02 - What is a Transformer & How Does it Work? (Step-Up & Step-Down Transformer Circuits)

welcome back to engineering circuit analysis in this lesson we're going to get an overview of transformers and mutual inductances and circuits now in the last section we reviewed the concept of inductance we talked about the concept of mutual inductance and then we drew a few circuits to kind of illustrate how how we can have and how we can have those kinds of circuits and real life and we're going to talk in more detail about how to solve them as the course proceeds and this lesson what I want to do is dive into the concept of a transformer because I know that everybody watching this has heard of what a transformer is and many of you probably already know more or less how transformers work what I want to do is I want to give you an overview so just keep in mind everything we talked about in this lesson we're going to be discussing in great great great detail much more detail than I will cover here as the course proceeds because there is more to it than what I'm going to talk about here but still at the beginning of this course it's really instructive to get a roadmap of where we're going so that as we cut through all of that math that we're going to get to you'll understand what the endgame is and why we're doing it so let's talk about the concept of a real transformer so I'm going to call it real transformer in a second you'll understand why transformer all right I call it a real transformer because in real life all circuit components are they're not perfect right so all circuit components have resistance and inductance and capacitance and we so what we do is we generally have to deal in the real world with real items but when we talk about circuits we have idealized components so what I'm gonna do now is I'm going to go a little backwards I'm gonna show you what a real transformer really looks like and then I'm going to draw an ideal transformer so you can see how it's much more simplified and then we're going to talk about how an ideal transformer will operate in a real circuit briefly and then you'll understand why in real life you don't ever get that performance because in real life we don't have ideal transformers so we're gonna start out with the real deal at least at least to the level that we can get to in this problem so what we have is on the left hand side will have some voltage source I'll call it V it's a sinusoidal source of course and then we have some source impedance we're just going to put it in a box and we're gonna call it Z s so this is some inductance capacitance resistance associated with the source all right and then over here I'm gonna put a dot here you'll understand why I do that in a second and then we'll have a resistance and then we'll have a coil of wire and then we'll tie it will have another dot here and it will tie it back around like this and then physically close to it but not touching it we will have another coil of wire don't pay too much attention to how I'm drawing my curls I'm doing that because it's a schematic in the real world it really does matter if you wind it this way or if you go the other direction see this way so it would be this way right the direction of the turning on the coils does matter and how the voltages and the polarities will work but for the purpose of the drawing here you don't feel worried about that stuff that's just a schematic and we're gonna get to those details later then there'll be some resistance here another dot I'll explain in a second and then over here we have some load resistance so I'll call that Z L and then here we'll have another dot and so here we go so this is your basic transformer circuit so let's label a couple of things we're gonna have first let me grab my red pin here first of all we're going to have I'm going to call this point a it's just gonna make it easier to reference point a point B Point C and point D in the circuit and then what we have here this resistance we're just going to call it R sub one we're going to call this resistance R sub two could be whatever usually they're very very small and then what we have here these resistances are basically modeling the resistance of the coil of wire itself of course you know the coil has inductance but it's made of physical matter so it also has an actual resistance of a couple million ohms or micro ohms or something if it's just a copper wire so this r1 is the resistance of the coil we just have to split it out because we have to draw them separate so this resistor is not a separate component it's actually the resistance of the wire same thing with this guy now the inductance of this coil this coil here is going to have its kind of kind of draw a little note here it's going to have in one turns and this coil over here is going to have in two turns and in one and then could two can be whatever you want your the circuit designer you can just do it however you need for your design but for this example let's just put some numbers in here let's say this is four milli henries and let's say this is 3 milli henries okay so when you write the inductance next to the coil that's the self inductance L so L 1 is 4 milli henries and L 2 is 3 milli henries so far so good but we've brought these things in such close proximity that whenever the current actually goes through this circuit and generates a magnetic field and it's an it's a sinusoid so it's getting bigger and smaller bigger and smaller we brought this coil close enough so the magnetic field of this wire of this coil is cutting through bigger and smaller the secondary one here alright and the closer we give them the more that interaction actually happens so in order to denote that like we showed you in the last section we draw a double-headed arrow pointing to from this coil to this one and we'll just put a number here just for the point of illustration we'll call it 1 milli Henry so this is the basic idea behind a ideal transformer now I mean I'm sorry real transformer