00:03:51.310 --> 00:03:56.450 align:middle line:84% across the inductor L, V sub L, has to have a 0 average balance. 00:03:56.450 --> 00:04:01.270 align:middle line:84% And what we get from that is that Vout over Vin 00:04:01.270 --> 00:04:08.090 align:middle line:84% is equal to minus D over 1 minus D. So it has a negative gain. 00:04:08.090 --> 00:04:10.960 align:middle line:84% The output voltage is negative if the input is positive. 00:04:10.960 --> 00:04:14.800 align:middle line:84% And I can make the output voltage smaller or larger 00:04:14.800 --> 00:04:17.500 align:middle line:84% in magnitude than the input based 00:04:17.500 --> 00:04:19.480 align:middle line:90% on how I select my duty ratio. 00:04:19.480 --> 00:04:27.830 align:middle line:84% So OK, I have of AC waveform at VL in the middle of my circuit. 00:04:27.830 --> 00:04:30.960 align:middle line:84% I could throw a transformer in there. 00:04:30.960 --> 00:04:32.210 align:middle line:90% So what happens if we do that? 00:04:32.210 --> 00:04:37.300 align:middle line:84% Suppose I come in and I just say, all right, 00:04:37.300 --> 00:04:39.940 align:middle line:84% let me throw a transformer in there. 00:04:39.940 --> 00:04:42.860 align:middle line:90% 00:04:42.860 --> 00:04:46.940 align:middle line:90% So here, I'll put in-- 00:04:46.940 --> 00:04:49.520 align:middle line:90% here's V sub L again. 00:04:49.520 --> 00:04:51.100 align:middle line:90% It would help if I had a switch. 00:04:51.100 --> 00:04:56.860 align:middle line:90% 00:04:56.860 --> 00:04:58.990 align:middle line:84% So I'll just throw a transformer in the middle 00:04:58.990 --> 00:05:09.180 align:middle line:90% of this circuit, N1 to N2. 00:05:09.180 --> 00:05:15.285 align:middle line:84% And all I've done is put a transformer in. 00:05:15.285 --> 00:05:18.570 align:middle line:90% 00:05:18.570 --> 00:05:19.650 align:middle line:90% And I'll make this Vout. 00:05:19.650 --> 00:05:23.130 align:middle line:90% 00:05:23.130 --> 00:05:29.220 align:middle line:84% All right, so if I do this, here, I have VL again. 00:05:29.220 --> 00:05:33.680 align:middle line:84% And so what has this thing done to my conversion ratio? 00:05:33.680 --> 00:05:36.120 align:middle line:84% Well, if I think about it, in the first part 00:05:36.120 --> 00:05:42.000 align:middle line:84% of the cycle, if I look at the average voltage across VL, 00:05:42.000 --> 00:05:42.840 align:middle line:90% I get-- 00:05:42.840 --> 00:05:54.320 align:middle line:84% that's equal to D times Vin plus 1 minus D times N1 over N2 00:05:54.320 --> 00:06:01.520 align:middle line:90% times Vout is equal to 0. 00:06:01.520 --> 00:06:07.280 align:middle line:84% And if I rearrange this, what I get is Vout over Vin 00:06:07.280 --> 00:06:17.030 align:middle line:84% is equal to minus D over 1 minus D times N2 over N1. 00:06:17.030 --> 00:06:20.480 align:middle line:84% So it's the same conversion ratio that I got up here. 00:06:20.480 --> 00:06:23.240 align:middle line:84% But because I put a transform in the middle, 00:06:23.240 --> 00:06:28.940 align:middle line:84% I get this scaling by the transformer turns ratio. 00:06:28.940 --> 00:06:33.830 align:middle line:84% And what that will let me do is get a certain voltage conversion 00:06:33.830 --> 00:06:36.590 align:middle line:84% ratio that gives me an extra way I can scale the output 00:06:36.590 --> 00:06:38.460 align:middle line:84% voltage compared to the input voltage, 00:06:38.460 --> 00:06:40.730 align:middle line:84% just fixed scaling that's set by the turns ratio. 00:06:40.730 --> 00:06:44.360 align:middle line:84% But nonetheless, it lets me pick my duty ratios the way I want. 00:06:44.360 --> 00:06:47.520 align:middle line:84% Any questions about that, rescaling? 00:06:47.520 --> 00:06:50.870 align:middle line:90% 00:06:50.870 --> 00:06:53.360 align:middle line:90% What else can we do here? 00:06:53.360 --> 00:06:56.780 align:middle line:84% Well, very conveniently, now, in this case, 00:06:56.780 --> 00:06:58.250 align:middle line:84% in addition to giving me a scaling, 00:06:58.250 --> 00:07:01.130 align:middle line:84% it says that now notice that this voltage is not reference 00:07:01.130 --> 00:07:04.220 align:middle line:90% at all to this voltage. 00:07:04.220 --> 00:07:06.950 align:middle line:84% So ideally speaking, there's no way for current to flow, 00:07:06.950 --> 00:07:10.940 align:middle line:84% say, from here to here or from here directly to here. 00:07:10.940 --> 00:07:14.570 align:middle line:84% So I've got some the potential to get galvanic isolation. 00:07:14.570 --> 00:07:17.720 align:middle line:84% But it also means that this node and this node 00:07:17.720 --> 00:07:19.740 align:middle line:84% are no longer referenced to one another. 00:07:19.740 --> 00:07:23.060 align:middle line:84% And I can put my grounds wherever 00:07:23.060 --> 00:07:24.990 align:middle line:90% I choose in this circuit now. 00:07:24.990 --> 00:07:26.570 align:middle line:84% So one thing I might choose to do 00:07:26.570 --> 00:07:32.860 align:middle line:84% is, if I look at this circuit, the gate drive for this circuit 00:07:32.860 --> 00:07:34.570 align:middle line:90% is referenced like this. 00:07:34.570 --> 00:07:36.370 align:middle line:84% I have to generate a voltage with respect 00:07:36.370 --> 00:07:39.580 align:middle line:84% to this node to drive this switch. 00:07:39.580 --> 00:07:41.470 align:middle line:84% And that's kind of a pain because this node 00:07:41.470 --> 00:07:43.030 align:middle line:84% is flapping up and down with respect 00:07:43.030 --> 00:07:46.210 align:middle line:90% to the negative of my input. 00:07:46.210 --> 00:07:50.210 align:middle line:84% So that's an inconvenient place to have to drive the switch. 00:07:50.210 --> 00:07:53.710 align:middle line:84% And I've got to usually put in a level-shifting gate 00:07:53.710 --> 00:07:55.790 align:middle line:84% drive or a flying gate driver to do that. 00:07:55.790 --> 00:07:58.340 align:middle line:90% That adds cost and complexity. 00:07:58.340 --> 00:08:01.310 align:middle line:84% Wouldn't it be nice if I could put the switch elsewhere? 00:08:01.310 --> 00:08:05.500 align:middle line:84% Well, look, I have Vin, this structure, 00:08:05.500 --> 00:08:07.310 align:middle line:90% and the switch in series. 00:08:07.310 --> 00:08:09.210 align:middle line:90% I could just rearrange that. 00:08:09.210 --> 00:08:12.820 align:middle line:84% So perhaps I could just simply do this-- 00:08:12.820 --> 00:08:16.330 align:middle line:90% Vin-- OK, I'll come along here. 00:08:16.330 --> 00:08:18.625 align:middle line:84% And let me just put my transformer and my inductor 00:08:18.625 --> 00:08:19.125 align:middle line:90% first. 00:08:19.125 --> 00:08:29.030 align:middle line:90% 00:08:29.030 --> 00:08:30.565 align:middle line:90% And I'll put the switch here. 00:08:30.565 --> 00:08:33.200 align:middle line:90% 00:08:33.200 --> 00:08:38.510 align:middle line:84% So now, this switch, if this is an in channel, 00:08:38.510 --> 00:08:41.299 align:middle line:84% his input is referenced right here. 00:08:41.299 --> 00:08:45.190 align:middle line:84% And my gate drive is very convenient to implement. 00:08:45.190 --> 00:08:48.050 align:middle line:84% So that's one nice thing I can do. 00:08:48.050 --> 00:08:51.980 align:middle line:84% What's another thing I could do here? 00:08:51.980 --> 00:08:55.490 align:middle line:84% There's nothing that says which way this output has 00:08:55.490 --> 00:08:59.360 align:middle line:84% to be referenced because, in the original circuit, 00:08:59.360 --> 00:09:03.560 align:middle line:84% I was forced to this inversion between output and input 00:09:03.560 --> 00:09:06.630 align:middle line:84% by the orientation of the inductor. 00:09:06.630 --> 00:09:11.570 align:middle line:84% Well, here, I could just flip this transformer around, 00:09:11.570 --> 00:09:12.385 align:middle line:90% if I wanted. 00:09:12.385 --> 00:09:14.010 align:middle line:84% And in fact, I can play the same trick. 00:09:14.010 --> 00:09:16.610 align:middle line:84% I could put the diode here or I can move it over here. 00:09:16.610 --> 00:09:19.010 align:middle line:84% So let me just flip this guy upside down. 00:09:19.010 --> 00:09:20.040 align:middle line:90% So I'll do it like this. 00:09:20.040 --> 00:09:21.410 align:middle line:90% Here's one dot. 00:09:21.410 --> 00:09:27.243 align:middle line:84% Now, I'll turn this upside down and do this. 00:09:27.243 --> 00:09:28.910 align:middle line:84% And I'm going to move the diode through. 00:09:28.910 --> 00:09:30.368 align:middle line:84% And I'm going to draw it like this. 00:09:30.368 --> 00:09:33.880 align:middle line:84% And I'm going to define a new output voltage, like this. 00:09:33.880 --> 00:09:39.110 align:middle line:90% 00:09:39.110 --> 00:09:41.720 align:middle line:90% So what does that do for me? 00:09:41.720 --> 00:09:46.230 align:middle line:84% Well, OK, in the first part of the cycle, 00:09:46.230 --> 00:09:48.970 align:middle line:90% I put Vin across the input. 00:09:48.970 --> 00:09:53.790 align:middle line:84% So I get D Vin is across the inductor. 00:09:53.790 --> 00:09:56.520 align:middle line:84% And when the diode is on, now, I'm 00:09:56.520 --> 00:10:02.820 align:middle line:84% applying minus Vout scaled by N1 over N2. 00:10:02.820 --> 00:10:16.080 align:middle line:84% So I get Din plus 1 minus D minus Vout times N1 over N2 00:10:16.080 --> 00:10:17.130 align:middle line:90% equals 0. 00:10:17.130 --> 00:10:23.790 align:middle line:84% And this just gives me Vout over Vin 00:10:23.790 --> 00:10:30.990 align:middle line:84% is equal to D over 1 minus D times N2 over N1. 00:10:30.990 --> 00:10:35.460 align:middle line:84% So I've gotten the same thing as I did before. 