This week we will discuss the realization of switches in our power converters using semiconductor devices such as power transistors and diodes. And there's really three major topics that we need to discuss. The first is, when we have an ideal switch, how do we decide whether to replace it with a transistor or diode or something else. In order to make it work in a power converter application. And I'm going to introduce in this lecture and the next several lectures. The ideas of single-quadrant, two-quadrant, and four-quadrant switches. And how to decide which of these to use, depending on the application. the second topic is, we need to talk a little bit about the real semiconductor devices. And so I'm going to discuss power diodes, power MOSFETs, and the power IGBT. Or insulated gate by polar transistor, which are some of the most popular and major power devices in use today. and I don't want to get too heavily into semiconductor device physics. But we're going to talk enough about them so that you can appreciate what are the the major limitations. And important features we need to think about from the stand point of their use and power electronics. And the third major topic is switching loss. so far we've talked about modelling conduction losses in switching the model but what one point in practice is that the conduction loss is not the largest. source of power loss at least in most applications. And, in fact, it's the switching loss that occurs during the switching transitions from the on to the off-state and, and in vice versa they're the largest loss in a converter. So what we're going to do is to refine our equivalent circuit models that we derived in chapter three. To include switching loss. And so that we'll have equivalent circuit models that include things like the diode reverse recovery and it's effect on the converter efficiency. Semiconductor devices are single-pole single-throw type devices. So they have two power terminals. And a transistor or a diode really acts as a on off single-pole single-throw switch like this. Now so far in the course I've been drawing single-pole double-throw switches, such as this one, in which the switch is either in position one or in position two. So, the first thing we have to do is to replace the single pole-double-throw switch with two single-pole single-throw switches like this. and then we can realize each of the single pole-single-throw switches with a semiconductor power device. Now this may seem like a trivial step, but in fact it's not. That, with a single-pole double-throw switch, there are only two possible positions. Whereas with the two single-pole-single throw switches, we have two more cases. The switch can be in position one or in position two, if switch A is on only, or switch B is on only. But we also have cases where we can turn both switches on or we can turn both switches off. And this really happens and it's something we need to consider. For this particular example of the [UNKNOWN] converter if you turn both switches on at once you probably destroy your switches. Because you showed up the power source and you can get a very large current flowing around this loop. That can destroy the devices or at least cause a lot of power loss. So we have to go to some lengths in our drive circuit to make sure that never happens even for a few nano seconds. The other case where both switches are off at the same time can happen, and it completely changes the characteristics of the converter when it does. And so we're going to talk about that case in chapter five and see that it leads to the discontinuous conduction mode. Which is something we haven't talked about yet, but we need to. Okay, we also talk about switches with respect to how many quadrants of operation do they have to work with. And this is really imposed on the switch by the rest of the converter. so here I plotted what we're talking about, the, the horizontal axis. Is the off-state voltage imposed on the switch by the converter when the switch is turned off. So, we also call this the blocking voltage. How much voltage does the switch have to block when it is off? So the switch off-state voltage generally is determined or given by the input voltage VG, or perhaps a capacitor voltage in the converter. And we have to see whether, or maybe the output voltage. But we have to see how large that voltage is, and whether it changes polarity. So perhaps it is positive at some values of duty cycle, and negative at others. And that affects how we realize the switch. Likewise the switch on-state current is the current imposed on the switch by the external converter, or by the converter itself when the switch is turned on. Generally the on-state current is an inductor current or some combination of inductor currents. and this can be a function of duty cycle also and perhaps its a function of the load current. So, again, we have to see what is the on-state current and how does it vary with duty cycle. Is it, say, always positive like sketched here or can it be positive sometimes and negatives other times? So what's sketched here is the case where both the off-state voltage and the on-state current are lying are positive. And so we say that this is in the first quadrant of this plane. And we call this a single-quadrant switch for this particular example. 