now the reason I put a and B and so on is so I can draw this dotted line here and I'm gonna get in the way of my words I don't like that but I'll go ahead and do it like this like this okay the reason I put the purple dotted line there is because everything inside of this dotted line is what we call the transformer when you buy a transformer from you know some circuit supply warehouse or if you make it yourself you're gonna get a bunch of coils and stuff and it's going to be generally wrapped in a lot of times it'll be even coated and plastic to protect the windings and all that stuff so you can't even really see them too well sometimes you can though and on one side of this thing there'll be two leads coming out we call that a and B and on the other side of the transformer we will have two more leads and we call that CMD so I'm just going to kind of label it like this for now we're not gonna use this ABCD too much but I wanted just to tell you that everything inside of the dotted line is what we call the quote of the transformer the primary winding is what we call the left-hand winding the secondary winding is what we call the right-hand winding the primary winding has an inductance of 4 milli henries and a resistance component of very very small usually a few milliohms or less and the secondary winding has an inductance self-inductance three millihenry again with a very small resistance component associated with it and then there's a mutual inductance between the coils of one milli Henry this mutual inductance just means that when this coil is activated its inducing a voltage over here right if I flip it around and put the source on the other side so I'm driving this one it means that the Vote the current swinging up up and down through here would induce a voltage in the other coil but since I have the source over here this is the driving side of the circuit so the secondary coil hasn't would have an induced voltage that would be given by the equation we talked about in the last section M di 1 DT so the mutual inductance times how fast the or the derivative of the current and the other side of the circuit okay so I have some notes here I just want to make sure I have gone through all of them I'm not gonna write them they'll take too long so basically this is what we call a real transformer it has losses in the source this is a source part driving as a Z sub s it has losses in the load that's the load whatever it is conductors or capacitors over here it has losses in coil 1 what I mean by losses is there's a resistance here so you have dissipative heat and it has losses in the secondary coil as a finite self inductance here in this case it's for a finite self inductance in coil number 2 L 1 & 2 and a finite mutual inductance in this case we call it 1 now what we're gonna do in a second is I'm gonna draw this circuit again but I'm gonna draw it in an idealized way because that's usually how you start these kinds of discussions talk about the ideal transformer it's a lot easier to understand and to do the analysis of it but I just want to let you know that after we get through all that math and we get through all the entire course the reason we're doing you know so much here is like a lot of introductory text books basic textbooks they'll talk or even hobbyist type things we'll talk about transformers and it will give you some equations for transformers but those equations usually given in the more basic books are very idealized perfect equations that we can't really use in real life or engineering because we don't have perfect transformers you can see that this guy has a resistance is everywhere mutual inductances and all kinds of things so for instance if I was going to stand at the source here and look for lack of a better word look through terminals a and B and look at this direction what would be the impedance looking back toward the low I mean typically if it's a source and you look at the your load then your load impedance is what you see but in this case I'm looking through a transformer so I've got this mutual inductance business which means it's very hard to understand what impedance I would see the load impedance is over there but it's not even physically connected to the coil so how does that play into it and then there's also these these impedances due to or these resistances due to the coil windings themselves so how does that play into it one of the things we're gonna spend a lot of time much later on talking about real transformers is we're gonna calculate what the impedance would look like if you're ahead if you put a basically a resistance meter between here and look that direction because the load impedance does factor into it all of these things factor all of these terms fact enter into it and it's kind of a complicated equation to derive it but once you have the answer you can calculate what that impedance looks like looking from the source you might need to know that because a lot of times you match your source impedance to be similar to your load impedance for power transfer reasons and other things or maybe you're designing a waveguide or some other something else and you have to know what that impedance looks like in order for your system to work right so you have to know how to calculate that stuff so I just want to let you know that in the real world is the math is more complicated but what we're gonna do now is transition from talking about the real transformer to an ideal transformer and we can have some fun playing around with what what how we could use that so or at least in an ideal way so we have the concept of an ideal transformer okay how does an ideal transformer differ from this guy I am gonna write these down first of all l1 the first coil and l2 equal infinity Henry's that's the first thing equal infinity Henry's now in real life you can't get infinite inductances but in an ideal transformer you can at least ideally right second thing is the mutual inductance between the two coils is infinity Henry's