WEBVTT 00:00:00.000 --> 00:00:01.976 align:middle line:90% [SQUEAKING] 00:00:01.976 --> 00:00:03.452 align:middle line:90% [RUSTLING] 00:00:03.452 --> 00:00:03.952 align:middle line:90% 00:00:03.952 --> 00:00:04.940 align:middle line:90% [CLICKING] 00:00:04.940 --> 00:00:09.047 align:middle line:90% 00:00:09.047 --> 00:00:09.880 align:middle line:90% DAVID PERREAULT: OK. 00:00:09.880 --> 00:00:11.520 align:middle line:90% Why don't we get started. 00:00:11.520 --> 00:00:14.320 align:middle line:84% We've been talking about DC to AC 00:00:14.320 --> 00:00:16.340 align:middle line:90% power conversion or inverters. 00:00:16.340 --> 00:00:20.170 align:middle line:84% And we've been talking about the full bridge-- 00:00:20.170 --> 00:00:22.360 align:middle line:84% what we would call the full bridge inverter or, more 00:00:22.360 --> 00:00:26.830 align:middle line:84% generally, you could call it the full bridge converter. 00:00:26.830 --> 00:00:27.943 align:middle line:90% So we have four switches. 00:00:27.943 --> 00:00:37.460 align:middle line:90% 00:00:37.460 --> 00:00:39.000 align:middle line:90% And we can use this. 00:00:39.000 --> 00:00:41.060 align:middle line:84% And depending upon how we switch them, 00:00:41.060 --> 00:00:46.370 align:middle line:84% we can use them to generate an AC output voltage. 00:00:46.370 --> 00:00:54.710 align:middle line:84% So we've been drawing a generic element that we're 00:00:54.710 --> 00:00:55.980 align:middle line:90% going to have as a filter. 00:00:55.980 --> 00:00:59.850 align:middle line:84% But imagine you constructed the structure like this. 00:00:59.850 --> 00:01:01.140 align:middle line:90% Suppose I did this. 00:01:01.140 --> 00:01:06.770 align:middle line:84% Suppose I had an inductor, a resistor, another inductor. 00:01:06.770 --> 00:01:09.740 align:middle line:84% Then I could consider that I'm synthesizing 00:01:09.740 --> 00:01:12.050 align:middle line:84% on this side of the circuit if I have 00:01:12.050 --> 00:01:17.090 align:middle line:84% q of 1 of t and its complement, so I have a duty 00:01:17.090 --> 00:01:20.250 align:middle line:84% ratio of the top switch on this side of the circuit, 00:01:20.250 --> 00:01:24.570 align:middle line:84% I could generate some output v x1. 00:01:24.570 --> 00:01:27.200 align:middle line:84% And that might be filtered through this inductor. 00:01:27.200 --> 00:01:29.910 align:middle line:90% Might generate me v o1. 00:01:29.910 --> 00:01:34.980 align:middle line:84% And likewise on this circuit, if I have q2 and q prime 2, 00:01:34.980 --> 00:01:39.300 align:middle line:84% I might generate if this is d1, this side I'm running 00:01:39.300 --> 00:01:43.570 align:middle line:90% with duty ratio d2 of t. 00:01:43.570 --> 00:01:50.530 align:middle line:84% And so I'm going to have an output voltage v x2 and v o3 00:01:50.530 --> 00:01:55.990 align:middle line:84% And if I thought of then this load network here, 00:01:55.990 --> 00:02:03.190 align:middle line:84% maybe if I thought of v x, I would have v 00:02:03.190 --> 00:02:09.610 align:middle line:90% x is equal to v x1 minus v x2. 00:02:09.610 --> 00:02:17.680 align:middle line:84% And I could then think of v out 1-- 00:02:17.680 --> 00:02:18.200 align:middle line:90% I'm sorry. 00:02:18.200 --> 00:02:19.930 align:middle line:84% I could think of my output voltage v out 00:02:19.930 --> 00:02:24.670 align:middle line:84% across the resistor as being v out as being 00:02:24.670 --> 00:02:29.440 align:middle line:90% equal to v o1 minus v o2. 00:02:29.440 --> 00:02:34.150 align:middle line:84% So another way to think about the full bridge 00:02:34.150 --> 00:02:39.680 align:middle line:84% is as a pair of back to back buck converters. 00:02:39.680 --> 00:02:42.460 align:middle line:84% Here's one synchronous buck converter 00:02:42.460 --> 00:02:48.520 align:middle line:84% switch pair and his filter and another synchronous bucks switch 00:02:48.520 --> 00:02:50.380 align:middle line:90% pair and his filter. 00:02:50.380 --> 00:02:53.170 align:middle line:84% And really what I'm doing is I'm taking 00:02:53.170 --> 00:02:57.820 align:middle line:84% the difference between the two outputs to get the AC output. 00:02:57.820 --> 00:02:58.960 align:middle line:90% Right. 00:02:58.960 --> 00:03:05.080 align:middle line:84% So, for example, if I made the average value of v x1, 00:03:05.080 --> 00:03:09.820 align:middle line:84% which I get to control anywhere between zero and v DC by how I 00:03:09.820 --> 00:03:13.960 align:middle line:84% switch these switches over a PWM cycle, 00:03:13.960 --> 00:03:21.740 align:middle line:84% I could make that equal to v times 1/2 plus cosine of omega 00:03:21.740 --> 00:03:29.360 align:middle line:84% AC t and maybe I can control v x2 to be equal to some voltage v 00:03:29.360 --> 00:03:35.330 align:middle line:90% times 1/2 cosine of 1/2-- 00:03:35.330 --> 00:03:40.530 align:middle line:90% sorry, minus cosine 1/2. 00:03:40.530 --> 00:03:42.390 align:middle line:84% This should be 1/2 plus 1/2 cosine. 00:03:42.390 --> 00:03:47.780 align:middle line:84% This should be 1 minus 1/2 cosine of omega AC t, 00:03:47.780 --> 00:03:51.050 align:middle line:90% which would then give me v x. 00:03:51.050 --> 00:03:53.120 align:middle line:84% If this is v x1 and this is v x2, 00:03:53.120 --> 00:03:54.800 align:middle line:84% v x is just the difference of those two 00:03:54.800 --> 00:03:57.680 align:middle line:84% and the DC part cancels out and I just 00:03:57.680 --> 00:04:01.490 align:middle line:84% get the difference in these AC parts, which gives me 00:04:01.490 --> 00:04:06.950 align:middle line:90% v cosine of omega AC t. 00:04:06.950 --> 00:04:10.340 align:middle line:84% So by basically synthesizing something 00:04:10.340 --> 00:04:13.310 align:middle line:84% with a DC component from the left buck converter 00:04:13.310 --> 00:04:16.700 align:middle line:84% and something with the same DC component, 00:04:16.700 --> 00:04:19.910 align:middle line:84% but a complementary AC component from the right hand buck 00:04:19.910 --> 00:04:23.300 align:middle line:84% converter, I generate an AC output voltage. 00:04:23.300 --> 00:04:27.620 align:middle line:84% So you could really think of a full bridge inverter 00:04:27.620 --> 00:04:31.580 align:middle line:84% as being two synchronous buck converters back to back. 00:04:31.580 --> 00:04:33.085 align:middle line:90% Any questions about that? 00:04:33.085 --> 00:04:35.990 align:middle line:90% 00:04:35.990 --> 00:04:42.848 align:middle line:84% Now the average voltage that we get is just due to PWM. 00:04:42.848 --> 00:04:44.390 align:middle line:84% So I can control this average voltage 00:04:44.390 --> 00:04:45.500 align:middle line:90% and this average voltage. 00:04:45.500 --> 00:04:49.260 align:middle line:84% The details of how much ripple I get 00:04:49.260 --> 00:04:52.530 align:middle line:84% and what its high frequency AC components 00:04:52.530 --> 00:04:55.050 align:middle line:84% are depend upon how we do the PWM. 00:04:55.050 --> 00:04:58.920 align:middle line:84% And we talked last time about different ways we could do that. 00:04:58.920 --> 00:05:01.530 align:middle line:90% But it's the same exact concept. 00:05:01.530 --> 00:05:03.330 align:middle line:90% All right. 00:05:03.330 --> 00:05:05.385 align:middle line:90% Why do I mention that one? 00:05:05.385 --> 00:05:07.260 align:middle line:84% Just because it's another way to look at what 00:05:07.260 --> 00:05:09.010 align:middle line:90% a full bridge inverter does. 00:05:09.010 --> 00:05:13.170 align:middle line:84% Another, just as an aside, which we're not going to dive into, 00:05:13.170 --> 00:05:17.760 align:middle line:84% is just because I used buck cells here 00:05:17.760 --> 00:05:20.510 align:middle line:84% doesn't mean that's the only converter I could use. 00:05:20.510 --> 00:05:26.190 align:middle line:84% So I could take two synchronous flyback converters, for example, 00:05:26.190 --> 00:05:28.770 align:middle line:84% and use each of those as a half cell 00:05:28.770 --> 00:05:30.480 align:middle line:84% and take the difference of their outputs 00:05:30.480 --> 00:05:34.360 align:middle line:84% and get a flyback-based inverter or a flyback inverter. 00:05:34.360 --> 00:05:35.320 align:middle line:90% And people do that. 00:05:35.320 --> 00:05:39.490 align:middle line:84% So people use different topologies to do this. 00:05:39.490 --> 00:05:42.630 align:middle line:84% This full bridge structure is, generally, 00:05:42.630 --> 00:05:46.830 align:middle line:84% the most preferred because buck converters 00:05:46.830 --> 00:05:47.747 align:middle line:90% are really low stress. 00:05:47.747 --> 00:05:49.122 align:middle line:84% They're really simple to control. 00:05:49.122 --> 00:05:50.640 align:middle line:84% They have a whole bunch of benefits. 00:05:50.640 --> 00:05:54.110 align:middle line:84% And it's about as simple as you can get to do the job. 00:05:54.110 --> 00:05:56.850 align:middle line:84% But if I had to put an AC transformer in the middle, 00:05:56.850 --> 00:06:00.900 align:middle line:84% maybe I'd think about something like a flyback inverter 00:06:00.900 --> 00:06:04.420 align:middle line:84% to give me isolation, and large step up, and everything else. 00:06:04.420 --> 00:06:06.495 align:middle line:90% Any questions about that? 00:06:06.495 --> 00:06:09.470 align:middle line:90% 00:06:09.470 --> 00:06:11.240 align:middle line:84% The second point I'd like to make 00:06:11.240 --> 00:06:15.560 align:middle line:84% is I've talked about power going from AC to DC-- 00:06:15.560 --> 00:06:17.900 align:middle line:90% I'm sorry-- DC to AC. 00:06:17.900 --> 00:06:21.890 align:middle line:84% And what the power flow looks like 00:06:21.890 --> 00:06:23.960 align:middle line:90% depends upon this current iL. 00:06:23.960 --> 00:06:26.090 align:middle line:84% What I'm really limited in this circuit by 00:06:26.090 --> 00:06:31.690 align:middle line:84% is what range of v x1 and v x2 I can synthesize. 00:06:31.690 --> 00:06:34.720 align:middle line:84% There's nothing wrong with using this circuit 00:06:34.720 --> 00:06:38.230 align:middle line:84% to flow power AC to DC so long as I have 00:06:38.230 --> 00:06:40.940 align:middle line:90% a source that could support it. 00:06:40.940 --> 00:06:47.050 align:middle line:84% So one thing I could think about is coming along and building 00:06:47.050 --> 00:06:50.620 align:middle line:90% the same basic structure. 00:06:50.620 --> 00:06:58.300 align:middle line:84% So here's v DC, And I'll put a pair of switches here. 00:06:58.300 --> 00:07:01.260 align:middle line:84% And I'll put a pair of switches here. 00:07:01.260 --> 00:07:03.660 align:middle line:84% And there's nothing that says I can't combine the filter 00:07:03.660 --> 00:07:04.600 align:middle line:90% elements. 00:07:04.600 --> 00:07:08.310 align:middle line:90% So here's iL again. 00:07:08.310 --> 00:07:11.160 align:middle line:84% I'll just combine those two inductors as one element. 00:07:11.160 --> 00:07:16.470 align:middle line:90% And maybe here I have v AC. 00:07:16.470 --> 00:07:17.090 align:middle line:90% Right. 