WEBVTT 00:00:00.000 --> 00:00:02.445 align:middle line:90% [SQUEAKING] 00:00:02.445 --> 00:00:04.401 align:middle line:90% [RUSTLING] 00:00:04.401 --> 00:00:05.379 align:middle line:90% [CLICKING] 00:00:05.379 --> 00:00:13.030 align:middle line:90% 00:00:13.030 --> 00:00:15.250 align:middle line:84% DAVID PERREAULT: OK, why don't we get going? 00:00:15.250 --> 00:00:18.760 align:middle line:84% What I wanted to do today was continue our discussion 00:00:18.760 --> 00:00:21.370 align:middle line:84% of resonant converters and specifically talk 00:00:21.370 --> 00:00:24.730 align:middle line:84% more about resonant DC-to-DC converters. 00:00:24.730 --> 00:00:29.170 align:middle line:84% And last time, just as we were running out of time, 00:00:29.170 --> 00:00:33.550 align:middle line:84% we talked about rectifiers, right. 00:00:33.550 --> 00:00:39.940 align:middle line:84% So I might have a rectifier for a resonant DC-to-DC converter, 00:00:39.940 --> 00:00:45.820 align:middle line:84% and I might like to model that rectifier as a resistor 00:00:45.820 --> 00:00:48.400 align:middle line:84% because everything I've said about resonant inverters, 00:00:48.400 --> 00:00:51.730 align:middle line:84% right, we're talking about, say, an LCR tank, 00:00:51.730 --> 00:00:54.590 align:middle line:84% so the question is, What's the resistance we have? 00:00:54.590 --> 00:00:58.090 align:middle line:84% So for example, suppose I just have 00:00:58.090 --> 00:01:00.850 align:middle line:84% a classical full-bridge rectifier. 00:01:00.850 --> 00:01:05.770 align:middle line:90% 00:01:05.770 --> 00:01:06.760 align:middle line:90% OK. 00:01:06.760 --> 00:01:10.900 align:middle line:84% And let's assume that I'm going to derive this 00:01:10.900 --> 00:01:16.535 align:middle line:84% from a perfect sinusoid, I sine omega t. 00:01:16.535 --> 00:01:19.220 align:middle line:90% 00:01:19.220 --> 00:01:21.980 align:middle line:90% OK. 00:01:21.980 --> 00:01:23.960 align:middle line:84% Where am I getting this I sine omega t? 00:01:23.960 --> 00:01:26.640 align:middle line:84% This is going to be coming from my resonant converter, 00:01:26.640 --> 00:01:29.150 align:middle line:84% and if I have the fundamental harmonic approximation, 00:01:29.150 --> 00:01:31.040 align:middle line:84% for example, in a series resonant tank, 00:01:31.040 --> 00:01:34.470 align:middle line:84% I can think of the tank current as being perfectly sinusoidal. 00:01:34.470 --> 00:01:37.370 align:middle line:84% So here's the sinusoidal current, right, 00:01:37.370 --> 00:01:46.880 align:middle line:84% and maybe I can say, OK, I have v rect here as the input voltage 00:01:46.880 --> 00:01:49.190 align:middle line:90% to the rectifier. 00:01:49.190 --> 00:01:53.990 align:middle line:84% Now, I'm going to consider a capacitively loaded 00:01:53.990 --> 00:01:59.050 align:middle line:84% full-bridge rectifier, OK, where we have C big here. 00:01:59.050 --> 00:02:06.140 align:middle line:84% OK, so the output voltage vd is approximately equal to its DC 00:02:06.140 --> 00:02:12.480 align:middle line:84% component, OK, and maybe I have a load resistor R dc over here. 00:02:12.480 --> 00:02:12.980 align:middle line:90% OK. 00:02:12.980 --> 00:02:19.510 align:middle line:84% So then the question is, What do the waveforms in this thing 00:02:19.510 --> 00:02:20.830 align:middle line:90% look like? 00:02:20.830 --> 00:02:26.070 align:middle line:84% And I could plot, for example, this current. 00:02:26.070 --> 00:02:29.620 align:middle line:90% I'll call this i sub x. 00:02:29.620 --> 00:02:35.810 align:middle line:84% i sub x, right, if this is a sine wave, 00:02:35.810 --> 00:02:39.170 align:middle line:84% when the sine wave is positive, these two diodes are on, 00:02:39.170 --> 00:02:42.800 align:middle line:84% and i sub x looks like I sine omega t. 00:02:42.800 --> 00:02:46.940 align:middle line:84% If I is negative, these two diodes are on, 00:02:46.940 --> 00:02:50.180 align:middle line:84% and ix looks like minus I sine omega t. 00:02:50.180 --> 00:02:55.070 align:middle line:84% So i sub x looks just like the rectified sine wave, right, 00:02:55.070 --> 00:03:05.270 align:middle line:84% where this is 2 pi over omega s in terms of this being t. 00:03:05.270 --> 00:03:05.900 align:middle line:90% OK. 00:03:05.900 --> 00:03:09.900 align:middle line:84% And the peak value here is just I, right. 00:03:09.900 --> 00:03:14.270 align:middle line:84% And if I said, What is the average value of i sub x? 00:03:14.270 --> 00:03:16.730 align:middle line:84% a simple analysis will show that the average value 00:03:16.730 --> 00:03:25.400 align:middle line:84% of i sub x here, OK, will be equal to 2 00:03:25.400 --> 00:03:30.360 align:middle line:84% over pi times I. It's a pretty straightforward analysis. 00:03:30.360 --> 00:03:30.860 align:middle line:90% OK. 00:03:30.860 --> 00:03:33.090 align:middle line:84% Why do I care about the average value of i sub x? 00:03:33.090 --> 00:03:35.870 align:middle line:84% Because clearly, in periodic steady state, 00:03:35.870 --> 00:03:40.610 align:middle line:84% the average current, it goes to the load resistor, 00:03:40.610 --> 00:03:43.170 align:middle line:84% and the ripple current goes to the capacitor, 00:03:43.170 --> 00:03:44.870 align:middle line:90% is the idealization. 00:03:44.870 --> 00:03:46.790 align:middle line:84% OK, and we know we don't get any DC current 00:03:46.790 --> 00:03:49.610 align:middle line:84% in the capacitor in periodic steady state. 00:03:49.610 --> 00:03:54.230 align:middle line:84% So if I wanted to analyze this thing, 00:03:54.230 --> 00:03:56.670 align:middle line:90% what do I get for output power? 00:03:56.670 --> 00:04:03.020 align:middle line:84% The average output power is simply equal to-- 00:04:03.020 --> 00:04:04.790 align:middle line:84% the average output power is simply 00:04:04.790 --> 00:04:11.300 align:middle line:84% equal to the average of vd times ix, which, 00:04:11.300 --> 00:04:14.600 align:middle line:84% if this capacitor is really big and vd is approximately 00:04:14.600 --> 00:04:18.230 align:middle line:84% constant, this is approximately equal to capital Vd times 00:04:18.230 --> 00:04:22.350 align:middle line:84% the average of ix, which we could say 00:04:22.350 --> 00:04:31.650 align:middle line:84% is equal to 2 over pi VD times I. 00:04:31.650 --> 00:04:34.240 align:middle line:84% And this is the power that's going to the load. 00:04:34.240 --> 00:04:35.620 align:middle line:90% This is the DC power. 00:04:35.620 --> 00:04:38.580 align:middle line:84% And of course, if these are just ideal diodes, 00:04:38.580 --> 00:04:45.670 align:middle line:84% then all that power came from the AC side, right. 00:04:45.670 --> 00:04:50.970 align:middle line:84% Looking at the AC side, what do I see on the AC side? 00:04:50.970 --> 00:04:57.875 align:middle line:84% What I see is a voltage v rect that looks like this. 00:04:57.875 --> 00:05:03.810 align:middle line:90% 00:05:03.810 --> 00:05:05.124 align:middle line:90% OK. 00:05:05.124 --> 00:05:07.210 align:middle line:90% It's a square wave. 00:05:07.210 --> 00:05:10.410 align:middle line:84% And this is, again, 2 pi over omega 00:05:10.410 --> 00:05:15.120 align:middle line:90% s, and this is pi over omega s. 00:05:15.120 --> 00:05:15.980 align:middle line:90% All right. 00:05:15.980 --> 00:05:26.520 align:middle line:84% This is vd, and this is minus vd, OK. 00:05:26.520 --> 00:05:30.490 align:middle line:84% And so the power on the AC side, right, 00:05:30.490 --> 00:05:36.062 align:middle line:84% would just be the integral of I sine omega t times v rect. 00:05:36.062 --> 00:05:36.562 align:middle line:90% OK. 00:05:36.562 --> 00:05:39.214 align:middle line:90% 00:05:39.214 --> 00:05:42.960 align:middle line:84% But we know that we only transfer power 00:05:42.960 --> 00:05:47.240 align:middle line:84% through voltages and currents at the same frequency, right. 00:05:47.240 --> 00:05:51.680 align:middle line:84% So if I make the fundamental harmonic approximation, 00:05:51.680 --> 00:05:55.460 align:middle line:84% then what I can say is, look, the only component 00:05:55.460 --> 00:05:57.650 align:middle line:90% of this voltage v rect-- 00:05:57.650 --> 00:05:59.360 align:middle line:84% and, boy, he doesn't look exactly square, 00:05:59.360 --> 00:06:02.840 align:middle line:84% but let's pretend he's square, OK-- 00:06:02.840 --> 00:06:09.260 align:middle line:84% the only component of v rect that generates power 00:06:09.260 --> 00:06:12.170 align:middle line:84% is the fundamental, right, because the current's 00:06:12.170 --> 00:06:12.670 align:middle line:90% fundamental. 00:06:12.670 --> 00:06:14.920 align:middle line:84% So it's only going to be the fundamental current times 00:06:14.920 --> 00:06:17.660 align:middle line:84% the fundamental voltage that are delivering power, or real power, 00:06:17.660 --> 00:06:22.805 align:middle line:84% and all other power components have to be reactive, right. 00:06:22.805 --> 00:06:30.350 align:middle line:84% So I might, then, just think about what v rect 1 looks like. 00:06:30.350 --> 00:06:36.380 align:middle line:84% v rect 1, if I did the analysis, the fundamental of a square wave 00:06:36.380 --> 00:06:39.610 align:middle line:84% is 4 over pi times the peak value of the square wave, 00:06:39.610 --> 00:06:43.130 align:middle line:84% right, so I might think of about a waveform that 00:06:43.130 --> 00:06:51.520 align:middle line:84% was the fundamental component, where this peak value 00:06:51.520 --> 00:06:58.570 align:middle line:90% is 4 over pi vdc-- 00:06:58.570 --> 00:07:06.435 align:middle line:84% or 4 over pi vd sine of omega st is equal to v rect 1 of t. 00:07:06.435 --> 00:07:13.690 align:middle line:90% 00:07:13.690 --> 00:07:15.940 align:middle line:84% Does that make sense to everybody? 00:07:15.940 --> 00:07:23.410 align:middle line:84% I'm sorry, this peak value, this peak value is 4 over pi vd, 00:07:23.410 --> 00:07:30.970 align:middle line:84% and this whole waveform is 4 over pi vd sine omega st. 00:07:30.970 --> 00:07:31.480 align:middle line:90% OK. 00:07:31.480 --> 00:07:35.320 align:middle line:84% So what I get-- with ideal diodes, at any rate-- 00:07:35.320 --> 00:07:38.530 align:middle line:84% is a square wave that's in phase with the drive current. 00:07:38.530 --> 00:07:40.820 align:middle line:84% Remember, the drive current looks something like this. 00:07:40.820 --> 00:07:44.680 align:middle line:90% This is Is sine omega t, right. 00:07:44.680 --> 00:07:46.760 align:middle line:90% So here's Is sine omega t-- 00:07:46.760 --> 00:07:49.390 align:middle line:90% 00:07:49.390 --> 00:07:51.520 align:middle line:90% I sine omega t-- 00:07:51.520 --> 00:07:54.730 align:middle line:90% I sine omega st. 00:07:54.730 --> 00:07:59.710 align:middle line:84% So what I get is a voltage whose fundamental component 00:07:59.710 --> 00:08:02.470 align:middle line:84% is in phase with the current, right. 00:08:02.470 --> 00:08:05.890 align:middle line:84% So for power transfer purposes, I 00:08:05.890 --> 00:08:09.550 align:middle line:84% might as well think of this thing as a resistor, right. 00:08:09.550 --> 00:08:12.710 align:middle line:84% Essentially, it's a describing function approach. 00:08:12.710 --> 00:08:15.550 align:middle line:84% It's the amplitude of the voltage divided by the amplitude 00:08:15.550 --> 00:08:16.450 align:middle line:90% of the current. 