00:10:35.460 --> 00:10:39.660 align:middle line:84% But because I was able to flip the way I did the transformer, 00:10:39.660 --> 00:10:43.210 align:middle line:90% I got rid of this negative sign. 00:10:43.210 --> 00:10:46.510 align:middle line:84% So if I want a positive output from this converter, 00:10:46.510 --> 00:10:50.860 align:middle line:84% now I can get a positive output relative to the input. 00:10:50.860 --> 00:10:53.440 align:middle line:84% If I still want a negative output, no problem. 00:10:53.440 --> 00:10:56.190 align:middle line:84% Nobody ever said I had to define Vout this way. 00:10:56.190 --> 00:10:58.690 align:middle line:84% I could define a new Vout inverted from that 00:10:58.690 --> 00:11:00.820 align:middle line:84% and time my output reference here. 00:11:00.820 --> 00:11:03.670 align:middle line:84% I can reference the output and the input to this circuit 00:11:03.670 --> 00:11:05.410 align:middle line:84% to different potentials and reference it 00:11:05.410 --> 00:11:07.810 align:middle line:84% any way I want because it's an isolated converter. 00:11:07.810 --> 00:11:09.110 align:middle line:90% And I'm good. 00:11:09.110 --> 00:11:11.960 align:middle line:90% So I can get positive outputs. 00:11:11.960 --> 00:11:15.310 align:middle line:84% I can get negative outputs, any way I want to do it. 00:11:15.310 --> 00:11:16.725 align:middle line:90% Any questions about that? 00:11:16.725 --> 00:11:19.890 align:middle line:90% 00:11:19.890 --> 00:11:22.620 align:middle line:90% Yeah? 00:11:22.620 --> 00:11:26.520 align:middle line:84% STUDENT: I guess, how strict is the galvanic isolation? 00:11:26.520 --> 00:11:30.330 align:middle line:84% How does that protect against like induced surge? 00:11:30.330 --> 00:11:32.470 align:middle line:84% DAVID PERREAULT: OK, so what would happen? 00:11:32.470 --> 00:11:39.990 align:middle line:84% Imagine that lightning strikes your circuit here. 00:11:39.990 --> 00:11:43.200 align:middle line:84% This ground, this node goes crazy because whatever 00:11:43.200 --> 00:11:47.160 align:middle line:84% this was tied to had some huge voltage across it. 00:11:47.160 --> 00:11:48.940 align:middle line:90% I'm applying that voltage. 00:11:48.940 --> 00:11:53.250 align:middle line:84% Suppose this is the ground you're connected to. 00:11:53.250 --> 00:11:56.580 align:middle line:90% That's applying a voltage here. 00:11:56.580 --> 00:11:58.590 align:middle line:84% Ideally, for an ideal transformer, 00:11:58.590 --> 00:11:59.790 align:middle line:90% that's just an open circuit. 00:11:59.790 --> 00:12:02.580 align:middle line:90% No current can flow this way. 00:12:02.580 --> 00:12:03.960 align:middle line:90% What would happen in reality? 00:12:03.960 --> 00:12:05.710 align:middle line:84% Maybe if there was a differential voltage, 00:12:05.710 --> 00:12:07.840 align:middle line:90% this transformer would saturate. 00:12:07.840 --> 00:12:10.570 align:middle line:84% But whatever happens, to the extent 00:12:10.570 --> 00:12:12.550 align:middle line:84% that this acts like an ideal transformer, 00:12:12.550 --> 00:12:15.190 align:middle line:84% you're not going to get current flow from here, through here, 00:12:15.190 --> 00:12:17.710 align:middle line:90% back to ground, and through you. 00:12:17.710 --> 00:12:23.780 align:middle line:90% In reality, this isn't perfect. 00:12:23.780 --> 00:12:26.395 align:middle line:84% This ability, the ability of the transformer 00:12:26.395 --> 00:12:27.770 align:middle line:84% to take voltage this way, depends 00:12:27.770 --> 00:12:29.743 align:middle line:84% upon how much insulation you have 00:12:29.743 --> 00:12:31.160 align:middle line:84% between the primary and secondary. 00:12:31.160 --> 00:12:32.460 align:middle line:90% And that's what's regulated. 00:12:32.460 --> 00:12:35.430 align:middle line:84% So it's a few thousand volts typically for a laptop adapter. 00:12:35.430 --> 00:12:37.730 align:middle line:84% And like I said, even if you have a fault on one 00:12:37.730 --> 00:12:39.920 align:middle line:84% of those layers of insulation, the other one 00:12:39.920 --> 00:12:43.703 align:middle line:84% should be big enough to block a few thousand volts. 00:12:43.703 --> 00:12:44.745 align:middle line:90% That answer the question? 00:12:44.745 --> 00:12:49.693 align:middle line:90% 00:12:49.693 --> 00:12:52.390 align:middle line:84% So the nice thing about the transformer 00:12:52.390 --> 00:12:54.195 align:middle line:84% is it lets us reference the output any way 00:12:54.195 --> 00:12:55.070 align:middle line:90% we want to the input. 00:12:55.070 --> 00:12:56.560 align:middle line:84% In addition to galvanic isolation, 00:12:56.560 --> 00:12:57.920 align:middle line:90% I can change the polarity. 00:12:57.920 --> 00:12:59.240 align:middle line:90% All very nice. 00:12:59.240 --> 00:13:00.800 align:middle line:90% But wait, there's more. 00:13:00.800 --> 00:13:02.110 align:middle line:90% What else can we do? 00:13:02.110 --> 00:13:04.450 align:middle line:90% Well, let's look at this thing. 00:13:04.450 --> 00:13:06.970 align:middle line:84% One thing I always have to pay attention to 00:13:06.970 --> 00:13:09.580 align:middle line:84% with the transformer is the fact that it 00:13:09.580 --> 00:13:13.070 align:middle line:84% has some parasitic magnetizing inductance. 00:13:13.070 --> 00:13:16.340 align:middle line:84% I ignored the magnetizing inductance in this thing. 00:13:16.340 --> 00:13:18.030 align:middle line:84% I treated it like an ideal transformer. 00:13:18.030 --> 00:13:19.780 align:middle line:84% Where would the magnetizing inductance be? 00:13:19.780 --> 00:13:21.590 align:middle line:84% If I referenced it to the primary, 00:13:21.590 --> 00:13:24.580 align:middle line:84% it would be right where this inductor is. 00:13:24.580 --> 00:13:26.080 align:middle line:84% Well, what says that I can't just 00:13:26.080 --> 00:13:32.830 align:middle line:84% then take this whole thing, OK, and build the transformer just 00:13:32.830 --> 00:13:33.500 align:middle line:90% like this. 00:13:33.500 --> 00:13:35.050 align:middle line:90% Here's my transformer. 00:13:35.050 --> 00:13:40.810 align:middle line:90% And then this L becomes L mu 1. 00:13:40.810 --> 00:13:43.900 align:middle line:90% And this becomes I mu one. 00:13:43.900 --> 00:13:46.360 align:middle line:84% And I use my magnetizing inductance 00:13:46.360 --> 00:13:49.335 align:middle line:84% of my transformer as my energy storage element. 00:13:49.335 --> 00:13:52.260 align:middle line:90% 00:13:52.260 --> 00:13:56.400 align:middle line:84% Done this way, this is often called a flyback converter. 00:13:56.400 --> 00:14:02.160 align:middle line:90% 00:14:02.160 --> 00:14:05.580 align:middle line:84% I believe where the term comes from is back in olden days 00:14:05.580 --> 00:14:07.260 align:middle line:84% when you used to have a cathode ray tube 00:14:07.260 --> 00:14:12.300 align:middle line:84% and you'd have some really high voltage causing the cursor 00:14:12.300 --> 00:14:17.620 align:middle line:84% to swing or fly, this was the kind of converter 00:14:17.620 --> 00:14:19.370 align:middle line:84% that was often in that because it got used 00:14:19.370 --> 00:14:20.760 align:middle line:90% to generate the high voltages. 00:14:20.760 --> 00:14:23.420 align:middle line:84% So it got into being called a flyback converter, as far 00:14:23.420 --> 00:14:25.610 align:middle line:90% as I understand it. 00:14:25.610 --> 00:14:28.370 align:middle line:84% But a flyback converter is essentially just 00:14:28.370 --> 00:14:30.270 align:middle line:84% an isolated buck boost converter. 00:14:30.270 --> 00:14:33.910 align:middle line:90% 00:14:33.910 --> 00:14:36.850 align:middle line:84% How would I design the transformer 00:14:36.850 --> 00:14:38.470 align:middle line:90% for this kind of thing? 00:14:38.470 --> 00:14:41.200 align:middle line:84% Well, what we would want to do is now, 00:14:41.200 --> 00:14:43.950 align:middle line:84% like an ideal transformer, I don't want any energy storage 00:14:43.950 --> 00:14:44.450 align:middle line:90% in it. 00:14:44.450 --> 00:14:46.480 align:middle line:84% The magnetizing, the parasitic, I usually 00:14:46.480 --> 00:14:48.740 align:middle line:84% want it to be infinite, if I can make it that way. 00:14:48.740 --> 00:14:51.910 align:middle line:84% But now, keep in mind that, in this converter, 00:14:51.910 --> 00:14:56.170 align:middle line:84% this yellow guy here is our energy storage element. 00:14:56.170 --> 00:14:57.820 align:middle line:84% So if I'm going to store energy in it, 00:14:57.820 --> 00:15:02.260 align:middle line:84% I usually would like to gap my magnetic structure so that it 00:15:02.260 --> 00:15:04.970 align:middle line:84% can efficiently store that energy in a small space 00:15:04.970 --> 00:15:07.360 align:middle line:84% because we put the energy storage in the gap. 00:15:07.360 --> 00:15:10.240 align:middle line:84% So the way we might build a transformer 00:15:10.240 --> 00:15:12.700 align:middle line:84% for this application-- this is an ideal transformer. 00:15:12.700 --> 00:15:14.925 align:middle line:84% This is an energy storage transformer. 00:15:14.925 --> 00:15:17.050 align:middle line:84% So what I might do is I might come up here and say, 00:15:17.050 --> 00:15:22.320 align:middle line:84% OK, I'll build some core, but I'll put a gap in it. 00:15:22.320 --> 00:15:29.930 align:middle line:90% And I'll put N1 one turns here. 00:15:29.930 --> 00:15:35.090 align:middle line:90% And here's V1 and I1. 00:15:35.090 --> 00:15:37.390 align:middle line:90% And then I'll put N2 turns here. 00:15:37.390 --> 00:15:41.140 align:middle line:90% 00:15:41.140 --> 00:15:43.930 align:middle line:84% And I'll have my dock goes this way, the way 00:15:43.930 --> 00:15:45.880 align:middle line:90% I've oriented the windings. 