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Lecture 1: Introduction to Power Electronics — Transcript

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0:12so I will just go through the
0:15oldfashioned paper uh syllabus so the
0:20course is going to be taught on canvas
0:21so the canvas site has been published uh
0:24we will for for uh homeworks and things
0:27like that they'll be handed out and
0:30turned in on paper but you can download
0:33them from canvas as
0:35well um the classes are going to be here
0:39Mondays Wednesdays and Thursdays so on
0:41usual class schedules 1
0:44pm uh I've mentioned the textbook there
0:47are some other textbooks that you might
0:49find Handy and I've listed those in the
0:51course handout those are completely
0:53optional you don't have to buy them the
0:55libraries also have
0:57copies um the way homeworks will work in
1:01this
1:02class is that will typically be issued
1:05on a Monday and do the following Monday
1:08okay and uh for the most part you are
1:12allowed to collaborate and talk about
1:15the homework problems so you feel free
1:17to get together and discuss the problems
1:19that there it's intended that you do so
1:22the only constraint we have is that you
1:24must hand in your own solution right so
1:26so you can trade ideas but in the end
1:28the thing you write up it can't be a
1:29copy your neighbors it has to be your
1:32solution but you can base it on uh you
1:35know ideas you've exchanged with others
1:37okay for those who don't know
1:42anybody or or don't have access to study
1:45partners and may have questions first of
1:46all there will be office hours uh Mon's
1:49office hours will be Thursdays 4: to 5:
1:52p.m. and Fridays 4 to 5:00 P p.m. in
1:5410178 in building 10 okay but there are
1:58also a number of students students in
2:00the Le laboratory 1050 who have had this
2:03class before will be happy to answer any
2:05questions and a few of those students
2:07are listed in the uh course
2:12description we've also decided not to
2:14have exams this term or in-class exams
2:19rather we're going to have assessments
2:22which are essentially take-home mini
2:24quizzes uh they will generally be uh um
2:31they'll be generally issued weekly and
2:33this says they're going to be issued
2:35starting on March 1st I should check if
2:38that yeah starting on March 1st they'll
2:40be issued weekly they'll be issued on a
2:42Wednesday that will be due the next day
2:44Thursday and those will be submitted
2:47through canvas through grade
2:50scope
2:52um as for homeworks we can take late
2:55homeworks if you arrange it ahead of
2:57time and there's some compelling reason
2:58why they're late assessments are a
3:00different
3:01story also the collaboration policy for
3:04assessments is different you cannot
3:06collaborate or discuss the problems at
3:08all for assessments and and you know we
3:11can't prove or not prove that you're
3:13doing so but this is you know this is an
3:15exam effectively so don't discuss it
3:17with your neighbors and don't discuss
3:19anything until the solutions are out
3:20because there may be people who have
3:22made some special arrangement for
3:24because they're traveling or or for
3:26whatever reason to hand it in late okay
3:28so we're going to have homework and
3:30assessments and the goal of the
3:32assessments really is instead of a you
3:34sort of very few high stakes
3:37opportunities to show your abilities the
3:40assessments are sort of distributed in
3:42low stakes and focused and gives you a
3:45better opportunity to show you what you
3:46really know okay so please complete them
3:50entirely on your own no consultation the
3:53only thing you're allowed to do is ask
3:54the core staff clarifying questions just
3:56the way you might in an exam okay
4:00and uh as for the assessments you can
4:03use any of the course materials you know
4:05read the book whatever you want
4:09uh do
4:10not go outside and try to use the
4:14worldwide web and for that matter the
4:16use of Bibles is also prohibited I know
4:18that there's collections of old 6334
4:22materials floating around you're not
4:24supposed to be Consulting those okay
4:27this just supposed to be a measure of
4:28what you've learned okay okay so the
4:31grading will be based on three
4:32components homeworks are going to be
4:3540% these assessments will be
4:3850% and there's also a final project
4:41which is 10% and the final project
4:44sounds like it's only 10% but it's the
4:46last thing we look at when we're going
4:48to assign a grade to everybody and it
4:50really is your opportunity to put
4:52together knowledge that you've learned
4:54throughout the class into a real it's on
4:57paper it's not a it's not a phys phical
5:00converter you will construct but it's a
5:01paper design but it's really your
5:03opportunity to show us how you've
5:04synthesized all this knowledge to be
5:06able to really design Power Electronics