00:08:16.450 --> 00:08:20.530 align:middle line:84% So I might think of an equivalent rectifier impedance, 00:08:20.530 --> 00:08:23.320 align:middle line:84% like looking into the rectifier from the AC side. 00:08:23.320 --> 00:08:34.770 align:middle line:84% Rac, OK, is going to be equal to v rect 1 over the current, which 00:08:34.770 --> 00:08:41.789 align:middle line:84% is going to give me 4 over pi vd divided by I. OK. 00:08:41.789 --> 00:08:45.990 align:middle line:84% This is the equivalent AC resistance 00:08:45.990 --> 00:08:48.330 align:middle line:84% that relates the fundamental drive 00:08:48.330 --> 00:08:51.540 align:middle line:84% current with the fundamental of the voltage. 00:08:51.540 --> 00:08:52.925 align:middle line:90% Any questions about that? 00:08:52.925 --> 00:08:56.800 align:middle line:90% 00:08:56.800 --> 00:09:00.460 align:middle line:84% Now, it turns out I can write this a couple of other ways 00:09:00.460 --> 00:09:02.390 align:middle line:90% which are useful to think about. 00:09:02.390 --> 00:09:03.850 align:middle line:90% One of these is as follows. 00:09:03.850 --> 00:09:06.670 align:middle line:84% Because I have this relationship between the current 00:09:06.670 --> 00:09:12.580 align:middle line:84% and the power, I could write this as being equal to 8 00:09:12.580 --> 00:09:19.450 align:middle line:84% over pi squared vd squared divided by the power. 00:09:19.450 --> 00:09:21.058 align:middle line:90% OK. 00:09:21.058 --> 00:09:22.760 align:middle line:84% So why would I think about it that way? 00:09:22.760 --> 00:09:25.450 align:middle line:84% Well, let's pretend I don't know what the resistance looks like. 00:09:25.450 --> 00:09:27.670 align:middle line:84% But I know I'm delivering a certain amount of power 00:09:27.670 --> 00:09:32.320 align:middle line:84% into the load, and I know I have a certain DC output voltage. 00:09:32.320 --> 00:09:36.580 align:middle line:84% Then I could express the equivalent AC resistance, 00:09:36.580 --> 00:09:39.520 align:middle line:84% owing to this rectifier, based on 8 00:09:39.520 --> 00:09:42.710 align:middle line:84% over pi squared vd squared over power. 00:09:42.710 --> 00:09:43.940 align:middle line:90% OK. 00:09:43.940 --> 00:09:48.560 align:middle line:84% Or equivalently, I know the relationship 00:09:48.560 --> 00:09:52.590 align:middle line:84% between the average current and vd is related to-- 00:09:52.590 --> 00:09:59.200 align:middle line:84% the average of ix times Rdc has to be vd, right. 00:09:59.200 --> 00:10:00.990 align:middle line:84% And if I apply that relationship, 00:10:00.990 --> 00:10:09.620 align:middle line:84% I can also write this as equal to being equal to 8 00:10:09.620 --> 00:10:11.043 align:middle line:90% over pi squared Rdc. 00:10:11.043 --> 00:10:16.130 align:middle line:90% 00:10:16.130 --> 00:10:17.366 align:middle line:90% OK. 00:10:17.366 --> 00:10:19.220 align:middle line:84% It's just a question of whether-- 00:10:19.220 --> 00:10:21.450 align:middle line:84% if I had some other load besides a resistor, 00:10:21.450 --> 00:10:23.450 align:middle line:84% I couldn't write it this way, but I could always 00:10:23.450 --> 00:10:24.630 align:middle line:90% write it this way. 00:10:24.630 --> 00:10:25.580 align:middle line:90% OK. 00:10:25.580 --> 00:10:27.320 align:middle line:84% Any questions about where I'm getting 00:10:27.320 --> 00:10:29.440 align:middle line:84% that notion of an equivalent resistance from? 00:10:29.440 --> 00:10:34.540 align:middle line:90% 00:10:34.540 --> 00:10:41.590 align:middle line:84% So I can take a rectifier and model it 00:10:41.590 --> 00:10:47.240 align:middle line:84% as an equivalent resistance for purposes of power transfer, 00:10:47.240 --> 00:10:50.320 align:middle line:84% assuming that it's being driven by a perfectly 00:10:50.320 --> 00:10:52.610 align:middle line:90% sinusoidal current. 00:10:52.610 --> 00:10:53.780 align:middle line:90% OK. 00:10:53.780 --> 00:10:56.360 align:middle line:84% And that's going to become really handy. 00:10:56.360 --> 00:10:58.110 align:middle line:90% Why is that going to be handy? 00:10:58.110 --> 00:11:00.170 align:middle line:84% That's going to be handy because we 00:11:00.170 --> 00:11:04.310 align:middle line:84% would like to model the behavior of a DC-to-DC converter, OK, 00:11:04.310 --> 00:11:07.370 align:middle line:84% and what I've been talking about up to now 00:11:07.370 --> 00:11:10.100 align:middle line:90% is series resonant inverters. 00:11:10.100 --> 00:11:17.700 align:middle line:84% Right, so let's think about what a series resonant inverter-- 00:11:17.700 --> 00:11:19.760 align:middle line:84% I'm sorry, a series resonant DC-to-DC converter 00:11:19.760 --> 00:11:20.790 align:middle line:90% might look like. 00:11:20.790 --> 00:11:22.840 align:middle line:90% It could look like this. 00:11:22.840 --> 00:11:28.370 align:middle line:84% Maybe I have an input voltage vdc, 00:11:28.370 --> 00:11:32.541 align:middle line:84% and then I will use a half-bridge inverter. 00:11:32.541 --> 00:11:36.930 align:middle line:84% Right, so this is just a simple half bridge, OK, 00:11:36.930 --> 00:11:41.360 align:middle line:84% and I'm going to call this v inv. 00:11:41.360 --> 00:11:44.360 align:middle line:84% That's the inverter voltage, v inv. 00:11:44.360 --> 00:11:47.070 align:middle line:90% What does v inv look like? 00:11:47.070 --> 00:11:48.655 align:middle line:90% v inv looks like this. 00:11:48.655 --> 00:11:51.950 align:middle line:90% 00:11:51.950 --> 00:11:52.580 align:middle line:90% OK. 00:11:52.580 --> 00:11:55.100 align:middle line:90% Here's v inv. 00:11:55.100 --> 00:12:01.200 align:middle line:84% It's modulating between-- someday, 00:12:01.200 --> 00:12:03.630 align:middle line:84% I'm going to get to this 50% duty ratio here-- he's 00:12:03.630 --> 00:12:07.260 align:middle line:84% modulating between v and 0, and this 00:12:07.260 --> 00:12:11.650 align:middle line:84% is 2 pi over omega s, whatever my switching frequency is. 00:12:11.650 --> 00:12:16.320 align:middle line:84% And this is pi over omega s in terms of time. 00:12:16.320 --> 00:12:17.850 align:middle line:90% OK. 00:12:17.850 --> 00:12:18.435 align:middle line:90% All right. 00:12:18.435 --> 00:12:20.940 align:middle line:90% 00:12:20.940 --> 00:12:25.410 align:middle line:84% Then I'm going to connect him up to some tank, right, 00:12:25.410 --> 00:12:30.095 align:middle line:84% and in this case, I'm going to use the series resonant tank. 00:12:30.095 --> 00:12:39.270 align:middle line:84% Right, so I'm going to have a capacitor C, an inductor L. OK. 00:12:39.270 --> 00:12:49.050 align:middle line:84% And I could kind think of that as running 00:12:49.050 --> 00:12:52.260 align:middle line:90% into whatever my net load is. 00:12:52.260 --> 00:12:52.950 align:middle line:90% OK. 00:12:52.950 --> 00:12:57.720 align:middle line:84% So let me just call this voltage over here v sub r. 00:12:57.720 --> 00:12:59.496 align:middle line:90% OK. 00:12:59.496 --> 00:13:01.890 align:middle line:84% And then maybe I go and I say, OK, I 00:13:01.890 --> 00:13:04.770 align:middle line:84% need a transformer here in the middle of my AC converter 00:13:04.770 --> 00:13:07.050 align:middle line:90% because now I have AC waveforms. 00:13:07.050 --> 00:13:12.046 align:middle line:84% Let me put in an n 1 to n2 transformer. 00:13:12.046 --> 00:13:14.870 align:middle line:90% 00:13:14.870 --> 00:13:16.975 align:middle line:90% OK. 00:13:16.975 --> 00:13:21.240 align:middle line:84% And I'm going to use this thing, and let me call this voltage v 00:13:21.240 --> 00:13:23.250 align:middle line:90% rect. 00:13:23.250 --> 00:13:26.520 align:middle line:84% And I'm going to run this into my rectifier. 00:13:26.520 --> 00:13:27.776 align:middle line:90% So here's my rectifier. 00:13:27.776 --> 00:13:46.510 align:middle line:90% 00:13:46.510 --> 00:13:48.110 align:middle line:90% All right, so what am I doing? 00:13:48.110 --> 00:13:52.810 align:middle line:84% I'm going DC to AC, running through my frequency-selective 00:13:52.810 --> 00:13:55.060 align:middle line:90% resonant tank. 00:13:55.060 --> 00:13:56.560 align:middle line:90% All right. 00:13:56.560 --> 00:13:59.637 align:middle line:84% Maybe I have an additional voltage transformation in here. 00:13:59.637 --> 00:14:01.220 align:middle line:84% Here, I'm doing it with a transformer. 00:14:01.220 --> 00:14:04.380 align:middle line:84% You can do it with other kinds of transforming elements, too. 00:14:04.380 --> 00:14:08.600 align:middle line:84% I'm running into a rectifier and getting my output voltage-- 00:14:08.600 --> 00:14:13.190 align:middle line:84% so I come from a DC input to a DC output. 00:14:13.190 --> 00:14:13.690 align:middle line:90% OK. 00:14:13.690 --> 00:14:15.945 align:middle line:84% Any questions about the structure of the system? 00:14:15.945 --> 00:14:20.880 align:middle line:90% 00:14:20.880 --> 00:14:24.660 align:middle line:84% So because I'm going to make the fundamental harmonic 00:14:24.660 --> 00:14:29.310 align:middle line:84% approximation, I'm going to assume that my current here, I 00:14:29.310 --> 00:14:36.090 align:middle line:84% sub L, is approximately sinusoidal, that this LC tank is 00:14:36.090 --> 00:14:40.110 align:middle line:84% high enough q when loaded by this rectifier system 00:14:40.110 --> 00:14:44.520 align:middle line:84% that I can ignore all the harmonic currents in iL. 00:14:44.520 --> 00:14:46.020 align:middle line:90% OK. 00:14:46.020 --> 00:14:48.450 align:middle line:84% If I do that, then the only thing that 00:14:48.450 --> 00:14:52.272 align:middle line:84% matters for power transfer, just as the only thing that mattered 00:14:52.272 --> 00:14:54.480 align:middle line:84% on the rectifier was the fundamental of the rectifier 00:14:54.480 --> 00:14:57.930 align:middle line:84% voltage, the only thing that matters on the inverter side 00:14:57.930 --> 00:15:00.200 align:middle line:84% is the fundamental of the inverter voltage. 00:15:00.200 --> 00:15:05.790 align:middle line:84% Right, so maybe I could just go focus on, for example, 00:15:05.790 --> 00:15:09.430 align:middle line:90% v inverter 1. 00:15:09.430 --> 00:15:11.060 align:middle line:90% It's fundamental. 00:15:11.060 --> 00:15:12.780 align:middle line:90% All right. 00:15:12.780 --> 00:15:15.640 align:middle line:84% Well, what does the inverter fundamental voltage look like? 00:15:15.640 --> 00:15:18.870 align:middle line:84% It's a square wave between 0 and vdc, 00:15:18.870 --> 00:15:22.690 align:middle line:84% but its DC components are going to get blocked anyway. 00:15:22.690 --> 00:15:26.620 align:middle line:84% So it's between plus vdc over 2 and minus vdc over 2, 00:15:26.620 --> 00:15:29.980 align:middle line:84% times 4 over pi for its fundamental, 00:15:29.980 --> 00:15:33.700 align:middle line:84% and I'm going to get an v inverter 1 that's basically 00:15:33.700 --> 00:15:47.150 align:middle line:84% equal to an amplitude of 2 over pi vdc.. 00:15:47.150 --> 00:15:51.110 align:middle line:84% And this is v inverter 1, OK, and this 00:15:51.110 --> 00:15:55.960 align:middle line:84% is the only thing that matters in terms of transferring power. 