WEBVTT 00:00:00.000 --> 00:00:08.947 align:middle line:84% [SQUEAKING] [RUSTLING] [CLICKING] 00:00:08.947 --> 00:00:09.780 align:middle line:90% DAVID PERREAULT: OK. 00:00:09.780 --> 00:00:11.340 align:middle line:90% Why don't we get started? 00:00:11.340 --> 00:00:14.850 align:middle line:84% So last class, we took up the topic 00:00:14.850 --> 00:00:17.280 align:middle line:90% of isolated DC/DC converters. 00:00:17.280 --> 00:00:20.850 align:middle line:84% And I'd like to expand on our discussion today. 00:00:20.850 --> 00:00:22.620 align:middle line:84% If you recall, the first converter 00:00:22.620 --> 00:00:29.760 align:middle line:84% we introduced last time was called the flyback converter. 00:00:29.760 --> 00:00:33.320 align:middle line:84% And this is sort of like an isolated buck boost. 00:00:33.320 --> 00:00:39.940 align:middle line:90% 00:00:39.940 --> 00:00:49.510 align:middle line:84% And the idea is I'll come in from, say, V-in. 00:00:49.510 --> 00:00:54.670 align:middle line:90% I will have a transformer. 00:00:54.670 --> 00:01:01.866 align:middle line:84% And that transformer will also have a magnetizing inductance. 00:01:01.866 --> 00:01:07.790 align:middle line:90% 00:01:07.790 --> 00:01:09.950 align:middle line:84% It has some magnetizing current that 00:01:09.950 --> 00:01:14.760 align:middle line:84% represents the energy stored in the transformer. 00:01:14.760 --> 00:01:22.870 align:middle line:84% Then I'll have a switch, Q of T, and a diode, 00:01:22.870 --> 00:01:25.730 align:middle line:90% and that's about it. 00:01:25.730 --> 00:01:27.550 align:middle line:90% And we worked this out. 00:01:27.550 --> 00:01:29.710 align:middle line:84% And we said, OK, in the first part of the cycle, 00:01:29.710 --> 00:01:32.750 align:middle line:84% I apply V-in across the magnetizing inductance. 00:01:32.750 --> 00:01:35.830 align:middle line:84% Second part of the cycle, I turn this switch off, 00:01:35.830 --> 00:01:46.210 align:middle line:84% and then I apply the reflected voltage from V-out 00:01:46.210 --> 00:01:48.370 align:middle line:84% across the magnetizing inductance. 00:01:48.370 --> 00:01:51.460 align:middle line:84% And I need a 0 average value across the magnetizing 00:01:51.460 --> 00:01:52.915 align:middle line:90% inductance. 00:01:52.915 --> 00:01:58.150 align:middle line:84% And if you apply that, what we get is V-out over V-in 00:01:58.150 --> 00:02:04.750 align:middle line:84% is equal to N2 over N1 times D over 1 minus D. 00:02:04.750 --> 00:02:10.648 align:middle line:84% So I could have made it minus N2 over N1 times V-in minus D. 00:02:10.648 --> 00:02:12.440 align:middle line:84% It's just a question of how I define V-out. 00:02:12.440 --> 00:02:15.490 align:middle line:84% And I can define it either way because this output 00:02:15.490 --> 00:02:17.600 align:middle line:84% circuit is electrically disconnected 00:02:17.600 --> 00:02:19.430 align:middle line:90% from the input-side circuit. 00:02:19.430 --> 00:02:23.030 align:middle line:84% So I can reference the output any way I want. 00:02:23.030 --> 00:02:27.500 align:middle line:84% And we said, OK, if I looked at L mu in this circuit 00:02:27.500 --> 00:02:31.803 align:middle line:84% and I looked at I mu, it ramps up 00:02:31.803 --> 00:02:33.470 align:middle line:84% in the first part of the cycle, and down 00:02:33.470 --> 00:02:36.890 align:middle line:84% in the second part of the cycle, and just does that. 00:02:36.890 --> 00:02:46.130 align:middle line:84% I mu-- or L mu acts exactly like the inductor in a buck boost 00:02:46.130 --> 00:02:47.420 align:middle line:90% converter. 00:02:47.420 --> 00:02:50.290 align:middle line:84% And so I'm storing energy in I mu. 00:02:50.290 --> 00:02:52.790 align:middle line:84% And I'm taking energy from the input and putting it in I mu. 00:02:52.790 --> 00:02:54.873 align:middle line:84% And then I'm taking that energy out and putting it 00:02:54.873 --> 00:02:57.890 align:middle line:84% into the output, just like a buck boost converter. 00:02:57.890 --> 00:03:04.380 align:middle line:84% So this is a very popular isolated converter. 00:03:04.380 --> 00:03:06.640 align:middle line:84% We looked at a different example. 00:03:06.640 --> 00:03:09.240 align:middle line:84% And I should say, by the way, in order to do this, 00:03:09.240 --> 00:03:15.330 align:middle line:84% because I'm storing all the energy in the magnetizing 00:03:15.330 --> 00:03:21.570 align:middle line:84% inductance, I usually use a gapped core 00:03:21.570 --> 00:03:24.960 align:middle line:84% because what I really want to do is 00:03:24.960 --> 00:03:28.320 align:middle line:84% store the magnetic energy in the gap 00:03:28.320 --> 00:03:30.920 align:middle line:84% to make the core as small as possible. 00:03:30.920 --> 00:03:34.950 align:middle line:84% So I'm using this transformer like an energy storage element, 00:03:34.950 --> 00:03:36.880 align:middle line:90% not like an ideal transformer. 00:03:36.880 --> 00:03:39.410 align:middle line:90% 00:03:39.410 --> 00:03:42.600 align:middle line:84% We also looked at a different converter 00:03:42.600 --> 00:03:46.330 align:middle line:84% here, which I will call a forward converter. 00:03:46.330 --> 00:03:49.300 align:middle line:90% 00:03:49.300 --> 00:03:50.980 align:middle line:84% And there's different versions of this. 00:03:50.980 --> 00:03:53.370 align:middle line:84% But this is basically an isolated buck. 00:03:53.370 --> 00:03:56.680 align:middle line:90% 00:03:56.680 --> 00:04:00.220 align:middle line:84% Sometimes, they would call this a buck-derived isolated 00:04:00.220 --> 00:04:00.950 align:middle line:90% converter. 00:04:00.950 --> 00:04:02.570 align:middle line:90% And the idea is this-- 00:04:02.570 --> 00:04:05.440 align:middle line:90% we will have V-in. 00:04:05.440 --> 00:04:09.100 align:middle line:90% 00:04:09.100 --> 00:04:13.030 align:middle line:84% And I'll use this transformer basically just 00:04:13.030 --> 00:04:14.886 align:middle line:90% to give me galvanic isolation. 00:04:14.886 --> 00:04:19.730 align:middle line:90% 00:04:19.730 --> 00:04:22.670 align:middle line:90% I'll add on a diode. 00:04:22.670 --> 00:04:27.590 align:middle line:84% And then I will have an inductor and get V-out. 00:04:27.590 --> 00:04:30.980 align:middle line:90% 00:04:30.980 --> 00:04:39.420 align:middle line:84% And the notion here is that this voltage-- 00:04:39.420 --> 00:04:40.530 align:middle line:90% I'll call this, say, Vx-- 00:04:40.530 --> 00:04:45.070 align:middle line:90% 00:04:45.070 --> 00:04:47.535 align:middle line:90% is when the switch is on. 00:04:47.535 --> 00:04:54.110 align:middle line:90% 00:04:54.110 --> 00:05:00.420 align:middle line:84% When the switch is on, I get V2 N2 over N1 V-in here. 00:05:00.420 --> 00:05:02.040 align:middle line:90% This diode is forward-biased. 00:05:02.040 --> 00:05:03.590 align:middle line:90% This diode is reverse-biased. 00:05:03.590 --> 00:05:10.580 align:middle line:84% And I get some scaled version of the input applied here at Vx. 00:05:10.580 --> 00:05:13.490 align:middle line:84% And then when I turn this switch off, 00:05:13.490 --> 00:05:16.560 align:middle line:84% this diode conducts and I get 0 at Vx. 00:05:16.560 --> 00:05:19.850 align:middle line:90% So this is DT. 00:05:19.850 --> 00:05:24.380 align:middle line:84% This is T. So as far as voltage Vx is concerned, 00:05:24.380 --> 00:05:27.020 align:middle line:84% this looks just like what a buck converter would do. 00:05:27.020 --> 00:05:33.080 align:middle line:84% So what I get in this voltage Vx is N2 over N1 V-in 00:05:33.080 --> 00:05:35.550 align:middle line:84% is what voltage is the peak voltage here. 00:05:35.550 --> 00:05:44.810 align:middle line:84% So what I get is V-out over V-in is equal to N2 over N1 times D. 00:05:44.810 --> 00:05:48.680 align:middle line:84% So it's just like that of a buck converter, but scaled by some 00:05:48.680 --> 00:05:51.120 align:middle line:90% turns ratio, N2 over N1. 00:05:51.120 --> 00:05:57.380 align:middle line:84% So In this converter, really what I'm doing 00:05:57.380 --> 00:06:03.090 align:middle line:84% is I'm using the inductor L here as my energy storage element. 00:06:03.090 --> 00:06:06.260 align:middle line:84% That's what's filtering this pulsating voltage 00:06:06.260 --> 00:06:09.890 align:middle line:90% Vx to give me a constant V-out. 00:06:09.890 --> 00:06:12.320 align:middle line:84% The transformer I'm really trying to use 00:06:12.320 --> 00:06:14.630 align:middle line:90% is an ideal transformer. 00:06:14.630 --> 00:06:17.600 align:middle line:84% I just want to apply an AC voltage across the transformer 00:06:17.600 --> 00:06:22.280 align:middle line:90% and generate this voltage-- 00:06:22.280 --> 00:06:24.410 align:middle line:84% generate a voltage here, which then gives me Vx. 00:06:24.410 --> 00:06:29.540 align:middle line:90% 00:06:29.540 --> 00:06:32.060 align:middle line:84% Nonetheless, I do have to respect the fact 00:06:32.060 --> 00:06:36.860 align:middle line:84% that any real transformer has some parasitic magnetizing 00:06:36.860 --> 00:06:37.470 align:middle line:90% inductance. 00:06:37.470 --> 00:06:44.980 align:middle line:84% I have L mu here and I have I mu here. 00:06:44.980 --> 00:06:48.650 align:middle line:84% So I do need to make the average voltage across the magnetizing 00:06:48.650 --> 00:06:51.530 align:middle line:84% inductance 0 or bad things will happen. 00:06:51.530 --> 00:06:53.990 align:middle line:84% The other thing I should recognize 00:06:53.990 --> 00:06:59.690 align:middle line:84% is that, in this circuit, if I plotted I mu, 00:06:59.690 --> 00:07:01.970 align:middle line:84% even if I start off with it being 00:07:01.970 --> 00:07:07.270 align:middle line:84% 0 at the beginning of the cycle, I mu rises for a time DT. 00:07:07.270 --> 00:07:07.770 align:middle line:90% Why? 00:07:07.770 --> 00:07:09.312 align:middle line:84% Because when the switch is on and I'm 00:07:09.312 --> 00:07:12.230 align:middle line:84% applying V-in across the magnetizing inductance, that 00:07:12.230 --> 00:07:15.060 align:middle line:84% magnetizing current stores energy. 00:07:15.060 --> 00:07:17.190 align:middle line:90% It has to have somewhere to go. 00:07:17.190 --> 00:07:21.000 align:middle line:84% And thus far, I have not provided it 00:07:21.000 --> 00:07:22.270 align:middle line:90% with any place to go. 00:07:22.270 --> 00:07:23.570 align:middle line:90% And that would be bad. 00:07:23.570 --> 00:07:27.270 align:middle line:84% I need to do something to so-called reset the core 00:07:27.270 --> 00:07:32.100 align:middle line:84% and give myself a means of recapturing that energy, 00:07:32.100 --> 00:07:34.690 align:middle line:84% either recapturing or dissipating that energy. 