00:15:45.880 --> 00:15:50.600 align:middle line:90% I'll have V2 and I2 and N2. 00:15:50.600 --> 00:15:53.840 align:middle line:90% And the notion is-- 00:15:53.840 --> 00:15:56.220 align:middle line:84% where is the energy stored in this? 00:15:56.220 --> 00:15:57.890 align:middle line:84% Well, physically, there's some current 00:15:57.890 --> 00:16:00.300 align:middle line:84% in winding 1 and some current in winding 2. 00:16:00.300 --> 00:16:03.650 align:middle line:84% And between the two of those, they're storing some-- 00:16:03.650 --> 00:16:06.800 align:middle line:84% they're having induction between the two coils. 00:16:06.800 --> 00:16:09.230 align:middle line:84% And there's some energy stored in the field, 00:16:09.230 --> 00:16:12.530 align:middle line:84% in the H field, which will mostly appear in the gap. 00:16:12.530 --> 00:16:15.810 align:middle line:84% So maybe there's a tiny bit in the core. 00:16:15.810 --> 00:16:18.020 align:middle line:90% And this is H that I'm drawing. 00:16:18.020 --> 00:16:21.860 align:middle line:84% But most of my energy is stored here. 00:16:21.860 --> 00:16:25.370 align:middle line:84% How is that reflected in this circuit diagram? 00:16:25.370 --> 00:16:27.930 align:middle line:84% It's reflected in the magnetizing current. 00:16:27.930 --> 00:16:34.010 align:middle line:84% 1/2 L mu 1 I mu 1 squared reflects the energy stored 00:16:34.010 --> 00:16:38.660 align:middle line:84% in the core and in this gap, mostly in the gap. 00:16:38.660 --> 00:16:41.830 align:middle line:90% It make sense to everybody? 00:16:41.830 --> 00:16:47.980 align:middle line:84% So the idea is, if I didn't have a second winding 00:16:47.980 --> 00:16:52.480 align:middle line:84% and I had current in here, the current in the winding 1 00:16:52.480 --> 00:16:56.770 align:middle line:84% would be precisely related to the energy stored in the gap. 00:16:56.770 --> 00:17:01.810 align:middle line:84% If I had no current in winding 1 and I had an energy storage gap, 00:17:01.810 --> 00:17:07.390 align:middle line:84% I'd have current in this winding that would carry current. 00:17:07.390 --> 00:17:11.560 align:middle line:84% And that 1/2 L I squared looked at from this side would 00:17:11.560 --> 00:17:13.540 align:middle line:90% represent that energy. 00:17:13.540 --> 00:17:16.510 align:middle line:84% So basically, I can think of this as an inductor 00:17:16.510 --> 00:17:18.444 align:middle line:84% from either side, but it's sort of 00:17:18.444 --> 00:17:21.040 align:middle line:84% like an inductor with an extra winding. 00:17:21.040 --> 00:17:25.175 align:middle line:84% And I can carry current in this winding to match that energy 00:17:25.175 --> 00:17:27.050 align:middle line:84% source or I can carry current in this winding 00:17:27.050 --> 00:17:28.530 align:middle line:90% to match that energy storage. 00:17:28.530 --> 00:17:30.980 align:middle line:84% And of course, the amount of current I need 00:17:30.980 --> 00:17:33.740 align:middle line:90% depends on the number of turns. 00:17:33.740 --> 00:17:36.850 align:middle line:84% So I can rescale the amount of current I have. 00:17:36.850 --> 00:17:39.070 align:middle line:90% Does that make sense? 00:17:39.070 --> 00:17:41.260 align:middle line:90% So what are we going to do? 00:17:41.260 --> 00:17:46.282 align:middle line:84% In the first part of the cycle in this converter, 00:17:46.282 --> 00:17:47.663 align:middle line:90% I turn on this switch. 00:17:47.663 --> 00:17:51.435 align:middle line:90% 00:17:51.435 --> 00:17:57.730 align:middle line:84% This magnetizing current basically circulates this way. 00:17:57.730 --> 00:18:01.690 align:middle line:84% And I'm applying Vin across the magnetizing inductance. 00:18:01.690 --> 00:18:05.680 align:middle line:84% And the current, I mu 1, is linearly increasing. 00:18:05.680 --> 00:18:14.080 align:middle line:84% So if I plotted I mu 1, I mu 1 would linearly 00:18:14.080 --> 00:18:17.140 align:middle line:84% increase in the first part of the cycle 00:18:17.140 --> 00:18:19.910 align:middle line:90% because I'm applying Vin. 00:18:19.910 --> 00:18:21.070 align:middle line:90% In I mu 2-- 00:18:21.070 --> 00:18:23.865 align:middle line:84% I'm sorry I2, on the secondary side 00:18:23.865 --> 00:18:25.240 align:middle line:84% with the diodes open-- so there's 00:18:25.240 --> 00:18:28.750 align:middle line:84% no current in the secondary winding. 00:18:28.750 --> 00:18:33.810 align:middle line:84% When I turn the switch off, if I thought about it, 00:18:33.810 --> 00:18:36.170 align:middle line:84% if I look at it, this circuit model, what's happening 00:18:36.170 --> 00:18:39.950 align:middle line:84% is the magnetizing current's circulating out of this dot 00:18:39.950 --> 00:18:43.510 align:middle line:90% and into this dot. 00:18:43.510 --> 00:18:45.460 align:middle line:84% So there's current in the secondary 00:18:45.460 --> 00:18:52.240 align:middle line:84% now, which is supporting this magnetizing energy storage. 00:18:52.240 --> 00:18:56.140 align:middle line:84% Because of the polarity, the voltage gets applied. 00:18:56.140 --> 00:18:57.880 align:middle line:84% And the current in the magnetizing 00:18:57.880 --> 00:18:59.300 align:middle line:90% inductance ramps down. 00:18:59.300 --> 00:19:03.180 align:middle line:90% So this is what I mu looks like. 00:19:03.180 --> 00:19:05.280 align:middle line:90% And I'll draw this as I mu 1. 00:19:05.280 --> 00:19:09.660 align:middle line:84% And I'm pretending it's a 1 to 1 turns ratio for the moment. 00:19:09.660 --> 00:19:12.040 align:middle line:84% Actually, I mu 1 is always going to look like this, 00:19:12.040 --> 00:19:13.450 align:middle line:90% the magnetizing current. 00:19:13.450 --> 00:19:18.900 align:middle line:84% If my winding 1 and winding 2 had the same turns, what 00:19:18.900 --> 00:19:23.340 align:middle line:84% I would see is, in the first part of the cycle, 00:19:23.340 --> 00:19:24.780 align:middle line:90% this would be I1. 00:19:24.780 --> 00:19:30.290 align:middle line:90% 00:19:30.290 --> 00:19:35.570 align:middle line:84% And in the second part of the cycle, 00:19:35.570 --> 00:19:40.460 align:middle line:84% I would have I2 would carry the current. 00:19:40.460 --> 00:19:45.590 align:middle line:90% This would be I2 here. 00:19:45.590 --> 00:19:48.590 align:middle line:84% So I've got a continuous magnetizing current and hence 00:19:48.590 --> 00:19:50.620 align:middle line:90% continuous energy storage. 00:19:50.620 --> 00:19:54.360 align:middle line:84% But I can carry that in the first part of the cycle. 00:19:54.360 --> 00:19:59.270 align:middle line:84% I put energy into the transformer 00:19:59.270 --> 00:20:00.823 align:middle line:90% by the first winding. 00:20:00.823 --> 00:20:02.240 align:middle line:84% In the second part of the cycle, I 00:20:02.240 --> 00:20:05.780 align:middle line:84% pull that out of the transformer via the second winding. 00:20:05.780 --> 00:20:07.620 align:middle line:90% So it's same kind of operation. 00:20:07.620 --> 00:20:11.820 align:middle line:84% I'm just using two separate windings instead of one winding. 00:20:11.820 --> 00:20:15.090 align:middle line:90% Questions? 00:20:15.090 --> 00:20:17.020 align:middle line:90% Let's see this in action. 00:20:17.020 --> 00:20:21.600 align:middle line:84% We actually have a flyback converter for you to see. 00:20:21.600 --> 00:20:23.645 align:middle line:84% So Mouncy's kindly put this together. 00:20:23.645 --> 00:20:26.660 align:middle line:90% 00:20:26.660 --> 00:20:31.130 align:middle line:84% And what we're showing you is precisely 00:20:31.130 --> 00:20:36.830 align:middle line:84% the two currents in the two transformer windings. 00:20:36.830 --> 00:20:38.300 align:middle line:84% Now, what you're going to see is, 00:20:38.300 --> 00:20:44.516 align:middle line:84% if you see the primary winding is channel 1, that's in yellow. 00:20:44.516 --> 00:20:47.910 align:middle line:84% And you can see the current in primary 1-- 00:20:47.910 --> 00:20:49.680 align:middle line:84% the current in the primary is ramping up. 00:20:49.680 --> 00:20:51.320 align:middle line:84% That's because I'm storing energy in the magnetizing 00:20:51.320 --> 00:20:52.040 align:middle line:90% inductance. 00:20:52.040 --> 00:20:54.965 align:middle line:84% And that's at 2 amps per division. 00:20:54.965 --> 00:20:57.110 align:middle line:84% In the second part of the cycle, we're 00:20:57.110 --> 00:21:02.060 align:middle line:84% showing you the purple waveform is the current winding 2. 00:21:02.060 --> 00:21:03.590 align:middle line:84% And you can see it's ramping down. 00:21:03.590 --> 00:21:08.340 align:middle line:84% But you notice, that's 1 amp per division. 00:21:08.340 --> 00:21:10.080 align:middle line:90% And the energy in the core-- 00:21:10.080 --> 00:21:13.110 align:middle line:84% the energy stored in the gap actually is continuous. 00:21:13.110 --> 00:21:15.060 align:middle line:84% And it's ramping up and ramping down. 00:21:15.060 --> 00:21:18.020 align:middle line:84% But it's reflected based on different input and output 00:21:18.020 --> 00:21:18.520 align:middle line:90% currents. 00:21:18.520 --> 00:21:21.420 align:middle line:84% And that's because I can use a turns ratio, in this case, 00:21:21.420 --> 00:21:24.870 align:middle line:84% a 2 to 1 turns ratio to help me do that. 00:21:24.870 --> 00:21:28.980 align:middle line:84% So we actually can get this nice scaling 00:21:28.980 --> 00:21:31.710 align:middle line:84% and think of this energy storage transformer 00:21:31.710 --> 00:21:36.620 align:middle line:84% as an inductor plus an ideal transformer. 00:21:36.620 --> 00:21:38.354 align:middle line:90% Questions? 