 I said there are three switches are there, I need to know the conducting state of these three switches. They will be either on or off, how many possible combinations are there? 8, 2 to the power 3 out of which 3 are completely on or 3 are completely off, I am now 0, 0, 0, 1, all are off, 0, 0, 1, so on up to 1, 1, 1. There are how many possible combinations? 8 combinations. All are 0, means all are off. That means these three are on. That means A is connected to negative bus, B is connected to negative bus, C is connected to negative bus, all three points are at the same potential. So, what is V AB? 0, what is B? Come on, A is also connected here, B is also connected here, C is also connected here, what is V AB? 0, what is B C? C, so all line voltages are 0, so phase voltages are also 0, so it is a 0 vector. All three are on, all three are on, A is connected here, B is connected here, C is connected here, again 0. So, now I have there are 6 states, these are active states and we are 2 are null states, null states, 2 are null states, 0, 0, 0 and 1, 1 more are null states and remaining 6 are active states, active states. Now, see from the equivalent circuit approach also you can determine. Now, I will I will show you, I must have taken the other from the equivalent circuit, do not have to worry about V or no, V or no whatever, see the circuit here. SCI is 1, SB is 0, SC is 0, what does it imply? Sir, what does this imply? Can you tell me the equivalent circuit of the inverter or this combination? Sir, energy, loss bench, what is the equivalent circuit for this? Quick, what is the equivalent circuit? SCI is 1, so A is connected to positive, A is connected to positive, there is a load, there is a neutral, S B is 0, load is on. So, B is connected to negative, C is 0, again C is connected to negative, loads are balanced. Now, what is VIN, what is VIN? Quick, this is VDC, this is 2 third of VDC, I do not know, Z, Z, Z, so Z by 2, so Z and Z by 2 VDC, so voltage here is 2 by 3 VDC, 1 third VDC. So, what is another possible combination you have? See there are, I said there are 6 possible combinations, out of which see here, one upper on, one upper on, two lower on or two lower on, one upper on, phases may differ, but the equivalent circuit is one upper on, two lower on or two upper on, one lower on, one upper one, when one upper one is on, what is the voltage? Two third VDC and these two are off, what is the voltage? Magnitude is one third, sine is negative, sine is negative, one third, this is two third. So, when this, when any two upper ones are on and one is off, what could be the voltage, what could be? Positive one third and negative two third, negative two third, negative two third, same equivalent circuit, same equivalent circuit, see here, so do not have to, one one C is lower one is off, that is equivalent circuit, so this voltage is now two third, two third VDC minus, this is one third, one third, only the signs are different, magnitude is the same, two third and one third, that is all. Now, you have to plot, now you have to plot, see assuming 180 degree conduction, what do you mean 180 degree conduction? Having turned on, no no, just 180 degree conduction, having turned on, you keep it in that state for 180, keep it on for 180, continuous, that is the reason we turned on A phase and kept on for 180 degrees, 180 degrees. So, A phase, so B phase should be turned on after 120, after 120 B comes in, after 240 C comes in, so this is 0 look something like this. So, here you just see, VA0 is positive, BB0 is lower negative, C upper, so upper, now I am plotting only VAN, I am not plotting VBN and VCN, that you can plot later, I will just teach you how to plot VAN, A is positive, A is positive and C is also positive, two upper switches are on, so what is the magnitude of voltage? Sir plus one-third, plus one-third, from two, this in this 60 degrees, A is positive, B is negative, C is also negative, only one device is on, only one device is, so magnitude is two-thirds, sin is also plus two-thirds, two-thirds and next 60 degrees is A is positive, B is also positive, but then C is, C is negative, so two devices are on, one-third, so hence the name six-step operation, how many steps are there in one cycle, how many steps are there in one cycle, six steps, what is the frequency of the predominant harmonic, what is the spectrum, fifth and seventh, if you take the harmonic series, fifth and seventh, so I am connecting to the grid, it is a 50 hertz grid, so frequency of predominant harmonic is 250 and 350, I want to filter it, what do we do? I can use the LC filter, no issues, what is the problem? Why straight away go to pulse width modulated in water, may be various limitations are there, you can use second order LC filter, there are being used, you can, you can, second one is, what is the, what is the second alternative, how do I wave shift, see my voltage, that is why I am telling output voltage of the inverter is non sinusoidal, output voltage of the inverter is non sinusoidal, now I