5:09and I should say just as an aside in
5:11this class we only have a paper design
5:13or or but this complements nicely the
5:18undergraduate Power Electronics class
5:20which has a lot of really nice lab
5:22activities and design activities there
5:24so even if you're a graduate student
5:26it's it can be a pretty good thing to
5:27take in terms of of uh rounding out the
5:30LA your lab skill set in this area
5:34Okay um if you have any necessary
5:39technical accommodations don't have
5:41access to uh iPads or whatever else you
5:44need for grade scope please let us know
5:46we'll try to assist uh assist with that
5:53okay so with that are there any
5:57questions about anything like associated
5:59with the course
6:03mechanics okay so let me um give you a
6:10sense of what this course is going to be
6:13about and uh this is one of my favorite
6:17photos is actually one that uh Nicola
6:20Tesla mocked up he wasn't really sitting
6:22next to his Tesla coil when he did this
6:23or he might have gotten killed um he
6:26kind of double exposed this but more to
6:28the point
6:30uh the quote from him is if we could
6:32produce electrical effects of the
6:33required quality this whole planet and
6:35the conditions of existence on it could
6:37be transformed and I think the sort of
6:40the more than a hundred years since he
6:42he said that or well more than 100 years
6:45since he said that uh have borne that
6:48out but it's also true that even
6:51today uh there's really revolutions
6:55happening in the way we use energy
6:57everything's being electrified from
6:59vehicles to transportation to power
7:02generation from renewable
7:04resources and um handling all that
7:08requires some means of processing
7:10controlling and converting energy and
7:12that's really what we're about
7:14processing controlling converting
7:15electrical
7:16energy if you look at what the uh itle e
7:21the which is sort of the governing body
7:23of electrical engineering says about
7:25Power Electronics it says this
7:27technology encompasses the use of
7:28electronic components
7:30the application of circuit Theory and
7:31design techniques and the development of
7:33analytical tools towards efficient
7:35electronic conversion control and
7:37conditioning of electric power and
7:39that's what we're really about here so
7:41we're going to do circuit Theory we're
7:43going to learn design techniques we're
7:44going to learn about all the components
7:46you need to do this we're going to learn
7:47about controls how do you put it all
7:50together to make energy conversion
7:52systems okay so as I mentioned the
7:56primary function of Power Electronics is
7:58to take sort of electrical energy in one
8:00form and convert it into some other form
8:03you need uh it's really a core
8:06technology in the electrical
8:07infrastructure it used to be that the AC
8:09grid was generators and you'd connect it
8:11up to things like directly things like
8:13Motors or lighting or whatever but
8:16that's pretty much changed at this point
8:18right lighting is LED lighting you need
8:20power supplies to go between the grid
8:22and the lighting same thing heavily
8:24loads computers Motors everything else
8:27you need energy tends to flow through
8:30one or even several layers of power
8:32conversion circuitry from the principal
8:35source to the final usage okay and so
8:38the Power Electronics first of all you
8:41know the efficiency of that is very
8:42important but also how you do it impacts
8:45the quality of the final system so the
8:48Power Electronics can really be a major
8:50factor impacting what you can and can't
8:52do and how well it works
8:56okay so if you showed up you know
8:59hundred years
9:01ago this is what Power Electronics would
9:03look like right some vacuum tubes and
9:05some Transformers and that kind of thing
9:09interestingly of course it's nothing
9:11like that today but with the techniques
9:14you're going to learn in this course you
9:15could actually go back and analyze this
9:17thing and figure out what it did right
9:19so some foundational ideas that we're
9:21going to come back to which can be 100
9:24years old but there's also elements that
9:26are extremely new okay and today you
9:29know this this was fancy 100 years ago
9:32today Power Electronics is everywhere
9:35from I say from mowatt to gigawatts and
9:38and it does actually use switch mode
9:39power conversion down at those power
9:41levels this is actually a a multi-watt
9:43power supply and this is literally at
9:45the gigawatt scale so if you if you go
9:48out to S the Sandy Pond terminal there
9:50is a power converter that takes two gws
9:53coming down from Canada hydro and
9:55converts it to AC to power homes and
9:58everything else around here right so and
10:00the techniques that we're going to learn
10:01in this class really span the entire
10:05range right so some of the details
10:06change and we'll learn about that but