00:21:38.354 --> 00:21:40.160 align:middle line:90% Yeah? 00:21:40.160 --> 00:21:41.827 align:middle line:90% STUDENT: What's the blue curve? 00:21:41.827 --> 00:21:43.160 align:middle line:90% DAVID PERREAULT: The blue curve? 00:21:43.160 --> 00:21:44.610 align:middle line:84% I don't actually know what the blue curve is. 00:21:44.610 --> 00:21:45.130 align:middle line:90% STUDENT: Primary voltage. 00:21:45.130 --> 00:21:46.963 align:middle line:84% DAVID PERREAULT: That's the primary voltage. 00:21:46.963 --> 00:21:47.570 align:middle line:90% Ah, OK. 00:21:47.570 --> 00:21:49.990 align:middle line:84% So one thing you would take away from this-- 00:21:49.990 --> 00:21:51.520 align:middle line:84% and it's a little bit hard to see. 00:21:51.520 --> 00:21:56.860 align:middle line:84% And I think there's some offset going on in here-- 00:21:56.860 --> 00:22:01.090 align:middle line:84% is that you have a positive and negative. 00:22:01.090 --> 00:22:05.460 align:middle line:84% So you have a purely AC voltage across the transformer, which 00:22:05.460 --> 00:22:07.960 align:middle line:84% is hard to see because it looks like there's a little offset 00:22:07.960 --> 00:22:08.510 align:middle line:90% in that. 00:22:08.510 --> 00:22:10.903 align:middle line:84% But it's supposed to reflect that you 00:22:10.903 --> 00:22:12.820 align:middle line:84% have a positive voltage in a part of the cycle 00:22:12.820 --> 00:22:15.070 align:middle line:84% and a negative voltage in the other part of the cycle. 00:22:15.070 --> 00:22:19.940 align:middle line:84% So when blue is high, the magnetizing current is rising. 00:22:19.940 --> 00:22:24.050 align:middle line:84% When blue is low, the magnetizing current is falling. 00:22:24.050 --> 00:22:27.230 align:middle line:90% OK, thank you. 00:22:27.230 --> 00:22:33.240 align:middle line:84% So that is how we would build a flyback transformer. 00:22:33.240 --> 00:22:35.220 align:middle line:84% It's not like an ideal transformer. 00:22:35.220 --> 00:22:36.950 align:middle line:84% It's an energy storage transformer. 00:22:36.950 --> 00:22:40.580 align:middle line:84% So it's more like an inductor design. 00:22:40.580 --> 00:22:43.520 align:middle line:84% So you want to design it with a gap to make it small. 00:22:43.520 --> 00:22:47.060 align:middle line:84% There's a lot of the same design considerations as 00:22:47.060 --> 00:22:51.170 align:middle line:84% for an inductor, but you're going to have a second winding. 00:22:51.170 --> 00:22:55.100 align:middle line:84% And like we said, because we have this nice isolation, 00:22:55.100 --> 00:22:57.290 align:middle line:84% I can reference the secondary either 00:22:57.290 --> 00:23:00.040 align:middle line:84% for positive or negative output voltages I choose. 00:23:00.040 --> 00:23:02.580 align:middle line:90% 00:23:02.580 --> 00:23:05.290 align:middle line:84% We get our nice ground reference active switch. 00:23:05.290 --> 00:23:08.340 align:middle line:84% The other thing I didn't mention is that why would 00:23:08.340 --> 00:23:09.640 align:middle line:90% we want this turns ratio? 00:23:09.640 --> 00:23:14.400 align:middle line:84% Because it can help us really design the converter better. 00:23:14.400 --> 00:23:22.560 align:middle line:84% Let's suppose I had a 1-kilowatt design. 00:23:22.560 --> 00:23:30.630 align:middle line:84% And what I want is for Vin to be 100 volts at 10 amps 00:23:30.630 --> 00:23:36.810 align:middle line:84% and Vout to be 10 volts at 100 amps. 00:23:36.810 --> 00:23:39.125 align:middle line:90% So it's a 10 to 1 step down. 00:23:39.125 --> 00:23:41.830 align:middle line:90% 00:23:41.830 --> 00:23:45.490 align:middle line:84% If I tried to do that with my original converter-- 00:23:45.490 --> 00:23:49.460 align:middle line:84% and forget about whether this is plus or minus. 00:23:49.460 --> 00:23:52.185 align:middle line:84% Suppose that doesn't really matter-- 00:23:52.185 --> 00:23:55.000 align:middle line:90% 00:23:55.000 --> 00:23:56.183 align:middle line:90% what would it look like? 00:23:56.183 --> 00:23:58.100 align:middle line:84% What would the stress on the switch look like? 00:23:58.100 --> 00:24:06.460 align:middle line:84% Well, for a for buck boost, what I'd end up with 00:24:06.460 --> 00:24:13.780 align:middle line:84% is V switch and V diode being 110 volts. 00:24:13.780 --> 00:24:19.720 align:middle line:84% And I switch and I diode would be 110 amps. 00:24:19.720 --> 00:24:24.760 align:middle line:84% So that's more than 10 KVA of switch rating there 00:24:24.760 --> 00:24:28.000 align:middle line:90% and diode rating. 00:24:28.000 --> 00:24:31.990 align:middle line:84% On the other hand, suppose I designed a flyback 00:24:31.990 --> 00:24:36.700 align:middle line:84% and I used a 10 to 1 transformer. 00:24:36.700 --> 00:24:40.540 align:middle line:90% So I'm going to get my scaling-- 00:24:40.540 --> 00:24:43.270 align:middle line:84% instead of just by using some extreme duty ratio, 00:24:43.270 --> 00:24:47.860 align:middle line:84% I'm going to get my scaling by putting it into the turns ratio. 00:24:47.860 --> 00:24:49.870 align:middle line:90% What does the turns ratio do? 00:24:49.870 --> 00:24:53.860 align:middle line:84% That rescales the high current seen 00:24:53.860 --> 00:24:56.380 align:middle line:84% at the secondary to the low current at the primary 00:24:56.380 --> 00:24:59.140 align:middle line:84% and the high voltage to the primary seen as a low voltage 00:24:59.140 --> 00:25:00.290 align:middle line:90% at the secondary. 00:25:00.290 --> 00:25:03.730 align:middle line:84% And what I would get is-- instead of the direct sum 00:25:03.730 --> 00:25:05.830 align:middle line:84% of the input and output voltages, 00:25:05.830 --> 00:25:11.830 align:middle line:84% what I would get is V switch would be equal to 100 volts plus 00:25:11.830 --> 00:25:15.230 align:middle line:84% the 10x scaled version of the output voltage. 00:25:15.230 --> 00:25:17.290 align:middle line:90% So it would be 200 volts. 00:25:17.290 --> 00:25:21.980 align:middle line:90% And this would be at 20 amps. 00:25:21.980 --> 00:25:24.580 align:middle line:84% Same thing, it would the 10 amps at the input 00:25:24.580 --> 00:25:28.540 align:middle line:84% plus the scaled 100 amps down by 10 at the output 00:25:28.540 --> 00:25:29.950 align:middle line:90% would give me 20 amps. 00:25:29.950 --> 00:25:41.450 align:middle line:84% And V diode would be 20 volts at 200 amps. 00:25:41.450 --> 00:25:45.520 align:middle line:84% So what it's let me do is instead of needing a switch that 00:25:45.520 --> 00:25:49.510 align:middle line:84% has both high voltage and high current, 00:25:49.510 --> 00:25:52.420 align:middle line:84% I get a high voltage, low current switch 00:25:52.420 --> 00:25:55.150 align:middle line:84% and a low voltage, high current diode. 00:25:55.150 --> 00:25:59.060 align:middle line:84% And I might be more easily able to buy those components. 00:25:59.060 --> 00:26:01.630 align:middle line:84% Or at any rate, I can choose my turns ratio 00:26:01.630 --> 00:26:05.200 align:middle line:84% to rescale voltages and currents to be more favorable. 00:26:05.200 --> 00:26:08.890 align:middle line:84% If I just thought about in terms of KVA. 00:26:08.890 --> 00:26:14.710 align:middle line:84% This is 4 KVA instead of 12 KVA or something, 00:26:14.710 --> 00:26:16.510 align:middle line:90% So it's much less VA. 00:26:16.510 --> 00:26:19.300 align:middle line:84% But it also means I can go pick a high voltage, 00:26:19.300 --> 00:26:24.930 align:middle line:84% low current switch and a low voltage, high current diode. 00:26:24.930 --> 00:26:29.000 align:middle line:84% And this would be easier to source. 00:26:29.000 --> 00:26:31.285 align:middle line:90% Any questions about that? 00:26:31.285 --> 00:26:36.020 align:middle line:90% 00:26:36.020 --> 00:26:38.360 align:middle line:84% So this kind of trick that we basically 00:26:38.360 --> 00:26:41.090 align:middle line:84% started with my indirect converter, 00:26:41.090 --> 00:26:42.800 align:middle line:84% throw a transformer in the middle, 00:26:42.800 --> 00:26:45.350 align:middle line:84% and we can get something that can perform better 00:26:45.350 --> 00:26:49.980 align:middle line:84% is the heart of the idea of isolated power conversion. 00:26:49.980 --> 00:26:53.480 align:middle line:84% We can do this with all kinds of converters 00:26:53.480 --> 00:26:56.600 align:middle line:84% and synthesize new ones that don't have a counterpart 00:26:56.600 --> 00:27:00.590 align:middle line:90% in the non-isolated regime. 00:27:00.590 --> 00:27:04.580 align:middle line:84% Let's take a look at another example. 00:27:04.580 --> 00:27:06.920 align:middle line:84% Let's think about a buck converter 00:27:06.920 --> 00:27:09.377 align:middle line:84% and play the same game with a buck converter. 00:27:09.377 --> 00:27:11.210 align:middle line:84% And that plays out a little bit differently. 00:27:11.210 --> 00:27:13.210 align:middle line:84% But we'll see it has some of the same advantages 00:27:13.210 --> 00:27:19.520 align:middle line:84% and some different design trade-offs. 00:27:19.520 --> 00:27:22.140 align:middle line:84% Let's think about-- in a buck converter, what do I have? 00:27:22.140 --> 00:27:24.770 align:middle line:90% I have an inductor. 00:27:24.770 --> 00:27:27.540 align:middle line:84% And this inductor is my energy storage inductor. 00:27:27.540 --> 00:27:29.480 align:middle line:90% And here's Vout. 00:27:29.480 --> 00:27:33.590 align:middle line:90% 00:27:33.590 --> 00:27:41.420 align:middle line:84% And what I'm really doing is I've got some voltage, Vx, 00:27:41.420 --> 00:27:43.290 align:middle line:90% that I'm synthesizing here. 00:27:43.290 --> 00:27:51.740 align:middle line:84% That's a pulse voltage between 0 and some other voltage 2 00:27:51.740 --> 00:27:54.650 align:middle line:84% that I filter and then get my output. 