want to make the current to be sinusoidal, because the current that I am feeding to the grid, after all the current that I am feeding to the grid should be sinusoidal, how do I make the current to be sinusoidal? How do I make the current to be sinusoidal? How do I make the current to be sinusoidal? Suppose, see there is an if I have an RL circuit see here, then we will see how PWM helps a DC is applied to an RL circuit. If tau time constant is very large compared to T or how does the initial portion of the current look like linear, initial portion of the current is linear. So, what I will do is instead of instead of keeping it having turned on having turned on keeping it for keeping it for 180 degrees, what I will do is what I will do is I will have I will have large number of pulses in this. Are you with me? How it tells you see, we will have a large number of pulses, I am achieving two things. What are they will see? There are large number of pulses, what will happen if there are large number of pulses? So, what will happen is I told you here what will happen? In the all of you all all of us agreed that initial portion is linear, I will turn it on. So, what will happen? Well, current increases linearly, here it is off, what will happen? Current decays, current decays again it is turned on decays. So, I can have almost a sinusoidal current, I can have almost a sinusoidal current, see I will show you. I will show it in the lab also, extended waveform, if I extend it you can see this for almost linear, I do not why I did not bring. If I extend this zone, you will see that this is linear, decay, linear, decay, linear, decay you can, these are storage oscilloscopic, if you do not have a question I have a question, no in the sense see I am not able to understand one thing. If I give a sinusoidal voltage, sinusoidal voltage to this circuit, current is sinusoidal are you with me? I am giving this sort of a waveform to this circuit current is again sinusoidal, so what is your conclusion? RL circuit you give any waveform it will be sinusoidal current, sir, I showed you and you told me sinusoidal, now you are saying that it is not sinusoidal. No, no of course, one I can see this is what it is, it is sinusoidal, almost sinusoidal, I do not, is it this is not, is it sinusoidal or no, come on, I do not think you can get a better sinusoidal than this, if I see if I take an oscilloscope and supply this voltage itself is non-sinusoidal with thanks to all this laptop voltage itself is non-sinusoidal. So, what do we, what we can infer, what is our inference, what do we conclude, sinusoidal current and sinusoidal current, what you can tell your students, if they are sir, what is their, where is the diagram, no, no I do not, may be I do not know, what my inference is looks like this waveform has a fundamental component which is sinus, fundamental component is sinusoidal and it has a high frequency component, a very high frequency for which this circuit be used like an open circuit, RL circuit, if the frequency of excitation is very high, how does it, what is the, what is the current due to that voltage, if the frequency of this supply is very high, this is almost an open circuit, open circuit, open circuit. So, if I use this, I can use the superposition theorem out of which one is 50 hertz current and, and, and a very high frequency component for which this circuit does not respond, does not respond, does not respond, is that okay. Now, my question to you is how do I choose this high frequency, what should be the frequency of the so called, so called predominant harmonic that is present, how do I hire the better, see come on, I want as the gentleman said that current waveform looks to him is approximately sinusoidal, not an almost sinusoidal, are you with me, to have a perfect sinusoid, to perfect sinusoidal, the harmonic spectrum should be, one is 50 hertz, another one is a very high, very high component should set, then only I may have a sinusoidal current, which is just not possible, what should be the frequency of the predominant harmonic, hire the better, which quantity will determine, hire the better, see number of pulses will determine the switching frequency, number of pulses will determine the switching frequency, are you with me, number of pulses will determine the switching frequency, which quantity will determine what should be the switching frequency, which quantity, how will I determine the switching frequency of the inverter, how will I determine or how will you decide what should be the switching frequency, no it is a power rating and the type of devices, see if you are designing a 10 kilowatt inverter and you are designing a 500 watt inverter, so type of devices are the same, for a 500 watt inverter, you can effort to have, you may choose a, you may choose a higher switching frequency, higher switching frequency, because every time you switch there is going to be on off losses, so as the power rating increases the switching frequency, switching frequency comes down, switching