00:15:55.960 --> 00:15:57.040 align:middle line:90% OK. 00:15:57.040 --> 00:16:03.070 align:middle line:84% So maybe, then, I could think of this system 00:16:03.070 --> 00:16:13.090 align:middle line:84% as being v inverter 1 right, the sinusoidal fundamental component 00:16:13.090 --> 00:16:16.090 align:middle line:84% of the square-wave voltage on synthesizing, 00:16:16.090 --> 00:16:24.830 align:middle line:84% running into a tank, first C, then L, right, 00:16:24.830 --> 00:16:35.160 align:middle line:84% and then I'm going through a transformer, 00:16:35.160 --> 00:16:38.110 align:middle line:90% OK, and back into a rectifier. 00:16:38.110 --> 00:16:39.860 align:middle line:84% But how did I model the rectifier? 00:16:39.860 --> 00:16:43.630 align:middle line:84% I modeled the rectifier as this Rac. 00:16:43.630 --> 00:16:45.850 align:middle line:90% Right, I just did this. 00:16:45.850 --> 00:16:47.410 align:middle line:90% What's my value of Rac? 00:16:47.410 --> 00:16:48.095 align:middle line:90% It's right here. 00:16:48.095 --> 00:16:51.070 align:middle line:90% 00:16:51.070 --> 00:16:54.790 align:middle line:90% OK, so I get some value of Rac. 00:16:54.790 --> 00:16:59.500 align:middle line:90% This is N1 to N2, right. 00:16:59.500 --> 00:17:04.030 align:middle line:84% Maybe I could say, What's the value of R sub r here? 00:17:04.030 --> 00:17:06.019 align:middle line:84% What's the resistance I see in here? 00:17:06.019 --> 00:17:07.394 align:middle line:84% Can anybody tell me what that is? 00:17:07.394 --> 00:17:16.930 align:middle line:90% 00:17:16.930 --> 00:17:20.740 align:middle line:84% If I had-- if this were, honest to god, a resistor here, 00:17:20.740 --> 00:17:26.410 align:middle line:84% right, then the ideal transformer scales 00:17:26.410 --> 00:17:29.240 align:middle line:84% impedances by the square of the turns ratio, right. 00:17:29.240 --> 00:17:35.540 align:middle line:84% So that means I ought to scale this up by N1 over N2 squared. 00:17:35.540 --> 00:17:41.050 align:middle line:84% So this ought to be R sub r ought to be N1 over N2 quantity 00:17:41.050 --> 00:17:45.590 align:middle line:90% squared, Rac, right. 00:17:45.590 --> 00:17:48.760 align:middle line:84% So I could think, looking this way, 00:17:48.760 --> 00:17:54.130 align:middle line:84% I could imagine I'm just seeing an AC resistance scaled 00:17:54.130 --> 00:17:56.110 align:middle line:90% by the transformation ratio. 00:17:56.110 --> 00:18:02.080 align:middle line:84% And all of that, so long as i sub L is sinusoidal, all of this 00:18:02.080 --> 00:18:04.360 align:middle line:84% preserves power transfer in the system 00:18:04.360 --> 00:18:07.040 align:middle line:84% because we're only transferring power through the fundamental. 00:18:07.040 --> 00:18:10.090 align:middle line:90% 00:18:10.090 --> 00:18:12.240 align:middle line:90% Any questions about that? 00:18:12.240 --> 00:18:12.960 align:middle line:90% Yeah? 00:18:12.960 --> 00:18:17.730 align:middle line:84% AUDIENCE: So is the voltage gain all coming from transformer? 00:18:17.730 --> 00:18:19.990 align:middle line:84% DAVID PERREAULT: That is an excellent question. 00:18:19.990 --> 00:18:24.193 align:middle line:84% No, it's not, but that's precisely-- 00:18:24.193 --> 00:18:25.610 align:middle line:84% you're very astute, because that's 00:18:25.610 --> 00:18:28.880 align:middle line:84% precisely how we want to think about the system, 00:18:28.880 --> 00:18:32.750 align:middle line:90% is in terms of the voltage gain. 00:18:32.750 --> 00:18:36.380 align:middle line:84% We get a lot-- we may get a lot of the voltage gain 00:18:36.380 --> 00:18:37.680 align:middle line:90% from the transformer. 00:18:37.680 --> 00:18:39.410 align:middle line:84% That's why we put-- that's one reason why 00:18:39.410 --> 00:18:40.618 align:middle line:90% we put the transformer there. 00:18:40.618 --> 00:18:44.930 align:middle line:84% One reason is I just want this voltage and this voltage 00:18:44.930 --> 00:18:46.830 align:middle line:84% to be isolated, so I get isolation. 00:18:46.830 --> 00:18:47.870 align:middle line:90% But I can also-- 00:18:47.870 --> 00:18:50.630 align:middle line:84% if I have a high-voltage input and a low-voltage output, 00:18:50.630 --> 00:18:53.060 align:middle line:90% maybe I do a big step-down here. 00:18:53.060 --> 00:19:03.860 align:middle line:84% But I also get some, some, voltage transformation 00:19:03.860 --> 00:19:06.630 align:middle line:90% from the tank, right. 00:19:06.630 --> 00:19:13.200 align:middle line:84% So maybe I think about this thing in the following way. 00:19:13.200 --> 00:19:22.423 align:middle line:84% I have some v inverter 1, right, then I have my LC network. 00:19:22.423 --> 00:19:25.650 align:middle line:90% 00:19:25.650 --> 00:19:29.190 align:middle line:84% And let me just preserve the order of my components, 00:19:29.190 --> 00:19:30.440 align:middle line:90% even though it doesn't matter. 00:19:30.440 --> 00:19:37.170 align:middle line:90% 00:19:37.170 --> 00:19:42.000 align:middle line:84% If I'm going to operate above resonance, 00:19:42.000 --> 00:19:47.255 align:middle line:84% this series resonant tank looks net inductive. 00:19:47.255 --> 00:19:51.050 align:middle line:84% Right, If I'm going to go above this natural resonant frequency, 00:19:51.050 --> 00:19:54.560 align:middle line:84% omega 0 1 over the square root of LC, this looks going to be-- 00:19:54.560 --> 00:19:57.060 align:middle line:84% whatever the cancellation between C and L is, 00:19:57.060 --> 00:20:01.730 align:middle line:84% this is going to give me some of L effective, which 00:20:01.730 --> 00:20:05.450 align:middle line:90% is some equivalent impedance. 00:20:05.450 --> 00:20:12.560 align:middle line:84% And so this is going to give me some net impedance, which then 00:20:12.560 --> 00:20:19.640 align:middle line:84% voltage-divides with R sub r to give me 00:20:19.640 --> 00:20:26.960 align:middle line:84% a voltage I'm calling v sub r, or v sub r 1 in this model. 00:20:26.960 --> 00:20:30.900 align:middle line:90% So this is v sub r 1, right. 00:20:30.900 --> 00:20:32.870 align:middle line:84% So I basically have a voltage divider 00:20:32.870 --> 00:20:35.060 align:middle line:84% between my inverter-generated voltage, 00:20:35.060 --> 00:20:37.250 align:middle line:84% the voltage generated by a half bridge, 00:20:37.250 --> 00:20:41.460 align:middle line:84% divided down by this with R sub r, right. 00:20:41.460 --> 00:20:44.240 align:middle line:84% And that's what we said, was one of the nice things 00:20:44.240 --> 00:20:47.510 align:middle line:84% about a resonant tank is the value 00:20:47.510 --> 00:20:50.540 align:middle line:84% of this effective impedance varies very quickly 00:20:50.540 --> 00:20:51.570 align:middle line:90% with frequency. 00:20:51.570 --> 00:20:53.420 align:middle line:84% That's why the admittance looking in here 00:20:53.420 --> 00:20:55.970 align:middle line:84% is varying very quickly with frequency. 00:20:55.970 --> 00:20:59.090 align:middle line:84% And hence, I get a frequency-dependent voltage 00:20:59.090 --> 00:21:04.340 align:middle line:84% divider between the effective resistance posed by my load 00:21:04.340 --> 00:21:09.350 align:middle line:84% and the resonant tank components themselves. 00:21:09.350 --> 00:21:11.290 align:middle line:90% OK. 00:21:11.290 --> 00:21:12.170 align:middle line:90% Excellent question. 00:21:12.170 --> 00:21:13.340 align:middle line:90% Any other questions? 00:21:13.340 --> 00:21:18.570 align:middle line:90% 00:21:18.570 --> 00:21:24.050 align:middle line:90% So how might I think about that? 00:21:24.050 --> 00:21:28.400 align:middle line:90% I might think about this gain. 00:21:28.400 --> 00:21:30.680 align:middle line:84% I might think of about my resonant tank 00:21:30.680 --> 00:21:41.900 align:middle line:84% gain, my resonant tank voltage gain, just 00:21:41.900 --> 00:21:44.780 align:middle line:84% owing to the operation of the resonant tank dividing 00:21:44.780 --> 00:21:46.500 align:middle line:90% with the equivalent load. 00:21:46.500 --> 00:21:50.960 align:middle line:84% I'll call that some gain G sub t, which 00:21:50.960 --> 00:21:56.780 align:middle line:84% I'm defining as being vr1, the magnitude of vr1, 00:21:56.780 --> 00:22:02.060 align:middle line:84% divided by the magnitude of v inv 1. 00:22:02.060 --> 00:22:03.206 align:middle line:90% OK. 00:22:03.206 --> 00:22:05.960 align:middle line:84% And this resonant tank gain is going 00:22:05.960 --> 00:22:12.000 align:middle line:84% to be frequency dependent, OK, because as I go up 00:22:12.000 --> 00:22:15.360 align:middle line:84% in frequency, if I were dead on resonance, 00:22:15.360 --> 00:22:18.680 align:middle line:84% what would the resonant tank gain be here? 00:22:18.680 --> 00:22:21.570 align:middle line:84% If I were to run this to where L and C exactly 00:22:21.570 --> 00:22:24.680 align:middle line:84% cancel in impedance, right, this would 00:22:24.680 --> 00:22:26.390 align:middle line:84% be a short circuit at the fundamental, 00:22:26.390 --> 00:22:30.840 align:middle line:84% and I'd have a gain of 1 between v inverter 1 and vr1. 00:22:30.840 --> 00:22:34.170 align:middle line:84% If I go above resonance or, for that matter, below resonance, 00:22:34.170 --> 00:22:36.870 align:middle line:84% this becomes a nonzero net reactance, 00:22:36.870 --> 00:22:40.290 align:middle line:84% and I get voltage division and I get a lower gain. 00:22:40.290 --> 00:22:41.030 align:middle line:90% OK. 00:22:41.030 --> 00:22:43.590 align:middle line:90% So I'm going to have-- 00:22:43.590 --> 00:22:49.120 align:middle line:84% this tank gain is a function of frequency. 00:22:49.120 --> 00:22:50.080 align:middle line:90% OK. 00:22:50.080 --> 00:22:52.660 align:middle line:84% The other thing I need to think about 00:22:52.660 --> 00:22:58.462 align:middle line:84% is, What is the effective quality factor of this tank? 00:22:58.462 --> 00:23:01.030 align:middle line:84% Right, and we said, when we're talking about the quality 00:23:01.030 --> 00:23:04.450 align:middle line:84% factor, what we're really meaning is, How sharply tuned 00:23:04.450 --> 00:23:07.045 align:middle line:90% is the behavior change? 00:23:07.045 --> 00:23:09.170 align:middle line:84% And I've got to be a little bit careful about that, 00:23:09.170 --> 00:23:14.830 align:middle line:84% but we could say that the Q0, the effective quality 00:23:14.830 --> 00:23:18.850 align:middle line:84% factor of the tank, I might write as the square root of L 00:23:18.850 --> 00:23:21.435 align:middle line:90% divided by C divided by R sub r. 00:23:21.435 --> 00:23:27.660 align:middle line:90% 00:23:27.660 --> 00:23:29.050 align:middle line:90% Does that make sense, everybody? 00:23:29.050 --> 00:23:32.840 align:middle line:90% 00:23:32.840 --> 00:23:38.660 align:middle line:84% So how does this play out in practice? 00:23:38.660 --> 00:23:43.070 align:middle line:84% First of all, let's recognize that this tank gain is 00:23:43.070 --> 00:23:50.560 align:middle line:84% a function of frequency, right, and it's also a function-- 00:23:50.560 --> 00:23:54.400 align:middle line:84% and the tank quality factor, the effective tank quality factor 00:23:54.400 --> 00:23:59.500 align:middle line:84% is, because it's a function of Rr and Rr is a function-- 00:23:59.500 --> 00:24:03.010 align:middle line:84% is determined by Rac, it's also a function of power 00:24:03.010 --> 00:24:04.980 align:middle line:90% as well as voltage. 