00:07:34.690 --> 00:07:36.850 align:middle line:84% There's a lot of ways you could do it. 00:07:36.850 --> 00:07:37.810 align:middle line:90% Here's one. 00:07:37.810 --> 00:07:40.050 align:middle line:84% Here's a different one than we used last time. 00:07:40.050 --> 00:07:44.160 align:middle line:84% Maybe I will add one more winding onto this transformer, 00:07:44.160 --> 00:07:49.320 align:middle line:90% like this, and the diode. 00:07:49.320 --> 00:07:53.520 align:middle line:84% And what I will then do is orient this, this way. 00:07:53.520 --> 00:07:59.190 align:middle line:84% And maybe this will have a number of turns, N sub r. 00:07:59.190 --> 00:08:02.880 align:middle line:84% So what then happens is that, when 00:08:02.880 --> 00:08:06.030 align:middle line:84% I turn the switch off, this magnetizing current, 00:08:06.030 --> 00:08:10.932 align:middle line:84% if I think of the white plus the plus-- 00:08:10.932 --> 00:08:16.190 align:middle line:84% plus this winding as being an ideal transformer 00:08:16.190 --> 00:08:18.410 align:middle line:84% and I deal with three-winding transformer, 00:08:18.410 --> 00:08:23.120 align:middle line:84% current will circulate out of that dot into this dot 00:08:23.120 --> 00:08:25.520 align:middle line:90% and come back to the input. 00:08:25.520 --> 00:08:29.670 align:middle line:84% So I could dump this energy into a Zener. 00:08:29.670 --> 00:08:32.429 align:middle line:84% Or I could use another winding, and recirculate, it 00:08:32.429 --> 00:08:34.350 align:middle line:90% and bring it back to the input. 00:08:34.350 --> 00:08:38.130 align:middle line:84% That's called a tertiary winding or an additional winding 00:08:38.130 --> 00:08:40.542 align:middle line:90% to recover the energy. 00:08:40.542 --> 00:08:42.000 align:middle line:84% Any questions about how that works? 00:08:42.000 --> 00:08:42.559 align:middle line:90% Yeah? 00:08:42.559 --> 00:08:46.490 align:middle line:84% STUDENT: So what happens in that winding when the switch is on? 00:08:46.490 --> 00:08:47.990 align:middle line:84% DAVID PERREAULT: Excellent question. 00:08:47.990 --> 00:08:52.730 align:middle line:84% So we said if this is series wound, 00:08:52.730 --> 00:08:58.430 align:middle line:84% this requires one core with three windings on it. 00:08:58.430 --> 00:09:01.580 align:middle line:84% So the core looks sort of like this. 00:09:01.580 --> 00:09:05.480 align:middle line:90% And I have N1. 00:09:05.480 --> 00:09:09.770 align:middle line:90% I have N2. 00:09:09.770 --> 00:09:14.720 align:middle line:84% And then I have some tertiary winding, like this. 00:09:14.720 --> 00:09:15.985 align:middle line:90% And this is. 00:09:15.985 --> 00:09:22.220 align:middle line:90% 00:09:22.220 --> 00:09:25.962 align:middle line:90% N3, like that. 00:09:25.962 --> 00:09:27.500 align:middle line:90% So what happens? 00:09:27.500 --> 00:09:31.230 align:middle line:84% So because these all link the same flux, 00:09:31.230 --> 00:09:34.340 align:middle line:84% their voltages are scaled versions of one another's. 00:09:34.340 --> 00:09:39.930 align:middle line:84% So what happens is, when I have Q of T on, I get V1 here. 00:09:39.930 --> 00:09:50.440 align:middle line:84% That means I get this way Nr over N1 V1 here. 00:09:50.440 --> 00:09:53.610 align:middle line:84% And it just reverse-biases this diode. 00:09:53.610 --> 00:09:57.400 align:middle line:84% So this winding is disconnected when the switch is on. 00:09:57.400 --> 00:09:59.825 align:middle line:84% And then it's connected when the switch is off. 00:09:59.825 --> 00:10:02.670 align:middle line:90% 00:10:02.670 --> 00:10:03.720 align:middle line:90% Any other questions? 00:10:03.720 --> 00:10:05.100 align:middle line:90% Yeah? 00:10:05.100 --> 00:10:06.560 align:middle line:90% Does that answer the question? 00:10:06.560 --> 00:10:07.660 align:middle line:90% STUDENT: [INAUDIBLE]. 00:10:07.660 --> 00:10:08.785 align:middle line:90% DAVID PERREAULT: All right. 00:10:08.785 --> 00:10:10.192 align:middle line:90% Yeah, go ahead. 00:10:10.192 --> 00:10:11.611 align:middle line:90% STUDENT: [INAUDIBLE]. 00:10:11.611 --> 00:10:14.460 align:middle line:90% 00:10:14.460 --> 00:10:16.793 align:middle line:90% DAVID PERREAULT: Yeah. 00:10:16.793 --> 00:10:18.210 align:middle line:84% STUDENT: But right, now the switch 00:10:18.210 --> 00:10:21.595 align:middle line:84% only affects the path for [INAUDIBLE]. 00:10:21.595 --> 00:10:27.440 align:middle line:90% 00:10:27.440 --> 00:10:29.430 align:middle line:90% Or does it matter? 00:10:29.430 --> 00:10:32.210 align:middle line:84% DAVID PERREAULT: Well, the switch is-- 00:10:32.210 --> 00:10:34.850 align:middle line:84% I mean, the switch is switching this 00:10:34.850 --> 00:10:38.150 align:middle line:90% winding on and off with V-in. 00:10:38.150 --> 00:10:42.620 align:middle line:84% Whether you say it's in series or not because of this path 00:10:42.620 --> 00:10:45.555 align:middle line:90% is another thing. 00:10:45.555 --> 00:10:47.305 align:middle line:84% The function of the switch hasn't changed. 00:10:47.305 --> 00:10:50.170 align:middle line:90% 00:10:50.170 --> 00:10:53.330 align:middle line:90% Does that answer your question? 00:10:53.330 --> 00:10:55.262 align:middle line:84% I mean, from the perspective of this winding, 00:10:55.262 --> 00:10:56.720 align:middle line:84% when the switch is on, this winding 00:10:56.720 --> 00:10:58.640 align:middle line:90% is connected across V-in. 00:10:58.640 --> 00:11:00.200 align:middle line:84% When the switch is off, this winding 00:11:00.200 --> 00:11:02.780 align:middle line:90% is disconnected from V-in. 00:11:02.780 --> 00:11:05.517 align:middle line:84% That's the function of the switch. 00:11:05.517 --> 00:11:07.350 align:middle line:84% Talking about whether it's in series or not, 00:11:07.350 --> 00:11:10.270 align:middle line:84% I mean, you wouldn't want to put the switch here. 00:11:10.270 --> 00:11:13.740 align:middle line:84% But you could put the switch here, if you wanted. 00:11:13.740 --> 00:11:17.220 align:middle line:84% And this is just acting as another uncontrolled switch 00:11:17.220 --> 00:11:19.420 align:middle line:90% that does what you want. 00:11:19.420 --> 00:11:22.300 align:middle line:84% Let me just come back to this question. 00:11:22.300 --> 00:11:23.680 align:middle line:84% STUDENT: Somewhat switch-related, 00:11:23.680 --> 00:11:26.200 align:middle line:84% not necessarily related to this implementation, 00:11:26.200 --> 00:11:30.460 align:middle line:84% but why are the switches coming after the transformer 00:11:30.460 --> 00:11:31.930 align:middle line:90% in these implementations? 00:11:31.930 --> 00:11:34.210 align:middle line:84% DAVID PERREAULT: Yeah, it's because if I 00:11:34.210 --> 00:11:38.850 align:middle line:84% have an N-channel transistor, the voltage 00:11:38.850 --> 00:11:42.610 align:middle line:84% I need to apply to run this is the gate source voltage. 00:11:42.610 --> 00:11:47.730 align:middle line:84% So I have some driver circuit here that can be referenced to-- 00:11:47.730 --> 00:11:49.125 align:middle line:84% if you imagine this is my ground, 00:11:49.125 --> 00:11:51.380 align:middle line:90% it can be referenced right here. 00:11:51.380 --> 00:11:55.340 align:middle line:84% If I put the switch up here, the source terminal, 00:11:55.340 --> 00:11:58.160 align:middle line:84% where my switch is referenced, is here. 00:11:58.160 --> 00:12:01.540 align:middle line:84% This node would be flapping up and down. 00:12:01.540 --> 00:12:04.210 align:middle line:84% So you'd like to put your switch usually 00:12:04.210 --> 00:12:07.880 align:middle line:84% where you can use a very simple driver to drive it. 00:12:07.880 --> 00:12:11.590 align:middle line:84% And that's the reason why both the flyback and the forward 00:12:11.590 --> 00:12:14.110 align:middle line:84% would tend to put their switch right here, because you can 00:12:14.110 --> 00:12:16.630 align:middle line:84% put all your logic here, and your driver here, 00:12:16.630 --> 00:12:18.670 align:middle line:90% and life is good. 00:12:18.670 --> 00:12:21.710 align:middle line:90% That make sense? 00:12:21.710 --> 00:12:23.680 align:middle line:84% STUDENT: I was wondering the current going back 00:12:23.680 --> 00:12:24.430 align:middle line:90% to the source. 00:12:24.430 --> 00:12:24.910 align:middle line:90% DAVID PERREAULT: Huh? 00:12:24.910 --> 00:12:27.050 align:middle line:84% STUDENT: How was the source able to reuse that? 00:12:27.050 --> 00:12:30.070 align:middle line:84% DAVID PERREAULT: Well, I mean, if I have a-- 00:12:30.070 --> 00:12:33.490 align:middle line:84% really, what would I have here in parallel 00:12:33.490 --> 00:12:36.020 align:middle line:84% with my whatever source and source resistance? 00:12:36.020 --> 00:12:38.150 align:middle line:84% I usually have a capacitor across the input. 00:12:38.150 --> 00:12:40.720 align:middle line:84% So basically, energy is coming out 00:12:40.720 --> 00:12:43.520 align:middle line:84% of that capacitor and the input and going into the magnetizing 00:12:43.520 --> 00:12:44.020 align:middle line:90% inductance. 00:12:44.020 --> 00:12:47.460 align:middle line:90% And then it's coming back. 00:12:47.460 --> 00:12:48.970 align:middle line:84% You can do a lot of other things. 00:12:48.970 --> 00:12:50.700 align:middle line:84% There's a converter called a fly forward, 00:12:50.700 --> 00:12:52.950 align:middle line:84% where they take that energy and throw it to the output 00:12:52.950 --> 00:12:54.730 align:middle line:90% instead of back to the input. 00:12:54.730 --> 00:12:57.040 align:middle line:84% It's not as widely done for a variety of reasons, 00:12:57.040 --> 00:12:58.050 align:middle line:90% but you could do that. 00:12:58.050 --> 00:13:01.130 align:middle line:90% 00:13:01.130 --> 00:13:06.660 align:middle line:84% So this design, we have to reset the core. 00:13:06.660 --> 00:13:10.130 align:middle line:84% So this purple winding, in other words, when the switch turns off 00:13:10.130 --> 00:13:12.620 align:middle line:84% and this diode turns on, the current 00:13:12.620 --> 00:13:15.940 align:middle line:90% will ramp back down to 0. 