00:27:54.650 --> 00:27:57.060 align:middle line:84% Well, why don't I play the same game? 00:27:57.060 --> 00:28:00.620 align:middle line:84% I'm going to throw a transformer in the middle of this thing. 00:28:00.620 --> 00:28:07.780 align:middle line:84% It turns out I'm going to need another diode here because I 00:28:07.780 --> 00:28:13.540 align:middle line:84% cannot apply a non-zero average to this transformer. 00:28:13.540 --> 00:28:15.350 align:middle line:90% So I need this diode. 00:28:15.350 --> 00:28:17.530 align:middle line:90% It's a new diode. 00:28:17.530 --> 00:28:20.260 align:middle line:84% I can play the same game and put my switch as a ground reference 00:28:20.260 --> 00:28:20.900 align:middle line:90% here. 00:28:20.900 --> 00:28:21.945 align:middle line:90% And so here's Vin. 00:28:21.945 --> 00:28:25.300 align:middle line:90% 00:28:25.300 --> 00:28:28.230 align:middle line:90% So what happens? 00:28:28.230 --> 00:28:31.050 align:middle line:90% Let me call this N1 to-- 00:28:31.050 --> 00:28:34.300 align:middle line:90% I'm sorry N1 to N2. 00:28:34.300 --> 00:28:36.690 align:middle line:90% So what does Vx look like? 00:28:36.690 --> 00:28:38.195 align:middle line:90% When the switch is on-- 00:28:38.195 --> 00:28:40.990 align:middle line:90% 00:28:40.990 --> 00:28:43.860 align:middle line:90% I'm going to plot Vx. 00:28:43.860 --> 00:28:49.590 align:middle line:84% When the switch is on, I'm applying Vn at the primary. 00:28:49.590 --> 00:28:55.080 align:middle line:84% So let me call this the voltage across the transformer. 00:28:55.080 --> 00:28:58.950 align:middle line:84% I get N2 over N1 times V transformer-- 00:28:58.950 --> 00:29:01.530 align:middle line:84% or I'll call this V21, V transformer 1-- 00:29:01.530 --> 00:29:04.140 align:middle line:90% N2 over N1 times Vn. 00:29:04.140 --> 00:29:06.010 align:middle line:84% This guy is going to be turned on. 00:29:06.010 --> 00:29:07.750 align:middle line:84% This guy is going to be turned off. 00:29:07.750 --> 00:29:15.870 align:middle line:84% So I'm going to get this voltage as being N2 over N1 Vn. 00:29:15.870 --> 00:29:20.510 align:middle line:84% And then when I turn this switch off, 00:29:20.510 --> 00:29:22.838 align:middle line:84% this diode is going to turn off, the load 00:29:22.838 --> 00:29:24.380 align:middle line:84% is going to carry through this diode, 00:29:24.380 --> 00:29:26.840 align:middle line:90% and Vx is going to go to 0. 00:29:26.840 --> 00:29:28.010 align:middle line:90% This is going to be Dt. 00:29:28.010 --> 00:29:29.840 align:middle line:84% And that's going to last until t. 00:29:29.840 --> 00:29:34.070 align:middle line:90% And this is the voltage, Vx. 00:29:34.070 --> 00:29:35.750 align:middle line:90% Well, what's the output of Vx? 00:29:35.750 --> 00:29:39.550 align:middle line:84% This inductor has to have an average voltage of 0. 00:29:39.550 --> 00:29:50.090 align:middle line:84% So what I get is V2 has to equal D times N2 over N1 Vin. 00:29:50.090 --> 00:29:54.060 align:middle line:90% So this is V2-- 00:29:54.060 --> 00:30:02.720 align:middle line:84% I'm sorry, Vout is equal to N2 over N1 D Vin. 00:30:02.720 --> 00:30:06.710 align:middle line:90% 00:30:06.710 --> 00:30:09.540 align:middle line:84% So it works just like a buck converter. 00:30:09.540 --> 00:30:12.660 align:middle line:90% 00:30:12.660 --> 00:30:14.130 align:middle line:90% And all I've gotten-- 00:30:14.130 --> 00:30:16.800 align:middle line:84% or what I've gotten out of putting this transformer in here 00:30:16.800 --> 00:30:18.100 align:middle line:90% is this scaling. 00:30:18.100 --> 00:30:21.270 align:middle line:84% Instead of applying the input voltage directly here 00:30:21.270 --> 00:30:23.940 align:middle line:84% through a switch, I'm applying a scaled version 00:30:23.940 --> 00:30:24.990 align:middle line:90% of the input voltage. 00:30:24.990 --> 00:30:27.240 align:middle line:90% And I get this nice rescaling. 00:30:27.240 --> 00:30:30.190 align:middle line:84% And I also get the electrical isolation. 00:30:30.190 --> 00:30:34.420 align:middle line:84% This port is no longer referenced to this node. 00:30:34.420 --> 00:30:36.916 align:middle line:84% So it's some of the same advantages. 00:30:36.916 --> 00:30:43.190 align:middle line:90% 00:30:43.190 --> 00:30:45.110 align:middle line:90% That's great. 00:30:45.110 --> 00:30:49.830 align:middle line:84% But notice that I again have a transformer here. 00:30:49.830 --> 00:30:51.620 align:middle line:84% And so I better think a little bit 00:30:51.620 --> 00:30:57.020 align:middle line:84% carefully about what the magnetizing inductance does. 00:30:57.020 --> 00:31:02.840 align:middle line:84% So let me come back here and say, OK, let me 00:31:02.840 --> 00:31:05.690 align:middle line:90% put in my magnetizing inductor. 00:31:05.690 --> 00:31:07.540 align:middle line:90% So here is L mu 1. 00:31:07.540 --> 00:31:11.480 align:middle line:90% 00:31:11.480 --> 00:31:13.195 align:middle line:90% And here's I mu 1. 00:31:13.195 --> 00:31:18.540 align:middle line:90% 00:31:18.540 --> 00:31:20.590 align:middle line:90% In the first part of the cycle-- 00:31:20.590 --> 00:31:23.000 align:middle line:84% so this is my real transformer model now. 00:31:23.000 --> 00:31:26.310 align:middle line:90% 00:31:26.310 --> 00:31:29.880 align:middle line:84% keep in mind, this inductor, L mu 1, 00:31:29.880 --> 00:31:33.630 align:middle line:84% is not my energy storage element the way 00:31:33.630 --> 00:31:35.790 align:middle line:90% it was in this converter. 00:31:35.790 --> 00:31:38.170 align:middle line:84% Here, I was using this as an energy storage element. 00:31:38.170 --> 00:31:42.660 align:middle line:84% Where is my energy storage element in this converter? 00:31:42.660 --> 00:31:45.250 align:middle line:90% For energy conversion purposes? 00:31:45.250 --> 00:31:46.620 align:middle line:90% STUDENT: By L? 00:31:46.620 --> 00:31:48.760 align:middle line:84% DAVID PERREAULT: Yeah, it's this inductor. 00:31:48.760 --> 00:31:53.432 align:middle line:84% This guy here-- basically, I'm applying a positive volt seconds 00:31:53.432 --> 00:31:55.390 align:middle line:84% across in the first cycle, storing energy here. 00:31:55.390 --> 00:31:57.515 align:middle line:84% In the second part of the cycle, I'm taking it out. 00:31:57.515 --> 00:32:00.880 align:middle line:84% So this is the energy storage I'm using for power conversion. 00:32:00.880 --> 00:32:06.290 align:middle line:84% This magnetizing inductance is purely a function of the fact 00:32:06.290 --> 00:32:08.260 align:middle line:84% that I don't have an ideal transformer. 00:32:08.260 --> 00:32:11.330 align:middle line:90% It has some magnetization to it. 00:32:11.330 --> 00:32:13.550 align:middle line:84% So it's a parasitic of a transformer. 00:32:13.550 --> 00:32:16.370 align:middle line:84% But I better think about what it does. 00:32:16.370 --> 00:32:17.583 align:middle line:90% And here's the catch. 00:32:17.583 --> 00:32:23.010 align:middle line:90% 00:32:23.010 --> 00:32:24.030 align:middle line:90% I turn on this switch. 00:32:24.030 --> 00:32:25.488 align:middle line:84% In the first part of the cycle, I'm 00:32:25.488 --> 00:32:28.500 align:middle line:84% applying a positive voltage, Vt1 here, 00:32:28.500 --> 00:32:31.650 align:middle line:90% which is appearing here, Vt1. 00:32:31.650 --> 00:32:35.010 align:middle line:84% That means this magnetizing inductance ramping up. 00:32:35.010 --> 00:32:37.960 align:middle line:84% The current in the magnetizing inductance is ramping up. 00:32:37.960 --> 00:32:40.740 align:middle line:84% Well, what happens in the second part of the cycle? 00:32:40.740 --> 00:32:44.580 align:middle line:84% When I turn this switch off, in the flyback converter, 00:32:44.580 --> 00:32:47.670 align:middle line:84% it circulated out of this door and into this dot-- 00:32:47.670 --> 00:32:53.850 align:middle line:84% or I'm sorry-- here, it can't do that because if the current 00:32:53.850 --> 00:32:56.370 align:middle line:84% flows here, there's no way for it to flow into here 00:32:56.370 --> 00:32:59.310 align:middle line:90% because this diode's here. 00:32:59.310 --> 00:33:04.720 align:middle line:84% So suddenly, I better provide some place for this magnetizing 00:33:04.720 --> 00:33:07.560 align:middle line:90% current to flow. 00:33:07.560 --> 00:33:09.400 align:middle line:84% And another thing I better think about 00:33:09.400 --> 00:33:12.880 align:middle line:84% is, in order for this transformer to work, 00:33:12.880 --> 00:33:16.270 align:middle line:84% the average volt seconds I apply across the transformer 00:33:16.270 --> 00:33:19.560 align:middle line:90% better be 0. 00:33:19.560 --> 00:33:23.110 align:middle line:84% Otherwise, it won't operate in periodic steady state. 00:33:23.110 --> 00:33:24.960 align:middle line:84% I have to respect this inductor, in terms 00:33:24.960 --> 00:33:28.230 align:middle line:84% of its need to have 0 average voltage to get 00:33:28.230 --> 00:33:31.626 align:middle line:90% to periodic steady state. 00:33:31.626 --> 00:33:34.050 align:middle line:90% So what would this look like? 00:33:34.050 --> 00:33:37.300 align:middle line:84% Well, let me-- actually, I'm going to change the color here. 00:33:37.300 --> 00:33:43.830 align:middle line:90% Let me call this V mu 1. 00:33:43.830 --> 00:33:45.040 align:middle line:90% That's the voltage. 00:33:45.040 --> 00:33:46.340 align:middle line:90% So what does that look like? 00:33:46.340 --> 00:33:49.000 align:middle line:90% 00:33:49.000 --> 00:33:51.340 align:middle line:84% And then let's think about what the magnetizing 00:33:51.340 --> 00:33:52.240 align:middle line:90% current looks like. 00:33:52.240 --> 00:33:57.190 align:middle line:84% In the first part of the cycle, I turn the switch on. 00:33:57.190 --> 00:34:00.680 align:middle line:90% And I'm applying Vin as V mu 1. 