WEBVTT 00:00:00.000 --> 00:00:01.476 align:middle line:90% [SQUEAKING] 00:00:01.476 --> 00:00:02.952 align:middle line:90% [RUSTLING] 00:00:02.952 --> 00:00:06.396 align:middle line:90% [CLICKING] 00:00:06.396 --> 00:00:09.860 align:middle line:90% 00:00:09.860 --> 00:00:11.780 align:middle line:84% DAVID PERREAULT: Why don't we get started? 00:00:11.780 --> 00:00:15.530 align:middle line:84% So last class, we were continuing 00:00:15.530 --> 00:00:18.230 align:middle line:84% to talk about DC-to-DC converters. 00:00:18.230 --> 00:00:22.310 align:middle line:84% And we saw both the buck and the boost converter, 00:00:22.310 --> 00:00:25.440 align:middle line:90% which could each be considered-- 00:00:25.440 --> 00:00:28.700 align:middle line:84% one way to look at it is to consider each of them 00:00:28.700 --> 00:00:33.190 align:middle line:84% a connection of a certain so-called canonical cell. 00:00:33.190 --> 00:00:36.470 align:middle line:84% So for example, we could have a structure 00:00:36.470 --> 00:00:40.370 align:middle line:84% like this, where we had one inductor, 00:00:40.370 --> 00:00:47.050 align:middle line:84% a single-pole, double-throw switch, and one capacitor. 00:00:47.050 --> 00:00:53.050 align:middle line:84% And connections of this two-port structure 00:00:53.050 --> 00:00:57.590 align:middle line:84% suddenly would let us build a converter. 00:00:57.590 --> 00:01:01.390 align:middle line:84% And one example-- and we often implement 00:01:01.390 --> 00:01:03.850 align:middle line:84% this single-pole, double-throw switch 00:01:03.850 --> 00:01:07.690 align:middle line:84% with two semiconductor devices acting 00:01:07.690 --> 00:01:09.730 align:middle line:84% as single-pole, single-throw switches. 00:01:09.730 --> 00:01:12.280 align:middle line:84% So for example, one way we could do this 00:01:12.280 --> 00:01:16.165 align:middle line:84% if we connected a source V1 here-- 00:01:16.165 --> 00:01:18.730 align:middle line:90% 00:01:18.730 --> 00:01:24.310 align:middle line:84% and then we would implement that single-pole, double-throw switch 00:01:24.310 --> 00:01:29.260 align:middle line:84% perhaps with a MOSFET and a diode. 00:01:29.260 --> 00:01:32.230 align:middle line:90% 00:01:32.230 --> 00:01:37.390 align:middle line:84% And we'd have an output voltage here that we connect to a load 00:01:37.390 --> 00:01:40.390 align:middle line:90% and call that V2. 00:01:40.390 --> 00:01:45.190 align:middle line:84% So we saw this converter, where we could deliver energy 00:01:45.190 --> 00:01:48.940 align:middle line:90% from a source V1 to a load V2. 00:01:48.940 --> 00:01:51.250 align:middle line:90% And we analyzed this operation. 00:01:51.250 --> 00:01:56.170 align:middle line:84% And we could say, suppose I turn this switch on with some signal 00:01:56.170 --> 00:01:59.050 align:middle line:90% q of t or a signal-- 00:01:59.050 --> 00:02:02.440 align:middle line:84% switching signal where when q of t is 1, the switch is on. 00:02:02.440 --> 00:02:04.360 align:middle line:84% When q of t is 0, the switch is off. 00:02:04.360 --> 00:02:09.639 align:middle line:84% So that's like saying q of t is 1 when the switch is 00:02:09.639 --> 00:02:11.740 align:middle line:90% in the down position. 00:02:11.740 --> 00:02:21.002 align:middle line:84% And so if we did that, something like this, 00:02:21.002 --> 00:02:22.580 align:middle line:90% with some duty ratio-- 00:02:22.580 --> 00:02:29.410 align:middle line:84% so here's DT and T, here's q of t-- 00:02:29.410 --> 00:02:32.320 align:middle line:84% we can analyze what's going on in part 00:02:32.320 --> 00:02:39.800 align:middle line:84% by looking at, for example, the voltage across this inductor. 00:02:39.800 --> 00:02:44.440 align:middle line:84% So if I call this V sub L, we could 00:02:44.440 --> 00:02:55.650 align:middle line:84% see that if the switch is on V sub L has V1 applied across it. 00:02:55.650 --> 00:02:58.480 align:middle line:90% So I could have a voltage V1. 00:02:58.480 --> 00:03:01.690 align:middle line:90% 00:03:01.690 --> 00:03:04.795 align:middle line:84% So I apply a voltage V1 in the first part of the cycle. 00:03:04.795 --> 00:03:07.720 align:middle line:90% 00:03:07.720 --> 00:03:11.930 align:middle line:84% And I will have a positive current in this inductor. 00:03:11.930 --> 00:03:16.210 align:middle line:84% And when I turn the switch off, this inductor 00:03:16.210 --> 00:03:19.720 align:middle line:84% will then turn on the diode and deliver that current 00:03:19.720 --> 00:03:21.700 align:middle line:90% to the output. 00:03:21.700 --> 00:03:23.197 align:middle line:84% So in the second part of the cycle, 00:03:23.197 --> 00:03:25.280 align:middle line:84% what do we have for a voltage across the inductor? 00:03:25.280 --> 00:03:27.990 align:middle line:90% We have V1 minus V2. 00:03:27.990 --> 00:03:29.560 align:middle line:90% So if we assume that's-- 00:03:29.560 --> 00:03:32.140 align:middle line:90% 00:03:32.140 --> 00:03:34.630 align:middle line:84% V2 is being held almost constant because the inductor 00:03:34.630 --> 00:03:36.850 align:middle line:84% and the capacitors are supposed to be big here, 00:03:36.850 --> 00:03:42.760 align:middle line:84% then we would have a voltage V1 minus V2 00:03:42.760 --> 00:03:45.760 align:middle line:84% across the inductor in the second part of the cycle. 00:03:45.760 --> 00:03:50.080 align:middle line:84% And what do we know about the average voltage 00:03:50.080 --> 00:03:54.010 align:middle line:84% across an inductor in periodic steady state? 00:03:54.010 --> 00:03:55.660 align:middle line:90% It's got to be 0. 00:03:55.660 --> 00:03:59.110 align:middle line:84% So if I'm going to be in periodic steady state, 00:03:59.110 --> 00:04:01.400 align:middle line:90% I need a 0 average voltage. 00:04:01.400 --> 00:04:04.870 align:middle line:84% That suggests that this voltage, V1 minus V2, 00:04:04.870 --> 00:04:09.940 align:middle line:84% had better be negative in order to get a 0 average 00:04:09.940 --> 00:04:10.970 align:middle line:90% voltage across it. 00:04:10.970 --> 00:04:15.310 align:middle line:84% So another way we could look at this periodic steady-state 00:04:15.310 --> 00:04:18.820 align:middle line:84% operating condition is to look at the voltage waveform 00:04:18.820 --> 00:04:25.690 align:middle line:84% across the inductor and then say, well, hey, 00:04:25.690 --> 00:04:33.145 align:middle line:84% I need the average value of VL equal to 0 in PSS. 00:04:33.145 --> 00:04:36.050 align:middle line:90% 00:04:36.050 --> 00:04:37.660 align:middle line:84% And what that means is essentially 00:04:37.660 --> 00:04:40.960 align:middle line:84% that this area, this positive area, 00:04:40.960 --> 00:04:45.140 align:middle line:84% must exactly balance this negative area 00:04:45.140 --> 00:04:48.640 align:middle line:84% because the average voltage across this inductor 00:04:48.640 --> 00:04:58.340 align:middle line:84% would simply be DV1 plus 1 minus D V1 minus V2. 00:04:58.340 --> 00:05:03.360 align:middle line:84% And if I then take and solve this equation, 00:05:03.360 --> 00:05:10.710 align:middle line:84% what I get is V2 in periodic steady state must equal V1 over 00:05:10.710 --> 00:05:19.980 align:middle line:84% 1 minus D. And since D is a fraction of a time-- this is DT, 00:05:19.980 --> 00:05:21.270 align:middle line:90% it's a fraction of a period-- 00:05:21.270 --> 00:05:24.190 align:middle line:90% 00:05:24.190 --> 00:05:27.100 align:middle line:84% V2 must end up being bigger than V1 such 00:05:27.100 --> 00:05:30.610 align:middle line:84% that V1 minus V2 is a negative number. 00:05:30.610 --> 00:05:33.520 align:middle line:84% So the way this converter will operate 00:05:33.520 --> 00:05:36.550 align:middle line:84% is if the output voltage isn't big enough, 00:05:36.550 --> 00:05:39.047 align:middle line:84% then I will have a positive average value 00:05:39.047 --> 00:05:39.880 align:middle line:90% across the inductor. 00:05:39.880 --> 00:05:41.800 align:middle line:84% And the inductor current will keep building up 00:05:41.800 --> 00:05:43.883 align:middle line:84% until it's delivering enough current to the output 00:05:43.883 --> 00:05:46.960 align:middle line:84% to raise the output voltage such that it's 00:05:46.960 --> 00:05:50.610 align:middle line:84% in this periodic steady-state operation. 00:05:50.610 --> 00:05:55.365 align:middle line:84% And what we would expect to see for an inductor current-- 00:05:55.365 --> 00:05:56.740 align:middle line:84% the ripple on this would be small 00:05:56.740 --> 00:05:58.640 align:middle line:84% if I assume the inductor is large. 00:05:58.640 --> 00:06:02.140 align:middle line:84% But if I was plotting-- if this is V sub L 00:06:02.140 --> 00:06:04.815 align:middle line:84% and I was plotting I sub L, maybe I 00:06:04.815 --> 00:06:08.890 align:middle line:84% sub L would go up in the first part of the cycle 00:06:08.890 --> 00:06:11.410 align:middle line:84% because I'm applying a positive voltage across it 00:06:11.410 --> 00:06:14.150 align:middle line:84% and would go down in the second part of the cycle. 00:06:14.150 --> 00:06:19.282 align:middle line:84% So it would be this triangular waveform, ideally speaking. 00:06:19.282 --> 00:06:21.520 align:middle line:84% And I'd be in periodic steady-state operation 00:06:21.520 --> 00:06:25.190 align:middle line:84% where it ended up just in the same place it started 00:06:25.190 --> 00:06:26.440 align:middle line:90% at the beginning of the cycle. 00:06:26.440 --> 00:06:31.884 align:middle line:84% And then that would be periodic steady-state operation. 00:06:31.884 --> 00:06:36.720 align:middle line:90% So this is the boost converter. 00:06:36.720 --> 00:06:38.310 align:middle line:90% I can also even look at this. 00:06:38.310 --> 00:06:47.960 align:middle line:84% And I can say, hey, if I have my rule here, 00:06:47.960 --> 00:06:54.320 align:middle line:84% V2 is equal to V1 over 1 minus D in periodic steady state, 00:06:54.320 --> 00:06:55.590 align:middle line:90% what else could I see? 00:06:55.590 --> 00:07:02.090 align:middle line:84% I could argue that I2 ought to be equal to I1 times 1 00:07:02.090 --> 00:07:08.570 align:middle line:84% minus D, where I'm defining in this case the DC current 00:07:08.570 --> 00:07:13.310 align:middle line:84% here as being I1, the DC component of this input 00:07:13.310 --> 00:07:19.180 align:middle line:84% current being I1, which is also IL, and this current being I2. 