Skip to main content
Loading Explore guides…
Power Electronics · Acedra
Home
Explore
Other
Power Electronics
Sign in to save
Chat
If YouTube asks you to sign in, open the video on YouTube.
Watch on YouTube
Reload player
Transcript
86 segments
Copy
Hide video
0:12
so I will just go through the oldfashioned paper uh syllabus so the course is going to be taught on canvas so the canvas site has been published uh we will for for uh homeworks and things like that they'll be handed out and turned in on paper but you can download them from canvas as well um the classes are going to be here Mondays Wednesdays and Thursdays so on usual class schedules 1 pm uh I've mentioned the textbook there are some other textbooks that you might
0:49
find Handy and I've listed those in the course handout those are completely optional you don't have to buy them the libraries also have copies um the way homeworks will work in this class is that will typically be issued on a Monday and do the following Monday okay and uh for the most part you are allowed to collaborate and talk about the homework problems so you feel free to get together and discuss the problems that there it's intended that you do so
1:22
the only constraint we have is that you must hand in your own solution right so so you can trade ideas but in the end the thing you write up it can't be a copy your neighbors it has to be your solution but you can base it on uh you know ideas you've exchanged with others okay for those who don't know anybody or or don't have access to study partners and may have questions first of all there will be office hours uh Mon's
1:49
office hours will be Thursdays 4: to 5: p.m. and Fridays 4 to 5:00 P p.m. in 10178 in building 10 okay but there are also a number of students students in the Le laboratory 1050 who have had this class before will be happy to answer any questions and a few of those students are listed in the uh course description we've also decided not to have exams this term or in-class exams rather we're going to have assessments which are essentially take-home mini
2:24
quizzes uh they will generally be uh um they'll be generally issued weekly and this says they're going to be issued starting on March 1st I should check if that yeah starting on March 1st they'll be issued weekly they'll be issued on a Wednesday that will be due the next day Thursday and those will be submitted through canvas through grade scope um as for homeworks we can take late homeworks if you arrange it ahead of
2:57
time and there's some compelling reason why they're late assessments are a different story also the collaboration policy for assessments is different you cannot collaborate or discuss the problems at all for assessments and and you know we can't prove or not prove that you're doing so but this is you know this is an exam effectively so don't discuss it with your neighbors and don't discuss anything until the solutions are out
3:20
because there may be people who have made some special arrangement for because they're traveling or or for whatever reason to hand it in late okay so we're going to have homework and assessments and the goal of the assessments really is instead of a you sort of very few high stakes opportunities to show your abilities the assessments are sort of distributed in low stakes and focused and gives you a better opportunity to show you what you really know okay so please complete them
3:50
entirely on your own no consultation the only thing you're allowed to do is ask the core staff clarifying questions just the way you might in an exam okay and uh as for the assessments you can use any of the course materials you know read the book whatever you want uh do not go outside and try to use the worldwide web and for that matter the use of Bibles is also prohibited I know that there's collections of old 6334 materials floating around you're not
4:24
supposed to be Consulting those okay this just supposed to be a measure of what you've learned okay okay so the grading will be based on three components homeworks are going to be 40% these assessments will be 50% and there's also a final project which is 10% and the final project sounds like it's only 10% but it's the last thing we look at when we're going to assign a grade to everybody and it really is your opportunity to put
4:52
together knowledge that you've learned throughout the class into a real it's on paper it's not a it's not a phys phical converter you will construct but it's a paper design but it's really your opportunity to show us how you've synthesized all this knowledge to be able to really design Power Electronics and I should say just as an aside in this class we only have a paper design or or but this complements nicely the
5:18
undergraduate Power Electronics class which has a lot of really nice lab activities and design activities there so even if you're a graduate student it's it can be a pretty good thing to take in terms of of uh rounding out the LA your lab skill set in this area Okay um if you have any necessary technical accommodations don't have access to uh iPads or whatever else you need for grade scope please let us know we'll try to assist uh assist with that
5:53
okay so with that are there any questions about anything like associated with the course
6:03
mechanics okay so let me um give you a sense of what this course is going to be about and uh this is one of my favorite photos is actually one that uh Nicola Tesla mocked up he wasn't really sitting next to his Tesla coil when he did this or he might have gotten killed um he kind of double exposed this but more to the point uh the quote from him is if we could produce electrical effects of the required quality this whole planet and the conditions of existence on it could
6:37