00:34:00.680 --> 00:34:01.770 align:middle line:90% So here's V mu 1. 00:34:01.770 --> 00:34:05.890 align:middle line:90% 00:34:05.890 --> 00:34:07.085 align:middle line:90% And I'm applying Vin. 00:34:07.085 --> 00:34:09.909 align:middle line:90% 00:34:09.909 --> 00:34:11.650 align:middle line:90% So what has to happen? 00:34:11.650 --> 00:34:14.080 align:middle line:84% In the second part of the cycle, I better 00:34:14.080 --> 00:34:17.469 align:middle line:84% do something so that, over the course of the cycle, 00:34:17.469 --> 00:34:22.380 align:middle line:84% the average voltage across this magnetizing inductance is 0. 00:34:22.380 --> 00:34:26.790 align:middle line:84% Well, I've provided no means for that to happen in this circuit. 00:34:26.790 --> 00:34:29.040 align:middle line:84% And probably, if I built it this way, 00:34:29.040 --> 00:34:31.770 align:middle line:90% unhappy things would happen. 00:34:31.770 --> 00:34:32.889 align:middle line:90% So what can I do? 00:34:32.889 --> 00:34:36.870 align:middle line:84% I've got to provide some other place for that magnetizing 00:34:36.870 --> 00:34:38.040 align:middle line:90% current to flow. 00:34:38.040 --> 00:34:41.460 align:middle line:84% And in the process, I need to apply a reverse voltage 00:34:41.460 --> 00:34:44.030 align:middle line:90% on V mu 1. 00:34:44.030 --> 00:34:46.820 align:middle line:84% Now, there's a lot of ways I could do that. 00:34:46.820 --> 00:34:50.780 align:middle line:84% One very popular way is to do something like this, 00:34:50.780 --> 00:34:56.120 align:middle line:84% is to provide a voltage here and maybe 00:34:56.120 --> 00:35:00.230 align:middle line:84% put, say, the equivalent of a Zener diode here. 00:35:00.230 --> 00:35:03.240 align:middle line:84% And then I will put a reverse diode here. 00:35:03.240 --> 00:35:07.280 align:middle line:84% And so what this does is this lets current, this magnetizing 00:35:07.280 --> 00:35:12.110 align:middle line:84% current, flow into this orange path against some Zener voltage, 00:35:12.110 --> 00:35:15.550 align:middle line:90% Vz, and back up here. 00:35:15.550 --> 00:35:17.920 align:middle line:84% So this orange path is another path for current 00:35:17.920 --> 00:35:19.630 align:middle line:90% to flow through. 00:35:19.630 --> 00:35:28.070 align:middle line:84% As a remembrance, I might think of this path 00:35:28.070 --> 00:35:36.050 align:middle line:84% that I just added as being equal to this, a zener voltage, Vz. 00:35:36.050 --> 00:35:39.260 align:middle line:84% So you could think of it this way, 00:35:39.260 --> 00:35:42.680 align:middle line:84% where the Zener breaks down and creates a voltage, Vc, 00:35:42.680 --> 00:35:47.480 align:middle line:84% when it's got current flowing into it this way. 00:35:47.480 --> 00:35:50.180 align:middle line:90% That make sense to everybody? 00:35:50.180 --> 00:35:53.090 align:middle line:84% So what would happen here if I did this? 00:35:53.090 --> 00:35:58.520 align:middle line:84% When the switch turns off, I mu 1 is going to flow this way. 00:35:58.520 --> 00:36:01.310 align:middle line:84% And the voltage across the primary 00:36:01.310 --> 00:36:02.680 align:middle line:90% is going to go to minus Vz. 00:36:02.680 --> 00:36:09.490 align:middle line:90% 00:36:09.490 --> 00:36:16.790 align:middle line:84% And what would happen to the current in that magnetizing 00:36:16.790 --> 00:36:17.730 align:middle line:90% inductance? 00:36:17.730 --> 00:36:22.550 align:middle line:90% So let me plot I mu 1. 00:36:22.550 --> 00:36:26.950 align:middle line:84% When I turn on the switch, it's going to ramp up. 00:36:26.950 --> 00:36:32.050 align:middle line:84% Let's assume it ramps up from 0, like this. 00:36:32.050 --> 00:36:36.420 align:middle line:90% And then I turn off the switch. 00:36:36.420 --> 00:36:41.360 align:middle line:84% This current, the magnetizing current, cycles into this. 00:36:41.360 --> 00:36:44.420 align:middle line:84% And it ramps down because I have a negative voltage. 00:36:44.420 --> 00:36:46.160 align:middle line:84% And eventually, what I would like 00:36:46.160 --> 00:36:49.160 align:middle line:84% is for this to hit 0 at some time. 00:36:49.160 --> 00:36:56.120 align:middle line:84% So if this is Dt, and t is over here somewhere, 00:36:56.120 --> 00:36:58.010 align:middle line:90% when would this happen? 00:36:58.010 --> 00:37:03.650 align:middle line:84% This would reach 0 basically when the average volt seconds-- 00:37:03.650 --> 00:37:08.570 align:middle line:90% this area equaled this area. 00:37:08.570 --> 00:37:11.150 align:middle line:84% Net volt seconds on my inductor would be 0. 00:37:11.150 --> 00:37:12.400 align:middle line:90% And then it would just stay 0. 00:37:12.400 --> 00:37:15.025 align:middle line:84% The current would have gone to 0 in the magnetizing inductance. 00:37:15.025 --> 00:37:16.050 align:middle line:90% And that's fine. 00:37:16.050 --> 00:37:20.550 align:middle line:84% And so the transformers are just open circuited at that point. 00:37:20.550 --> 00:37:23.010 align:middle line:90% Any questions about that? 00:37:23.010 --> 00:37:23.510 align:middle line:90% Yeah? 00:37:23.510 --> 00:37:25.468 align:middle line:84% STUDENT: Why did you choose to use Zener diodes 00:37:25.468 --> 00:37:28.683 align:middle line:84% and not like one freewheeling diode? 00:37:28.683 --> 00:37:30.600 align:middle line:84% DAVID PERREAULT: Zener diodes instead of what? 00:37:30.600 --> 00:37:33.350 align:middle line:84% STUDENT: Why would you not use one freewheeling diode 00:37:33.350 --> 00:37:35.030 align:middle line:90% instead of the Zener diodes? 00:37:35.030 --> 00:37:36.295 align:middle line:90% DAVID PERREAULT: Ah, because-- 00:37:36.295 --> 00:37:36.920 align:middle line:90% think about it. 00:37:36.920 --> 00:37:39.560 align:middle line:84% A freewheeling diode has a forward drop that's 00:37:39.560 --> 00:37:41.120 align:middle line:90% like 0.7 and a reverse drop. 00:37:41.120 --> 00:37:43.370 align:middle line:84% You don't want to try to put a current through a diode 00:37:43.370 --> 00:37:44.600 align:middle line:90% backwards, right? 00:37:44.600 --> 00:37:50.150 align:middle line:84% The Zener is designed to hold a constant voltage when 00:37:50.150 --> 00:37:51.990 align:middle line:90% it's breaking down in reverse. 00:37:51.990 --> 00:37:53.480 align:middle line:90% And I might not use a Zener. 00:37:53.480 --> 00:37:58.550 align:middle line:84% I might use some other element that can absorb energy 00:37:58.550 --> 00:38:00.030 align:middle line:90% in the reverse direction. 00:38:00.030 --> 00:38:10.310 align:middle line:84% So I could have replaced it with, for example, a capacitor, 00:38:10.310 --> 00:38:18.230 align:middle line:84% and then bled the capacitor to Vin, for example. 00:38:18.230 --> 00:38:22.940 align:middle line:84% So there's a lot of different circuits. 00:38:22.940 --> 00:38:23.940 align:middle line:90% Or maybe I should have-- 00:38:23.940 --> 00:38:27.190 align:middle line:90% 00:38:27.190 --> 00:38:28.970 align:middle line:84% maybe I should have drawn it differently. 00:38:28.970 --> 00:38:30.762 align:middle line:84% But essentially, there's a lot of circuits. 00:38:30.762 --> 00:38:32.800 align:middle line:84% I've just got to give this current a path 00:38:32.800 --> 00:38:35.170 align:middle line:84% to flow into a voltage source that's 00:38:35.170 --> 00:38:38.320 align:middle line:84% going to apply enough negative voltage to drive the magnetizing 00:38:38.320 --> 00:38:39.790 align:middle line:90% current to 0. 00:38:39.790 --> 00:38:41.450 align:middle line:90% A lot of ways I can do that. 00:38:41.450 --> 00:38:46.005 align:middle line:84% The Zener was just my model for the easiest one to show you. 00:38:46.005 --> 00:38:48.460 align:middle line:90% Does that explain things? 00:38:48.460 --> 00:38:49.570 align:middle line:90% Other questions? 00:38:49.570 --> 00:38:50.530 align:middle line:90% Yeah? 00:38:50.530 --> 00:38:52.960 align:middle line:84% STUDENT: So in this case, is the Zener diode just acting 00:38:52.960 --> 00:38:55.300 align:middle line:90% like a sink, like a resistor? 00:38:55.300 --> 00:38:57.226 align:middle line:84% DAVID PERREAULT: It's just acting like a-- 00:38:57.226 --> 00:39:00.550 align:middle line:84% yeah, like a resistor, except that it's a fixed voltage. 00:39:00.550 --> 00:39:01.610 align:middle line:90% It clamps it. 00:39:01.610 --> 00:39:03.750 align:middle line:90% And the reason I was drawing-- 00:39:03.750 --> 00:39:08.320 align:middle line:84% you could replace that with a capacitor, 00:39:08.320 --> 00:39:12.730 align:middle line:84% and then bleed that capacitor back down to some average value, 00:39:12.730 --> 00:39:15.050 align:middle line:90% like Vin. 00:39:15.050 --> 00:39:19.080 align:middle line:84% So you could have connected it like this, too. 00:39:19.080 --> 00:39:21.130 align:middle line:90% You would have needed-- 00:39:21.130 --> 00:39:23.920 align:middle line:90% sorry, you would have needed a-- 00:39:23.920 --> 00:39:25.875 align:middle line:84% you would have still needed a diode there. 00:39:25.875 --> 00:39:33.570 align:middle line:90% 00:39:33.570 --> 00:39:38.780 align:middle line:84% I've got to be careful to let this ramp down to 0. 00:39:38.780 --> 00:39:40.940 align:middle line:90% What happens if I don't? 00:39:40.940 --> 00:39:44.370 align:middle line:84% If I don't, suppose I don't apply-- 00:39:44.370 --> 00:39:46.910 align:middle line:84% suppose I choose too low a Zener voltage. 