00:07:19.180 --> 00:07:22.470 align:middle line:90% 00:07:22.470 --> 00:07:24.150 align:middle line:90% And how do I get that? 00:07:24.150 --> 00:07:29.160 align:middle line:84% It's because V2I2 has to equal V1I1. 00:07:29.160 --> 00:07:31.615 align:middle line:84% I'm assuming it's lossless in that example. 00:07:31.615 --> 00:07:34.146 align:middle line:90% 00:07:34.146 --> 00:07:39.770 align:middle line:84% So we can very quickly get to how we think 00:07:39.770 --> 00:07:41.610 align:middle line:90% this circuit ought to operate. 00:07:41.610 --> 00:07:44.670 align:middle line:84% Are there any questions about the boost converter? 00:07:44.670 --> 00:07:48.397 align:middle line:90% 00:07:48.397 --> 00:07:50.230 align:middle line:84% AUDIENCE: I'm just looking at the notation-- 00:07:50.230 --> 00:07:53.880 align:middle line:84% so with the orange curve that we've drawn, I is changing. 00:07:53.880 --> 00:07:55.750 align:middle line:90% But then we wrote a capital I1. 00:07:55.750 --> 00:07:56.890 align:middle line:90% Can you say more from that? 00:07:56.890 --> 00:07:58.390 align:middle line:84% DAVID PERREAULT: Excellent question. 00:07:58.390 --> 00:08:06.710 align:middle line:84% So strictly speaking-- it's a very good question. 00:08:06.710 --> 00:08:09.840 align:middle line:84% Strictly speaking, this is I sub L of T. 00:08:09.840 --> 00:08:16.450 align:middle line:84% So I've plotted I sub L of T here. 00:08:16.450 --> 00:08:25.650 align:middle line:84% And then I1-- if I wanted to put I1 in here, it would be, 00:08:25.650 --> 00:08:28.480 align:middle line:90% essentially, its average value. 00:08:28.480 --> 00:08:31.485 align:middle line:90% This would be IL is equal to I1. 00:08:31.485 --> 00:08:34.086 align:middle line:90% 00:08:34.086 --> 00:08:36.000 align:middle line:84% And of course, if I make the inductor 00:08:36.000 --> 00:08:42.080 align:middle line:84% induct bigger and bigger and bigger, there's no distinction. 00:08:42.080 --> 00:08:45.020 align:middle line:84% The reason I wanted to plot the ripple 00:08:45.020 --> 00:08:47.570 align:middle line:84% here is because in the first part of the cycle, 00:08:47.570 --> 00:08:50.360 align:middle line:84% you can see we're putting energy into the inductor 00:08:50.360 --> 00:08:52.340 align:middle line:84% because the inductor current's rising. 00:08:52.340 --> 00:08:53.840 align:middle line:84% And in the second part of the cycle, 00:08:53.840 --> 00:08:55.840 align:middle line:84% we're taking the energy back out of the inductor 00:08:55.840 --> 00:08:58.640 align:middle line:90% and putting it to the output. 00:08:58.640 --> 00:08:59.265 align:middle line:90% Great question. 00:08:59.265 --> 00:09:02.691 align:middle line:90% 00:09:02.691 --> 00:09:06.990 align:middle line:84% So that was an example converter. 00:09:06.990 --> 00:09:09.360 align:middle line:84% And you can see that we implemented 00:09:09.360 --> 00:09:12.120 align:middle line:84% this single-pole, double-throw switch as a pair 00:09:12.120 --> 00:09:14.730 align:middle line:90% of semiconductor devices. 00:09:14.730 --> 00:09:17.790 align:middle line:84% I'd like to talk a little bit more 00:09:17.790 --> 00:09:21.750 align:middle line:84% about how we would implement that. 00:09:21.750 --> 00:09:27.120 align:middle line:84% Typically, I would implement any device 00:09:27.120 --> 00:09:31.590 align:middle line:84% like this as some pair of devices, 00:09:31.590 --> 00:09:34.860 align:middle line:84% two actual physical semiconductor devices, 00:09:34.860 --> 00:09:38.010 align:middle line:84% because what I get is single-pole, 00:09:38.010 --> 00:09:40.080 align:middle line:84% single-throw switches from a device. 00:09:40.080 --> 00:09:43.110 align:middle line:90% I turn them on or off. 00:09:43.110 --> 00:09:45.390 align:middle line:84% But what I can do with my converter 00:09:45.390 --> 00:09:49.080 align:middle line:84% depends upon how I implement those devices. 00:09:49.080 --> 00:09:52.800 align:middle line:84% So let's talk about the capabilities 00:09:52.800 --> 00:09:55.437 align:middle line:84% of different semiconductor switch devices. 00:09:55.437 --> 00:09:57.270 align:middle line:84% By the way, there's nothing that says I have 00:09:57.270 --> 00:09:58.570 align:middle line:90% to use a semiconductor device. 00:09:58.570 --> 00:10:00.362 align:middle line:84% In theory, I could use a mechanical switch. 00:10:00.362 --> 00:10:03.066 align:middle line:84% But it'd just be pretty horrible. 00:10:03.066 --> 00:10:06.120 align:middle line:84% And people have tried other things historically. 00:10:06.120 --> 00:10:07.830 align:middle line:84% But in the modern world, everybody 00:10:07.830 --> 00:10:10.350 align:middle line:90% uses semiconductor devices. 00:10:10.350 --> 00:10:13.800 align:middle line:84% So let's think about the capabilities of different kinds 00:10:13.800 --> 00:10:17.460 align:middle line:90% of power semiconductor devices. 00:10:17.460 --> 00:10:22.370 align:middle line:84% Perhaps one very common device would be the power MOSFET. 00:10:22.370 --> 00:10:27.530 align:middle line:90% 00:10:27.530 --> 00:10:32.840 align:middle line:84% And I'll focus on the end channel one 00:10:32.840 --> 00:10:37.130 align:middle line:84% because that's perhaps the most common because 00:10:37.130 --> 00:10:38.880 align:middle line:90% of its good performance. 00:10:38.880 --> 00:10:42.250 align:middle line:84% So the symbol for this device would be like this. 00:10:42.250 --> 00:10:46.750 align:middle line:90% 00:10:46.750 --> 00:10:50.140 align:middle line:84% And a power MOSFET, by the way, is a vertical device. 00:10:50.140 --> 00:10:53.360 align:middle line:84% It conducts current through the thickness of the device. 00:10:53.360 --> 00:10:57.270 align:middle line:84% So it's a little bit different than a typical device 00:10:57.270 --> 00:10:59.770 align:middle line:84% on an integrated circuit, which is usually a lateral device. 00:10:59.770 --> 00:11:03.220 align:middle line:84% But you can use lateral power MOSFETs, as well, 00:11:03.220 --> 00:11:07.240 align:middle line:84% if you're doing an integrated semiconductor process. 00:11:07.240 --> 00:11:11.170 align:middle line:84% How might I think of this device if this was the drain, 00:11:11.170 --> 00:11:12.710 align:middle line:90% the source, and the gate? 00:11:12.710 --> 00:11:15.490 align:middle line:90% What would it do? 00:11:15.490 --> 00:11:20.080 align:middle line:84% Well, this device can carry positive-- it can block. 00:11:20.080 --> 00:11:24.520 align:middle line:84% If I thought of this as V switch and I thought of this 00:11:24.520 --> 00:11:33.430 align:middle line:84% as I switch, it can block positive voltage 00:11:33.430 --> 00:11:39.780 align:middle line:84% and carry positive or negative current. 00:11:39.780 --> 00:11:46.390 align:middle line:84% And in fact, if you look inside a power MOSFET at its structure, 00:11:46.390 --> 00:11:49.990 align:middle line:84% for free, what you get is a built-in-- people 00:11:49.990 --> 00:11:51.160 align:middle line:90% often don't draw this. 00:11:51.160 --> 00:11:56.320 align:middle line:84% But you get a built-in so-called body diode. 00:11:56.320 --> 00:11:59.950 align:middle line:84% So whether you want it or not, there's an effective diode here 00:11:59.950 --> 00:12:02.800 align:middle line:84% that if you try to put reverse voltage on, it will turn on. 00:12:02.800 --> 00:12:05.180 align:middle line:84% And it can carry current in the negative direction, 00:12:05.180 --> 00:12:07.690 align:middle line:84% or you can turn the device on physically through its gate 00:12:07.690 --> 00:12:09.290 align:middle line:84% and carry current in the channel. 00:12:09.290 --> 00:12:13.530 align:middle line:84% But the point is I can block positive voltage. 00:12:13.530 --> 00:12:17.080 align:middle line:84% I can't block negative voltage because of this device, 00:12:17.080 --> 00:12:19.490 align:middle line:84% because of this internal parasitic device. 00:12:19.490 --> 00:12:23.360 align:middle line:84% But I can carry current in both directions. 00:12:23.360 --> 00:12:25.720 align:middle line:84% The way you might think of a power 00:12:25.720 --> 00:12:31.160 align:middle line:84% MOSFET as a simplified model is with something like this. 00:12:31.160 --> 00:12:36.700 align:middle line:84% Maybe it has some parasitic on-state resistance, 00:12:36.700 --> 00:12:41.900 align:middle line:84% a switch that you control with the gate, and then 00:12:41.900 --> 00:12:43.000 align:middle line:90% a reverse diode. 00:12:43.000 --> 00:12:47.370 align:middle line:90% 00:12:47.370 --> 00:12:50.950 align:middle line:84% So that might be the way you could mentally model a device. 00:12:50.950 --> 00:12:55.020 align:middle line:84% And of course, an ideal device would have 0 resistance. 00:12:55.020 --> 00:12:59.850 align:middle line:84% But real device has real resistance, and so forth. 00:12:59.850 --> 00:13:01.420 align:middle line:90% A lot of other devices-- 00:13:01.420 --> 00:13:03.630 align:middle line:84% actually, a lot of other semiconductor devices 00:13:03.630 --> 00:13:06.540 align:middle line:84% that you can put into active circuitry 00:13:06.540 --> 00:13:08.590 align:middle line:90% behave in a similar fashion. 00:13:08.590 --> 00:13:12.120 align:middle line:84% So for example, very popular lately 00:13:12.120 --> 00:13:18.030 align:middle line:84% are gallium nitride HEMTs, high-electron-mobility 00:13:18.030 --> 00:13:18.700 align:middle line:90% transistors. 00:13:18.700 --> 00:13:21.193 align:middle line:84% The symbol for that is very similar, actually. 00:13:21.193 --> 00:13:23.110 align:middle line:84% People use different symbols for these things. 00:13:23.110 --> 00:13:25.440 align:middle line:90% Sometimes they look like this. 00:13:25.440 --> 00:13:27.720 align:middle line:84% But they behave effectively similarly. 00:13:27.720 --> 00:13:29.070 align:middle line:90% They don't have a body diode. 00:13:29.070 --> 00:13:30.960 align:middle line:90% But they act like they do. 00:13:30.960 --> 00:13:33.420 align:middle line:90% They'll turn on and reverse. 00:13:33.420 --> 00:13:38.878 align:middle line:84% So there's a whole class of devices that will act like this. 00:13:38.878 --> 00:13:40.170 align:middle line:90% They'll block positive voltage. 00:13:40.170 --> 00:13:43.030 align:middle line:84% And they'll carry positive and negative current. 00:13:43.030 --> 00:13:50.720 align:middle line:84% If I thought of the I-V plane for the devices, 00:13:50.720 --> 00:13:56.930 align:middle line:84% I might think of if this is the current-carrying direction 00:13:56.930 --> 00:13:59.100 align:middle line:84% and this is the voltage-blocking direction, 00:13:59.100 --> 00:14:00.910 align:middle line:90% maybe I have four quadrants. 