WEBVTT 00:00:00.000 --> 00:00:00.994 align:middle line:90% 00:00:00.994 --> 00:00:02.485 align:middle line:90% [SQUEAKING] 00:00:02.485 --> 00:00:04.473 align:middle line:90% [RUSTLING] 00:00:04.473 --> 00:00:05.964 align:middle line:90% [CLICKING] 00:00:05.964 --> 00:00:12.740 align:middle line:90% 00:00:12.740 --> 00:00:15.020 align:middle line:84% DAVID PERREAULT: OK, why don't we get started? 00:00:15.020 --> 00:00:20.790 align:middle line:84% My computer decided to tank right now, 00:00:20.790 --> 00:00:22.290 align:middle line:84% but we can get started without that. 00:00:22.290 --> 00:00:25.790 align:middle line:90% And then we'll see what it says. 00:00:25.790 --> 00:00:28.580 align:middle line:84% I'd like to continue our discussion 00:00:28.580 --> 00:00:32.950 align:middle line:84% of soft-switched power converters today. 00:00:32.950 --> 00:00:36.910 align:middle line:84% And if you'll recall, when we think of soft switching, 00:00:36.910 --> 00:00:39.220 align:middle line:84% we're thinking of these switching transitions 00:00:39.220 --> 00:00:41.980 align:middle line:84% when we're commutating between devices. 00:00:41.980 --> 00:00:45.490 align:middle line:84% And we said, if I'm going to consider soft switching, 00:00:45.490 --> 00:00:49.750 align:middle line:84% I can consider 0 voltage switching, ZVS, 00:00:49.750 --> 00:00:53.290 align:middle line:90% and 0 current switching, ZCS. 00:00:53.290 --> 00:00:55.290 align:middle line:84% And some switching transitions, you 00:00:55.290 --> 00:00:57.310 align:middle line:84% can get a combination of both of these, 00:00:57.310 --> 00:00:59.130 align:middle line:90% depending upon the design. 00:00:59.130 --> 00:01:04.540 align:middle line:84% But we also have to think about switch turn-off 00:01:04.540 --> 00:01:05.680 align:middle line:90% and switch turn-on. 00:01:05.680 --> 00:01:10.290 align:middle line:90% 00:01:10.290 --> 00:01:15.030 align:middle line:84% So we said, in a turn-off transition, 00:01:15.030 --> 00:01:20.190 align:middle line:84% what we're doing is this the switch current, i switch, 00:01:20.190 --> 00:01:23.760 align:middle line:84% is going from whatever its maximum value is down to 0 00:01:23.760 --> 00:01:25.390 align:middle line:90% in some finite time. 00:01:25.390 --> 00:01:28.500 align:middle line:84% And if I did a hard-switch converter, just 00:01:28.500 --> 00:01:30.720 align:middle line:84% a straight-up buck converter or something, what 00:01:30.720 --> 00:01:32.580 align:middle line:84% I would see that, usually, what would happen 00:01:32.580 --> 00:01:35.850 align:middle line:84% is the voltage on the switch would rise, 00:01:35.850 --> 00:01:37.980 align:middle line:84% and then the current on the switch would fall. 00:01:37.980 --> 00:01:40.930 align:middle line:84% To do a soft-switch transition, we 00:01:40.930 --> 00:01:43.930 align:middle line:84% want to somehow delay the voltage rise, which 00:01:43.930 --> 00:01:46.690 align:middle line:84% we can do by putting a capacitor across the device 00:01:46.690 --> 00:01:49.060 align:middle line:84% as one means of doing this, in which case 00:01:49.060 --> 00:01:51.680 align:middle line:84% we'd see a voltage rise which did something like this. 00:01:51.680 --> 00:01:55.660 align:middle line:84% Maybe it would do this, like this. 00:01:55.660 --> 00:01:57.290 align:middle line:90% And we would delay the rise. 00:01:57.290 --> 00:01:59.950 align:middle line:90% 00:01:59.950 --> 00:02:06.610 align:middle line:84% The comparison to that is if I did a zero-voltage switch 00:02:06.610 --> 00:02:07.840 align:middle line:90% turn-on. 00:02:07.840 --> 00:02:10.870 align:middle line:84% In a switch turn-on, what we expect to have 00:02:10.870 --> 00:02:14.711 align:middle line:84% is that the current in the device falls. 00:02:14.711 --> 00:02:16.503 align:middle line:84% I'm sorry, the current in the device rises. 00:02:16.503 --> 00:02:22.990 align:middle line:90% 00:02:22.990 --> 00:02:27.010 align:middle line:84% So if pink is the switch voltage and green 00:02:27.010 --> 00:02:30.620 align:middle line:84% is the switch current, what I get 00:02:30.620 --> 00:02:34.903 align:middle line:84% at switch turn-on is, usually, the current in the switch 00:02:34.903 --> 00:02:35.403 align:middle line:90% rising. 00:02:35.403 --> 00:02:38.620 align:middle line:90% 00:02:38.620 --> 00:02:40.510 align:middle line:90% So here's i switch. 00:02:40.510 --> 00:02:43.660 align:middle line:84% And usually, what happens is if I'm 00:02:43.660 --> 00:02:47.320 align:middle line:84% doing a hard-switch transition, the switch current comes up, 00:02:47.320 --> 00:02:51.250 align:middle line:84% and then the switch voltage falls some time after that. 00:02:51.250 --> 00:02:53.470 align:middle line:84% In a zero-voltage turn-on, what I do 00:02:53.470 --> 00:02:56.380 align:middle line:84% is try to make some kind of circuit magic 00:02:56.380 --> 00:03:00.790 align:middle line:84% such that I will already make the voltage on the switch 0 00:03:00.790 --> 00:03:05.480 align:middle line:84% somehow before I turn the switch on and the current rises. 00:03:05.480 --> 00:03:08.800 align:middle line:84% So I'm going to have some kind of circuit magic 00:03:08.800 --> 00:03:10.610 align:middle line:90% that lets me make the voltage 0. 00:03:10.610 --> 00:03:12.190 align:middle line:84% Or another way to look at it is-- 00:03:12.190 --> 00:03:16.210 align:middle line:84% and I only turn on the switch when the voltage is 0. 00:03:16.210 --> 00:03:18.070 align:middle line:90% Now, that's ZVS. 00:03:18.070 --> 00:03:21.970 align:middle line:84% And ZVS just turns out to be best for really high-frequency 00:03:21.970 --> 00:03:22.480 align:middle line:90% designs. 00:03:22.480 --> 00:03:24.940 align:middle line:84% Because I also take care of issues 00:03:24.940 --> 00:03:29.470 align:middle line:84% with discharging the switch capacitance at the switching 00:03:29.470 --> 00:03:31.660 align:middle line:90% turn-off transition. 00:03:31.660 --> 00:03:36.790 align:middle line:84% But I can also do zero-current switching. 00:03:36.790 --> 00:03:41.850 align:middle line:84% So zero-current turn-on is the dual of zero-voltage turn-off. 00:03:41.850 --> 00:03:45.620 align:middle line:84% So what we have here is that the switch voltage is falling. 00:03:45.620 --> 00:03:48.970 align:middle line:90% 00:03:48.970 --> 00:03:51.040 align:middle line:90% So this is v switch. 00:03:51.040 --> 00:03:54.820 align:middle line:84% And normally, what we would have is the switch current 00:03:54.820 --> 00:04:00.890 align:middle line:84% rising before the switch voltage falls. 00:04:00.890 --> 00:04:05.210 align:middle line:84% But maybe I can delay that somehow and really 00:04:05.210 --> 00:04:13.160 align:middle line:84% reduce this overlap, like this, and get a reduced switch overlap 00:04:13.160 --> 00:04:14.790 align:middle line:90% between turn-on and turn-off. 00:04:14.790 --> 00:04:17.100 align:middle line:90% And I can usually do this delay. 00:04:17.100 --> 00:04:19.160 align:middle line:84% One way to do it is to put an inductor in series 00:04:19.160 --> 00:04:19.860 align:middle line:90% with the device. 00:04:19.860 --> 00:04:23.180 align:middle line:84% So when I turn it on, the inductor takes up the voltage 00:04:23.180 --> 00:04:26.990 align:middle line:84% and, hence, we can have low voltage 00:04:26.990 --> 00:04:29.510 align:middle line:84% while the switch is still turning on. 00:04:29.510 --> 00:04:34.580 align:middle line:84% And lastly, we can have a zero-current switch turn-off, 00:04:34.580 --> 00:04:41.720 align:middle line:84% which is the dual here, which is what I'm going to have is, 00:04:41.720 --> 00:04:43.370 align:middle line:84% when I'm turning the switch off, I'm 00:04:43.370 --> 00:04:46.015 align:middle line:84% going to have a rise in the switch voltage, like this. 00:04:46.015 --> 00:04:51.720 align:middle line:90% 00:04:51.720 --> 00:04:55.080 align:middle line:84% And normally, the current and the switch 00:04:55.080 --> 00:04:59.700 align:middle line:84% can only fall after the switch voltage rises. 00:04:59.700 --> 00:05:01.028 align:middle line:90% So here's i switch. 00:05:01.028 --> 00:05:02.570 align:middle line:84% And what we're going to do is somehow 00:05:02.570 --> 00:05:04.820 align:middle line:84% play some kind of magic game where 00:05:04.820 --> 00:05:07.520 align:middle line:84% we're going to make sure that the current and the switch 00:05:07.520 --> 00:05:12.611 align:middle line:84% is 0 before I ever try to turn it off. 00:05:12.611 --> 00:05:15.320 align:middle line:84% So I can use any combination of these kind 00:05:15.320 --> 00:05:21.410 align:middle line:84% of switching transitions in order to get soft switching. 00:05:21.410 --> 00:05:25.010 align:middle line:84% And we saw a few examples in DC to DC converters 00:05:25.010 --> 00:05:28.280 align:middle line:90% where we did that last time. 00:05:28.280 --> 00:05:30.380 align:middle line:84% Let me pause there and just ask if there's 00:05:30.380 --> 00:05:32.353 align:middle line:84% any questions about the general concept. 00:05:32.353 --> 00:05:38.580 align:middle line:90% 00:05:38.580 --> 00:05:39.150 align:middle line:90% OK. 00:05:39.150 --> 00:05:43.640 align:middle line:84% So what do I get out of soft switching? 00:05:43.640 --> 00:05:49.010 align:middle line:84% Soft switching, it's implied that if I'm snubbing the switch 00:05:49.010 --> 00:05:52.050 align:middle line:84% transition, I'm doing it in a pseudo lossless fashion, 00:05:52.050 --> 00:05:54.500 align:middle line:84% meaning if I put a capacitor across the device 00:05:54.500 --> 00:05:57.230 align:middle line:84% for the turn-off loss, I'm going to recover that energy. 00:05:57.230 --> 00:06:03.170 align:middle line:84% So one thing I can get out of it is I reduce the switching loss. 00:06:03.170 --> 00:06:11.280 align:middle line:84% So one thing I can get out of this is the switching-- 00:06:11.280 --> 00:06:15.590 align:middle line:84% I'm sorry-- P switching goes down. 00:06:15.590 --> 00:06:18.710 align:middle line:84% And I can either use that to make the switching frequency 00:06:18.710 --> 00:06:22.070 align:middle line:84% higher because the switching loss is 00:06:22.070 --> 00:06:23.160 align:middle line:90% proportional to frequency. 00:06:23.160 --> 00:06:25.827 align:middle line:84% So if I've turned it down, I can turn the switching frequency up 00:06:25.827 --> 00:06:27.860 align:middle line:84% and then make my components smaller. 00:06:27.860 --> 00:06:30.380 align:middle line:84% So one benefit of this is I typically 00:06:30.380 --> 00:06:32.480 align:middle line:84% can push up my switching frequency 00:06:32.480 --> 00:06:35.300 align:middle line:90% and push down my converter size. 00:06:35.300 --> 00:06:38.443 align:middle line:84% The other thing I can do is push up my efficiency. 