frequency comes down, switching frequency comes down, it is a power level that will decide, power level that will decide, power level that will decide, it is a power level and the type of devices that will decide, it is like this, in a sense you may say, no it is, there are various parameters, suppose fine let the switching frequency high, losses will increase, I will use a, I will use a, I will use a better heatsink cooling or something like that, another thing what will happen, another thing is a THD, total harmonic distortion, total harmonic distortion, THD, suppose you are feeding power to the grid, as per certain standards, if the THD should be less than 5 percent, then you have no choice but to switch at a high frequency or use a filter, or use a filter, or use a filter, there are various guidelines, because it is a filter, not the thumb rule, device 10 kilowatt inverter may be you can switch at may be 10 kilowatts or so, but then is it that is sufficient, then what are you going to do with the 10 kilowatt inverter that will decide, if you are feeding to the in grid, if the THD is less, yes, if you want to, you have to reduce the THD further, you have to worry about something else, technology available or you are definitely the so called switched converter, we will see, what is the problem as you increase the switching frequency, what happens, see every time you switch apart from the losses, see that voltage from 0 to, what is this voltage, VDC, I think DC link voltage if you see, and what is the rise time, what is the rise time, now you cannot, it cannot be 0, it is almost turn on time is quite fast, see that DVP DT, see the DVP DT, suppose if I using this, this of course, this load either this fan has to take, your load so motor has to withstand, are you with me, see the DVP DT, the motor winding has to withstand, which parameter is there, very high DVP DT, there are windings there, so inter winding capacitance, what about inter winding capacitance in a machine, come on, distributed capacitance, and there is a very high DVP DT, so capacitor charging discharge current will be very high, insulation background, all those issues are there, is not only the losses, so the question is how do I, we will come to that, how do I reduce all these, the so called stress, not only the losses, is the voltage across the device also, see this is the voltage across, this is voltage across the conducting device, so in a voltage source inverter is complementary, is not it, whatever that happens, if this voltage goes from 0 to VDC, same voltage this also will be facing, is not it, come on, when this is on, instantly the entire voltage comes across it, when this is off voltage across it is 0, so device voltage across it, device also rises very fast, and so device stress also more, how do I reduce this device stress, how do I reduce this device stress, how do I reduce, there are issues, we will see, come to that, definitely, definitely, so retrofitting may not be a solution, I have a motor which is designed for a sine wave, sine wave is a beautiful wave form, you can differentiate it, you can integrate it, you can still get a sine, I am not, so motor winding there is no transient at all, all of a sudden you have, that motor is been designed for 50 hertz sinusoidal supply, now you are feeding, feeding this inverter output, where the DVB DT is very high, now you need to really properly think and only then you need to go on for all this, if you are going to be inverter, it has to be, you may have to increase the insulation level, you may have to, it is subject by itself, we will see this later, any questions, I do not know, that is a typically, what it comes to, I do not know, I will just give an example, what could be the switching frequency of a small SMPF that is used in a PC, what could be, yes of that order, what is the frequency of the inverter, see we have Rajdhani and Shatabdi trains, these are all AC locomotives, AC drive, there is also an inverter, over rating is of the order of 1 rake is of the order of 1 MVA, thumb rule, 1 rake of the order 1 MVA, what is the frequency, switching frequency, what is the switching frequency of the order of 550 to 600 hertz, all depends on the switching frequency, sorry it all depends on the power level and afterwards what you do afterwards, will you put a LC filter, see here in the sense, what I will do is, in the output voltage of this inverter is pulse width modulated, output, if I am using pulse width modulation, output voltage is going to be pulses, now if I want to feed a sinusoidal voltage, I can use a LC filter, filter it out and give, it is possible, there are various or change the control strategy itself, change the power circuit configuration itself, may be in my next lecture I will cover, which is better, then you need to decide which is better, just 5 minutes are there, I do not think I will start another topic, if you have any questions feel free, feel free. No, it does not, no the sense, it will turn off, turn off time is, see how do you