00:14:00.910 --> 00:14:04.430 align:middle line:90% 00:14:04.430 --> 00:14:08.570 align:middle line:84% This device can block positive voltage 00:14:08.570 --> 00:14:11.010 align:middle line:84% and can carry positive or negative current. 00:14:11.010 --> 00:14:13.326 align:middle line:84% So it operates in these two quadrants. 00:14:13.326 --> 00:14:16.670 align:middle line:90% 00:14:16.670 --> 00:14:18.630 align:middle line:84% What other kinds of devices could I get? 00:14:18.630 --> 00:14:19.920 align:middle line:90% Why do I focus on that? 00:14:19.920 --> 00:14:22.520 align:middle line:84% Well, suppose I went out and bought 00:14:22.520 --> 00:14:28.080 align:middle line:84% an IGBT, an insulated-gate bipolar transistor. 00:14:28.080 --> 00:14:31.010 align:middle line:84% These, in recent years, have been very popular 00:14:31.010 --> 00:14:33.240 align:middle line:84% for motor drives, things like that. 00:14:33.240 --> 00:14:35.240 align:middle line:84% They don't go to very high frequencies. 00:14:35.240 --> 00:14:36.380 align:middle line:90% But they're inexpensive. 00:14:36.380 --> 00:14:38.880 align:middle line:90% And they carry a lot of current. 00:14:38.880 --> 00:14:41.460 align:middle line:90% And so an IGBT-- 00:14:41.460 --> 00:14:43.490 align:middle line:84% the symbol for it looks like this. 00:14:43.490 --> 00:14:46.680 align:middle line:90% 00:14:46.680 --> 00:14:49.000 align:middle line:84% So it's like a bipolar transistor 00:14:49.000 --> 00:14:50.560 align:middle line:90% with an isolated gate. 00:14:50.560 --> 00:14:54.910 align:middle line:84% You can think of it as a isolated-gate controlled bipolar 00:14:54.910 --> 00:14:55.700 align:middle line:90% transistor. 00:14:55.700 --> 00:14:58.190 align:middle line:84% One could use a bipolar junction transistor. 00:14:58.190 --> 00:14:59.740 align:middle line:90% And back in the day, people did. 00:14:59.740 --> 00:15:02.530 align:middle line:84% But almost nobody would use these devices anymore 00:15:02.530 --> 00:15:05.080 align:middle line:84% because they're kind of horrible. 00:15:05.080 --> 00:15:09.760 align:middle line:84% These devices have a slightly different characteristic. 00:15:09.760 --> 00:15:16.155 align:middle line:84% These can block positive voltage and carry positive current. 00:15:16.155 --> 00:15:20.108 align:middle line:90% 00:15:20.108 --> 00:15:23.280 align:middle line:84% But if you try to shove current in the reverse direction 00:15:23.280 --> 00:15:27.570 align:middle line:84% through this or put a reverse voltage on it to do so, 00:15:27.570 --> 00:15:30.130 align:middle line:90% you'll generally blow them up. 00:15:30.130 --> 00:15:34.230 align:middle line:84% So that would be an unhappy thing to do. 00:15:34.230 --> 00:15:37.620 align:middle line:84% If you're going to use that device, don't do that. 00:15:37.620 --> 00:15:42.400 align:middle line:84% I should say there are exceptions to everything. 00:15:42.400 --> 00:15:44.670 align:middle line:84% There are something called reverse blocking IGBTs. 00:15:44.670 --> 00:15:46.190 align:middle line:90% But they're not very common. 00:15:46.190 --> 00:15:48.210 align:middle line:84% So you always have to look at the data sheet. 00:15:48.210 --> 00:15:51.734 align:middle line:90% But most can't do that. 00:15:51.734 --> 00:15:57.370 align:middle line:84% So what would I do if there was some chance I might get current 00:15:57.370 --> 00:16:00.740 align:middle line:84% going negative here and I wanted to deal with that? 00:16:00.740 --> 00:16:07.620 align:middle line:84% Well, I might go and say, let me go take my IGBT. 00:16:07.620 --> 00:16:10.840 align:middle line:90% 00:16:10.840 --> 00:16:14.600 align:middle line:84% And it can block voltage this way 00:16:14.600 --> 00:16:17.480 align:middle line:90% and can carry current this way. 00:16:17.480 --> 00:16:25.160 align:middle line:84% And what I'll do is I will go out and buy a diode. 00:16:25.160 --> 00:16:27.440 align:middle line:84% And I will stick a diode in antiparallel 00:16:27.440 --> 00:16:33.290 align:middle line:84% with it, for example, so that now this diode 00:16:33.290 --> 00:16:35.663 align:middle line:84% can carry current in the reverse direction 00:16:35.663 --> 00:16:37.580 align:middle line:84% and can still block in the positive direction. 00:16:37.580 --> 00:16:44.120 align:middle line:84% And this hybrid switch can block positive voltage 00:16:44.120 --> 00:16:48.020 align:middle line:84% and carry positive and negative current. 00:16:48.020 --> 00:16:50.270 align:middle line:84% So a lot of circuits-- you actually 00:16:50.270 --> 00:16:55.220 align:middle line:84% do add diodes to your-- in antiparallel with your IGBTs 00:16:55.220 --> 00:16:58.250 align:middle line:84% because the circuit may get into a situation, at least 00:16:58.250 --> 00:17:00.950 align:middle line:84% transiently, where you do carry negative current. 00:17:00.950 --> 00:17:01.640 align:middle line:90% Yeah? 00:17:01.640 --> 00:17:03.620 align:middle line:84% AUDIENCE: Sorry, can you just remind 00:17:03.620 --> 00:17:05.822 align:middle line:90% me, what do you mean by block? 00:17:05.822 --> 00:17:07.280 align:middle line:84% DAVID PERREAULT: So in other words, 00:17:07.280 --> 00:17:10.940 align:middle line:84% in this case, if I turn the switch off, 00:17:10.940 --> 00:17:13.250 align:middle line:84% if I think of it as a switch that's off, 00:17:13.250 --> 00:17:17.490 align:middle line:84% here's V switch And let me repeat the question. 00:17:17.490 --> 00:17:20.359 align:middle line:84% The question is, what do I mean by it can block 00:17:20.359 --> 00:17:22.170 align:middle line:90% a certain direction of voltage? 00:17:22.170 --> 00:17:24.890 align:middle line:84% If I define this as voltage V switch 00:17:24.890 --> 00:17:27.170 align:middle line:84% and I go and turn the switch off, 00:17:27.170 --> 00:17:31.930 align:middle line:84% it can allow a polarity of voltage this way. 00:17:31.930 --> 00:17:33.020 align:middle line:90% And it will be happy. 00:17:33.020 --> 00:17:34.450 align:middle line:90% It'll just stay off. 00:17:34.450 --> 00:17:38.410 align:middle line:84% But if I ran around and tried to put a voltage polarity across it 00:17:38.410 --> 00:17:43.270 align:middle line:84% this way, bad things will happen. 00:17:43.270 --> 00:17:47.680 align:middle line:84% So it can act as a switch and open circuit itself, 00:17:47.680 --> 00:17:51.750 align:middle line:84% but only in one direction of applied voltage. 00:17:51.750 --> 00:17:56.960 align:middle line:84% So this one won't allow me to block reverse voltage, either. 00:17:56.960 --> 00:17:59.880 align:middle line:84% But it will allow me to carry reverse current 00:17:59.880 --> 00:18:02.490 align:middle line:84% because this one-- if I try to shove current through it 00:18:02.490 --> 00:18:04.082 align:middle line:90% the wrong way, it'll die. 00:18:04.082 --> 00:18:06.540 align:middle line:84% AUDIENCE: Following on that, then, sorry, if the switch was 00:18:06.540 --> 00:18:07.873 align:middle line:90% closed, it would be a short? 00:18:07.873 --> 00:18:08.790 align:middle line:90% DAVID PERREAULT: Yeah. 00:18:08.790 --> 00:18:11.555 align:middle line:84% If the switch is closed, an IGBT alone-- 00:18:11.555 --> 00:18:12.930 align:middle line:84% if the switch is closed, it looks 00:18:12.930 --> 00:18:16.330 align:middle line:84% like a short or some kind of very small drop 00:18:16.330 --> 00:18:18.910 align:middle line:90% for positive currents. 00:18:18.910 --> 00:18:21.160 align:middle line:84% But it doesn't look like a short for negative currents 00:18:21.160 --> 00:18:22.840 align:middle line:90% because bad things will happen. 00:18:22.840 --> 00:18:26.530 align:middle line:84% If I add this diode, then it can carry positively 00:18:26.530 --> 00:18:28.640 align:middle line:84% through the IGBT and negatively through the diode. 00:18:28.640 --> 00:18:31.540 align:middle line:84% And then it's happy as a bidirectional current-carrying 00:18:31.540 --> 00:18:34.050 align:middle line:90% device. 00:18:34.050 --> 00:18:36.930 align:middle line:84% AUDIENCE: So then when we're determining what the polarity is 00:18:36.930 --> 00:18:39.420 align:middle line:84% across the switch, if it was in a circuit 00:18:39.420 --> 00:18:42.030 align:middle line:84% and you had some voltage source, then the switch would 00:18:42.030 --> 00:18:43.230 align:middle line:90% act like a load, right? 00:18:43.230 --> 00:18:45.360 align:middle line:84% And so it would be in the opposite direction 00:18:45.360 --> 00:18:46.450 align:middle line:90% of the voltage source. 00:18:46.450 --> 00:18:48.480 align:middle line:90% Is that how we would do it? 00:18:48.480 --> 00:18:52.750 align:middle line:84% Because I always think of it in terms of current and then 00:18:52.750 --> 00:18:54.310 align:middle line:84% determine the voltage [INAUDIBLE]. 00:18:54.310 --> 00:18:55.450 align:middle line:90% That might be [INAUDIBLE]. 00:18:55.450 --> 00:18:56.825 align:middle line:84% DAVID PERREAULT: And that's fine. 00:18:56.825 --> 00:18:58.510 align:middle line:84% So if you thought of it as being open, 00:18:58.510 --> 00:19:00.940 align:middle line:84% if you thought about it as being open, 00:19:00.940 --> 00:19:03.920 align:middle line:84% then you could calculate all the voltages and currents in this. 00:19:03.920 --> 00:19:06.580 align:middle line:84% If you treat it as an open circuit 00:19:06.580 --> 00:19:09.430 align:middle line:84% and you go analyze your circuit and then you say, 00:19:09.430 --> 00:19:13.010 align:middle line:84% which way is the polarity of that voltage-- 00:19:13.010 --> 00:19:14.990 align:middle line:84% and if it's the wrong polarity, you're unhappy. 00:19:14.990 --> 00:19:16.865 align:middle line:84% And if it's the right polarity, you're happy. 00:19:16.865 --> 00:19:20.270 align:middle line:90% 00:19:20.270 --> 00:19:24.110 align:middle line:84% So what about if I want-- but this, again, will get me 00:19:24.110 --> 00:19:25.080 align:middle line:90% to those two quadrants. 00:19:25.080 --> 00:19:26.580 align:middle line:84% What if I want a different quadrant? 00:19:26.580 --> 00:19:32.420 align:middle line:84% I could come up here and I could say, let me take my IGBT. 00:19:32.420 --> 00:19:35.030 align:middle line:84% And now I'll put a diode in series with it. 00:19:35.030 --> 00:19:39.410 align:middle line:84% And to be clear, I mean a separate diode. 