00:24:04.980 --> 00:24:05.480 align:middle line:90% OK. 00:24:05.480 --> 00:24:14.560 align:middle line:84% So how might I model this whole DC-to-DC conversion system? 00:24:14.560 --> 00:24:17.320 align:middle line:84% OK, let's break it up, and now I'm 00:24:17.320 --> 00:24:21.160 align:middle line:84% going beyond like-- sort of a resonant inverter's very simple. 00:24:21.160 --> 00:24:23.650 align:middle line:84% I just have to think about my gain 00:24:23.650 --> 00:24:26.410 align:middle line:84% from my inverter to my fundamental and what happens 00:24:26.410 --> 00:24:28.020 align:middle line:90% and how I control power. 00:24:28.020 --> 00:24:34.180 align:middle line:84% But now I have sort of DC on the input side, DC on the output 00:24:34.180 --> 00:24:37.750 align:middle line:84% side, but I'm mediating it through purely sinusoidal 00:24:37.750 --> 00:24:38.870 align:middle line:90% waveforms. 00:24:38.870 --> 00:24:39.370 align:middle line:90% OK. 00:24:39.370 --> 00:24:42.580 align:middle line:84% So maybe here's how I might think about my DC-to-DC 00:24:42.580 --> 00:24:43.490 align:middle line:90% converter. 00:24:43.490 --> 00:24:49.220 align:middle line:84% Maybe I would think about this thing as, you know, 00:24:49.220 --> 00:24:57.670 align:middle line:84% I come from my DC input VDC, and maybe I have an inverter gain-- 00:24:57.670 --> 00:25:01.610 align:middle line:84% and I'm going to call this the gain of the inverter, OK-- 00:25:01.610 --> 00:25:06.160 align:middle line:84% which basically gives me the AC fundamental 00:25:06.160 --> 00:25:09.820 align:middle line:90% divided by the DC voltage. 00:25:09.820 --> 00:25:18.600 align:middle line:84% So this is sort of v inverter 1 divided by v DC. 00:25:18.600 --> 00:25:20.230 align:middle line:90% OK. 00:25:20.230 --> 00:25:21.830 align:middle line:84% I've already told you what that is. 00:25:21.830 --> 00:25:25.110 align:middle line:84% It's basically I come in from vdc in DC, 00:25:25.110 --> 00:25:27.720 align:middle line:90% and I get 2 over pi vdc AC. 00:25:27.720 --> 00:25:34.170 align:middle line:84% So in my example here, this is equal to 2 over pi, right. 00:25:34.170 --> 00:25:36.960 align:middle line:84% If I use a full-bridge inverter, maybe it 00:25:36.960 --> 00:25:39.272 align:middle line:84% would be 4, and square wave, it would be 4 over pi. 00:25:39.272 --> 00:25:41.730 align:middle line:84% If I use some other inverter that I haven't told you about, 00:25:41.730 --> 00:25:44.080 align:middle line:84% it could be some other value, again. 00:25:44.080 --> 00:25:48.390 align:middle line:84% But this is just to say, OK, going through the switch 00:25:48.390 --> 00:25:55.050 align:middle line:84% portion of my inverter, there's some gain 00:25:55.050 --> 00:25:58.530 align:middle line:84% between the DC input and the fundamental AC output 00:25:58.530 --> 00:26:02.160 align:middle line:84% that I'm getting from my inverter. 00:26:02.160 --> 00:26:05.490 align:middle line:90% That make sense to everybody? 00:26:05.490 --> 00:26:10.230 align:middle line:84% The next thing I have is the tank gain. 00:26:10.230 --> 00:26:15.050 align:middle line:84% It's basically this model here, right. 00:26:15.050 --> 00:26:17.150 align:middle line:90% This is G sub tank. 00:26:17.150 --> 00:26:21.050 align:middle line:84% So maybe I will put that in yellow, right. 00:26:21.050 --> 00:26:28.310 align:middle line:84% So now I have G sub tank, OK, and G sub tank 00:26:28.310 --> 00:26:33.860 align:middle line:84% is the magnitude v sub r 1 divided 00:26:33.860 --> 00:26:38.330 align:middle line:84% by the magnitude of v inverter 1. 00:26:38.330 --> 00:26:40.710 align:middle line:90% OK. 00:26:40.710 --> 00:26:45.215 align:middle line:84% And this thing is a function of the tank. 00:26:45.215 --> 00:26:48.270 align:middle line:90% 00:26:48.270 --> 00:26:51.780 align:middle line:84% It's a function of, like, is it a series tank 00:26:51.780 --> 00:26:54.840 align:middle line:84% or a parallel tank, and the values of the tank. 00:26:54.840 --> 00:26:57.690 align:middle line:90% It's a function of frequency. 00:26:57.690 --> 00:27:00.785 align:middle line:90% It's a function of power. 00:27:00.785 --> 00:27:04.110 align:middle line:84% OK, but importantly, it's a function of the switching 00:27:04.110 --> 00:27:05.140 align:middle line:90% frequency, right. 00:27:05.140 --> 00:27:10.200 align:middle line:84% So basically, I get to control this tank gain by controlling 00:27:10.200 --> 00:27:12.560 align:middle line:90% my switching frequency. 00:27:12.560 --> 00:27:13.230 align:middle line:90% All right. 00:27:13.230 --> 00:27:18.590 align:middle line:84% The output of this thing, we said was vr 1, 00:27:18.590 --> 00:27:22.660 align:middle line:84% the fundamental of the voltage here. 00:27:22.660 --> 00:27:23.160 align:middle line:90% OK. 00:27:23.160 --> 00:27:24.967 align:middle line:90% And this should be-- 00:27:24.967 --> 00:27:26.550 align:middle line:84% what does this voltage look like here? 00:27:26.550 --> 00:27:27.570 align:middle line:90% It's actually a square wave. 00:27:27.570 --> 00:27:28.560 align:middle line:90% This is a square wave. 00:27:28.560 --> 00:27:29.450 align:middle line:84% On the other side of the transformer, 00:27:29.450 --> 00:27:30.350 align:middle line:90% I get a square wave. 00:27:30.350 --> 00:27:32.180 align:middle line:84% But it has a fundamental component 00:27:32.180 --> 00:27:34.520 align:middle line:84% that we looked at up there, so we can kind of treat 00:27:34.520 --> 00:27:35.560 align:middle line:90% it as fundamental. 00:27:35.560 --> 00:27:38.450 align:middle line:90% Then I have my transformer gain. 00:27:38.450 --> 00:27:40.170 align:middle line:84% I put my transformer in green, right. 00:27:40.170 --> 00:27:43.910 align:middle line:90% So let me call this G sub x. 00:27:43.910 --> 00:27:45.450 align:middle line:90% That's for the transformer. 00:27:45.450 --> 00:27:52.010 align:middle line:84% This is magnitude of v rect 1 over vr 1. 00:27:52.010 --> 00:27:56.680 align:middle line:84% And this is simply equal to, in my example, N2 over N1. 00:27:56.680 --> 00:28:00.820 align:middle line:90% 00:28:00.820 --> 00:28:03.230 align:middle line:84% Does that make sense to everybody? 00:28:03.230 --> 00:28:06.160 align:middle line:84% And what's on the output side of this guy? 00:28:06.160 --> 00:28:11.035 align:middle line:90% It's simply equal to v rect 1. 00:28:11.035 --> 00:28:14.450 align:middle line:90% 00:28:14.450 --> 00:28:17.090 align:middle line:84% And then the last thing I have to think about is, What 00:28:17.090 --> 00:28:18.810 align:middle line:90% is the effect of this inverter? 00:28:18.810 --> 00:28:22.670 align:middle line:84% And what I'm interested in is, for this kind of model, 00:28:22.670 --> 00:28:24.710 align:middle line:84% the conversion between the fundamental 00:28:24.710 --> 00:28:29.040 align:middle line:84% of the rectifier voltage to the DC output voltage. 00:28:29.040 --> 00:28:31.760 align:middle line:84% So this gain's sort of an AC-to-DC gain, 00:28:31.760 --> 00:28:35.540 align:middle line:84% but I'm going to use it from the fundamental to the output. 00:28:35.540 --> 00:28:36.140 align:middle line:90% OK. 00:28:36.140 --> 00:28:37.260 align:middle line:90% What would that be? 00:28:37.260 --> 00:28:40.250 align:middle line:84% Well, I've already I've already shown you that, right. 00:28:40.250 --> 00:28:46.760 align:middle line:84% The fundamental at the input of the rectifier is 4 over pi vd, 00:28:46.760 --> 00:28:50.150 align:middle line:84% and the output of the rectifier, the DC output, is just vd. 00:28:50.150 --> 00:28:54.670 align:middle line:84% So the gain must then be pi over 4. 00:28:54.670 --> 00:28:58.260 align:middle line:90% Right, so here's the rectifier. 00:28:58.260 --> 00:28:59.440 align:middle line:90% What did I call that? 00:28:59.440 --> 00:29:03.720 align:middle line:84% I guess I called it G sub r, the gain of the rectifier. 00:29:03.720 --> 00:29:05.560 align:middle line:90% And this is, in my-- 00:29:05.560 --> 00:29:12.480 align:middle line:84% this is magnitude of vd divided by v rect 1, right. 00:29:12.480 --> 00:29:16.980 align:middle line:84% And this is equal to pi over 4 because it's 00:29:16.980 --> 00:29:19.080 align:middle line:90% a full-bridge rectifier. 00:29:19.080 --> 00:29:23.460 align:middle line:84% If I had to use a so-called voltage-doubler rectifier, which 00:29:23.460 --> 00:29:27.240 align:middle line:84% would basically be a half bridge with a capacitor, 00:29:27.240 --> 00:29:30.470 align:middle line:90% it would be pi over 2. 00:29:30.470 --> 00:29:33.740 align:middle line:84% If I used a voltage-multiplying rectifier, 00:29:33.740 --> 00:29:35.345 align:middle line:84% like a Cockcroft-Walton rectifier, 00:29:35.345 --> 00:29:37.200 align:middle line:90% it could be a different gain. 00:29:37.200 --> 00:29:37.700 align:middle line:90% OK. 00:29:37.700 --> 00:29:40.970 align:middle line:84% So I can pick, Do I use a half bridge or a full bridge 00:29:40.970 --> 00:29:42.420 align:middle line:90% or some other inverter? 00:29:42.420 --> 00:29:44.640 align:middle line:84% Do I use-- what kind of rectifier do I use? 00:29:44.640 --> 00:29:46.230 align:middle line:90% What kind of tank do I use? 00:29:46.230 --> 00:29:48.540 align:middle line:84% all of which helps me shape this gain. 00:29:48.540 --> 00:29:51.740 align:middle line:84% And the output of this thing is then vd, right. 00:29:51.740 --> 00:29:58.460 align:middle line:84% So what I get is, in my output, I get vd over vdc, right. 00:29:58.460 --> 00:30:01.250 align:middle line:84% This is the voltage gain of my converter, right. 00:30:01.250 --> 00:30:04.550 align:middle line:84% I come in from vdc, and I get vd at the output. 00:30:04.550 --> 00:30:11.870 align:middle line:84% And that's simply just going to be G sub i times G sub tank 00:30:11.870 --> 00:30:20.800 align:middle line:90% times G sub x times G sub r. 00:30:20.800 --> 00:30:22.480 align:middle line:90% OK. 00:30:22.480 --> 00:30:25.180 align:middle line:84% And what I'm going to do in this whole game 00:30:25.180 --> 00:30:27.670 align:middle line:84% is I'm trying to build a power converter that's 00:30:27.670 --> 00:30:32.270 align:middle line:84% going to regulate vd for a given input voltage. 00:30:32.270 --> 00:30:35.610 align:middle line:84% The thing I'm going to control is the tank gain. 00:30:35.610 --> 00:30:37.910 align:middle line:90% Right, everything else is fixed. 00:30:37.910 --> 00:30:42.210 align:middle line:84% I choose it to get the gain, some range I want, 00:30:42.210 --> 00:30:48.560 align:middle line:84% but how do I deal with variations in power and voltage, 00:30:48.560 --> 00:30:50.480 align:middle line:84% or especially very interesting volts? 00:30:50.480 --> 00:30:52.736 align:middle line:90% I vary the tank gain. 00:30:52.736 --> 00:30:54.500 align:middle line:84% Does that makes sense to everybody? 00:30:54.500 --> 00:30:57.890 align:middle line:90% 00:30:57.890 --> 00:30:58.730 align:middle line:90% Questions? 00:30:58.730 --> 00:31:04.690 align:middle line:90% 00:31:04.690 --> 00:31:08.280 align:middle line:90% So let's think about this. 00:31:08.280 --> 00:31:12.600 align:middle line:90% This is the same picture, right. 