be transformed and I think the sort of the more than a hundred years since he he said that or well more than 100 years since he said that uh have borne that out but it's also true that even today uh there's really revolutions happening in the way we use energy everything's being electrified from vehicles to transportation to power generation from renewable resources and um handling all that requires some means of processing controlling and converting energy and
7:12
that's really what we're about processing controlling converting electrical energy if you look at what the uh itle e the which is sort of the governing body of electrical engineering says about Power Electronics it says this technology encompasses the use of electronic components the application of circuit Theory and design techniques and the development of analytical tools towards efficient electronic conversion control and conditioning of electric power and
7:39
that's what we're really about here so we're going to do circuit Theory we're going to learn design techniques we're going to learn about all the components you need to do this we're going to learn about controls how do you put it all together to make energy conversion systems okay so as I mentioned the primary function of Power Electronics is to take sort of electrical energy in one form and convert it into some other form
8:03
you need uh it's really a core technology in the electrical infrastructure it used to be that the AC grid was generators and you'd connect it up to things like directly things like Motors or lighting or whatever but that's pretty much changed at this point right lighting is LED lighting you need power supplies to go between the grid and the lighting same thing heavily loads computers Motors everything else you need energy tends to flow through
8:30
one or even several layers of power conversion circuitry from the principal source to the final usage okay and so the Power Electronics first of all you know the efficiency of that is very important but also how you do it impacts the quality of the final system so the Power Electronics can really be a major factor impacting what you can and can't do and how well it works okay so if you showed up you know hundred years ago this is what Power Electronics would
9:03
look like right some vacuum tubes and some Transformers and that kind of thing interestingly of course it's nothing like that today but with the techniques you're going to learn in this course you could actually go back and analyze this thing and figure out what it did right so some foundational ideas that we're going to come back to which can be 100 years old but there's also elements that are extremely new okay and today you
9:29
know this this was fancy 100 years ago today Power Electronics is everywhere from I say from mowatt to gigawatts and and it does actually use switch mode power conversion down at those power levels this is actually a a multi-watt power supply and this is literally at the gigawatt scale so if you if you go out to S the Sandy Pond terminal there is a power converter that takes two gws coming down from Canada hydro and converts it to AC to power homes and everything else around here right so and
10:00
the techniques that we're going to learn in this class really span the entire range right so some of the details change and we'll learn about that but there's underlying principles that that cut across all kinds of electrical energy conversion systems okay what kind of applications well portable Electronics this slightly older an iPhone 5 and you think okay iPhones got radio transmitters and displays and other stuff in it but it turns out that
10:27
a large fraction of the volume and board area is actually associated with energy conversion in the thing because no matter what you're doing you're processing energy to process information right so something like 40% in this of the motherboard in this example was associated with power conversion likewise you know at some point you're going to charge your phone or your or your iPad or your computer into the wall that's mostly Power
10:52
Electronics too all kinds of computers if you're in a data center there's several layers of power conversion between the AC group GD and the final set of processors okay this is more of what it looks like inside your home computer we'll actually learn exactly about those kind of converters and about all the components that are in them if you're going to communicate right the transmitters we tend to think of this as analog circuits to to make RF
11:21
transmitters but in fact Power Electronics are heavily embedded in any real communication systems to increase the efficiency of transmission all kinds of commercial applications whether you're you know doing LED lighting or this is actually from some water Purity device but of course it requires a power supply right so almost any use of energy these days requires a power supply even in your home I mentioned that it used to be that you'd connect
11:54
Motors up to the grid and they'd run and maybe You' turn them on and off something like that but no longer right if you want high performance you need to be able to modulate that energy so two examples here this is for an air conditioning unit and it uses an inverter a DC to AC converter inside it to drive the motor much more quietly and much more modulated for higher overall system efficiency even your dishwasher these days has power converters in it
12:23
because it's more efficient in this case quieter to do it that way okay IDE is that you might not think of as power converters medical applications this is this is actually a uh magnetic stimulator generates 5,000 amps pulse trains in a transducer coil to throw up magnetic fields that can trigger nerves this is an interesting one it's actually homework zero so the thing you're analyzing in the first homework just to break the rust off is actually this box
12:53