00:06:38.443 --> 00:06:39.860 align:middle line:84% So if I have lower switching loss, 00:06:39.860 --> 00:06:43.460 align:middle line:84% I just take that out as efficiency or some combination 00:06:43.460 --> 00:06:44.250 align:middle line:90% thereof. 00:06:44.250 --> 00:06:49.180 align:middle line:84% And that's one major reason to do soft switching. 00:06:49.180 --> 00:06:51.040 align:middle line:84% A second reason to do soft switching 00:06:51.040 --> 00:06:52.720 align:middle line:90% is a little bit more subtle. 00:06:52.720 --> 00:06:57.750 align:middle line:84% We spent a bunch of time talking about EMI. 00:06:57.750 --> 00:07:03.240 align:middle line:84% And one of the things is for a given switching transition, 00:07:03.240 --> 00:07:09.070 align:middle line:84% if I had a very rapid, say, dv/dt here, 00:07:09.070 --> 00:07:11.470 align:middle line:84% if I'm going to soft switch, usually, 00:07:11.470 --> 00:07:16.090 align:middle line:84% what I'm doing is I'm arranging so that the voltage slope is 00:07:16.090 --> 00:07:17.370 align:middle line:90% lower. 00:07:17.370 --> 00:07:27.980 align:middle line:84% So I can reduce EMI in a soft switch converter 00:07:27.980 --> 00:07:29.570 align:middle line:90% in a lot of cases. 00:07:29.570 --> 00:07:31.700 align:middle line:84% So another reason people will often 00:07:31.700 --> 00:07:34.370 align:middle line:84% use soft switching is because they 00:07:34.370 --> 00:07:38.930 align:middle line:84% want to get nice, smooth waveforms 00:07:38.930 --> 00:07:42.440 align:middle line:84% and, hence, reduced EMI in the converter. 00:07:42.440 --> 00:07:44.950 align:middle line:90% So if we were to think about-- 00:07:44.950 --> 00:07:48.590 align:middle line:84% let me think about, before we talk more about soft switching, 00:07:48.590 --> 00:07:53.650 align:middle line:84% let me think about this in a little bit more detail. 00:07:53.650 --> 00:07:55.270 align:middle line:90% If I were to come back-- 00:07:55.270 --> 00:07:58.660 align:middle line:90% and give me one moment here-- 00:07:58.660 --> 00:08:03.290 align:middle line:84% let's think about the soft switching impacts on EMI. 00:08:03.290 --> 00:08:07.060 align:middle line:84% So if I thought about my buck converter, for example-- 00:08:07.060 --> 00:08:09.850 align:middle line:90% so here's my buck converter. 00:08:09.850 --> 00:08:13.690 align:middle line:84% And usually, I'm going to put some input filter here. 00:08:13.690 --> 00:08:17.560 align:middle line:90% But in the buck converter-- 00:08:17.560 --> 00:08:20.200 align:middle line:84% in the input filter, maybe I consider the input capacitor, 00:08:20.200 --> 00:08:20.810 align:middle line:90% too-- 00:08:20.810 --> 00:08:22.562 align:middle line:84% let me just think of this as IDC. 00:08:22.562 --> 00:08:27.750 align:middle line:90% 00:08:27.750 --> 00:08:31.800 align:middle line:84% If I were to look at this current, 00:08:31.800 --> 00:08:35.850 align:middle line:84% this current that I'm drawing through the input switch-- 00:08:35.850 --> 00:08:38.370 align:middle line:90% I'll call that ix-- 00:08:38.370 --> 00:08:40.785 align:middle line:90% is, more or less, a square wave. 00:08:40.785 --> 00:08:44.780 align:middle line:90% 00:08:44.780 --> 00:08:47.180 align:middle line:84% It has some finite slope on it, but I'm 00:08:47.180 --> 00:08:50.210 align:middle line:84% looking at some kind of square wave slope 00:08:50.210 --> 00:08:53.840 align:middle line:84% With time, so if I were to look at this. 00:08:53.840 --> 00:08:59.490 align:middle line:84% And so the frequency content is what drives my filter. 00:08:59.490 --> 00:09:05.310 align:middle line:84% And then that's what sets what shows up, say, at my input. 00:09:05.310 --> 00:09:09.240 align:middle line:90% Likewise, if I looked at-- 00:09:09.240 --> 00:09:12.750 align:middle line:84% be helpful if I put a diode here instead of a capacitor. 00:09:12.750 --> 00:09:16.260 align:middle line:84% If I looked at the switch voltage-- 00:09:16.260 --> 00:09:19.180 align:middle line:90% let me call this vy-- 00:09:19.180 --> 00:09:21.510 align:middle line:90% vy has the same sort of shape. 00:09:21.510 --> 00:09:26.460 align:middle line:84% I have high for some time DT and then 00:09:26.460 --> 00:09:29.520 align:middle line:84% low for the rest of the cycle, for T. 00:09:29.520 --> 00:09:34.890 align:middle line:84% And I've got this very sharp-edged waveform right here. 00:09:34.890 --> 00:09:37.615 align:middle line:84% Now, that doesn't appear specifically 00:09:37.615 --> 00:09:38.490 align:middle line:90% out of the converter. 00:09:38.490 --> 00:09:44.040 align:middle line:84% But remember, maybe I might have some parasitic capacitance 00:09:44.040 --> 00:09:47.490 align:middle line:84% coming back here and either into my filter somewhere 00:09:47.490 --> 00:09:49.090 align:middle line:90% or towards my input somewhere. 00:09:49.090 --> 00:09:54.360 align:middle line:84% So basically, this very sharp voltage injects currents back. 00:09:54.360 --> 00:09:58.110 align:middle line:84% And that can appear as noise, either within my circuit 00:09:58.110 --> 00:10:02.685 align:middle line:84% or at the input or output somewhere. 00:10:02.685 --> 00:10:06.030 align:middle line:84% So one of the things that influences 00:10:06.030 --> 00:10:08.310 align:middle line:84% how much EMI your converter generates 00:10:08.310 --> 00:10:21.333 align:middle line:84% is the di/dt here or the dv/dt here. 00:10:21.333 --> 00:10:22.750 align:middle line:84% Does that make sense to everybody? 00:10:22.750 --> 00:10:29.180 align:middle line:90% 00:10:29.180 --> 00:10:40.210 align:middle line:84% So let's think about what's the impact of square wave switching. 00:10:40.210 --> 00:10:42.320 align:middle line:90% Because what are we going to do? 00:10:42.320 --> 00:10:46.480 align:middle line:84% Maybe if I use zero-voltage switching here, instead of 00:10:46.480 --> 00:10:51.310 align:middle line:84% having a really steep waveform vy, maybe what I would have 00:10:51.310 --> 00:10:56.680 align:middle line:84% is a more slew rate limited waveform here. 00:10:56.680 --> 00:11:01.120 align:middle line:84% And so what's the impact of this slew rate on dv/dt 00:11:01.120 --> 00:11:06.970 align:middle line:84% or the slew rate on di/dt if I had lower di/dt switching 00:11:06.970 --> 00:11:11.500 align:middle line:84% transitions on the fundamental waveforms? 00:11:11.500 --> 00:11:21.190 align:middle line:84% And here is what we can say about a square wave waveform. 00:11:21.190 --> 00:11:24.220 align:middle line:84% And it doesn't matter what the shape of the square wave is. 00:11:24.220 --> 00:11:31.320 align:middle line:84% But let's just say this was a current i of t. 00:11:31.320 --> 00:11:34.140 align:middle line:84% And here's the waveform I'm going to consider. 00:11:34.140 --> 00:11:37.860 align:middle line:84% I'm going to say, OK, it's going to have some finite slew rate up 00:11:37.860 --> 00:11:43.210 align:middle line:84% to a maximum current I. And it's going 00:11:43.210 --> 00:11:45.208 align:middle line:90% to have some slew rate down. 00:11:45.208 --> 00:11:46.750 align:middle line:84% And at the end of this, here is going 00:11:46.750 --> 00:11:48.820 align:middle line:84% to be some period T. And let me call 00:11:48.820 --> 00:11:55.160 align:middle line:84% this period to the middle of the rise some time period DT. 00:11:55.160 --> 00:11:59.720 align:middle line:90% 00:11:59.720 --> 00:12:03.520 align:middle line:84% And then I'm also going to worry about-- 00:12:03.520 --> 00:12:06.540 align:middle line:90% I'm going to call this t rise. 00:12:06.540 --> 00:12:07.880 align:middle line:90% I'm going to call this t rise. 00:12:07.880 --> 00:12:11.170 align:middle line:84% Let me assume the rising and falling slopes are the same. 00:12:11.170 --> 00:12:12.910 align:middle line:84% They may not be in the real circuit, 00:12:12.910 --> 00:12:17.090 align:middle line:84% but, for purposes of analysis, we can consider that way. 00:12:17.090 --> 00:12:21.480 align:middle line:84% So I'm exaggerating this rectangle wave 00:12:21.480 --> 00:12:24.480 align:middle line:84% into a trapezoid wave just for illustrative purposes. 00:12:24.480 --> 00:12:26.900 align:middle line:84% Does that make sense to everybody? 00:12:26.900 --> 00:12:30.230 align:middle line:84% Here is what the magnitude of the n-th Fourier coefficient 00:12:30.230 --> 00:12:31.290 align:middle line:90% looks like. 00:12:31.290 --> 00:12:33.180 align:middle line:90% You can derive this. 00:12:33.180 --> 00:12:38.120 align:middle line:84% I actually took this version from Ott's Electromagnetic 00:12:38.120 --> 00:12:42.770 align:middle line:84% Compatibility book, but it's also in KPBS. 00:12:42.770 --> 00:12:43.670 align:middle line:90% It looks like this-- 00:12:43.670 --> 00:12:48.790 align:middle line:90% 2ID, or it's 2ID. 00:12:48.790 --> 00:12:59.720 align:middle line:84% I'm sorry, it's 2I times the duty ratio times sine of n pi D 00:12:59.720 --> 00:13:17.750 align:middle line:84% over pi n D times sine of n pi tr over T divided by pi n pi tr 00:13:17.750 --> 00:13:25.670 align:middle line:84% over T. So This is the n-th coefficient. 00:13:25.670 --> 00:13:29.840 align:middle line:84% And the whole waveform has the sum of these individual Fourier 00:13:29.840 --> 00:13:32.450 align:middle line:90% coefficients. 00:13:32.450 --> 00:13:36.200 align:middle line:90% So why am I raising this? 00:13:36.200 --> 00:13:39.080 align:middle line:84% Each of these is a sinc function. 00:13:39.080 --> 00:13:46.730 align:middle line:84% This is a sinc function in terms of the duty ratio. 00:13:46.730 --> 00:13:48.546 align:middle line:90% And this is a sinc function-- 00:13:48.546 --> 00:13:52.230 align:middle line:90% 00:13:52.230 --> 00:13:58.230 align:middle line:84% this is a sinc function in terms of the percentage rise time. 00:13:58.230 --> 00:14:00.280 align:middle line:84% And this is for the n-th harmonic, 00:14:00.280 --> 00:14:03.060 align:middle line:84% so it's at the n-th frequency, So this 00:14:03.060 --> 00:14:05.460 align:middle line:84% is multiples of the switching frequency, 00:14:05.460 --> 00:14:07.180 align:middle line:90% essentially, where these appear. 00:14:07.180 --> 00:14:09.420 align:middle line:84% And then this sinc function is related 00:14:09.420 --> 00:14:15.030 align:middle line:84% to the slew rate normalized to the period, the percentage rise 00:14:15.030 --> 00:14:18.200 align:middle line:90% time, if you will. 00:14:18.200 --> 00:14:20.850 align:middle line:90% Why do I raise that? 00:14:20.850 --> 00:14:26.520 align:middle line:84% Because think about what a sinc function looks like, 00:14:26.520 --> 00:14:30.960 align:middle line:90% A sinc function looks like this. 00:14:30.960 --> 00:14:33.220 align:middle line:90% It falls off. 00:14:33.220 --> 00:14:35.820 align:middle line:90% It starts at a certain height 1. 