So, good evening all of you, I am Sandeep Anand, I am a PhD student of Professor Farnandes, so he won't be presenting this particular session, instead of him I will be doing that. Okay, so today in this session we will talk about battery charger systems, is it fine? We will talk about battery charge systems for specifically for solar photovoltaic arrays. This is the outline of the presentation, first I will start with what are the different types of batteries used, particularly for power energy storage, then what are the charging characteristics of these batteries, how can we effectively charge those batteries, finally these are the two popular batteries which everybody might have heard of, one is the vented lead acid battery which almost everybody has seen in his car, and the second is VRLA that is wall regulated lead acid battery, somebody call it gel batteries, finally we will see how can we implement those charge controllers, not in detail, but just the overview of that, after that what are the typical AC charges, so by AC charges what I mean is that how can I use the AC power to charge the battery, okay, so those I will look upon, after that coming to the main point that is PV charges, what are the different charges available for PV power, so that we can charge the battery, okay, finally I will just take a brief example in a telecom system, because telecom system as a like one of the most they use batteries for the abundance, so I will take just their example, what are the different topologies they use, and how can PV be integrated in the telecom sector, okay, so these are the two pictures of the most popular batteries used, so actually both are lead acid batteries, one is ball vented or flooded cell what we call, and the other one the newer one is sealed maintenance free or there are many other names for the same, then the third battery which is also used in the systems are nickel cadmium batteries, niacad batteries popularly known as, but more or less they are very costly, so typically we would not go for that particular kind of batteries in a typical system, unless until it requires a very high, it is a very critical application for example space applications, so usually we will go for lead acid batteries one of these two types, okay, so this is like a brief comparison between the two batteries, one is nickel cadmium battery other one is lead acid battery, so you can see what are, what are, what is the comparison, so if you talk about life, definitely niacad has a better life, if you talk about high energy density again niacad, if you talk about deep discharge again niacad is a clear winner, then the performance at low temperature if you go for a very low temperature, then the performance of a niacad battery is much much better than that of a lead acid battery, just one problem with niacad that is the cost, so that is the main driver for the lead acid batteries and is a reason for the success of the lead acid batteries, okay, I hope it is visible, I will just compare these two batteries, these are the, these are taken from a data sheet of a battery manufacturing company, they manufacture both type of batteries niacad as well as lead acid, so they have just compared these two based on some parameters, so the first graph you see over this one is the average self discharge rate for niacad battery, so what will happen is that if you charge a battery completely, you keep it alone, you come after maybe one year or two year, you will see it is almost discharged, so that is called the self discharge rate of the battery, it will discharge by itself, so you can see that now compare these two, these two curves, these are for the same self discharge rate, but this is for niacad and this is for lead acid, so you can see niacad discharge is self discharge is much faster, okay, so lead acid sustains its energy for a longer time as compared to the niacad, so that is also a benefit of a lead acid batteries, now if you see again bottom two curves, these are again the comparison, these are the life of the batteries for depth of discharge, now I assume that most of you will know what is the depth of discharge, that is the percentage of the discharge you will take it to, for example if there is a battery which is capable of providing x power, x energy, then you discharge it to 0.1x, that means you have 10 percent, you have 10 percent discharge the battery, okay, so that is depth of discharge, so the more you discharge it, the deeper you discharge it, the lesser becomes the life, that is true for both the batteries, but for the same depth of discharge, if you compare these two batteries, then niacad has better life, better lives, number of charged discharge cycles, okay, so that is the second difference, comes the third difference at low temperature, you can see the life of niacad battery is much higher than that of lead acid battery, specifically at low temperatures, okay, so these are the three major differences between the two batteries, so I won't go into the type, the chemistry of the battery much because even I am not aware of those things, I will go into the charging circuits, just the basic terminology of the battery is like the most basic thing, the battery capacity is nothing but a number of hours you can discharge it and the current with which you can discharge it, the multiplication of these two, then what is the charge coefficient? Charge coefficient as we have discussed that the power you put into the battery, you cannot take out the same amount of power, there will be some loss in the battery, that quantifies the charge coefficient, that is quantified by the charge coefficient, so it is the amount of charge you give it, divided by the amount of charge you get back, so you can clearly see the battery efficiency, if you can say something like that, will be inversely proportional to the, this charge coefficient, okay, so lower the charge coefficient, better it is, fine, so you can see that lead acid battery offers a relatively lower charge coefficient as compared to the niacad battery, this was also seen in terms of the self discharge rate also, the same thing we can see in this particular equation also, okay, moving on there is something called as gassing voltage of the battery, gassing voltage is a voltage typically at that particular voltage, if you apply it to the battery, there will be certain reactions going inside the battery which may not be very fruitful, okay, so that is a particular voltage, at which there will be some gases forming in the battery and it will consume the electrolytic much rapidly as compared to the normal case, so typically as a battery charger, as we are designing a battery charger, we would not like to go above the gassing voltage, specifically what is its impact we will see later, so for lead acid it is 2.5, 4 volt per cell and for niacad it is about 1.5 to 1.65 volt per cell, okay, moving on now, what are, it comes, now comes the power electronics, what is the charging characteristics curve, this I have shown as a battery, okay, this circuit is a battery, I have just represented it as the simplest way possible which is like a voltage source in series with the resistance, I have shown a arrow on both the things that is both are variable with the depth of discharge, how much power is left in the battery depending on that, what is the age of the battery, depending on that these parameters vary, so I have shown as variable parameters, these are, there is a battery, now if I want to charge the battery, there are two ways possible, I can force a current, now if I close this upper switch, this is the current source, always a current, constant current flowing through this, so constant current will flow through the battery, okay, so battery is positive terminal here, negative terminal here, current is going inside, battery will get charged, fine, so that is one way, the other way of doing the same thing is that I will close this switch, instead of closing the upper switch, I close the bottom switch and this voltage is more than this voltage, so definitely since this voltage is higher, there will be a current flowing in the resistance and since the current will flow into this direction, into the battery, it will again charge the battery, okay, so I can use either of the ways to charge the battery, so what I have to figure out in next couple of slides is that what could be the better way to do that, either it is one of these two or maybe the third one, also if you have any doubt, you can stop me in between and you can ask me because otherwise I would not be aware of whether I will be communicating, whether I am communicating in a particular way or not, so please ask me doubts if there are any, yeah please, okay, so fine that will also we will come in the next slide, the speed of the charging, so which method will give me a faster charging method, which method will give me a slower charging method that all we will see in the next slide, okay, so since we have seen there are two primary methods, one is at constant current, charging one is constant voltage charging, so here I have just written those things, constant current CC I will call it, constant voltage CV, if you see voltage versus current current, so for the constant current charging irrespective of the battery voltage, I will force a constant current, for the constant voltage charging irrespective of the current flowing into, I will maintain the voltage at the battery terminals, okay, these