right here okay scientific applications you may not be processing energy but even if you just need to generate electric High electrical fields for whatever reason or magnetic fields as in the magnetic stimulator you need energy conversion circuits to do it then there's the sort of the more maybe the applications you might think of Transportation right let say that electric vehicle or a hybrid vehicle right you need Power Electronics to drive the energy conversion and this is not a
13:24
small thing first of all you need the Power Electronics to drive these things right secondly in fact as in one example they redes they redesigned the power converter for a Prius the the power train for the Prius the fuel economy went up by 5% just by redesigning the Power Electronics to be better so it has a huge impact on the overall application and of course that's um electric vehicles but traction right trains that's higher power but the same issue
13:59
actually even future trains this it's a little hard to see behind this railing that's a maglev magnetically levitated train along the Wayside over in the back corner you see this big building here inside that big building as these racks of Power Electronics now you better have pretty reliable Power Electronics if your vehicle's flying along at 400 kmers an hour floating on you know that far off the ground right so not only do you need efficiency but you need reliability
14:26
and precision okay even Strang things uh this is this is an example of a drone just by powered by high voltage right you just apply high voltage it breaks down the air accelerates ions and you can use that for propulsion that's the first demonstration of it but it actually it's very similar in some regards to what people use for space propulsion you've heard of ion engines right the twin ion engine TIE fighter or what more practically they use to uh to
14:57
reposition satellites those require Power Electronics to generate high voltages and accelerate ions okay Power transmission and generation right that's so you're getting your energy from somewhere and increasingly we're getting it from renewable resources well generally the way things are trending you take some mechanical or solar or other source of energy and you transition it not only through a generator but through Power Electronics
15:25
to get there and that's true for terrestrial things things like this is a house rooftop PV system this is a micro inverter um Automotive Systems or even much smaller things like uh uh Power harvesting energy harvesting techniques you need Power Electronics in it also all kinds of industrial applications whether you're doing uh plasma processing for Semiconductor processing or you know you want to refine metals like a DC Arc furnace you need Power Electronics there too okay so
16:04
that's just sort of a way long way of saying power electronics are in almost everything you care about these days and it's only getting more so because we have to be better about how we use energy okay so what's inside a power converter and we're going to talk about this in much greater detail but if you want to think about it what we have is typically some kind of energy storage elements these could be inductors or capacitors or sometimes other things and
16:38
what we're going to do is we're going to use semiconductor switches and we're going to draw energy from some Source we're going to manipulate it somehow so we store it in these energy storage elements and then we're going to put it to the output and we're going to repeat that right so draw transform put it to the output okay because we do this on a cyclic basis we generate sort of Ripple and potentially noise that could interfere
17:04
with things like television or Electronics so you generally need filters to do that too we also of course need to control that flow of energy right we can't be stupid about it we have especially for something high performance like a microprocessor which might be changing its operation very very fast we need to control that flow so there's control circuitry we're going to be learning about all of the aspects of Designing all of these kinds of elements okay
17:36
so we're leveraging sort of everything from circuit design semiconductor devices passive components and materials increasingly packaging and Cooling and controls also matter and things have been getting better and better and better both because the um ways we can manufacture things get better and because the devices which we have our access to in order to implement these things get better okay and so we're going to look at some of the
18:06
different ways you can do that I'll just give you uh one example this is what you would find something like in a data center right so they come in they rectify the voltage they get it to sort of 400 Volts for reasons we'll go into this converter here was designed to take that 400 volts and bring it down to 12 volts okay that that tiny little thing a little bit bigger than a penny there actually can handle a kilowatt then you need more converters to take it down from there to
18:36
the one VT that the processor uses okay so the sort of a long way of saying all kinds of things are limited by energy and how we can control it right across all these applications and what we're usually trying to do is how figure out how to make them smaller and lighter right if you're taking up 40% of your iPhone you want make that thing smaller so it doesn't take that up and you can replace that volume either with nothing or with things that are more interesting to you
19:06
we need higher efficiency both for the converters and the systems how we process energy can matter to the not only the ultimate efficiency of the converter but the efficiency of the system how it uses energy can be determined by the Power Electronics we want higher performance that could mean higher bandwidth or other aspects and then there's all kinds of means that we we can use better electrical processing to enable new applications so these are
19:33