00:07:17.090 --> 00:07:19.470 align:middle line:84% There's absolutely nothing that says 00:07:19.470 --> 00:07:21.870 align:middle line:84% that I can't now use this circuit 00:07:21.870 --> 00:07:24.520 align:middle line:90% to run power from AC to DC. 00:07:24.520 --> 00:07:28.390 align:middle line:84% It's just a question of what the phase of iL is compared to v AC. 00:07:28.390 --> 00:07:33.090 align:middle line:90% 00:07:33.090 --> 00:07:36.060 align:middle line:84% And in fact, if I think about it then, 00:07:36.060 --> 00:07:39.780 align:middle line:84% that's very much like from AC to DC, 00:07:39.780 --> 00:07:42.490 align:middle line:84% this acting as a pair of back to back boost converters. 00:07:42.490 --> 00:07:45.150 align:middle line:84% It's taking energy from here, boosting it up 00:07:45.150 --> 00:07:48.090 align:middle line:90% to a higher DC output voltage. 00:07:48.090 --> 00:07:50.400 align:middle line:84% So just like we talked on early in the lecture, 00:07:50.400 --> 00:07:55.500 align:middle line:84% I can either think of this as a buck inverter or a boost 00:07:55.500 --> 00:07:57.360 align:middle line:90% rectifier. 00:07:57.360 --> 00:08:01.840 align:middle line:90% Any questions about that? 00:08:01.840 --> 00:08:06.130 align:middle line:84% And in fact, people often do this. 00:08:06.130 --> 00:08:07.910 align:middle line:90% Where might you do this? 00:08:07.910 --> 00:08:13.440 align:middle line:84% Well, imagine for a second that this whole thing-- 00:08:13.440 --> 00:08:19.320 align:middle line:84% this box-- maybe this is the back EMF and winding 00:08:19.320 --> 00:08:21.660 align:middle line:90% of a generator. 00:08:21.660 --> 00:08:25.080 align:middle line:84% So I can then extract energy from the generator 00:08:25.080 --> 00:08:27.270 align:middle line:84% so there's a mechanical input in. 00:08:27.270 --> 00:08:30.120 align:middle line:84% It generates a back EMF voltage and I take power out 00:08:30.120 --> 00:08:35.159 align:middle line:84% and throw it out to the DC side or maybe this is a motor drive. 00:08:35.159 --> 00:08:39.900 align:middle line:84% And sometimes I'm driving power into the back EMF of the motor 00:08:39.900 --> 00:08:41.230 align:middle line:90% to generate torque. 00:08:41.230 --> 00:08:45.390 align:middle line:84% And sometimes I'm regeneratively braking and absorbing power 00:08:45.390 --> 00:08:47.490 align:middle line:84% from the AC side back to the DC side. 00:08:47.490 --> 00:08:52.380 align:middle line:84% So I can either generate positive torque with respect 00:08:52.380 --> 00:08:56.400 align:middle line:84% to speed and deliver mechanical power or absorb mechanical power 00:08:56.400 --> 00:08:57.900 align:middle line:90% and slow down. 00:08:57.900 --> 00:09:00.480 align:middle line:90% Any questions about that? 00:09:00.480 --> 00:09:04.740 align:middle line:84% So just because I often call this an inverter, 00:09:04.740 --> 00:09:09.360 align:middle line:84% we might really think of it as a converter, meaning it 00:09:09.360 --> 00:09:11.310 align:middle line:84% can be an inverter or a rectifier, 00:09:11.310 --> 00:09:14.600 align:middle line:84% depending upon how I'm controlling it. 00:09:14.600 --> 00:09:17.400 align:middle line:90% And this is very common. 00:09:17.400 --> 00:09:20.070 align:middle line:84% The other places it could be is the AC grid. 00:09:20.070 --> 00:09:24.080 align:middle line:84% So if I had a solar panel stack here 00:09:24.080 --> 00:09:29.030 align:middle line:84% and I wanted to shove energy out into the AC grid, 00:09:29.030 --> 00:09:31.920 align:middle line:84% perhaps I use exactly this structure. 00:09:31.920 --> 00:09:32.420 align:middle line:90% OK. 00:09:32.420 --> 00:09:34.350 align:middle line:84% So there's another place you might do it. 00:09:34.350 --> 00:09:37.550 align:middle line:90% 00:09:37.550 --> 00:09:42.020 align:middle line:84% And that's just many applications of an inverter. 00:09:42.020 --> 00:09:42.860 align:middle line:90% Yeah. 00:09:42.860 --> 00:09:44.660 align:middle line:84% STUDENT: When you're generating breaking, 00:09:44.660 --> 00:09:47.210 align:middle line:84% do you have to use the switch the way the switches are 00:09:47.210 --> 00:09:50.360 align:middle line:90% switching [INAUDIBLE]? 00:09:50.360 --> 00:09:53.990 align:middle line:84% DAVID PERREAULT: Well, we talked last time about 00:09:53.990 --> 00:09:55.940 align:middle line:90% how I might control current. 00:09:55.940 --> 00:10:00.560 align:middle line:84% So I could think to measure the current here. 00:10:00.560 --> 00:10:05.780 align:middle line:84% And I could either generate the PWM to generate 00:10:05.780 --> 00:10:08.930 align:middle line:90% the average voltage vx. 00:10:08.930 --> 00:10:11.570 align:middle line:84% If the current is too low, I turn up vx 00:10:11.570 --> 00:10:12.620 align:middle line:90% to make the current high. 00:10:12.620 --> 00:10:15.500 align:middle line:84% And I put a closed loop so I can control the current 00:10:15.500 --> 00:10:17.420 align:middle line:84% or I could use a hysteretic current controller 00:10:17.420 --> 00:10:18.870 align:middle line:90% is another way we talked about. 00:10:18.870 --> 00:10:20.600 align:middle line:84% So really, it's really a question 00:10:20.600 --> 00:10:26.120 align:middle line:84% of whether a power is flowing AC to DC is just me deciding, well, 00:10:26.120 --> 00:10:28.400 align:middle line:84% relative to this voltage, what do 00:10:28.400 --> 00:10:30.800 align:middle line:84% I want the phase of that current to be. 00:10:30.800 --> 00:10:33.860 align:middle line:84% It could be exactly in phase and then 00:10:33.860 --> 00:10:36.170 align:middle line:84% I'm just purely delivering DC to AC. 00:10:36.170 --> 00:10:39.660 align:middle line:84% It could be iL could have the exact opposite sign to v AC 00:10:39.660 --> 00:10:42.240 align:middle line:84% and then I'm just purely delivering energy AC-DC 00:10:42.240 --> 00:10:44.580 align:middle line:90% or something in between. 00:10:44.580 --> 00:10:48.180 align:middle line:84% So yes, it's exactly how I control the switches determines 00:10:48.180 --> 00:10:51.120 align:middle line:84% the power flow direction in this generalized picture, 00:10:51.120 --> 00:10:54.220 align:middle line:84% understanding that there's limits on what the load can do. 00:10:54.220 --> 00:10:57.210 align:middle line:84% Now if I had a current source inverter, 00:10:57.210 --> 00:11:01.920 align:middle line:84% here I'm talking about deciding power flow direction based 00:11:01.920 --> 00:11:05.530 align:middle line:84% on the sign of this current where the voltages I apply 00:11:05.530 --> 00:11:06.280 align:middle line:90% are the same sign. 00:11:06.280 --> 00:11:08.410 align:middle line:84% If I had a current source inverter, I'd do the reverse. 00:11:08.410 --> 00:11:10.210 align:middle line:84% The current would have the same direction. 00:11:10.210 --> 00:11:12.550 align:middle line:84% I'd do it at a different voltage polarity. 00:11:12.550 --> 00:11:15.190 align:middle line:90% 00:11:15.190 --> 00:11:16.220 align:middle line:90% Any other questions? 00:11:16.220 --> 00:11:16.720 align:middle line:90% Yeah. 00:11:16.720 --> 00:11:19.990 align:middle line:84% STUDENT: I have a question on the one on the top. 00:11:19.990 --> 00:11:24.010 align:middle line:84% You have the average voltages, but they have the cosine omega t 00:11:24.010 --> 00:11:24.590 align:middle line:90% term. 00:11:24.590 --> 00:11:27.058 align:middle line:84% So is that some special AC average 00:11:27.058 --> 00:11:28.600 align:middle line:84% that gives you the fundamentals here? 00:11:28.600 --> 00:11:28.990 align:middle line:90% DAVID PERREAULT: Yeah. 00:11:28.990 --> 00:11:30.470 align:middle line:90% That's a very good question. 00:11:30.470 --> 00:11:33.790 align:middle line:84% What I meant to convey here-- and I wasn't very clear about 00:11:33.790 --> 00:11:35.620 align:middle line:90% it-- 00:11:35.620 --> 00:11:39.550 align:middle line:84% is imagine I have a really high switching frequency, 00:11:39.550 --> 00:11:42.850 align:middle line:84% 100 kilohertz, but omega AC is maybe 00:11:42.850 --> 00:11:45.370 align:middle line:90% some lower frequency, 60 hertz. 00:11:45.370 --> 00:11:50.740 align:middle line:84% So from the perspective of the switching frequency, maybe 00:11:50.740 --> 00:11:55.640 align:middle line:84% omega AC is really low and so think about as DC. 00:11:55.640 --> 00:11:58.600 align:middle line:84% So instead of being, you know, average 00:11:58.600 --> 00:12:01.390 align:middle line:84% over infinite time, it's average over just some time 00:12:01.390 --> 00:12:04.780 align:middle line:84% this long compared to the PWM cycle, hundreds or thousands 00:12:04.780 --> 00:12:05.870 align:middle line:90% of PWM cycles. 00:12:05.870 --> 00:12:10.090 align:middle line:84% So I slowly vary my duty cycle, d of t, 00:12:10.090 --> 00:12:13.600 align:middle line:84% not within a switching cycle but slowly 00:12:13.600 --> 00:12:17.860 align:middle line:84% compared to the switching period of the inverter 00:12:17.860 --> 00:12:23.390 align:middle line:84% and on the time scale of the AC output I want to synthesize. 00:12:23.390 --> 00:12:24.877 align:middle line:84% So if I want to synthesize music, 00:12:24.877 --> 00:12:26.710 align:middle line:84% I'd better have a switching frequency that's 00:12:26.710 --> 00:12:30.400 align:middle line:84% much higher than 20 kilohertz bandwidth you can hear 00:12:30.400 --> 00:12:34.430 align:middle line:84% kind of thing or, in my case, 8 or 10 kilohertz, 00:12:34.430 --> 00:12:37.550 align:middle line:90% but that's life. 00:12:37.550 --> 00:12:41.370 align:middle line:90% Any other questions? 00:12:41.370 --> 00:12:42.570 align:middle line:90% Yeah. 00:12:42.570 --> 00:12:46.440 align:middle line:84% STUDENT: Can the top one be used to excite 00:12:46.440 --> 00:12:54.150 align:middle line:84% the excitation of the [INAUDIBLE] for rectification? 00:12:54.150 --> 00:12:55.690 align:middle line:84% DAVID PERREAULT: For rectification. 00:12:55.690 --> 00:12:56.190 align:middle line:90% Yeah. 00:12:56.190 --> 00:12:58.430 align:middle line:90% I don't see why not. 00:12:58.430 --> 00:12:59.060 align:middle line:90% Yeah. 00:12:59.060 --> 00:13:01.550 align:middle line:84% As long as you have a DC voltage that's 00:13:01.550 --> 00:13:04.380 align:middle line:84% greater than whatever the AC output in amplitude is. 00:13:04.380 --> 00:13:04.880 align:middle line:90% Right. 00:13:04.880 --> 00:13:07.460 align:middle line:84% This thing, because it's based on a buck converter, 00:13:07.460 --> 00:13:09.560 align:middle line:84% I can't synthesize an AC waveform 00:13:09.560 --> 00:13:12.590 align:middle line:84% to drive current that's bigger than the thing 00:13:12.590 --> 00:13:13.680 align:middle line:90% I'm trying to drive. 00:13:13.680 --> 00:13:16.010 align:middle line:84% STUDENT: If you were to have the stator in the middle 00:13:16.010 --> 00:13:23.247 align:middle line:84% and then use that to excite the rotor field winding. 00:13:23.247 --> 00:13:24.080 align:middle line:90% DAVID PERREAULT: Oh. 00:13:24.080 --> 00:13:25.190 align:middle line:90% Could I? 00:13:25.190 --> 00:13:25.850 align:middle line:90% Yes. 00:13:25.850 --> 00:13:29.360 align:middle line:84% You can play games like that, but maybe that's better. 