00:14:35.820 --> 00:14:41.860 align:middle line:84% And it falls off like this, like this. 00:14:41.860 --> 00:14:46.710 align:middle line:84% At really low frequencies, a sinc function asymptotes to 1. 00:14:46.710 --> 00:14:49.960 align:middle line:90% 00:14:49.960 --> 00:14:58.250 align:middle line:84% Above x equals 1-- if this is sinc of x, above x equals 1, 00:14:58.250 --> 00:15:08.590 align:middle line:84% you get an asymptote that does this, that goes as 1 over x. 00:15:08.590 --> 00:15:10.815 align:middle line:84% So what I'm looking at isn't the actual value 00:15:10.815 --> 00:15:12.190 align:middle line:84% of the sinc function at any point 00:15:12.190 --> 00:15:15.080 align:middle line:84% but what does the envelope of the peaks of the sinc function 00:15:15.080 --> 00:15:16.380 align:middle line:90% do. 00:15:16.380 --> 00:15:17.820 align:middle line:90% That make sense to everybody? 00:15:17.820 --> 00:15:21.530 align:middle line:90% So at low frequencies, it's DC. 00:15:21.530 --> 00:15:22.860 align:middle line:90% It's constant. 00:15:22.860 --> 00:15:25.350 align:middle line:84% And at high frequencies, it falls off as 1 00:15:25.350 --> 00:15:27.360 align:middle line:90% over x, whatever x is. 00:15:27.360 --> 00:15:29.160 align:middle line:84% And we have the product of two state 00:15:29.160 --> 00:15:33.390 align:middle line:90% functions for our waveform. 00:15:33.390 --> 00:15:34.990 align:middle line:90% So what does that mean? 00:15:34.990 --> 00:15:36.990 align:middle line:84% Well, let's just start by saying, 00:15:36.990 --> 00:15:41.220 align:middle line:84% suppose I have a perfect square wave. 00:15:41.220 --> 00:15:47.670 align:middle line:84% Suppose I have a design where, yeah, these walls are so steep, 00:15:47.670 --> 00:15:49.600 align:middle line:84% it's, more or less, instantaneous. 00:15:49.600 --> 00:15:51.947 align:middle line:84% What would the frequency distribution of that look like? 00:15:51.947 --> 00:15:53.530 align:middle line:84% And what would the waveform look like? 00:15:53.530 --> 00:15:54.610 align:middle line:90% Well, here we go. 00:15:54.610 --> 00:15:59.880 align:middle line:84% And I should say that I'm taking these very nice slides 00:15:59.880 --> 00:16:02.940 align:middle line:84% from a presentation done by John McCloskey, who's 00:16:02.940 --> 00:16:06.480 align:middle line:84% the chief electromagnetic compatibility engineer for NASA. 00:16:06.480 --> 00:16:10.950 align:middle line:84% And he put together a really nice presentation on this. 00:16:10.950 --> 00:16:14.880 align:middle line:84% So this just shows, suppose I have 00:16:14.880 --> 00:16:19.810 align:middle line:84% a square wave, or a rectangle wave, of duty ratio D. 00:16:19.810 --> 00:16:22.540 align:middle line:84% And here's the individual harmonic terms. 00:16:22.540 --> 00:16:24.710 align:middle line:84% And as I add up more and more harmonics, 00:16:24.710 --> 00:16:26.440 align:middle line:90% you get a square wave. 00:16:26.440 --> 00:16:28.030 align:middle line:90% That make sense to everybody? 00:16:28.030 --> 00:16:35.560 align:middle line:84% And because I've ignored, I've made tr over T to 0, 00:16:35.560 --> 00:16:39.170 align:middle line:84% this whole factor just becomes 1. 00:16:39.170 --> 00:16:44.560 align:middle line:84% So I get harmonics that fall off as a sinc function in frequency. 00:16:44.560 --> 00:16:46.630 align:middle line:90% So what does that look like? 00:16:46.630 --> 00:16:49.870 align:middle line:90% That looks exactly like this. 00:16:49.870 --> 00:16:52.550 align:middle line:84% So here's exactly the envelope I'm talking about. 00:16:52.550 --> 00:16:58.990 align:middle line:90% This is in a linear scale. 00:16:58.990 --> 00:17:01.030 align:middle line:84% So at low frequency, it has constant, 00:17:01.030 --> 00:17:04.270 align:middle line:84% and then it falls off as 1 over x. 00:17:04.270 --> 00:17:09.400 align:middle line:84% If I looked at this on a log-log plot, what I get 00:17:09.400 --> 00:17:15.520 align:middle line:84% is constant up to x equals 1 and then falls off as 1 00:17:15.520 --> 00:17:17.775 align:middle line:84% over x, which is minus 20 db per decade. 00:17:17.775 --> 00:17:20.316 align:middle line:90% 00:17:20.316 --> 00:17:21.960 align:middle line:90% So why am I bringing this up? 00:17:21.960 --> 00:17:24.690 align:middle line:84% What I'm trying to say is, Where is the energy content 00:17:24.690 --> 00:17:26.550 align:middle line:90% in my square wave waveform? 00:17:26.550 --> 00:17:31.440 align:middle line:84% It's sitting at a bunch of harmonics. 00:17:31.440 --> 00:17:34.870 align:middle line:84% And I'm not really worried about the individual harmonics. 00:17:34.870 --> 00:17:36.640 align:middle line:84% I'm just worried about how the envelope 00:17:36.640 --> 00:17:39.920 align:middle line:84% of those harmonic amplitudes fall off. 00:17:39.920 --> 00:17:42.490 align:middle line:84% So an individual harmonic might be really low, 00:17:42.490 --> 00:17:48.240 align:middle line:84% but they will be no bigger than the envelope dictated 00:17:48.240 --> 00:17:50.030 align:middle line:90% by the sinc function. 00:17:50.030 --> 00:17:52.170 align:middle line:90% Some of them will get 0. 00:17:52.170 --> 00:17:53.620 align:middle line:90% Some of them will be maximum. 00:17:53.620 --> 00:17:56.970 align:middle line:84% But if I'm just looking at how the energy goes down overall, 00:17:56.970 --> 00:18:00.350 align:middle line:84% it goes as 1 over frequency for higher frequencies. 00:18:00.350 --> 00:18:03.060 align:middle line:84% So if I looked at my square wave, in this case, 00:18:03.060 --> 00:18:04.420 align:middle line:90% this is what happens. 00:18:04.420 --> 00:18:06.150 align:middle line:84% Essentially, I have the fundamental. 00:18:06.150 --> 00:18:08.190 align:middle line:84% And then everything tends to fall off 00:18:08.190 --> 00:18:12.260 align:middle line:84% with an envelope that goes as 1 over the frequency. 00:18:12.260 --> 00:18:13.435 align:middle line:90% Any questions about that? 00:18:13.435 --> 00:18:17.400 align:middle line:90% 00:18:17.400 --> 00:18:21.990 align:middle line:84% So now, what happens if I then say, 00:18:21.990 --> 00:18:25.500 align:middle line:84% all right, I don't switch my waveforms and exchange there. 00:18:25.500 --> 00:18:29.580 align:middle line:84% I don't have really fast gate drives and no capacitance 00:18:29.580 --> 00:18:31.000 align:middle line:90% at my switching node. 00:18:31.000 --> 00:18:34.260 align:middle line:84% And I, instead, allow something that 00:18:34.260 --> 00:18:36.360 align:middle line:84% limits the slew rate and voltage or current, 00:18:36.360 --> 00:18:37.777 align:middle line:84% depending upon whether I'm talking 00:18:37.777 --> 00:18:39.780 align:middle line:90% about a voltage or current. 00:18:39.780 --> 00:18:42.060 align:middle line:84% This would be exactly the impact of, 00:18:42.060 --> 00:18:45.330 align:middle line:84% instead of having really hard and fast switching transitions, 00:18:45.330 --> 00:18:49.080 align:middle line:84% maybe I put a capacitor across my device that limited 00:18:49.080 --> 00:18:51.810 align:middle line:90% the dv/dt to a reduced value. 00:18:51.810 --> 00:18:55.080 align:middle line:84% Maybe this would instead turn into some kind 00:18:55.080 --> 00:18:57.000 align:middle line:90% of trapezoid waveform. 00:18:57.000 --> 00:19:02.370 align:middle line:84% And what I get is this second sinc function factor, which 00:19:02.370 --> 00:19:04.680 align:middle line:84% is related to the percentage of time 00:19:04.680 --> 00:19:07.170 align:middle line:90% it spends rising and falling. 00:19:07.170 --> 00:19:09.810 align:middle line:84% Does that make sense to everybody? 00:19:09.810 --> 00:19:13.640 align:middle line:90% So here's what happens. 00:19:13.640 --> 00:19:16.070 align:middle line:84% From the original square wave, I get 00:19:16.070 --> 00:19:20.060 align:middle line:84% something that starts off at DC and then falls at 1 over f. 00:19:20.060 --> 00:19:23.150 align:middle line:84% And then, at higher frequencies, I 00:19:23.150 --> 00:19:27.350 align:middle line:84% get this additional attenuation of another 20 db per decade. 00:19:27.350 --> 00:19:30.500 align:middle line:84% And that's because of the roll-off of the second product 00:19:30.500 --> 00:19:33.200 align:middle line:90% of the sinc function. 00:19:33.200 --> 00:19:36.090 align:middle line:90% Make sense to everybody? 00:19:36.090 --> 00:19:36.990 align:middle line:90% Yeah, Loren? 00:19:36.990 --> 00:19:41.160 align:middle line:84% AUDIENCE: So why would they not have [INAUDIBLE] frequencies? 00:19:41.160 --> 00:19:43.140 align:middle line:84% DAVID PERREAULT: Because, remember, 00:19:43.140 --> 00:19:48.060 align:middle line:84% the sinc starts falling, sinc of x 00:19:48.060 --> 00:19:53.560 align:middle line:84% starts falling, when the asymptote is above x. 00:19:53.560 --> 00:19:56.560 align:middle line:84% So it's going to start rolling off 00:19:56.560 --> 00:19:58.810 align:middle line:84% when whatever the argument of the sinc function is 00:19:58.810 --> 00:20:00.520 align:middle line:90% becomes greater than 1. 00:20:00.520 --> 00:20:07.730 align:middle line:84% So what that means is when tr over T 00:20:07.730 --> 00:20:12.060 align:middle line:84% is really small, it doesn't attenuate. 00:20:12.060 --> 00:20:15.010 align:middle line:84% And then, when I get to higher frequencies, it does attenuate. 00:20:15.010 --> 00:20:18.740 align:middle line:90% 00:20:18.740 --> 00:20:21.160 align:middle line:84% So what that should mean, then, is 00:20:21.160 --> 00:20:25.660 align:middle line:84% that, compared to having pure, sharp square waveforms, if I can 00:20:25.660 --> 00:20:29.230 align:middle line:84% do something that slows the dv/dt or the di/dt down, 00:20:29.230 --> 00:20:32.640 align:middle line:84% I should get reduced high-frequency content. 00:20:32.640 --> 00:20:34.430 align:middle line:84% And that should make it easier to filter. 00:20:34.430 --> 00:20:37.620 align:middle line:90% 00:20:37.620 --> 00:20:38.752 align:middle line:90% Let's see this in action. 00:20:38.752 --> 00:20:40.710 align:middle line:84% And this is what I love about this presentation 00:20:40.710 --> 00:20:41.585 align:middle line:90% that he put together. 00:20:41.585 --> 00:20:45.500 align:middle line:90% 00:20:45.500 --> 00:20:47.960 align:middle line:84% What the author of the original presentation did 00:20:47.960 --> 00:20:50.330 align:middle line:84% was build a setup, get a signal generator, 00:20:50.330 --> 00:20:53.210 align:middle line:84% measure the voltage waveform, and then measure 00:20:53.210 --> 00:20:56.150 align:middle line:84% the spectral content so you can see exactly what happens 00:20:56.150 --> 00:20:58.100 align:middle line:90% with the actual waveform. 