the kind of things that we're going to learn about this term I'll pause there i' I've been going on a while are there any questions about any of this before we get going this is just to sort of Orient you as to what we're going to focus the term
19:49
on I can put the slides on canvas sure any other questions okay okay I will just give you a slight notion okay just and this is a favorite thing I like to bring in just to show you the kind of things we're going to look at this term this is a piece of commercial Hardware from a company called MKS instruments that I just happen to have in my office this input piece is a filter so you don't create electrom magnetic interference and you don't generate noise you don't
20:31
want then this piece here takes energy from the 60 HZ grid and generates DC from it and it has to do it while making the whole thing look like a resistor to the grid so you don't mess up the grid okay that's what this part does then it has these isolated dcdc converters that can take that DC voltage and generate other DC voltages referenced in other ways and without worrying about uh sort of currents going back to ground okay it's galvanically isolated and then it
21:04
takes that energy and goes back DC to AC okay now in some systems you might go DC to AC for 60 hertz to to generate into the Grid or for a motor or something else this particular one has these outputs that are at 13 megahertz for driving plasmas to process semiconductors okay but you get all these kind of functions AC to DC DC to DC DC to AC and we're going to learn the first of all the underlying uh principles of doing all these things and how to design them okay
21:34
so the the the real goal is by the time you walk out of here you should have all the tools to go off and design Power Electronics for all kinds of applications and and in fact graduates of this class have worked on electric vehicles Char battery charger solar uh communication systems data centers the in fact the the power supply I usually use for my laptop and the in fact the wireless charger for my eyewatch were all designed or the teams were led by graduates of this class
22:13
right so this the goal is to give you the tools you need to go do these things okay so with that um let me start by just giving you a sense of um what goes on inside Power
22:40
Electronics so let's think of the simplest case I have some DC input voltage and I'd like some other DC voltage so suppose I have some input that's you know maybe it's 9 volts to 6 16 Vols I'm making that up arbitrarily but that's roughly what you might get in a typical vehicle right out of the cigarette lighter okay and suppose I want and I'll call this VN and suppose I want here's some load
23:16
that I'm going to represent with a resistor I'm going to call that V out okay and suppose I want EG 5 volts right to power something that takes five volts right what's the most obvious and simple way to get 5 volts at my output from some higher
23:41
voltage voltage divider precisely right I could come up here I could say okay let me put in some volt variable resistor and I'll drop down this voltage to give me the voltage I want and I'm done and in fact a lot of systems that's exactly more or less what they have inside them in fact inside most integrated circuits there's lots of these things going on okay well okay they don't do it quite this way what do they really do
24:18
they will take VN and what they will do is they'll use some kind of transistor a mosfet or a bipolar transistor and they will treat that essentially as a variable resistor right so I implement the variable resistor with a controlled transistor and I will come and I'll have some feedback loop I'll Fe feed in a reference voltage and I'll measure the output voltage and I'll control the Gate of this transistor and essentially make
24:49
that transistor look like a variable resistor and control the voltage division so that even if this voltage varies between 9 and 16 volts I always get my 5 Vols output Okay and like I said that's very common but what's the problem with this well there's a whole lot of problems with this right why why wouldn't you want to do this uh in typical operation efficiency terrible efficiency yes exactly so let's think about this if I
25:25
accept the fact let me call this current I in
25:33
okay and this current I out okay if this thing does act exactly like a variable resistor the input currents equal to the output current now this actually a real system might have some current that actually also goes to ground let's take the best case where the output current is equal to the input current okay what would be the efficiency of this Beast well the
26:05
efficiency the efficiency is equal to the output power over the input power right I'm drawing energy maybe from my car battery or whatever my battery source is and I'm delivering it to the output but not all of it's getting to the output so the output power is V out time I out and my input power is VN time I in and I just told you that I out was equal to I in in the best case so that's V out over VN right so if I'm coming in from 15
26:41
volts and I'm getting five volts that's 33% efficiency right I've taken 2/3 of my energy and thrown it away now if I got lots of energy floating around and I'm processing a microwatt maybe maybe I don't care maybe I'll live with that because this thing's pretty simple right it's a transistor it's a power transistor and some controls and they can often put all that on one integrated circuit or even as a subblock
27:09
on an integrated circuit I might still need some filtering it's not it's not quite as easy as it sounds but um pretty much it's relatively simple but my efficiency is miserable now if I thought about in your in your computer right your desktop computer typically the intermediate Supply that you're getting after it's sort of come in from the grid and been transformed down you get 12 volts right and let's say your computer is it sort of it