00:13:29.360 --> 00:13:31.172 align:middle line:90% Yeah. 00:13:31.172 --> 00:13:32.630 align:middle line:84% That would require more explanation 00:13:32.630 --> 00:13:34.320 align:middle line:84% than I have time to give, unfortunately. 00:13:34.320 --> 00:13:35.155 align:middle line:90% But yes, you can. 00:13:35.155 --> 00:13:38.250 align:middle line:90% 00:13:38.250 --> 00:13:42.840 align:middle line:84% So that's-- whether I think about this as an inverter, 00:13:42.840 --> 00:13:49.910 align:middle line:84% or rectifier, or just a converter is up to you. 00:13:49.910 --> 00:13:51.980 align:middle line:84% But I would like to note that there 00:13:51.980 --> 00:13:54.840 align:middle line:84% are some times when I only really want to go one direction. 00:13:54.840 --> 00:13:56.870 align:middle line:84% In fact, there's times when I only 00:13:56.870 --> 00:14:01.410 align:middle line:84% want to take power from the wall and put it out to the DC side. 00:14:01.410 --> 00:14:05.120 align:middle line:84% If I'm building a computer power supply, 00:14:05.120 --> 00:14:09.200 align:middle line:84% at least in ones today, there's no real reason for me 00:14:09.200 --> 00:14:12.200 align:middle line:84% to do anything except absorb power from the AC side 00:14:12.200 --> 00:14:13.400 align:middle line:90% and put it to the DC side. 00:14:13.400 --> 00:14:13.900 align:middle line:90% Right. 00:14:13.900 --> 00:14:18.140 align:middle line:84% And if that's the only thing I want to do, 00:14:18.140 --> 00:14:20.113 align:middle line:90% I can do the conversion. 00:14:20.113 --> 00:14:21.530 align:middle line:84% I could do that with this circuit. 00:14:21.530 --> 00:14:23.290 align:middle line:84% I could connect this to the AC grid. 00:14:23.290 --> 00:14:29.150 align:middle line:90% 00:14:29.150 --> 00:14:32.200 align:middle line:84% I could connect this thing to the AC grid, 00:14:32.200 --> 00:14:35.350 align:middle line:84% and control the switches, and dump energy 00:14:35.350 --> 00:14:38.410 align:middle line:84% into the DC side, which then I'd use to power my computer, 00:14:38.410 --> 00:14:39.050 align:middle line:90% for example. 00:14:39.050 --> 00:14:40.002 align:middle line:90% Right. 00:14:40.002 --> 00:14:42.070 align:middle line:84% But if that's all I want to do, this 00:14:42.070 --> 00:14:46.000 align:middle line:84% is kind of a more complicated circuit than you need to do it. 00:14:46.000 --> 00:14:49.630 align:middle line:84% So for things like computer power supplies, which 00:14:49.630 --> 00:14:52.360 align:middle line:84% are kind of ubiquitous these days, or something 00:14:52.360 --> 00:14:55.990 align:middle line:84% like my laptop adapter there, that's 00:14:55.990 --> 00:14:59.710 align:middle line:84% a pretty expensive circuit to be using because it has way 00:14:59.710 --> 00:15:02.920 align:middle line:90% more capability than we need. 00:15:02.920 --> 00:15:08.140 align:middle line:84% So mostly if we're going to deliver power from AC or DC, 00:15:08.140 --> 00:15:09.740 align:middle line:90% we use simpler circuits. 00:15:09.740 --> 00:15:12.880 align:middle line:84% One way to do this and the oldie-fashioned way to do 00:15:12.880 --> 00:15:15.310 align:middle line:84% is to use what's known as a phase controlled rectifier. 00:15:15.310 --> 00:15:16.977 align:middle line:84% And there's a chapter in the book on it. 00:15:16.977 --> 00:15:18.610 align:middle line:90% At high powers, it's still done. 00:15:18.610 --> 00:15:21.070 align:middle line:84% But I'm going to skip over that as an approach 00:15:21.070 --> 00:15:28.270 align:middle line:84% because it's less relevant to high frequency converters 00:15:28.270 --> 00:15:32.620 align:middle line:84% and also because, if you think about things like computer power 00:15:32.620 --> 00:15:36.580 align:middle line:84% supplies, not so much in the sub-75 watt range 00:15:36.580 --> 00:15:38.660 align:middle line:84% but higher power like your desktop, 00:15:38.660 --> 00:15:41.320 align:middle line:84% there are very strict requirements in how 00:15:41.320 --> 00:15:43.340 align:middle line:90% it looks to the AC grid. 00:15:43.340 --> 00:15:45.940 align:middle line:84% So we talked about uncontrolled rectifiers 00:15:45.940 --> 00:15:47.410 align:middle line:90% at the beginning of the term. 00:15:47.410 --> 00:15:50.590 align:middle line:84% And they tend to have ugly AC waveforms. 00:15:50.590 --> 00:15:53.890 align:middle line:84% And that means they have low power factor. 00:15:53.890 --> 00:15:56.950 align:middle line:84% So a goal of many switch mode rectifiers 00:15:56.950 --> 00:15:59.830 align:middle line:84% is to take energy from AC to DC only, 00:15:59.830 --> 00:16:02.770 align:middle line:84% but to do it at a very good power factor. 00:16:02.770 --> 00:16:03.340 align:middle line:90% OK. 00:16:03.340 --> 00:16:05.420 align:middle line:84% So let's think about how we might do that. 00:16:05.420 --> 00:16:08.830 align:middle line:84% Maybe I might draw this generalized box 00:16:08.830 --> 00:16:10.640 align:middle line:90% as something like this. 00:16:10.640 --> 00:16:14.370 align:middle line:90% I have some AC voltage, v AC. 00:16:14.370 --> 00:16:14.870 align:middle line:90% Right. 00:16:14.870 --> 00:16:16.640 align:middle line:84% That's the line voltage typically. 00:16:16.640 --> 00:16:18.375 align:middle line:90% Maybe I'll call it v line. 00:16:18.375 --> 00:16:22.900 align:middle line:90% 00:16:22.900 --> 00:16:25.690 align:middle line:90% It goes into a box. 00:16:25.690 --> 00:16:27.700 align:middle line:90% OK. 00:16:27.700 --> 00:16:30.590 align:middle line:90% That box is a rectifier. 00:16:30.590 --> 00:16:33.610 align:middle line:90% And maybe it just feeds-- 00:16:33.610 --> 00:16:34.720 align:middle line:90% I'll put a capacitor here. 00:16:34.720 --> 00:16:36.880 align:middle line:84% And we'll talk more about this capacitor later. 00:16:36.880 --> 00:16:40.240 align:middle line:84% But maybe it feeds some load v DC. 00:16:40.240 --> 00:16:46.630 align:middle line:84% And I would like, generally, this line current i line 00:16:46.630 --> 00:16:50.200 align:middle line:90% to have very nice waveforms. 00:16:50.200 --> 00:16:51.070 align:middle line:90% OK. 00:16:51.070 --> 00:16:53.660 align:middle line:90% What would nice be defined as? 00:16:53.660 --> 00:16:58.110 align:middle line:90% Well, you know, here is v line. 00:16:58.110 --> 00:17:05.640 align:middle line:90% 00:17:05.640 --> 00:17:08.500 align:middle line:90% This is the line frequency. 00:17:08.500 --> 00:17:13.150 align:middle line:84% This is 60hz or 50hz, depending upon where you are. 00:17:13.150 --> 00:17:17.910 align:middle line:84% The best I can do in terms of power factor 00:17:17.910 --> 00:17:21.089 align:middle line:84% is to make my whole converter look like a resistor. 00:17:21.089 --> 00:17:25.740 align:middle line:84% So my goal might be to have a current waveform that looks just 00:17:25.740 --> 00:17:26.584 align:middle line:90% like this. 00:17:26.584 --> 00:17:29.400 align:middle line:90% 00:17:29.400 --> 00:17:30.403 align:middle line:90% Here's i line. 00:17:30.403 --> 00:17:33.240 align:middle line:90% 00:17:33.240 --> 00:17:42.930 align:middle line:84% And maybe I would make i line something like i line of t 00:17:42.930 --> 00:17:49.140 align:middle line:84% is just equal to some constant g times v line of t. 00:17:49.140 --> 00:17:52.320 align:middle line:84% Now, clearly, the amount of power I'm going to get 00:17:52.320 --> 00:17:54.750 align:middle line:90% is going to vary with g. 00:17:54.750 --> 00:17:58.850 align:middle line:84% But for any value of g, I'll get some amount of average power out 00:17:58.850 --> 00:17:59.350 align:middle line:90% of the line. 00:17:59.350 --> 00:18:02.730 align:middle line:84% And this is about as good as I can do in terms of power factor. 00:18:02.730 --> 00:18:03.270 align:middle line:90% OK. 00:18:03.270 --> 00:18:07.980 align:middle line:84% So done that way, this is called a unity power factor rectifier 00:18:07.980 --> 00:18:13.050 align:middle line:84% because the line current, ideally, just 00:18:13.050 --> 00:18:15.960 align:middle line:84% looks like-- it makes the converter look like a resistor. 00:18:15.960 --> 00:18:22.600 align:middle line:84% It's a variable resistor depending upon this constant. 00:18:22.600 --> 00:18:26.590 align:middle line:84% So as I vary the g to vary the amount of power I draw, 00:18:26.590 --> 00:18:29.290 align:middle line:84% I vary the equivalent resistance. 00:18:29.290 --> 00:18:32.690 align:middle line:84% But nonetheless, at any given load, it looks like a resistor. 00:18:32.690 --> 00:18:33.190 align:middle line:90% OK. 00:18:33.190 --> 00:18:35.940 align:middle line:84% Does that make sense to everybody? 00:18:35.940 --> 00:18:39.630 align:middle line:84% So that's called a unity power factor rectifier or a UPF 00:18:39.630 --> 00:18:40.700 align:middle line:90% rectifier. 00:18:40.700 --> 00:18:43.200 align:middle line:84% More generally, in modern terms, people 00:18:43.200 --> 00:18:47.700 align:middle line:84% talk about a PFC or power factor corrected rectifier. 00:18:47.700 --> 00:18:50.940 align:middle line:84% And what's meant by that is I've shown 00:18:50.940 --> 00:18:54.450 align:middle line:84% you the idealized case where this draws a perfect sinusoid. 00:18:54.450 --> 00:18:57.840 align:middle line:84% You may have converters that don't draw perfect sinusoids 00:18:57.840 --> 00:19:01.160 align:middle line:84% but are close enough that the power factor is very, very high. 00:19:01.160 --> 00:19:03.640 align:middle line:84% And so that would be called a PFC converter. 00:19:03.640 --> 00:19:06.120 align:middle line:84% And if you look at many applications like computer power 00:19:06.120 --> 00:19:08.430 align:middle line:84% supplies or for different kinds of tools, 00:19:08.430 --> 00:19:12.190 align:middle line:84% they all have slightly different requirements put together. 00:19:12.190 --> 00:19:14.560 align:middle line:84% But generally, the power factor has to be pretty high. 00:19:14.560 --> 00:19:16.320 align:middle line:84% They limit the distortion in the current 00:19:16.320 --> 00:19:21.930 align:middle line:84% or they limit how non-sinusoidal the line current looks. 00:19:21.930 --> 00:19:24.180 align:middle line:84% So what I'm going to do is I'm going to tell you now-- 00:19:24.180 --> 00:19:26.010 align:middle line:84% I'll give you as in one example of this, 00:19:26.010 --> 00:19:29.048 align:middle line:84% I'll show you what's at the front end or some variant 00:19:29.048 --> 00:19:30.840 align:middle line:84% of what's at the front end of most computer 00:19:30.840 --> 00:19:32.950 align:middle line:90% power supplies for single phase. 00:19:32.950 --> 00:19:35.710 align:middle line:90% And this is the idea. 00:19:35.710 --> 00:19:36.210 align:middle line:90% OK. 00:19:36.210 --> 00:19:38.640 align:middle line:84% Whereas we had all these active switches, 00:19:38.640 --> 00:19:41.610 align:middle line:84% it turns out I don't need all those active switches. 