10:08there's underlying principles that that
10:10cut across all kinds of electrical
10:12energy conversion systems
10:16okay what kind of applications well
10:18portable Electronics this slightly older
10:20an iPhone 5 and you think okay iPhones
10:23got radio transmitters and displays and
10:25other stuff in it but it turns out that
10:27a large fraction of the volume and board
10:30area is actually associated with energy
10:33conversion in the thing because no
10:34matter what you're doing you're
10:35processing energy to process information
10:37right so something like 40% in this of
10:39the motherboard in this example was
10:41associated with power
10:43conversion likewise you know at some
10:45point you're going to charge your phone
10:47or your or your iPad or your computer
10:49into the wall that's mostly Power
10:52Electronics too all kinds of computers
10:54if you're in a data center there's
10:56several layers of power conversion
10:58between the AC group GD and the final
11:01set of
11:02processors okay this is more of what it
11:05looks like inside your home computer
11:07we'll actually learn exactly about those
11:10kind of converters and about all the
11:12components that are in them if you're
11:14going to communicate right the
11:16transmitters we tend to think of this as
11:19analog circuits to to make RF
11:21transmitters but in fact Power
11:22Electronics are heavily embedded in any
11:25real communication systems to increase
11:27the efficiency of transmission
11:31all kinds of commercial applications
11:33whether you're you know doing LED
11:35lighting or this is actually from some
11:38water
11:39Purity device but of course it requires
11:42a power supply right
11:45so almost any use of energy these days
11:48requires a power
11:50supply even in your home I mentioned
11:52that it used to be that you'd connect
11:54Motors up to the grid and they'd run and
11:56maybe You' turn them on and off
11:58something like that but no longer right
11:59if you want high performance you need to
12:02be able to modulate that energy so two
12:04examples here this is for an air
12:07conditioning unit and it uses an
12:10inverter a DC to AC converter inside it
12:12to drive the motor much more quietly and
12:15much more modulated for higher overall
12:17system efficiency even your dishwasher
12:20these days has power converters in it
12:23because it's more efficient in this case
12:25quieter to do it that way okay IDE is
12:30that you might not think of as power
12:33converters medical applications this is
12:35this is actually a uh magnetic
12:39stimulator generates 5,000 amps pulse
12:41trains in a transducer coil to throw up
12:43magnetic fields that can trigger nerves
12:46this is an interesting one it's actually
12:47homework zero so the thing you're
12:49analyzing in the first homework just to
12:51break the rust off is actually this box
12:53right here okay scientific applications
12:57you may not be processing energy but
12:59even if you just need to generate
13:01electric High electrical fields for
13:03whatever reason or magnetic fields as in
13:05the magnetic stimulator you need energy
13:07conversion circuits to do it then
13:10there's the sort of the more maybe the
13:12applications you might think of
13:14Transportation right let say that
13:17electric vehicle or a hybrid vehicle
13:19right you
13:21need Power Electronics to drive the
13:23energy conversion and this is not a
13:24small thing first of all you need the
13:25Power Electronics to drive these things
13:28right secondly in fact as in one
13:31example they redes they
13:34redesigned the power converter for a
13:37Prius the the power train for the Prius
13:40the fuel economy went up by 5% just by
13:43redesigning the Power Electronics to be
13:45better so it has a huge impact on the
13:48overall application and of course that's
13:52um electric vehicles but traction right
13:56trains that's higher power but the same
13:58issue
13:59actually even future trains this it's a
14:01little hard to see behind this railing
14:03that's a maglev magnetically levitated
14:05train along the Wayside over in the back
14:08corner you see this big building here
14:10inside that big building as these racks
14:12of Power Electronics now you better have
14:14pretty reliable Power Electronics if
14:16your vehicle's flying along at 400 kmers
14:19an hour floating on you know that far
14:20off the ground right so not only do you
14:23need efficiency but you need reliability
14:26and precision okay even Strang
14:29things uh this is this is an example of
14:32a drone just by powered by high voltage
14:37right you just apply high voltage it
14:38breaks down the air accelerates ions and
14:41you can use that for propulsion that's
14:43the first demonstration of it but it
14:45actually it's very similar in some
14:47regards to what people use for space
14:49propulsion you've heard of ion engines