27:37
depends on what it's doing but say it's operating at a volt right so then you're less than 10% efficient right and if you think that you know you can have a microprocessor that's taking 200 amps at a volt or few hundred Watts suddenly if I've got less than 10% efficiency on 200 Watts that means I need to put in a few kilowatts well you can't even plug that into the wall never mind the fact you've just made a massive room heater right
28:03
that's that's like that'd be great for heating your dorm room um but pretty terrible for the overall system okay so the number one reason we don't like this solution is efficiency good thing it's simple bad thing it's terrible efficiency this technique I should have noted is what's known for historical reasons as a quote unquote linear power supply why linear I think only because analog circuits kind of a category of
28:43
them became known as quote unquote linear circuits there's nothing really that linear about it but this would be called a linear power converter or or some sometimes a linear regulator is what it would be called okay for obvious reasons I hate throwing away energy we're not going to talk about linear Regulators at all in this class and there's plenty of classes where you can learn about that we want to do things some better way that's not
29:09
going to burn lots of energy okay so ideally you know in my world the goal is to take as much of the input energy in and put it to the output right and that's important because think about it this way I I showed you a photo graph of something that was you know really tiny maybe that big right and that thick and was processing a kilowatt right if I don't do that at really high efficiency that thing will burn up right so in order to make something small I need to
29:45
make it efficient all right so we want almost all of the energy at the input to get to the output well how can we do that let's think of a completely different way we might achieve this same function function all right and here's the idea here's my
30:09
input I'm going to create a switch here single pole double throw switch now we're not going to go get physical switches we're probably going to get semiconductor devices and make it do something like this but we could use anything any technology that was practical as a switch okay and let me just Define if I'm going to define a switching function that I'm going to call Q of T if Q of T is one I'll connect the switch to the input if Q of T is
30:41
zero I'll connect the switch to the ground okay so this notion this voltage okay maybe I'll call this voltage
30:54
VX all right so one thing I could do is I could say okay let me just hook this up to my load here's my resistive load whatever it is and I'll call this V out all right well all right what would that look like well let me Define my switching
31:22
function I'm going to put the switch in the up position for a little while then I'll put it in the down position by setting the switching function to zero and then I'll just repeat that so I said we're going to operate in some kind of repetitive fashion here and so forth let me operate with some period T okay that's mean my switching period in this example I'm showing you is a fixed switching period okay and I will
31:50
keep the switch in the up position some fraction of the time that I'll call DT so D is a fraction zero is less than D is less than one okay so if I do that then what do I get for VX VX is going to look something like this okay um when the switch is in the up position VX equals
32:21
VN so this is VX when the switch is in the down position VX is equal to zero
32:31
okay and I rinse and repeat and I get this now now I have this pulsating voltage VX okay what's the average value of that voltage VX right I can take you know simple integration right one over T the integral of VX of T over a period T okay and what I would find is the average voltage of VX is equal to D * VN all right so I can create a waveform here whose average value is something different than VN just by controlling this timing D all right so now if my load resistor
33:19
here was a space heater you know maybe this is some load resistance RL and I wanted to modulate the power to that load resistance by controlling the average voltage on the load resistance then this technique would work great if on the other hand my load was a microprocessor and I start you know pulsing 12 volts between 12 volts and zero on it I'm probably going to blow it up right so that's no good all right but this notion is at least that I can
33:49
control an average voltage by pulsing a set a switch okay and this would be known as pwm or pulse width modulation because I control the average volage by the fraction of the time the switch is in one position versus the other okay so that's that's the basic concept we're going to be using how do I fix this little problem of in practice right what I wanted was a DC voltage what I got was a pulsating voltage that just happened to have the right average value well I
34:23
could go do something like this maybe I'll go back and say okay let me throw in a filter and extract out the component I want right I want the average value of VX so maybe I'll come back here and say okay let me throw in a filter and I'll use an inductor
34:47
here an l and if I want optionally I can put a capacitor here C okay and you know I think people can look at this filter block and recognize that as a low pass filter the DC component of VX passes through the filter to the output and the AC component of VX gets rejected by the filter and doesn't get to the output so in this case I might get an output voltage V out that looks something like this I'm going to sort of make this up but you know I'm amplifying
35:24