00:19:41.610 --> 00:19:43.980 align:middle line:84% And the active switches, and their controllers, 00:19:43.980 --> 00:19:45.670 align:middle line:84% and all that stuff are expensive. 00:19:45.670 --> 00:19:47.440 align:middle line:84% Maybe I could do something like this. 00:19:47.440 --> 00:19:49.020 align:middle line:90% Maybe I could come in. 00:19:49.020 --> 00:19:53.160 align:middle line:90% And here's my v AC. 00:19:53.160 --> 00:19:58.950 align:middle line:90% 00:19:58.950 --> 00:20:00.810 align:middle line:90% Here's my AC line voltage. 00:20:00.810 --> 00:20:05.290 align:middle line:84% I'll run that into a diode rectifier. 00:20:05.290 --> 00:20:05.790 align:middle line:90% OK. 00:20:05.790 --> 00:20:12.625 align:middle line:90% 00:20:12.625 --> 00:20:19.010 align:middle line:84% So if I plotted v line of t here-- 00:20:19.010 --> 00:20:24.060 align:middle line:90% 00:20:24.060 --> 00:20:27.255 align:middle line:84% and again, I'm plotting things on the line frequency time scale 00:20:27.255 --> 00:20:29.130 align:middle line:84% so I'm going to have a switching circuit that 00:20:29.130 --> 00:20:30.860 align:middle line:90% runs much faster than that. 00:20:30.860 --> 00:20:39.120 align:middle line:84% So this time period t line might be 1 over 60 hertz. 00:20:39.120 --> 00:20:44.310 align:middle line:90% So I have v line here. 00:20:44.310 --> 00:20:48.470 align:middle line:84% Maybe what I will get then is a voltage vx, 00:20:48.470 --> 00:20:50.970 align:middle line:84% depending upon how I make the rest of the circuit look like, 00:20:50.970 --> 00:20:52.470 align:middle line:90% vx that looks like this. 00:20:52.470 --> 00:20:54.780 align:middle line:90% So this is vx of t. 00:20:54.780 --> 00:20:56.640 align:middle line:90% I will make vx of t. 00:20:56.640 --> 00:20:59.310 align:middle line:84% When v line is positive, these two diodes 00:20:59.310 --> 00:21:02.100 align:middle line:90% are on and v line equals-- 00:21:02.100 --> 00:21:03.180 align:middle line:90% vx equals v line. 00:21:03.180 --> 00:21:05.370 align:middle line:84% And when v line is negative, these two diodes are on 00:21:05.370 --> 00:21:07.240 align:middle line:90% and vx equals minus v line. 00:21:07.240 --> 00:21:09.650 align:middle line:84% So now I get something that does this. 00:21:09.650 --> 00:21:16.240 align:middle line:90% 00:21:16.240 --> 00:21:16.740 align:middle line:90% OK. 00:21:16.740 --> 00:21:18.670 align:middle line:84% That's a pretty bad half sine wave. 00:21:18.670 --> 00:21:19.320 align:middle line:90% So right. 00:21:19.320 --> 00:21:20.450 align:middle line:90% So here's v line. 00:21:20.450 --> 00:21:26.210 align:middle line:90% 00:21:26.210 --> 00:21:27.300 align:middle line:90% Here's v x. 00:21:27.300 --> 00:21:29.840 align:middle line:90% 00:21:29.840 --> 00:21:32.370 align:middle line:84% Does that make sense to everybody? 00:21:32.370 --> 00:21:32.870 align:middle line:90% Now. 00:21:32.870 --> 00:21:37.180 align:middle line:84% The beauty of this is I've made it unipolar. 00:21:37.180 --> 00:21:40.347 align:middle line:84% And so then I can build the rest of my circuit. 00:21:40.347 --> 00:21:42.430 align:middle line:84% And maybe one way I'd build the rest of my circuit 00:21:42.430 --> 00:21:44.260 align:middle line:84% is just to build a boost converter. 00:21:44.260 --> 00:21:45.260 align:middle line:90% So here we go. 00:21:45.260 --> 00:21:46.990 align:middle line:90% I only have one active switch. 00:21:46.990 --> 00:21:49.420 align:middle line:90% q of t runs this switch. 00:21:49.420 --> 00:21:51.880 align:middle line:84% And he's now referenced to this node. 00:21:51.880 --> 00:21:57.670 align:middle line:84% And then I can put a diode and a capacitor and get v DC out. 00:21:57.670 --> 00:22:01.510 align:middle line:90% 00:22:01.510 --> 00:22:04.170 align:middle line:90% And what's my goal? 00:22:04.170 --> 00:22:13.410 align:middle line:84% My goal might be to control my input current i x. 00:22:13.410 --> 00:22:17.486 align:middle line:84% And maybe I'll make this current i x. 00:22:17.486 --> 00:22:22.050 align:middle line:90% 00:22:22.050 --> 00:22:27.470 align:middle line:84% And i x maybe I'll control to look like this, on average. 00:22:27.470 --> 00:22:31.050 align:middle line:84% There's going to be some switching component to it. 00:22:31.050 --> 00:22:37.530 align:middle line:84% But maybe I'll make i x, if this is a voltage v s-- 00:22:37.530 --> 00:22:42.260 align:middle line:84% peak voltage v s, maybe I'll make his peak g times v s. 00:22:42.260 --> 00:22:42.760 align:middle line:90% All right. 00:22:42.760 --> 00:22:45.900 align:middle line:84% So it's going to have a sinusoidal reference current. 00:22:45.900 --> 00:22:47.880 align:middle line:90% And I'm going to track it. 00:22:47.880 --> 00:22:48.390 align:middle line:90% OK. 00:22:48.390 --> 00:22:51.870 align:middle line:84% Well, if this is the current i x, 00:22:51.870 --> 00:22:55.810 align:middle line:84% it has to ultimately come from the diode bridge. 00:22:55.810 --> 00:22:58.140 align:middle line:84% So when these two diodes are on, which 00:22:58.140 --> 00:23:02.430 align:middle line:84% happens when v line is positive, it goes through one way 00:23:02.430 --> 00:23:04.080 align:middle line:84% and then i x goes through the other 00:23:04.080 --> 00:23:06.070 align:middle line:84% when the other two diodes are positive. 00:23:06.070 --> 00:23:13.060 align:middle line:84% So then if I plotted i line, what would i line look like? 00:23:13.060 --> 00:23:15.480 align:middle line:90% i line would look like this. 00:23:15.480 --> 00:23:18.570 align:middle line:90% So this is i x. 00:23:18.570 --> 00:23:21.750 align:middle line:90% And i line would look like this. 00:23:21.750 --> 00:23:26.165 align:middle line:84% It would look like i x in the positive half cycle minus x 00:23:26.165 --> 00:23:27.290 align:middle line:90% in the negative half cycle. 00:23:27.290 --> 00:23:29.530 align:middle line:90% And this would be i line. 00:23:29.530 --> 00:23:33.370 align:middle line:84% So suddenly, what happens is I only 00:23:33.370 --> 00:23:39.220 align:middle line:84% have to control this simple DC to DC boost converter 00:23:39.220 --> 00:23:44.110 align:middle line:84% to generate a time varying current over the line cycle. 00:23:44.110 --> 00:23:46.750 align:middle line:84% And the diode bridge naturally unfolds that. 00:23:46.750 --> 00:23:48.390 align:middle line:84% Give me a sinusoidal input current. 00:23:48.390 --> 00:23:51.390 align:middle line:90% 00:23:51.390 --> 00:23:54.840 align:middle line:90% Any questions about that? 00:23:54.840 --> 00:23:56.550 align:middle line:84% This is kind of cool because I've 00:23:56.550 --> 00:24:00.950 align:middle line:84% thrown out four active switches and a bunch of control 00:24:00.950 --> 00:24:04.090 align:middle line:90% for basically one active switch. 00:24:04.090 --> 00:24:06.470 align:middle line:84% And yeah, I got some diodes, but so what. 00:24:06.470 --> 00:24:08.927 align:middle line:84% Those diodes don't require any control. 00:24:08.927 --> 00:24:09.510 align:middle line:90% They're cheap. 00:24:09.510 --> 00:24:10.350 align:middle line:90% They're simple. 00:24:10.350 --> 00:24:11.930 align:middle line:90% Life is good. 00:24:11.930 --> 00:24:12.680 align:middle line:90% OK. 00:24:12.680 --> 00:24:15.830 align:middle line:84% Now this kind of boost rectifier-- 00:24:15.830 --> 00:24:17.760 align:middle line:84% this would be called a boost rectifier-- 00:24:17.760 --> 00:24:21.650 align:middle line:90% 00:24:21.650 --> 00:24:26.160 align:middle line:84% is very much in the spirit of my full bridge. 00:24:26.160 --> 00:24:28.770 align:middle line:84% I just don't have to worry about all the phase shift. 00:24:28.770 --> 00:24:31.800 align:middle line:84% Now, that said, it can only rectify. 00:24:31.800 --> 00:24:34.220 align:middle line:84% Power is only going to flow this way because of these four 00:24:34.220 --> 00:24:35.070 align:middle line:90% diodes. 00:24:35.070 --> 00:24:36.450 align:middle line:90% That's the price I paid. 00:24:36.450 --> 00:24:39.470 align:middle line:84% I can't phase shift my current with respect to the line 00:24:39.470 --> 00:24:41.227 align:middle line:90% or do any other fancy things. 00:24:41.227 --> 00:24:42.560 align:middle line:90% But, generally, I don't want to. 00:24:42.560 --> 00:24:44.310 align:middle line:84% I don't want to get energy out of the line 00:24:44.310 --> 00:24:47.240 align:middle line:84% and put it into a power supply for my computer. 00:24:47.240 --> 00:24:50.030 align:middle line:84% The other thing about this, of course, 00:24:50.030 --> 00:24:53.900 align:middle line:84% is this particular circuit is a boost converter. 00:24:53.900 --> 00:24:56.525 align:middle line:84% Like if I look at it from here, that just looks like a boost DC 00:24:56.525 --> 00:24:58.280 align:middle line:90% to DC converter. 00:24:58.280 --> 00:25:02.460 align:middle line:84% That means that this DC output voltage must be bigger 00:25:02.460 --> 00:25:04.800 align:middle line:90% than the peak line voltage. 00:25:04.800 --> 00:25:05.400 align:middle line:90% OK. 00:25:05.400 --> 00:25:09.420 align:middle line:84% Now what that means practically is most places in the US 00:25:09.420 --> 00:25:13.500 align:middle line:84% the peak line voltage is 170 but it 00:25:13.500 --> 00:25:18.390 align:middle line:84% can be plus 10%, minus 15%, around that in practice 00:25:18.390 --> 00:25:19.660 align:middle line:90% or sometimes even worse. 00:25:19.660 --> 00:25:22.410 align:middle line:84% But then I also have to make it run in some places in Japan 00:25:22.410 --> 00:25:28.380 align:middle line:84% where the line voltage might go down to like 90 VACRMS. 00:25:28.380 --> 00:25:30.240 align:middle line:84% And I got to make it run in Europe where 00:25:30.240 --> 00:25:32.040 align:middle line:90% it can get much higher. 00:25:32.040 --> 00:25:34.560 align:middle line:84% So most of the time, what people will do 00:25:34.560 --> 00:25:36.780 align:middle line:84% is they'll make this like 400 volts 00:25:36.780 --> 00:25:38.550 align:middle line:84% for a single phase line, which means 00:25:38.550 --> 00:25:44.600 align:middle line:84% it can take anywhere in the world's single phase AC voltage. 00:25:44.600 --> 00:25:47.120 align:middle line:90% 00:25:47.120 --> 00:25:48.650 align:middle line:84% The other thing I should point out 00:25:48.650 --> 00:25:54.440 align:middle line:84% is notice that if this is hot and this is neutral, 00:25:54.440 --> 00:25:59.210 align:middle line:84% which is near ground, notice that this node is not 00:25:59.210 --> 00:26:02.540 align:middle line:90% referenced to this node. 00:26:02.540 --> 00:26:05.060 align:middle line:84% So don't make the mistake of saying, 00:26:05.060 --> 00:26:07.910 align:middle line:84% OK, I'm going to connect my ground clip here 00:26:07.910 --> 00:26:11.060 align:middle line:84% because grounds are neutral and bad things are going to happen. 00:26:11.060 --> 00:26:13.910 align:middle line:84% Usually, bad things means your circuit explodes. 00:26:13.910 --> 00:26:17.370 align:middle line:90% And I've been there. 