00:13:15.940 --> 00:13:20.030 align:middle line:84% And then it'll stay 0 until the beginning of the next cycle. 00:13:20.030 --> 00:13:23.570 align:middle line:84% So this is T. And this is some reset time here. 00:13:23.570 --> 00:13:29.390 align:middle line:84% And so the smallest transformer I can get, 00:13:29.390 --> 00:13:31.890 align:middle line:84% if I think about the energy source of the transformer, which 00:13:31.890 --> 00:13:35.520 align:middle line:84% is essentially the energy stored in this magnetizing inductance, 00:13:35.520 --> 00:13:39.000 align:middle line:84% tends to be smaller when the magnetizing inductance is 00:13:39.000 --> 00:13:39.690 align:middle line:90% bigger. 00:13:39.690 --> 00:13:42.330 align:middle line:84% And that ends up meaning that you typically 00:13:42.330 --> 00:13:45.270 align:middle line:84% used an uncapped core or a minimally gapped core 00:13:45.270 --> 00:13:47.780 align:middle line:90% in this kind of converter. 00:13:47.780 --> 00:13:50.738 align:middle line:84% So in this design, you want sort of an ideal transformer, 00:13:50.738 --> 00:13:52.530 align:middle line:84% but you've got to deal with its parasitics. 00:13:52.530 --> 00:13:57.180 align:middle line:84% In the flyback design, you are really 00:13:57.180 --> 00:14:00.250 align:middle line:84% using it like an inductor with an extra winding on it. 00:14:00.250 --> 00:14:02.840 align:middle line:90% 00:14:02.840 --> 00:14:09.080 align:middle line:84% Now, these are only two of a plethora of isolated converter 00:14:09.080 --> 00:14:10.910 align:middle line:90% designs I could choose from. 00:14:10.910 --> 00:14:14.590 align:middle line:84% Why might I choose from one versus the other? 00:14:14.590 --> 00:14:17.620 align:middle line:84% What's the real benefit of the flyback? 00:14:17.620 --> 00:14:21.170 align:middle line:84% Look, it's got one magnetic component-- 00:14:21.170 --> 00:14:25.320 align:middle line:84% it's both my transformer and my inductor-- 00:14:25.320 --> 00:14:28.480 align:middle line:84% one ground reference switch, and one diode, and some capacitors. 00:14:28.480 --> 00:14:30.010 align:middle line:90% Very, very simple. 00:14:30.010 --> 00:14:31.650 align:middle line:90% Very few components. 00:14:31.650 --> 00:14:34.740 align:middle line:84% So in a low power circuit, where component count and cost 00:14:34.740 --> 00:14:37.540 align:middle line:84% is really important, that's a great circuit. 00:14:37.540 --> 00:14:42.690 align:middle line:84% And in fact, a lot of laptop adapters or little wall warts 00:14:42.690 --> 00:14:45.240 align:middle line:84% that use some version of that circuit. 00:14:45.240 --> 00:14:46.263 align:middle line:90% They'll put a rectifier. 00:14:46.263 --> 00:14:48.180 align:middle line:84% And then they'll use that as a DC/DC converter 00:14:48.180 --> 00:14:50.760 align:middle line:90% to supply your outputs. 00:14:50.760 --> 00:14:55.170 align:middle line:84% So flyback is really good for low component 00:14:55.170 --> 00:14:56.910 align:middle line:90% count and simplicity. 00:14:56.910 --> 00:14:59.920 align:middle line:84% On the other hand, we said it's an isolated version of a buck 00:14:59.920 --> 00:15:00.420 align:middle line:90% boost. 00:15:00.420 --> 00:15:01.980 align:middle line:84% And we said buck boost converters 00:15:01.980 --> 00:15:03.670 align:middle line:84% have a lot of stress on the components. 00:15:03.670 --> 00:15:05.280 align:middle line:90% It has a very big inductor. 00:15:05.280 --> 00:15:08.950 align:middle line:84% It has high voltage and current stresses on the switches. 00:15:08.950 --> 00:15:13.590 align:middle line:84% And so as I go up in power, that starts to become unpleasant. 00:15:13.590 --> 00:15:18.070 align:middle line:84% The forward converter now has two magnetic components. 00:15:18.070 --> 00:15:20.300 align:middle line:84% So that's more magnetic components. 00:15:20.300 --> 00:15:24.650 align:middle line:84% On the other hand, this is based around a buck. 00:15:24.650 --> 00:15:27.215 align:middle line:84% So this inductor requires typically 00:15:27.215 --> 00:15:29.590 align:middle line:84% a lot less energy storage than the magnetizing inductance 00:15:29.590 --> 00:15:30.340 align:middle line:90% of the buck boost. 00:15:30.340 --> 00:15:33.904 align:middle line:90% 00:15:33.904 --> 00:15:36.817 align:middle line:84% And so while I've got to throw in a transformer, 00:15:36.817 --> 00:15:38.400 align:middle line:84% maybe I can make this transformer very 00:15:38.400 --> 00:15:40.330 align:middle line:90% compact at high power levels. 00:15:40.330 --> 00:15:43.530 align:middle line:84% And so maybe in the balance I have more components 00:15:43.530 --> 00:15:45.030 align:middle line:90% in this design. 00:15:45.030 --> 00:15:47.940 align:middle line:84% But at a higher power level, maybe this one 00:15:47.940 --> 00:15:50.160 align:middle line:84% can be more efficient or smaller because there's less 00:15:50.160 --> 00:15:52.320 align:middle line:90% stresses on all the components. 00:15:52.320 --> 00:15:56.910 align:middle line:84% So this is something you might do at hundreds of watts 00:15:56.910 --> 00:15:59.380 align:middle line:90% or above or a kilowatt. 00:15:59.380 --> 00:16:04.680 align:middle line:84% So the designer will always play some trade-off 00:16:04.680 --> 00:16:07.350 align:middle line:84% between higher complexity and component 00:16:07.350 --> 00:16:11.880 align:middle line:84% account versus simplicity based on what components you can get 00:16:11.880 --> 00:16:15.070 align:middle line:84% and what that implies for the design. 00:16:15.070 --> 00:16:18.810 align:middle line:84% But you will see a lot of telecom converters, for example, 00:16:18.810 --> 00:16:20.880 align:middle line:90% they come in-- 00:16:20.880 --> 00:16:28.270 align:middle line:84% you might find in a cell base station or powered from 48 volts 00:16:28.270 --> 00:16:35.390 align:middle line:84% to supply some voltage to run a board in a microprocessor rack 00:16:35.390 --> 00:16:37.050 align:middle line:90% system or something. 00:16:37.050 --> 00:16:38.820 align:middle line:84% Forward converters, especially the active 00:16:38.820 --> 00:16:40.410 align:middle line:84% clamp forward converter, which has 00:16:40.410 --> 00:16:42.360 align:middle line:84% a slightly different configuration 00:16:42.360 --> 00:16:43.830 align:middle line:84% of the clamping circuit, but it's 00:16:43.830 --> 00:16:47.246 align:middle line:84% the same basic circuit, very popular in that application. 00:16:47.246 --> 00:16:51.460 align:middle line:90% 00:16:51.460 --> 00:16:55.600 align:middle line:84% Both of these, we said, what are the reasons why we wanted 00:16:55.600 --> 00:16:58.660 align:middle line:90% to use an isolated converter? 00:16:58.660 --> 00:17:00.410 align:middle line:90% One is galvanic isolation. 00:17:00.410 --> 00:17:02.740 align:middle line:84% And both of these mean I can be isolated 00:17:02.740 --> 00:17:05.720 align:middle line:84% from primary to secondary for protection, for safety. 00:17:05.720 --> 00:17:08.300 align:middle line:84% They also help you with large conversion ratios. 00:17:08.300 --> 00:17:08.890 align:middle line:90% Why? 00:17:08.890 --> 00:17:13.240 align:middle line:84% Because if I wanted to do a 10 to 1 00:17:13.240 --> 00:17:15.400 align:middle line:84% voltage conversion with a buck converter, 00:17:15.400 --> 00:17:16.880 align:middle line:90% I need a 10% duty ratio. 00:17:16.880 --> 00:17:19.550 align:middle line:84% If I want a 20 to 1, I need a 5% duty ratio. 00:17:19.550 --> 00:17:21.050 align:middle line:90% I'm just pulsing the switch. 00:17:21.050 --> 00:17:23.609 align:middle line:90% I've got a lot of stress. 00:17:23.609 --> 00:17:25.079 align:middle line:90% It's not very easy to do. 00:17:25.079 --> 00:17:28.860 align:middle line:84% Here, I can pick a turns ratio, and rescale 00:17:28.860 --> 00:17:32.460 align:middle line:84% that, and, by using a 10 to 1 or 20 to 1 turns ratio, 00:17:32.460 --> 00:17:34.770 align:middle line:84% suddenly be running at 50% duty cycle again 00:17:34.770 --> 00:17:36.160 align:middle line:90% and have lower stresses. 00:17:36.160 --> 00:17:38.730 align:middle line:84% So I get an additional design freedom 00:17:38.730 --> 00:17:41.585 align:middle line:84% that helps me get to wide conversion ratio ranges. 00:17:41.585 --> 00:17:45.850 align:middle line:90% 00:17:45.850 --> 00:17:49.980 align:middle line:84% The third reason-- first of all, let me stop there. 00:17:49.980 --> 00:17:51.730 align:middle line:84% Are there any other questions about either 00:17:51.730 --> 00:17:53.920 align:middle line:84% of these circuits as examples of different ways 00:17:53.920 --> 00:17:57.410 align:middle line:84% you might do isolated converters? 00:17:57.410 --> 00:18:00.320 align:middle line:84% STUDENT: Could you quickly go over how to do the component 00:18:00.320 --> 00:18:02.240 align:middle line:90% stresses? 00:18:02.240 --> 00:18:04.363 align:middle line:84% DAVID PERREAULT: Right, so what we said was-- 00:18:04.363 --> 00:18:07.120 align:middle line:90% 00:18:07.120 --> 00:18:11.230 align:middle line:84% for example, in this circuit, if I ignore the magnetizing 00:18:11.230 --> 00:18:17.060 align:middle line:84% currents because it's small, when I turn the switch on, 00:18:17.060 --> 00:18:25.520 align:middle line:84% if this is an output current I2 and it's almost constant, 00:18:25.520 --> 00:18:31.580 align:middle line:84% when I turn the switch on, I2 is coming this way, which 00:18:31.580 --> 00:18:33.440 align:middle line:90% means I2 is coming this way. 00:18:33.440 --> 00:18:38.760 align:middle line:84% And I see N2 over N1 I2 through the switch. 00:18:38.760 --> 00:18:41.430 align:middle line:84% When the switch is off, I see the reset voltage, 00:18:41.430 --> 00:18:44.710 align:middle line:84% which is some minimum multiple of V-in. 00:18:44.710 --> 00:18:50.750 align:middle line:84% So I can relate the switch voltage 00:18:50.750 --> 00:18:54.230 align:middle line:84% to-- in this case, the input voltage and the switch current 00:18:54.230 --> 00:18:55.620 align:middle line:90% to the output current. 00:18:55.620 --> 00:18:57.990 align:middle line:84% And then it helps me pick my switches. 00:18:57.990 --> 00:19:00.530 align:middle line:84% I can do the same thing for the indirect kind of converter. 