00:31:12.600 --> 00:31:14.640 align:middle line:84% I've got my half-bridge inverter, 00:31:14.640 --> 00:31:18.600 align:middle line:84% which gives me my inverter gain here, and that generates a-- 00:31:18.600 --> 00:31:21.130 align:middle line:84% I consider the fundamental AC voltage here. 00:31:21.130 --> 00:31:23.130 align:middle line:84% I go through the tank gain-- which is a function 00:31:23.130 --> 00:31:24.510 align:middle line:90% of frequency-- 00:31:24.510 --> 00:31:27.660 align:middle line:84% the transformer gain, the rectifier gain, and then I 00:31:27.660 --> 00:31:29.490 align:middle line:90% get my DC output again. 00:31:29.490 --> 00:31:30.660 align:middle line:90% OK. 00:31:30.660 --> 00:31:33.480 align:middle line:84% What is-- the important thing in all of this, the thing 00:31:33.480 --> 00:31:36.030 align:middle line:84% I'm controlling, is the tank gain. 00:31:36.030 --> 00:31:41.170 align:middle line:84% And my model for my tank gain is essentially right here, right. 00:31:41.170 --> 00:31:44.880 align:middle line:84% If I thought about this as being an equivalent 00:31:44.880 --> 00:31:46.930 align:middle line:84% resistor-- actually, it's right here, right. 00:31:46.930 --> 00:31:50.070 align:middle line:84% This models the tank gain right here. 00:31:50.070 --> 00:31:51.850 align:middle line:84% Well, this circuit, I could analyze. 00:31:51.850 --> 00:31:57.780 align:middle line:84% If I tell you R sub r, then I know the operating, I know Q0, 00:31:57.780 --> 00:32:01.660 align:middle line:84% and I can calculate the tank gain versus frequency, right. 00:32:01.660 --> 00:32:03.310 align:middle line:90% What does that look like? 00:32:03.310 --> 00:32:05.670 align:middle line:90% It looks like this. 00:32:05.670 --> 00:32:06.310 align:middle line:90% All right. 00:32:06.310 --> 00:32:10.270 align:middle line:84% So what I've plotted is, for Q0, which 00:32:10.270 --> 00:32:15.860 align:middle line:84% would be Rr is equal to the square root of L over C, 00:32:15.860 --> 00:32:17.240 align:middle line:90% q0 equals 1. 00:32:17.240 --> 00:32:19.860 align:middle line:90% It looks like this. 00:32:19.860 --> 00:32:20.970 align:middle line:90% All right. 00:32:20.970 --> 00:32:23.340 align:middle line:84% So if I had an equivalent resistance that 00:32:23.340 --> 00:32:26.580 align:middle line:84% looked like that, then if I'm operating right at resonance, 00:32:26.580 --> 00:32:27.640 align:middle line:90% the tank gain's 1. 00:32:27.640 --> 00:32:28.140 align:middle line:90% Why? 00:32:28.140 --> 00:32:30.780 align:middle line:84% Because this thing looks like a short circuit, 00:32:30.780 --> 00:32:33.870 align:middle line:84% and I'm just applying the fundamental to the load. 00:32:33.870 --> 00:32:38.760 align:middle line:84% If I go above resonance, right, this looks like a net reactance, 00:32:38.760 --> 00:32:41.910 align:middle line:84% and I get a voltage divider and it droops down. 00:32:41.910 --> 00:32:44.940 align:middle line:84% And if my operating tank Q is low, 00:32:44.940 --> 00:32:46.980 align:middle line:90% it droops down kind of slowly. 00:32:46.980 --> 00:32:48.090 align:middle line:90% OK. 00:32:48.090 --> 00:32:53.040 align:middle line:84% If, on the other hand, my effective Rr were small, 00:32:53.040 --> 00:32:56.250 align:middle line:84% right, my tank quality factor would be high, 00:32:56.250 --> 00:32:58.770 align:middle line:84% square root of L over C over R would get big, 00:32:58.770 --> 00:33:02.460 align:middle line:84% and maybe it would look like tank quality factor of 5, 00:33:02.460 --> 00:33:08.380 align:middle line:84% in which case the change in gain with frequency is very steep. 00:33:08.380 --> 00:33:11.900 align:middle line:84% Does that make sense to everybody? 00:33:11.900 --> 00:33:16.240 align:middle line:90% So what do we have to do? 00:33:16.240 --> 00:33:22.170 align:middle line:84% Well, suppose I know my input voltage, my DC input voltage, 00:33:22.170 --> 00:33:24.030 align:middle line:84% and I know the output voltage that I'm 00:33:24.030 --> 00:33:26.160 align:middle line:90% regulating the output to. 00:33:26.160 --> 00:33:26.700 align:middle line:90% OK. 00:33:26.700 --> 00:33:31.830 align:middle line:84% That sets a voltage conversion ratio, right. 00:33:31.830 --> 00:33:35.670 align:middle line:84% And so I know this conversion ratio, 00:33:35.670 --> 00:33:39.600 align:middle line:84% and I have to pick Gt to match that conversion 00:33:39.600 --> 00:33:41.980 align:middle line:84% ratio if I'm going to-- if I'm going to operate there. 00:33:41.980 --> 00:33:48.900 align:middle line:84% That means, essentially, suppose I needed to operate at a net-- 00:33:48.900 --> 00:33:51.510 align:middle line:84% total conversion ratio, right, this 00:33:51.510 --> 00:33:54.300 align:middle line:84% is 2 over pi times pi over 4 times 00:33:54.300 --> 00:33:55.950 align:middle line:90% whatever my transformer gain is. 00:33:55.950 --> 00:33:57.047 align:middle line:90% Factor all those out. 00:33:57.047 --> 00:33:59.130 align:middle line:84% Let's just pretend those are all 1 for the moment, 00:33:59.130 --> 00:34:01.620 align:middle line:90% even though they're not 1 here. 00:34:01.620 --> 00:34:05.500 align:middle line:84% Suppose I needed a-- or, to get to the correct ratio here, 00:34:05.500 --> 00:34:08.880 align:middle line:84% suppose that I needed a tank gain of a half, right. 00:34:08.880 --> 00:34:15.980 align:middle line:84% That means I'd have to operate somewhere here. 00:34:15.980 --> 00:34:17.150 align:middle line:90% OK. 00:34:17.150 --> 00:34:20.225 align:middle line:84% So I'd have to be sitting on this line of exactly the tank 00:34:20.225 --> 00:34:22.420 align:middle line:90% gain's a half. 00:34:22.420 --> 00:34:24.620 align:middle line:90% And which curve am I sitting on? 00:34:24.620 --> 00:34:27.070 align:middle line:84% Well, it depends what power I'm operating at, right, 00:34:27.070 --> 00:34:31.449 align:middle line:84% or, equivalently, which load resistance 00:34:31.449 --> 00:34:36.520 align:middle line:84% I'm operating at, because for a smaller load resistance, 00:34:36.520 --> 00:34:39.070 align:middle line:84% the AC resistance gets smaller, the tank gain 00:34:39.070 --> 00:34:41.449 align:middle line:84% gets higher-- the tank Q gets higher. 00:34:41.449 --> 00:34:44.440 align:middle line:84% But between those two, for a given operating power, 00:34:44.440 --> 00:34:48.199 align:middle line:84% that's going to determine one of these tank gain curves. 00:34:48.199 --> 00:34:54.280 align:middle line:84% And I'm going to go sit here, and maybe if my tank 00:34:54.280 --> 00:34:57.550 align:middle line:84% loaded quality factor is 2, that means 00:34:57.550 --> 00:35:01.900 align:middle line:84% I need to operate at 1.5 times the resonant frequency to get 00:35:01.900 --> 00:35:06.640 align:middle line:90% the conversion I wanted, right. 00:35:06.640 --> 00:35:12.340 align:middle line:84% Now, if my output voltage stayed the same but my input voltage 00:35:12.340 --> 00:35:17.110 align:middle line:84% went down, maybe I would only need a tank gain-- 00:35:17.110 --> 00:35:20.440 align:middle line:84% instead of tank gain of a half, I need a tank gain of 2/3, 00:35:20.440 --> 00:35:24.480 align:middle line:84% I'd jump up here, OK, and in here, 00:35:24.480 --> 00:35:26.870 align:middle line:84% and I'd have to operate at a different frequency to sit 00:35:26.870 --> 00:35:28.310 align:middle line:90% at the same power level. 00:35:28.310 --> 00:35:29.150 align:middle line:90% OK. 00:35:29.150 --> 00:35:33.170 align:middle line:84% So basically, when I think about a resonant converter, 00:35:33.170 --> 00:35:35.540 align:middle line:84% it's like a resonant inverter in the sense 00:35:35.540 --> 00:35:39.810 align:middle line:84% that I'm doing voltage division with the tank 00:35:39.810 --> 00:35:41.880 align:middle line:84% or I'm controlling power by controlling 00:35:41.880 --> 00:35:44.730 align:middle line:84% the net impedance of this thing to feed power 00:35:44.730 --> 00:35:46.230 align:middle line:90% through to my load resistor. 00:35:46.230 --> 00:35:48.990 align:middle line:84% But at the same time, I have to think 00:35:48.990 --> 00:35:51.300 align:middle line:84% that because I have a rectifier, it's 00:35:51.300 --> 00:35:53.620 align:middle line:84% not a fixed resistor I'm running into, 00:35:53.620 --> 00:35:57.480 align:middle line:84% but it's a resistor that's a function of, equivalently, 00:35:57.480 --> 00:36:01.990 align:middle line:84% DC load resistance or operating power and output voltage. 00:36:01.990 --> 00:36:02.810 align:middle line:90% OK. 00:36:02.810 --> 00:36:05.290 align:middle line:84% So maybe what I could do is, by knowing 00:36:05.290 --> 00:36:08.200 align:middle line:84% the range of powers that I have to operate at 00:36:08.200 --> 00:36:10.690 align:middle line:84% and the range of voltage conversion ratios I could 00:36:10.690 --> 00:36:13.330 align:middle line:84% operate at, I can kind of put a bounding box 00:36:13.330 --> 00:36:16.240 align:middle line:84% for a given tank gain on what frequency 00:36:16.240 --> 00:36:17.660 align:middle line:90% range I need to run over. 00:36:17.660 --> 00:36:18.160 align:middle line:90% OK. 00:36:18.160 --> 00:36:19.900 align:middle line:84% And there's an example in Principles 00:36:19.900 --> 00:36:25.470 align:middle line:84% of Power Electronics that works over just this such a range. 00:36:25.470 --> 00:36:30.810 align:middle line:84% So that's the basic notion of how 00:36:30.810 --> 00:36:34.680 align:middle line:84% we think about resonant DC-to-DC converters, OK, 00:36:34.680 --> 00:36:39.060 align:middle line:84% or a typical resonant DC-to-DC converter, 00:36:39.060 --> 00:36:43.740 align:middle line:84% where we're going to basically pick all the designs to help us 00:36:43.740 --> 00:36:45.190 align:middle line:90% get the voltage gain we want. 00:36:45.190 --> 00:36:47.580 align:middle line:84% I might pick my inverter and rectifier topologies 00:36:47.580 --> 00:36:50.560 align:middle line:84% to help me get part of the gain, and the rest of the gain, 00:36:50.560 --> 00:36:53.175 align:middle line:84% I'm going to get out of picking the right tank. 00:36:53.175 --> 00:36:55.800 align:middle line:84% And I'm going to pick the tank components such that the quality 00:36:55.800 --> 00:36:58.170 align:middle line:84% factors, the operating quality factors I'm going to get 00:36:58.170 --> 00:37:01.800 align:middle line:84% are going to put me in sort of an allowable range of frequency, 00:37:01.800 --> 00:37:04.320 align:middle line:84% and then I'm going to sort of operate there 00:37:04.320 --> 00:37:08.140 align:middle line:90% to get the conversion I want. 00:37:08.140 --> 00:37:09.060 align:middle line:90% Questions about that? 00:37:09.060 --> 00:37:13.810 align:middle line:90% 00:37:13.810 --> 00:37:14.740 align:middle line:90% Yeah? 00:37:14.740 --> 00:37:16.660 align:middle line:84% AUDIENCE: We're playing with the LC reactants 00:37:16.660 --> 00:37:18.250 align:middle line:84% to do this sort of voltage division, 00:37:18.250 --> 00:37:20.950 align:middle line:84% but is the power factor of these kind of systems 00:37:20.950 --> 00:37:21.800 align:middle line:90% bad because of that? 00:37:21.800 --> 00:37:22.300 align:middle line:90% Or-- 00:37:22.300 --> 00:37:24.530 align:middle line:84% DAVID PERREAULT: So that's an excellent question. 