00:39:46.910 --> 00:39:49.080 align:middle line:84% What would happen is, in the first cycle, 00:39:49.080 --> 00:39:50.330 align:middle line:90% the magnetizing would ramp up. 00:39:50.330 --> 00:39:51.848 align:middle line:84% And it'd come partly the way down. 00:39:51.848 --> 00:39:54.140 align:middle line:84% And then it would ramp up and come partly the way down. 00:39:54.140 --> 00:39:56.250 align:middle line:84% And it would start to walk away on me. 00:39:56.250 --> 00:39:58.970 align:middle line:84% And keep in mind, the magnetizing current 00:39:58.970 --> 00:40:01.490 align:middle line:84% is proportional to the flux in the core. 00:40:01.490 --> 00:40:03.987 align:middle line:84% And eventually, that flux would exceed the saturation flux 00:40:03.987 --> 00:40:04.820 align:middle line:90% density of the core. 00:40:04.820 --> 00:40:06.260 align:middle line:84% And then the core would saturate. 00:40:06.260 --> 00:40:07.980 align:middle line:84% And then your converter would blow up. 00:40:07.980 --> 00:40:09.210 align:middle line:90% Bad things would happen. 00:40:09.210 --> 00:40:12.890 align:middle line:84% So whatever this clamp is going to settle to, 00:40:12.890 --> 00:40:18.950 align:middle line:84% it's got to settle to a big enough voltage 00:40:18.950 --> 00:40:26.100 align:middle line:84% that it can drive the magnetizing current back to 0 00:40:26.100 --> 00:40:28.390 align:middle line:90% each cycle. 00:40:28.390 --> 00:40:30.080 align:middle line:90% So what does that say? 00:40:30.080 --> 00:40:32.395 align:middle line:84% Well, what is this peak magnetizing current? 00:40:32.395 --> 00:40:35.740 align:middle line:90% 00:40:35.740 --> 00:40:40.070 align:middle line:84% I mu 1 peak ought to be equal to what? 00:40:40.070 --> 00:40:42.183 align:middle line:90% Well, V is equal to L dI/dt. 00:40:42.183 --> 00:40:44.980 align:middle line:90% 00:40:44.980 --> 00:40:48.930 align:middle line:90% So this would be V1-- 00:40:48.930 --> 00:40:59.420 align:middle line:84% or Vin dt over L mu 1 is the peak current I hit here. 00:40:59.420 --> 00:41:01.400 align:middle line:90% Does that make sense? 00:41:01.400 --> 00:41:08.900 align:middle line:84% And lambda 1 is equal to L mu 1 I 00:41:08.900 --> 00:41:15.770 align:middle line:84% mu 1 is equal to N1 B in the core 00:41:15.770 --> 00:41:17.970 align:middle line:84% times the cross-sectional core area. 00:41:17.970 --> 00:41:19.088 align:middle line:90% Lambda's LI. 00:41:19.088 --> 00:41:19.880 align:middle line:90% And it's also NBAC. 00:41:19.880 --> 00:41:23.568 align:middle line:90% 00:41:23.568 --> 00:41:33.250 align:middle line:84% So we can calculate the core flux, VC, as being equal to-- 00:41:33.250 --> 00:41:45.920 align:middle line:84% or the peak core flux as being L mu 1 I mu 1 over N1 AC. 00:41:45.920 --> 00:41:47.800 align:middle line:84% And we've got to keep this peak core 00:41:47.800 --> 00:41:51.405 align:middle line:84% flux below the saturation flux density of the core. 00:41:51.405 --> 00:41:58.760 align:middle line:90% 00:41:58.760 --> 00:42:01.610 align:middle line:84% Actually, I should have substituted. 00:42:01.610 --> 00:42:08.940 align:middle line:84% I could rewrite this as Vin dt over N1 AC. 00:42:08.940 --> 00:42:11.730 align:middle line:90% That's another way to write it. 00:42:11.730 --> 00:42:15.500 align:middle line:90% So what do I need? 00:42:15.500 --> 00:42:18.080 align:middle line:90% Well, what I need is-- 00:42:18.080 --> 00:42:19.530 align:middle line:90% what's the minimum? 00:42:19.530 --> 00:42:20.460 align:middle line:90% Zener voltage. 00:42:20.460 --> 00:42:21.490 align:middle line:90% I need to do this? 00:42:21.490 --> 00:42:24.140 align:middle line:90% 00:42:24.140 --> 00:42:30.620 align:middle line:84% What I need is Vz times 1 minus D 00:42:30.620 --> 00:42:38.210 align:middle line:84% has to be greater than Vin times D, 00:42:38.210 --> 00:42:42.080 align:middle line:84% in order for that volt seconds to go to 0 because otherwise I 00:42:42.080 --> 00:42:44.030 align:middle line:84% won't get enough negative volt seconds 00:42:44.030 --> 00:42:46.040 align:middle line:84% to offset the positive volt seconds. 00:42:46.040 --> 00:42:53.240 align:middle line:84% And that means that Vz has to be greater than or equal to Vin 00:42:53.240 --> 00:43:00.770 align:middle line:84% times D over 1 minus D. That make sense to everybody? 00:43:00.770 --> 00:43:02.750 align:middle line:84% So what does that say about what happens 00:43:02.750 --> 00:43:04.640 align:middle line:90% to the switch in this circuit? 00:43:04.640 --> 00:43:07.023 align:middle line:84% Well, if I look at the circuit, the switch-- 00:43:07.023 --> 00:43:12.010 align:middle line:90% 00:43:12.010 --> 00:43:15.810 align:middle line:84% obviously, when the switch is on-- 00:43:15.810 --> 00:43:21.300 align:middle line:84% if I think about this as being Vswitch, when the switch is on, 00:43:21.300 --> 00:43:23.340 align:middle line:90% he has 0 volts. 00:43:23.340 --> 00:43:26.670 align:middle line:84% When the switch is off and the Zener is conducting, 00:43:26.670 --> 00:43:30.000 align:middle line:90% he has Vin plus Vz across him. 00:43:30.000 --> 00:43:35.220 align:middle line:84% So the peak switch voltage I'm going to get 00:43:35.220 --> 00:43:36.365 align:middle line:90% is going to be what? 00:43:36.365 --> 00:43:40.150 align:middle line:90% 00:43:40.150 --> 00:43:45.580 align:middle line:84% It's going to be equal to Vin plus Vz, which 00:43:45.580 --> 00:43:50.230 align:middle line:90% is equal to Vin plus-- 00:43:50.230 --> 00:43:55.570 align:middle line:84% let's suppose I use the minimum value, Vin times D over 1 00:43:55.570 --> 00:44:02.980 align:middle line:84% minus D. I could rewrite this as Vin times 1 minus D over 1 00:44:02.980 --> 00:44:04.100 align:middle line:90% minus D, if I wanted. 00:44:04.100 --> 00:44:05.210 align:middle line:90% That's the same thing. 00:44:05.210 --> 00:44:11.110 align:middle line:84% And this gives me equal to Vin over 1 minus D. All right, 00:44:11.110 --> 00:44:14.380 align:middle line:84% so if I pick a big enough Zener voltage 00:44:14.380 --> 00:44:18.910 align:middle line:84% based on this requirement to get to the 0 volt seconds balance 00:44:18.910 --> 00:44:23.300 align:middle line:84% on my transformer, I get this voltage. 00:44:23.300 --> 00:44:27.220 align:middle line:84% So if I was at D is equal to 0.5, 00:44:27.220 --> 00:44:32.200 align:middle line:84% that would give me Vswitch is equal to 2Vin. 00:44:32.200 --> 00:44:35.500 align:middle line:84% If I went up to a 75% duty ratio, 00:44:35.500 --> 00:44:40.230 align:middle line:84% that would give me Vswitch is equal to 4Vin. 00:44:40.230 --> 00:44:43.190 align:middle line:84% That's getting kind of ugly, My switch voltage 00:44:43.190 --> 00:44:45.390 align:middle line:84% is bigger than my input voltage considerably. 00:44:45.390 --> 00:44:48.150 align:middle line:84% What would it be if I just built a regular buck converter? 00:44:48.150 --> 00:44:51.040 align:middle line:90% 00:44:51.040 --> 00:44:52.450 align:middle line:90% Anybody recall that offhand? 00:44:52.450 --> 00:44:53.980 align:middle line:90% STUDENT: 1 minus V to the n? 00:44:53.980 --> 00:44:57.060 align:middle line:84% DAVID PERREAULT: It actually would be just Vn, 00:44:57.060 --> 00:44:59.790 align:middle line:84% because, in a normal buck converter, 00:44:59.790 --> 00:45:02.220 align:middle line:84% the switch is just blocking the input voltage. 00:45:02.220 --> 00:45:04.600 align:middle line:84% And the diode is circulating in the second part. 00:45:04.600 --> 00:45:06.360 align:middle line:84% So it's got the input voltage across it. 00:45:06.360 --> 00:45:09.870 align:middle line:84% Here, even a 50% duty ratio has twice the input voltage. 00:45:09.870 --> 00:45:11.140 align:middle line:90% It gets worse. 00:45:11.140 --> 00:45:14.130 align:middle line:84% It keeps getting worse at higher duty ratios. 00:45:14.130 --> 00:45:22.153 align:middle line:84% So I'm going to pay a price in the isolated buck converter. 00:45:22.153 --> 00:45:23.820 align:middle line:84% And I should have mentioned, by the way, 00:45:23.820 --> 00:45:27.750 align:middle line:84% an isolated-- this converter is called a forward converter. 00:45:27.750 --> 00:45:34.890 align:middle line:90% 00:45:34.890 --> 00:45:37.040 align:middle line:90% And that equals isolated buck. 00:45:37.040 --> 00:45:40.410 align:middle line:90% 00:45:40.410 --> 00:45:42.750 align:middle line:84% And I have no idea why it's called a forward converter, 00:45:42.750 --> 00:45:43.917 align:middle line:90% but that's what it's called. 00:45:43.917 --> 00:45:47.690 align:middle line:90% 00:45:47.690 --> 00:45:49.638 align:middle line:84% The forward converter has much greater stress. 00:45:49.638 --> 00:45:51.680 align:middle line:84% So when I put the transformer in the middle of it 00:45:51.680 --> 00:45:53.513 align:middle line:84% to give me galvanic isolation, suddenly I've 00:45:53.513 --> 00:45:56.780 align:middle line:84% paid a penalty in my device voltage stress. 00:45:56.780 --> 00:45:58.280 align:middle line:84% And I've paid that penalty because I 00:45:58.280 --> 00:46:00.440 align:middle line:90% need to reset the transformer. 00:46:00.440 --> 00:46:06.140 align:middle line:84% And that's a different trade-off compared to this design 00:46:06.140 --> 00:46:10.940 align:middle line:84% where, coincidentally or not, the magnetizing inductance 00:46:10.940 --> 00:46:13.760 align:middle line:84% turned out to be just the energy storage element I wanted. 00:46:13.760 --> 00:46:17.792 align:middle line:84% Here, the transformer is not doing me any favors. 00:46:17.792 --> 00:46:19.250 align:middle line:84% It's just there because that's what 00:46:19.250 --> 00:46:20.417 align:middle line:90% I need to get the isolation. 