14:51right the twin ion engine TIE fighter or
14:54what more practically they use to uh to
14:57reposition satellites those require
14:59Power Electronics to generate high
15:00voltages and accelerate ions okay Power
15:05transmission and generation right that's
15:08so you're getting your energy from
15:10somewhere and increasingly we're getting
15:11it from renewable resources well
15:13generally the way things are trending
15:16you take some mechanical or solar or
15:19other source of energy and you
15:21transition it not only through a
15:24generator but through Power Electronics
15:25to get there and that's true for
15:27terrestrial things things like this is a
15:30house rooftop PV system this is a micro
15:33inverter
15:35um
15:36Automotive Systems or even much smaller
15:39things like uh
15:42uh Power harvesting energy harvesting
15:45techniques you need Power Electronics in
15:48it also all kinds of industrial
15:50applications whether you're doing uh
15:53plasma processing for Semiconductor
15:56processing or you know you want to
15:58refine metals like a DC Arc furnace you
16:02need Power Electronics there too okay so
16:04that's just sort of a way long way of
16:06saying power electronics are in almost
16:09everything you care about these days and
16:11it's only getting more so because we
16:13have to be better about how we use
16:15energy
16:19okay so what's inside a power converter
16:22and we're going to talk about this in
16:23much greater detail but if you want to
16:26think about it what we have
16:30is typically some kind of energy storage
16:33elements these could be inductors or
16:35capacitors or sometimes other things and
16:38what we're going to do is we're going to
16:40use semiconductor switches and we're
16:42going to draw energy from some Source
16:44we're going to manipulate it somehow so
16:46we store it in these energy storage
16:48elements and then we're going to put it
16:49to the output and we're going to repeat
16:51that right so draw transform put it to
16:55the output okay because we do this on a
16:58cyclic
16:59basis we generate sort of Ripple and
17:02potentially noise that could interfere
17:04with things like television or
17:05Electronics so you generally need
17:08filters to do that too we also of course
17:11need to control that flow of energy
17:13right we can't be stupid about it we
17:15have especially for something high
17:16performance like a microprocessor which
17:18might be changing its operation very
17:21very fast we need to control that flow
17:24so there's control circuitry we're going
17:26to be learning about all of the aspects
17:27of Designing
17:29all of these kinds of elements
17:34okay
17:36so we're leveraging sort of everything
17:38from circuit design semiconductor
17:41devices passive components and materials
17:43increasingly packaging and Cooling and
17:46controls also matter and things have
17:49been getting better and better and
17:51better both because the um ways we can
17:55manufacture things get better and
17:57because the devices which we have
18:00our access to in order to implement
18:03these things get better okay and so
18:05we're going to look at some of the
18:06different ways you can do that I'll just
18:09give you
18:11uh one example this is what you would
18:14find something like in a data center
18:16right so they come in they rectify the
18:18voltage they get it to sort of 400 Volts
18:21for reasons we'll go into this converter
18:24here was designed to take that 400 volts
18:26and bring it down to 12 volts okay
18:29that that tiny little thing a little bit
18:31bigger than a penny there actually can
18:32handle a kilowatt then you need more
18:35converters to take it down from there to
18:36the one VT that the processor uses okay
18:42so the sort of a long way of saying all
18:45kinds of things are limited by energy
18:48and how we can control it right across
18:49all these applications and what we're
18:52usually trying to do is how figure out
18:53how to make them smaller and lighter
18:55right if you're taking up 40% of your
18:57iPhone you want
18:59make that thing smaller so it doesn't
19:00take that up and you can replace that
19:02volume either with nothing or with
19:04things that are more interesting to you
19:06we need higher efficiency both for the
19:08converters and the systems how we
19:10process energy can matter to the not
19:12only the ultimate efficiency of the
19:14converter but the efficiency of the
19:15system how it uses energy can be
19:17determined by the Power Electronics we
19:19want higher performance that could mean
19:21higher bandwidth or other aspects and
19:25then there's all kinds of means that we
19:28we can use better electrical processing
19:31to enable new applications so these are
19:33the kind of things that we're going to
19:35learn about this term I'll pause there
19:38i' I've been going on a while are there
19:39any questions about any of this before