00:20:58.100 --> 00:21:01.610 align:middle line:90% And here's the applied waveform. 00:21:01.610 --> 00:21:04.190 align:middle line:84% He's just doing exactly what we said. 00:21:04.190 --> 00:21:07.230 align:middle line:90% And he's varying the parameters. 00:21:07.230 --> 00:21:08.370 align:middle line:90% And here we go. 00:21:08.370 --> 00:21:11.720 align:middle line:84% He's got a 100-microsecond waveform that's, like, 00:21:11.720 --> 00:21:12.630 align:middle line:90% 10 kilohertz. 00:21:12.630 --> 00:21:15.380 align:middle line:84% So this is low frequency, easy to measure, 00:21:15.380 --> 00:21:16.920 align:middle line:90% easy to generate and measure. 00:21:16.920 --> 00:21:19.350 align:middle line:84% And what you can see is exactly what he said. 00:21:19.350 --> 00:21:21.630 align:middle line:90% It's a 50% duty ratio waveform. 00:21:21.630 --> 00:21:25.580 align:middle line:84% It's not 0 rise and fall time, but it's pretty small. 00:21:25.580 --> 00:21:30.710 align:middle line:84% And what you can see is exactly that it falls above-- 00:21:30.710 --> 00:21:32.600 align:middle line:84% the fundamental falls off as 1 over f, 00:21:32.600 --> 00:21:35.700 align:middle line:84% basically, exactly what we would expect to see. 00:21:35.700 --> 00:21:39.050 align:middle line:84% And here, you can see, OK, the even harmonics are low, 00:21:39.050 --> 00:21:41.210 align:middle line:84% and the odd harmonics are high because this 00:21:41.210 --> 00:21:43.730 align:middle line:90% is, ideally, a 50% waveform. 00:21:43.730 --> 00:21:47.890 align:middle line:84% And there's no even harmonics in it, 00:21:47.890 --> 00:21:50.180 align:middle line:84% except that it's not precisely 50%. 00:21:50.180 --> 00:21:53.980 align:middle line:84% So at high frequencies, there is some content. 00:21:53.980 --> 00:21:57.730 align:middle line:84% What happens if you go from 40 nanoseconds 00:21:57.730 --> 00:22:02.140 align:middle line:84% to 360 nanoseconds for rise and fall time? 00:22:02.140 --> 00:22:05.820 align:middle line:90% So that's 0.36%. 00:22:05.820 --> 00:22:09.510 align:middle line:84% When you get to a high enough frequency, boy, 00:22:09.510 --> 00:22:13.840 align:middle line:84% some of the high-frequency content starts to go away. 00:22:13.840 --> 00:22:15.690 align:middle line:84% What if I were to slow it down more? 00:22:15.690 --> 00:22:19.390 align:middle line:84% What if I were to make this, instead of 0.36% rise 00:22:19.390 --> 00:22:23.530 align:middle line:90% time, 3.6% rise time? 00:22:23.530 --> 00:22:24.030 align:middle line:90% Wow. 00:22:24.030 --> 00:22:26.570 align:middle line:84% I'm really killing off the high frequencies. 00:22:26.570 --> 00:22:29.480 align:middle line:84% If I make it 10% rise time, I'm really 00:22:29.480 --> 00:22:30.980 align:middle line:90% killing off high frequencies. 00:22:30.980 --> 00:22:35.210 align:middle line:84% Now, maybe in a reality, maybe I wouldn't let my transitions take 00:22:35.210 --> 00:22:36.840 align:middle line:90% that long, or maybe I would. 00:22:36.840 --> 00:22:40.310 align:middle line:84% If you looked at the transitions in some of those waveforms 00:22:40.310 --> 00:22:42.620 align:middle line:84% we showed you in the last class, they 00:22:42.620 --> 00:22:44.870 align:middle line:84% were pretty slow compared to the switching period 00:22:44.870 --> 00:22:48.900 align:middle line:84% because you're using it to get the ZVS. 00:22:48.900 --> 00:22:52.400 align:middle line:84% So what you really get, one of the effects you get, 00:22:52.400 --> 00:22:57.590 align:middle line:84% is as you as you slow up the slew rates, 00:22:57.590 --> 00:23:04.150 align:middle line:84% you start to kill off a bunch of high-frequency content. 00:23:04.150 --> 00:23:07.990 align:middle line:84% Now, your filter is sized, typically, 00:23:07.990 --> 00:23:10.750 align:middle line:90% for the lowest frequencies. 00:23:10.750 --> 00:23:12.640 align:middle line:84% But when you put parasitics in there, 00:23:12.640 --> 00:23:16.180 align:middle line:84% you remember that we saw the circuit parasitics make 00:23:16.180 --> 00:23:21.640 align:middle line:84% the filter start to drop out its capabilities at high frequency 00:23:21.640 --> 00:23:22.900 align:middle line:90% because the parasitics. 00:23:22.900 --> 00:23:25.750 align:middle line:84% So you might argue that the best way to get rid 00:23:25.750 --> 00:23:28.090 align:middle line:84% of the high-frequency noise is, instead 00:23:28.090 --> 00:23:31.780 align:middle line:84% of generating and filtering it, just don't generate it. 00:23:31.780 --> 00:23:35.620 align:middle line:84% Or the stuff that's most likely to couple 00:23:35.620 --> 00:23:37.750 align:middle line:84% through, say, a parasitic capacitance 00:23:37.750 --> 00:23:39.520 align:middle line:90% is the highest frequencies. 00:23:39.520 --> 00:23:41.590 align:middle line:84% So if you just never generate them, 00:23:41.590 --> 00:23:44.230 align:middle line:84% it's a lot easier to filter them. 00:23:44.230 --> 00:23:46.330 align:middle line:84% So you might not design your whole converter 00:23:46.330 --> 00:23:51.310 align:middle line:84% around this thought, but it really does help you 00:23:51.310 --> 00:23:52.818 align:middle line:90% with reduced filter size. 00:23:52.818 --> 00:23:54.860 align:middle line:84% And we've seen that, with soft-switch converters, 00:23:54.860 --> 00:23:59.650 align:middle line:84% you can often really make your filtering job easier. 00:23:59.650 --> 00:24:01.865 align:middle line:90% So questions. 00:24:01.865 --> 00:24:02.990 align:middle line:90% AUDIENCE: I figured it out. 00:24:02.990 --> 00:24:04.610 align:middle line:84% DAVID PERREAULT: Figured it out, OK. 00:24:04.610 --> 00:24:05.790 align:middle line:90% Other questions? 00:24:05.790 --> 00:24:09.270 align:middle line:90% 00:24:09.270 --> 00:24:14.340 align:middle line:84% So I wanted to argue that one of the things we can get out 00:24:14.340 --> 00:24:18.480 align:middle line:84% of soft switching is reduced switching loss, which 00:24:18.480 --> 00:24:22.170 align:middle line:84% lets us either get efficiency or higher frequencies and, hence, 00:24:22.170 --> 00:24:25.200 align:middle line:84% possibly higher power densities, smaller component size. 00:24:25.200 --> 00:24:27.360 align:middle line:84% And for a given switching frequency, 00:24:27.360 --> 00:24:28.920 align:middle line:90% we can reduce the EMI. 00:24:28.920 --> 00:24:31.290 align:middle line:84% And even when you're pushing frequency, 00:24:31.290 --> 00:24:33.900 align:middle line:84% that can help you because you might have a high switching 00:24:33.900 --> 00:24:37.590 align:middle line:84% frequency converter that doesn't have increased really 00:24:37.590 --> 00:24:38.630 align:middle line:90% high-frequency content. 00:24:38.630 --> 00:24:42.680 align:middle line:90% 00:24:42.680 --> 00:24:43.290 align:middle line:90% All right. 00:24:43.290 --> 00:24:48.783 align:middle line:84% Well, last time, I introduced some power converter examples 00:24:48.783 --> 00:24:49.700 align:middle line:90% that were soft switch. 00:24:49.700 --> 00:24:52.280 align:middle line:84% And I showed you DC to DC converter examples. 00:24:52.280 --> 00:24:55.070 align:middle line:90% And I was a little bit rushed. 00:24:55.070 --> 00:24:57.220 align:middle line:90% But we said that-- 00:24:57.220 --> 00:25:00.770 align:middle line:84% and I should say that there's all kinds of ways 00:25:00.770 --> 00:25:03.050 align:middle line:84% that people try to break down different classes 00:25:03.050 --> 00:25:04.850 align:middle line:90% of soft-switching converters. 00:25:04.850 --> 00:25:08.960 align:middle line:84% There's a whole variety of techniques. 00:25:08.960 --> 00:25:12.090 align:middle line:84% And you can mix these techniques any different ways. 00:25:12.090 --> 00:25:13.680 align:middle line:90% What's a good way? 00:25:13.680 --> 00:25:16.760 align:middle line:84% Well, it depends upon, first of all, your device 00:25:16.760 --> 00:25:17.700 align:middle line:90% characteristics. 00:25:17.700 --> 00:25:21.080 align:middle line:84% I make it sound like all devices are the same, but it turns out, 00:25:21.080 --> 00:25:21.980 align:middle line:90% they're not. 00:25:21.980 --> 00:25:24.290 align:middle line:84% So what soft-switching technique might really 00:25:24.290 --> 00:25:27.110 align:middle line:84% be suitable does relate back to the details 00:25:27.110 --> 00:25:30.440 align:middle line:84% of the type of semiconductor device you're using. 00:25:30.440 --> 00:25:32.240 align:middle line:84% There are some devices that just don't like 00:25:32.240 --> 00:25:34.100 align:middle line:90% to turn on under 0 voltage. 00:25:34.100 --> 00:25:37.490 align:middle line:84% So you probably wouldn't want to use zero-voltage switching 00:25:37.490 --> 00:25:38.640 align:middle line:90% for that kind of device. 00:25:38.640 --> 00:25:43.980 align:middle line:84% So you have to match the soft-switching technique 00:25:43.980 --> 00:25:46.750 align:middle line:90% to the device type you're using. 00:25:46.750 --> 00:25:51.640 align:middle line:84% And you have to match the particular circuit or technique 00:25:51.640 --> 00:25:53.260 align:middle line:90% to the circuit application. 00:25:53.260 --> 00:25:55.750 align:middle line:84% Because it depends upon the voltage range 00:25:55.750 --> 00:25:58.690 align:middle line:84% you want to operate over or the power 00:25:58.690 --> 00:26:00.040 align:middle line:90% range you want to operate over. 00:26:00.040 --> 00:26:03.670 align:middle line:84% You might change which circuit implementation of soft switching 00:26:03.670 --> 00:26:05.710 align:middle line:84% is a good idea versus a bad idea. 00:26:05.710 --> 00:26:08.800 align:middle line:84% And that's why there's so many different techniques people use, 00:26:08.800 --> 00:26:11.650 align:middle line:84% or versions of the general idea people use, 00:26:11.650 --> 00:26:16.470 align:middle line:84% is because there's not one size fits all. 00:26:16.470 --> 00:26:19.890 align:middle line:90% I showed you a few examples. 00:26:19.890 --> 00:26:23.730 align:middle line:84% And maybe the broadest split I could 00:26:23.730 --> 00:26:27.630 align:middle line:84% make in the ideas of how soft switching is implemented 00:26:27.630 --> 00:26:30.300 align:middle line:84% is there's some designs in which you 00:26:30.300 --> 00:26:35.610 align:middle line:84% will design the whole circuit to achieve some particular kind 00:26:35.610 --> 00:26:37.150 align:middle line:90% of soft-switch operation. 00:26:37.150 --> 00:26:41.040 align:middle line:84% And that usually means that the way the circuit's component 00:26:41.040 --> 00:26:44.460 align:middle line:84% values are chosen, the whole control scheme, everything 00:26:44.460 --> 00:26:48.040 align:middle line:84% is geared around meeting the requirements of soft switching. 