00:26:17.370 --> 00:26:20.160 align:middle line:84% Let me just illustrate this for you. 00:26:20.160 --> 00:26:22.360 align:middle line:90% This is a simulation. 00:26:22.360 --> 00:26:26.440 align:middle line:84% So here's my sine wave voltage source, four diodes. 00:26:26.440 --> 00:26:30.620 align:middle line:90% Here's my boost converter. 00:26:30.620 --> 00:26:31.640 align:middle line:90% OK. 00:26:31.640 --> 00:26:32.548 align:middle line:90% Let me run it. 00:26:32.548 --> 00:26:34.090 align:middle line:84% This is just a simulation we can run. 00:26:34.090 --> 00:26:45.930 align:middle line:90% 00:26:45.930 --> 00:26:46.430 align:middle line:90% OK. 00:26:46.430 --> 00:26:48.222 align:middle line:84% Let's take a look at some of the waveforms. 00:26:48.222 --> 00:26:49.123 align:middle line:90% Let me look at the-- 00:26:49.123 --> 00:26:52.320 align:middle line:90% 00:26:52.320 --> 00:26:53.830 align:middle line:84% actually, let me take a look at-- 00:26:53.830 --> 00:27:00.110 align:middle line:90% 00:27:00.110 --> 00:27:05.590 align:middle line:84% let me take a look at the AC input voltage. 00:27:05.590 --> 00:27:07.446 align:middle line:90% Right. 00:27:07.446 --> 00:27:09.950 align:middle line:84% Looks like that's the AC input voltage. 00:27:09.950 --> 00:27:12.800 align:middle line:84% Let me look at the AC input current. 00:27:12.800 --> 00:27:15.410 align:middle line:84% And actually, I looked at them with the wrong phase. 00:27:15.410 --> 00:27:16.910 align:middle line:84% Let me just change the phase here. 00:27:16.910 --> 00:27:20.540 align:middle line:90% Minus 1 times that current. 00:27:20.540 --> 00:27:27.080 align:middle line:84% So this is very much generating a very sinusoidal looking input. 00:27:27.080 --> 00:27:30.110 align:middle line:84% If I looked at this current, for example, 00:27:30.110 --> 00:27:34.330 align:middle line:84% the current in the inductor, he is the rectified version 00:27:34.330 --> 00:27:34.830 align:middle line:90% of that. 00:27:34.830 --> 00:27:36.650 align:middle line:90% So it's exactly what I said. 00:27:36.650 --> 00:27:38.360 align:middle line:84% But of course, keep in mind, we're 00:27:38.360 --> 00:27:39.930 align:middle line:90% looking at a long time scale. 00:27:39.930 --> 00:27:41.520 align:middle line:90% This is 60 hertz. 00:27:41.520 --> 00:27:44.270 align:middle line:84% If I zoomed in close, what I would see 00:27:44.270 --> 00:27:47.580 align:middle line:90% is a lot of PWM switching. 00:27:47.580 --> 00:27:48.913 align:middle line:90% So I have a switching frequency. 00:27:48.913 --> 00:27:51.163 align:middle line:84% Actually, I don't remember what it is in this example, 00:27:51.163 --> 00:27:53.250 align:middle line:84% but it's probably like 500 kilohertz or something 00:27:53.250 --> 00:27:54.130 align:middle line:90% like that. 00:27:54.130 --> 00:27:58.170 align:middle line:84% And I'm using it to create a 60 hertz rectification 00:27:58.170 --> 00:28:01.320 align:middle line:84% and drawing energy from the line at essentially unity power 00:28:01.320 --> 00:28:04.150 align:middle line:90% factor. 00:28:04.150 --> 00:28:06.720 align:middle line:90% Any questions about that? 00:28:06.720 --> 00:28:07.600 align:middle line:90% Yeah. 00:28:07.600 --> 00:28:10.715 align:middle line:84% STUDENT: So I may have missed this, but why isn't there a way 00:28:10.715 --> 00:28:13.200 align:middle line:90% you could introduce [INAUDIBLE]? 00:28:13.200 --> 00:28:15.350 align:middle line:84% DAVID PERREAULT: Ah, that's a very good question 00:28:15.350 --> 00:28:20.630 align:middle line:84% because what I'm doing is if I had some passive kind of thing 00:28:20.630 --> 00:28:21.990 align:middle line:90% going on, I might. 00:28:21.990 --> 00:28:24.680 align:middle line:84% But what I'm really doing is I'm-- 00:28:24.680 --> 00:28:26.840 align:middle line:84% I can do this control in a bunch of ways, 00:28:26.840 --> 00:28:29.450 align:middle line:90% but I'm sensing this current. 00:28:29.450 --> 00:28:33.230 align:middle line:90% And then I'm chopping this-- 00:28:33.230 --> 00:28:37.810 align:middle line:84% I'm chopping the switch in order to regulate the current 00:28:37.810 --> 00:28:39.670 align:middle line:90% in the inductor i x. 00:28:39.670 --> 00:28:43.630 align:middle line:84% So this would be like what i x is doing according 00:28:43.630 --> 00:28:46.900 align:middle line:84% to following a reference which is exactly in phase 00:28:46.900 --> 00:28:48.310 align:middle line:90% with the input voltage. 00:28:48.310 --> 00:28:49.170 align:middle line:90% OK. 00:28:49.170 --> 00:28:52.820 align:middle line:84% Any phase shift that would go on I can deal with. 00:28:52.820 --> 00:28:56.530 align:middle line:84% And keep in mind this inductor at the line frequency 00:28:56.530 --> 00:29:00.850 align:middle line:84% is really small so this doesn't have much impedance at the line 00:29:00.850 --> 00:29:01.880 align:middle line:90% frequency. 00:29:01.880 --> 00:29:03.920 align:middle line:84% It has impedance at the switching frequency. 00:29:03.920 --> 00:29:06.920 align:middle line:84% So I need to switch way faster than the line frequency. 00:29:06.920 --> 00:29:10.167 align:middle line:90% 00:29:10.167 --> 00:29:11.750 align:middle line:84% STUDENT: How is it possible to control 00:29:11.750 --> 00:29:15.800 align:middle line:90% both i x and DC [INAUDIBLE]? 00:29:15.800 --> 00:29:17.705 align:middle line:84% DAVID PERREAULT: So I'm not controlling-- 00:29:17.705 --> 00:29:19.357 align:middle line:90% oh, v DC? 00:29:19.357 --> 00:29:19.940 align:middle line:90% STUDENT: Yeah. 00:29:19.940 --> 00:29:22.670 align:middle line:84% Like if the output power is set by the load 00:29:22.670 --> 00:29:25.580 align:middle line:84% and you're trying to maintain the DC at 400 volts 00:29:25.580 --> 00:29:28.580 align:middle line:84% while also having a [INAUDIBLE] on it. 00:29:28.580 --> 00:29:30.660 align:middle line:84% How do you control that with the one switch? 00:29:30.660 --> 00:29:32.160 align:middle line:84% DAVID PERREAULT: Excellent question. 00:29:32.160 --> 00:29:33.160 align:middle line:90% Let me put that on hold. 00:29:33.160 --> 00:29:35.077 align:middle line:84% I'm going to answer that in about two minutes. 00:29:35.077 --> 00:29:36.340 align:middle line:90% But it's a perfect question. 00:29:36.340 --> 00:29:39.320 align:middle line:90% 00:29:39.320 --> 00:29:42.110 align:middle line:90% How do we do that? 00:29:42.110 --> 00:29:43.380 align:middle line:90% Let's think about that. 00:29:43.380 --> 00:29:45.150 align:middle line:84% I mean that's a very good question. 00:29:45.150 --> 00:29:46.700 align:middle line:84% In fact, that's the main thing I want 00:29:46.700 --> 00:29:49.885 align:middle line:84% to convey in the next section of the lecture. 00:29:49.885 --> 00:29:53.250 align:middle line:90% 00:29:53.250 --> 00:29:54.880 align:middle line:90% How would I control that? 00:29:54.880 --> 00:29:58.140 align:middle line:84% Well, here's the scheme that we'll generally use. 00:29:58.140 --> 00:30:03.610 align:middle line:84% The magic thing I have is this constant g. 00:30:03.610 --> 00:30:09.270 align:middle line:84% So this constant g is essentially what sets the power. 00:30:09.270 --> 00:30:10.870 align:middle line:90% So what does the power-- 00:30:10.870 --> 00:30:13.730 align:middle line:84% what does the power look like here? 00:30:13.730 --> 00:30:21.110 align:middle line:84% p of t is equal to i line times v 00:30:21.110 --> 00:30:29.780 align:middle line:84% line, which is ultimately equal to g times v line 00:30:29.780 --> 00:30:31.250 align:middle line:90% square root of t. 00:30:31.250 --> 00:30:32.010 align:middle line:90% Right. 00:30:32.010 --> 00:30:33.500 align:middle line:90% So if this is-- 00:30:33.500 --> 00:30:40.100 align:middle line:84% this could be then g times v s squared sine squared of omega 00:30:40.100 --> 00:30:52.520 align:middle line:84% t, which I could also write as g vs squared over 2 times 1 00:30:52.520 --> 00:30:56.270 align:middle line:90% minus cosine of 2 omega t. 00:30:56.270 --> 00:31:03.500 align:middle line:84% So if I were to draw that out for you, 00:31:03.500 --> 00:31:07.370 align:middle line:84% what the power would look like is this. 00:31:07.370 --> 00:31:10.410 align:middle line:90% So this is p of t. 00:31:10.410 --> 00:31:14.880 align:middle line:90% 00:31:14.880 --> 00:31:21.101 align:middle line:84% It would have an average value that's gvs squared over 2. 00:31:21.101 --> 00:31:21.601 align:middle line:90% Right. 00:31:21.601 --> 00:31:24.487 align:middle line:90% 00:31:24.487 --> 00:31:31.280 align:middle line:84% And then it would pulsate up and down like this. 00:31:31.280 --> 00:31:32.550 align:middle line:90% That's all that equation says. 00:31:32.550 --> 00:31:34.260 align:middle line:90% Why does it pulsate up and down? 00:31:34.260 --> 00:31:37.970 align:middle line:84% Because when v and i are equal to zero, 00:31:37.970 --> 00:31:41.450 align:middle line:84% when the line voltage is zero, you're not drawing any power 00:31:41.450 --> 00:31:42.540 align:middle line:90% from the line. 00:31:42.540 --> 00:31:44.030 align:middle line:84% When the line voltage is really big 00:31:44.030 --> 00:31:45.920 align:middle line:84% and the current's really big, you're drawing a lot of power 00:31:45.920 --> 00:31:46.503 align:middle line:90% from the line. 00:31:46.503 --> 00:31:48.930 align:middle line:84% And on average, you get gvs squared over 2. 00:31:48.930 --> 00:31:49.430 align:middle line:90% OK. 00:31:49.430 --> 00:31:52.580 align:middle line:84% So the whole magic of the control 00:31:52.580 --> 00:31:54.440 align:middle line:84% is controlling what g is because I 00:31:54.440 --> 00:31:59.540 align:middle line:84% get to pick g because I'm picking how big I'm 00:31:59.540 --> 00:32:01.520 align:middle line:90% tracking my current to be. 00:32:01.520 --> 00:32:04.670 align:middle line:90% So here's how you'd go do it. 00:32:04.670 --> 00:32:15.680 align:middle line:84% You might say, OK, let me come in and let me take v line of t. 00:32:15.680 --> 00:32:16.410 align:middle line:90% OK. 00:32:16.410 --> 00:32:21.200 align:middle line:84% And I'm going to multiply v line of t, the instantaneous value, 00:32:21.200 --> 00:32:28.260 align:middle line:84% or, actually, maybe I just measure v x 00:32:28.260 --> 00:32:31.500 align:middle line:90% as the magnitude of v line of t. 00:32:31.500 --> 00:32:35.300 align:middle line:84% And I multiply it by some constant g. 00:32:35.300 --> 00:32:39.920 align:middle line:84% And this gives me i ref, which then I 00:32:39.920 --> 00:32:43.550 align:middle line:84% feed to my current controller for my boost converter. 00:32:43.550 --> 00:32:50.210 align:middle line:84% So an input to my control is what I chose g of t to be. 00:32:50.210 --> 00:32:55.260 align:middle line:84% Now what I'll do is I will measure v out. 00:32:55.260 --> 00:32:58.370 align:middle line:84% I'll have an output reference v ref. 00:32:58.370 --> 00:33:00.980 align:middle line:90% You know, maybe that's 400v. 00:33:00.980 --> 00:33:04.880 align:middle line:90% I will measure v out. 00:33:04.880 --> 00:33:06.960 align:middle line:84% So I'll go to the output of the boost converter. 