19:41we get going this is just to sort of
19:43Orient you as to what we're going to
19:44focus the term
19:49on I can put the slides on canvas
19:53sure any other
19:57questions okay
20:01okay I will just give
20:05you a slight
20:07notion okay just and this is a
20:11favorite thing I like to bring in just
20:13to show you the kind of things we're
20:16going to look at this
20:17term this is a piece of commercial
20:20Hardware from a company called MKS
20:22instruments that I just happen to have
20:23in my
20:24office this input piece is a filter so
20:27you don't create electrom magnetic
20:29interference and you don't generate
20:30noise you don't
20:31want then this piece here takes energy
20:35from the 60 HZ grid and generates DC
20:37from it and it has to do it while making
20:40the whole thing look like a resistor to
20:42the grid so you don't mess up the grid
20:44okay that's what this part does then it
20:46has these isolated dcdc converters that
20:49can take that DC voltage and generate
20:51other DC voltages referenced in other
20:54ways and without worrying about uh sort
20:58of currents going back to ground okay
21:00it's galvanically isolated and then it
21:04takes that energy and goes back DC to AC
21:07okay now in some systems you might go DC
21:09to AC for 60 hertz to to generate into
21:11the Grid or for a motor or something
21:13else this particular one has these
21:15outputs that are at 13 megahertz for
21:17driving plasmas to process
21:20semiconductors okay but you get all
21:22these kind of functions AC to DC DC to
21:25DC DC to AC and we're going to learn the
21:28first of all the
21:29underlying uh principles of doing all
21:31these things and how to design them okay
21:34so the the the real goal
21:38is by the time you walk out of here you
21:41should have all the tools to go off and
21:43design Power
21:44Electronics for all kinds of
21:47applications and and in fact graduates
21:49of this
21:50class have worked on electric vehicles
21:53Char battery charger
21:55solar
21:57uh communication
21:59systems data
22:01centers the in fact the the power supply
22:04I usually use for my laptop and the in
22:06fact the wireless charger for my
22:08eyewatch were all designed or the teams
22:11were led by graduates of this class
22:13right so this the goal is to give you
22:15the tools you need to go do these things
22:18okay so with
22:21that um let me
22:25start by just giving you a sense
22:29of
22:31um what goes on inside Power
22:40Electronics so let's think of the
22:43simplest case I have some DC input
22:46voltage and I'd like some other DC
22:49voltage so suppose I have some
22:54input that's you know maybe it's 9 volts
22:58to 6 16
22:59Vols I'm making that up arbitrarily but
23:02that's roughly what you might get in a
23:04typical vehicle right out of the
23:06cigarette lighter
23:09okay and suppose I want and I'll call
23:11this
23:13VN and suppose I want here's some load
23:16that I'm going to represent with a
23:18resistor I'm going to call that V out
23:21okay and suppose I want EG 5
23:25volts right to power something that
23:27takes five volts
23:29right what's the most obvious and simple
23:33way to get 5 volts at my output from
23:36some higher
23:41voltage voltage divider precisely right
23:44I could come up here I could say okay
23:47let me put
23:50in some volt variable
23:53resistor and I'll drop down this voltage
23:56to give me the voltage I want and I'm
23:58done and in fact a lot of systems that's
24:02exactly more or less what they have
24:03inside them in fact inside most
24:07integrated circuits there's lots of
24:09these things going on okay well okay
24:12they don't do it quite this way what do
24:14they really do
24:18they will take VN and what they will do
24:21is they'll use some kind of transistor a
24:24mosfet or a bipolar
24:26transistor and they will treat that
24:31essentially as a variable resistor right
24:34so I implement the variable resistor
24:35with a controlled transistor and I will
24:38come and I'll have some feedback loop
24:40I'll Fe feed in a reference
24:43voltage and I'll measure the output
24:45voltage and I'll control the Gate of
24:47this transistor and essentially make
24:49that transistor look like a variable
24:51resistor and control the voltage
24:53division so that even if this voltage
24:55varies between 9 and 16 volts I always
24:58get my 5 Vols output
25:01Okay and like I said that's very
25:05common but what's the problem with this
25:07well there's a whole lot of problems
25:08with this right why why wouldn't you
25:10want to do this uh
25:13in typical
25:15operation efficiency terrible efficiency
25:19yes
25:20exactly so let's think about this if I
25:25accept the fact let me call this current
25:27I in
25:33okay and this current I
25:37out
25:38okay if this thing does act exactly like
25:42a variable resistor the input currents
25:45equal to the output current now this
25:47actually a real system might have some