are the basic two, now comes the third one which is the constant power charging, now what I do is that, I will measure the current and I will apply a voltage such that the power going into the battery is constant, so if the battery is fully discharged, still some power will be going and as battery gets charged, still the same amount of power will be going into the battery, okay, yeah, for which case, no definitely not because since you have to force the same power, your voltage will continuously vary with time, as battery gets charged the voltage will become higher and higher and the current will become lower and lower, but the power remains the same going into the battery, no, the voltage we are talking about right now is that the voltage, while we are charging the battery, while we are charging the battery, that voltage we are talking about right now, when the battery is kept idle, that voltage is something else, that is for the nominal voltage, if you leave a battery idle, that is the nominal voltage, this voltage we are talking about is that we have connected an external circuit to the battery and we are pushing in power and what is the voltage we are maintaining across the terminal of the battery and for the constant power, since our aim itself is to maintain the constant power and if the battery gets charged more and more, so the voltage, the voltage and current has to vary to make the power constant, okay, constant current, constant voltage, yeah, you can, so actually thing is that these are not very good methods, though these are theoretically possible, but practically they do not give such a good yield, so we never use it in a product or so you will never see in a product, but theoretically these are possible and if you want you can have a prototype where you can show constant current charging and things like that, okay, now we will see some of the more complicated charging curves, we saw the three basic curves, constant current, constant voltage, constant power, now I will just mix up these, couple of these and make, form new, new curves, so just see the first one, this one, what I have done is that I have made two constant currents, what I would say, if the battery is completely discharged, that means the battery voltage is low, I will force a higher current, I will maintain it to a constant value until the battery voltage is read to a particular value, above that value of the battery voltage, I will maintain a different current which is also constant, but it is lesser than the first current, okay, so this is, I have derived it and called it as C C C C, like double C C, constant current, constant current charging, so this is the first curve, going to the second curve, called it as C P C P, so one constant power curve and another constant power curve, at higher voltage I will force lesser power, at lower voltage I will force a little larger power, okay, so this is like a C P C P curve, the third comes the C C C V, which is, which is the most popularly heard about, the constant current, constant voltage charging curve, you can see in this curve, what I do is that, if the battery voltage is very low, I will maintain, I force a constant current into that, okay, as battery voltage rises, I will not allow the battery voltage to go above this particular value and I will try to maintain the voltage constant, if the battery reaches this value, so if the battery is fully discharged, I will force a constant current, as battery gets charged, what will happen is that, even if I try to force the same current, if the battery is fully discharged, its voltage will become much higher, so at that point I limit the voltage and maintain the constant voltage, so this is called constant current, constant voltage charging, okay, what are the benefit pros and cons of these different curves as compared to each other, I will come in the next slide, but this is just to introduce that, what are the possibilities we have, okay, so this is like the third one, now going, yeah, you can call it, but this is a popular name given to it, like almost everybody calls, so if, so if the battery is completely discharged, yes, CC is carried out first, yeah, so maybe that's why it might be the reason, yeah, okay, okay, so the last one is there, last one is, is even further modified, CC, CV, CC, so make constant current, make constant voltage and again make a constant current, so just a small step here, okay, so No, because this graph never shows you time axis, this graph never shows you time axis, this is just a voltage in the current graph, if there would be, yeah, so if there would be a time axis then it will go to the right, it's a xy a plot, it's sort of a time plot, okay, so now let's see how these two things merge together, one is the popular batteries we have seen, the two batteries and how can we charge it, so vented lead acid battery, so this is like, this is like the same battery as is present in any scooter or any car to start the battery, it's almost of the same type, almost, so what is the requirement, so as we have already discussed about the gassing voltage, so gassing voltage is at 2.4 volt per cell, so what is the requirement is that you would like to limit the current flowing into the battery at gassing voltage, that is the thumb rule, that is the basic requirement while charging the battery, so other than this everything is what is for our good but this is like a limitation while charging the battery, at gassing voltage you cannot force high current in the battery, otherwise battery will show, it may show a very low life or it may explode also, so this is like a basic limit, okay, so now what I will do is that I will take all the methods which we have already discussed and just try to figure out which method choose this particular requirement the best and that we will choose as a method for our particular application, so first let's see constant power charging, okay, now since this limitation is there, the constant power charging forces the constant power into the battery, how do I calculate that constant power, I will multiply this gassing voltage by the current allowed at that gassing voltage, that will give me the constant power, okay and I am limited to force that much power even when the battery is fully discharged, so you see the drawback, now I am limited because of the state when the battery is almost fully charged, at that point I calculate the constant power value and I have to force the same power even if the battery is not fully charged, so my rate of charge, rate of charging the battery actually reduces to a very lower value, is that fine this thing, yeah, so the limit is that at constant at the gassing voltage I want to limit the current, okay, at gassing voltage I want to limit the current, now since my characteristics is constant power, so my characteristics is I will feed the same power when irrespective of the battery charge, so I have to calculate that constant power as the gassing voltage into that small current and even if the battery is fully discharged, I have to still force that small power, I can still force that small power, so the time it takes from a battery to fully charge is long, okay, so that is the first point, now second point is again, now if I have multiple arrays of battery, I have connected multiple arrays of battery together, my this requirement says that at 2.4 volt per cell the current going into each cell or each battery should be limited to a particular value, but if I connected all together and I am just maintaining constant power into the bunch of the batteries, I cannot ensure the current limit of each of the each battery, okay, so I can ensure the current limit of maybe or the power limit of total system, total battery bank but I cannot ensure the current limit of each battery, so this is also a drawback, so this method is not popularly used because of these two reasons which I have just gave you, one is like paralleling is not possible, parallel battery charging is not possible and the other one is like it's a very slow method of charging the batteries, it will be good for, still not because it's a very, very slow method, so anyways nobody uses it, I will just include it for the completeness but nobody uses it because of it's very slow thing, but definitely the second method which is like a CPCP, now what I have done is I have taken two constant power limits and whatever I have shown you here, now I have two constant power limits, so I can keep one constant power limit very small which will actually satisfy this limit and the other CPCP limit I can make a little larger, so it will give me a faster alternative to constant power charging but again if I have parallel charging of the of the ventilated battery there will be a problem, next constant current I can always use this but whatever was the problem with constant power will still remain here because this constant current will be limited by this particular requirement, so the problem with constant power remains almost the same with constant current, both the problems remain the same, so CCCC again will give me a faster alternative but parallel charging of the battery is not very effective, so now directly going to the last option CCCC which should be the winner, so what it does is that it first maintain constant current which I can keep any value, by any value I mean is not limited by this particular requirement and when this particular voltage is reached I will