00:26:48.040 --> 00:26:48.630 align:middle line:90% Why? 00:26:48.630 --> 00:26:53.740 align:middle line:84% Because maybe I have to make the circuit do something magic, 00:26:53.740 --> 00:26:55.573 align:middle line:84% and I only want to turn the switch 00:26:55.573 --> 00:26:58.240 align:middle line:84% on when the voltage is already 0 across the switch or something. 00:26:58.240 --> 00:27:01.080 align:middle line:84% So that prevents me from just doing 00:27:01.080 --> 00:27:02.670 align:middle line:90% standard fixed-frequency PWM. 00:27:02.670 --> 00:27:06.550 align:middle line:84% And I just work really hard to make that happen. 00:27:06.550 --> 00:27:11.360 align:middle line:84% So that's one very broad category of circuits. 00:27:11.360 --> 00:27:14.420 align:middle line:84% Another category of circuits is, jeez, 00:27:14.420 --> 00:27:16.970 align:middle line:84% I don't want to redesign and conceive 00:27:16.970 --> 00:27:21.717 align:middle line:84% this whole funny operation of this circuit in order 00:27:21.717 --> 00:27:22.800 align:middle line:90% to achieve soft switching. 00:27:22.800 --> 00:27:24.342 align:middle line:84% What I'd like to do is, more or less, 00:27:24.342 --> 00:27:26.180 align:middle line:84% design a PWM converter like we've 00:27:26.180 --> 00:27:29.120 align:middle line:84% been talking about all semester and somehow add 00:27:29.120 --> 00:27:31.310 align:middle line:84% in some auxiliary circuit that's going 00:27:31.310 --> 00:27:34.410 align:middle line:90% to help me get soft switching. 00:27:34.410 --> 00:27:39.090 align:middle line:84% Both of those kind of strategies are used. 00:27:39.090 --> 00:27:42.360 align:middle line:84% And I'm going to show you one of each today. 00:27:42.360 --> 00:27:47.080 align:middle line:84% And since last time, we talked about DC to DC converters, 00:27:47.080 --> 00:27:49.380 align:middle line:84% today, I'm going to talk about DC to AC converters, 00:27:49.380 --> 00:27:50.910 align:middle line:90% or inverters. 00:27:50.910 --> 00:27:55.170 align:middle line:84% And you can use the same kind of ideas on rectifiers, naturally. 00:27:55.170 --> 00:28:00.045 align:middle line:84% So let's talk about a couple of examples of soft switching in DC 00:28:00.045 --> 00:28:03.510 align:middle line:90% to DC converters. 00:28:03.510 --> 00:28:08.940 align:middle line:84% Here is one soft-switch inverter. 00:28:08.940 --> 00:28:12.350 align:middle line:84% So I want to take a DC input voltage. 00:28:12.350 --> 00:28:16.870 align:middle line:84% And here, for simplicity, I'm illustrating something 00:28:16.870 --> 00:28:18.745 align:middle line:90% with a DC bus split in two. 00:28:18.745 --> 00:28:20.120 align:middle line:84% You don't have to do it this way. 00:28:20.120 --> 00:28:23.800 align:middle line:84% It's just easy for educational purposes 00:28:23.800 --> 00:28:25.350 align:middle line:90% to illustrate this this way. 00:28:25.350 --> 00:28:28.730 align:middle line:90% So this is my DC input, Vdc. 00:28:28.730 --> 00:28:34.130 align:middle line:84% My output is the voltage across this capacitor here, Vcf. 00:28:34.130 --> 00:28:37.010 align:middle line:84% So I want to generate a low-frequency AC 00:28:37.010 --> 00:28:40.740 align:middle line:90% voltage across that capacitor. 00:28:40.740 --> 00:28:45.320 align:middle line:84% And that AC voltage is going to be applied to the load. 00:28:45.320 --> 00:28:53.870 align:middle line:84% So maybe you could imagine this is some low-frequency AC output 00:28:53.870 --> 00:28:55.820 align:middle line:84% that I want to synthesize to deliver power 00:28:55.820 --> 00:28:58.490 align:middle line:84% at low-frequency AC, single phase. 00:28:58.490 --> 00:29:02.600 align:middle line:84% And I'm willing to switch this inverter at a high frequency 00:29:02.600 --> 00:29:05.965 align:middle line:90% in order to do that. 00:29:05.965 --> 00:29:10.460 align:middle line:84% And this first design is called a resonant pole inverter. 00:29:10.460 --> 00:29:11.710 align:middle line:90% Well, that's one of its names. 00:29:11.710 --> 00:29:14.970 align:middle line:90% It's very often used. 00:29:14.970 --> 00:29:17.760 align:middle line:84% It's one of these techniques where the whole circuit is 00:29:17.760 --> 00:29:20.190 align:middle line:84% designed and controlled to achieve soft switching 00:29:20.190 --> 00:29:23.340 align:middle line:84% and to achieve high-frequency operation. 00:29:23.340 --> 00:29:26.640 align:middle line:84% And what we can see is, here's my switch. 00:29:26.640 --> 00:29:30.390 align:middle line:84% And I'm showing like an IGBT, or bipolar, with a diode across it, 00:29:30.390 --> 00:29:32.100 align:middle line:90% but this could be a MOSFET. 00:29:32.100 --> 00:29:36.300 align:middle line:84% And each of the two MOSFETs in this bridge leg-- 00:29:36.300 --> 00:29:38.880 align:middle line:84% this is clearly a bridge leg, or half bridge-- 00:29:38.880 --> 00:29:41.370 align:middle line:90% has a capacitor across it. 00:29:41.370 --> 00:29:45.660 align:middle line:84% So what does that suggest to you about what 00:29:45.660 --> 00:29:48.095 align:middle line:84% kind of soft switching I'm going to be doing? 00:29:48.095 --> 00:29:51.990 align:middle line:84% I got capacitance across my devices. 00:29:51.990 --> 00:29:53.790 align:middle line:84% It's going to be zero-voltage switching 00:29:53.790 --> 00:29:56.550 align:middle line:84% because when I put a capacitor across my device, 00:29:56.550 --> 00:30:00.840 align:middle line:84% I can delay the rise and get zero-voltage turn-off. 00:30:00.840 --> 00:30:03.790 align:middle line:84% And I'd better turn the switch on when I have 0 voltage. 00:30:03.790 --> 00:30:05.910 align:middle line:84% Otherwise, that energy in this capacitor 00:30:05.910 --> 00:30:07.340 align:middle line:90% will be dumped into the switch. 00:30:07.340 --> 00:30:09.920 align:middle line:84% So this is going to be a zero-voltage switch circuit. 00:30:09.920 --> 00:30:14.040 align:middle line:84% This capacitance might be an external capacitor. 00:30:14.040 --> 00:30:17.180 align:middle line:84% It might entirely comprise the parasitic capacitance 00:30:17.180 --> 00:30:18.820 align:middle line:90% of the device-- 00:30:18.820 --> 00:30:21.790 align:middle line:90% just depends on the design. 00:30:21.790 --> 00:30:23.380 align:middle line:90% So what's the idea here? 00:30:23.380 --> 00:30:28.030 align:middle line:84% We can assume that over any switching cycle, 00:30:28.030 --> 00:30:33.140 align:middle line:84% the voltage Vcf across this capacitor is constant. 00:30:33.140 --> 00:30:40.220 align:middle line:84% It might vary anywhere between plus Vdc over 2 and minus Vdc 00:30:40.220 --> 00:30:40.820 align:middle line:90% over 2. 00:30:40.820 --> 00:30:43.220 align:middle line:84% But within a switching cycle, I can think of it 00:30:43.220 --> 00:30:45.680 align:middle line:90% as quasi constant. 00:30:45.680 --> 00:30:49.340 align:middle line:90% So what are we going to do? 00:30:49.340 --> 00:30:54.010 align:middle line:84% Suppose I want to deliver an average, a local average, 00:30:54.010 --> 00:30:56.320 align:middle line:84% current over a switching cycle iL 00:30:56.320 --> 00:30:59.567 align:middle line:84% into the load filter combination. 00:30:59.567 --> 00:31:01.900 align:middle line:84% Well, what I'm going to do is I'm going to, for example, 00:31:01.900 --> 00:31:04.210 align:middle line:90% turn on the top switch S1. 00:31:04.210 --> 00:31:06.380 align:middle line:90% Suppose the top switch S1 is on. 00:31:06.380 --> 00:31:11.950 align:middle line:84% So long as Vcf is smaller than Vdc over 2, 00:31:11.950 --> 00:31:14.020 align:middle line:84% I've got a positive voltage across the inductor, 00:31:14.020 --> 00:31:16.400 align:middle line:84% and the inductor current is going to ramp up. 00:31:16.400 --> 00:31:23.290 align:middle line:84% So that's going to be some positive-rising current here. 00:31:23.290 --> 00:31:26.980 align:middle line:84% When I get to some peak-commanded current that I 00:31:26.980 --> 00:31:29.650 align:middle line:84% desire-- this is a current-controlled converter-- 00:31:29.650 --> 00:31:35.440 align:middle line:84% I will turn off S1 under zero-voltage switching 00:31:35.440 --> 00:31:39.070 align:middle line:84% because this capacitor is snubbing the switching 00:31:39.070 --> 00:31:41.290 align:middle line:90% transition. 00:31:41.290 --> 00:31:42.280 align:middle line:90% What will happen then? 00:31:42.280 --> 00:31:44.980 align:middle line:84% When these two switches are off, the current 00:31:44.980 --> 00:31:48.400 align:middle line:84% will actually split between these two resonant capacitors, 00:31:48.400 --> 00:31:50.740 align:middle line:84% and the bus voltage will resonate down 00:31:50.740 --> 00:31:52.430 align:middle line:90% until the bottom diode turns on. 00:31:52.430 --> 00:31:55.300 align:middle line:90% 00:31:55.300 --> 00:31:59.642 align:middle line:84% So now I've got the bottom diode on. 00:31:59.642 --> 00:32:01.600 align:middle line:84% And I'm still delivering current to the output. 00:32:01.600 --> 00:32:06.370 align:middle line:84% But now, the voltage across the inductor is negative, 00:32:06.370 --> 00:32:09.820 align:middle line:84% and the current is going to slow down in the inductor. 00:32:09.820 --> 00:32:11.450 align:middle line:90% But notice something. 00:32:11.450 --> 00:32:14.860 align:middle line:84% As long as this diode's on, what is the voltage 00:32:14.860 --> 00:32:16.005 align:middle line:90% across the bottom switch? 00:32:16.005 --> 00:32:21.310 align:middle line:90% 00:32:21.310 --> 00:32:23.050 align:middle line:90% 0. 00:32:23.050 --> 00:32:26.440 align:middle line:84% So, in fact, by turning off the top device 00:32:26.440 --> 00:32:29.470 align:middle line:84% and having this inductor ring with these capacitors 00:32:29.470 --> 00:32:33.270 align:middle line:84% and turn the bottom diode on, I am, essentially-- 00:32:33.270 --> 00:32:37.050 align:middle line:84% boom-- creating a case where the bottom switch voltage is 0. 00:32:37.050 --> 00:32:41.470 align:middle line:84% That means, at any point after this node voltage rings 00:32:41.470 --> 00:32:45.060 align:middle line:84% down from Vdc to 0, I can turn on this switch. 00:32:45.060 --> 00:32:47.856 align:middle line:90% 00:32:47.856 --> 00:32:53.870 align:middle line:84% So I have zero-voltage turn-off, zero-voltage turn-on. 00:32:53.870 --> 00:32:55.710 align:middle line:84% I will turn on the bottom switch. 00:32:55.710 --> 00:32:57.260 align:middle line:84% And what will eventually happen is, 00:32:57.260 --> 00:33:00.650 align:middle line:84% because the current's slowing down, 00:33:00.650 --> 00:33:03.350 align:middle line:84% the inductor current will reverse. 