25:49current that actually also goes to
25:50ground let's take the best case where
25:52the output current is equal to the input
25:54current okay what would be the
25:56efficiency of this Beast well the
26:05efficiency the efficiency is equal to
26:07the output power over the input power
26:11right I'm drawing energy maybe from my
26:13car battery or whatever my battery
26:15source is and I'm delivering it to the
26:17output but not all of it's getting to
26:19the output so the output power is V out
26:23time I
26:24out and my input power is VN time I in
26:30and I just told you that I out was equal
26:33to I in in the best case so that's V out
26:36over
26:37VN right so if I'm coming in from 15
26:41volts and I'm getting five
26:44volts that's 33% efficiency right I've
26:47taken 2/3 of my energy and thrown it
26:50away
26:52now if I got lots of energy floating
26:54around and I'm processing a microwatt
26:58maybe maybe I don't care maybe I'll live
26:59with that because this thing's pretty
27:01simple right it's a transistor it's a
27:03power transistor and some controls and
27:05they can often put all that on one
27:06integrated circuit or even as a subblock
27:09on an integrated circuit I might still
27:11need some filtering it's not it's not
27:13quite as easy as it sounds but um pretty
27:17much it's relatively simple but my
27:21efficiency is miserable now if I thought
27:23about in your in your
27:24computer right your desktop computer
27:27typically the intermediate Supply that
27:29you're getting after it's sort of come
27:31in from the grid and been transformed
27:33down you get 12 volts right and let's
27:35say your computer is it sort of it
27:37depends on what it's doing but say it's
27:40operating at a volt right so then you're
27:42less than 10% efficient right and if you
27:45think that you know you can have a
27:47microprocessor that's taking 200 amps at
27:49a volt or few hundred Watts suddenly if
27:53I've got less than 10% efficiency on 200
27:55Watts that means I need to put in a few
27:58kilowatts well you can't even plug that
27:59into the wall never mind the fact you've
28:01just made a massive room heater right
28:03that's that's like that'd be great for
28:06heating your dorm room um but pretty
28:10terrible for the overall system okay so
28:13the number one reason we don't like this
28:17solution is
28:19efficiency good thing it's simple bad
28:21thing it's terrible efficiency this
28:24technique I should have noted
28:28is what's known for historical reasons
28:30as a quote unquote
28:33linear power
28:35supply why linear I think only because
28:40analog circuits kind of a category of
28:43them became known as quote unquote
28:45linear circuits there's nothing really
28:47that linear about it but this would be
28:49called a linear power converter or or
28:51some sometimes a linear regulator is
28:54what it would be called
28:56okay for obvious reasons I hate throwing
28:59away energy we're not going to talk
29:01about linear Regulators at all in this
29:03class and there's plenty of classes
29:04where you can learn about that we want
29:06to do things some better way that's not
29:09going to burn lots of energy okay so
29:13ideally you know in my world the goal is
29:18to take as much of the input energy in
29:22and put it to the output right and
29:24that's important because think about it
29:26this way I I showed you a photo graph of
29:29something that was you know really tiny
29:31maybe that big right and that thick and
29:35was processing a kilowatt right if I
29:38don't do that at really high efficiency
29:40that thing will burn up right so in
29:42order to make something small I need to
29:45make it efficient all right so we want
29:48almost all of the energy at the input to
29:50get to the output well how can we do
29:52that let's think of a completely
29:55different way we might achieve this same
29:57function function all right and here's
30:00the idea here's my
30:09input I'm going to create a switch here
30:12single pole double throw switch now
30:15we're not going to go get physical
30:16switches we're probably going to get
30:17semiconductor devices and make it do
30:19something like this but we could use
30:22anything any technology that was
30:24practical as a switch okay and let me
30:27just Define if I'm going to define a
30:29switching function that I'm going to
30:30call Q of T if Q of T is
30:33one I'll connect the switch to the input
30:37if Q of T is
30:41zero I'll connect the switch to the
30:43ground okay so this notion this voltage
30:47okay maybe I'll call this voltage
30:54VX all right so one thing I could do is
30:57I could say okay let me just hook this
30:59up to my load here's my resistive
31:02load whatever it is and I'll call this V
31:06out all right well all right what would
31:10that look like well let me Define my
31:12switching
31:22function I'm going to put the switch in
31:25the up position for a little while then