just maintain the battery at this particular voltage, so I will never allow the battery voltage to rise this particular value, so in that way even if I have multiple batteries connected in parallel I can regulate the voltage of each and every battery, so each and every battery voltage is is regulated to 2.4 volt and if their battery voltage is regulated to 2.4 volt each battery then it is it is automatically ensured that the current going into the battery is less than the limit current, so this particular method constant current constant voltage that is the reason for its popularity in use, so it has actually satisfied my both both the things it will be a pretty fast method and secondly I can have parallel battery connections and charge the batteries in parallel, I will just in brief field, so this one was vented lead acid I will see VRLA that is the sealed batteries which do not have opening which need not be poured with water or electrolyte additional, so for this particular battery since there are no openings, so typically we would like to restrict the voltage to less than the gassing voltage, at gassing voltage some gases will be produced, so since these kinds of batteries are sealed they do not have any openings, so we would like to restrict the charging voltage to a slightly lower value that is said to be 2.35 volt instead of 2.4 volt, so prevent formation of gas inside the battery, so we will use this particular voltage again if we go on the comparison almost CCCV will come out to be as a better option for this particular charging, so after after seeing after seeing the ways to charge the battery in terms of the characteristics the next question which might be in the mind is that how do we actually implement these particular characteristics, I have a battery I have let us say AC source how do we actually have a converter and its control, so that battery gets charged, so that should be the next question in mind and just with the help of this example I will try to explain you that, so what I am doing in this example is that I have a DC source, I have a hypothetical DC source which may be derived from solar or may be derived from AC source by rectifying it in may be different ways, I have a AC source or DC source sorry, I have battery and there is a DC to DC bug converter, so this is the piece of the hardware I have and this is the control which should be used to charge the battery in CCCV mode, we will look upon each component just in the struggle like to ask before proceeding that DC to DC bug converters Professor Fernandes would have taken in the class, so this is the same circuit DC to DC bug converter, one switch, second switch and inductor and finally the battery, we do not need a capacitor here because already battery is present at the output, there are two parameters which I am sensing in this circuit for control, one is the battery voltage, another one is the battery current, this battery current is same as the inductor current because inductor is created in series to the battery, so these two things I am sensing in my control, so let us say how I am achieving that, so first I will compare the battery voltage with V ref, V ref is the voltage for example, it is 2.4 for that tubular batteries and 2.35 voltage, so it is a gassing voltage, it is the voltage to which I want to limit the battery voltage, I will just compare these two and whatever is the error out of these two, I will pass it through a controller which is most of the time PI in our case, this PI can be any other controller also, any intelligent controller also but for most of our application we use a simple proportional plus integral control, now since everybody all of you are not from the same background, should I actually explain what is the PI or can I go ahead with the term, I made it very small, that is fine, so what I am doing here is that, so this is the input let us say, I will multiply it with the proportional gain, this is just again constant multiplication, in the same input I will integrate also and multiply with another gain K2 and finally I will add these two components to give me the output, so just to give a, so this is like a controller, I can always, I can remove this part, I can just use the proportional part or I can add a differential part also, I can have one more term which is D by DT multiplied by the third gain, I can use it or I can go together and change this whole thing and form some sort of intelligent controller, so everything is possible, so essentially this controller ensures that at steady state the error is 0, at steady state since the output should be constant, this input will become 0 because there is an integral in it, since the output will be constant at steady state whenever it is reached, there is an integral here, so the input has to be 0 and that is the whole purpose of using an integral part, integral here, yeah that is a much involved process and so typical, I will just tell you the steps how I do it, you have to take the circuit, you have to model it, maybe a small signal model of that, then you have to draw either root locus, Nyquist plot or any of the other methods and then you can include this KPKI in the model and accordingly you can choose values of K and K1 and K2, there are certain thumb rules also available, so you can do either way like you can actually do it or you can use the thumb rule, so that is nothing but this PI, now output of this PI I have put to a limiter, this limiter is nothing but a saturator, so input of this can be anything, output of this is limited by this particular value, so output of this will be 0 to IRF, if the input is more than IRF output will be saturated to IRF, if the input is less than IRF output is same as input, so that is the function of this block limit. Next, so actually this gives me the reference for the current and I will compare this value with the inductor current or the battery current I call it, again I will pass it through a PI and I finally use it to control my buck converter, so this was just the description of the converter, now I will explain how it will work, so for the basic operation let us forget about this part, let us just forget about this part, fine. So, typically LEM based Hall effect sensors are used which are very high bandwidth sensors, for this particular application they use such sort of sensors. So, if I take the battery voltage and I compare it with the reference, now assume battery voltage is slightly lesser than my reference voltage, battery voltage slightly lesser than my reference voltage. So, the output of this is a positive value, the output of this is a positive value I will pass it through a PI, the output of this, so since there is a integral the output of this will increase, output of the PI will increase in this particular case, since the output of PI will increase, my duty cycle will increase, just forget about this part and just let us say we connect this to this terminal. So, since the output of the PI has increased, my duty cycle has increased and because duty cycle is increased, my output voltage should increase, that is operation of the basic buck converter, okay. So, this is like a closed loop control where I will maintain the output voltage equal to the reference voltage, if I just use this out voltage loop, now I have introduced a current loop inside, this current loop has two functional function, one is that it will limit the current, since my aim is to have constant voltage, constant current, okay. So, if my this constant voltage loop gives me output, which says that you should force a current higher than the reference current, okay. To maintain the same voltage, if my voltage loop tells me that you should force a current higher than the reference current, then this limiter will limit that current. So, this limiter what the function of this limiter is to give me the constant current characteristics in picture to bring that into picture. If I remove this limiter, it is a constant voltage charging characteristics. So, that is that is the thing, now this is just a sawtooth generation or triangle wave generation and this is the final comparison. And finally, I am feeding to these two with some phase shift. So, this is like the basic, so this controller actually implements CCCV in the most basic format. There are other, there will be definitely be other circuits involved, yes. The voltage of source is less than battery, is greater than battery voltage. No, if this is a voltage source, then it is definitely not advisable to charge the battery without using any sort of DC to DC converter. It may be a buck converter, it may be some some other form of converter. If the power level is very low, it may be a linear regulator. No, it is like shorting two sources with different voltages. So, you have two DC sources and if you short these two, what will happen? Yeah, it is a bi-directional. So, yeah. So, I have just drawn it as bi-directional. It can be either you can use it as a unidirectional also. I will remove this gating pulse till the operation remains the same because for this particular application, we just need power from source to battery, but I have drawn it as a generic circuit, that is it. Yeah. So, I will come to that. I will come to that definitely. Sure. So, hall effect sensors are, so current sensing we can either do by a simple current transformer. We can have a transformer with CT, typical CT, but the problem with typical CTs are it is accuracy in terms of the voltage and second it is bandwidth. So, there will be lots of parasitic. So, the waveform you will get from this will be a flow bandwidth. It will not show high bandwidth phenomena of high frequency. So, that is the reason we go for hall effect sensors. And most of the power electrons applications for control purpose, if you want to sense the current, we will use a hall effect sensors. And those are the closed loop, those are also called, also named as closed loop CTs or LEM. LEM is actually a company who manufactures it, but they are now popular as the name itself LEM, L-E-N. So, coming to protection, yeah, so no, it is proportional to the current. So, if the current is. So, yeah, depending on the current and the type of the hall effect sensor. So, there are hall effect sensors which will give you AC output. There are hall effect sensors which will give you a phase shifted output. They will just shift the voltage and give you the DC output. So, depending on the type of the hall effect sensor you use.  