00:37:24.530 --> 00:37:28.900 align:middle line:84% Yes, so if I thought about the power factor seen 00:37:28.900 --> 00:37:31.567 align:middle line:84% by this inverter, right, first of all, 00:37:31.567 --> 00:37:33.400 align:middle line:84% he's putting out a square wave, and then I'm 00:37:33.400 --> 00:37:35.360 align:middle line:84% only delivering power via the sine wave. 00:37:35.360 --> 00:37:38.660 align:middle line:84% So that's sort of, in some sense, a distortion factor, 00:37:38.660 --> 00:37:39.160 align:middle line:90% right. 00:37:39.160 --> 00:37:42.390 align:middle line:84% But also, yeah, the current's phase-shifted from the voltage, 00:37:42.390 --> 00:37:43.330 align:middle line:90% right. 00:37:43.330 --> 00:37:48.690 align:middle line:84% So if I compared this to just doing some kind of PWM isolated 00:37:48.690 --> 00:37:50.440 align:middle line:84% converter, like we've talked about before, 00:37:50.440 --> 00:37:52.810 align:middle line:84% where we're putting more or less square waves 00:37:52.810 --> 00:37:58.220 align:middle line:84% through our converter, we end up with higher peak voltage 00:37:58.220 --> 00:38:01.100 align:middle line:84% and current stresses in a resonant converter 00:38:01.100 --> 00:38:06.260 align:middle line:90% than I do in a PWM converter. 00:38:06.260 --> 00:38:06.980 align:middle line:90% OK. 00:38:06.980 --> 00:38:10.230 align:middle line:84% So you are paying, definitely paying something. 00:38:10.230 --> 00:38:13.040 align:middle line:84% And I think you'll concede, this is a heck of a lot more complex 00:38:13.040 --> 00:38:15.248 align:middle line:84% to think about than, say, a forward converter, right. 00:38:15.248 --> 00:38:19.070 align:middle line:84% It's-- and the models, and we haven't even talked about 00:38:19.070 --> 00:38:20.490 align:middle line:84% control modeling for these things. 00:38:20.490 --> 00:38:21.620 align:middle line:90% It's really tricky. 00:38:21.620 --> 00:38:24.446 align:middle line:90% OK. 00:38:24.446 --> 00:38:27.950 align:middle line:84% So you give up a lot to do a resonant DC-to-DC 00:38:27.950 --> 00:38:28.940 align:middle line:90% converter, right. 00:38:28.940 --> 00:38:31.130 align:middle line:90% So why would I do that? 00:38:31.130 --> 00:38:37.160 align:middle line:84% The reason I might do it is because, we said before, 00:38:37.160 --> 00:38:44.150 align:middle line:84% if my load looks inductive, I can soft-switch these-- 00:38:44.150 --> 00:38:47.690 align:middle line:84% I can soft-switch these transistors, right. 00:38:47.690 --> 00:38:51.560 align:middle line:84% So I can get zero-voltage switching of my inverter 00:38:51.560 --> 00:38:54.770 align:middle line:84% and, hence, run him at a really high frequency. 00:38:54.770 --> 00:38:59.420 align:middle line:84% Likewise, I'm putting sinusoidal currents in here, 00:38:59.420 --> 00:39:03.290 align:middle line:84% so these diodes kind of switch nicely, too, or if I'm using-- 00:39:03.290 --> 00:39:05.390 align:middle line:84% depending on if I'm using diodes or FETs 00:39:05.390 --> 00:39:06.720 align:middle line:90% or whatever I'm using there. 00:39:06.720 --> 00:39:07.220 align:middle line:90% OK. 00:39:07.220 --> 00:39:10.100 align:middle line:84% So the thing I can get about it is the ability 00:39:10.100 --> 00:39:12.200 align:middle line:84% to push up to pretty darn high frequencies 00:39:12.200 --> 00:39:15.350 align:middle line:84% and keep good efficiency and, hence, get down to small sizes. 00:39:15.350 --> 00:39:17.330 align:middle line:84% So a lot of high-performance designs, 00:39:17.330 --> 00:39:20.430 align:middle line:84% despite all the complexity of doing this, will do that. 00:39:20.430 --> 00:39:23.345 align:middle line:84% And in fact, if you look at this, this is a rectifier. 00:39:23.345 --> 00:39:25.130 align:middle line:84% Right, this comes from line voltage 00:39:25.130 --> 00:39:27.490 align:middle line:84% and eventually gives me the voltage from my laptop. 00:39:27.490 --> 00:39:29.930 align:middle line:84% This has a resonant converter in it. 00:39:29.930 --> 00:39:36.030 align:middle line:84% It's tiny for 65 watts, and it's north of 96% efficient. 00:39:36.030 --> 00:39:40.970 align:middle line:84% And the reason it can be not hot and very tiny 00:39:40.970 --> 00:39:44.720 align:middle line:84% is because they went to the great lengths of designing 00:39:44.720 --> 00:39:46.520 align:middle line:84% the right kind of very high-frequency 00:39:46.520 --> 00:39:48.160 align:middle line:90% resonant converter. 00:39:48.160 --> 00:39:49.530 align:middle line:90% OK. 00:39:49.530 --> 00:39:51.300 align:middle line:90% So would you always do this? 00:39:51.300 --> 00:39:52.170 align:middle line:90% No. 00:39:52.170 --> 00:39:54.180 align:middle line:84% Right, the design time and everything else 00:39:54.180 --> 00:39:55.360 align:middle line:90% is going to cost you a lot. 00:39:55.360 --> 00:39:57.095 align:middle line:84% But what you will find is a lot of very 00:39:57.095 --> 00:39:58.470 align:middle line:84% high-performance systems, they're 00:39:58.470 --> 00:40:01.260 align:middle line:84% going to go through the effort of figuring all this stuff out 00:40:01.260 --> 00:40:02.345 align:middle line:90% to get you there. 00:40:02.345 --> 00:40:05.460 align:middle line:90% 00:40:05.460 --> 00:40:06.440 align:middle line:90% Questions about that? 00:40:06.440 --> 00:40:09.230 align:middle line:90% 00:40:09.230 --> 00:40:09.778 align:middle line:90% Yeah? 00:40:09.778 --> 00:40:10.820 align:middle line:90% AUDIENCE: What would be-- 00:40:10.820 --> 00:40:13.300 align:middle line:84% for this laptop charger that you have, 00:40:13.300 --> 00:40:15.045 align:middle line:84% what would be the load variation on it? 00:40:15.045 --> 00:40:16.920 align:middle line:84% DAVID PERREAULT: That's a very good question. 00:40:16.920 --> 00:40:20.030 align:middle line:84% The load variation's essentially infinite, right. 00:40:20.030 --> 00:40:23.300 align:middle line:84% So that brings me to another point. 00:40:23.300 --> 00:40:26.720 align:middle line:84% I've talked about essentially one mode of power control 00:40:26.720 --> 00:40:28.340 align:middle line:90% in this thing, right. 00:40:28.340 --> 00:40:31.850 align:middle line:84% I've talked about essentially varying the switching frequency 00:40:31.850 --> 00:40:34.470 align:middle line:84% to vary where you're sitting on these curves, right. 00:40:34.470 --> 00:40:37.730 align:middle line:84% And that is a good method of power control, 00:40:37.730 --> 00:40:39.790 align:middle line:84% but it'll only get you so far, right. 00:40:39.790 --> 00:40:45.760 align:middle line:84% Or another way to think about it is, if my current goes to zero 00:40:45.760 --> 00:40:51.100 align:middle line:84% and my power goes to zero, my effective AC resistance is 00:40:51.100 --> 00:40:52.390 align:middle line:90% going through the roof, right. 00:40:52.390 --> 00:40:54.220 align:middle line:84% So what will happen eventually is maybe 00:40:54.220 --> 00:40:55.845 align:middle line:84% you enter a different mode of operation 00:40:55.845 --> 00:40:57.440 align:middle line:84% where you can't keep soft-switching. 00:40:57.440 --> 00:41:00.580 align:middle line:84% So people will do all kinds of different other things 00:41:00.580 --> 00:41:01.850 align:middle line:90% to control power. 00:41:01.850 --> 00:41:03.880 align:middle line:90% They might burst the converter. 00:41:03.880 --> 00:41:05.530 align:middle line:84% They run the converter at full power 00:41:05.530 --> 00:41:07.150 align:middle line:84% or some nominal power for some time 00:41:07.150 --> 00:41:10.240 align:middle line:84% and then shut it off, burst it on and off, 00:41:10.240 --> 00:41:12.640 align:middle line:84% and use the output capacitor here 00:41:12.640 --> 00:41:15.197 align:middle line:84% to hold the voltage so that when it's running, 00:41:15.197 --> 00:41:16.780 align:middle line:84% it's running at high power and then it 00:41:16.780 --> 00:41:18.440 align:middle line:90% runs at zero power for a while. 00:41:18.440 --> 00:41:21.670 align:middle line:84% That's called on-off control or burst control. 00:41:21.670 --> 00:41:26.800 align:middle line:84% If I had a different kind of inverter in the input, maybe 00:41:26.800 --> 00:41:31.630 align:middle line:84% I can do phase shift or some degree of kind of PWM control, 00:41:31.630 --> 00:41:36.470 align:middle line:84% OK, or what's known as out-phasing control 00:41:36.470 --> 00:41:38.600 align:middle line:84% if you're doing it with sinusoids. 00:41:38.600 --> 00:41:40.760 align:middle line:84% So there's a lot of other control techniques 00:41:40.760 --> 00:41:45.230 align:middle line:84% you can bring in to deal with the really light-load cases. 00:41:45.230 --> 00:41:49.080 align:middle line:84% The other piece of it is, is there's other kinds of tanks. 00:41:49.080 --> 00:41:51.920 align:middle line:84% This tank really doesn't going down to zero power 00:41:51.920 --> 00:41:54.440 align:middle line:84% because when the load resistance goes to infinity, 00:41:54.440 --> 00:41:58.240 align:middle line:84% the tank goes to zero, and you'd get really wide frequency 00:41:58.240 --> 00:41:58.740 align:middle line:90% ranges. 00:41:58.740 --> 00:42:00.157 align:middle line:84% That wouldn't be very good, right. 00:42:00.157 --> 00:42:02.720 align:middle line:84% On the other hand, if I used a parallel resonant tank, 00:42:02.720 --> 00:42:05.750 align:middle line:84% I could do something different, and it can go down 00:42:05.750 --> 00:42:07.820 align:middle line:90% to zero load just happily. 00:42:07.820 --> 00:42:09.480 align:middle line:90% It has circulating current. 00:42:09.480 --> 00:42:12.350 align:middle line:84% Maybe the efficiency decreases, but it doesn't mind. 00:42:12.350 --> 00:42:13.070 align:middle line:90% Why? 00:42:13.070 --> 00:42:17.830 align:middle line:84% Because if I look at a parallel tank, in a parallel tank, 00:42:17.830 --> 00:42:20.440 align:middle line:90% q goes up as r gets bigger. 00:42:20.440 --> 00:42:22.150 align:middle line:84% And so my frequency range goes down, 00:42:22.150 --> 00:42:24.130 align:middle line:84% so I can go to zero load with that. 00:42:24.130 --> 00:42:27.760 align:middle line:84% Or maybe I use an LCC tank, which 00:42:27.760 --> 00:42:29.230 align:middle line:84% has some of the properties of both, 00:42:29.230 --> 00:42:33.730 align:middle line:84% or an LLC tank, which has two inductors and one capacitor. 00:42:33.730 --> 00:42:35.377 align:middle line:84% That's a very popular one for very 00:42:35.377 --> 00:42:36.710 align:middle line:90% high-performance converters, OK. 00:42:36.710 --> 00:42:41.020 align:middle line:84% So you can basically trade simplicity 00:42:41.020 --> 00:42:44.110 align:middle line:84% and still use frequency control but then 00:42:44.110 --> 00:42:46.060 align:middle line:84% go to burst control or outphasing control 00:42:46.060 --> 00:42:48.540 align:middle line:90% or other control mechanisms. 00:42:48.540 --> 00:42:49.870 align:middle line:90% And people do that. 00:42:49.870 --> 00:42:51.860 align:middle line:90% And is it worth the complexity? 00:42:51.860 --> 00:42:54.510 align:middle line:90% It depends on the application. 