00:19:00.530 --> 00:19:02.697 align:middle line:84% And what you'll see is, for a given conversion ratio 00:19:02.697 --> 00:19:05.960 align:middle line:84% with optimally chosen turns ratios, it's worse for that one 00:19:05.960 --> 00:19:07.250 align:middle line:90% than it is for this one. 00:19:07.250 --> 00:19:08.750 align:middle line:84% Moreover, you can see the same thing 00:19:08.750 --> 00:19:11.600 align:middle line:84% about the energy stored in that magnetizing 00:19:11.600 --> 00:19:17.215 align:middle line:84% inductance versus this physical inductance. 00:19:17.215 --> 00:19:24.490 align:middle line:84% So what was the other reason I said we wanted to do, 00:19:24.490 --> 00:19:26.980 align:middle line:84% quote unquote, "isolated converters," not for isolation, 00:19:26.980 --> 00:19:29.280 align:middle line:84% but its ease of doing multiple outputs. 00:19:29.280 --> 00:19:32.060 align:middle line:90% 00:19:32.060 --> 00:19:32.940 align:middle line:90% Why? 00:19:32.940 --> 00:19:36.770 align:middle line:84% Because, A, I often need multiple related outputs. 00:19:36.770 --> 00:19:44.340 align:middle line:84% But B, I can often do that just by adding windings 00:19:44.340 --> 00:19:45.580 align:middle line:90% to my transformer. 00:19:45.580 --> 00:19:49.540 align:middle line:84% So for example, suppose I have a forward converter. 00:19:49.540 --> 00:19:53.350 align:middle line:90% 00:19:53.350 --> 00:19:59.176 align:middle line:84% And all I might do is say, OK, I'll build this transformer. 00:19:59.176 --> 00:20:03.200 align:middle line:90% 00:20:03.200 --> 00:20:06.650 align:middle line:84% And what I can do is I can say, OK, here's N1. 00:20:06.650 --> 00:20:08.460 align:middle line:90% I'll have a second winding, N2. 00:20:08.460 --> 00:20:10.375 align:middle line:90% This is my first output. 00:20:10.375 --> 00:20:21.070 align:middle line:90% 00:20:21.070 --> 00:20:22.450 align:middle line:90% That's V2. 00:20:22.450 --> 00:20:24.430 align:middle line:84% And then I could just build another 00:20:24.430 --> 00:20:35.432 align:middle line:84% winding on my same transformer and call that V3 00:20:35.432 --> 00:20:38.310 align:middle line:90% with a number of turns, N3. 00:20:38.310 --> 00:20:40.710 align:middle line:84% So all I do is I throw one more winding 00:20:40.710 --> 00:20:43.560 align:middle line:84% on my transformer-- same idea, series-wound, 00:20:43.560 --> 00:20:45.060 align:middle line:90% just like this guy. 00:20:45.060 --> 00:20:46.830 align:middle line:84% And then, yes, I've got to add two more 00:20:46.830 --> 00:20:49.080 align:middle line:84% diodes and another inductor, but I get another output. 00:20:49.080 --> 00:20:52.110 align:middle line:84% So it's not like I've got to build a whole nother converter. 00:20:52.110 --> 00:20:55.080 align:middle line:84% I just add a few more components to my existing converter. 00:20:55.080 --> 00:20:56.450 align:middle line:90% And what should I get? 00:20:56.450 --> 00:21:01.980 align:middle line:84% Ideally, whereas this voltage became 00:21:01.980 --> 00:21:04.650 align:middle line:84% N2 over N1 scaled times V-in, this voltage 00:21:04.650 --> 00:21:06.600 align:middle line:90% becomes N3 over N1 times V-in. 00:21:06.600 --> 00:21:10.800 align:middle line:84% So what I get is V3 is equal to D times-- 00:21:10.800 --> 00:21:19.840 align:middle line:84% is equal to-- I'm sorry, V2 is equal to N2 over N1 V1 times D. 00:21:19.840 --> 00:21:26.980 align:middle line:84% And V3 is equal to, ideally, N3 over N1 V1 times D. 00:21:26.980 --> 00:21:30.760 align:middle line:84% So if I wanted a 5-volt output and a 12-volt output, 00:21:30.760 --> 00:21:35.110 align:middle line:90% I just make N3 12/5 of N2. 00:21:35.110 --> 00:21:41.180 align:middle line:84% And boom, I've got my extra output and life is good. 00:21:41.180 --> 00:21:43.460 align:middle line:90% That make sense to everybody? 00:21:43.460 --> 00:21:44.910 align:middle line:90% And of course, I'm not showing-- 00:21:44.910 --> 00:21:48.090 align:middle line:84% I still need a reset mechanism over here, 00:21:48.090 --> 00:21:49.855 align:middle line:84% whether it's that one or some other one. 00:21:49.855 --> 00:21:56.900 align:middle line:90% 00:21:56.900 --> 00:22:01.100 align:middle line:84% So we often see converters with a lot of outputs 00:22:01.100 --> 00:22:03.850 align:middle line:90% when we're building them. 00:22:03.850 --> 00:22:07.390 align:middle line:84% We do have to, however, start thinking, especially when we 00:22:07.390 --> 00:22:11.260 align:middle line:84% have many windings, what are the impacts of all the transformer 00:22:11.260 --> 00:22:15.310 align:middle line:84% parasitics beyond the magnetizing inductance? 00:22:15.310 --> 00:22:18.070 align:middle line:84% And that's why we spent time thinking about what 00:22:18.070 --> 00:22:20.050 align:middle line:90% are the transformer parasitics. 00:22:20.050 --> 00:22:22.120 align:middle line:90% So let's think about this. 00:22:22.120 --> 00:22:25.700 align:middle line:90% If I did this-- 00:22:25.700 --> 00:22:29.510 align:middle line:84% Suppose I come back to my single output magnetizing-- 00:22:29.510 --> 00:22:33.840 align:middle line:90% my single output design here. 00:22:33.840 --> 00:22:38.142 align:middle line:84% What other kind of transformer parasitics might I have? 00:22:38.142 --> 00:22:40.010 align:middle line:90% STUDENT: [INAUDIBLE]. 00:22:40.010 --> 00:22:42.020 align:middle line:84% DAVID PERREAULT: Leakage inductances, yes. 00:22:42.020 --> 00:22:47.480 align:middle line:84% So this circuit, this extra winding in the diode, 00:22:47.480 --> 00:22:51.410 align:middle line:84% will help me capture, recapture, recycle the magnetizing energy 00:22:51.410 --> 00:22:52.670 align:middle line:90% back to the input. 00:22:52.670 --> 00:22:55.353 align:middle line:84% So whereas in the converter I showed you last time, 00:22:55.353 --> 00:22:57.770 align:middle line:84% I threw it away, here, I can recycle it back to the input. 00:22:57.770 --> 00:23:01.550 align:middle line:84% On the other hand, suppose I have some primary leakage here, 00:23:01.550 --> 00:23:03.440 align:middle line:90% LL1. 00:23:03.440 --> 00:23:07.840 align:middle line:84% Energy stored there doesn't get caught. 00:23:07.840 --> 00:23:10.122 align:middle line:90% That won't get recycled. 00:23:10.122 --> 00:23:11.330 align:middle line:90% It's in series with a switch. 00:23:11.330 --> 00:23:12.705 align:middle line:84% I turn the switch off, it's going 00:23:12.705 --> 00:23:14.300 align:middle line:90% to get dumped into the switch. 00:23:14.300 --> 00:23:18.310 align:middle line:84% Now, maybe I just rate my switch to take that energy when 00:23:18.310 --> 00:23:19.940 align:middle line:90% it turns off and eat it. 00:23:19.940 --> 00:23:21.380 align:middle line:90% And you often do that. 00:23:21.380 --> 00:23:25.570 align:middle line:84% Or maybe I go and I add a little Zener diode, or a clamp, 00:23:25.570 --> 00:23:28.090 align:middle line:84% or some other thing, a snubber, which 00:23:28.090 --> 00:23:34.246 align:middle line:84% we'll talk about next class, snubbers, to eat that energy. 00:23:34.246 --> 00:23:36.110 align:middle line:90% But I have to think about that. 00:23:36.110 --> 00:23:38.308 align:middle line:84% And because we're going to be interfacing switches 00:23:38.308 --> 00:23:40.600 align:middle line:84% and transformers, we often have to worry about leakages 00:23:40.600 --> 00:23:42.910 align:middle line:84% that are bigger than I have to think about 00:23:42.910 --> 00:23:46.270 align:middle line:90% in a non-isolated converter. 00:23:46.270 --> 00:23:49.040 align:middle line:90% All right, I can do that. 00:23:49.040 --> 00:23:55.490 align:middle line:84% Let's think about the impact of leakage in a different scenario. 00:23:55.490 --> 00:23:57.470 align:middle line:90% Let's again just simply-- 00:23:57.470 --> 00:24:00.170 align:middle line:84% let's ignore the primary side leakage. 00:24:00.170 --> 00:24:04.400 align:middle line:84% This circuit would take care of eating any primary side leakage 00:24:04.400 --> 00:24:05.272 align:middle line:90% effects. 00:24:05.272 --> 00:24:06.980 align:middle line:84% But let's think about the leakage effects 00:24:06.980 --> 00:24:08.560 align:middle line:90% on the secondary side. 00:24:08.560 --> 00:24:10.975 align:middle line:84% So suppose I build my forward converter again. 00:24:10.975 --> 00:24:14.650 align:middle line:90% 00:24:14.650 --> 00:24:21.030 align:middle line:84% And here is my transformer, my ideal transformer. 00:24:21.030 --> 00:24:24.300 align:middle line:90% 00:24:24.300 --> 00:24:30.660 align:middle line:84% And I am going to run out of room if I draw it that way. 00:24:30.660 --> 00:24:36.930 align:middle line:90% 00:24:36.930 --> 00:24:40.680 align:middle line:90% So here's my transformer. 00:24:40.680 --> 00:24:42.820 align:middle line:90% Here's my V1. 00:24:42.820 --> 00:24:44.620 align:middle line:90% Here's my transformer. 00:24:44.620 --> 00:24:52.710 align:middle line:90% Here's my switch, N1 to N2. 00:24:52.710 --> 00:24:56.980 align:middle line:84% Now, let me worry about a second element. 00:24:56.980 --> 00:24:59.420 align:middle line:90% Let me worry about L leakage 2. 00:24:59.420 --> 00:25:04.450 align:middle line:90% 00:25:04.450 --> 00:25:08.050 align:middle line:84% This is the secondary side leakage inductance. 00:25:08.050 --> 00:25:11.715 align:middle line:84% And then this runs into this diode pair. 00:25:11.715 --> 00:25:17.420 align:middle line:90% 00:25:17.420 --> 00:25:19.860 align:middle line:84% And then this runs into an inductor. 00:25:19.860 --> 00:25:21.510 align:middle line:90% I'll call that current I2. 00:25:21.510 --> 00:25:23.720 align:middle line:84% Let's assume this inductor is really big. 00:25:23.720 --> 00:25:24.830 align:middle line:90% And then I get V2. 00:25:24.830 --> 00:25:29.730 align:middle line:90% 00:25:29.730 --> 00:25:36.130 align:middle line:84% Well, what happens in this circuit when I'm switching? 00:25:36.130 --> 00:25:40.000 align:middle line:84% Well, I might think about a voltage 00:25:40.000 --> 00:25:41.260 align:middle line:90% that I'm going to call Vy. 00:25:41.260 --> 00:25:45.970 align:middle line:90% 00:25:45.970 --> 00:25:48.700 align:middle line:90% Let me use this color for Vy. 00:25:48.700 --> 00:25:52.090 align:middle line:90% Here's Vy, here. 00:25:52.090 --> 00:25:54.110 align:middle line:90% What does Vy look like? 00:25:54.110 --> 00:26:03.680 align:middle line:84% Vy, when I turn the switch on, Vy looks like N2 over N1 V1. 