31:28I'll put it in the down
31:29position by setting the switching
31:31function to zero and then I'll just
31:33repeat that so I said we're going to
31:35operate in some kind of repetitive
31:36fashion here and so
31:39forth let me operate with some period
31:43T okay that's mean my switching period
31:46in this example I'm showing you is a
31:47fixed switching period okay and I will
31:50keep the switch in the up position some
31:52fraction of the time that I'll call DT
31:56so D is a fraction zero is less than D
31:59is less than
32:01one
32:03okay so if I do that then what do I get
32:07for VX VX is going to look something
32:09like
32:11this okay um when the switch is in the
32:15up position VX equals
32:21VN so this is VX when the switch is in
32:24the down position VX is equal to zero
32:31okay and I rinse and repeat and I get
32:34this now now I have this pulsating
32:36voltage VX okay what's the average value
32:40of that voltage
32:42VX right I can take you know simple
32:45integration right one over T the
32:47integral of VX of T over a period
32:50T okay and what I would
32:53find is the average voltage of VX
32:58is equal to D *
33:01VN all right so I can create a waveform
33:05here whose average value is something
33:08different than VN just by controlling
33:11this timing
33:13D all right so now if my load resistor
33:19here was a space heater you know maybe
33:22this is some load resistance RL and I
33:25wanted to modulate the power to that
33:27load resistance by controlling the
33:29average voltage on the load resistance
33:32then this technique would work
33:35great if on the other hand my load was a
33:38microprocessor and I start you know
33:40pulsing 12 volts between 12 volts and
33:43zero on it I'm probably going to blow it
33:44up right so that's no good all right but
33:47this notion is at least that I can
33:49control an average voltage by pulsing a
33:52set a switch okay and this would be
33:55known as pwm or pulse width modulation
33:58because I control the average volage by
34:01the fraction of the time the switch is
34:02in one position versus the
34:05other okay so that's that's the basic
34:08concept we're going to be using how do I
34:11fix this
34:12little problem of in practice right what
34:16I wanted was a DC voltage what I got was
34:19a pulsating voltage that just happened
34:21to have the right average value well I
34:23could go do something like this maybe
34:25I'll go back and say okay let me throw
34:28in a
34:30filter and extract out the component I
34:33want right I want the average value of
34:36VX so maybe I'll come back here and say
34:39okay let me throw in a filter and I'll
34:43use an inductor
34:47here an l and if I want optionally I can
34:50put a capacitor here
34:53C okay and you know I think people can
34:57look at
34:59this filter block and recognize that as
35:02a low pass filter the DC component of VX
35:07passes through the filter to the
35:09output and the AC component of VX gets
35:13rejected by the filter and doesn't get
35:15to the output so in this case I might
35:17get an output voltage V out that looks
35:19something like this I'm going to sort of
35:22make this up but you know I'm amplifying
35:24the Ripple but eventually it's going to
35:27filter
35:28the energy content of that and the
35:30fundamental and higher harmonic terms of
35:33VX are going to go away and the DC terms
35:35going to go through and I get an output
35:37voltage V out that's very close to
35:40whatever value I want and if I'm
35:43basically make the filter cut off hard
35:46enough I can't distinguish between V out
35:49and the average value of VX and I get
35:51exactly what I wanted Okay so we've
35:55essentially now created
36:00a voltage
36:04converter that lets me use this
36:07pulsewidth modulation by controlling
36:09this duty cycle D to regulate the output
36:13just the way I wanted so instead of you
36:15know here I'm just changing the gate
36:17voltage on my transistor to control the
36:19output here I'm changing timing I'm
36:21going to control
36:23timing okay and by controlling timing I
36:26control average value and then I get
36:27what I want right any questions about
36:31that what's what's the
36:33efficiency that is an excellent question
36:37the answer is
36:42um ideally theoretically the efficiency
36:46can be
36:47100% in reality it can't be why do I say
36:51the efficiency can ideally be
36:54100% well how would I implement
36:58this box in the real world usually I I
37:02don't get semiconductor single pole
37:04double throw switches the way I would
37:06usually build this Beast is like
37:08this okay I would usually have a first
37:11switch and a second switch implemented
37:14like this so I close this when Q of T is
37:17equal to
37:18one and I close this one when Q of T is
37:21equal to
37:22zero okay and then I build my filter
37:30and then I put my load on here okay
37:35so what would be the efficiency of this