00:33:03.350 --> 00:33:05.568 align:middle line:84% And now I'll be building up negative current 00:33:05.568 --> 00:33:06.235 align:middle line:90% in the inductor. 00:33:06.235 --> 00:33:08.855 align:middle line:90% 00:33:08.855 --> 00:33:10.230 align:middle line:84% What I'm going to do is I'm going 00:33:10.230 --> 00:33:12.300 align:middle line:84% to let this negative current build up 00:33:12.300 --> 00:33:16.340 align:middle line:90% to a minimum particular value. 00:33:16.340 --> 00:33:18.170 align:middle line:90% And then I'm going to-- 00:33:18.170 --> 00:33:21.800 align:middle line:84% I'll call that ip minus, for example. 00:33:21.800 --> 00:33:25.380 align:middle line:84% And eventually, I can turn off this bottom switch. 00:33:25.380 --> 00:33:27.662 align:middle line:84% And the precharged current in this inductor 00:33:27.662 --> 00:33:29.870 align:middle line:84% is going to resonate with these two capacitors again. 00:33:29.870 --> 00:33:31.640 align:middle line:84% And again, I turn off the bottom switch 00:33:31.640 --> 00:33:34.560 align:middle line:84% with zero-voltage switching because of the capacitors. 00:33:34.560 --> 00:33:37.260 align:middle line:84% This inductor will ring with these two capacitors 00:33:37.260 --> 00:33:39.990 align:middle line:90% until the top diode turns on. 00:33:39.990 --> 00:33:41.910 align:middle line:84% And once the top diode turns on, I'm 00:33:41.910 --> 00:33:45.030 align:middle line:84% getting zero-voltage turn-on on the top device again. 00:33:45.030 --> 00:33:47.220 align:middle line:90% And now I'm back. 00:33:47.220 --> 00:33:50.820 align:middle line:84% When I turn the switch on, I can get back to here. 00:33:50.820 --> 00:33:55.740 align:middle line:84% So I'm alternating between top device on and bottom device on 00:33:55.740 --> 00:34:00.520 align:middle line:84% but with dead times in between that let the bus voltage 00:34:00.520 --> 00:34:01.950 align:middle line:90% ring down and ring up. 00:34:01.950 --> 00:34:05.260 align:middle line:90% 00:34:05.260 --> 00:34:06.390 align:middle line:90% Any questions about that? 00:34:06.390 --> 00:34:09.580 align:middle line:90% 00:34:09.580 --> 00:34:12.780 align:middle line:84% Now, what's the magic trick of this? 00:34:12.780 --> 00:34:16.350 align:middle line:84% In order to get zero-voltage switching-- 00:34:16.350 --> 00:34:17.770 align:middle line:90% let's consider this case. 00:34:17.770 --> 00:34:19.780 align:middle line:84% I'm delivering negative current in the inductor. 00:34:19.780 --> 00:34:21.989 align:middle line:84% The inductor current's gone negative. 00:34:21.989 --> 00:34:26.610 align:middle line:84% In order for the voltage in this state 00:34:26.610 --> 00:34:29.250 align:middle line:84% to ring all the way up such that the top diode turns on, 00:34:29.250 --> 00:34:33.280 align:middle line:84% there's a negative minimum current I need in this inductor. 00:34:33.280 --> 00:34:35.710 align:middle line:84% That negative minimum current is, actually, 00:34:35.710 --> 00:34:40.889 align:middle line:90% a function of the voltage. 00:34:40.889 --> 00:34:44.343 align:middle line:84% So if I just didn't have enough current, 00:34:44.343 --> 00:34:47.010 align:middle line:84% this voltage would ring up, but it wouldn't ring up all the way. 00:34:47.010 --> 00:34:49.530 align:middle line:84% And then it would die, and I wouldn't get there. 00:34:49.530 --> 00:34:51.701 align:middle line:84% So I have to have a certain positive current 00:34:51.701 --> 00:34:54.159 align:middle line:84% to make sure I can ring down and a certain negative current 00:34:54.159 --> 00:34:55.600 align:middle line:90% to make sure I can ring up. 00:34:55.600 --> 00:34:57.870 align:middle line:84% But if I ignore the short durations of the switching 00:34:57.870 --> 00:35:00.540 align:middle line:84% transitions, the average current delivered 00:35:00.540 --> 00:35:02.280 align:middle line:84% into the capacitor over a switching cycle 00:35:02.280 --> 00:35:04.950 align:middle line:84% is really the average of the peak positive current 00:35:04.950 --> 00:35:07.560 align:middle line:90% and the peak negative current. 00:35:07.560 --> 00:35:12.520 align:middle line:84% So this is very much a hysteretically controlled 00:35:12.520 --> 00:35:15.400 align:middle line:84% inverter-- hysteretic current control. 00:35:15.400 --> 00:35:19.570 align:middle line:84% But what I'm doing is I'm making the positive current I deliver 00:35:19.570 --> 00:35:22.210 align:middle line:84% always positive enough that I can bring the voltage down 00:35:22.210 --> 00:35:24.800 align:middle line:84% and the negative current always negative enough-- 00:35:24.800 --> 00:35:29.710 align:middle line:84% and notice that the current's reversing here-- 00:35:29.710 --> 00:35:32.600 align:middle line:84% so that I can always ring the bus voltage the other way. 00:35:32.600 --> 00:35:36.800 align:middle line:84% And I'm delivering the average of the two in a switching cycle. 00:35:36.800 --> 00:35:39.397 align:middle line:84% So I can work out the math that says 00:35:39.397 --> 00:35:41.480 align:middle line:84% how negative does the negative current have to be, 00:35:41.480 --> 00:35:43.820 align:middle line:84% how positive does the positive current have to be, 00:35:43.820 --> 00:35:48.140 align:middle line:84% create a current-based switching cycle that will always give me 00:35:48.140 --> 00:35:50.000 align:middle line:84% soft switching and will let me deliver 00:35:50.000 --> 00:35:52.490 align:middle line:84% either positive or negative average current 00:35:52.490 --> 00:35:58.180 align:middle line:84% into the capacitor independent of the capacitor voltage. 00:35:58.180 --> 00:36:03.700 align:middle line:84% And hence, I can deliver a low-frequency AC output 00:36:03.700 --> 00:36:07.900 align:middle line:84% component by modulating the positive and negative peak 00:36:07.900 --> 00:36:09.000 align:middle line:90% current over a cycle. 00:36:09.000 --> 00:36:13.020 align:middle line:90% 00:36:13.020 --> 00:36:14.820 align:middle line:84% The exact values that you need to do 00:36:14.820 --> 00:36:18.510 align:middle line:84% that make for wonderful homework problems, not that hard 00:36:18.510 --> 00:36:20.430 align:middle line:90% to work out. 00:36:20.430 --> 00:36:24.960 align:middle line:84% But this technique is taking advantage of the fact 00:36:24.960 --> 00:36:28.030 align:middle line:84% that you have a high ripple current in the inductor. 00:36:28.030 --> 00:36:30.690 align:middle line:84% So the inductor current has to go in both directions in order 00:36:30.690 --> 00:36:32.460 align:middle line:84% to, generally, give you your output. 00:36:32.460 --> 00:36:36.105 align:middle line:84% So you have to turn off the top switch when the inductor 00:36:36.105 --> 00:36:38.355 align:middle line:84% current's positive and turn off the bottom switch when 00:36:38.355 --> 00:36:39.940 align:middle line:90% the inductor current's negative. 00:36:39.940 --> 00:36:42.270 align:middle line:84% I have to have a high ripple to make this thing work. 00:36:42.270 --> 00:36:44.040 align:middle line:84% But if I'm willing to get that, I 00:36:44.040 --> 00:36:46.050 align:middle line:84% can get soft switching in my devices 00:36:46.050 --> 00:36:47.735 align:middle line:84% and deliver the average current I want. 00:36:47.735 --> 00:36:50.920 align:middle line:90% 00:36:50.920 --> 00:36:52.080 align:middle line:90% Any questions about that? 00:36:52.080 --> 00:36:56.060 align:middle line:90% 00:36:56.060 --> 00:36:59.100 align:middle line:84% This, again, has variable switching frequency. 00:36:59.100 --> 00:37:00.510 align:middle line:90% It has all kinds of challenges. 00:37:00.510 --> 00:37:01.730 align:middle line:90% It has high ripple. 00:37:01.730 --> 00:37:04.590 align:middle line:84% But it can be very compact and efficient. 00:37:04.590 --> 00:37:09.520 align:middle line:90% 00:37:09.520 --> 00:37:13.973 align:middle line:84% I should say one of the ways people think about this-- 00:37:13.973 --> 00:37:16.640 align:middle line:84% and we're going to come back to this because we're going to look 00:37:16.640 --> 00:37:23.510 align:middle line:84% at classes of converter that use this kind of zero-voltage 00:37:23.510 --> 00:37:25.610 align:middle line:90% soft-switch technique a lot-- 00:37:25.610 --> 00:37:31.220 align:middle line:84% usually, what you have is when you're 00:37:31.220 --> 00:37:33.620 align:middle line:84% going to turn off your device, you usually 00:37:33.620 --> 00:37:35.923 align:middle line:84% have some inductor current that carries a current 00:37:35.923 --> 00:37:37.340 align:middle line:84% in the right direction to give you 00:37:37.340 --> 00:37:39.640 align:middle line:90% the switch direction you want. 00:37:39.640 --> 00:37:41.740 align:middle line:84% So usually, when you look at this kind of circuit, 00:37:41.740 --> 00:37:44.650 align:middle line:84% you say, OK, when the device is turning off, 00:37:44.650 --> 00:37:48.820 align:middle line:84% it's loaded by some impedance that, typically, looks inductive 00:37:48.820 --> 00:37:50.580 align:middle line:84% or, basically, is carrying a current 00:37:50.580 --> 00:37:53.260 align:middle line:84% in a direction that will help charge 00:37:53.260 --> 00:37:55.030 align:middle line:84% those capacitances in the right direction 00:37:55.030 --> 00:37:57.830 align:middle line:84% to give you soft switching is the way to think about it. 00:37:57.830 --> 00:38:01.220 align:middle line:90% 00:38:01.220 --> 00:38:01.910 align:middle line:90% Questions? 00:38:01.910 --> 00:38:05.910 align:middle line:90% 00:38:05.910 --> 00:38:08.760 align:middle line:90% OK. 00:38:08.760 --> 00:38:12.480 align:middle line:84% This circuit works under variable switching frequency 00:38:12.480 --> 00:38:15.710 align:middle line:84% and variable duty ratio based on hysteretic current control. 00:38:15.710 --> 00:38:20.640 align:middle line:84% So everything about it is governed by the desire 00:38:20.640 --> 00:38:22.760 align:middle line:90% to get soft switching. 00:38:22.760 --> 00:38:25.580 align:middle line:90% So if I told you, you know what? 00:38:25.580 --> 00:38:31.990 align:middle line:84% We want to do harmonic illumination 00:38:31.990 --> 00:38:33.803 align:middle line:90% PWM with this inverter leg. 00:38:33.803 --> 00:38:34.470 align:middle line:90% Can you do that? 00:38:34.470 --> 00:38:37.750 align:middle line:90% 00:38:37.750 --> 00:38:38.900 align:middle line:90% Not really, right? 00:38:38.900 --> 00:38:41.530 align:middle line:84% You don't really have the means to do it. 00:38:41.530 --> 00:38:45.310 align:middle line:84% You can't just generate switching angles at your command 00:38:45.310 --> 00:38:47.680 align:middle line:84% because everything's governed by what 00:38:47.680 --> 00:38:52.470 align:middle line:84% the ripple current in that resonant inductor is doing. 