the Ripple but eventually it's going to filter the energy content of that and the fundamental and higher harmonic terms of VX are going to go away and the DC terms going to go through and I get an output voltage V out that's very close to whatever value I want and if I'm basically make the filter cut off hard enough I can't distinguish between V out and the average value of VX and I get exactly what I wanted Okay so we've essentially now created
36:00
a voltage converter that lets me use this pulsewidth modulation by controlling this duty cycle D to regulate the output just the way I wanted so instead of you know here I'm just changing the gate voltage on my transistor to control the output here I'm changing timing I'm going to control timing okay and by controlling timing I control average value and then I get what I want right any questions about that what's what's the
36:33
efficiency that is an excellent question the answer is um ideally theoretically the efficiency can be 100% in reality it can't be why do I say the efficiency can ideally be 100% well how would I implement this box in the real world usually I I don't get semiconductor single pole double throw switches the way I would usually build this Beast is like this okay I would usually have a first switch and a second switch implemented like this so I close this when Q of T is equal to
37:18
one and I close this one when Q of T is equal to zero okay and then I build my filter and then I put my load on here okay so what would be the efficiency of this thing well let's think about this um this is voltage Vex and this is voltage vout all
37:50
right what power is theoretically dissipated in my switch if I have an ideal switch has zero resistance when it's on and has infinite resistance when it's off what's that zero power why because the power dissipated the power that goes into this box let me call this V switch let me call this I switch okay well P switch the power going into the switch the power being dissipated in the switch is going to be V switch time I switch
38:28
okay well if it's an ideal switch then if the switch is on V switch is zero right it's ideal so it has no voltage drop when it's on so the power when it's on is zero when the switch is off it has infinite resistance so the switch is current zero so basically the power going into the switch if it's an ideal switch um is ideally zero so these these elements this ideal switch is a lossless element right likewise I wasn't I didn't just randomly
39:07
choose any filter here right I chose an LC filter why did I choose an LC filter I choose an LC filter because inductors and capacitors are energy storage elements if they're ideal then they store energy but they don't dissipate energy right so basically everything in the box here everything between the input and the output is a lossless element so then one would assume that if every element's lossless any energy walking in to the left comes
39:39
out to the right right and that's how that that kilowatt little 400 volt to 12vt converter I showed you um in the photo is about 97% efficient it's not 100% because you know the wires have some resistance and the switches have some on-state resistance a whole bunch of things that contribute to loss and we'll talk about that um but I can make it really close to 100% even though I might be doing a huge step down right so if I tried to build a linear regulator
40:09
that was going from 400 to 12 volts that' be about 2 and a half% efficient right so if I want to generate a kilowatt at 2 and a half% efficiency what is that 40 kilowatt input and instead what I get is sort of like 1.03 kilowatt input to generate a kilowatt output right so the whole Magic that we're going to talk about this term is how can I use sort of perfectly lossless elements draw energy in process it and put it out the other side okay and by the way I should
40:41
say not only did I say oh inductors and capacitors are lossless in principle lossless elements uh it wasn't an accident that we put an inductor here right because think about it when this switch is closed right I have V in on this side of the inductor and V out on this side of the inductor and I have current flowing this way right well what's happening when this switch is closed basically there's voltage across this inductor and current going through it we are storing
41:17
energy in that inductor so the difference in voltage between the input and the output is basically putting energy in the inductor in this the other part of the cycle when I turn this switch off and this switch on basically I'm taking now I have a negative voltage across the inductor I'm taking energy out of the inductor and put it in the output so essentially I'm using this inductor as a filter but it's also an intermediate store of energy
41:45
that lets me kind of take energy from the input and transfer to the output with a voltage conversion without losing any of the energy excellent question long answer to a short question any other
42:04
questions okay so as I said um my goal is to sort of first of all teach you a lot of the underlying principles this is the this is the world's if you will simplest switching power converter so the when we use this technique we also often say we're switched mode all right with the notion that we're going to use switches and energy storage elements to process energy and that's sort of what sits at the core of Power Electronics okay and as I said we're
42:35
going to look at all of the aspects how do you design these things how do you control them how do you design the components and by the time we're done you should be able to put it all together and and start designing Power Electronics of your own and you will for the final project okay so any final questions
42:59
okay we'll wrap up today and I will see everybody on Wednesday
Here to help you learn
Sign in to keep a private conversation with your course tutor.
Ask me anything about the material…
Sign in to chat