00:26:03.680 --> 00:26:07.450 align:middle line:84% This is Vy in the first part of the cycle. 00:26:07.450 --> 00:26:11.440 align:middle line:84% In the second part of the cycle, it 00:26:11.440 --> 00:26:15.640 align:middle line:84% goes negative to some value that's determined by the clamp 00:26:15.640 --> 00:26:16.580 align:middle line:90% that I'm not showing. 00:26:16.580 --> 00:26:19.150 align:middle line:84% There's some transformer reset mechanism 00:26:19.150 --> 00:26:22.510 align:middle line:84% that's going to make this node clamped, 00:26:22.510 --> 00:26:27.170 align:middle line:84% whether I use this method or some other method. 00:26:27.170 --> 00:26:29.920 align:middle line:84% And it's going to clamp to some value. 00:26:29.920 --> 00:26:32.320 align:middle line:84% And then maybe it'll go to 0 before the beginning 00:26:32.320 --> 00:26:34.160 align:middle line:84% of the next cycle, something like that. 00:26:34.160 --> 00:26:36.640 align:middle line:84% So this is what voltage Vy looks like. 00:26:36.640 --> 00:26:37.530 align:middle line:90% Everybody buy that? 00:26:37.530 --> 00:26:40.110 align:middle line:90% 00:26:40.110 --> 00:26:45.240 align:middle line:84% So let's think about what happens where I have 00:26:45.240 --> 00:26:47.230 align:middle line:90% this secondary side leakage. 00:26:47.230 --> 00:26:49.830 align:middle line:84% And I particularly want to look at-- 00:26:49.830 --> 00:26:53.640 align:middle line:90% I'll call this I leakage 2. 00:26:53.640 --> 00:26:56.970 align:middle line:90% And let me call this device-- 00:26:56.970 --> 00:26:57.763 align:middle line:90% I'll call this D1. 00:26:57.763 --> 00:26:58.680 align:middle line:90% And I'll call this D2. 00:26:58.680 --> 00:27:01.630 align:middle line:90% 00:27:01.630 --> 00:27:02.685 align:middle line:90% So let's plot that. 00:27:02.685 --> 00:27:10.570 align:middle line:90% 00:27:10.570 --> 00:27:12.490 align:middle line:90% So here's my voltage, Vy. 00:27:12.490 --> 00:27:18.367 align:middle line:90% 00:27:18.367 --> 00:27:20.075 align:middle line:84% And it's going to do something like this. 00:27:20.075 --> 00:27:27.360 align:middle line:90% 00:27:27.360 --> 00:27:30.240 align:middle line:84% And I don't have to worry about what happens. 00:27:30.240 --> 00:27:32.015 align:middle line:84% As long as the core resets, I'm happy. 00:27:32.015 --> 00:27:34.630 align:middle line:90% 00:27:34.630 --> 00:27:41.460 align:middle line:84% So this is N2 over N1 times V1 here. 00:27:41.460 --> 00:27:44.420 align:middle line:90% So let's think about that. 00:27:44.420 --> 00:27:48.890 align:middle line:84% And I can really think about Vy as just 00:27:48.890 --> 00:27:51.652 align:middle line:84% being an equivalent source there. 00:27:51.652 --> 00:27:58.040 align:middle line:84% So what's going to happen to that current, IL leakage 2? 00:27:58.040 --> 00:28:00.340 align:middle line:84% So here's what that's going to look like. 00:28:00.340 --> 00:28:06.760 align:middle line:90% 00:28:06.760 --> 00:28:14.920 align:middle line:84% When I turned on the switch L leakage 2 had no current in it 00:28:14.920 --> 00:28:19.370 align:middle line:84% because, before I turned on the switch, D2 was conducting. 00:28:19.370 --> 00:28:21.670 align:middle line:90% So over here, D2 is conducting. 00:28:21.670 --> 00:28:24.430 align:middle line:90% 00:28:24.430 --> 00:28:28.067 align:middle line:84% And there's no current through D1 and no current 00:28:28.067 --> 00:28:28.900 align:middle line:90% through I leakage 2. 00:28:28.900 --> 00:28:29.640 align:middle line:90% So he's 0. 00:28:29.640 --> 00:28:32.440 align:middle line:90% 00:28:32.440 --> 00:28:35.810 align:middle line:84% What's going to happen when I turn the switch on? 00:28:35.810 --> 00:28:37.990 align:middle line:84% Well, suddenly Vy becomes positive. 00:28:37.990 --> 00:28:41.430 align:middle line:90% 00:28:41.430 --> 00:28:43.500 align:middle line:84% On the other hand, I can't change the current 00:28:43.500 --> 00:28:44.640 align:middle line:90% through L leakage 2. 00:28:44.640 --> 00:28:46.560 align:middle line:90% So D2 can't turn off. 00:28:46.560 --> 00:28:49.233 align:middle line:90% D1, however, turns on. 00:28:49.233 --> 00:28:50.650 align:middle line:84% So what I'm going to get-- this is 00:28:50.650 --> 00:28:52.310 align:middle line:84% what we talked about at the beginning of class. 00:28:52.310 --> 00:28:54.250 align:middle line:84% We're going to get a commutation interval. 00:28:54.250 --> 00:28:57.460 align:middle line:84% So what happens is I'm going to get an interval where 00:28:57.460 --> 00:29:01.774 align:middle line:90% D1 and D2 are on. 00:29:01.774 --> 00:29:05.210 align:middle line:84% And so I can think of this circuit 00:29:05.210 --> 00:29:07.460 align:middle line:84% as being like this during that interval. 00:29:07.460 --> 00:29:17.410 align:middle line:84% I have Vy, which is exactly this. 00:29:17.410 --> 00:29:24.100 align:middle line:90% Then I have I leakage 2. 00:29:24.100 --> 00:29:26.260 align:middle line:90% This is L leakage 2. 00:29:26.260 --> 00:29:32.020 align:middle line:84% And then I have D2 one is on and D2 is on. 00:29:32.020 --> 00:29:34.630 align:middle line:84% And maybe I think of the output network 00:29:34.630 --> 00:29:36.890 align:middle line:84% as just being constant during this time. 00:29:36.890 --> 00:29:39.340 align:middle line:90% So this is I 2. 00:29:39.340 --> 00:29:43.810 align:middle line:84% So this is a simplified circuit model there for the interval 00:29:43.810 --> 00:29:48.020 align:middle line:84% after the switch turns on, when D1 and D2 are on. 00:29:48.020 --> 00:29:51.470 align:middle line:84% Does that make sense to everybody? 00:29:51.470 --> 00:29:52.680 align:middle line:90% So what should happen? 00:29:52.680 --> 00:29:56.310 align:middle line:84% I basically have Vy applied across L leakage 2. 00:29:56.310 --> 00:29:59.820 align:middle line:84% And so I have a constant voltage across L leakage. 00:29:59.820 --> 00:30:05.840 align:middle line:84% So I should expect that I leakage 2 should just 00:30:05.840 --> 00:30:09.770 align:middle line:90% ramp up like this, linearly. 00:30:09.770 --> 00:30:12.030 align:middle line:84% How long is it going to ramp up linearly? 00:30:12.030 --> 00:30:14.000 align:middle line:84% It's going to ramp up linearly until I 00:30:14.000 --> 00:30:19.970 align:middle line:84% leakage 2 equals I2, at which point this diode will turn off. 00:30:19.970 --> 00:30:29.450 align:middle line:84% So once I hit I2, then this is going to cease increasing. 00:30:29.450 --> 00:30:30.920 align:middle line:90% This diode is going to turn on. 00:30:30.920 --> 00:30:33.310 align:middle line:84% And then I leakage 2 is just going to carry I2. 00:30:33.310 --> 00:30:36.720 align:middle line:90% And it's going to do this. 00:30:36.720 --> 00:30:38.370 align:middle line:84% If I followed the rest of the cycle, 00:30:38.370 --> 00:30:42.210 align:middle line:84% it'll do the same thing in this, after I turn off the switch. 00:30:42.210 --> 00:30:43.650 align:middle line:90% There's D2. 00:30:43.650 --> 00:30:49.360 align:middle line:84% And it'll go back to 0 the beginning of the next cycle. 00:30:49.360 --> 00:30:53.440 align:middle line:84% So this is what happens with I leakage 2 in this case. 00:30:53.440 --> 00:31:00.840 align:middle line:84% And all I'm doing-- and during this interval, D2 is-- 00:31:00.840 --> 00:31:02.790 align:middle line:90% D1 is on. 00:31:02.790 --> 00:31:08.210 align:middle line:84% So I go from D2 on to D1 and D2 on to D1 on. 00:31:08.210 --> 00:31:11.040 align:middle line:90% Everybody follow that? 00:31:11.040 --> 00:31:13.100 align:middle line:84% So why am I dragging you through this? 00:31:13.100 --> 00:31:14.650 align:middle line:90% Because of the following-- 00:31:14.650 --> 00:31:17.280 align:middle line:90% 00:31:17.280 --> 00:31:20.950 align:middle line:84% let me look at a different voltage now. 00:31:20.950 --> 00:31:24.840 align:middle line:90% Let me look at the voltage Vx. 00:31:24.840 --> 00:31:27.420 align:middle line:90% It's this voltage here. 00:31:27.420 --> 00:31:40.615 align:middle line:84% This voltage is going to be 0 whenever D2 is on. 00:31:40.615 --> 00:31:44.750 align:middle line:90% 00:31:44.750 --> 00:31:51.110 align:middle line:84% So what I'm going to get Is D2 is on. 00:31:51.110 --> 00:31:53.710 align:middle line:90% Vx was 0 because D2 is on. 00:31:53.710 --> 00:32:01.990 align:middle line:84% After this switch turns on, it stays 0 until D2 turns off. 00:32:01.990 --> 00:32:05.800 align:middle line:84% And once D2 turns off, IL2 has a constant current through it. 00:32:05.800 --> 00:32:07.520 align:middle line:90% So it has no drop across it. 00:32:07.520 --> 00:32:11.440 align:middle line:84% And then this will just jump up to a value 00:32:11.440 --> 00:32:16.120 align:middle line:90% that is N2 over N1 times V1. 00:32:16.120 --> 00:32:19.480 align:middle line:90% And it'll stay there until DT. 00:32:19.480 --> 00:32:24.520 align:middle line:84% Then D2 will turn on again and so forth until T. 00:32:24.520 --> 00:32:26.570 align:middle line:90% So let me call this time-- 00:32:26.570 --> 00:32:28.370 align:middle line:84% I didn't specify what this time is called. 00:32:28.370 --> 00:32:32.446 align:middle line:84% Let me call this delta T. And this is DT. 00:32:32.446 --> 00:32:34.970 align:middle line:90% 00:32:34.970 --> 00:32:41.000 align:middle line:84% And the question we have is, what is the average output 00:32:41.000 --> 00:32:43.270 align:middle line:90% voltage of this circuit? 00:32:43.270 --> 00:32:48.010 align:middle line:84% Well, clearly, V2 is just equal to the average voltage of Vx. 00:32:48.010 --> 00:32:50.550 align:middle line:90% 00:32:50.550 --> 00:32:56.800 align:middle line:84% So V2, It's the average of this voltage. 00:32:56.800 --> 00:32:59.350 align:middle line:84% V2 is equal to the average voltage 00:32:59.350 --> 00:33:09.840 align:middle line:84% of vx, which is equal to D minus delta T over T 00:33:09.840 --> 00:33:14.250 align:middle line:90% times N2 over N1 times V1. 00:33:14.250 --> 00:33:16.890 align:middle line:90% 00:33:16.890 --> 00:33:19.610 align:middle line:84% Does that make sense to everybody? 00:33:19.610 --> 00:33:21.260 align:middle line:90% Well, what's delta T? 00:33:21.260 --> 00:33:24.020 align:middle line:90% We have V is equal to L dI/dT. 00:33:24.020 --> 00:33:26.570 align:middle line:90% 00:33:26.570 --> 00:33:32.120 align:middle line:84% So delta T is simply going to be equal to L leakage 2 times 00:33:32.120 --> 00:33:40.080 align:middle line:84% delta I, which is I2 over V, which is N2 over N1 V1. 