00:19:39.410 --> 00:19:45.170 align:middle line:84% I take two physical devices, And I use them to make one switch. 00:19:45.170 --> 00:19:51.250 align:middle line:84% And I'll call that V switch and this I switch. 00:19:51.250 --> 00:19:59.165 align:middle line:84% This device can block positive and negative voltage. 00:19:59.165 --> 00:20:01.390 align:middle line:84% If I put a positive voltage across it, 00:20:01.390 --> 00:20:04.640 align:middle line:90% I can turn it off with the IGBT. 00:20:04.640 --> 00:20:06.350 align:middle line:84% If I put a negative voltage across it, 00:20:06.350 --> 00:20:09.570 align:middle line:84% this diode will naturally block it. 00:20:09.570 --> 00:20:11.740 align:middle line:84% But it can only carry positive current. 00:20:11.740 --> 00:20:14.960 align:middle line:90% 00:20:14.960 --> 00:20:18.710 align:middle line:84% So if that's what I need for the circuit I'm building, 00:20:18.710 --> 00:20:20.970 align:middle line:90% that's what I would do. 00:20:20.970 --> 00:20:21.470 align:middle line:90% Yeah? 00:20:21.470 --> 00:20:24.195 align:middle line:84% AUDIENCE: So are these just considered semi-controlled? 00:20:24.195 --> 00:20:28.575 align:middle line:90% 00:20:28.575 --> 00:20:31.780 align:middle line:84% DAVID PERREAULT: This would be considered a-- 00:20:31.780 --> 00:20:36.880 align:middle line:84% it's a fully controlled device under these conditions. 00:20:36.880 --> 00:20:41.360 align:middle line:84% Yes, it does act like a diode in the reverse direction. 00:20:41.360 --> 00:20:44.750 align:middle line:84% So if your circuit happens to do that, then it's uncontrolled. 00:20:44.750 --> 00:20:46.280 align:middle line:90% You can't tell it to turn on. 00:20:46.280 --> 00:20:46.830 align:middle line:90% That's right. 00:20:46.830 --> 00:20:50.040 align:middle line:90% 00:20:50.040 --> 00:20:53.460 align:middle line:84% I can extend this one level further. 00:20:53.460 --> 00:20:55.950 align:middle line:84% So a very common thing I might do 00:20:55.950 --> 00:21:04.850 align:middle line:84% is take two MOSFETs in antiparallel, like this. 00:21:04.850 --> 00:21:08.330 align:middle line:84% And just to remember, inside of my MOSFET, 00:21:08.330 --> 00:21:11.480 align:middle line:90% this guy has a diode this way. 00:21:11.480 --> 00:21:14.930 align:middle line:84% And this guy has a diode this way. 00:21:14.930 --> 00:21:17.930 align:middle line:84% So by controlling these two gates, 00:21:17.930 --> 00:21:23.210 align:middle line:84% I can block positive and negative voltage 00:21:23.210 --> 00:21:28.370 align:middle line:84% or carry positive and negative current. 00:21:28.370 --> 00:21:32.313 align:middle line:90% So this switch can do anything. 00:21:32.313 --> 00:21:34.730 align:middle line:84% It can just look like a switch, turn on whenever you want, 00:21:34.730 --> 00:21:36.200 align:middle line:90% and turn off whenever you want. 00:21:36.200 --> 00:21:38.340 align:middle line:84% And there are other implementations 00:21:38.340 --> 00:21:39.090 align:middle line:90% that will do that. 00:21:39.090 --> 00:21:40.715 align:middle line:84% I put a couple of other implementations 00:21:40.715 --> 00:21:43.774 align:middle line:84% that people often use in the lecture notes. 00:21:43.774 --> 00:21:49.790 align:middle line:84% So I certainly can get a switch that will do absolutely anything 00:21:49.790 --> 00:21:53.400 align:middle line:90% that I tell it to do. 00:21:53.400 --> 00:21:55.795 align:middle line:84% Why would I not want to do this all the time? 00:21:55.795 --> 00:22:02.020 align:middle line:90% 00:22:02.020 --> 00:22:07.550 align:middle line:84% It's expensive-- more loss, more device drops. 00:22:07.550 --> 00:22:09.050 align:middle line:84% I got to buy twice as many switches. 00:22:09.050 --> 00:22:10.750 align:middle line:84% So if I only need one MOSFET, I only 00:22:10.750 --> 00:22:12.940 align:middle line:84% have to block in one direction, I certainly 00:22:12.940 --> 00:22:14.360 align:middle line:84% don't want to add the capability. 00:22:14.360 --> 00:22:18.400 align:middle line:84% So designers are very sensitive to, 00:22:18.400 --> 00:22:20.590 align:middle line:84% what's the minimum thing I need to do in order 00:22:20.590 --> 00:22:22.080 align:middle line:90% to get the capability I need? 00:22:22.080 --> 00:22:25.380 align:middle line:90% 00:22:25.380 --> 00:22:29.310 align:middle line:84% So depending upon how I implement my switches, 00:22:29.310 --> 00:22:32.980 align:middle line:84% different converters will do different things. 00:22:32.980 --> 00:22:35.050 align:middle line:90% And when we're going to go-- 00:22:35.050 --> 00:22:41.140 align:middle line:84% coming back to this notion of I just drew this or I built a-- 00:22:41.140 --> 00:22:47.740 align:middle line:84% I designed a converter and I just draw some abstract switch, 00:22:47.740 --> 00:22:51.850 align:middle line:84% you don't necessarily know what that converter can do 00:22:51.850 --> 00:22:54.400 align:middle line:84% or you don't know what it will do, necessarily, 00:22:54.400 --> 00:22:56.590 align:middle line:90% unless you know more things. 00:22:56.590 --> 00:22:58.690 align:middle line:84% So very often, what might you need 00:22:58.690 --> 00:23:02.260 align:middle line:84% to know in order to figure out what a converter is really 00:23:02.260 --> 00:23:02.780 align:middle line:90% going to do? 00:23:02.780 --> 00:23:05.650 align:middle line:84% Well, you might need to know the switch implementation. 00:23:05.650 --> 00:23:08.560 align:middle line:90% 00:23:08.560 --> 00:23:13.008 align:middle line:84% You might need to know the control. 00:23:13.008 --> 00:23:14.800 align:middle line:84% If I don't tell you how I'm controlling it, 00:23:14.800 --> 00:23:17.940 align:middle line:84% you may not be able to tell what it's doing. 00:23:17.940 --> 00:23:19.485 align:middle line:84% You might need to know-- even then, 00:23:19.485 --> 00:23:21.360 align:middle line:84% you might need to know the external networks. 00:23:21.360 --> 00:23:24.330 align:middle line:90% 00:23:24.330 --> 00:23:26.970 align:middle line:84% So you might need a whole bunch of information 00:23:26.970 --> 00:23:31.572 align:middle line:84% to really analyze the behavior of a converter. 00:23:31.572 --> 00:23:35.930 align:middle line:84% So let me illustrate what I mean by that. 00:23:35.930 --> 00:23:37.890 align:middle line:84% Suppose I were to show you this converter. 00:23:37.890 --> 00:23:44.120 align:middle line:84% I have a voltage source V1 here, an inductor, 00:23:44.120 --> 00:23:49.440 align:middle line:84% and maybe I'll implement my single-pole, 00:23:49.440 --> 00:23:52.770 align:middle line:84% double-throw switches, two switches. 00:23:52.770 --> 00:23:53.860 align:middle line:90% And here I go. 00:23:53.860 --> 00:23:56.040 align:middle line:90% And then I'll have a capacitor. 00:23:56.040 --> 00:23:58.330 align:middle line:84% And I will have some other voltage. 00:23:58.330 --> 00:23:59.135 align:middle line:90% I'll call it V2. 00:23:59.135 --> 00:24:02.720 align:middle line:90% 00:24:02.720 --> 00:24:06.180 align:middle line:84% Can I tell which way power is going to flow in this converter? 00:24:06.180 --> 00:24:08.790 align:middle line:90% 00:24:08.790 --> 00:24:11.550 align:middle line:84% Can I tell even what the polarity is? 00:24:11.550 --> 00:24:14.860 align:middle line:90% Is V1 positive or negative? 00:24:14.860 --> 00:24:16.220 align:middle line:90% Not really. 00:24:16.220 --> 00:24:18.010 align:middle line:90% I don't have enough information. 00:24:18.010 --> 00:24:21.670 align:middle line:84% Now, if I then came back and said, well, you know what-- 00:24:21.670 --> 00:24:24.640 align:middle line:90% here's some more detail. 00:24:24.640 --> 00:24:27.520 align:middle line:90% Here's V1. 00:24:27.520 --> 00:24:34.330 align:middle line:84% I'm going to implement this switch as a power MOSFET. 00:24:34.330 --> 00:24:37.995 align:middle line:84% And I'll implement this switch as a power MOSFET. 00:24:37.995 --> 00:24:48.220 align:middle line:90% 00:24:48.220 --> 00:24:53.040 align:middle line:84% And just to remind you, while it's not necessary to draw this, 00:24:53.040 --> 00:24:57.630 align:middle line:84% and people don't normally-- but I will just remind you that 00:24:57.630 --> 00:25:01.620 align:middle line:84% inside this device, it has this magic-- 00:25:01.620 --> 00:25:05.345 align:middle line:90% it has this internal body diode. 00:25:05.345 --> 00:25:06.720 align:middle line:84% Whether you like it or not, there 00:25:06.720 --> 00:25:10.560 align:middle line:84% are diodes there because I've used the MOSFET. 00:25:10.560 --> 00:25:13.670 align:middle line:84% If I look at this network, can I tell which way power is flowing? 00:25:13.670 --> 00:25:19.210 align:middle line:90% 00:25:19.210 --> 00:25:23.890 align:middle line:84% I would argue you can't because think about it this way. 00:25:23.890 --> 00:25:27.893 align:middle line:84% If I left this device off and I switched this MOSFET, 00:25:27.893 --> 00:25:29.310 align:middle line:84% I could use it as a buck converter 00:25:29.310 --> 00:25:30.720 align:middle line:90% to transfer energy that way. 00:25:30.720 --> 00:25:33.570 align:middle line:84% That's exactly the buck converter circuit we had-- 00:25:33.570 --> 00:25:39.600 align:middle line:84% or if I turned this switch off and just switch this device, 00:25:39.600 --> 00:25:41.670 align:middle line:84% it would be acting just like a boost converter, 00:25:41.670 --> 00:25:44.910 align:middle line:90% throwing energy this way. 00:25:44.910 --> 00:25:47.160 align:middle line:84% And by the way, I might not do that. 00:25:47.160 --> 00:25:49.960 align:middle line:84% I might actually use both devices. 00:25:49.960 --> 00:25:51.980 align:middle line:84% In fact, this circuit can actually 00:25:51.980 --> 00:25:55.210 align:middle line:84% act as a buck converter or a boost converter. 00:25:55.210 --> 00:25:58.210 align:middle line:84% Just to illustrate that, I brought one with me. 00:25:58.210 --> 00:26:01.870 align:middle line:84% This beast is actually made for a certain kind of car that 00:26:01.870 --> 00:26:03.850 align:middle line:90% had two battery voltages in it. 00:26:03.850 --> 00:26:06.200 align:middle line:84% And it's actually five such converters. 00:26:06.200 --> 00:26:07.420 align:middle line:90% Here's the inductors. 