obviously we can't have that either the third thing is we have no losses so the main difference between an ideal transformer and this real one is that in an ideal transformer this is zero there is no loss due to one resistance loss this is zero because there's no loss here this inductance is not for milli henries it's infinity Henry's this is infinity Henry's and then this is infinity Henry's also and you might say how can I even be possible well I can't be it's not possible but I haven't even talked about this yet we'll talk about a lot more later when we wind these inductors or these transformers in order to make the inductance is really really high to approach the ideal inductor case and to make the mutual inductance closer to infinity as close as we can get we don't line these coils on air right what we do is we wind them on iron or nickel or something like that that's a magnetic material I'm going to talk about this a lot more later but what that does is when you whine your inductor on top of the material that's magnetically iron or that's able to be magnetized like iron then what happens is the magnetic field of the coil here interacts with the iron and it lines up all of the atoms inside of the iron so that they're kind of oriented they start slapping to place so that they're oriented in a common direction which then allows that iron to generate a magnetic field that adds up with the magnetic field that you're kind of supplying the circuit with and the end result of it is if you wind a coil on iron you get a much much long larger inductance because the magnetic field you can generate by winding on iron is much much bigger than you could generate by winding on air like if I just wound an inductor on this thing and then removed it so that I had a coil of wire with air inside I could generate some magnetic field there by cooking a current source up to it of course I could but if I wound this thing on iron or some other magnetic material then for the same current I'm supplying into the coil I would generate a much larger magnetic field and that's because the coil is generating a magnetic field but it's also aligning the iron atoms so that they start spinning in the common direction to the coil and that generates a magnetic field from the iron that's an induced magnetic magnetization that then adds up with the original one so it's much much bigger overall so the bottom line of all of that is yes it looks ridiculous to have infinity inductances in infinity mutual inductance but you can get hi inductances by just winding everything on iron and or whatever other magnetic material you have and that's why almost every transformer is wound on some material when you actually look at it it's not wound on air it's a wound on something like either iron or cobalt or nickel or something like that and that's the reason why get higher magnetic fields higher inductance is higher mutual inductance because you wind it on the same physical structure or put them very close together to get that hot so this is what an ideal transform it looks like that's how we accomplish the goal how do we continue on from there so what we have for this ideal transformer now that we kind of know we're talking about here is we have the voltage source driving on the primary side and we have some source impedance which we always have for a source right and then we have this terminal a that we talked about in the past and we have a coil of wire but notice there's no resistance there's no resistor in that model because we've said that it's equal to zero and then on the secondary side we again have some coil that's physically close to the first one again no resistance here and then there is some load resistance over here right and then we'll call this terminal C and this terminal D so the ideal transformer comparing it with the first case I guess I use purple again since that's what I did in the first time is I will say well it basically includes everything here so that the only thing sticking out are these terminals a B C and D notice now that the only thing inside of here is the coils there are the coils there's no there's no resistor here there's no losses due to that stuff and then just to be absolutely clear you don't typically have to write this down because we know we all know what an ideal transformer is but what we'll do is we'll just say that right here this primary inductance is infinity Henry's and then we will then say that the secondary inductor is infinity Henry's and then we will then say that the mutual inductance between the two m is also equal to infinity Henry's now again we don't have to write all that stuff but we typically do and then we'll say we have n turns of the primary inductor and in two turns of the secondary inductor so literally we can't build this in real life but what it is compared to the original guys is exactly the same drawing except we've taken these out we've made this infinity this infinity and this infinity that everything else is the same in one in two turns everything else is the same here we go now to physically build this we can't do it but what we can do is we can build two tightly coupled coils that are literally bound wound either very close to each other or literally on top of one another sharing a common core which is has a very high or yields very high inductances which would be like an iron core or cobalt core or something like that something magnetic something that can be magnetized by the magnetic field that is generated by the current flowing through those coils now this is the kind of thing you'll typically see I mean you don't see all the infinities everywhere but this is the kind of thing the ideal transformer is typically what you see in a basic electronics electronics textbook or a hobbyist textbook or something because it's a great idealized thing if you have a coil a coil in one turns meaning like maybe 50 turns in two turns can be you know 120 turns whatever but what is the point of this thing why do I want to build