00:33:40.080 --> 00:33:44.050 align:middle line:84% So this is my expression for this time. 00:33:44.050 --> 00:33:46.180 align:middle line:90% It's just V is equal to L dI/dT. 00:33:46.180 --> 00:33:48.710 align:middle line:90% 00:33:48.710 --> 00:33:50.600 align:middle line:84% That's how long delta T has to be 00:33:50.600 --> 00:33:52.460 align:middle line:90% with a constant applied voltage. 00:33:52.460 --> 00:34:04.040 align:middle line:84% So I can rewrite this as being equal to D N2 over N1 V1 minus 00:34:04.040 --> 00:34:09.790 align:middle line:84% delta T times N2 over N1 V1 L leakage 2 00:34:09.790 --> 00:34:21.020 align:middle line:84% I2, which just gives me minus L leakage 2 over T times I2. 00:34:21.020 --> 00:34:21.710 align:middle line:90% And this is V2. 00:34:21.710 --> 00:34:26.170 align:middle line:90% 00:34:26.170 --> 00:34:30.070 align:middle line:84% Does that make sense to everybody? 00:34:30.070 --> 00:34:32.260 align:middle line:84% This is precisely load regulation, 00:34:32.260 --> 00:34:34.440 align:middle line:84% just like we talked about with rectifiers before. 00:34:34.440 --> 00:34:36.940 align:middle line:84% But we don't have sinusoidal waveforms anymore because we're 00:34:36.940 --> 00:34:39.100 align:middle line:90% building a DC/DC converter. 00:34:39.100 --> 00:34:44.739 align:middle line:84% But the point is that the output voltage V2 no longer just 00:34:44.739 --> 00:34:46.929 align:middle line:84% depends upon the input and voltage and duty ratio. 00:34:46.929 --> 00:34:50.163 align:middle line:84% But it depends upon my load current. 00:34:50.163 --> 00:34:55.000 align:middle line:84% This load current influences my output voltage. 00:34:55.000 --> 00:34:58.980 align:middle line:84% As I2 gets bigger, V2 tends to droop. 00:34:58.980 --> 00:35:02.010 align:middle line:90% 00:35:02.010 --> 00:35:03.360 align:middle line:90% Is that a problem? 00:35:03.360 --> 00:35:04.460 align:middle line:90% Well, not really. 00:35:04.460 --> 00:35:08.070 align:middle line:90% It's a little bit of a problem. 00:35:08.070 --> 00:35:12.510 align:middle line:84% If I have a low load current, if I2 goes towards 0, 00:35:12.510 --> 00:35:14.800 align:middle line:84% well, I just get my ideal relationship. 00:35:14.800 --> 00:35:16.920 align:middle line:84% If I get heavier and heavier load, 00:35:16.920 --> 00:35:18.870 align:middle line:84% depending upon how big our leakage is, 00:35:18.870 --> 00:35:20.218 align:middle line:90% the output voltage droops. 00:35:20.218 --> 00:35:22.260 align:middle line:84% So all I would have to do is to get the right V2, 00:35:22.260 --> 00:35:24.750 align:middle line:84% to the one I really wanted, I'd use a slightly larger duty 00:35:24.750 --> 00:35:25.250 align:middle line:90% ratio. 00:35:25.250 --> 00:35:27.951 align:middle line:90% 00:35:27.951 --> 00:35:28.530 align:middle line:90% Yeah? 00:35:28.530 --> 00:35:30.458 align:middle line:84% STUDENT: Would it also affect the [INAUDIBLE]? 00:35:30.458 --> 00:35:32.250 align:middle line:84% DAVID PERREAULT: Ah, you've put your finger 00:35:32.250 --> 00:35:34.010 align:middle line:90% on the real problem of this. 00:35:34.010 --> 00:35:36.630 align:middle line:90% Yes. 00:35:36.630 --> 00:35:41.460 align:middle line:84% It probably doesn't matter very much in-- 00:35:41.460 --> 00:35:44.290 align:middle line:84% I mean, if L leakage is huge, then I've always got a problem. 00:35:44.290 --> 00:35:49.440 align:middle line:84% But if L leakage is small, maybe I don't care so much. 00:35:49.440 --> 00:35:51.460 align:middle line:84% But it's exactly what you're saying. 00:35:51.460 --> 00:35:53.760 align:middle line:84% Suppose I have my two-output converter. 00:35:53.760 --> 00:35:55.870 align:middle line:90% I only have one duty ratio. 00:35:55.870 --> 00:35:58.350 align:middle line:84% Both of those outputs are being regulated by the same duty 00:35:58.350 --> 00:35:59.290 align:middle line:90% ratio. 00:35:59.290 --> 00:36:04.140 align:middle line:84% And if I wanted ratiometric outputs scaled by N3 over N2, 00:36:04.140 --> 00:36:05.460 align:middle line:90% that's fine. 00:36:05.460 --> 00:36:08.460 align:middle line:84% But now, once I put in leakage, suddenly 00:36:08.460 --> 00:36:12.030 align:middle line:84% I have this term where I have to vary duty ratio based 00:36:12.030 --> 00:36:13.120 align:middle line:90% on the load of L2. 00:36:13.120 --> 00:36:14.490 align:middle line:90% I can only control one output. 00:36:14.490 --> 00:36:16.880 align:middle line:84% And the other output, I get what I get. 00:36:16.880 --> 00:36:18.860 align:middle line:84% And so what will happen is I'll get something 00:36:18.860 --> 00:36:20.650 align:middle line:90% called cross regulation. 00:36:20.650 --> 00:36:24.480 align:middle line:84% That is, suppose I'm controlling V2. 00:36:24.480 --> 00:36:28.200 align:middle line:84% I'm picking duty ratio by my controller to get the V2 I want. 00:36:28.200 --> 00:36:32.040 align:middle line:84% If I get a heavier load, I turn D up, 00:36:32.040 --> 00:36:35.520 align:middle line:84% V2 goes back to where I wanted, but V1 00:36:35.520 --> 00:36:38.350 align:middle line:84% changes because I changed the duty ratio. 00:36:38.350 --> 00:36:42.930 align:middle line:84% So the load on output two affects the voltage on output 3. 00:36:42.930 --> 00:36:44.590 align:middle line:90% And I tend not to like that. 00:36:44.590 --> 00:36:46.900 align:middle line:90% I'm stuck with that. 00:36:46.900 --> 00:36:48.010 align:middle line:90% Yeah? 00:36:48.010 --> 00:36:50.110 align:middle line:84% STUDENT: Doesn't that work the other way around? 00:36:50.110 --> 00:36:53.530 align:middle line:84% Couldn't you do the same analysis for circuit 3, 00:36:53.530 --> 00:36:55.630 align:middle line:90% and then get an equivalent? 00:36:55.630 --> 00:36:56.922 align:middle line:90% DAVID PERREAULT: That's right. 00:36:56.922 --> 00:36:58.630 align:middle line:84% It depends if there's much leakage there, 00:36:58.630 --> 00:37:01.740 align:middle line:90% too, with respect to winding 1. 00:37:01.740 --> 00:37:04.990 align:middle line:90% Yes, certainly. 00:37:04.990 --> 00:37:06.260 align:middle line:90% So there's two points. 00:37:06.260 --> 00:37:08.140 align:middle line:84% First of all, the two outputs are 00:37:08.140 --> 00:37:12.140 align:middle line:84% going to influence one another, which I don't like. 00:37:12.140 --> 00:37:13.890 align:middle line:84% Generally, if I want 5 volts at my output, 00:37:13.890 --> 00:37:15.190 align:middle line:90% I want 5 volts in my output. 00:37:15.190 --> 00:37:17.160 align:middle line:90% What can I do about that? 00:37:17.160 --> 00:37:18.250 align:middle line:90% A few things. 00:37:18.250 --> 00:37:20.310 align:middle line:84% One thing I might do is the output 00:37:20.310 --> 00:37:22.330 align:middle line:84% I really care about that has to be precise, 00:37:22.330 --> 00:37:23.605 align:middle line:90% that's the one I regulate. 00:37:23.605 --> 00:37:25.980 align:middle line:84% And then the other one, if it drifts around a little bit, 00:37:25.980 --> 00:37:27.220 align:middle line:90% maybe I don't care. 00:37:27.220 --> 00:37:30.100 align:middle line:84% Or maybe I put a linear rate, I make it go a little high, 00:37:30.100 --> 00:37:32.305 align:middle line:84% so when it drifts around, it's always high enough. 00:37:32.305 --> 00:37:33.930 align:middle line:84% And then I put a linear regulator there 00:37:33.930 --> 00:37:36.700 align:middle line:84% or I put another conversion stage there. 00:37:36.700 --> 00:37:39.720 align:middle line:84% But now, I'm adding complexity, and loss, and everything else. 00:37:39.720 --> 00:37:44.170 align:middle line:84% So an upside to these multiple output converters 00:37:44.170 --> 00:37:46.690 align:middle line:84% is that I can get multiple outputs. 00:37:46.690 --> 00:37:48.820 align:middle line:84% The downside is maybe I can only get one of them 00:37:48.820 --> 00:37:50.140 align:middle line:90% to be precisely what I want. 00:37:50.140 --> 00:37:52.160 align:middle line:84% And the other moves around a little bit. 00:37:52.160 --> 00:37:53.630 align:middle line:90% How much does it move around? 00:37:53.630 --> 00:37:55.620 align:middle line:84% It depends on your transformer parasitics. 00:37:55.620 --> 00:37:58.120 align:middle line:84% And that's where you start to think very carefully about how 00:37:58.120 --> 00:38:01.655 align:middle line:90% you design your transformer. 00:38:01.655 --> 00:38:02.530 align:middle line:90% Questions about that? 00:38:02.530 --> 00:38:06.120 align:middle line:90% 00:38:06.120 --> 00:38:10.020 align:middle line:84% STUDENT: This might be simple, but can you 00:38:10.020 --> 00:38:13.890 align:middle line:84% explain [INAUDIBLE] in terms of current being commutated, 00:38:13.890 --> 00:38:16.590 align:middle line:84% could you explain like the current paths? 00:38:16.590 --> 00:38:18.140 align:middle line:90% DAVID PERREAULT: Sure. 00:38:18.140 --> 00:38:25.410 align:middle line:84% So what's happening is that what I would ideally like-- 00:38:25.410 --> 00:38:32.750 align:middle line:84% if I didn't have any leakage, before the switch is on, 00:38:32.750 --> 00:38:34.920 align:middle line:90% the current's coming through D2. 00:38:34.920 --> 00:38:37.780 align:middle line:84% The output current is considered I2 constant. 00:38:37.780 --> 00:38:39.360 align:middle line:90% It's coming through D2. 00:38:39.360 --> 00:38:42.080 align:middle line:84% When I turn the switch on, what I would like 00:38:42.080 --> 00:38:45.260 align:middle line:84% is the current come out of this winding of the transformer 00:38:45.260 --> 00:38:47.430 align:middle line:84% and into this winding of the transformer. 00:38:47.430 --> 00:38:50.740 align:middle line:90% 00:38:50.740 --> 00:38:52.420 align:middle line:84% That's easy to do in a buck converter 00:38:52.420 --> 00:38:54.617 align:middle line:84% because I'm connecting those nodes together. 00:38:54.617 --> 00:38:56.450 align:middle line:84% But here, I've got a transformer in between. 00:38:56.450 --> 00:38:57.130 align:middle line:90% He has some leakage. 00:38:57.130 --> 00:38:58.630 align:middle line:84% And that's what causes the headache. 