00:38:52.470 --> 00:38:58.500 align:middle line:84% So this is nice that it lets you generate 00:38:58.500 --> 00:39:01.500 align:middle line:84% a low-frequency component plus high frequency into an output 00:39:01.500 --> 00:39:03.810 align:middle line:84% and get filtered and get what you want. 00:39:03.810 --> 00:39:06.700 align:middle line:84% But it's very constrained in how you have to operate it. 00:39:06.700 --> 00:39:10.550 align:middle line:84% It's in that first category of converters I talked about. 00:39:10.550 --> 00:39:13.960 align:middle line:84% What if I, instead, said, you know what? 00:39:13.960 --> 00:39:15.950 align:middle line:90% I've got some motor drive. 00:39:15.950 --> 00:39:17.750 align:middle line:84% And I, basically, know how I want 00:39:17.750 --> 00:39:22.150 align:middle line:84% to control it in terms of switching between my top switch 00:39:22.150 --> 00:39:23.393 align:middle line:90% and my bottom main switch. 00:39:23.393 --> 00:39:26.090 align:middle line:90% 00:39:26.090 --> 00:39:29.462 align:middle line:84% But I don't like this notion that I don't get any control. 00:39:29.462 --> 00:39:31.670 align:middle line:84% I just want to switch this inverter because I already 00:39:31.670 --> 00:39:34.790 align:middle line:84% have a control system in mind for what this inverter's going 00:39:34.790 --> 00:39:35.720 align:middle line:90% to drive. 00:39:35.720 --> 00:39:40.500 align:middle line:84% And maybe in the thing you want to drive-- 00:39:40.500 --> 00:39:43.410 align:middle line:84% this has an LC filter at the output-- 00:39:43.410 --> 00:39:45.770 align:middle line:84% maybe I just want to run this inverter into a motor. 00:39:45.770 --> 00:39:48.380 align:middle line:84% So I don't really want to have this extra stage 00:39:48.380 --> 00:39:50.750 align:middle line:90% of high-frequency stuff. 00:39:50.750 --> 00:39:52.280 align:middle line:90% What could I do? 00:39:52.280 --> 00:39:56.450 align:middle line:84% Well, maybe, I would imagine this. 00:39:56.450 --> 00:39:59.720 align:middle line:90% And this is often done. 00:39:59.720 --> 00:40:02.690 align:middle line:84% Suppose I said, all right, here's my bus voltage. 00:40:02.690 --> 00:40:04.750 align:middle line:84% Maybe I'll, again, just for simplicity, 00:40:04.750 --> 00:40:07.015 align:middle line:84% let me split my bus voltage in two. 00:40:07.015 --> 00:40:09.580 align:middle line:90% 00:40:09.580 --> 00:40:14.470 align:middle line:84% And I could do this with just splitting capacitors. 00:40:14.470 --> 00:40:19.990 align:middle line:84% Maybe I would just have a pair of devices, a first device 00:40:19.990 --> 00:40:22.240 align:middle line:90% and a second device. 00:40:22.240 --> 00:40:23.860 align:middle line:84% And maybe this thing is just going 00:40:23.860 --> 00:40:27.618 align:middle line:84% to drive some load current iL of t. 00:40:27.618 --> 00:40:29.410 align:middle line:84% And I don't know what this load current is, 00:40:29.410 --> 00:40:31.960 align:middle line:84% but maybe this is some motor or something. 00:40:31.960 --> 00:40:34.570 align:middle line:84% And what my goal is is to, basically, 00:40:34.570 --> 00:40:42.200 align:middle line:84% generate this voltage vx according to some command. 00:40:42.200 --> 00:40:45.640 align:middle line:90% I either want to make VDC or 0. 00:40:45.640 --> 00:40:48.650 align:middle line:84% I want to make vx go to VDC or 0. 00:40:48.650 --> 00:40:51.730 align:middle line:84% I want to use standard motor drive techniques. 00:40:51.730 --> 00:40:54.250 align:middle line:84% I don't want to deal with all this funny behavior. 00:40:54.250 --> 00:41:02.460 align:middle line:84% And yet maybe I would like to reduce the slew rate of vx. 00:41:02.460 --> 00:41:03.150 align:middle line:90% Why? 00:41:03.150 --> 00:41:07.030 align:middle line:84% Because I do have EMI going out towards my motor. 00:41:07.030 --> 00:41:10.370 align:middle line:84% So maybe I want to reduce that dv/dt. 00:41:10.370 --> 00:41:13.610 align:middle line:84% Or maybe I want a PWM at pretty high frequency 00:41:13.610 --> 00:41:17.840 align:middle line:84% with high efficiency, use a high-power system. 00:41:17.840 --> 00:41:20.600 align:middle line:90% So how could I do that? 00:41:20.600 --> 00:41:23.010 align:middle line:84% And here's one thing you could do. 00:41:23.010 --> 00:41:28.430 align:middle line:84% Maybe we can look at this thing and add some auxiliary circuitry 00:41:28.430 --> 00:41:31.520 align:middle line:84% that lets me switch these two devices between these two 00:41:31.520 --> 00:41:36.110 align:middle line:84% devices any time I want but will give me 00:41:36.110 --> 00:41:37.770 align:middle line:90% a soft-switch transition. 00:41:37.770 --> 00:41:40.440 align:middle line:90% 00:41:40.440 --> 00:41:42.300 align:middle line:90% Here's how we could do it. 00:41:42.300 --> 00:41:44.330 align:middle line:90% Maybe I will go-- 00:41:44.330 --> 00:41:47.700 align:middle line:84% the first thing I'll do is I'll add some capacitance 00:41:47.700 --> 00:41:49.200 align:middle line:90% across each device. 00:41:49.200 --> 00:41:51.570 align:middle line:84% And that would include the intrinsic capacitor 00:41:51.570 --> 00:41:53.250 align:middle line:90% in the device. 00:41:53.250 --> 00:41:55.530 align:middle line:84% So if I'm going to do that, is this 00:41:55.530 --> 00:42:00.860 align:middle line:84% going to be a ZVS converter or a ZCS converter? 00:42:00.860 --> 00:42:04.040 align:middle line:84% ZVS because I know that I'm going to be playing 00:42:04.040 --> 00:42:07.250 align:middle line:90% with ZVS switching transitions. 00:42:07.250 --> 00:42:09.690 align:middle line:84% What is my auxiliary circuit going to look like? 00:42:09.690 --> 00:42:13.220 align:middle line:90% It's going to look like this. 00:42:13.220 --> 00:42:18.500 align:middle line:84% I'm going to add a resonant inductor, Lr, and then maybe 00:42:18.500 --> 00:42:20.160 align:middle line:90% a pair of back-to-back switches. 00:42:20.160 --> 00:42:22.070 align:middle line:90% But let me just think of this-- 00:42:22.070 --> 00:42:25.040 align:middle line:84% well, I'll draw it as a pair of back-to-back switches, 00:42:25.040 --> 00:42:25.855 align:middle line:90% just to be clear. 00:42:25.855 --> 00:42:28.490 align:middle line:90% 00:42:28.490 --> 00:42:29.960 align:middle line:84% If I had a bidirectional switch, I 00:42:29.960 --> 00:42:31.470 align:middle line:84% could do this with a bidirectional switch, 00:42:31.470 --> 00:42:32.770 align:middle line:90% but maybe I'll do it like this. 00:42:32.770 --> 00:42:41.400 align:middle line:90% 00:42:41.400 --> 00:42:44.350 align:middle line:84% Actually, I could have put them back to back the other way. 00:42:44.350 --> 00:42:45.600 align:middle line:90% It might have been better. 00:42:45.600 --> 00:42:48.670 align:middle line:84% But here's my back-to-back switch. 00:42:48.670 --> 00:42:53.280 align:middle line:84% So this thing here is just a controllable bidirectional 00:42:53.280 --> 00:42:54.990 align:middle line:90% switch. 00:42:54.990 --> 00:42:57.660 align:middle line:84% Now this bidirectional switch has 00:42:57.660 --> 00:43:00.042 align:middle line:90% an inductor in series with it. 00:43:00.042 --> 00:43:01.500 align:middle line:84% So do you think I'm going to switch 00:43:01.500 --> 00:43:03.840 align:middle line:84% this switch with zero-voltage switching 00:43:03.840 --> 00:43:06.950 align:middle line:90% or zero-current switching? 00:43:06.950 --> 00:43:08.780 align:middle line:90% Zero current. 00:43:08.780 --> 00:43:12.140 align:middle line:84% So this circuit, the pink circuit, 00:43:12.140 --> 00:43:18.860 align:middle line:84% is an auxiliary circuit, which is 00:43:18.860 --> 00:43:23.060 align:middle line:84% going to give me zero-voltage switching on my main devices 00:43:23.060 --> 00:43:26.400 align:middle line:84% and, itself, is going to operate with zero-current switching. 00:43:26.400 --> 00:43:29.680 align:middle line:90% 00:43:29.680 --> 00:43:33.110 align:middle line:84% And what we're going to do is this pink circuit 00:43:33.110 --> 00:43:37.250 align:middle line:84% is only going to operate transiently at the times 00:43:37.250 --> 00:43:42.570 align:middle line:84% when I want to switch between the bottom and top main device. 00:43:42.570 --> 00:43:45.740 align:middle line:84% This circuit is called an auxiliary resonant commutated 00:43:45.740 --> 00:43:48.020 align:middle line:90% pole inverter. 00:43:48.020 --> 00:43:52.220 align:middle line:84% It was invented in the early '90s. 00:43:52.220 --> 00:43:56.000 align:middle line:84% It was actually an extension of a notion called the McMurray 00:43:56.000 --> 00:43:56.750 align:middle line:90% snubber. 00:43:56.750 --> 00:43:57.980 align:middle line:90% This was developed at GE. 00:43:57.980 --> 00:44:01.430 align:middle line:84% And McMurray, before this particular invention, 00:44:01.430 --> 00:44:04.700 align:middle line:84% was a very famous power electronics researcher 00:44:04.700 --> 00:44:06.260 align:middle line:90% and designer at GE. 00:44:06.260 --> 00:44:10.910 align:middle line:84% And a guy named Rik De Doncker came up with this circuit. 00:44:10.910 --> 00:44:12.710 align:middle line:84% And he actually originally demonstrated it 00:44:12.710 --> 00:44:15.710 align:middle line:90% in high-power motor drives. 00:44:15.710 --> 00:44:18.050 align:middle line:90% And here's how it works. 00:44:18.050 --> 00:44:21.450 align:middle line:84% For any transition, regardless of this load current, 00:44:21.450 --> 00:44:24.560 align:middle line:84% if I want to go between this device and this device, 00:44:24.560 --> 00:44:28.220 align:middle line:84% there is some way I can operate the auxiliary circuit 00:44:28.220 --> 00:44:30.740 align:middle line:84% to let me transition between the two devices 00:44:30.740 --> 00:44:34.572 align:middle line:90% with zero-voltage switching. 00:44:34.572 --> 00:44:37.400 align:middle line:90% So here is the notion. 00:44:37.400 --> 00:44:43.490 align:middle line:84% This is actually from De Doncker's original PESC '91 00:44:43.490 --> 00:44:47.390 align:middle line:90% tutorial on the ARCP converter. 00:44:47.390 --> 00:44:50.490 align:middle line:90% So he uses funny device symbols. 00:44:50.490 --> 00:44:54.230 align:middle line:84% I think these may have been MCCs at the time. 00:44:54.230 --> 00:44:57.083 align:middle line:84% But he's using these device symbols. 00:44:57.083 --> 00:44:59.750 align:middle line:84% And here's the auxiliary circuit that's going to be zero-current 00:44:59.750 --> 00:45:00.597 align:middle line:90% switched. 00:45:00.597 --> 00:45:02.180 align:middle line:84% Here's the main devices that are going 00:45:02.180 --> 00:45:03.780 align:middle line:90% to be zero-voltage switched. 