00:42:54.510 --> 00:42:57.660 align:middle line:84% In some cases, straight up flyback converter 00:42:57.660 --> 00:42:59.265 align:middle line:90% is the right thing to do. 00:42:59.265 --> 00:43:02.550 align:middle line:84% Right, you don't have to do this to do a DC-to-DC converter, 00:43:02.550 --> 00:43:04.620 align:middle line:84% but in some high-performance applications, 00:43:04.620 --> 00:43:07.690 align:middle line:90% this is very popular. 00:43:07.690 --> 00:43:08.740 align:middle line:90% Other questions? 00:43:08.740 --> 00:43:11.510 align:middle line:84% I should say, by the way, why else-- looking at this, 00:43:11.510 --> 00:43:14.380 align:middle line:84% why else might I choose a parallel resonant tank, 00:43:14.380 --> 00:43:16.950 align:middle line:84% besides the fact that it goes down to zero load happily? 00:43:16.950 --> 00:43:22.060 align:middle line:90% 00:43:22.060 --> 00:43:23.470 align:middle line:90% Voltage gain, right? 00:43:23.470 --> 00:43:26.557 align:middle line:84% Here, a series resonant tank, the best I can do 00:43:26.557 --> 00:43:28.390 align:middle line:84% is make this thing look like a short circuit 00:43:28.390 --> 00:43:29.620 align:middle line:90% and get a gain of 1. 00:43:29.620 --> 00:43:32.703 align:middle line:84% With a parallel resonant tank, especially 00:43:32.703 --> 00:43:34.120 align:middle line:84% if I'm going to operate up here, I 00:43:34.120 --> 00:43:35.870 align:middle line:84% can get a lot of voltage gain out of that. 00:43:35.870 --> 00:43:39.850 align:middle line:84% And in fact, if you want to build a really high-gain 00:43:39.850 --> 00:43:45.220 align:middle line:84% DC-to-DC converter-- and a design that was done in my group 00:43:45.220 --> 00:43:48.410 align:middle line:84% some time ago went from 200 volts to 40,000 volts-- 00:43:48.410 --> 00:43:52.180 align:middle line:84% one thing you might do, you might pick a voltage-multiplying 00:43:52.180 --> 00:43:54.890 align:middle line:84% rectifier, a rectifier with a huge voltage gain. 00:43:54.890 --> 00:43:58.180 align:middle line:84% You might pair that with a parallel resonant tank 00:43:58.180 --> 00:44:01.120 align:middle line:84% that would help give you voltage gain from the tank, right. 00:44:01.120 --> 00:44:04.720 align:middle line:90% So all these design decisions-- 00:44:04.720 --> 00:44:06.935 align:middle line:84% I might choose, instead of a half-bridge inverter, 00:44:06.935 --> 00:44:09.310 align:middle line:84% maybe I'll choose a full-bridge inverter, because instead 00:44:09.310 --> 00:44:12.025 align:middle line:84% of getting a gain of 2 over pi, I get a gain of 4 over pi. 00:44:12.025 --> 00:44:14.590 align:middle line:84% Right, so there's, all kinds of games 00:44:14.590 --> 00:44:17.860 align:middle line:84% that can be played to help you get to some large conversion 00:44:17.860 --> 00:44:19.360 align:middle line:84% ratio that you might want to get to, 00:44:19.360 --> 00:44:21.990 align:middle line:84% which might be hard with a standard PWM converter. 00:44:21.990 --> 00:44:25.400 align:middle line:90% 00:44:25.400 --> 00:44:26.030 align:middle line:90% OK. 00:44:26.030 --> 00:44:27.530 align:middle line:90% I would like to say-- 00:44:27.530 --> 00:44:31.370 align:middle line:84% and we're getting close to the end here-- 00:44:31.370 --> 00:44:37.638 align:middle line:84% that not all resonant power converters are quite as-- 00:44:37.638 --> 00:44:39.180 align:middle line:84% I don't want to say "simple as this," 00:44:39.180 --> 00:44:41.970 align:middle line:84% because this is not simple, but that are quite as clean as this. 00:44:41.970 --> 00:44:45.450 align:middle line:84% In this version of a resonant converter, 00:44:45.450 --> 00:44:47.760 align:middle line:84% we have this intermediate current waveform 00:44:47.760 --> 00:44:50.130 align:middle line:84% that was purely sinusoidal, right, 00:44:50.130 --> 00:44:52.490 align:middle line:84% and that helped us think about the analysis, 00:44:52.490 --> 00:44:56.250 align:middle line:84% just thinking about sinusoids throughout the converter. 00:44:56.250 --> 00:44:58.140 align:middle line:90% You don't always get that. 00:44:58.140 --> 00:45:04.730 align:middle line:84% Sometimes you get waveforms that are quasi-sinusoidal, 00:45:04.730 --> 00:45:08.100 align:middle line:84% and sometimes they'll call that a quasi-resonant converter, 00:45:08.100 --> 00:45:11.950 align:middle line:90% OK, depending upon the type. 00:45:11.950 --> 00:45:15.930 align:middle line:84% But I wanted to show you an example, a very 00:45:15.930 --> 00:45:19.750 align:middle line:90% a very useful home example. 00:45:19.750 --> 00:45:25.600 align:middle line:84% And what this thing is, this is your standard home induction 00:45:25.600 --> 00:45:26.590 align:middle line:90% cooker. 00:45:26.590 --> 00:45:29.710 align:middle line:84% Right, if you want to go out and spend-- 00:45:29.710 --> 00:45:31.570 align:middle line:84% I don't know, what did you spend for these? 00:45:31.570 --> 00:45:32.155 align:middle line:90% DAVID OTTEN: $50. 00:45:32.155 --> 00:45:33.590 align:middle line:84% DAVID PERREAULT: $50 for one of these things. 00:45:33.590 --> 00:45:36.280 align:middle line:84% These were so cheap, we went out and bought multiple of them 00:45:36.280 --> 00:45:38.950 align:middle line:90% and took them all apart. 00:45:38.950 --> 00:45:45.243 align:middle line:84% Actually, I have the following slides that Dave prepared. 00:45:45.243 --> 00:45:46.660 align:middle line:84% So I don't know if, Dave, you want 00:45:46.660 --> 00:45:49.340 align:middle line:84% to present the topology and everything that's going on 00:45:49.340 --> 00:45:51.760 align:middle line:84% and then show it, show it off, that'd be great. 00:45:51.760 --> 00:45:53.010 align:middle line:90% DAVID OTTEN: No, no, go ahead. 00:45:53.010 --> 00:45:53.990 align:middle line:84% DAVID PERREAULT: All right, I'll describe it. 00:45:53.990 --> 00:45:55.240 align:middle line:90% OK, I'll describe the circuit. 00:45:55.240 --> 00:45:59.920 align:middle line:84% Here's the circuit, OK, and it turns out a lot of the-- 00:45:59.920 --> 00:46:05.620 align:middle line:84% a lot of the systems are designed like this. 00:46:05.620 --> 00:46:09.200 align:middle line:90% And here you can see the coil. 00:46:09.200 --> 00:46:18.130 align:middle line:84% Now, this coil both serves as the inductor-- 00:46:18.130 --> 00:46:20.560 align:middle line:84% both serves as sort of an inductor to store energy, 00:46:20.560 --> 00:46:22.540 align:middle line:84% but it also couples in to the pan 00:46:22.540 --> 00:46:26.470 align:middle line:84% to deliver the fields from this inductor, hit your pan, 00:46:26.470 --> 00:46:29.570 align:middle line:84% and make a effective resistive load on the tank. 00:46:29.570 --> 00:46:30.070 align:middle line:90% OK. 00:46:30.070 --> 00:46:33.920 align:middle line:84% And then here you can see it's an interesting circuit. 00:46:33.920 --> 00:46:36.830 align:middle line:90% OK, here's the topology. 00:46:36.830 --> 00:46:37.330 align:middle line:90% OK. 00:46:37.330 --> 00:46:43.360 align:middle line:84% We can pass these around, but please, I need them back. 00:46:43.360 --> 00:46:46.753 align:middle line:84% But let's see what's inside this toy. 00:46:46.753 --> 00:46:49.420 align:middle line:84% DAVID OTTEN: Note the pieces of ferrite on the back of the coil, 00:46:49.420 --> 00:46:53.280 align:middle line:84% to deflect the field into your pan and not into the circuit. 00:46:53.280 --> 00:46:54.530 align:middle line:90% DAVID PERREAULT: That's right. 00:46:54.530 --> 00:46:57.430 align:middle line:84% Yeah, so the field's supposed to go into the pan side, 00:46:57.430 --> 00:47:00.550 align:middle line:84% and the ferrite chunks there help you out. 00:47:00.550 --> 00:47:04.700 align:middle line:84% And Dave has kind of taken this thing apart and instrumented it. 00:47:04.700 --> 00:47:06.190 align:middle line:90% OK. 00:47:06.190 --> 00:47:07.790 align:middle line:90% Here you see the top. 00:47:07.790 --> 00:47:09.220 align:middle line:90% This is where the pan goes. 00:47:09.220 --> 00:47:12.160 align:middle line:84% The bottom, you can see these ferrite pieces to force 00:47:12.160 --> 00:47:13.990 align:middle line:90% the fields to the other side. 00:47:13.990 --> 00:47:15.110 align:middle line:90% Here's the circuit board. 00:47:15.110 --> 00:47:16.640 align:middle line:90% Here's what it looks like. 00:47:16.640 --> 00:47:17.420 align:middle line:90% OK. 00:47:17.420 --> 00:47:24.850 align:middle line:84% It has a sort of input filter and a line-frequency rectifier 00:47:24.850 --> 00:47:27.160 align:middle line:84% followed by a low-frequency filter, 00:47:27.160 --> 00:47:31.090 align:middle line:84% so that at least at one point in the line cycle, 00:47:31.090 --> 00:47:33.970 align:middle line:84% you could imagine this being a DC voltage. 00:47:33.970 --> 00:47:34.480 align:middle line:90% OK. 00:47:34.480 --> 00:47:37.060 align:middle line:84% Essentially, this voltage goes almost 00:47:37.060 --> 00:47:39.290 align:middle line:90% as the rectified sine voltage. 00:47:39.290 --> 00:47:39.790 align:middle line:90% OK. 00:47:39.790 --> 00:47:43.090 align:middle line:90% And here's the circuit. 00:47:43.090 --> 00:47:47.252 align:middle line:84% This is the inductor slash transformer, right, 00:47:47.252 --> 00:47:50.210 align:middle line:84% so that that's the coil right here. 00:47:50.210 --> 00:47:53.090 align:middle line:84% There's a capacitor across the coil, OK, 00:47:53.090 --> 00:47:55.850 align:middle line:84% so this is going to give us our resonance swing. 00:47:55.850 --> 00:47:56.350 align:middle line:90% OK. 00:47:56.350 --> 00:48:00.420 align:middle line:84% But this circuit only has one switch. 00:48:00.420 --> 00:48:01.120 align:middle line:90% OK. 00:48:01.120 --> 00:48:04.290 align:middle line:84% So what's essentially going to happen is-- 00:48:04.290 --> 00:48:09.180 align:middle line:84% so think about this voltage as being a constant input voltage. 00:48:09.180 --> 00:48:11.130 align:middle line:84% We're going to turn on the switch 00:48:11.130 --> 00:48:14.070 align:middle line:84% and apply a constant voltage across the inductor 00:48:14.070 --> 00:48:16.640 align:middle line:84% and ramp up current in the inductor. 00:48:16.640 --> 00:48:18.990 align:middle line:84% Then we're going to turn off the switch. 00:48:18.990 --> 00:48:20.880 align:middle line:84% And this is connected to a voltage source, 00:48:20.880 --> 00:48:23.120 align:middle line:84% and this thing is going to go through essentially 00:48:23.120 --> 00:48:24.390 align:middle line:90% a parallel resonance. 00:48:24.390 --> 00:48:26.480 align:middle line:84% It's going to-- the voltage is going to ring up, 00:48:26.480 --> 00:48:28.410 align:middle line:84% and it's going to ring back down. 00:48:28.410 --> 00:48:31.900 align:middle line:84% And when it rings back down, we can turn on the switch. 00:48:31.900 --> 00:48:32.580 align:middle line:90% OK. 00:48:32.580 --> 00:48:37.270 align:middle line:84% And so in this AC ring, we're coupling energy via induction 00:48:37.270 --> 00:48:39.800 align:middle line:84% into the output, which is essentially 00:48:39.800 --> 00:48:43.500 align:middle line:90% sort of the resistance. 00:48:43.500 --> 00:48:45.050 align:middle line:90% Everybody get the basic idea? 00:48:45.050 --> 00:48:48.030 align:middle line:84% So this thing, it doesn't quite have sinusoidal waveforms 00:48:48.030 --> 00:48:51.500 align:middle line:84% at all, but it is using a resonance. 