00:33:06.960 --> 00:33:10.100 align:middle line:84% Or I called it v DC so let me call it v DC. 00:33:10.100 --> 00:33:12.860 align:middle line:84% I'll take the difference between these two 00:33:12.860 --> 00:33:16.040 align:middle line:90% and I'll have an error voltage. 00:33:16.040 --> 00:33:19.555 align:middle line:84% And then I'm going to run that into a compensator h of s. 00:33:19.555 --> 00:33:22.380 align:middle line:90% 00:33:22.380 --> 00:33:24.180 align:middle line:90% OK. 00:33:24.180 --> 00:33:25.140 align:middle line:90% h of s. 00:33:25.140 --> 00:33:26.780 align:middle line:90% And this is a high gain. 00:33:26.780 --> 00:33:30.240 align:middle line:90% 00:33:30.240 --> 00:33:34.570 align:middle line:84% And that's going to give me g of t. 00:33:34.570 --> 00:33:40.140 align:middle line:84% So if v DC falls below vref, v error gets bigger. 00:33:40.140 --> 00:33:43.620 align:middle line:84% I amplify that and I increase g of t. 00:33:43.620 --> 00:33:47.790 align:middle line:84% So I'm going to pick g of t big enough 00:33:47.790 --> 00:33:52.500 align:middle line:84% that I get enough power that the output voltage matches 00:33:52.500 --> 00:33:56.385 align:middle line:84% whatever I want, in this case, as I said, 400 volts. 00:33:56.385 --> 00:33:57.260 align:middle line:90% Does that make sense? 00:33:57.260 --> 00:33:59.890 align:middle line:90% 00:33:59.890 --> 00:34:04.180 align:middle line:84% So this is a typical kind of controller for a PFC control. 00:34:04.180 --> 00:34:06.830 align:middle line:84% Let me explain a couple of things here. 00:34:06.830 --> 00:34:11.714 align:middle line:84% Keep in mind what's the bandwidth of this thing? 00:34:11.714 --> 00:34:15.699 align:middle line:84% Well, g is supposed to be a constant over a cycle 00:34:15.699 --> 00:34:19.630 align:middle line:84% so that the AC current that I draw 00:34:19.630 --> 00:34:22.750 align:middle line:84% isn't wildly varying over half a line cycle. 00:34:22.750 --> 00:34:25.090 align:middle line:84% So the bandwidth of this controller 00:34:25.090 --> 00:34:29.290 align:middle line:84% tends to be really slow, like less than-- 00:34:29.290 --> 00:34:31.750 align:middle line:84% it shouldn't vary its output voltage 00:34:31.750 --> 00:34:35.380 align:middle line:84% very much over half a line cycle because if it starts doing that, 00:34:35.380 --> 00:34:37.900 align:middle line:84% then the current no longer looks sinusoidal. 00:34:37.900 --> 00:34:41.590 align:middle line:84% And it can only respond to slow variations. 00:34:41.590 --> 00:34:44.679 align:middle line:84% But as we'll see, what that mainly 00:34:44.679 --> 00:34:49.630 align:middle line:84% implies is because the bandwidth of this loop is low, 00:34:49.630 --> 00:34:52.030 align:middle line:84% this capacitor size here needs to be 00:34:52.030 --> 00:34:55.540 align:middle line:90% pretty big to hold things up. 00:34:55.540 --> 00:34:56.277 align:middle line:90% All right. 00:34:56.277 --> 00:34:58.610 align:middle line:84% And in fact, we're going to talk about that in a minute. 00:34:58.610 --> 00:35:00.620 align:middle line:84% That size of this capacitor right 00:35:00.620 --> 00:35:07.130 align:middle line:84% here tends to be very dominant things in most PFC rectifiers. 00:35:07.130 --> 00:35:12.440 align:middle line:84% Just to illustrate that, I've got one with me here. 00:35:12.440 --> 00:35:17.480 align:middle line:84% This part on your very left is basically the line filter, 00:35:17.480 --> 00:35:21.290 align:middle line:84% because we're switching and I got to keep the PWM junk out 00:35:21.290 --> 00:35:22.830 align:middle line:90% of the line. 00:35:22.830 --> 00:35:23.970 align:middle line:90% Has a fan. 00:35:23.970 --> 00:35:25.880 align:middle line:84% Then you'll see if you look carefully, 00:35:25.880 --> 00:35:27.360 align:middle line:84% you'll see these four diodes here. 00:35:27.360 --> 00:35:28.320 align:middle line:90% One, two, three, four. 00:35:28.320 --> 00:35:29.403 align:middle line:90% Those are the four diodes. 00:35:29.403 --> 00:35:31.870 align:middle line:90% 00:35:31.870 --> 00:35:35.230 align:middle line:84% The inductor is a little bit hard 00:35:35.230 --> 00:35:36.885 align:middle line:84% to see because it's buried in here. 00:35:36.885 --> 00:35:40.620 align:middle line:90% 00:35:40.620 --> 00:35:45.390 align:middle line:84% Then the main thing that you see is this block right here, 00:35:45.390 --> 00:35:47.580 align:middle line:90% which is all these capacitors. 00:35:47.580 --> 00:35:50.055 align:middle line:90% And that's this guy right here. 00:35:50.055 --> 00:35:51.930 align:middle line:84% So we're going to come back and talk to that. 00:35:51.930 --> 00:36:00.240 align:middle line:84% And then the rest of this thing is this top board is essentially 00:36:00.240 --> 00:36:02.730 align:middle line:90% this first stage. 00:36:02.730 --> 00:36:05.315 align:middle line:84% Then we got to talk about what we do after that. 00:36:05.315 --> 00:36:10.455 align:middle line:90% 00:36:10.455 --> 00:36:14.480 align:middle line:84% It's a little bit hard to see the inductor. 00:36:14.480 --> 00:36:16.810 align:middle line:84% But does that answer your question about control? 00:36:16.810 --> 00:36:21.930 align:middle line:84% So we need a very low bandwidth controller but we modulate that. 00:36:21.930 --> 00:36:23.480 align:middle line:84% We ultimately modulate one switch 00:36:23.480 --> 00:36:26.030 align:middle line:84% to control the current that then controls the output. 00:36:26.030 --> 00:36:28.100 align:middle line:90% Multiple loops. 00:36:28.100 --> 00:36:29.180 align:middle line:90% Yeah. 00:36:29.180 --> 00:36:31.370 align:middle line:84% STUDENT: I don't understand how [INAUDIBLE] 00:36:31.370 --> 00:36:35.562 align:middle line:90% remaining half cycle. 00:36:35.562 --> 00:36:37.520 align:middle line:84% DAVID PERREAULT: Because I'm telling it to you? 00:36:37.520 --> 00:36:38.900 align:middle line:90% In some sense, right? 00:36:38.900 --> 00:36:42.000 align:middle line:90% 00:36:42.000 --> 00:36:45.210 align:middle line:84% Suppose this compensator is acting really 00:36:45.210 --> 00:36:48.420 align:middle line:84% slowly so that g is, roughly speaking, 00:36:48.420 --> 00:36:50.670 align:middle line:90% a constant for some time period. 00:36:50.670 --> 00:36:53.940 align:middle line:84% Then all I'm doing is I'm measuring the line voltage. 00:36:53.940 --> 00:36:58.050 align:middle line:84% I'm making a multiple of it and creating a current reference. 00:36:58.050 --> 00:37:00.720 align:middle line:84% And then I have another inner loop, maybe 00:37:00.720 --> 00:37:03.180 align:middle line:84% a hysteretic current control, that switch-- 00:37:03.180 --> 00:37:07.620 align:middle line:84% if the inductor current is too far below i ref, 00:37:07.620 --> 00:37:09.840 align:middle line:84% I turn the switch on until it ramps up. 00:37:09.840 --> 00:37:12.180 align:middle line:84% And once it gets a little bit too big, I turn it off 00:37:12.180 --> 00:37:14.490 align:middle line:84% and then the diode turns on and the current ramps down. 00:37:14.490 --> 00:37:16.530 align:middle line:84% And I'll get this kind of choppy current 00:37:16.530 --> 00:37:20.820 align:middle line:90% that roughly follows i ref. 00:37:20.820 --> 00:37:21.990 align:middle line:90% That make sense? 00:37:21.990 --> 00:37:24.540 align:middle line:84% That's all happening at some high frequency, the switching 00:37:24.540 --> 00:37:25.690 align:middle line:90% frequency. 00:37:25.690 --> 00:37:29.280 align:middle line:84% The component I care about for power factor purposes 00:37:29.280 --> 00:37:33.180 align:middle line:84% is the local average of that current 00:37:33.180 --> 00:37:34.900 align:middle line:84% because that's what's being fed back. 00:37:34.900 --> 00:37:36.240 align:middle line:84% And there's some additional filtering here 00:37:36.240 --> 00:37:37.282 align:middle line:90% to get rid of the ripple. 00:37:37.282 --> 00:37:39.850 align:middle line:90% 00:37:39.850 --> 00:37:41.180 align:middle line:90% Any other questions? 00:37:41.180 --> 00:37:45.070 align:middle line:90% 00:37:45.070 --> 00:37:50.510 align:middle line:84% So that's the basic idea of a PFC rectifier control. 00:37:50.510 --> 00:37:51.640 align:middle line:90% Now note one thing. 00:37:51.640 --> 00:37:53.120 align:middle line:90% I mentioned this before. 00:37:53.120 --> 00:37:57.370 align:middle line:84% This node is nothing like this node. 00:37:57.370 --> 00:37:59.800 align:middle line:84% These aren't at the same potential. 00:37:59.800 --> 00:38:02.080 align:middle line:84% So it's a little bit hard to use because if I'm 00:38:02.080 --> 00:38:04.580 align:middle line:84% plugging into the wall and one of one of the sides 00:38:04.580 --> 00:38:06.580 align:middle line:84% of this thing that I'm plugging into is neutral, 00:38:06.580 --> 00:38:08.270 align:middle line:90% that's very close to the ground. 00:38:08.270 --> 00:38:12.100 align:middle line:84% It's ultimately a DC connected to ground. 00:38:12.100 --> 00:38:12.610 align:middle line:90% Yeah. 00:38:12.610 --> 00:38:14.277 align:middle line:84% I better not connect this node to ground 00:38:14.277 --> 00:38:15.850 align:middle line:90% because bad things will happen. 00:38:15.850 --> 00:38:18.070 align:middle line:84% But on the other hand, my computer-- 00:38:18.070 --> 00:38:20.830 align:middle line:84% first of all, it doesn't need 400 volts. 00:38:20.830 --> 00:38:23.750 align:middle line:84% It needs, ultimately, one volt. Right. 00:38:23.750 --> 00:38:26.810 align:middle line:84% But intermediate in your desktop machine, 00:38:26.810 --> 00:38:28.730 align:middle line:84% it probably steps it down to 12 volts 00:38:28.730 --> 00:38:30.700 align:middle line:84% and then there's another converter 00:38:30.700 --> 00:38:34.220 align:middle line:84% that goes from 12 volts to 1 volt to run the processor. 00:38:34.220 --> 00:38:40.830 align:middle line:84% So ultimately, we need, first of all, isolation, 00:38:40.830 --> 00:38:43.840 align:middle line:84% because this node isn't galvanically isolated from here. 00:38:43.840 --> 00:38:46.627 align:middle line:84% And we do need our microprocessor really 00:38:46.627 --> 00:38:48.210 align:middle line:84% referenced to ground because you don't 00:38:48.210 --> 00:38:50.790 align:middle line:84% want to touch the case of your computer and get shocked. 00:38:50.790 --> 00:38:53.150 align:middle line:90% So you need some isolation. 00:38:53.150 --> 00:38:55.390 align:middle line:84% We also need a large voltage conversion. 00:38:55.390 --> 00:38:59.940 align:middle line:84% So usually, after this PFC stage, 00:38:59.940 --> 00:39:01.920 align:middle line:84% the thing I drew as a resistor here 00:39:01.920 --> 00:39:04.180 align:middle line:90% is some other DC to DC stage. 00:39:04.180 --> 00:39:08.110 align:middle line:84% So what does that DC to DC stage look like? 00:39:08.110 --> 00:39:10.770 align:middle line:84% It could look like any kind of isolated DC to DC converter 00:39:10.770 --> 00:39:11.760 align:middle line:90% we're talking about. 