00:26:07.420 --> 00:26:10.100 align:middle line:84% The two MOSFETs are bolted down to the heat sink. 00:26:10.100 --> 00:26:11.300 align:middle line:90% There's five copies of this. 00:26:11.300 --> 00:26:12.920 align:middle line:90% They're so-called interleaved. 00:26:12.920 --> 00:26:15.820 align:middle line:84% They're paralleled and operated in a certain manner. 00:26:15.820 --> 00:26:18.010 align:middle line:84% But you can actually-- there's actually 00:26:18.010 --> 00:26:21.070 align:middle line:84% a switch on the front of this thing. 00:26:21.070 --> 00:26:23.570 align:middle line:84% If I can switch it up, it controls to boost. 00:26:23.570 --> 00:26:26.230 align:middle line:84% That means it regulates the high voltage from the low voltage. 00:26:26.230 --> 00:26:28.360 align:middle line:84% Switch the other way, it goes the other direction, 00:26:28.360 --> 00:26:30.915 align:middle line:84% or you can control it from our computer. 00:26:30.915 --> 00:26:33.340 align:middle line:84% So the notion is you can build circuits 00:26:33.340 --> 00:26:39.510 align:middle line:84% that are bidirectional power flow capable if you choose. 00:26:39.510 --> 00:26:42.590 align:middle line:84% What could I tell about this thing? 00:26:42.590 --> 00:26:44.870 align:middle line:84% Well, I can tell a couple of things. 00:26:44.870 --> 00:26:47.700 align:middle line:84% In periodic steady-state operation, 00:26:47.700 --> 00:26:49.670 align:middle line:84% I know that the magnitude of V2 has 00:26:49.670 --> 00:26:51.620 align:middle line:84% to be bigger than the magnitude of V1 00:26:51.620 --> 00:26:56.277 align:middle line:84% because we showed if I'm boosting, V2 is bigger than V1. 00:26:56.277 --> 00:26:57.860 align:middle line:84% If I'm bucking from this side to this, 00:26:57.860 --> 00:27:00.210 align:middle line:84% this voltage is bigger than this voltage. 00:27:00.210 --> 00:27:05.240 align:middle line:84% So that I know because of periodic steady-state analysis. 00:27:05.240 --> 00:27:06.690 align:middle line:90% What else can I tell about it? 00:27:06.690 --> 00:27:09.050 align:middle line:84% I could also argue that I can tell you 00:27:09.050 --> 00:27:13.130 align:middle line:84% the polarities of allowable voltages here. 00:27:13.130 --> 00:27:14.270 align:middle line:90% Why? 00:27:14.270 --> 00:27:19.880 align:middle line:90% Well, let's look at V2. 00:27:19.880 --> 00:27:22.180 align:middle line:84% If I told you I was going to make V2 negative, 00:27:22.180 --> 00:27:23.680 align:middle line:84% what would be the problem with that? 00:27:23.680 --> 00:27:29.810 align:middle line:90% 00:27:29.810 --> 00:27:32.047 align:middle line:84% The two diodes would just turn on and short 00:27:32.047 --> 00:27:33.380 align:middle line:90% the negative voltage source out. 00:27:33.380 --> 00:27:35.060 align:middle line:84% And then bad things would happen. 00:27:35.060 --> 00:27:37.510 align:middle line:90% So V2 must be positive. 00:27:37.510 --> 00:27:40.400 align:middle line:84% I can actually even look at V1 independently of that 00:27:40.400 --> 00:27:41.610 align:middle line:90% and tell it must be positive. 00:27:41.610 --> 00:27:42.140 align:middle line:90% Why? 00:27:42.140 --> 00:27:45.380 align:middle line:84% Because the average voltage in periodic steady state 00:27:45.380 --> 00:27:49.500 align:middle line:84% at this node must be the same as this node, and likewise. 00:27:49.500 --> 00:27:52.740 align:middle line:84% So that means this has an average voltage of V1. 00:27:52.740 --> 00:27:55.860 align:middle line:84% And that means this diode would turn on 00:27:55.860 --> 00:27:57.600 align:middle line:90% if I tried to make V1 negative. 00:27:57.600 --> 00:27:59.170 align:middle line:84% So I can tell something about this. 00:27:59.170 --> 00:28:03.360 align:middle line:84% I can tell what polarities of voltage are allowable. 00:28:03.360 --> 00:28:06.300 align:middle line:84% I could build a buck converter or a boost converter-- 00:28:06.300 --> 00:28:08.320 align:middle line:84% went from negative voltage to negative voltage. 00:28:08.320 --> 00:28:10.500 align:middle line:84% I just have to change my switch implementation, 00:28:10.500 --> 00:28:16.020 align:middle line:84% or I could build one that, for example, would allow 00:28:16.020 --> 00:28:17.500 align:middle line:90% either polarity of voltage. 00:28:17.500 --> 00:28:19.860 align:middle line:84% What I would have to do then is go rethink 00:28:19.860 --> 00:28:21.380 align:middle line:90% how I implement these switches. 00:28:21.380 --> 00:28:27.047 align:middle line:90% 00:28:27.047 --> 00:28:32.330 align:middle line:84% Of course, if I came back to you and said, 00:28:32.330 --> 00:28:35.510 align:middle line:84% I don't really have two voltage sources or two batteries here, 00:28:35.510 --> 00:28:37.760 align:middle line:90% this guy over here-- 00:28:37.760 --> 00:28:38.980 align:middle line:90% he's actually a resistor. 00:28:38.980 --> 00:28:42.610 align:middle line:90% 00:28:42.610 --> 00:28:46.120 align:middle line:84% Well, then you can tell what it can do in steady state, anyways, 00:28:46.120 --> 00:28:49.900 align:middle line:84% because I can't source energy from at least positive 00:28:49.900 --> 00:28:50.930 align:middle line:90% resistors. 00:28:50.930 --> 00:28:52.990 align:middle line:84% So I would know that this converter 00:28:52.990 --> 00:28:58.140 align:middle line:84% was designed to flow power this way, at least on average. 00:28:58.140 --> 00:29:01.620 align:middle line:84% So that's a little bit about what people think about 00:29:01.620 --> 00:29:03.120 align:middle line:90% in switch implementation. 00:29:03.120 --> 00:29:06.150 align:middle line:84% You've got to go for what voltage 00:29:06.150 --> 00:29:08.400 align:middle line:84% amplitudes and polarities you need 00:29:08.400 --> 00:29:11.177 align:middle line:84% and then you-- and what current and what power carrying 00:29:11.177 --> 00:29:12.010 align:middle line:90% directions you need. 00:29:12.010 --> 00:29:14.580 align:middle line:84% And then you work back from that to the simplest switches you 00:29:14.580 --> 00:29:18.710 align:middle line:90% can use to give what you want. 00:29:18.710 --> 00:29:19.650 align:middle line:90% Any questions? 00:29:19.650 --> 00:29:25.012 align:middle line:90% 00:29:25.012 --> 00:29:27.195 align:middle line:84% So the buck and the boost converter-- 00:29:27.195 --> 00:29:28.570 align:middle line:84% whether this is a buck or a boost 00:29:28.570 --> 00:29:30.030 align:middle line:84% depends on power flow direction-- 00:29:30.030 --> 00:29:33.870 align:middle line:84% are examples of what are known as direct power converters. 00:29:33.870 --> 00:29:35.620 align:middle line:84% And they're called direct power converters 00:29:35.620 --> 00:29:38.680 align:middle line:84% because in one of the two switch states, 00:29:38.680 --> 00:29:41.950 align:middle line:84% we transfer energy directly via current 00:29:41.950 --> 00:29:45.530 align:middle line:90% from the source to the load. 00:29:45.530 --> 00:29:47.940 align:middle line:84% You can build other kinds of converters. 00:29:47.940 --> 00:29:51.500 align:middle line:84% And in fact, if I took this original canonical cell 00:29:51.500 --> 00:29:56.040 align:middle line:84% that I drew, this guy, and turned its-- on its end, 00:29:56.040 --> 00:29:58.710 align:middle line:84% I changed which ports I was using, its input and output, 00:29:58.710 --> 00:30:02.270 align:middle line:84% I could build a different kind of converter. 00:30:02.270 --> 00:30:03.308 align:middle line:90% It could look like this. 00:30:03.308 --> 00:30:04.350 align:middle line:90% This is one way to do it. 00:30:04.350 --> 00:30:06.350 align:middle line:90% It looks like this. 00:30:06.350 --> 00:30:11.680 align:middle line:84% I will have a single-pole, double-throw switch. 00:30:11.680 --> 00:30:15.640 align:middle line:90% I will put my capacitor here. 00:30:15.640 --> 00:30:17.880 align:middle line:90% I'll put the inductor here. 00:30:17.880 --> 00:30:20.140 align:middle line:84% And then I'll put the other port here. 00:30:20.140 --> 00:30:29.250 align:middle line:84% So then I can connect up, for example, if I made this V1 00:30:29.250 --> 00:30:31.640 align:middle line:90% and I made this V2. 00:30:31.640 --> 00:30:34.580 align:middle line:90% 00:30:34.580 --> 00:30:38.870 align:middle line:84% That would be another possible way I could build a converter. 00:30:38.870 --> 00:30:43.490 align:middle line:84% And I can make this switch in this position. 00:30:43.490 --> 00:30:45.620 align:middle line:84% When q of t is equal to 1, it's in this position. 00:30:45.620 --> 00:30:49.200 align:middle line:84% When q of t is equal to 0, it's the other position. 00:30:49.200 --> 00:30:54.220 align:middle line:84% So we could go analyze this circuit. 00:30:54.220 --> 00:30:58.240 align:middle line:84% I should say, by the way, that when people implement 00:30:58.240 --> 00:31:01.300 align:middle line:90% this circuit, they often-- 00:31:01.300 --> 00:31:04.270 align:middle line:84% this is a nice pedagogical description. 00:31:04.270 --> 00:31:07.870 align:middle line:84% But they often implement it by splitting this capacitor. 00:31:07.870 --> 00:31:11.660 align:middle line:84% So instead of having some voltage Vc here-- 00:31:11.660 --> 00:31:14.920 align:middle line:84% if this voltage V-- if V1 is constant and Vc-- 00:31:14.920 --> 00:31:17.620 align:middle line:84% and the capacitor is really big so that Vc 00:31:17.620 --> 00:31:19.840 align:middle line:84% is almost constant, then clearly, 00:31:19.840 --> 00:31:21.640 align:middle line:84% V2 is going to be almost constant. 00:31:21.640 --> 00:31:26.880 align:middle line:84% So this capacitor can act to stabilize voltage V2. 00:31:26.880 --> 00:31:31.620 align:middle line:84% But perhaps more common would be to build it this way, 00:31:31.620 --> 00:31:37.590 align:middle line:90% have V1 a switch like this. 00:31:37.590 --> 00:31:41.820 align:middle line:84% And maybe put a capacitor here and another capacitor here 00:31:41.820 --> 00:31:47.610 align:middle line:84% and the load like this and call that V2. 00:31:47.610 --> 00:31:50.830 align:middle line:84% So that might be a very typical way 00:31:50.830 --> 00:31:54.260 align:middle line:84% to actually implement this circuit. 00:31:54.260 --> 00:31:59.210 align:middle line:84% So let's think about what would this circuit do 00:31:59.210 --> 00:32:00.710 align:middle line:90% in the real world. 