So, it is all depending on the specific occasions of that. So, I have not, I have missed one of the component in this circuit actually. I have not shown you because I do not want to discuss it, but there is one more thing which is called driver circuits. And this controller, driver and power electronics hardware are together. So, controller output may be 3 volt, 3.3 volt or 5 volt. So, getting signals might be 0 to 3.3 or 0 to 5 volt. Then it goes to the driver circuit which actually drives these switches. So, in case if these are MOSFETs, something else, in case if these are IGBTs it has to be something else. So, there will be another driver circuit. So, driver has to ensure that switch is closed or switch is open depending on its input. So, in addition to these basic circuits, there has to be yeah, you can definitely use, you can either use micro controller or you can use a DSP or you can have an analog implementation of this. Anything can be used. Most of the time micro controller DSP nowadays they will use. So, that is in electric vehicles. So, what I will do is that because we are not battery experts. So, I may not be able to answer this particular question because so, for us battery is just the CCCV curve, nothing more than that. So, it will be difficult for me to answer on that, but may be professor Fernandez will be able to answer that. Okay. So, moving on, I will go to the protection circuit. So, what are the different protections we would need in this particular kind of charges? One is a maximum current. So, even if there is some fault anywhere, the current through the inductor or current flowing into the battery should not rise to a very, very high value.  This loop is there which will try to regulate the current, but what I am saying is that if there is any fault, if there is any fault in this loop, let us say this connection gets open, anything like that, then there should be a master protection circuit just to avoid the hazard. So, maximum current should be limited. Again, maximum voltage at the output terminal should be limited. Then shoot through should not be there. So, shoot through is like if both the switches accidentally gets turned on, this is like a short circuit of the source. Okay. So, that should be avoided. And something called as VCE protection is there in ICBT, which is pretty much natural with their drivers. Finally, over temperature. So, since there are devices, there will be heat sinks inside that. I think tomorrow's lab session if we will go, we will even see the hall effect sensors there in the lab and we will see the heat sinks and everything. So, heat sinks are there which will dissipate the heat of these devices. So, the temperature of those heat sinks should not be more than a certain value. Otherwise, something is definitely wrong. So, we should turn off the system. And there might be other faults, maybe an external fault input or something like that. If the battery is fully charged, by that I assume you mean that battery voltage is equal to Vref. Okay. In that particular case, the ratio of these two switches will be Vout by Vin. So, what will happen is that there will be some. So, first of all, we turn this switch. Now, this battery voltage is. Yeah. Yeah, that protection. Yeah. Okay. So, depending on the application, no, battery will definitely not going to discharge, because that's fine, but this voltage is higher. Okay. So, the current in this Okay. Okay. Let's say battery discharges and it charges this inductor in this way. Okay. Now, if I open this switch, I have to close this switch after a certain time. In that case, current will flow into the source. Okay. Now, this particular thing will only happen if I choose my duty cycle such that, if I slightly increase the duty cycle, this thing won't happen. And this in steady state, the current will be positive in this particular direction. So, the circuit is capable of doing that. So, best thing is what the gentleman suggests is that it would have been much better if I did not show this particular thing. Okay. This particular thing I may not show. And it's just one switch and a diode. That would be much simpler to explain. Okay. But anyways, even if the switch is there, the power doesn't go back because this controller ensures so. But it will take some time for me to explain that. Yeah. In practical charge, it can be either. It can be a diode or it can be a switch also because MOSFETs if you see, if you turn on the MOSFETs, the voltage across it is 0.3 volt. Whereas, instead of that MOSFET, if you are using a diode, it's 0.7 volt. So, to increase the efficiency, you might considering using a MOSFET instead of just a diode here. That's just an example. So, it can be either way depending on the application. For this particular application, it depends on the application. This is like a UPS application, uninterrupted power supply. The objective is to charge the battery from the source. And when the source is not available, force the battery power back to the source. So, in that particular case, we have to go for this particular thing. There is no other way out. But if the application is a use battery just to maybe light a lamp or something on this side, then I can use just a unidirectional converter also. No, what I am saying is that? Yeah. In case of UPS, okay, what I will do is that I will. So, what is the different? So, in UPS, we will definitely use a battery, right? So, but UPS, the application of battery in a UPS is different from that of a standalone system. So, for example, in UPS, the aim of the battery is to get charged from the source and throw back the battery power into the source. One way of doing that is the typical UPS, which we have in our home. They will just use a very crude method and rectify the voltage and charge the battery, okay? And when the power is gone, they will switch on some other circuits and throw the battery, throw the battery power. So, in higher cost UPS, they will use a common circuit to charge the battery as well as discharge the battery. If that is the case, if this switch is not present, I can only charge the battery using the source. But if the switch is present, I can even discharge the battery and throw power back to the source. My load is connected somewhere here, okay? Then I will use a bi-directional. If my load is connected on this side, I may not require a bi-directional power flow, okay? So, I will move on with the next slide. Now, we have seen the basic charge controller. I will just briefly touch upon the various possibilities of how a battery can be charged using AC power. I will come to the PV power after this. So, this is like, I have an AC supply in my home, either a single phase or a three phase. How can I use that to charge my battery? This next section is on that. So, typically, what would be the parameters in that? So, I have shown it here, okay? Is there anything I am missing here? So, like, definitely the converter efficiency should be good. The battery charger efficiency should be good. Definitely the input power factor of the charger should be close to unity. It should have lesser harmonics because it will adversely affect my grid conditions. It can be controllable. I will come to this point maybe later, okay? So, have I missed anything out of anything more you would like to have in your charger? If you want a charger with charges your battery from the AC source, what all would you need? Yeah, voltage is anyways there. So, voltage, some converter would be there from AC to DC to AC. But these are two requirements I mentioned. One is the efficiency should be good. Otherwise, nobody will buy it and then the input power factor should be good. Otherwise, the buyer will have to face the penalty. Yeah, cost should be one factor, definitely cost should be one factor and the reason I have not put here is that because nowadays since this factor is these two factors are so much stressing that cost has gone out of picture for this particular low power application because you can maybe pay a little higher cost and if you save on efficiency, if you get better efficiency then your cost will be recovered in soon. Anything other than that cost anything else? Okay, I hope we have covered everything and so this is like the most cheapest method of doing that. I have AC voltage in my home. I will use a transformer, AC transformer, step down to a LSL voltage, some protection switch is there. Use a diode bridge