00:39:11.760 --> 00:39:17.310 align:middle line:84% It could be just maybe I split the bus in two 00:39:17.310 --> 00:39:21.780 align:middle line:84% and I have a pair of switches and a transformer, 00:39:21.780 --> 00:39:24.780 align:middle line:84% and then I run the other side of this transformer 00:39:24.780 --> 00:39:26.476 align:middle line:90% into a diode rectifier. 00:39:26.476 --> 00:39:29.790 align:middle line:90% 00:39:29.790 --> 00:39:32.970 align:middle line:84% And that comes out to my 12 volts, for example. 00:39:32.970 --> 00:39:36.710 align:middle line:84% And that powers my next power supply. 00:39:36.710 --> 00:39:40.810 align:middle line:84% Or maybe I have multiple outputs from next stage. 00:39:40.810 --> 00:39:45.160 align:middle line:84% You have plus and minus 12 and plus 5, whatever I need. 00:39:45.160 --> 00:39:48.410 align:middle line:84% But I will usually have some subsequent stage. 00:39:48.410 --> 00:39:51.010 align:middle line:84% And in fact, the other part of that converter, the other board 00:39:51.010 --> 00:39:53.320 align:middle line:84% I'm passing around, is the subsequent stages 00:39:53.320 --> 00:39:56.530 align:middle line:84% to provide from the high voltage rectifier 00:39:56.530 --> 00:39:59.530 align:middle line:90% down to lower voltage loads. 00:39:59.530 --> 00:40:03.730 align:middle line:84% And 400 volts is kind of standard, A, 00:40:03.730 --> 00:40:07.000 align:middle line:84% because it matches across what all 00:40:07.000 --> 00:40:09.280 align:middle line:84% the different universal input voltages across 00:40:09.280 --> 00:40:13.307 align:middle line:84% around the world for line inputs and, as a consequence, 00:40:13.307 --> 00:40:14.890 align:middle line:84% you can get really good energy storage 00:40:14.890 --> 00:40:18.760 align:middle line:84% capacitors and a bunch of other really good cheap elements 00:40:18.760 --> 00:40:20.270 align:middle line:90% to build your converter there. 00:40:20.270 --> 00:40:21.860 align:middle line:90% And so then you have two stages. 00:40:21.860 --> 00:40:24.023 align:middle line:84% You have a first stage that does that, then you 00:40:24.023 --> 00:40:26.440 align:middle line:84% have a transformation and isolation stage, which gives you 00:40:26.440 --> 00:40:28.762 align:middle line:84% some low voltage, typically 12 volts, 00:40:28.762 --> 00:40:30.970 align:middle line:84% but it can be other voltages, and servers, and things 00:40:30.970 --> 00:40:31.840 align:middle line:90% like that. 00:40:31.840 --> 00:40:33.662 align:middle line:84% And then you have usually another converter 00:40:33.662 --> 00:40:36.370 align:middle line:84% that gets like this more or less a buck converter or some variant 00:40:36.370 --> 00:40:38.260 align:middle line:84% that gets you very high bandwidth control 00:40:38.260 --> 00:40:40.512 align:middle line:90% over your microprocessor supply. 00:40:40.512 --> 00:40:43.220 align:middle line:84% So hence you can see we're going through lots of power conversion 00:40:43.220 --> 00:40:46.210 align:middle line:90% stages here. 00:40:46.210 --> 00:40:46.990 align:middle line:90% Questions? 00:40:46.990 --> 00:40:50.570 align:middle line:90% 00:40:50.570 --> 00:40:53.300 align:middle line:84% STUDENT: What do you refer to by bandwidth in this case? 00:40:53.300 --> 00:40:55.220 align:middle line:84% DAVID PERREAULT: So what I mean by bandwidth 00:40:55.220 --> 00:41:00.183 align:middle line:90% is this gain stage-- 00:41:00.183 --> 00:41:01.850 align:middle line:84% maybe that's an integrator or maybe it's 00:41:01.850 --> 00:41:06.560 align:middle line:84% a PI controller-- oughtn't vary this signal 00:41:06.560 --> 00:41:13.040 align:middle line:84% on a time scale that approaches half of a line cycle. 00:41:13.040 --> 00:41:16.780 align:middle line:84% So maybe if half of a line cycle is 120 hertz, 00:41:16.780 --> 00:41:19.930 align:middle line:84% maybe this thing varies only like 10 hertz or something 00:41:19.930 --> 00:41:24.160 align:middle line:84% like that or it can be very slow. 00:41:24.160 --> 00:41:24.660 align:middle line:90% OK. 00:41:24.660 --> 00:41:27.390 align:middle line:84% That means you need a lot of energy storage 00:41:27.390 --> 00:41:29.800 align:middle line:84% to hold things up in the intermediate time 00:41:29.800 --> 00:41:32.930 align:middle line:90% but that's necessary. 00:41:32.930 --> 00:41:35.180 align:middle line:90% OK. 00:41:35.180 --> 00:41:40.530 align:middle line:84% That brings me to my next point, which is the following. 00:41:40.530 --> 00:41:42.330 align:middle line:90% When we talked about-- 00:41:42.330 --> 00:41:45.210 align:middle line:84% even when we talked about inverters, 00:41:45.210 --> 00:41:48.430 align:middle line:90% I kind of brushed over-- 00:41:48.430 --> 00:41:51.600 align:middle line:84% I just said, oh, I have a perfect DC source 00:41:51.600 --> 00:41:56.340 align:middle line:84% and he's going to provide whatever I want. 00:41:56.340 --> 00:41:59.460 align:middle line:84% But I didn't worry how much power pulsations were 00:41:59.460 --> 00:42:01.140 align:middle line:90% coming from this DC source. 00:42:01.140 --> 00:42:01.700 align:middle line:90% Right. 00:42:01.700 --> 00:42:06.095 align:middle line:84% In reality, I almost always have some capacitor here. 00:42:06.095 --> 00:42:08.631 align:middle line:90% 00:42:08.631 --> 00:42:14.460 align:middle line:84% In this application, I said I'm going to have-- 00:42:14.460 --> 00:42:17.045 align:middle line:84% this isn't really necessarily exactly going to be a resistor. 00:42:17.045 --> 00:42:19.570 align:middle line:84% This is going to be another power supply stage. 00:42:19.570 --> 00:42:23.640 align:middle line:84% But this next power supply stage, really, it 00:42:23.640 --> 00:42:24.750 align:middle line:90% wants a DC voltage. 00:42:24.750 --> 00:42:26.430 align:middle line:90% It wants to draw a DC current. 00:42:26.430 --> 00:42:33.330 align:middle line:84% So really, this capacitor is going 00:42:33.330 --> 00:42:35.580 align:middle line:84% to take the difference between instantaneous-- 00:42:35.580 --> 00:42:38.460 align:middle line:84% whatever power this thing is going to provide instantaneously 00:42:38.460 --> 00:42:41.760 align:middle line:84% and whatever the next stage instantaneously wants. 00:42:41.760 --> 00:42:42.390 align:middle line:90% OK. 00:42:42.390 --> 00:42:44.290 align:middle line:90% So if we thought of-- 00:42:44.290 --> 00:42:44.790 align:middle line:90% let's see. 00:42:44.790 --> 00:42:45.957 align:middle line:90% Where's my original drawing? 00:42:45.957 --> 00:42:48.570 align:middle line:84% If we thought of this box over here 00:42:48.570 --> 00:42:52.590 align:middle line:84% as being an AC to DC rectifier, I just 00:42:52.590 --> 00:42:58.860 align:middle line:84% plotted for you what the power versus 00:42:58.860 --> 00:43:05.310 align:middle line:90% time that is coming out of-- 00:43:05.310 --> 00:43:09.610 align:middle line:84% that's the power versus time that's crossing this node. 00:43:09.610 --> 00:43:14.560 align:middle line:84% This p of t is basically what's coming out of this device 00:43:14.560 --> 00:43:16.330 align:middle line:90% into this network. 00:43:16.330 --> 00:43:18.790 align:middle line:84% And what you can see is it's actually pulsating 00:43:18.790 --> 00:43:20.240 align:middle line:90% at twice the line frequency. 00:43:20.240 --> 00:43:26.930 align:middle line:84% So this basically every half cycle-- 00:43:26.930 --> 00:43:28.270 align:middle line:90% maybe I'll move this up. 00:43:28.270 --> 00:43:31.070 align:middle line:90% 00:43:31.070 --> 00:43:35.480 align:middle line:84% Every half cycle, both the line current and the line voltage 00:43:35.480 --> 00:43:36.913 align:middle line:90% go back to zero. 00:43:36.913 --> 00:43:39.080 align:middle line:84% And when the line current and line voltage are zero, 00:43:39.080 --> 00:43:40.663 align:middle line:84% there's no power coming from the line. 00:43:40.663 --> 00:43:42.525 align:middle line:84% In fact, it doesn't matter what current I 00:43:42.525 --> 00:43:43.650 align:middle line:90% want to draw from the line. 00:43:43.650 --> 00:43:45.690 align:middle line:84% If there's no line voltage, I can't get any current. 00:43:45.690 --> 00:43:47.023 align:middle line:90% I can't get any power out of it. 00:43:47.023 --> 00:43:53.030 align:middle line:84% So that's why I have this square law power versus time. 00:43:53.030 --> 00:43:54.410 align:middle line:90% OK. 00:43:54.410 --> 00:44:03.560 align:middle line:84% Now if I imagined that the orange is what's being sourced-- 00:44:03.560 --> 00:44:06.330 align:middle line:84% so that's what power is coming to here. 00:44:06.330 --> 00:44:15.380 align:middle line:84% If I imagined what I want going to my load is DC power, 00:44:15.380 --> 00:44:16.710 align:middle line:90% what does that look like? 00:44:16.710 --> 00:44:19.250 align:middle line:84% Well, if I have a DC voltage and a DC current drawn 00:44:19.250 --> 00:44:21.290 align:middle line:84% by my next stage, my next converter 00:44:21.290 --> 00:44:23.220 align:middle line:84% stage-- it's not really a resistor-- 00:44:23.220 --> 00:44:26.000 align:middle line:84% it basically wants to look like this. 00:44:26.000 --> 00:44:27.620 align:middle line:84% That's what I'm controlling is I'm 00:44:27.620 --> 00:44:32.850 align:middle line:84% controlling the average power going to the load right here. 00:44:32.850 --> 00:44:36.420 align:middle line:84% So what about the difference between the instantaneous power 00:44:36.420 --> 00:44:37.930 align:middle line:90% and the average power? 00:44:37.930 --> 00:44:41.270 align:middle line:90% Where is that being stored? 00:44:41.270 --> 00:44:43.680 align:middle line:84% Conservation of energy is flowing in one place 00:44:43.680 --> 00:44:45.000 align:middle line:90% and flowing out the other. 00:44:45.000 --> 00:44:48.450 align:middle line:84% If they're not equal, it's got to be stored somewhere. 00:44:48.450 --> 00:44:52.140 align:middle line:84% And precisely where it's stored is in that capacitor. 00:44:52.140 --> 00:44:52.640 align:middle line:90% OK. 00:44:52.640 --> 00:44:55.040 align:middle line:84% Now the most common place on a PFC converter 00:44:55.040 --> 00:44:59.510 align:middle line:84% is to store it across this high voltage DC output 00:44:59.510 --> 00:45:03.920 align:middle line:84% because you can buy very good capacitors there. 00:45:03.920 --> 00:45:07.910 align:middle line:84% But what I'm trying to tell you is the energy going 00:45:07.910 --> 00:45:12.380 align:middle line:84% into that capacitor, basically, in the first part 00:45:12.380 --> 00:45:15.560 align:middle line:84% of the line cycle, I said this is kind of t over 2. 00:45:15.560 --> 00:45:17.210 align:middle line:90% This is t over 4. 00:45:17.210 --> 00:45:19.790 align:middle line:90% 00:45:19.790 --> 00:45:22.640 align:middle line:84% In the first part of the line cycle-- and if I went negative, 00:45:22.640 --> 00:45:24.500 align:middle line:90% it would do this. 00:45:24.500 --> 00:45:36.180 align:middle line:84% So this is, in this time period, basically, the line 00:45:36.180 --> 00:45:38.010 align:middle line:90% isn't sourcing enough energy. 