transformers what is it useful for well the first thing that you obviously see this makes transformers useful is that you're physically separating the left-hand side of the circuit from the right-hand side of the circuit so there are a lot of applications in circuits and engineering in general where you really want to isolate the left-hand side from the right-hand side now they're not totally isolated because you have current here which generates a magnetic field the magnetic field cuts into the second one which can generate a voltage here so you can influence you are influencing the second half of the circuit by things that are happening in the first right but still a physical break here is often very very good for lots of things like surge protection lightning strikes there there are many other noise types applications where you have a noise going on you want to eliminate the noise on the second hand side I mean you still have to develop your circuit and stuff to make it work right you can just put a transformer in there and say it's done but there are cases when you want to physically isolate the left hand of the right hand signed and the transformer does do that although you obviously have an influence on the secondary side based on what's happening on the first stands I'm there's a physical break there the main reason though that you build a transformer is because it has a property that we were about to talk about now that basically allows you to take whatever voltage you see on the input side of this transformer and either step-up that voltage or step-down that voltage on the output side of the secondary part of that transformer so in other words I could drive this transformer with some known voltage source and then I can use the transformer to make that voltage actually larger on the output right maybe I start with 50 volts on the primary side and I can make the output a hundred volts right pretty neat right all alternatively which is actually is more commonly instead of stepping things that well stepping things up happens a lot with power generation but typically in your house you're always stepping things down you know like you have a 120 volts coming out of your wall but you don't want a hundred and twenty volts to plug into your iPhone or to your tablet or whatever so for the charger that's in there you only want five volts or whatever it is seven volts 5 volts whatever it is so in many cases you'll have a transformer that's a lot of times what's inside of the power brick that you're plugging into the wall there's two coils of wire that's taking the primary which is the wall and it's actually lowering the voltage to to whatever device you're trying to plug it into because the voltage you have coming into that secondary device needs to be smaller a lot of times if it's a computer device with delicate electronic circuitry it could be damaged with higher voltage so you you want those devices to operate at a lower voltage so you step it down so the transformer can step the voltage up step the voltage down now you might ask yourself that's pretty neat you can step up or step down the voltage it sounds like I'm getting free energy right sounds like I'm just getting free stuff because I make the voltage higher well it turns out that there's no free lunch in the universe you cannot get free energy out of the system and we'll talk about that here in just a second but basically yes you can step up the voltage up and down the punch line is if you step the voltage up on the output on the output side then by definition the current flow on the out is stepped down from what's on the other side and vice versa so if I try to design this thing to increase the voltage on the outside on the output it sounds like I'm getting something for free well you're really not because when you do that the current that's flowing on the front side is going to be then stepped down to a lower value on the out on the output so if you increase the voltage by a step-up transformer then the current has been decreased on the output compared to the input if I go the opposite way if I step down the voltage then the current is stepped up on the output side so that basically means that you're not getting something for nothing because the current is being adjusted indirectly on lots of lockstep with the voltage and it's all because of the physics involved now what we're gonna do later on in the class is we're gonna derive a lot of relations but I'm gonna give you the punchline right here because you can learn a lot just from the punchline and then just know that as we go on in the class we're gonna derive these relations you know you'll already have an idea about why they're useful and why we care about them so let's go and take a look at they're very simple okay so for an ideal transformer the following relations are true you have a voltage relation a voltage relation which is V 1 over N 1 is equal to V 2 over N 2 and that's so important that I'm actually going to circle it now you might see this equation written in different ways in different books but the way that you know I'm writing it is V 1 over N 1 that means the voltage across this coil divided by the number of turns of coil 1 is the same exact ratio as the voltage across coil 2 I haven't drawn the voltages but it's the voltage across coil 2 divided by the number of turns in coil 2 now this is a nice way to remember the relation because it's symmetrical but really a more instructive way to remember it is like this if I just solve for V 1 here I'm sorry solve for V 2 V 2 by moving in over here is going to be n 2 over N 1 just multiply by hand 2 times V 1 so what this equation means remember I told you could step up the output or step down the output right so I told you so what this means is the output voltage V 2 is whatever V 1 is but multiplied by something so if I choose n 1 and n 2 properly I can make the output voltage because I'll be taking the input voltage and more vote multiplying by something now let's