rectifier maybe half wave, full wave whatever and just connect it to the battery terminals. I can do that and charge the battery. And actually that is the way the batteries are getting charged in the cars also. So, this method is uncontrolled. Why I call it uncontrolled? Because I cannot whatever we talked about in last 10 or 15 slight constant current, constant voltage, constant power, I cannot do anything in this particular circuit. Whatever is the voltage here, accordingly the voltage will appear here and the battery will get some current. I cannot regulate anything. So, my battery life will be very, very low. So, less battery life is one of the disadvantage. Low cost, then low input power factor. Now, if you are aware of the input current, so if this is the AC voltage, input current will look something like this. So, everybody must have seen this sort of input current. In a PC also, you will see this sort of input current. So, the power factor is very poor. Am I right? Yeah. So, the power factor is very poor. It is not unity. Even though they are in phase, the power factor is still poor because of the distortion. So, this kind of circuits can be used for very small power level, but definitely for the power level above 1 kilowatt, nobody would even think of using it nowadays especially. Moving to the next slide and on the better option is mixed better option is half control thyristor bridge. So, this is the AC source. Followed by that there may be a transformer, there may not be a transformer. What I am doing is that instead of using 4 diodes, now I am using 2 thyristors and 2 diodes. So, the function of these thyristors is that the property of thyristors, definitely we all know that we can turn on it whenever we want to, but we do not have any control over its turn off. Whenever the current becomes 0, it will get turned off automatically. So, it is sort of semi controlled devices. So, we have 2 diodes and 2 thyristors. Just briefly I will explain how it works. So, this is let us say this voltage. This voltage VAB, I will call it VAB. So, this is that voltage. Consider the positive half cycle. Now, this is the battery. Let us say battery is this much voltage. Battery is a DC voltage. So, this much voltage is the battery voltage. Now, let us say I turn on this device. So, when both the devices are turned off, there is no current flowing anywhere. When I turn on T1, let us say this is the time when I turn on T1. This is the time. This G1 is a gate signal for T1 and I turn on thyristor 1 at this particular time. So, as soon as I turn on T1, what will happen is that this voltage will appear here. This voltage will appear here and since this voltage is more than battery voltage, you can see this voltage is more than battery voltage. So, current will start flowing from this inductor. So, you can see on this, this is the inductor current. So, you can see as soon as I turn on the thyristor, current in inductor rises. Because voltage difference is positive equal to L diability, current has to rise. So, from this way current will flow through D2 and it will go back and from T1 it will come and goes through this way. So, that is fine. Now, consider the second situation when both the voltages become equal. Now, current is rising. Now, both the voltage has to become equal somewhere sometime or the other in the negative slope VAB will become equal to battery voltage. In that particular instant, now V is equal to 0, V equal to L diability. So, diability has to be 0. So, it sorts of reaches its maximum value, diability is 0. And after that V is higher than this voltage. So, V equal to L diability where V is negative. So, diability has to be negative. So, current should decrease. So, after that current starts decreasing. I am just using that basic law for the inductor in trying to explain it. So, current will start decreasing. Yeah, there is a specific reason because these sort of topologies are called current sourced topologies and what they do is that they draw current from here. So, we would like to have a very good sinusoid voltage at this particular point. Because you can see the source current. If you see the source current, the current suddenly goes from some value to zero value. This is the source current. This is the current I draw from this branch. So, it can go from a certain value to a zero value in a fraction of second it can go. But if there is no capacitor, this is like an inductor. So, in inductor you cannot change the current so rapidly, otherwise a spark would come. So, to avoid those kinds of situations, there has to be a capacitor in it. Because capacitor can supply that peaky current. Capacitor does not have any problem you supply those current. So, moving on on this. So, eventually current should become. So, this is like an inductor current. Every time every half cycle it will I will turn on gate. So, same thing happens with T4 D3 also I will not go into that. So, I will turn on the gate the current will increase it will become maximum it will decrease. Finally, again after sometime for the next half cycle the same thing will repeat. And if you see the source current it will be something like this. So, this is the shape of shape of the source current. So, the shape here was very peaky very sharp you can see the shape here. Now, it is debatable, but I could say that power factor should be better here in this case as compared to the previous case. Because it looks more smoother to me. So, distortion power factor will definitely be reduced. There will be displacement power factor, but that may not be substantial. So, but still I would not call it a unity power factor. It is not even close to a unity power factor. Again now even though this is control you can see the current going into the battery. This is this is the current going into the battery. This is the inductor current. This is the current going into the battery. You can see it will always rise come back rise come back and this is like a 20 millisecond cycle. So, the life of the battery is less in this particular method. It is more than this particular method, but still not a very good value. The best best we will get we actually got in terms of the DC-DC converter when the current was constant flowing into the battery. That was the best possible case we had. So, moving on on this next method. Now, can we have actually unity power factor? Is it possible to have unity power factor? You just observe. Just do not look at this circuit. Just look on the right hand side. This is like a DC to DC converter. Do you resemble it of some DC to DC converter? Just do not look at this. Just look at this. Yeah, it is a boost converter. It is a boost converter. It is a same boost converter which sir might have taught. The only difference is that instead of having a DC voltage here, constant DC voltage, what I have done is that I have removed that DC voltage capacitor instead connected a diode bridge rectifier. So, there is a diode bridge rectifier and then there is a DC-DC converter. Just the most basic way to explain it is if this inductor current somehow I can manage to make this inductor current vary as this particular thing. If I can make the inductor current follow this envelope, this diode bridge will nothing but unfold this envelope and give me a sinusoid current, same as the sinusoid voltage. Now, since as we know the duty cycle relates the input voltage to the output voltage, duty cycle also relates the input current to the output current. So, we can always manipulate the duty cycle to achieve this particular shape of the current. While studying DC to DC converter, you must have seen this current to be a constant value. In this particular case, I am saying that we can always maintain it to this, we can give it this sort of shape. It is fine. Now, how to actually give it that is a little complicated, I would not go into that, but it is possible. So, if we do that, then the input current becomes almost unity power factor. So, this is a diode bridge plus boost rectifier, boost converter. So, high input power factor, it is a control charging, but still the battery life will not be that much good, but I can call it at least better than the previous converter. This is very popularly used in low power rating. So, above 5 kilowatt, I do not think anybody would use it, but less than 5 kilowatt may be 1 kilowatt or so people use it very happily. So, this is like the last AC charger. Now, I should not go into that, but this is the charger which can give you unity power factor, which can give you a very good life of your battery and everything else. So, it can give you almost anything and especially if you have a three phase equivalent, there is nothing better than that, but I would not go into that. This is called fully controlled IGBT or MOSFET based charger. So, let us come to the topic of our interest, that is PV chargers. Okay. So, before moving on, I like to have suggestions on what is the possibility, how can we charge a battery using a PV panel? Anything on that? How can we charge a battery using a PV panel? Yeah, but what could be the scheme or what could be the converter? Do we need a converter? We can cannot we directly shot the battery to the solar panel? What is the problem if I directly shot the battery to the solar panel? Yeah, DC to DC converter. Boost converter. Boost converter, we can use considering if the panel voltage is lesser and the battery voltages are higher or I can use a bug boost also if