00:45:03.780 --> 00:45:06.590 align:middle line:84% And what you'll see is that this is-- 00:45:06.590 --> 00:45:08.090 align:middle line:84% when you trip the auxiliary circuit, 00:45:08.090 --> 00:45:09.715 align:middle line:84% you can go from the bottom switch being 00:45:09.715 --> 00:45:11.060 align:middle line:90% on to the top switch being on. 00:45:11.060 --> 00:45:15.680 align:middle line:84% And hence, you can get very nice soft transitions, which 00:45:15.680 --> 00:45:17.570 align:middle line:84% helps reduce the EMI of the circuit 00:45:17.570 --> 00:45:20.810 align:middle line:90% and reduces the switching loss. 00:45:20.810 --> 00:45:22.820 align:middle line:84% Now, there's all kinds of switching transitions 00:45:22.820 --> 00:45:24.000 align:middle line:90% to the circuit. 00:45:24.000 --> 00:45:28.880 align:middle line:84% You have to think about what's the load current and everything 00:45:28.880 --> 00:45:31.627 align:middle line:84% else to figure out what sequence of steps 00:45:31.627 --> 00:45:33.710 align:middle line:84% you go through to get between the bottom switch on 00:45:33.710 --> 00:45:35.700 align:middle line:84% and the top switch on, or vice versa. 00:45:35.700 --> 00:45:38.570 align:middle line:84% I'll just show you one transition as an example. 00:45:38.570 --> 00:45:40.960 align:middle line:84% And this is, again, from his original tutorial. 00:45:40.960 --> 00:45:43.130 align:middle line:90% Suppose the bottom diode-- 00:45:43.130 --> 00:45:45.060 align:middle line:84% and now he's showing it with GTOs-- 00:45:45.060 --> 00:45:49.650 align:middle line:84% suppose the bottom diode's conducting to the output. 00:45:49.650 --> 00:45:52.410 align:middle line:90% So this is one case. 00:45:52.410 --> 00:45:54.025 align:middle line:84% And I get to the time of my cycle. 00:45:54.025 --> 00:45:54.900 align:middle line:90% I say, you know what? 00:45:54.900 --> 00:45:57.567 align:middle line:84% The bottom diode was on, but now I want the top switch to be on. 00:45:57.567 --> 00:45:58.950 align:middle line:90% What do I do? 00:45:58.950 --> 00:46:00.880 align:middle line:90% Well, what he says is this. 00:46:00.880 --> 00:46:05.880 align:middle line:84% He says, OK, let me trip on this auxiliary circuit. 00:46:05.880 --> 00:46:09.540 align:middle line:90% I'm going to close this switch. 00:46:09.540 --> 00:46:13.990 align:middle line:84% I'm going to close this switch with zero-current switching. 00:46:13.990 --> 00:46:17.850 align:middle line:84% And what's going to happen is, because the bottom diode's on, 00:46:17.850 --> 00:46:20.225 align:middle line:84% current's going to ramp up in this resonant inductor. 00:46:20.225 --> 00:46:22.876 align:middle line:90% 00:46:22.876 --> 00:46:25.040 align:middle line:84% And then what he's going to do is 00:46:25.040 --> 00:46:28.850 align:middle line:84% he's going to turn the bottom switch on at 0 voltage 00:46:28.850 --> 00:46:33.913 align:middle line:84% because he's going to turn this device on when he's able. 00:46:33.913 --> 00:46:35.330 align:middle line:84% And since this diode's conducting, 00:46:35.330 --> 00:46:37.300 align:middle line:84% he can turn this guy on at 0 voltage. 00:46:37.300 --> 00:46:40.850 align:middle line:84% He charges up current in this resonant inductor. 00:46:40.850 --> 00:46:43.730 align:middle line:84% And then he turns off the bottom device. 00:46:43.730 --> 00:46:45.980 align:middle line:84% And then it's very much like the other circuit. 00:46:45.980 --> 00:46:50.680 align:middle line:84% This resonant inductor rings with the two capacitors 00:46:50.680 --> 00:46:52.200 align:middle line:90% until the top diode conducts. 00:46:52.200 --> 00:46:55.154 align:middle line:90% 00:46:55.154 --> 00:46:59.740 align:middle line:84% Then, he can turn on the top device. 00:46:59.740 --> 00:47:04.520 align:middle line:84% And then he just waits until this current ramps down 00:47:04.520 --> 00:47:11.240 align:middle line:84% and goes to 0 and this auxiliary switch turns off at 0 current. 00:47:11.240 --> 00:47:14.830 align:middle line:84% And then the top device is conducting the output current. 00:47:14.830 --> 00:47:17.660 align:middle line:84% So I've gotten from the bottom diode conducting 00:47:17.660 --> 00:47:20.210 align:middle line:84% to the top switch conducting by triggering 00:47:20.210 --> 00:47:22.180 align:middle line:90% the auxiliary circuit. 00:47:22.180 --> 00:47:27.400 align:middle line:84% And if you think of every other possible switching transmission 00:47:27.400 --> 00:47:29.140 align:middle line:84% and direction of the load current, 00:47:29.140 --> 00:47:30.730 align:middle line:84% you can find a sequence that will 00:47:30.730 --> 00:47:32.110 align:middle line:84% let you use the auxiliary circuit 00:47:32.110 --> 00:47:36.085 align:middle line:90% to make that transition for you. 00:47:36.085 --> 00:47:40.450 align:middle line:84% And so this is a complicated circuit, relatively speaking, 00:47:40.450 --> 00:47:43.057 align:middle line:84% especially when he did this in the late '80s, early '90s. 00:47:43.057 --> 00:47:44.890 align:middle line:84% This is controls and sensing, and everything 00:47:44.890 --> 00:47:46.400 align:middle line:90% was really complicated. 00:47:46.400 --> 00:47:49.630 align:middle line:84% On the other hand, at high powers, you don't really mind. 00:47:49.630 --> 00:47:52.150 align:middle line:84% Compared to the previous inverter I showed you, 00:47:52.150 --> 00:47:55.162 align:middle line:84% the control for that, it has a lot of stuff, 00:47:55.162 --> 00:47:56.120 align:middle line:90% but it's pretty simple. 00:47:56.120 --> 00:47:58.703 align:middle line:84% You just get a sense current and make your switching decisions 00:47:58.703 --> 00:48:01.500 align:middle line:90% based on commanded currents. 00:48:01.500 --> 00:48:03.150 align:middle line:90% This is much more complicated. 00:48:03.150 --> 00:48:05.570 align:middle line:84% But, on the other hand, it lets you PWM any way you want. 00:48:05.570 --> 00:48:07.028 align:middle line:84% They were running motors with this, 00:48:07.028 --> 00:48:09.970 align:middle line:84% and they were running all kinds of special motor controls. 00:48:09.970 --> 00:48:15.300 align:middle line:84% So this is a really good circuit for this kind of application. 00:48:15.300 --> 00:48:17.880 align:middle line:84% And the things you get are reduced switching loss 00:48:17.880 --> 00:48:22.020 align:middle line:84% in the main devices for a small extra auxiliary circuit, which 00:48:22.020 --> 00:48:23.790 align:middle line:90% is also soft switched. 00:48:23.790 --> 00:48:27.480 align:middle line:84% And you get-- this is another set of computations going 00:48:27.480 --> 00:48:29.280 align:middle line:90% the other way-- 00:48:29.280 --> 00:48:32.880 align:middle line:84% you get, because of the snubber capacitors, 00:48:32.880 --> 00:48:36.420 align:middle line:84% you get reduced dv/dt on the switching transmission 00:48:36.420 --> 00:48:38.645 align:middle line:84% and, hence, reduced EMI driving your motor. 00:48:38.645 --> 00:48:42.060 align:middle line:90% 00:48:42.060 --> 00:48:47.550 align:middle line:84% So that is a lightning introduction to soft switching 00:48:47.550 --> 00:48:50.010 align:middle line:84% and some of its benefits and just an introduction 00:48:50.010 --> 00:48:52.260 align:middle line:84% to some of the ways you might go about it. 00:48:52.260 --> 00:48:53.840 align:middle line:90% Yeah? 00:48:53.840 --> 00:48:57.725 align:middle line:84% AUDIENCE: How do you so abruptly turn off the current in the Lr? 00:48:57.725 --> 00:48:59.100 align:middle line:84% DAVID PERREAULT: Well, you don't. 00:48:59.100 --> 00:49:08.210 align:middle line:84% What you do is suppose you're going from bottom to top. 00:49:08.210 --> 00:49:11.480 align:middle line:84% If I turn this switch on and leave this switch off-- 00:49:11.480 --> 00:49:13.220 align:middle line:90% this diode conducts-- 00:49:13.220 --> 00:49:16.820 align:middle line:84% I will charge current positively in Lr. 00:49:16.820 --> 00:49:19.970 align:middle line:84% And eventually, this node's going to ring from the bottom 00:49:19.970 --> 00:49:20.930 align:middle line:90% to the top. 00:49:20.930 --> 00:49:24.230 align:middle line:84% And then Lr has a negative voltage across it. 00:49:24.230 --> 00:49:27.110 align:middle line:90% And so Lr will reduce down to 0. 00:49:27.110 --> 00:49:31.900 align:middle line:84% And when it hits 0, this switch just naturally turns off 00:49:31.900 --> 00:49:35.140 align:middle line:90% because this diode will block. 00:49:35.140 --> 00:49:38.910 align:middle line:84% So what you can do is, by how you control this switch, 00:49:38.910 --> 00:49:43.130 align:middle line:84% this current will just resonate back to 0 and stay at 0. 00:49:43.130 --> 00:49:44.005 align:middle line:90% Does that make sense? 00:49:44.005 --> 00:49:48.960 align:middle line:90% 00:49:48.960 --> 00:49:49.920 align:middle line:90% Kind of. 00:49:49.920 --> 00:49:52.060 align:middle line:84% Let's talk a little bit after class. 00:49:52.060 --> 00:49:57.090 align:middle line:84% But yeah, the idea is to let voltages or currents ring 00:49:57.090 --> 00:49:58.450 align:middle line:90% up or down and then be clamped. 00:49:58.450 --> 00:50:00.600 align:middle line:84% In this case, it's clamped by this switch 00:50:00.600 --> 00:50:02.720 align:middle line:90% going naturally open. 00:50:02.720 --> 00:50:05.070 align:middle line:84% In the other case, it's ring up is clamped 00:50:05.070 --> 00:50:08.100 align:middle line:90% by the body diode of the FET. 00:50:08.100 --> 00:50:11.780 align:middle line:90% And you go along that route. 00:50:11.780 --> 00:50:15.230 align:middle line:84% So that's a lightning introduction to soft switching. 00:50:15.230 --> 00:50:17.990 align:middle line:84% Next class, we'll start talking about a whole class 00:50:17.990 --> 00:50:20.420 align:middle line:84% of converters called resonant converters, 00:50:20.420 --> 00:50:23.210 align:middle line:84% which are a subset of the world of soft-switch converters 00:50:23.210 --> 00:50:27.740 align:middle line:84% that are very, very widely used in high-performance power 00:50:27.740 --> 00:50:28.290 align:middle line:90% converters. 00:50:28.290 --> 00:50:31.460 align:middle line:84% In fact, the converter inside my laptop adapter 00:50:31.460 --> 00:50:34.910 align:middle line:84% here is based on a certain kind of high-frequency resonant 00:50:34.910 --> 00:50:35.810 align:middle line:90% converter. 00:50:35.810 --> 00:50:39.150 align:middle line:84% So have a great day, and we'll take this up next class. 00:50:39.150 --> 00:50:41.970 align:middle line:84% And yeah, Kaito is wandering around somewhere. 00:50:41.970 --> 00:50:42.790 align:middle line:90% I will find him. 00:50:42.790 --> 00:50:44.770 align:middle line:90% Have a great day. 00:50:44.770 --> 00:50:53.000 align:middle line:90%