00:32:00.710 --> 00:32:04.070 align:middle line:90% Well, here's my signal, q of t. 00:32:04.070 --> 00:32:12.242 align:middle line:90% 00:32:12.242 --> 00:32:13.950 align:middle line:84% So I'm going to operate it periodically-- 00:32:13.950 --> 00:32:19.610 align:middle line:84% DT, T. In order to analyze the other circuit there, 00:32:19.610 --> 00:32:23.920 align:middle line:84% what did I do to analyze its behavior? 00:32:23.920 --> 00:32:26.230 align:middle line:84% How did I figure out what its steady state operating 00:32:26.230 --> 00:32:27.150 align:middle line:90% characteristics were? 00:32:27.150 --> 00:32:32.790 align:middle line:90% 00:32:32.790 --> 00:32:35.370 align:middle line:84% If you came back here, what I really looked at 00:32:35.370 --> 00:32:39.780 align:middle line:84% is what was the average voltage on the inductor. 00:32:39.780 --> 00:32:43.110 align:middle line:90% So why don't I do that again? 00:32:43.110 --> 00:32:48.210 align:middle line:84% Again, I'll plot the average voltage on the inductor here, 00:32:48.210 --> 00:32:55.250 align:middle line:90% V sub L. So let me plot V sub L. 00:32:55.250 --> 00:33:05.860 align:middle line:84% So when this q of t is 1, then the switch is in this position 00:33:05.860 --> 00:33:07.550 align:middle line:90% and VL is equal to V1. 00:33:07.550 --> 00:33:11.380 align:middle line:84% So let me make V1 positive for sake of this analysis. 00:33:11.380 --> 00:33:14.800 align:middle line:90% So I have V1 here. 00:33:14.800 --> 00:33:18.010 align:middle line:84% When q of t is equal to 0 and the switch flips, 00:33:18.010 --> 00:33:21.915 align:middle line:90% VL is equal to V2. 00:33:21.915 --> 00:33:23.970 align:middle line:90% So VL is equal to V2. 00:33:23.970 --> 00:33:26.730 align:middle line:84% And I know I need the average voltage 00:33:26.730 --> 00:33:29.490 align:middle line:90% on this inductor to be 0. 00:33:29.490 --> 00:33:31.830 align:middle line:84% Then that must mean that V2 is going 00:33:31.830 --> 00:33:35.210 align:middle line:90% to be some negative number. 00:33:35.210 --> 00:33:38.030 align:middle line:90% So V2 is going to be possibly-- 00:33:38.030 --> 00:33:40.650 align:middle line:90% 00:33:40.650 --> 00:33:41.650 align:middle line:90% look like this. 00:33:41.650 --> 00:33:47.000 align:middle line:90% 00:33:47.000 --> 00:33:49.090 align:middle line:84% And what I know is-- so here's the voltage 00:33:49.090 --> 00:33:51.650 align:middle line:90% across this inductor. 00:33:51.650 --> 00:33:54.220 align:middle line:84% And what I know is that the average voltage here 00:33:54.220 --> 00:33:55.040 align:middle line:90% has to be 0. 00:33:55.040 --> 00:33:58.840 align:middle line:84% That means that this positive area, this volt-seconds 00:33:58.840 --> 00:34:01.450 align:middle line:84% positively on the inductor, must be balanced 00:34:01.450 --> 00:34:05.330 align:middle line:84% by this negative volt-seconds on the inductor, 00:34:05.330 --> 00:34:07.210 align:middle line:84% or another way I could look at that is I 00:34:07.210 --> 00:34:10.239 align:middle line:84% could say that the average voltage V sub 00:34:10.239 --> 00:34:13.040 align:middle line:90% L is equal to what? 00:34:13.040 --> 00:34:24.610 align:middle line:84% It's equal to D times V1 plus 1 minus D V2. 00:34:24.610 --> 00:34:31.150 align:middle line:84% So that means that V2 must be equal to minus 00:34:31.150 --> 00:34:34.364 align:middle line:90% D over 1 minus D V1. 00:34:34.364 --> 00:34:38.219 align:middle line:90% 00:34:38.219 --> 00:34:41.920 align:middle line:84% Does that make sense to everybody? 00:34:41.920 --> 00:34:45.370 align:middle line:84% So I can tell two things from this. 00:34:45.370 --> 00:34:49.790 align:middle line:90% One is this is a number-- 00:34:49.790 --> 00:34:53.120 align:middle line:84% D over 1 minus D is a number that for D 0 to 1 00:34:53.120 --> 00:34:57.499 align:middle line:84% goes between, basically, 0 and infinity. 00:34:57.499 --> 00:35:02.700 align:middle line:84% So the first thing I can say is the voltage V2 must be negative. 00:35:02.700 --> 00:35:05.940 align:middle line:84% I'm applying a positive voltage here 00:35:05.940 --> 00:35:07.390 align:middle line:90% in the first part of the cycle. 00:35:07.390 --> 00:35:10.910 align:middle line:84% So V2 in the second part of the cycle must be negative. 00:35:10.910 --> 00:35:13.875 align:middle line:90% 00:35:13.875 --> 00:35:15.810 align:middle line:84% So first of all, I can tell that this circuit 00:35:15.810 --> 00:35:17.110 align:middle line:90% is going to invert the voltage. 00:35:17.110 --> 00:35:18.600 align:middle line:84% So if I have a positive input voltage, 00:35:18.600 --> 00:35:20.683 align:middle line:84% it's going to be give me a negative output voltage 00:35:20.683 --> 00:35:21.770 align:middle line:90% in periodic steady state. 00:35:21.770 --> 00:35:24.470 align:middle line:90% 00:35:24.470 --> 00:35:26.470 align:middle line:84% The other thing about it, though, as I can tell, 00:35:26.470 --> 00:35:29.860 align:middle line:84% is that I said this number, D over 1 minus D, 00:35:29.860 --> 00:35:33.570 align:middle line:84% varies anywhere between 0 and infinity. 00:35:33.570 --> 00:35:37.240 align:middle line:84% So this circuit-- if I put aside the polarity of the output 00:35:37.240 --> 00:35:39.880 align:middle line:84% voltage-- sometimes I want an output voltage 00:35:39.880 --> 00:35:43.040 align:middle line:84% that's the opposite polarity of my input voltage-- 00:35:43.040 --> 00:35:46.200 align:middle line:84% I can make the magnitude of the output voltage anything I want, 00:35:46.200 --> 00:35:50.180 align:middle line:84% bigger or smaller than the input voltage, 00:35:50.180 --> 00:35:54.740 align:middle line:84% because this scaling factor, by choosing D-- 00:35:54.740 --> 00:35:59.690 align:middle line:84% if I make D equal to 0.5, V2 exactly equals V1. 00:35:59.690 --> 00:36:02.310 align:middle line:90% It's the opposite of V1. 00:36:02.310 --> 00:36:05.350 align:middle line:84% If I make it bigger than 0.5, the magnitude of V2 00:36:05.350 --> 00:36:06.600 align:middle line:90% is going to be bigger than V1. 00:36:06.600 --> 00:36:08.683 align:middle line:84% If I make it less than 0.5, the magnitude of V2 00:36:08.683 --> 00:36:09.850 align:middle line:90% is going to be less than V1. 00:36:09.850 --> 00:36:11.470 align:middle line:84% So this is a very flexible circuit. 00:36:11.470 --> 00:36:13.080 align:middle line:84% It will let me do whatever I want. 00:36:13.080 --> 00:36:15.900 align:middle line:84% Whereas a buck converter can only step down voltages 00:36:15.900 --> 00:36:18.360 align:middle line:84% and a boost converter can only step up voltages, 00:36:18.360 --> 00:36:20.610 align:middle line:84% this, at least in the terms of the voltage magnitude, 00:36:20.610 --> 00:36:24.350 align:middle line:84% will do whatever the heck I like. 00:36:24.350 --> 00:36:27.710 align:middle line:90% Any questions about that? 00:36:27.710 --> 00:36:28.210 align:middle line:90% Yeah? 00:36:28.210 --> 00:36:29.918 align:middle line:84% AUDIENCE: Does the capacitor up top still 00:36:29.918 --> 00:36:32.000 align:middle line:84% help to filter out the output voltage? 00:36:32.000 --> 00:36:33.010 align:middle line:90% DAVID PERREAULT: Yes. 00:36:33.010 --> 00:36:34.120 align:middle line:90% Excellent question. 00:36:34.120 --> 00:36:36.938 align:middle line:84% The question is, does the capacitor still help you-- 00:36:36.938 --> 00:36:39.480 align:middle line:84% if I place it here, still help you filter the output voltage? 00:36:39.480 --> 00:36:43.090 align:middle line:84% And the answer is yes because if this node is 00:36:43.090 --> 00:36:46.780 align:middle line:84% at a constant potential because, say, V1 is constant 00:36:46.780 --> 00:36:50.770 align:middle line:84% and the capacitor here is really big 00:36:50.770 --> 00:36:53.200 align:middle line:84% such that Vc doesn't have any ripple, 00:36:53.200 --> 00:36:55.750 align:middle line:90% then V2 doesn't have any ripple. 00:36:55.750 --> 00:36:58.450 align:middle line:84% So yes, this capacitor placed here 00:36:58.450 --> 00:37:04.160 align:middle line:84% can certainly help stabilize V2 as long as V1 is stable. 00:37:04.160 --> 00:37:05.508 align:middle line:90% So we could build it that way. 00:37:05.508 --> 00:37:06.550 align:middle line:90% And sometimes, people do. 00:37:06.550 --> 00:37:09.110 align:middle line:90% 00:37:09.110 --> 00:37:10.710 align:middle line:90% So let's think about this. 00:37:10.710 --> 00:37:15.200 align:middle line:84% Let's look at an implementation of this circuit. 00:37:15.200 --> 00:37:26.500 align:middle line:84% Suppose I wanted to do it for V1 greater than 0, V2 less than 0. 00:37:26.500 --> 00:37:29.020 align:middle line:84% So maybe I would implement it like this. 00:37:29.020 --> 00:37:33.140 align:middle line:90% Here's my voltage source V1. 00:37:33.140 --> 00:37:35.140 align:middle line:90% Maybe I'll use a power MOSFET. 00:37:35.140 --> 00:37:36.995 align:middle line:90% I could use an IGBT as well. 00:37:36.995 --> 00:37:51.745 align:middle line:90% 00:37:51.745 --> 00:37:53.120 align:middle line:84% We can implement this either way. 00:37:53.120 --> 00:37:54.805 align:middle line:84% But maybe I'll implement it like this. 00:37:54.805 --> 00:38:01.396 align:middle line:90% 00:38:01.396 --> 00:38:02.665 align:middle line:90% And this is V2. 00:38:02.665 --> 00:38:07.298 align:middle line:90% 00:38:07.298 --> 00:38:14.370 align:middle line:84% So if I thought about the power flow direction of this, 00:38:14.370 --> 00:38:15.700 align:middle line:90% what do I know? 00:38:15.700 --> 00:38:18.630 align:middle line:84% I know that V1 must be bigger than 0 because 00:38:18.630 --> 00:38:23.340 align:middle line:84% of this internal body diode here because otherwise, 00:38:23.340 --> 00:38:27.981 align:middle line:84% then V1 would get shorted out on average. 00:38:27.981 --> 00:38:31.130 align:middle line:90% So V1 must be greater than 0. 00:38:31.130 --> 00:38:33.598 align:middle line:90% V2 must be less than 0. 00:38:33.598 --> 00:38:36.450 align:middle line:90% 00:38:36.450 --> 00:38:38.588 align:middle line:84% I1, the average current flowing in 00:38:38.588 --> 00:38:41.130 align:middle line:84% here-- if I pretended that this capacitor filtered everything 00:38:41.130 --> 00:38:45.290 align:middle line:84% perfectly, this would give me I2 on average. 00:38:45.290 --> 00:38:47.650 align:middle line:90% This would give me a current I2. 00:38:47.650 --> 00:38:52.290 align:middle line:90% 00:38:52.290 --> 00:38:53.810 align:middle line:90% And what do I know? 00:38:53.810 --> 00:38:57.870 align:middle line:90% I know that I2 must be positive. 