both are almost the same value. Okay. So, typically it is good now the battery voltage also comes in the fraction of 12, the panel voltage also comes in the fraction of 12 and typically for very high power we will use panel number of panels in series to make higher voltage, number of batteries in series to make higher voltage. So, the voltage, the nominal voltage is of the both sections will almost be same for the same power level. So, that is a good thing, but why can't we directly shot the panel to the battery? It is not consistent, but then what will I lose? Will it harm my circuit or will it harm the battery or will I lose something else? Okay, backflow I can avoid by using just a diode, I will put a diode and that will avoid the backflow. So, cost is actually the cheapest possible way, that is a good thing, but what is bad about this particular circuit? Protection I can have using one switch maybe, I will just when I think the battery is fully charged, I will open that switch and disconnect the battery from the panel. Yeah, idea is to trap the maximum power from the TV. So, even though this is a better method, panel will never be damaged because panel is neither a voltage source nor a current source. So, if you connect anything to fit, it won't get damaged. Yeah, so, correct. So, to sum up actually, the basic aim is the same that we want to extract maximum power. If I connect my battery directly to the panel, it will not harm the system, neither it will reduce the life of the system, because my panel will give me a constant current, DC current and my battery will get the DC current. It may so happen if the cloud comes, there is no current at all. So, that is possibility, but the aim is to charge with maximum power available with the panel, because panel is the most expensive thing we have in our system. So, we would not like to underutilize that asset. So, here what we want, we want higher efficiency definitely. Then there is a concept of leakage current, which I am, I do not know whether I will be able to cover it or not, but then this is also a very motivating factor for TV based charges. Just this is what we discussed. So, this is what we discussed, right. I will take a battery, somebody suggested protection. So, I will put a switch, somebody said back power flow, I will put a diode and connect a panel. So, these are the different panel characteristics at different radiation, for with radiation current varies. So, these are different characteristics. So, let us say my battery is some 12 volt battery. So, how can I find what is the current going into the battery? Let us say I consider this particular curve. So, this is my panel curve. I will draw a battery curve, which is a constant voltage at here 12 volt, wherever the intersection point that amount that much current will flow into the battery. It is fine. And for example, if I see in this particular case, 12 volt lies somewhere here. So, this is the point of operation, whereas the maximum power I get is at this particular point. And you can almost see I am losing almost one fourth of the available power. The power you can see that this between this point and this point, there is almost one fourth power I am losing, because currents are more or less the same, but voltage is almost one fourth of the maximum power point voltage. So, that is the main aim, like if I can direct battery to the panel, I will lose on power. And I do not want to do that, because panels are most expensive things. So, what comes the next? The thing which was suggested first that use a DC to DC converter. That is the next thing to do. Now, which DC to DC converter that we will look upon, just for the time being we can consider there is a DC to DC converter, which we are using. So, the specifics of the DC to DC converter will depend on many factors like power, the voltage levels on both the sides and all those things. So, this DC to DC converter controls charging. So, I can have a maximum power point tracking algorithm incorporated in DC to DC converter, which will operate always try to extract maximum power from the PV, that is fine. So, and definitely I can condition the battery, I can still use those characteristics, whichever we have talked about in the beginning of the lecture. So, the life of the battery is definitely going to be much better in this particular case. So, these are the two aims we have, use PV power and battery capacity to fullest. If there is a power available, if there is a space where I can store it, I should store it, I should not waste it. Then second objective is that again what we have studied before, the battery voltage should not exceed the maximum limit. So, since we discussed about constant current constant voltage. So, the conclusion of that section was that we should not allow the battery voltage to go above its cashing voltage and that should be kept with this particular converter also. So, I should satisfy both these constraints in this circuit. Now, I will just for the thought I will say that you can think of I will say this one DC to DC converter. So, whatever power I will feed into the battery has to come from PV, that is fine. Whatever power I will feed into the battery has to come from DC. If I want to satisfy this particular constraint which says use PV power and battery capacity to fullest. So, if PV power is available, I will try to extract the maximum power. I do not have any place any other place to dump the power. So, I will dump it into the battery, but then it may so happen that battery voltage might exceed its maximum limit during that particular time, because I am trying to force more power. Now, assume that battery is about to get discharged may be 80 percent charge or something like that, but I will throw the maximum power. So, it will take my battery voltage to higher value. It will avoid this second condition may not be satisfied in this particular case. So, there are actually I will say there are two control objectives and there is only one control variable. There are two objectives, there are only one variable, there is only one variable. That is the problem we are facing right now. So, somehow I have to club these two objectives and bring to a common conclusion and use that common variable. The common variable is the duty cycle of the converter. So, this is how I achieve that. So, what I am showing you is just one method, there can be many possibilities. So, one method is that operate PV on maximum power point MPPT as long as voltage of the battery is less than the maximum allowed. When the maximum allowed battery voltage is reached then just try to maintain the battery voltage. Even then forget about MPPT, the battery gassing voltage is reached just try to maintain the battery voltage forget about MPPT even if the power is getting lost there is nothing you can do about it, because your capacity is already full. So, this will ensure both the things good utilization of PV as well as longer battery life. I just termed it as CPCV charging constant power, because initially you have to maximum power point. So, it is a constant power then constant voltage finally. So, this is a relatively fast method and it is a good method for this particular application. So, this block diagram represents how I do that. I will compare the battery voltage with the maximum voltage and depending on this value I will either use a voltage controller, which I have showed you on the previous couple of previous slides. Or I will use a maximum power point controller, which we till now have not discussed maybe in some of the next sessions you will see that. So, that is the other way of doing it. And finally, it will give me maybe the duty cycle of the converter or some other control variables, but just one control variable out of these two objectives. So, this way I can achieve it. So, you can have both the things maximum power as well as long life of the battery that is what we wanted. Just see let us see. Now, what is the options we have? Now, in the previous slide I told you that we can use some DC to DC converter. What is the option of the DC to DC converter do I have? So, I have this full thing here and actually there are many more if I take, but these are just those which are popularly used in the industry. If I talk about papers they will be like I do not know going to infinity all the lines. So, basic DC to DC converter can be categorized as either non-isolated or an isolated topology. The non-isolated topology does not have a high frequency transformer in that. An isolated topology will have a high frequency transformer in that. Have you studied any of these isolated topologies? Sir has as sir told about any of these isolated topologies. He has fly back that is fine. So, you know the basic difference between these two. Then in non-isolated conventionally these are the four very well known bug, bug boost, boost, chuk, sepec these are all very well known. Now, there is thing called soft switch which also he might have just spoken about. So, soft switch we can have either 0 voltage switching, 0 current switching maybe couple of more topologies. In isolated also similarly we have a simple in isolated also we can have a conventional topologies without soft switching we can have a soft switching topologies. And there are more there is research definitely research going on this and there are more number of topologies coming around. And specifically this one has been proposed by one of one of the