00:38:58.630 --> 00:39:03.210 align:middle line:90% 00:39:03.210 --> 00:39:09.260 align:middle line:84% Nonetheless, we can often get away 00:39:09.260 --> 00:39:12.050 align:middle line:84% with still having just multiple windings. 00:39:12.050 --> 00:39:14.593 align:middle line:84% And many, many converters are built exactly that way. 00:39:14.593 --> 00:39:16.010 align:middle line:84% So I'm not saying it's impossible. 00:39:16.010 --> 00:39:17.040 align:middle line:84% I'm just saying it's another thing you've 00:39:17.040 --> 00:39:19.430 align:middle line:84% got to watch out about, is how precise can you 00:39:19.430 --> 00:39:22.275 align:middle line:84% get your winding outputs and which output 00:39:22.275 --> 00:39:23.400 align:middle line:90% do you care the most about. 00:39:23.400 --> 00:39:25.275 align:middle line:84% And that's the one you'll precisely regulate. 00:39:25.275 --> 00:39:30.670 align:middle line:90% 00:39:30.670 --> 00:39:32.290 align:middle line:90% Let's keep going. 00:39:32.290 --> 00:39:38.010 align:middle line:84% I've only introduced two isolated converters. 00:39:38.010 --> 00:39:41.640 align:middle line:84% And there are arbitrary numbers of kinds of isolated converters 00:39:41.640 --> 00:39:43.620 align:middle line:90% you can build. 00:39:43.620 --> 00:39:47.220 align:middle line:84% But one of the things we said was, well, 00:39:47.220 --> 00:39:49.730 align:middle line:84% why would I choose a forward instead of a flyback? 00:39:49.730 --> 00:39:53.910 align:middle line:84% Because when I get higher power, this 00:39:53.910 --> 00:39:56.760 align:middle line:84% tends to be more compact, even though it has more components. 00:39:56.760 --> 00:39:59.370 align:middle line:84% Particularly, it has more devices and everything. 00:39:59.370 --> 00:40:03.180 align:middle line:84% But because the energy storage elements are smaller, 00:40:03.180 --> 00:40:04.230 align:middle line:90% I'm happier. 00:40:04.230 --> 00:40:05.880 align:middle line:84% And the energy storage elements tend 00:40:05.880 --> 00:40:07.120 align:middle line:90% to dominate the overall size. 00:40:07.120 --> 00:40:09.540 align:middle line:84% What happens if I went still further up in power? 00:40:09.540 --> 00:40:11.230 align:middle line:90% What might I think about doing? 00:40:11.230 --> 00:40:14.610 align:middle line:84% Well, I might end up-- it turns out that these are both 00:40:14.610 --> 00:40:17.740 align:middle line:84% considered, quote unquote, "single-ended" converters. 00:40:17.740 --> 00:40:21.300 align:middle line:84% They drive the transformer one way, 00:40:21.300 --> 00:40:25.380 align:middle line:84% and then let something else reset the core, 00:40:25.380 --> 00:40:29.930 align:middle line:84% apply the voltage that resets the transformer or drives 00:40:29.930 --> 00:40:31.350 align:middle line:90% the transformer flux to 0. 00:40:31.350 --> 00:40:33.560 align:middle line:90% I could get more clever. 00:40:33.560 --> 00:40:36.750 align:middle line:84% Let me show you a different circuit. 00:40:36.750 --> 00:40:39.280 align:middle line:84% It is very closely related to the forward converter. 00:40:39.280 --> 00:40:40.750 align:middle line:90% And maybe it looks like this. 00:40:40.750 --> 00:40:43.550 align:middle line:84% Maybe I will get a full bridge inverter. 00:40:43.550 --> 00:40:48.620 align:middle line:90% 00:40:48.620 --> 00:40:50.230 align:middle line:90% I'll have two switches here. 00:40:50.230 --> 00:41:02.230 align:middle line:90% 00:41:02.230 --> 00:41:07.220 align:middle line:90% So I'll have a transformer. 00:41:07.220 --> 00:41:11.070 align:middle line:90% 00:41:11.070 --> 00:41:18.760 align:middle line:84% And let me call this Q1, Q2, Q3, and Q4. 00:41:18.760 --> 00:41:23.410 align:middle line:84% So now, instead of one switch, I have four. 00:41:23.410 --> 00:41:28.420 align:middle line:90% Here's my transformer, N1 to N2. 00:41:28.420 --> 00:41:31.003 align:middle line:84% Now, I'm going to take the secondary winding 00:41:31.003 --> 00:41:32.920 align:middle line:84% and I'm going to do the same thing, except I'm 00:41:32.920 --> 00:41:34.003 align:middle line:90% going to have four diodes. 00:41:34.003 --> 00:41:36.930 align:middle line:90% 00:41:36.930 --> 00:41:38.930 align:middle line:84% And there's a lot of different versions of this. 00:41:38.930 --> 00:41:40.840 align:middle line:90% I'm just showing you one. 00:41:40.840 --> 00:41:43.540 align:middle line:90% And I'll call this I2. 00:41:43.540 --> 00:41:45.340 align:middle line:90% And here's my output, V2. 00:41:45.340 --> 00:41:50.680 align:middle line:90% 00:41:50.680 --> 00:41:58.330 align:middle line:84% And I will connect this one this way, like this. 00:41:58.330 --> 00:42:00.738 align:middle line:90% So now, what have I done? 00:42:00.738 --> 00:42:02.530 align:middle line:84% Instead of having a forward converter where 00:42:02.530 --> 00:42:05.770 align:middle line:84% I have one switch and some reset mechanism, 00:42:05.770 --> 00:42:07.700 align:middle line:90% I've got four switches. 00:42:07.700 --> 00:42:10.250 align:middle line:84% Instead of having two diodes, I've got four diodes. 00:42:10.250 --> 00:42:12.930 align:middle line:84% So this looks like-- geez, I wouldn't like this very much, 00:42:12.930 --> 00:42:13.430 align:middle line:90% would I? 00:42:13.430 --> 00:42:15.200 align:middle line:84% Because I've got a lot more components. 00:42:15.200 --> 00:42:16.360 align:middle line:90% But what happens? 00:42:16.360 --> 00:42:18.220 align:middle line:90% Let's think about this. 00:42:18.220 --> 00:42:21.850 align:middle line:84% Let me show you the switching patterns of this guy. 00:42:21.850 --> 00:42:26.700 align:middle line:84% What we're going to do is we're going to control this 00:42:26.700 --> 00:42:34.890 align:middle line:84% so that-- let me call this voltage V sub mu. 00:42:34.890 --> 00:42:39.490 align:middle line:90% 00:42:39.490 --> 00:42:42.580 align:middle line:84% And keep in mind, I do have a magnetizing inductance 00:42:42.580 --> 00:42:45.700 align:middle line:84% and a magnetizing current I mu here. 00:42:45.700 --> 00:42:49.690 align:middle line:84% So what I'm going to get is this. 00:42:49.690 --> 00:42:52.890 align:middle line:84% I'm going to control this thing in the following way. 00:42:52.890 --> 00:42:58.870 align:middle line:90% 00:42:58.870 --> 00:43:02.850 align:middle line:84% First, I'll turn on Q1 and Q2 so that I 00:43:02.850 --> 00:43:04.350 align:middle line:90% will apply a V mu that's V1. 00:43:04.350 --> 00:43:11.160 align:middle line:90% 00:43:11.160 --> 00:43:14.060 align:middle line:90% This is V mu. 00:43:14.060 --> 00:43:18.120 align:middle line:84% It's going to go to V1 until some time DT. 00:43:18.120 --> 00:43:21.240 align:middle line:90% 00:43:21.240 --> 00:43:23.190 align:middle line:90% So here, I've got Q1 Q2. 00:43:23.190 --> 00:43:25.800 align:middle line:90% 00:43:25.800 --> 00:43:28.380 align:middle line:90% Then I'll turn on Q2 Q3. 00:43:28.380 --> 00:43:30.540 align:middle line:84% So I'll just short circuit the transformer. 00:43:30.540 --> 00:43:34.970 align:middle line:84% And I'll get V mu is equal to 0 until some time 00:43:34.970 --> 00:43:47.148 align:middle line:84% T. So here's Q2 Q3 until time T. And then I'll turn Q3 Q4 on. 00:43:47.148 --> 00:43:49.690 align:middle line:84% So now, I'm going to apply the voltage across the transformer 00:43:49.690 --> 00:43:50.390 align:middle line:90% the reverse way. 00:43:50.390 --> 00:43:53.140 align:middle line:90% And this is minus V1. 00:43:53.140 --> 00:44:00.510 align:middle line:84% So this is Q3 Q4 until T plus DT. 00:44:00.510 --> 00:44:06.870 align:middle line:90% 00:44:06.870 --> 00:44:21.920 align:middle line:84% And then I'll have Q4 Q1 until 2T, like this, 00:44:21.920 --> 00:44:24.230 align:middle line:90% and then I'll repeat, so forth. 00:44:24.230 --> 00:44:25.730 align:middle line:84% So what I'm going to do is I'm going 00:44:25.730 --> 00:44:32.990 align:middle line:84% to go Q1 Q2 Q2 Q3 Q3 Q4 and Q4 Q1, and then I repeat. 00:44:32.990 --> 00:44:37.500 align:middle line:84% So my actual repeating pattern is in some time 2T. 00:44:37.500 --> 00:44:38.770 align:middle line:90% Why do I do that? 00:44:38.770 --> 00:44:42.150 align:middle line:84% If I apply V mu, I just get a scaled version 00:44:42.150 --> 00:44:44.260 align:middle line:90% of that on the secondary. 00:44:44.260 --> 00:44:50.440 align:middle line:84% And then if I look at this voltage, 00:44:50.440 --> 00:44:53.030 align:middle line:84% remember this voltage here, we had some voltage Vx. 00:44:53.030 --> 00:44:55.630 align:middle line:90% 00:44:55.630 --> 00:44:59.470 align:middle line:84% Let's look at Vx now on this one. 00:44:59.470 --> 00:45:00.705 align:middle line:90% Here's Vx again. 00:45:00.705 --> 00:45:03.250 align:middle line:90% 00:45:03.250 --> 00:45:06.430 align:middle line:84% Vx is just going to take the scaled version of V mu 00:45:06.430 --> 00:45:10.040 align:middle line:84% and then rectify it with this full bridge rectifier. 00:45:10.040 --> 00:45:12.650 align:middle line:84% So it's going to be a flipped version of that 00:45:12.650 --> 00:45:15.130 align:middle line:84% and scaled by the transformer turns ratio. 00:45:15.130 --> 00:45:18.100 align:middle line:90% 00:45:18.100 --> 00:45:20.790 align:middle line:84% And what I'm going to get is this. 00:45:20.790 --> 00:45:27.020 align:middle line:90% 00:45:27.020 --> 00:45:30.150 align:middle line:90% It's going to look like this. 00:45:30.150 --> 00:45:37.780 align:middle line:84% This is going to be N2 over N1 V1 for DT. 00:45:37.780 --> 00:45:39.130 align:middle line:90% And then it's going to be 0. 00:45:39.130 --> 00:45:43.240 align:middle line:84% And then at T plus DT, it's going to be positive again. 00:45:43.240 --> 00:45:45.160 align:middle line:84% And at 2T, it's going to be here. 00:45:45.160 --> 00:45:52.190 align:middle line:84% So this is DT T T plus DT 2T and et cetera. 00:45:52.190 --> 00:45:54.880 align:middle line:84% And what's V2 going to be equal to? 00:45:54.880 --> 00:45:56.800 align:middle line:84% V2 is going to be the average value of Vx. 00:45:56.800 --> 00:46:00.030 align:middle line:90% 00:46:00.030 --> 00:46:06.600 align:middle line:84% It's just going to be equal to D N2 over N1 V1. 00:46:06.600 --> 00:46:09.990 align:middle line:84% So this circuit does the exact same thing 00:46:09.990 --> 00:46:12.960 align:middle line:84% as my standard forward converter-- 00:46:12.960 --> 00:46:17.460 align:middle line:84% turns ratio N2 to N1, control it like D. 00:46:17.460 --> 00:46:19.920 align:middle line:90% It's basically a buck converter. 