well we'll get into an example in a second but if you choose the coil the number of coils on the on the right hand side bigger than the number of coils on the primary this number will be bigger than one multiplied by the input voltage means your output voltage will be larger than the input voltage and if you do it in the reverse way where this is smaller than this then this will be a decimal and you'll cut the voltage down so that's what I'm saying you can step up the voltage you can step down the voltage and for an ideal transformer ideal transformer that relationship that tells you if you're gonna step the voltage up or down is just called the turns ratio it's basically the output turns on the output side divided by the input turns alright now let me write in one more equation because I gave you the punchline already I told you the current also varies so for the current it varies as follows I sub one times n sub 1 is equal to I sub 2 n sub 2 now I have it labeled i but you know what n 1 and n 2 are I 1 is the current circulating through this inductor the current going through inductor one that's I 1 the current going through this inductor here is called I 2 so you see this is a nice symmetric way to remember this equation because this is basically V 1 over N 1 V 2 over into I 1 times N 1 I want to times into so they're symmetric they look different ones a fraction and ones not but it's all the ones on one side all the twos on the other side for both equations now again this is the way it's easy to remember but I think a more instructive way is to write it as follows let me solve for the output current so i2 is equal to we're gonna divide by n 2 so on the left you're gonna have I 1 over I'm sorry I said the wrong thing already it's gonna be in 1 over N 2 times I sub 1 so forget about the voltage just look at the current what this is telling you is that the current on the output side of the transformer is going to be equal to the current on the input side of the transformer multiplied its time some some ratio so you see depending on if you choose N 1 and n 2 correctly whether it's bigger or smaller than 1 when I multiply it I can get a bigger or smaller output current then I have on the input side but here's the crazy thing about it let's go back to our first example let's say I want to make the voltage bigger the voltage just say I want to get bigger so if I want to make this voltage bigger I need to have into bigger than n1 in other words I have to have more turns on the right-hand side or the output then turns on that on the input side so that's gonna make a number bigger than one so I'm gonna have a bigger output voltage but if I choose into bigger up here to do that then into is bigger down here that means that if I choose it to be a larger ratio here because it's flipped upside down then every time I make this a bigger number than one this one's going to be smaller than one which means that every time I make the current the voltage larger using that turns ratio equation then because I'm inverting it in the equation down here it makes the current smaller than the input current so if I step up the output voltage that's great sounds it gets something for free but then you realize wait a minute the current went down as a result of that it's all because of the math here if I make the voltage go down on the output side then because the ratios flipped over I'm gonna make the output current actually bigger okay so let's do a quick quick quick example this is not really an engineering level example it's not a hard example but it's illustrative to show you what I'm talking about so let's say I want to make the output voltage bigger I want to make the output voltage bigger I want to get free energy let's say I'm gonna tell you right now you're not gonna get free energy but I would like that so what I'm gonna do is I'm gonna say well I'm gonna make this ratio bigger than one so I'm gonna make in two I'm gonna make it equal to fifty turns that means this coil here in two is 50 turns around its core and one has to be less than that so I'm going to call it ten turns I could make up any numbers I want to illustrate the point but I'm choosing simple numbers so because n 2 is bigger than N 1 I know this fraction is going to be large so I'm going to multiply times this and V 2 should be bigger let's calculate what V 2 actually is and by the way we can take this and we can say that in 2 over in 1 is 50 over 10 just basically plug in the numbers n so I have a turns ratio of 5 that means that this ratio here is 5 so whatever the input voltage I stick in there the outputs gonna be five times that right that's pretty cool it's like almost like free energy you think you're getting but again I'm telling you ahead of time you're not gonna get any real free energy out of it because what's gonna happen is the following let's calculate the output voltage v2 it's just as we said the second go into over n1 times v1 into we already know is fifty divided by ten times what is the input voltage well I haven't given you any input voltage yet because I forgot to to do that so let's pick some input voltage let's say we just pick anything literally v1 let's say it's equal to 10 volts and let's say I want the current on the primary side of the transformer is 2 amps what we're saying here is we've defined an ideal transformer we've said this turn over here is 10 this turn over here is 50 so the output turn is larger and we've set on the input side this voltage here across the inductor is 10 volts the current going through that inductor is 2 amps so these are the input on the input side of the transformer we've just listed it and now we have a known turns ratio so now that we have that we have a turns ratio times this is just given in the problem statement times 10 so what we're gonna have is 5 times 10 so what you're gonna get for v2 is 50 volts 50 volts so it looks like you're getting free energy right because you started with 10 volts on the primary side but then the output