37:37thing well let's think about
37:40this um this is voltage Vex and this is
37:44voltage
37:46vout all
37:50right what power is theoretically
37:54dissipated in my switch if I have an
37:56ideal switch has zero resistance when
37:59it's on and has infinite resistance when
38:01it's
38:02off what's that zero power why because
38:06the power dissipated the power that goes
38:08into this box let me call this V
38:12switch let me call this I switch okay
38:17well P switch the power going into the
38:19switch the power being dissipated in the
38:22switch is going to be V switch time I
38:25switch
38:28okay well if it's an ideal switch then
38:32if the switch is on V switch is
38:35zero right it's ideal so it has no
38:37voltage drop when it's on so the power
38:40when it's on is
38:42zero when the switch is off it has
38:44infinite resistance so the switch is
38:46current zero so basically the power
38:50going into the switch if it's an ideal
38:52switch
38:54um is ideally zero so these these
38:57elements this ideal switch is a lossless
39:01element
39:02right
39:05likewise I wasn't I didn't just randomly
39:07choose any filter here right I chose an
39:10LC filter why did I choose an LC filter
39:14I choose an LC filter because inductors
39:16and capacitors are energy storage
39:17elements if they're ideal then they
39:19store energy but they don't dissipate
39:21energy right so basically
39:25everything in the box here everything
39:28between the input and the output is a
39:30lossless element so then one would
39:33assume that if every element's lossless
39:36any energy walking in to the left comes
39:39out to the right right and that's how
39:42that that kilowatt little 400 volt to
39:4412vt converter I showed you um in the
39:48photo is about 97% efficient it's not
39:51100% because you know the wires have
39:54some resistance and the switches have
39:55some on-state resistance a whole bunch
39:57of things that contribute to loss and
39:58we'll talk about that um but I can make
40:02it really close to 100% even though I
40:05might be doing a huge step down right so
40:08if I tried to build a linear regulator
40:09that was going from 400 to 12 volts
40:11that' be about 2 and a half% efficient
40:13right so if I want to generate a
40:14kilowatt at 2 and a half% efficiency
40:16what is that 40 kilowatt input and
40:19instead what I get is sort of like 1.03
40:24kilowatt input to generate a kilowatt
40:26output right
40:27so the whole Magic that we're going to
40:30talk about this term is how can I use
40:33sort of perfectly lossless elements draw
40:36energy in process it and put it out the
40:38other side okay and by the way I should
40:41say not only did I say oh inductors and
40:43capacitors are lossless in principle
40:45lossless elements uh it wasn't an
40:50accident that we put an inductor
40:54here right because think about it when
40:57this switch is
40:59closed right I have V in on this side of
41:03the inductor and V out on this side of
41:04the inductor and I have current flowing
41:07this way right well what's happening
41:10when this switch is closed basically
41:13there's voltage across this inductor and
41:15current going through it we are storing
41:17energy in that inductor so the
41:19difference in voltage between the input
41:21and the output is basically putting
41:22energy in the
41:24inductor in this the other part of the
41:26cycle
41:28when I turn this switch off and this
41:30switch
41:31on basically I'm taking now I have a
41:34negative voltage across the inductor I'm
41:36taking energy out of the inductor and
41:38put it in the output so essentially I'm
41:40using this inductor as a filter but it's
41:43also an intermediate store of energy
41:45that lets me kind of take energy from
41:48the input and transfer to the output
41:50with a voltage conversion without losing
41:52any of the
41:54energy excellent question long answer to
41:57a short question any other
42:04questions okay so as I said um my goal
42:09is to sort of first of all teach you a
42:12lot of the underlying principles this is
42:14the this is the world's if you will
42:16simplest switching power converter so
42:18the when we use this technique we also
42:20often say we're switched
42:24mode all right with the notion that
42:26we're going to use
42:27switches and energy storage elements to
42:29process energy and that's sort of what
42:31sits at the core of Power
42:33Electronics okay and as I said we're
42:35going to look at all of the aspects how
42:38do you design these things how do you
42:39control them how do you design the
42:41components and by the time we're done
42:43you should be able to put it all
42:44together and and start designing Power
42:46Electronics of your own and you will for
42:49the final project
42:52okay so any final questions
42:59okay we'll wrap up today and I will see
43:01everybody on Wednesday

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