00:46:20.417 --> 00:46:21.630 align:middle line:90% I've got to pay for that. 00:46:21.630 --> 00:46:22.670 align:middle line:90% Yeah, Jack? 00:46:22.670 --> 00:46:27.092 align:middle line:84% STUDENT: Would you use the core converter or the buck converter? 00:46:27.092 --> 00:46:29.420 align:middle line:84% DAVID PERREAULT: Ah, that's a very good question. 00:46:29.420 --> 00:46:33.320 align:middle line:90% That comes back to-- 00:46:33.320 --> 00:46:34.980 align:middle line:90% and we'll talk more about this. 00:46:34.980 --> 00:46:37.730 align:middle line:84% That comes back to how big it is. 00:46:37.730 --> 00:46:39.540 align:middle line:84% So we're going to come back to this. 00:46:39.540 --> 00:46:43.160 align:middle line:84% But remember, a buck converter is a direct converter 00:46:43.160 --> 00:46:45.860 align:middle line:84% and has very low stress on its switches 00:46:45.860 --> 00:46:49.430 align:middle line:84% and low energy storage in its components. 00:46:49.430 --> 00:46:53.450 align:middle line:84% The flyback converter is based on an indirect topology, which 00:46:53.450 --> 00:46:55.490 align:middle line:90% has lots of energy storage. 00:46:55.490 --> 00:46:58.850 align:middle line:84% So it turns out that, depending upon the design regime, 00:46:58.850 --> 00:47:00.980 align:middle line:84% a forward converter can actually be a lot smaller 00:47:00.980 --> 00:47:02.570 align:middle line:90% because the magnets-- 00:47:02.570 --> 00:47:05.280 align:middle line:84% keep in mind, this transformer doesn't really 00:47:05.280 --> 00:47:06.348 align:middle line:90% need to store any energy. 00:47:06.348 --> 00:47:07.890 align:middle line:84% The only real energy storage element, 00:47:07.890 --> 00:47:10.020 align:middle line:84% which is the size-limiting element, 00:47:10.020 --> 00:47:11.160 align:middle line:90% ought to be that inductor. 00:47:11.160 --> 00:47:16.140 align:middle line:84% And that inductor is smaller than this flyback transformer. 00:47:16.140 --> 00:47:18.990 align:middle line:84% So you'd pick it for the same reason 00:47:18.990 --> 00:47:26.420 align:middle line:84% you might do a buck converter instead of a buck boost 00:47:26.420 --> 00:47:28.110 align:middle line:90% converter. 00:47:28.110 --> 00:47:30.870 align:middle line:84% We'll come back to design trade-offs moving forward, 00:47:30.870 --> 00:47:33.650 align:middle line:84% like when might you choose what topology. 00:47:33.650 --> 00:47:34.440 align:middle line:90% Great question. 00:47:34.440 --> 00:47:35.580 align:middle line:90% Any other questions? 00:47:35.580 --> 00:47:38.160 align:middle line:90% 00:47:38.160 --> 00:47:45.870 align:middle line:84% Let me just come back to this means of resetting the core. 00:47:45.870 --> 00:47:46.990 align:middle line:90% So we've reset the core. 00:47:46.990 --> 00:47:49.510 align:middle line:84% We have increased voltage stress on our switches. 00:47:49.510 --> 00:47:51.930 align:middle line:84% The other thing we have is increased dissipation 00:47:51.930 --> 00:47:54.100 align:middle line:90% because what am I doing here? 00:47:54.100 --> 00:47:57.390 align:middle line:84% Every cycle, I'm storing a little bit of energy 00:47:57.390 --> 00:48:00.780 align:middle line:90% in that magnetizing inductance. 00:48:00.780 --> 00:48:01.950 align:middle line:90% Magnetizing current ramps. 00:48:01.950 --> 00:48:03.490 align:middle line:84% I put energy in the magnetizing inductance. 00:48:03.490 --> 00:48:04.740 align:middle line:90% What do I do with that energy? 00:48:04.740 --> 00:48:08.750 align:middle line:90% 00:48:08.750 --> 00:48:10.500 align:middle line:90% I dump it into a Zener diode. 00:48:10.500 --> 00:48:12.490 align:middle line:90% I throw it away. 00:48:12.490 --> 00:48:14.650 align:middle line:90% So I hate throwing away energy. 00:48:14.650 --> 00:48:16.750 align:middle line:84% But this circuit, that orange circuit, 00:48:16.750 --> 00:48:18.770 align:middle line:90% is throwing away energy. 00:48:18.770 --> 00:48:21.816 align:middle line:84% Well, how much energy do I dissipate? 00:48:21.816 --> 00:48:26.140 align:middle line:90% 00:48:26.140 --> 00:48:27.940 align:middle line:84% And by the way, this process of driving 00:48:27.940 --> 00:48:32.230 align:middle line:84% the magnetizing current back to 0 is called resetting the core. 00:48:32.230 --> 00:48:38.190 align:middle line:84% How much energy do I lose in resetting the core back 00:48:38.190 --> 00:48:39.670 align:middle line:90% to 0 flux density? 00:48:39.670 --> 00:48:49.390 align:middle line:84% Well, that would be 1/2 L mu 1 times I mu 1 quantity squared. 00:48:49.390 --> 00:48:52.320 align:middle line:90% So that would be 1/2 L mu 1-- 00:48:52.320 --> 00:48:53.650 align:middle line:90% what's I mu 1? 00:48:53.650 --> 00:48:54.950 align:middle line:90% I wrote it up there. 00:48:54.950 --> 00:49:04.660 align:middle line:84% That's going to be Vin dt over L mu 1 squared. 00:49:04.660 --> 00:49:16.590 align:middle line:84% This works out to be 1/2 L mu 1 times Vin squared D squared t 00:49:16.590 --> 00:49:17.850 align:middle line:90% squared. 00:49:17.850 --> 00:49:21.570 align:middle line:84% And then if I wanted to say what's the power dissipation, 00:49:21.570 --> 00:49:24.960 align:middle line:84% I have to multiply that by the frequency of 1 over t. 00:49:24.960 --> 00:49:34.930 align:middle line:84% And what I get is 2 L mu 1 times Vin squared D squared t. 00:49:34.930 --> 00:49:38.220 align:middle line:84% So if my t is really small or I have a high frequency, 00:49:38.220 --> 00:49:40.990 align:middle line:84% I dissipate very little energy in resetting 00:49:40.990 --> 00:49:43.840 align:middle line:90% the core for a given size. 00:49:43.840 --> 00:49:47.050 align:middle line:84% If my magnetizing inductance is big, 00:49:47.050 --> 00:49:49.120 align:middle line:84% I don't store much energy in the core, 00:49:49.120 --> 00:49:50.900 align:middle line:90% and then I don't dissipate much. 00:49:50.900 --> 00:49:54.700 align:middle line:84% So in this design, I would like my magnetizing inductance 00:49:54.700 --> 00:49:56.020 align:middle line:90% to be as big as I can. 00:49:56.020 --> 00:49:59.320 align:middle line:84% I want this to be as close to an ideal transformer as possible 00:49:59.320 --> 00:50:01.780 align:middle line:84% in order to reduce the amount of energy I store in the core 00:50:01.780 --> 00:50:04.020 align:middle line:90% and throw away. 00:50:04.020 --> 00:50:05.135 align:middle line:90% Any questions about that? 00:50:05.135 --> 00:50:08.330 align:middle line:90% 00:50:08.330 --> 00:50:13.790 align:middle line:84% So just one or two final points here-- 00:50:13.790 --> 00:50:16.770 align:middle line:84% of course, I don't like throwing away energy like that. 00:50:16.770 --> 00:50:21.500 align:middle line:84% And there's a lot of other ways that you can not 00:50:21.500 --> 00:50:22.920 align:middle line:90% throw that energy away. 00:50:22.920 --> 00:50:26.180 align:middle line:84% I put energy in the magnetizing inductance. 00:50:26.180 --> 00:50:27.900 align:middle line:90% Maybe I can take it back out. 00:50:27.900 --> 00:50:29.640 align:middle line:84% And there's lots of ways I can do that. 00:50:29.640 --> 00:50:32.630 align:middle line:84% One way I might do that-- and there's others in the notes-- 00:50:32.630 --> 00:50:33.720 align:middle line:90% is the following. 00:50:33.720 --> 00:50:35.540 align:middle line:90% Maybe I do this. 00:50:35.540 --> 00:50:49.460 align:middle line:84% I will, in the first part of the cycle, 00:50:49.460 --> 00:50:53.990 align:middle line:84% apply a positive voltage through a pair of switches. 00:50:53.990 --> 00:50:58.580 align:middle line:84% In the second part of the cycle, I'll turn on this. 00:50:58.580 --> 00:51:02.360 align:middle line:84% This is Q of t and this is Q of t. 00:51:02.360 --> 00:51:05.103 align:middle line:84% So I apply a positive Vin across the transformer, 00:51:05.103 --> 00:51:06.270 align:middle line:90% just the way I did up there. 00:51:06.270 --> 00:51:08.630 align:middle line:84% In the second part of the cycle, the switches turn off 00:51:08.630 --> 00:51:09.680 align:middle line:90% and the diodes turn on. 00:51:09.680 --> 00:51:13.940 align:middle line:84% And I return the magnetizing inductance energy to the input. 00:51:13.940 --> 00:51:17.690 align:middle line:84% This can work up to a duty ratio of 50%. 00:51:17.690 --> 00:51:20.840 align:middle line:84% Or I could create another winding. 00:51:20.840 --> 00:51:23.162 align:middle line:84% And instead of throwing the energy into a Zener diode, 00:51:23.162 --> 00:51:24.620 align:middle line:84% I could throw it back to the input. 00:51:24.620 --> 00:51:26.550 align:middle line:84% That's another way I could do it. 00:51:26.550 --> 00:51:29.520 align:middle line:84% So there's lots of ways to recover that energy. 00:51:29.520 --> 00:51:31.470 align:middle line:84% And the trade-offs of how you do that 00:51:31.470 --> 00:51:33.750 align:middle line:84% separates different versions of the forward converter 00:51:33.750 --> 00:51:34.580 align:middle line:90% from one another. 00:51:34.580 --> 00:51:36.430 align:middle line:84% So I don't want you to walk away with the notion that says, 00:51:36.430 --> 00:51:39.150 align:middle line:84% I have to throw away the energy stored in the transformer. 00:51:39.150 --> 00:51:39.790 align:middle line:90% I don't. 00:51:39.790 --> 00:51:41.020 align:middle line:90% I can recover it. 00:51:41.020 --> 00:51:45.314 align:middle line:84% But it adds complexity and adds some trade-offs. 00:51:45.314 --> 00:51:48.991 align:middle line:90% Any final questions? 00:51:48.991 --> 00:51:52.840 align:middle line:84% OK, we will pick up isolated converters again next class. 00:51:52.840 --> 00:51:54.680 align:middle line:90% Have a great day. 00:51:54.680 --> 00:51:58.000 align:middle line:90%