turn off the MOSFET, no multi-level inverter we will discuss, that is the next topic that I have discussed, this is the question of multi-level inverter, we will see when we discuss multi-level inverter. I have a square wave, output voltage is a square wave, output voltage waveform is a square wave, okay, 180 degree, what is the harmonic spectrum, what is the harmonic spectrum, in a 3 phase circuit, 1, 5, 7, 11, 13, so on, okay, okay, so what the, what the feedback is, if there are n switches for quarter cycle, n minus 1 harmonics can be eliminated and fundamental can be controlled, so if there are 6 switches per quarter cycle, 5 harmonics we can eliminate, what are they, what are they, 5, 7, 11, 5, 7, 11, 13, 17, these harmonics you can eliminate and the predominant harmonic that is present is 19, predominant harmonic that is present is 19, if there are 6 switches per quarter cycle, so what is the question, how can I tell, is there a predominant harmonic, I don't know, the question is predominant harmonic that is present is now 19, I don't know sir, who am I to tell it is around or not, is the predominant harmonic that present is 90, what is the frequency, 50 into 90, 950 hertz, 950 hertz is the frequency of the predominant harmonic, okay, now depending upon your circuit parameters, what is the current that it will draw from that 19th harmonic that you need to know, what I am saying, no, no there is a one lecture on harmonical elimination, if you want me to give, I will give, but then you need to give me a slot, these are, this wave, if I write the Fourier series or whatever, first 5, 7, 11, 13 so on, if there are 6 switchings means 17, these harmonics are eliminated, predominant harmonic is now, okay, so what will be the equivalent circuit for the 19th harmonic, V19th and may be R, R I can neglect if it is an RL circuit because L will be, this L will be now 19 into omega 1 into L, okay, now omega 1 is 50 a fundamental, okay, 19 omega, so your impedance has increased by 19 times, 19 times, so depending upon the magnitude it will draw, drive some, small current I do not, it depends on L, no, it will drive some current, now that will affect your THD, that will affect your THD, so will it be okay or not, it all depends on your circuit parameters and the THD, suppose this would not do, then you may have to increase the switchings per cycle, it has one has to take a paper and a pencil and write is it sufficient or not, I cannot say is it okay, is it allowed or not allowed, because one has to go as per, as per certain standards, there are certain standards, that will tell you, go ahead, quick, quick, inverters are not recommended for refrigerator and what could be the reason, in the sense one is, what sort of air conditioner, see the window air conditioner, no, but what could be the reason, is it the interest current, is the interest current, see 1 k way inverter, I use it for a one turn AC, this is my gut feeling and telling you, I do not know, suppose I use a one k way inverter for a, for a, for a, whatever this one, what will happen, when I put, when I turn on the air condition, what will happen, initially huge interest current, your inverter may not be able to supply, if the inverter is able to supply, why not, all the data centers, all the data centers, here they are backed up by, backed up by, air conditions are backed up by UPSs, air conditions are there, backed up by UPS, but then I need to choose a, I need to choose a, higher rating in water, higher rating in water, higher rating in water, see one way is, we have to see, what it could be the reason, one way is, if the motor is run for 50 hertz, now we are feeding a voltage, some fast rising voltage, that may affect your, retrofitting is not possible, you should really think, point number one, are you with me, yeah. The second is, you can definitely use an inverter for AC, choose a suitable rating, you cannot say one k way inverter, one turn is required around this one, I can use it, no, why you come to IIT, there are data centers, computer centers running continuously, whether there is a, for supply or not, you can, anything else, we do not have a very stiff source, now source is weak, it cannot, does not have a high capacity, so your devices may fail, and this until you have over load capacity, or you need to have a soft start, what is hf means, what does it mean, it is all depends on your CHD and type of load, over rating, no, no, maybe those are all final details, we will discuss, how to choose, what is the harmonic spectrum, see which book you are referring, I do not know, but then, see it all depends on frequency spectrum, it all depends on the frequency spectrum, n is multiple, so it requires time to discuss this, so called minor details, whether for a given number of persons, what should be the harmonic spectrum, after all, after all it only depends on power level, and what is the harmonic spectrum, harmonic, sorry harmonic content that a load you can, load that you can, that can withstand, that is all, nothing else.