00:38:57.870 --> 00:38:58.990 align:middle line:90% Why do I know that? 00:38:58.990 --> 00:39:02.340 align:middle line:84% Because if this is the average or DC current coming this way, 00:39:02.340 --> 00:39:05.010 align:middle line:84% no DC current goes into the capacitor. 00:39:05.010 --> 00:39:06.670 align:middle line:84% So it must go through this diode. 00:39:06.670 --> 00:39:12.015 align:middle line:84% And we know this diode can only carry current in one direction. 00:39:12.015 --> 00:39:16.590 align:middle line:84% So I know that V2 is negative and I2 is positive. 00:39:16.590 --> 00:39:22.550 align:middle line:84% So V1 greater than 0, I1 greater than 0, V2 less than 0, 00:39:22.550 --> 00:39:24.820 align:middle line:90% I2 greater than 0-- 00:39:24.820 --> 00:39:27.560 align:middle line:84% so power can only flow from this side to this side. 00:39:27.560 --> 00:39:31.350 align:middle line:90% 00:39:31.350 --> 00:39:33.485 align:middle line:84% That's just an example of doing this. 00:39:33.485 --> 00:39:37.400 align:middle line:90% 00:39:37.400 --> 00:39:39.880 align:middle line:84% What else could I tell about this converter? 00:39:39.880 --> 00:39:43.350 align:middle line:90% 00:39:43.350 --> 00:39:49.410 align:middle line:84% If I thought of the voltage on this capacitor, Vc, 00:39:49.410 --> 00:39:52.380 align:middle line:84% how big is that capacitor voltage? 00:39:52.380 --> 00:39:55.200 align:middle line:84% Well, I could argue that the DC value of Vc-- 00:39:55.200 --> 00:39:58.070 align:middle line:90% 00:39:58.070 --> 00:39:59.670 align:middle line:90% the DC value-- 00:39:59.670 --> 00:40:04.655 align:middle line:84% I can do average KVL around this loop. 00:40:04.655 --> 00:40:09.900 align:middle line:84% So I could say that V1 minus Vc minus V2 00:40:09.900 --> 00:40:20.000 align:middle line:84% is 0 or, written a different way, Vc is equal to V1 minus V2, 00:40:20.000 --> 00:40:22.880 align:middle line:84% or if I wanted to take the magnitude here, 00:40:22.880 --> 00:40:26.150 align:middle line:84% I could say that the magnitude of Vc 00:40:26.150 --> 00:40:30.240 align:middle line:84% is equal to the magnitude of V1 plus the magnitude of V2. 00:40:30.240 --> 00:40:30.740 align:middle line:90% Why? 00:40:30.740 --> 00:40:33.282 align:middle line:90% Because V2 is negative. 00:40:33.282 --> 00:40:36.230 align:middle line:84% So in this example, this capacitor voltage-- 00:40:36.230 --> 00:40:38.940 align:middle line:84% because V2 is negative and V1 is positive, 00:40:38.940 --> 00:40:42.080 align:middle line:84% this capacitor blocks a lot of voltage 00:40:42.080 --> 00:40:43.440 align:middle line:90% if I place the capacitor there. 00:40:43.440 --> 00:40:48.360 align:middle line:90% 00:40:48.360 --> 00:40:54.210 align:middle line:84% What can I say about the current? 00:40:54.210 --> 00:40:57.430 align:middle line:84% What would I say about IL, for example? 00:40:57.430 --> 00:41:02.150 align:middle line:84% And now I'm going to talk about the DC component, capital IL. 00:41:02.150 --> 00:41:05.280 align:middle line:84% I'll pretend this inductor is so big, it doesn't have any ripple. 00:41:05.280 --> 00:41:07.410 align:middle line:90% And it's instantaneous equally-- 00:41:07.410 --> 00:41:08.945 align:middle line:90% equal to its average current. 00:41:08.945 --> 00:41:11.580 align:middle line:90% 00:41:11.580 --> 00:41:13.900 align:middle line:90% Well, what could I say? 00:41:13.900 --> 00:41:18.150 align:middle line:84% I can do average KCL analysis on this. 00:41:18.150 --> 00:41:25.635 align:middle line:84% Imagine I come and I draw a supernode in this circuit. 00:41:25.635 --> 00:41:36.315 align:middle line:90% 00:41:36.315 --> 00:41:38.700 align:middle line:84% What do I know about that supernode? 00:41:38.700 --> 00:41:42.510 align:middle line:84% The average current going into that dotted dashed box 00:41:42.510 --> 00:41:44.780 align:middle line:90% must be 0. 00:41:44.780 --> 00:41:48.020 align:middle line:84% So the average current going in here is I2. 00:41:48.020 --> 00:41:50.760 align:middle line:84% The average current coming in here is I1. 00:41:50.760 --> 00:41:53.470 align:middle line:84% And the only place for those currents to come out is IL. 00:41:53.470 --> 00:41:56.240 align:middle line:90% So what I can say is that IL-- 00:41:56.240 --> 00:42:00.080 align:middle line:84% the magnitude of IL is equal to the magnitude 00:42:00.080 --> 00:42:03.470 align:middle line:90% of I1 plus the magnitude of I2. 00:42:03.470 --> 00:42:07.340 align:middle line:84% IL, I1, and I2 are all positive in this example 00:42:07.340 --> 00:42:11.140 align:middle line:84% because we've already said I1 and I2 have to be positive. 00:42:11.140 --> 00:42:16.210 align:middle line:84% So basically, the inductor current 00:42:16.210 --> 00:42:19.815 align:middle line:84% carries the sum of the input and output DC currents. 00:42:19.815 --> 00:42:23.270 align:middle line:90% 00:42:23.270 --> 00:42:26.532 align:middle line:84% Does that make sense to everybody? 00:42:26.532 --> 00:42:28.240 align:middle line:84% AUDIENCE: Why don't we use the supernode? 00:42:28.240 --> 00:42:30.400 align:middle line:84% Couldn't we just look at the node inside? 00:42:30.400 --> 00:42:33.300 align:middle line:90% 00:42:33.300 --> 00:42:36.010 align:middle line:90% DAVID PERREAULT: But this node-- 00:42:36.010 --> 00:42:36.860 align:middle line:90% you could. 00:42:36.860 --> 00:42:39.340 align:middle line:84% But keep in mind this current I can think 00:42:39.340 --> 00:42:40.583 align:middle line:90% of as almost being current-- 00:42:40.583 --> 00:42:43.250 align:middle line:84% constant all the time because of the filtering of the capacitor. 00:42:43.250 --> 00:42:44.500 align:middle line:90% This current is pulsating. 00:42:44.500 --> 00:42:46.930 align:middle line:84% So I'd have to think about it more carefully. 00:42:46.930 --> 00:42:49.060 align:middle line:84% So I was just trying to limit myself 00:42:49.060 --> 00:42:53.900 align:middle line:84% to currents flowing in that are, ideally, close to DC. 00:42:53.900 --> 00:42:56.730 align:middle line:90% Excellent question. 00:42:56.730 --> 00:42:57.480 align:middle line:90% I don't know. 00:42:57.480 --> 00:42:59.890 align:middle line:84% The first time I saw this circuit, it bothered me. 00:42:59.890 --> 00:43:03.500 align:middle line:84% I was like, why does that inductor really 00:43:03.500 --> 00:43:06.220 align:middle line:84% carry the sum of the input and output currents? 00:43:06.220 --> 00:43:08.820 align:middle line:84% But let's think about what's going on in this circuit. 00:43:08.820 --> 00:43:12.360 align:middle line:84% Let me pretend that this capacitor is 00:43:12.360 --> 00:43:17.770 align:middle line:84% doing a really good job of filtering so that it carries 00:43:17.770 --> 00:43:19.580 align:middle line:90% all of the AC current. 00:43:19.580 --> 00:43:23.470 align:middle line:84% And so the I2 and I1 are almost constant. 00:43:23.470 --> 00:43:25.990 align:middle line:84% What does the current flow look like? 00:43:25.990 --> 00:43:30.550 align:middle line:84% Well, let me look at, for example, the switch 00:43:30.550 --> 00:43:32.570 align:middle line:90% current flow. 00:43:32.570 --> 00:43:38.030 align:middle line:84% So if I looked at this switch current flow, I switch, 00:43:38.030 --> 00:43:39.925 align:middle line:84% what does the switch current look like? 00:43:39.925 --> 00:43:42.440 align:middle line:90% 00:43:42.440 --> 00:43:44.810 align:middle line:84% Well, in the first part of the cycle-- 00:43:44.810 --> 00:43:47.060 align:middle line:84% or the switch current's carrying IL 00:43:47.060 --> 00:43:48.823 align:middle line:90% in the first part of the cycle. 00:43:48.823 --> 00:43:50.240 align:middle line:84% So in the first part of the cycle, 00:43:50.240 --> 00:43:51.700 align:middle line:90% the switch current carries IL. 00:43:51.700 --> 00:43:58.310 align:middle line:90% 00:43:58.310 --> 00:44:01.270 align:middle line:90% So this is I switch. 00:44:01.270 --> 00:44:03.250 align:middle line:84% And in the second part of the cycle, 00:44:03.250 --> 00:44:06.572 align:middle line:90% the switch carries nothing. 00:44:06.572 --> 00:44:10.060 align:middle line:84% So the switch pulsates between carrying some big current 00:44:10.060 --> 00:44:14.230 align:middle line:90% and carrying 0 and doing this. 00:44:14.230 --> 00:44:17.600 align:middle line:84% And what's the average switch current got to be equal to? 00:44:17.600 --> 00:44:21.940 align:middle line:84% Well, there's no average current coming up through the capacitor. 00:44:21.940 --> 00:44:25.730 align:middle line:84% So on average, the switch current must carry I1. 00:44:25.730 --> 00:44:27.670 align:middle line:90% So this switch has some-- 00:44:27.670 --> 00:44:30.310 align:middle line:90% I switch of T is pulsating. 00:44:30.310 --> 00:44:34.410 align:middle line:84% But his average value has to be I1. 00:44:34.410 --> 00:44:38.850 align:middle line:90% 00:44:38.850 --> 00:44:40.925 align:middle line:84% If I looked at the diode current-- 00:44:40.925 --> 00:44:43.860 align:middle line:90% 00:44:43.860 --> 00:44:47.450 align:middle line:90% here's the diode current-- 00:44:47.450 --> 00:44:52.120 align:middle line:84% when the switch is on, he's carrying 0. 00:44:52.120 --> 00:44:55.850 align:middle line:84% When the switch is off, the diode's carrying IL. 00:44:55.850 --> 00:44:56.650 align:middle line:90% So he steps up. 00:44:56.650 --> 00:44:59.690 align:middle line:90% And he carries all of IL. 00:44:59.690 --> 00:45:02.710 align:middle line:84% So he's switching the opposite way. 00:45:02.710 --> 00:45:05.830 align:middle line:84% And by the same argument, the average of the diode current 00:45:05.830 --> 00:45:06.810 align:middle line:90% must be I2. 00:45:06.810 --> 00:45:13.220 align:middle line:90% 00:45:13.220 --> 00:45:21.020 align:middle line:84% So it turns out that IL is the sum of I1 plus I2 in order 00:45:21.020 --> 00:45:24.250 align:middle line:90% that it be carried-- 00:45:24.250 --> 00:45:27.950 align:middle line:84% it's constantly carrying the sum of I1-- 00:45:27.950 --> 00:45:30.610 align:middle line:84% I switch plus ID is always equal to IL. 00:45:30.610 --> 00:45:34.790 align:middle line:84% So when I add these two up, I get IL. 00:45:34.790 --> 00:45:37.240 align:middle line:84% So that's why the inductor current 00:45:37.240 --> 00:45:40.180 align:middle line:84% has to really carry the sum of the average input and output 00:45:40.180 --> 00:45:42.910 align:middle line:90% currents. 