00:48:51.500 --> 00:48:55.710 align:middle line:84% And in fact, we do get zero-voltage switching 00:48:55.710 --> 00:48:57.990 align:middle line:90% with a single switch here. 00:48:57.990 --> 00:49:00.070 align:middle line:84% There are many inverters that actually only need 00:49:00.070 --> 00:49:02.070 align:middle line:84% a single switch, one of the most famous of which 00:49:02.070 --> 00:49:04.360 align:middle line:90% is the Class-E inverter. 00:49:04.360 --> 00:49:06.810 align:middle line:84% This is a variant on that concept. 00:49:06.810 --> 00:49:09.570 align:middle line:84% To control power, we're going to vary how long we hold up 00:49:09.570 --> 00:49:14.091 align:middle line:84% the switch and ramp up current in the inductor, 00:49:14.091 --> 00:49:16.632 align:middle line:84% but at a given power level, that's going to be fixed. 00:49:16.632 --> 00:49:18.090 align:middle line:84% Now, the beautiful thing about this 00:49:18.090 --> 00:49:20.790 align:middle line:84% is, is the amount current ramps up in this 00:49:20.790 --> 00:49:23.760 align:middle line:84% is proportional to this voltage, which 00:49:23.760 --> 00:49:25.440 align:middle line:90% varies over the line cycle. 00:49:25.440 --> 00:49:29.010 align:middle line:84% So almost for free, this thing operates at super high power 00:49:29.010 --> 00:49:31.650 align:middle line:84% factor because the switching frequency of this thing 00:49:31.650 --> 00:49:34.000 align:middle line:90% is way above the line frequency. 00:49:34.000 --> 00:49:37.440 align:middle line:84% And so we're going to draw power that 00:49:37.440 --> 00:49:41.610 align:middle line:84% is proportional to the square of the line voltage, which lets 00:49:41.610 --> 00:49:43.850 align:middle line:90% us get very high power factor. 00:49:43.850 --> 00:49:44.350 align:middle line:90% OK. 00:49:44.350 --> 00:49:46.600 align:middle line:84% So basically, with one active switch 00:49:46.600 --> 00:49:50.290 align:middle line:84% and some resonant components, plus a diode rectifier 00:49:50.290 --> 00:49:53.200 align:middle line:84% and some filters, we get basically an induction heater, 00:49:53.200 --> 00:49:56.380 align:middle line:84% which is why they can do it for $50. 00:49:56.380 --> 00:49:59.200 align:middle line:84% I will now turn it over to Dave, and he can sort of 00:49:59.200 --> 00:50:00.483 align:middle line:90% explain what's going on. 00:50:00.483 --> 00:50:01.150 align:middle line:90% DAVID OTTEN: OK. 00:50:01.150 --> 00:50:12.170 align:middle line:84% So I've got-- so let me tell you-- 00:50:12.170 --> 00:50:14.220 align:middle line:84% let me tell you what we're working with here. 00:50:14.220 --> 00:50:19.070 align:middle line:84% So I want to adjust this so that it triggers. 00:50:19.070 --> 00:50:23.450 align:middle line:84% So the pink waveform is the input voltage 00:50:23.450 --> 00:50:24.650 align:middle line:90% after the rectifier. 00:50:24.650 --> 00:50:26.700 align:middle line:84% So it doesn't go all the way down to zero, 00:50:26.700 --> 00:50:28.530 align:middle line:84% but you can see it has some humps in it. 00:50:28.530 --> 00:50:29.090 align:middle line:90% OK. 00:50:29.090 --> 00:50:33.030 align:middle line:84% The blue waveform is the voltage across the switch. 00:50:33.030 --> 00:50:35.280 align:middle line:84% So you can see it's zero for a period of time. 00:50:35.280 --> 00:50:36.840 align:middle line:90% That's when the switch is on. 00:50:36.840 --> 00:50:38.540 align:middle line:84% When the switch turns off, then you 00:50:38.540 --> 00:50:41.867 align:middle line:84% see that the voltage resonates up and then down again. 00:50:41.867 --> 00:50:43.700 align:middle line:84% Now, the real thing that we're interested in 00:50:43.700 --> 00:50:45.210 align:middle line:90% is the current in the coil. 00:50:45.210 --> 00:50:46.620 align:middle line:90% That's the yellow waveform. 00:50:46.620 --> 00:50:48.950 align:middle line:84% So you can see that when the blue waveform is flat, 00:50:48.950 --> 00:50:51.330 align:middle line:84% the switch is on, the current ramps up. 00:50:51.330 --> 00:50:54.680 align:middle line:84% At some point, the switch turns off, the voltage builds up, 00:50:54.680 --> 00:50:55.690 align:middle line:90% the current goes down. 00:50:55.690 --> 00:50:56.190 align:middle line:90% OK. 00:50:56.190 --> 00:50:59.600 align:middle line:84% And so that's the current waveform that's actually 00:50:59.600 --> 00:51:00.990 align:middle line:90% being used for the heat. 00:51:00.990 --> 00:51:05.100 align:middle line:90% Now, if I change the power-- 00:51:05.100 --> 00:51:06.560 align:middle line:90% so that was 1,200 watts. 00:51:06.560 --> 00:51:08.840 align:middle line:84% I'm going to go to 700 watts, and I'm 00:51:08.840 --> 00:51:11.910 align:middle line:84% going to adjust the thing so that it triggers. 00:51:11.910 --> 00:51:12.410 align:middle line:90% OK. 00:51:12.410 --> 00:51:17.460 align:middle line:84% You can see that the current is lower. 00:51:17.460 --> 00:51:18.500 align:middle line:90% OK. 00:51:18.500 --> 00:51:20.300 align:middle line:84% And now while it's running, I'm going 00:51:20.300 --> 00:51:22.220 align:middle line:90% to try to turn up the voltage-- 00:51:22.220 --> 00:51:23.180 align:middle line:90% turn up the power. 00:51:23.180 --> 00:51:25.220 align:middle line:84% And you can see that the control system 00:51:25.220 --> 00:51:29.270 align:middle line:84% is going to increase the time that the switch is on. 00:51:29.270 --> 00:51:31.700 align:middle line:84% That allows the current to build up more. 00:51:31.700 --> 00:51:34.320 align:middle line:84% It turns out that it makes the frequency go down, 00:51:34.320 --> 00:51:37.770 align:middle line:84% but I think that the time is what's more important. 00:51:37.770 --> 00:51:38.270 align:middle line:90% OK. 00:51:38.270 --> 00:51:42.690 align:middle line:84% Now, there are several ways to look at this circuit. 00:51:42.690 --> 00:51:44.420 align:middle line:84% OK, right now, I'm sort of showing 00:51:44.420 --> 00:51:46.500 align:middle line:90% you one high-frequency signal. 00:51:46.500 --> 00:51:49.820 align:middle line:84% Now I'm going to change the time scale so that we look 00:51:49.820 --> 00:51:52.320 align:middle line:90% at one full cycle of 60 cycles. 00:51:52.320 --> 00:51:53.866 align:middle line:90% So let me adjust the triggering. 00:51:53.866 --> 00:52:06.660 align:middle line:90% 00:52:06.660 --> 00:52:08.910 align:middle line:90% Maybe one more. 00:52:08.910 --> 00:52:11.285 align:middle line:90% OK. 00:52:11.285 --> 00:52:15.870 align:middle line:84% And then let me go down in power because this one triggers 00:52:15.870 --> 00:52:17.440 align:middle line:90% more reasonably. 00:52:17.440 --> 00:52:20.310 align:middle line:84% So now you can see the feature that I was talking about, 00:52:20.310 --> 00:52:24.690 align:middle line:84% where during one period of 60 cycles-- 00:52:24.690 --> 00:52:26.730 align:middle line:84% this is really 120 hertz, so it's twice 00:52:26.730 --> 00:52:28.920 align:middle line:84% that-- you can see that the input voltage, which 00:52:28.920 --> 00:52:32.850 align:middle line:84% is the pink, goes basically to zero and up again. 00:52:32.850 --> 00:52:35.530 align:middle line:84% Then the current is the yellow waveform, 00:52:35.530 --> 00:52:38.000 align:middle line:84% so that has an envelope of a sine wave. 00:52:38.000 --> 00:52:41.200 align:middle line:84% OK, and then the voltage matches that. 00:52:41.200 --> 00:52:41.700 align:middle line:90% OK. 00:52:41.700 --> 00:52:44.350 align:middle line:84% I should point out this is the parallel resonance circuit, 00:52:44.350 --> 00:52:48.820 align:middle line:84% and so the peak voltage is 700, 800 volts. 00:52:48.820 --> 00:52:49.492 align:middle line:90% OK. 00:52:49.492 --> 00:52:53.040 align:middle line:84% The peak current when we get up to full power, 1,800 watts, 00:52:53.040 --> 00:52:56.230 align:middle line:84% is about 70 amps, so it's serious. 00:52:56.230 --> 00:52:58.410 align:middle line:84% OK, let me just turn up the power, 00:52:58.410 --> 00:53:03.360 align:middle line:84% and you should see the current is building up. 00:53:03.360 --> 00:53:06.180 align:middle line:90% So this is 1,400 watts. 00:53:06.180 --> 00:53:08.680 align:middle line:90% This is 1,600. 00:53:08.680 --> 00:53:11.880 align:middle line:84% And whether we get 1,800 actually has something to do 00:53:11.880 --> 00:53:13.070 align:middle line:90% with the line voltage, OK. 00:53:13.070 --> 00:53:14.430 align:middle line:90% So I'll just turn it down. 00:53:14.430 --> 00:53:18.810 align:middle line:84% Now if I-- we were talking about different modes of control 00:53:18.810 --> 00:53:22.510 align:middle line:84% before I programmed the thing for 500 watts. 00:53:22.510 --> 00:53:25.560 align:middle line:84% OK, so it runs, and then all of a sudden, it stops. 00:53:25.560 --> 00:53:27.150 align:middle line:84% OK, so this circuit doesn't really 00:53:27.150 --> 00:53:29.280 align:middle line:84% want to work at really low power, 00:53:29.280 --> 00:53:31.803 align:middle line:90% and so it pulses on and off. 00:53:31.803 --> 00:53:33.720 align:middle line:84% Normally, if you're just trying to heat water, 00:53:33.720 --> 00:53:35.350 align:middle line:84% that doesn't really make a difference, 00:53:35.350 --> 00:53:39.030 align:middle line:84% and so they can get away with this type of operation. 00:53:39.030 --> 00:53:43.224 align:middle line:84% Notice how the soft start, it slowly, slowly builds itself up. 00:53:43.224 --> 00:53:43.724 align:middle line:90% OK. 00:53:43.724 --> 00:53:44.884 align:middle line:90% OK. 00:53:44.884 --> 00:53:46.800 align:middle line:84% DAVID PERREAULT: Yeah, OK, so just 00:53:46.800 --> 00:53:48.215 align:middle line:84% to show that this thing is real-- 00:53:48.215 --> 00:54:12.210 align:middle line:90% 00:54:12.210 --> 00:54:15.400 align:middle line:84% let's see how fast we can cook with 1,200 watts. 00:54:15.400 --> 00:54:16.340 align:middle line:90% And there we go. 00:54:16.340 --> 00:54:17.530 align:middle line:90% Wow, that's pretty quick. 00:54:17.530 --> 00:54:18.750 align:middle line:90% Anybody hungry? 00:54:18.750 --> 00:54:20.525 align:middle line:90% It's just after lunch. 00:54:20.525 --> 00:54:26.912 align:middle line:90% 00:54:26.912 --> 00:54:27.870 align:middle line:90% DAVID OTTEN: All right. 00:54:27.870 --> 00:54:30.212 align:middle line:84% DAVID PERREAULT: All right, there we go, one cooked egg. 00:54:30.212 --> 00:54:31.420 align:middle line:90% We'll wrap it up for the day. 00:54:31.420 --> 00:54:33.660 align:middle line:84% But there you can see how even resonant principles 00:54:33.660 --> 00:54:34.690 align:middle line:90% can be applied. 00:54:34.690 --> 00:54:38.490 align:middle line:84% We've got zero-voltage switching pushing 1,800 watts with 00:54:38.490 --> 00:54:39.820 align:middle line:90% a single active switch. 00:54:39.820 --> 00:54:42.517 align:middle line:84% So that's sort of on the clever end of the trickery 00:54:42.517 --> 00:54:44.850 align:middle line:84% you can do with resonant converters, but as I mentioned, 00:54:44.850 --> 00:54:47.190 align:middle line:84% they're in a lot of kinds of applications. 00:54:47.190 --> 00:54:48.160 align:middle line:90% Have a great day. 00:54:48.160 --> 00:54:52.644 align:middle line:90% [APPLAUSE] 00:54:52.644 --> 00:55:00.000 align:middle line:90%