00:46:19.920 --> 00:46:22.890 align:middle line:90% Make sense to everybody? 00:46:22.890 --> 00:46:25.750 align:middle line:84% So why would I go through all this trouble to do that? 00:46:25.750 --> 00:46:29.280 align:middle line:84% There's a couple reasons I might do it. 00:46:29.280 --> 00:46:32.220 align:middle line:90% Let's look at I mu. 00:46:32.220 --> 00:46:34.090 align:middle line:90% What does I mu look like? 00:46:34.090 --> 00:46:36.030 align:middle line:84% Well, I mu, when I'm applying positive, 00:46:36.030 --> 00:46:38.080 align:middle line:90% it's flowing positive like this. 00:46:38.080 --> 00:46:39.760 align:middle line:90% Then it's 0. 00:46:39.760 --> 00:46:41.850 align:middle line:90% Then it slows down to negative. 00:46:41.850 --> 00:46:45.990 align:middle line:84% And then it's 0, change, and then it shows positive again. 00:46:45.990 --> 00:46:48.090 align:middle line:90% So this is I mu. 00:46:48.090 --> 00:46:53.490 align:middle line:84% And this is delta I mu peak to peak, 00:46:53.490 --> 00:46:57.930 align:middle line:84% which is proportional to delta B peak to peak in the core. 00:46:57.930 --> 00:47:00.680 align:middle line:90% So here's the idea. 00:47:00.680 --> 00:47:02.180 align:middle line:84% There's a whole bunch of reasons why 00:47:02.180 --> 00:47:05.840 align:middle line:84% this circuit's a lot prettier, in terms of its performance. 00:47:05.840 --> 00:47:10.190 align:middle line:84% Here, my transformer flux or my magnetizing current 00:47:10.190 --> 00:47:11.460 align:middle line:90% swung in one direction. 00:47:11.460 --> 00:47:13.500 align:middle line:84% It swung between 0 and a positive value. 00:47:13.500 --> 00:47:14.870 align:middle line:90% Maybe that could be limited. 00:47:14.870 --> 00:47:17.030 align:middle line:84% If I translate the magnetizing current 00:47:17.030 --> 00:47:19.100 align:middle line:84% to magnetic flux [INAUDIBLE] it's 00:47:19.100 --> 00:47:21.740 align:middle line:84% limited to B-max, which is below B-sat. 00:47:21.740 --> 00:47:28.730 align:middle line:84% Here, I get to use the negative to the positive. 00:47:28.730 --> 00:47:33.500 align:middle line:84% So I can swing my transformer flux more before I saturate it. 00:47:33.500 --> 00:47:36.710 align:middle line:84% So if I'm limited by saturation, this converter 00:47:36.710 --> 00:47:38.592 align:middle line:84% is going to lead to a smaller transformer 00:47:38.592 --> 00:47:40.800 align:middle line:84% than the forward converter because it's double-ended. 00:47:40.800 --> 00:47:42.780 align:middle line:84% It swings the flux in both directions. 00:47:42.780 --> 00:47:45.710 align:middle line:90% 00:47:45.710 --> 00:47:52.070 align:middle line:84% Even in cases where you're not limited by the saturation, 00:47:52.070 --> 00:47:54.670 align:middle line:90% you're limited by core loss. 00:47:54.670 --> 00:47:57.810 align:middle line:84% Some core materials actually tend to have-- 00:47:57.810 --> 00:47:59.150 align:middle line:90% well, we didn't cover this. 00:47:59.150 --> 00:48:03.390 align:middle line:84% Some core materials tend to have less loss if you don't 00:48:03.390 --> 00:48:05.600 align:middle line:90% have an offset flux in them. 00:48:05.600 --> 00:48:07.800 align:middle line:90% So this can still be better. 00:48:07.800 --> 00:48:09.740 align:middle line:84% Even if you're not caring about saturation, 00:48:09.740 --> 00:48:10.610 align:middle line:90% this can be still better. 00:48:10.610 --> 00:48:12.193 align:middle line:84% And you get more headroom with respect 00:48:12.193 --> 00:48:15.890 align:middle line:84% to your saturation with this circuit than that circuit. 00:48:15.890 --> 00:48:17.930 align:middle line:84% The other thing that happens is, notice, 00:48:17.930 --> 00:48:24.120 align:middle line:84% these switches all switch once for every 2T. 00:48:24.120 --> 00:48:28.040 align:middle line:84% But the ripple frequency that's on that output inductor 00:48:28.040 --> 00:48:33.650 align:middle line:84% is every T. So what that means is, for the same switching 00:48:33.650 --> 00:48:37.520 align:middle line:84% frequency, I can have higher ripple frequency and hence 00:48:37.520 --> 00:48:40.670 align:middle line:84% a smaller inductor in this circuit. 00:48:40.670 --> 00:48:43.773 align:middle line:84% So what you can see then is I'm making some trade-off. 00:48:43.773 --> 00:48:45.690 align:middle line:84% I'm saying, I'm going to have more components. 00:48:45.690 --> 00:48:46.910 align:middle line:84% Now, I'm going to have four switches. 00:48:46.910 --> 00:48:48.327 align:middle line:84% And I'm going to have four diodes. 00:48:48.327 --> 00:48:51.880 align:middle line:84% But my transformer got better and my inductor got better. 00:48:51.880 --> 00:48:53.980 align:middle line:84% And this is a very typical trade-off 00:48:53.980 --> 00:48:56.620 align:middle line:84% that you see in power electronics design generally, 00:48:56.620 --> 00:48:58.840 align:middle line:84% but in isolated converters especially, 00:48:58.840 --> 00:49:02.230 align:middle line:84% that I will throw more components at it, 00:49:02.230 --> 00:49:06.670 align:middle line:84% I'll have more sophisticated flux swings or controls. 00:49:06.670 --> 00:49:09.790 align:middle line:84% But what I get is smaller passive components. 00:49:09.790 --> 00:49:12.510 align:middle line:84% And so if your life is dominated by the physical size 00:49:12.510 --> 00:49:15.930 align:middle line:84% of your passive components and not by the total component 00:49:15.930 --> 00:49:18.100 align:middle line:90% count, this strategy is better. 00:49:18.100 --> 00:49:22.590 align:middle line:84% So this strategy would be good for 5 kilowatts or 10 kilowatts. 00:49:22.590 --> 00:49:24.930 align:middle line:84% Maybe I would do something like this. 00:49:24.930 --> 00:49:27.370 align:middle line:84% There's a whole bunch of other advantages and trade-offs 00:49:27.370 --> 00:49:29.550 align:middle line:84% I'm not talking about, relating to soft switching 00:49:29.550 --> 00:49:29.970 align:middle line:90% and other things. 00:49:29.970 --> 00:49:31.887 align:middle line:84% And we'll talk about those later in the class. 00:49:31.887 --> 00:49:35.760 align:middle line:84% But this is just to show you the idea from the progression 00:49:35.760 --> 00:49:38.640 align:middle line:84% from simple circuits that maybe have high stresses 00:49:38.640 --> 00:49:41.460 align:middle line:84% to more sophistication, to more sophistication, 00:49:41.460 --> 00:49:43.380 align:middle line:84% to get higher levels of performance, 00:49:43.380 --> 00:49:46.095 align:middle line:84% which tend to become more important at higher power 00:49:46.095 --> 00:49:46.595 align:middle line:90% levels. 00:49:46.595 --> 00:49:49.200 align:middle line:90% 00:49:49.200 --> 00:49:52.110 align:middle line:84% I should say, as a final comment, 00:49:52.110 --> 00:49:55.440 align:middle line:84% there are lots of other kinds of isolated converters. 00:49:55.440 --> 00:49:57.690 align:middle line:84% I show you a converter on the last page of the lecture 00:49:57.690 --> 00:50:01.050 align:middle line:84% notes, which is essentially like an isolated boost converter. 00:50:01.050 --> 00:50:03.060 align:middle line:84% But there are isolated converters 00:50:03.060 --> 00:50:05.100 align:middle line:84% that don't really have any counterpart 00:50:05.100 --> 00:50:07.170 align:middle line:84% in the non-isolated world because they just 00:50:07.170 --> 00:50:08.760 align:middle line:90% choose to use transformers. 00:50:08.760 --> 00:50:14.950 align:middle line:84% And that's your advantage as a good designer, is saying, 00:50:14.950 --> 00:50:19.120 align:middle line:84% I'm going to be more clever than my colleague about which circuit 00:50:19.120 --> 00:50:22.300 align:middle line:84% I choose to use for what and hence have a smaller, cheaper, 00:50:22.300 --> 00:50:25.180 align:middle line:84% higher performance, more efficient circuit, 00:50:25.180 --> 00:50:29.650 align:middle line:84% and hence win in the competition of who's going to make a better 00:50:29.650 --> 00:50:31.500 align:middle line:90% overall system. 00:50:31.500 --> 00:50:32.410 align:middle line:90% So I'm done there. 00:50:32.410 --> 00:50:35.870 align:middle line:84% Are there any final questions before we wrap up today? 00:50:35.870 --> 00:50:37.620 align:middle line:84% STUDENT: Are these other converter designs 00:50:37.620 --> 00:50:38.530 align:middle line:90% in the textbook? 00:50:38.530 --> 00:50:39.990 align:middle line:90% DAVID PERREAULT: Yeah, sure. 00:50:39.990 --> 00:50:41.800 align:middle line:90% And many I didn't talk about. 00:50:41.800 --> 00:50:45.430 align:middle line:84% So I'm just trying to illustrate how things go. 00:50:45.430 --> 00:50:47.370 align:middle line:84% But yes, the isolated converters chapter, 00:50:47.370 --> 00:50:49.560 align:middle line:84% it goes even beyond any of the ones I'm showing here 00:50:49.560 --> 00:50:52.750 align:middle line:84% and shows a whole bunch of other ways to do it. 00:50:52.750 --> 00:50:56.830 align:middle line:84% And the last thing I'll note is next class, 00:50:56.830 --> 00:50:58.330 align:middle line:90% we're going to come back-- 00:50:58.330 --> 00:50:59.590 align:middle line:90% I'm actually not going to-- 00:50:59.590 --> 00:51:02.140 align:middle line:90% Dr. Zahn is going to present. 00:51:02.140 --> 00:51:05.170 align:middle line:84% But he's going to talk about some very important things. 00:51:05.170 --> 00:51:08.890 align:middle line:84% How do you deal with stuff like leakages 00:51:08.890 --> 00:51:10.277 align:middle line:90% and capturing that energy? 00:51:10.277 --> 00:51:11.860 align:middle line:84% And then we'll talk about other things 00:51:11.860 --> 00:51:15.010 align:middle line:84% like thermal, like how do I deal with all the heat 00:51:15.010 --> 00:51:16.850 align:middle line:84% that we don't want to generate, but we do. 00:51:16.850 --> 00:51:18.040 align:middle line:84% So in the next couple of classes, 00:51:18.040 --> 00:51:20.350 align:middle line:84% we're going to talk about some of these very practical 00:51:20.350 --> 00:51:21.710 align:middle line:90% implementation issues. 00:51:21.710 --> 00:51:23.640 align:middle line:90% Have a great day. 00:51:23.640 --> 00:51:26.000 align:middle line:90%