00:45:42.910 --> 00:45:44.750 align:middle line:84% If I thought about the capacitor, 00:45:44.750 --> 00:45:46.700 align:middle line:90% what's the capacitor doing here? 00:45:46.700 --> 00:45:48.580 align:middle line:84% Let me plot the capacitor current. 00:45:48.580 --> 00:45:50.520 align:middle line:84% And maybe we can get some insight from that. 00:45:50.520 --> 00:45:53.300 align:middle line:90% 00:45:53.300 --> 00:45:57.330 align:middle line:84% When the switch is on, IL is coming through here. 00:45:57.330 --> 00:45:59.630 align:middle line:84% Where does I2 go, the average current I2? 00:45:59.630 --> 00:46:02.100 align:middle line:84% It must come negatively through the capacitor. 00:46:02.100 --> 00:46:05.630 align:middle line:84% So the capacitor is carrying minus I2 00:46:05.630 --> 00:46:07.820 align:middle line:90% in the first part of the cycle. 00:46:07.820 --> 00:46:11.840 align:middle line:84% And in the second part of the cycle, when this is off, 00:46:11.840 --> 00:46:14.870 align:middle line:84% I1 must be going positively through the capacitor, 00:46:14.870 --> 00:46:15.775 align:middle line:90% like this. 00:46:15.775 --> 00:46:20.870 align:middle line:90% 00:46:20.870 --> 00:46:23.930 align:middle line:90% And this is I C of T. 00:46:23.930 --> 00:46:28.410 align:middle line:84% What do I know about the average value of I C of T? 00:46:28.410 --> 00:46:29.130 align:middle line:90% 0. 00:46:29.130 --> 00:46:46.040 align:middle line:84% So that must mean that DI2 must equal 1 minus DI1, 00:46:46.040 --> 00:46:54.160 align:middle line:84% or I could write I2 is equal to 1 minus D over D times I1. 00:46:54.160 --> 00:46:58.090 align:middle line:90% 00:46:58.090 --> 00:46:59.740 align:middle line:90% Well, guess what? 00:46:59.740 --> 00:47:02.570 align:middle line:84% That's exactly the complement allowing 00:47:02.570 --> 00:47:07.185 align:middle line:84% for the sign of the voltage conversion ratio, which 00:47:07.185 --> 00:47:09.560 align:middle line:84% comes back to the fact that this thing is supposed to be, 00:47:09.560 --> 00:47:12.250 align:middle line:90% ideally, 100% efficient. 00:47:12.250 --> 00:47:15.670 align:middle line:84% So basically, all of the AC currents 00:47:15.670 --> 00:47:18.910 align:middle line:84% run around in this loop, allowing DC 00:47:18.910 --> 00:47:19.957 align:middle line:90% at the input and output. 00:47:19.957 --> 00:47:22.540 align:middle line:84% But the result of that is that the inductor current must carry 00:47:22.540 --> 00:47:26.030 align:middle line:90% the sum of those currents. 00:47:26.030 --> 00:47:28.090 align:middle line:90% That make sense? 00:47:28.090 --> 00:47:39.730 align:middle line:84% So this is, by the way, known as a buck-boost converter 00:47:39.730 --> 00:47:43.900 align:middle line:84% because it can either step up voltage or down voltage 00:47:43.900 --> 00:47:46.720 align:middle line:84% or step up current or step down current. 00:47:46.720 --> 00:47:50.050 align:middle line:84% It's sometimes known as an inverting buck-boost converter 00:47:50.050 --> 00:47:52.550 align:middle line:84% to distinguish it from other kinds of buck-boost converters. 00:47:52.550 --> 00:47:55.760 align:middle line:84% But this would be the buck-boost converter. 00:47:55.760 --> 00:47:59.086 align:middle line:84% Let me just show you by way of illustration this operation. 00:47:59.086 --> 00:48:02.460 align:middle line:90% 00:48:02.460 --> 00:48:09.570 align:middle line:84% So what I created here, if my computer will wake up, 00:48:09.570 --> 00:48:13.210 align:middle line:84% is a simulation of a very simple buck-boost converter. 00:48:13.210 --> 00:48:18.150 align:middle line:84% So I split the capacitors in this example. 00:48:18.150 --> 00:48:21.810 align:middle line:84% But I'm running from 8.5 volts input. 00:48:21.810 --> 00:48:25.320 align:middle line:84% And we've set our duty ratio to 0.75. 00:48:25.320 --> 00:48:27.050 align:middle line:90% So let me just simulate this. 00:48:27.050 --> 00:48:30.895 align:middle line:90% 00:48:30.895 --> 00:48:33.510 align:middle line:84% And let me just look at what the output does. 00:48:33.510 --> 00:48:36.900 align:middle line:84% At T equals 0, the output is initialized to 0. 00:48:36.900 --> 00:48:40.090 align:middle line:84% And what we can see is the output starts at 0 volts. 00:48:40.090 --> 00:48:41.430 align:middle line:90% But then he goes negative. 00:48:41.430 --> 00:48:44.280 align:middle line:84% And he goes through all this transient-- and stuff happening. 00:48:44.280 --> 00:48:46.560 align:middle line:84% We'll talk about the dynamics of this converter. 00:48:46.560 --> 00:48:50.975 align:middle line:84% But eventually, it gets to periodic steady state out here. 00:48:50.975 --> 00:48:53.700 align:middle line:90% 00:48:53.700 --> 00:48:54.460 align:middle line:90% So what do we see? 00:48:54.460 --> 00:48:57.450 align:middle line:90% There's the output voltage. 00:48:57.450 --> 00:48:58.840 align:middle line:90% Here's the input voltage. 00:48:58.840 --> 00:49:02.040 align:middle line:84% So it's coming from plus 8.5 volts 00:49:02.040 --> 00:49:05.500 align:middle line:90% and going to minus 27 volts. 00:49:05.500 --> 00:49:07.680 align:middle line:84% We can see that this inductor voltage 00:49:07.680 --> 00:49:11.400 align:middle line:90% is pulsing between the two. 00:49:11.400 --> 00:49:13.620 align:middle line:84% So it's acting-- what is it doing 00:49:13.620 --> 00:49:15.470 align:middle line:90% in the first part of the cycle? 00:49:15.470 --> 00:49:17.850 align:middle line:84% It's sucking energy from the input 00:49:17.850 --> 00:49:20.360 align:middle line:90% and storing it in the inductor. 00:49:20.360 --> 00:49:22.040 align:middle line:84% And in the second part of the cycle, 00:49:22.040 --> 00:49:24.210 align:middle line:84% that energy is then being thrown to the output. 00:49:24.210 --> 00:49:26.150 align:middle line:84% So all of the energy in this circuit 00:49:26.150 --> 00:49:28.010 align:middle line:90% is going through the inductor. 00:49:28.010 --> 00:49:31.610 align:middle line:84% The only way energy gets from the input is from the input 00:49:31.610 --> 00:49:32.670 align:middle line:90% into the inductor. 00:49:32.670 --> 00:49:34.520 align:middle line:84% And the only way energy gets to the output 00:49:34.520 --> 00:49:36.440 align:middle line:84% is from the inductor to the output. 00:49:36.440 --> 00:49:40.010 align:middle line:84% So it's an indirect conversion in that all of the energy flow 00:49:40.010 --> 00:49:42.570 align:middle line:84% is mediated through the inductor. 00:49:42.570 --> 00:49:44.130 align:middle line:90% You can see that here. 00:49:44.130 --> 00:49:46.130 align:middle line:84% If I plotted the inductor current, 00:49:46.130 --> 00:49:48.260 align:middle line:84% you can see that in the first part of the cycle, 00:49:48.260 --> 00:49:50.198 align:middle line:84% the inductor's-- current's going up. 00:49:50.198 --> 00:49:51.740 align:middle line:84% In the second part of the cycle, it's 00:49:51.740 --> 00:49:53.433 align:middle line:84% going down because I'm charging up 00:49:53.433 --> 00:49:55.850 align:middle line:84% the inductor from the input in the first part of the cycle 00:49:55.850 --> 00:49:58.310 align:middle line:84% and discharging it into the output in the second part 00:49:58.310 --> 00:49:59.790 align:middle line:90% of the cycle. 00:49:59.790 --> 00:50:02.030 align:middle line:84% So this is a very flexible converter. 00:50:02.030 --> 00:50:04.910 align:middle line:84% But what we're going to see is that it's also 00:50:04.910 --> 00:50:07.910 align:middle line:90% a very high-stress converter. 00:50:07.910 --> 00:50:09.000 align:middle line:90% Why? 00:50:09.000 --> 00:50:12.200 align:middle line:84% Because the inductor has to carry 00:50:12.200 --> 00:50:15.110 align:middle line:84% the sum of the input and output currents. 00:50:15.110 --> 00:50:17.090 align:middle line:84% The capacitor, if I put it here, would 00:50:17.090 --> 00:50:19.350 align:middle line:84% have to block some of the input and output voltages, 00:50:19.350 --> 00:50:20.720 align:middle line:84% or if I have two capacitors, I-- then I 00:50:20.720 --> 00:50:22.100 align:middle line:84% have two capacitors, one of which 00:50:22.100 --> 00:50:24.620 align:middle line:84% blocks the input and one of which blocks the output. 00:50:24.620 --> 00:50:27.920 align:middle line:90% And notice that the switch-- 00:50:27.920 --> 00:50:30.800 align:middle line:84% when it's off, it sees the capacitor voltage 00:50:30.800 --> 00:50:34.220 align:middle line:84% or the sum of the magnitudes of the input and the output 00:50:34.220 --> 00:50:35.850 align:middle line:90% voltage. 00:50:35.850 --> 00:50:39.060 align:middle line:84% When it's on, it's carrying the full inductor current, 00:50:39.060 --> 00:50:42.820 align:middle line:84% which is the sum of the average input and output currents. 00:50:42.820 --> 00:50:47.800 align:middle line:84% So I'll go into this more detail next class. 00:50:47.800 --> 00:50:50.430 align:middle line:84% But what we find is this is a very flexible converter. 00:50:50.430 --> 00:50:53.850 align:middle line:84% But because it modulate or mediates all the power flow 00:50:53.850 --> 00:50:56.520 align:middle line:84% through the inductor-- end ups with very high 00:50:56.520 --> 00:50:59.410 align:middle line:84% stresses on the inductors and capacitors and switches. 00:50:59.410 --> 00:51:02.528 align:middle line:84% And so it tends to be a more expensive converter than a buck 00:51:02.528 --> 00:51:03.820 align:middle line:90% converter or a boost converter. 00:51:03.820 --> 00:51:04.980 align:middle line:90% So if I could only do-- 00:51:04.980 --> 00:51:07.650 align:middle line:84% if I only need a buck function, I don't want to build this guy. 00:51:07.650 --> 00:51:11.130 align:middle line:84% But if I need to raise my voltage 00:51:11.130 --> 00:51:14.620 align:middle line:84% above and below the input, maybe this is a great way to do it. 00:51:14.620 --> 00:51:15.920 align:middle line:90% We're out of time. 00:51:15.920 --> 00:51:17.240 align:middle line:90% We will take this up. 00:51:17.240 --> 00:51:19.180 align:middle line:84% We will see you, remember, next Tuesday 00:51:19.180 --> 00:51:20.540 align:middle line:90% because Monday is a holiday. 00:51:20.540 --> 00:51:23.760 align:middle line:90% So have a great holiday weekend. 00:51:23.760 --> 00:51:26.000 align:middle line:90%