research scholar here. So, this is actually these topologies are meant for high power applications. So, you need isolation DC DC converter for high power. So, you can go for one of these topologies. Just to give the hint that telecom applications for telecom application if you see the newer converter. So, just telecom application is actually nothing, but I will come to the telecom example next, but they use this LLC topology very frequently. They are very happy with that. LLC means for inductor inductor capacitor. So, how do we select the DC DC converter out of this family? It is not specific it is just some basic overview that if you have a very low power level you can use either of these three or four basic converters without isolation. Typically for low power level you might not require isolation. So, you can go for either of these three or four converters. As the power level increases things become interesting and isolation may be required to protect from lightning or avoid leakage currents. So, these are the two reasons for isolation. So, you may need isolation. So, then you have to choose your topologies accordingly. Now, source switching may be required because for high power level you would definitely like to have better efficiency. You do not want to lose your power. Now, if you are talking about much higher power then you may have to modular your design. So, you will build one converter with a lesser power and multiple it in parallel to achieve that high power level. So, that is the technique popularly used. Now, definitely if you have multiple converters then you will achieve the benefit of multiple MPP trackers also which will overcome something called as shading effect. So, finally, this is the last section. It is an example I am taking for telecom based battery charging systems. This is the example. Now, a telecom station which we call as BTS based transmission station that can be of power level going from 1.4 to 22 kilowatt. Now, most of you would know that battery nominal voltage is 48 volts in telecom system and it is actually minus 48 volts because the positive is earth instead of negative. Now, here so this is the circuit. So, there are AC voltage available. Then this is some converter which is used to charge these batteries. This is the AC to DC converter which is used to charge the battery here. And on all the DC loads all the critical loads telecommunication loads are connected on this 48 volt bus. So, till date this is the structure. This part is the structure which is used. Now, our aim is actually to introduce PV panel into the system and use the panel power to charge the battery. Definitely, we would still keep this option open because in case if there is no sound and things like that, I should be able to charge my battery with AC also. But primarily, I would like to charge my batteries using PV panel. So, this is what I have added. This is the PV panel, a DC to DC converter connected to the battery system. So, the panel voltage can be anything depending on what panels I choose. I can either choose from right from 28 to 480 volt depends on the design what I choose. Now, in this particular application if you are talking about this power level, you would see that this AC to DC converter has an isolation inside it. Telecom AC to DC converters 48 volt battery chargers telecom base has an isolation inside it. That has couple of reasons behind it. First of all, the voltage matching. So, this if you rectify this voltage you will get 325. This is 48 volt. You need a large voltage jump. So, you may use isolated topology that is a benefit with isolated topologies. But more important reasons are one is the protection. So, if there is any lightning strike nearby, it should not harm the owner's battery system or its load. So, that is also one reason why they use transformer inside that. Any lightning in the nearby area should not harm my battery and my load. So, I will put a transformer and keep myself safe. Then the third is the leakage current which is also one phenomena which is essentially the current flowing through the ground wire. So, which is the leakage current nothing but the current flowing through the ground. So, it is a common mode current. It comes from the 3 phases together. It is the same magnitude in all the 3 phases and goes through the ground. So, that is also something we do not want and there are actually there are standards on that as to what value to be limited to and transformers helps in maintaining restricting those currents to that particular value. So, that is the third reason for using a transformer isolation in here. Okay. So, I have explained you what is the system right now. Now, let us see I connect my panel and a DC to DC converter. Okay. Now, what all do I need in DC to DC converter? First of all, do I need a isolation or I do not need a isolation in DC to DC converter? I have explained you everything about what is present in the system. Now, I want to introduce one more component of the system like a panel based on that a battery charging system. Now, what is this DC to DC converter should be? Should be isolated converter or should it be a non-isolated converter? Because the voltage is now is not a constraint. I can still have the voltage of this may be of the order of 100 volt or 48 volt. This is also 48. So, I can use may be a conventional converter also. Okay. So, what should I use? Should I use isolated? Should I use a non-isolated? I should use a non-isolated. Anything else? Anybody for isolated? Anybody for isolated? Isolated is the answer. Anybody for isolated? For what? Why should we go for isolated? I will take the ground. So, when you clear, you can round the system. Yeah. So, correct. So, if I do not use isolation, the ground of the battery system is will be coming to the panel. So, I cannot separately ground this system. I cannot do that. I am restricted for the same. I will use the same ground. In that case, if there is a now panels are spread over the field, right? They occupy huge space. If there is a lightning on that panel, the path for the lightning to go inside the ground is through this particular ground. Okay. There is no other way out for the lightning to go. Definitely, there will be lightning or stress and all those sort of things. But if there is a major strut, then it has to flow through this ground. And while flying through this ground, the lightning will actually take the DC loads and the battery along with it. So, everything will be gone. So, definitely, we would like to have a separate ground for the PV system. And again, the leakage current is also the second issue in that for having a different ground. So, we would like to have an isolated system. We will put an isolation here and we will ground either negative or positive of this system. We will have a separate dig and just ground it. A more advantage is controlling the converters. Control circuit would now, for the new type of converter anyways, we would like to have the converters. Actually, it will become difficult because now you have two, you have switches on both the side of the converters. On this side also, you have switches. This side also, you have switches. So, you have to turn on and off both the switches. And you have to have two separate supplies for that, two separate driver circuits for that. So, I would not, I mean, in certain application, it might be, but… The other side is… This is a DC to DC converter. This one. This one typically used at single phase converters. So, we are talking about this DC to DC converter right now. So, in this DC to DC converter, even if it is isolated, things might get little messy. So, that way or in fact, if we talk about cost and all, we might go to for unisolated, but should go for isolation. In fact, this is the thing. This is the reason which is not still well understood. So, people still in telecom might, who are trying to start with the things, might use DC to DC converter without isolation considering its very low cost, but that may not be a sustainable solution. So, it may not hamper the system today, but maybe 5 years down the line, it will take the whole system down. So, one possibility of this converter, now since we have all agreed for the isolation is the LLC converter topology. I won't go into the detail of that, but this is, I am suggesting this because this is very well popularly understood by people who manufacture this particular converters. This is a software topology. So, they use this topology in this converter. This is a transformer based DC to DC converter. They use here. So, it is very easy to modify it and use it for this particular converter as well. So, that way, that is the reason why I am with which I am justifying that LLC converter should be used for this particular topology. That is it.