00:45:38.010 --> 00:45:41.890 align:middle line:84% It's sourcing less than the average. 00:45:41.890 --> 00:45:43.800 align:middle line:84% So during this time period, energy 00:45:43.800 --> 00:45:46.230 align:middle line:90% is coming out of the capacitor. 00:45:46.230 --> 00:45:50.010 align:middle line:84% And then in this time period, I'm 00:45:50.010 --> 00:45:52.540 align:middle line:84% drawing more energy out of the line than my load's using. 00:45:52.540 --> 00:45:54.720 align:middle line:84% And I'm recharging the capacitor. 00:45:54.720 --> 00:45:58.080 align:middle line:84% So at twice the line frequency, I'm charging and discharging 00:45:58.080 --> 00:45:59.610 align:middle line:90% that capacitor. 00:45:59.610 --> 00:46:02.280 align:middle line:84% So that capacitor has to be physically big enough 00:46:02.280 --> 00:46:04.680 align:middle line:84% or it has to be energy storage-wise big enough 00:46:04.680 --> 00:46:07.560 align:middle line:90% to store that much energy. 00:46:07.560 --> 00:46:12.210 align:middle line:84% And that sets a bound on the energy storage requirement. 00:46:12.210 --> 00:46:16.080 align:middle line:84% Now the same thing is true in the inverter. 00:46:16.080 --> 00:46:22.070 align:middle line:84% Suppose this was the AC grid and this was a solar panel. 00:46:22.070 --> 00:46:26.420 align:middle line:84% I don't want my solar panel pulsating. 00:46:26.420 --> 00:46:28.520 align:middle line:90% I don't want my solar panel-- 00:46:28.520 --> 00:46:31.820 align:middle line:84% he doesn't want it delivering 100 watts 00:46:31.820 --> 00:46:35.310 align:middle line:84% in one time frame and 0 watts in the next for an average of 50. 00:46:35.310 --> 00:46:39.780 align:middle line:84% He wants to source DC current and DC voltage. 00:46:39.780 --> 00:46:44.930 align:middle line:84% So that means-- but if I'm going to deliver energy into the grid 00:46:44.930 --> 00:46:48.410 align:middle line:84% at unity power factor, which is what I want to do, 00:46:48.410 --> 00:46:51.930 align:middle line:84% that means this power into the AC grid is pulsating. 00:46:51.930 --> 00:46:54.610 align:middle line:84% It's just the reverse of that waveform. 00:46:54.610 --> 00:46:59.350 align:middle line:84% So I still need some big capacitor to buffer the energy. 00:46:59.350 --> 00:47:01.540 align:middle line:84% So whether I'm going AC to DC or DC 00:47:01.540 --> 00:47:08.200 align:middle line:84% to AC, if I have pure DC power flow on one side and unity power 00:47:08.200 --> 00:47:11.020 align:middle line:84% factor AC on the other, there is no way around the fact 00:47:11.020 --> 00:47:12.910 align:middle line:84% that I got to store some energy somewhere. 00:47:12.910 --> 00:47:14.410 align:middle line:84% And you'll find people that say, I 00:47:14.410 --> 00:47:17.140 align:middle line:84% got this magic technique that's going to do it, 00:47:17.140 --> 00:47:21.762 align:middle line:84% except that conservation of energy rather forbids that. 00:47:21.762 --> 00:47:24.620 align:middle line:84% And I have feel like I got this magic way around it. 00:47:24.620 --> 00:47:28.400 align:middle line:84% No, you don't because, you know, conservation of energy holds. 00:47:28.400 --> 00:47:30.430 align:middle line:90% So somewhere in your circuit-- 00:47:30.430 --> 00:47:33.340 align:middle line:84% it doesn't have to be across the input or the output, 00:47:33.340 --> 00:47:43.360 align:middle line:84% but if you're going to have AC voltage and AC current 00:47:43.360 --> 00:47:46.840 align:middle line:84% on the other side that's at unity power factor and a DC 00:47:46.840 --> 00:47:54.500 align:middle line:84% voltage on the other and a DC current-- 00:47:54.500 --> 00:47:58.140 align:middle line:84% so this is i AC and this is i DC-- 00:47:58.140 --> 00:48:00.430 align:middle line:84% somewhere in your circuit you either need 00:48:00.430 --> 00:48:02.510 align:middle line:90% an inductor or a capacitor. 00:48:02.510 --> 00:48:05.020 align:middle line:84% You need some third place that's going 00:48:05.020 --> 00:48:09.970 align:middle line:84% to store the instantaneous power between v DC i DC, 00:48:09.970 --> 00:48:14.200 align:middle line:84% and the pulsating AC power v AC i AC. 00:48:14.200 --> 00:48:17.700 align:middle line:84% Does that make sense to everybody? 00:48:17.700 --> 00:48:21.780 align:middle line:84% Now I'm running out of time here, 00:48:21.780 --> 00:48:25.110 align:middle line:84% but it's very clear if I basically just integrate, 00:48:25.110 --> 00:48:29.617 align:middle line:84% if I take the integral of this right, that's 00:48:29.617 --> 00:48:30.450 align:middle line:90% an amount of energy. 00:48:30.450 --> 00:48:33.320 align:middle line:84% And that's how much energy that capacitor has to store. 00:48:33.320 --> 00:48:35.070 align:middle line:84% If I work through the integral, what I get 00:48:35.070 --> 00:48:43.620 align:middle line:84% is e store is exactly equal to p average, the DC power, 00:48:43.620 --> 00:48:47.220 align:middle line:84% divided by the AC line frequency. 00:48:47.220 --> 00:48:50.460 align:middle line:84% So it's worse at 50 hertz than 60 hertz by a little bit 00:48:50.460 --> 00:48:54.060 align:middle line:84% because I have to store it for longer. 00:48:54.060 --> 00:48:54.960 align:middle line:90% OK. 00:48:54.960 --> 00:48:58.530 align:middle line:84% So when we said I want to increase the switching 00:48:58.530 --> 00:49:01.190 align:middle line:84% frequency of my converter to make the components smaller, 00:49:01.190 --> 00:49:04.170 align:middle line:84% That's all well and good, but if I'm delivering energy 00:49:04.170 --> 00:49:06.720 align:middle line:84% to the line at unity power factor, 00:49:06.720 --> 00:49:08.910 align:middle line:84% I need to store a certain amount of energy 00:49:08.910 --> 00:49:13.410 align:middle line:84% inside my converter for unity power factor anyways 00:49:13.410 --> 00:49:17.520 align:middle line:84% that's related to the line frequency. 00:49:17.520 --> 00:49:20.460 align:middle line:84% And that's going to set a minimum size on the capacitors, 00:49:20.460 --> 00:49:22.360 align:middle line:90% or inductors, or whatever I use. 00:49:22.360 --> 00:49:26.040 align:middle line:84% Most people use capacitors because they have better energy 00:49:26.040 --> 00:49:27.540 align:middle line:84% density, at least at small scales, 00:49:27.540 --> 00:49:30.390 align:middle line:84% like the single phase line scales. 00:49:30.390 --> 00:49:34.767 align:middle line:84% So any scheme you're going to come up with, 00:49:34.767 --> 00:49:36.100 align:middle line:90% you're going to have to do this. 00:49:36.100 --> 00:49:38.490 align:middle line:84% Now it turns out that this stored energy 00:49:38.490 --> 00:49:41.290 align:middle line:84% is the minimum that I need if I have unity power factor. 00:49:41.290 --> 00:49:43.650 align:middle line:84% If you allow me to cheat a little bit, 00:49:43.650 --> 00:49:46.260 align:middle line:84% maybe I don't have perfect unity power factor, 00:49:46.260 --> 00:49:48.280 align:middle line:84% you can effectively reduce that a bit. 00:49:48.280 --> 00:49:50.250 align:middle line:84% And essentially, you're using the line 00:49:50.250 --> 00:49:54.210 align:middle line:84% as your storage mechanism, which is allowed over a limited range. 00:49:54.210 --> 00:49:57.810 align:middle line:84% Real computer power supplies don't have 00:49:57.810 --> 00:49:59.320 align:middle line:90% to have perfect power factor. 00:49:59.320 --> 00:50:01.900 align:middle line:84% They just have to have good enough power factor. 00:50:01.900 --> 00:50:05.440 align:middle line:84% And so you can reduce this maybe by a factor of 2 or something 00:50:05.440 --> 00:50:08.850 align:middle line:84% if you're willing to let your line waveforms distort a bit. 00:50:08.850 --> 00:50:14.100 align:middle line:84% But generally, it's on this scale. 00:50:14.100 --> 00:50:16.290 align:middle line:84% And the details of how much you can do 00:50:16.290 --> 00:50:19.960 align:middle line:84% depend very much on what power level, what your application 00:50:19.960 --> 00:50:20.660 align:middle line:90% space is. 00:50:20.660 --> 00:50:23.200 align:middle line:84% There's rules regarding how much distortion 00:50:23.200 --> 00:50:27.730 align:middle line:84% you can have in line connected equipment depending upon, like I 00:50:27.730 --> 00:50:29.620 align:middle line:84% said, application and power level. 00:50:29.620 --> 00:50:31.360 align:middle line:84% But what that means is you've got 00:50:31.360 --> 00:50:33.313 align:middle line:84% to get clever in how you store this. 00:50:33.313 --> 00:50:35.230 align:middle line:84% And by the way, this is the amount of energy-- 00:50:35.230 --> 00:50:37.300 align:middle line:90% this is the swing in energy. 00:50:37.300 --> 00:50:40.420 align:middle line:84% So if I'm going to store that with very small ripple on that 00:50:40.420 --> 00:50:45.280 align:middle line:84% capacitor, that's 1/2 cv max squared by minus 1/2 cv min 00:50:45.280 --> 00:50:45.840 align:middle line:90% squared. 00:50:45.840 --> 00:50:48.580 align:middle line:84% If my ripple on my capacitor voltage becomes smaller, 00:50:48.580 --> 00:50:50.440 align:middle line:84% the energy storage rating of that capacitor 00:50:50.440 --> 00:50:53.260 align:middle line:84% is even bigger than this number by a lot. 00:50:53.260 --> 00:50:58.420 align:middle line:90% So there are pretty-- 00:50:58.420 --> 00:51:01.893 align:middle line:84% there are games you can play, but this 00:51:01.893 --> 00:51:04.310 align:middle line:84% is a minimum energy storage you're going to need to store. 00:51:04.310 --> 00:51:06.685 align:middle line:84% And generally, if you want small ripple on the capacitor, 00:51:06.685 --> 00:51:08.180 align:middle line:84% you even need much more than that. 00:51:08.180 --> 00:51:10.210 align:middle line:84% And the lecture notes and the text 00:51:10.210 --> 00:51:13.650 align:middle line:84% go into the details of those calculations. 00:51:13.650 --> 00:51:15.640 align:middle line:84% So I'm out of time to talk about this. 00:51:15.640 --> 00:51:18.180 align:middle line:84% Are there any final questions before we wrap up and move on 00:51:18.180 --> 00:51:18.860 align:middle line:90% to a new topic? 00:51:18.860 --> 00:51:21.890 align:middle line:90% 00:51:21.890 --> 00:51:22.710 align:middle line:90% OK, great. 00:51:22.710 --> 00:51:26.300 align:middle line:84% So next class, we'll have a little fun. 00:51:26.300 --> 00:51:28.275 align:middle line:84% And then when we come back after spring break, 00:51:28.275 --> 00:51:29.900 align:middle line:84% we're going to start to talk about what 00:51:29.900 --> 00:51:31.650 align:middle line:84% happens when I go up in power and we start 00:51:31.650 --> 00:51:32.880 align:middle line:90% to use three phase systems. 00:51:32.880 --> 00:51:35.930 align:middle line:84% So have a great-- if I don't see you, have a great break. 00:51:35.930 --> 00:51:38.440 align:middle line:90% And hope to see you tomorrow. 00:51:38.440 --> 00:51:41.000 align:middle line:90%