is 50 volts so that's why I said you can step it up you could step it down but let's take a look a little more closely at what's happening to the current in this situation right we're given the initial conditions here what happens to the current i2 is equal to what we said right here it's the turns ratio but flipped upside down times the input current so it's n1 over n2 times the input current but in one is the primary turn is 10 and the other turn is 50 so it's literally this ratio flipped upside down times the input current I'm giving to you is 2 amps so what do I have well I have 1/5 times two which is two-fifths right and so when I do two-fifths what do I get by - 0.4 amps okay 0.4 m/s so what happened here you see is that I chose a turns ratio to give me a bigger voltage I calculate the output voltage and it does indeed turn out to be larger than the input voltage but with that same turns ratio when I plug the turns in because it's a flipped upside down for the current equation here I started with the current of two amps but I didn't get a higher current I got a lower current a much lower current 0.4 amps right point forums so these are the initial guys these were the final values I want to do one more thing to really show you why you're not getting a free lunch let's look at the power on the input side we're gonna calculate the power and on the output side we're gonna calculate the power right on the input side current times voltage is 2 and 10 so we have p1 on the input I 1 times v1 that's the current the voltage going across that transformer it's basically what I said it was 2 amps and 10 volts right two amps 10 volts so the primary power is 20 watts on the output side after we stepped it all up and down with the transformer we got point 4 amps and we got 50 what do you think is gonna happen so it's going to be p2 is I 2 V 2 the current was point 4 50 I think was the voltage right and so p2 when you stick that in your calculator and get 20 watts these are equal so you have no free lunch okay so what is literally going on here is we have indeed stepped up the voltage on the right hand side but the laws of physics tell us that this coil even though the voltage is higher is physically incapable of supplying more current than point four amps because of the law of conservation of energy and science in math and physics right so a lot of times people think well I'm gonna snip this transformer up to 20,000 volts that's like a huge voltage of and getting something free but reality no because it can't supply very much current can't push very many electrons and that's because the source of the energy for lack of a better word on the right hand side trying to push those electrons is ultimately coming from the left hand side it's just going through an intermediary which is called the magnetic field everything is coming from the source it's going into the current here which goes into this thing called a magnetic field which induces a voltage through mutual inductance in the secondary coil which generates an output voltage which pushes electrons in the secondary circuit but ultimately from a load point of view the current and the voltage here yields a certain power which is joules per second right that's what power is and that power here supplied here has to be exactly the same as the power going in you can't have a free lunch the power going into this box has got to be the same as the power going out of that box if you can build a box that puts more power out than what you're getting on the inside then you just won the Nobel Prize and you're the richest person on the planet because you obviously could sell that but you can't do that so that is an introduction to transformers and mutual inductance as well I wanted to give you these relations not so that you can be an expert in ideal transformers not so that you can be an expert right now at real transformers with all of these resistances but just so you have an idea of the roadmap of where we're trying to go right because what we're gonna do in the remainder of the course is we're gonna dive more into the physics we're going to talk about that concept of inductance more and we're gonna talk about the physics associated of where it comes from and then we're going to talk about mutual inductance and the physics associative of where that comes from and then we're gonna write a bunch of circuits down then dealing with mutual inductance so that we can get some comfortable comfortable writing some equations down for circuits that you could build and then we're going to talk about transformers we're going to drive lots of relations for the ideal transformer in which case these equations are going to apply but then we're going to also spend some time talking about real transformers because we're gonna in many cases we're going to be very interested in calculating the impedance looking this direction through from the source looking towards the load and that requires a lot more math so rather than bogging you down with all that math upfront I wanted you to know where we're going so we have a summary here of the next however many hours it's going to take to get through that so continue on with me to the next section and we'll roll up our sleeves and won't get serious about it but now you have a roadmap so you can keep this in the back of your mind as we conquer those topics in engineering

Channel: Math and Science

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Keywords: transformer, what is a transformer, power transformer, ac transformer, current transformer, voltage transformer, step up voltage, step up voltage circuit, step up voltage converter, mutual inductance, inductor, self inductance, physics, electrical engineering, circuit analysis, circuit theory, electricity, magnetism, alternating current, ferrite core, ferrite bead, flux, magnetic flux, faraday's law, engineering, step up transformer, step down transformer

Id: Wa1PvQ7Bqeo

Length: 33min 49sec (2029 seconds)

Published: Thu Oct 11 2018