We are going to discuss the three activities which are reported in any cash flow statement. Now operational activities, in operation activities, we start with cash flow from operation, the cash generated from the business and good sale of goods and services after paying the cost of inputs and operation. Now let me tell you in detail what include in operating activity. Look if we are a trading business, we are buying goods and we are selling them. And if we are in a manufacturing business, then we buy raw material, put it in the process, then it is finished and then sold. So the material coming in the process will be your cash outflow. And after the goods are ready for sale, you are moving to sell it and then whatever money coming in that is the inflow. But at the same time, that is one item, raw material. What about the other administrative expenses? Selling distribution expenses, they are also equally important. So in this activity, we look into that how those expenses are going to be paid out. The selling admin, we put it together operating expense. Similarly, in this case, we have taxes paid. So the tax we pay that also be recorded here. Similarly, interest we pay that also be recorded here. Another important issue in this activity is direct method is simple, but so far indirect method is concerned. We start with profit and we do adjustments in those profit figures for those items which are not involving cash flow, but they are reported in the income statement and major items as depreciations, losses, or any other adjustment where the cash is not involved that will be adjusted back, added back to the profits. Similarly, if there is a gain which is separately, you are selling an asset and you are making certain gain on it, that gain is added to the profit. But that money which you are selling for the assets, that will go to the investment activity. The profit you added, gain you added to profit will be subtracted. So then we have another section here, the adjustments of working capital. And this is also a very important one. Working capital is basically current assets and current liability. So the change in current assets and the change in current liability that will also be reported as inflow or outflow. Now here some people are feeling difficulties like debtors, receivables. If you got let's say 100,000 receivable at the beginning of the year and now it is 80,000. So it means there is a drop of 20,000. What happened to that? That 20,000 you have collected. Similarly, if you look into creditors, you got a creditors of let's say 10,000 at the beginning of the year and now it is 7,000. So it means you paid of 3,000. But if you look the other way, you just look the other way that not necessarily it happens that all the time opening is more and closing is less. No. Investing activity shows the cash paid for capital expenditure, incorporate investment acquisitions, cash received from sale of long term assets. In financing activities, it shows the cash raised or paid to the firm stockholders and the debtors, debt holders. Normally this is regarding the lenders and the shareholders, whether how much money they are putting in and how much we are paying back. Thank you very much.


Hello everyone. Welcome to this video lecture. Myself Dipali Vardhakar working as assistant professor at WIT, Solarpur. Today we will study the pulse width modulation. At the end of this video lecture, student will be able to illustrate working of PWM modulator and demodulator with its waveform. Student will be able to illustrate the application of PWM. These are the content introduction to PWM, PWM modulator, PWM demodulator, advantages and disadvantages of PWM, then application of PWM. Now the pulse width modulation, it is the technique for delivering partial power to the load through digital means. So, this is the one of the example how this pulse width modulation will transmit a partial power to the load. So, what is the pulse width modulation? In the pulse width modulation, the continuous time signal or message signal is suppose X of t, the carrier pulses is train of pulses. In PWM, the width of this carrier signal changes according to the amplitude of continuous time signal. Here, the amplitude of all pulses remains same. So, the information in the PWM is in the form of change of width of pulses. Next is a duty cycle. In PWM, how long a rectangular pulse stays on within a constant period is determined by the value of information signal. So, duty cycle is measured in percentage. So, what is the duty cycle? Suppose this clock pulse having total time period t and it remains on for this time period. So, its duty cycle is nothing but on time upon total time and percentage duty cycle is equal to on time upon total time period into 100. Next is a PWM generator. The PWM generator consists a comparator circuit. The analog signal is applied to the non-inverting terminal of this comparator and the sawtooth wave is applied to the inverting terminal of the comparator. Here, this sawtooth wave act as a sampling function and its frequency is fs. So, this frequency fs is always greater than the frequency of continuous time signal x of t. Now, this comparator gives output high as long as this continuous time signal remains higher than this RAM signal. Let us see the working of this comparator. The comparator gives the output high at the falling edge of this RAM signal and this output remains high up to the point where the continuous time signal and RAM signal coincide with each other. So, after this point the comparator output becomes low. So, in this way the starting edge of this PWM is decided by the falling edge of this RAM signal which are as fixed interval of time and the ending edge of this PWM is decided by the continuous time signal and the point at which the continuous time signal and RAM signal coincide with each other. So, see here again at this point this when the falling edge of RAM signal comes comparator output becomes high and then this output remains high up to the point where the continuous time signal is higher than this RAM signal and at this point the comparator output becomes low. So, in this way as the continuous time signal goes to the positive peak the width of this PWM signal is high as the continuous time signal goes to the negative side or negative peak the width of PWM signal is less. So, as the amplitude of this continuous time signal changes the width of PWM signal changes. So, in this way the PWM signal is obtained at the output of this comparator. Now, the demodulation of this PWM signal. So, first what is the demodulation? It is the act for extracting the original information bearing signal from modulated carrier wave. It is used to recover the information content from the modulated carrier signal. Now, let us see the PWM demodulator block diagram. So, this is the first PWM signal which is to be demodulated. This PWM signal is given to the RAMP generator. Same PWM signal is also given to the synchronous pulse generator. The output of RAMP's generator and synchronous pulse generator is given to the adder. Then this adder output is given to the clipper circuit and next the clipper circuit output is given to the low pass filter. Let us see one by one working of each block. Now, first PWM signal which is to be demodulated, this PWM signal having different width and its position and its amplitude is same. Next RAMP generator, PWM signal is given to the RAMP generator. This RAMP generator will generate a RAMP signal. The height of this RAMP signal is proportional to the width of this input PWM signal. So, at the end of this RAMP signal, the sample and hole circuit which is present inside this RAMP generator circuit, this will hold this amplitude and for the rest of this cycle. Next, synchronous pulse generator. So, the synchronous pulse generator will generate a train of pulses and these pulses having constant amplitude, constant width. But these pulses are synchronized with the leading edge of PWM. Then the RAMP generator output and synchronous pulse generator output given to the adder circuit. Then this adder will add this train of pulses or reference pulses with the RAMP signal and we get the output like this. RAMP signal and on that this reference pulse generator output. Now, this output of adder is given to the clipper circuit. Now, the question what is the function of clipper? Pause the video for a while and think. So, the clipper is a device which is used to remove or to limit some portion from the waveform at one particular level. So, it will remove some positive part or some negative part or maybe both the parts from the waveforms and remaining portion remains as it is. So, a tube biased clipper is used here which will clips off this part and gives the PAM at the output. Now, this PAM signal is passed through a low pass filter and it gives a continuous time signal X of t. So, in this way the continuous time signal X of t is recovered from a PWM signal. Now, next that is the advantages as the amplitude of a PWM signal is constant. So, effect of noise is less. So, it has good noise immunity. Here, the synchronization is not required between transmitter and receiver. It is easy to reconstruct the PWM signal from a noise-contaminated PWM signal. So, it is possible to separate out signal from a noise in case of PWM modulation. Next, in PWM the width of pulses varies. So, the power of this all the pulses also variable. So, the transmission system must be powerful enough to handle the variation in the width of pulses. The bandwidth required for the PWM communication is large as compared to pulse amplitude modulation system. Then applications, PWM system is used in a telecommunication. PWM is also used to control the speed of robots by controlling the motors. It is PWM is used to control the power which is delivered to the load without noise. So, it is used in RC devices. It is used in audio and amplification purpose. Also, it is used in video effects. The sum class of amplifiers use the PWM techniques. PWM also used in embedded application. It is also used in analog and digital applications. These are the references. Thank you.