'Kay, there are many different possibilities in these. In different applications, we may require one or more of these. So the single-quadrant switch that I just mentioned is one example. And in fact, which quadrant does it have to operate in? You can see there are four possible quadrants, and so there are four ways, in that sense, to realize a single-quadrant switch. the next case here is called a current bidirectional two-quadrant switch where the, switch must conduct both positive and negative currents. So, perhaps at one duty cycle the current is positive and at another, it's negative. But it only has to block positive voltage when it's off and so we call this a current bidirectional two-quadrant switch. There are two possibilities here depending on whether the blocking voltage is positive or negative. The third example is a voltage bidirectional two-quadrant switch in which the switch has to block both polarities of voltage when it is off. But only conduct one polarity of current. And finally the four-quadrant switch is the most general case where the switch may have to do anything. It can. Block either positive or negative voltage when it is turned off and it can conduct either positive or negative current when it is turned on. So this is the most complex case, to both control and to realize with semiconductor devices but there are examples. most notably AC to AC type converters. That, that need four-quadrant switches. Okay, so let's talk here about the single-quadrant case. so here I've defined a switch, an ideal switch. I've defined a voltage across the switch with some polarity. And I've defined the current is flowing from the plus terminal to the negative terminal of the reference voltage of the switch. And so if the, the on-state current and the off-state voltage are of a single polarity, then we have a single-quadrant switch. further, we have what are called active switches. And in these switches a switch state, whether it's on or off, is controlled only by a control terminal, like the gate of a MOSFET or IGBT. And so, if you, we know at any given time the, the conducting state of the switch, by the control signal that we have applied to it. On the other hand a passive switch doesn't have a control terminal, for example a diode. And instead its switch state is controlled by the converter waveforms that are applied to the switch. So if the converter voltage or current forward biases the diode then it will, the switch will be on for example. The silicon controlled rectifier or SCR is a special case. it is turned on with a control signal, so the turn on transition is active. But once it's on, it behaves like a diode in which it won't turn off until the, the external circuit, or the power converter circuit, reverse biases the SCR. Okay, so here's the diode and what I've drawn here is different than the on-state current and off-state voltage. This is the voltage versus current characteristic of the diodes. You know you can think of this as the classic exponential characteristic of the diode. That looks like this, and I've diodized it here to ignore the forward voltage drop and put the IV characteristic right along the axis. Okay, so, when the diode is on basically it conducts positive current. And when the diode is off, it blocks negative voltage. So in the planes that we have been drawing in the previous slides, the off-state voltage is negative. And the on-state current is positive and so the diode operates then, in this quadrant, the second quadrant. So, if we work out these quantities by solving the converter to find its voltages and currents and see what it applies to the. The switch and it turns out that we get quadrant two, then we can realize it with the diode like this. Incidentally, suppose I had this define voltage in the other direction, I'm free to do that. We could just as well define voltage upside down and this is an arbitrary choice of the outset. So if we define voltage that way then we have to define current consistently as flowing from the reference positive to negative terminals. And if we did that we would find that the diode would operate in the fourth-quadrant instead of the second. So if we do our analysis. Of the converter, and see the applied voltages and currents on our switch. And it turns out to be in this fourth-quadrant, then we know we need to connect a diode in the opposite direction, to to, realize the switch. Okay power transistors such as the bipolar junction transistor or the newer, insulated gate bipolar transistor. are devices that have, if we plot the instantaneous voltage and current, they have characteristics like this. Depending on the gate voltage of the IGBT or the, the base current of the VJT and so these devices. when they're on they operate with a voltage on this part of the, the curve that is close to zero voltage, and they conduct positive current. When they're turned off by their control terminals then the characteristic is here. And they can block positive voltage. On the other hand, practical transistors su, such as these generally are not capable of blocking significant negative voltage. And if you plot their reverse characteristic, it does something like this. and the device will break down if you apply more than a few voltage. A few volts of reverse voltage. so this is a practical detail in how the devices are built. So they are not capable of blocking significant reverse voltage, and basically we, then we can approximate the instantaneous IV characteristic of this. Like this. The off-state is on the positive horizontal axis, and the on-state is nearly on the the positive vertical axis. And so we, we actually have a single-quadrant switch that operates on the first quadrant. The MOSFET is, is very similar. It's also a power transistor in wide use, that similar forward characteristics. So, it can conduct positive current and block positive voltage. In addition the power MOSFET channel is symmetric and it can actually conduct reverse current. As well. but in addition to that, the MOSFET also has what is called a body diode. That is a built-in diode that comes from shorting the substrate of the MOSFET to the source of the MOSFET. That adds an extra PN junction that effectively acts like a diode in parallel with the MOSFET channel. And so that diode can also conduct reverse current. So in that sense, the MOSFET is a current bidirectionally device. I have to add a few caveats to that though because the body diode in many MOSFETs is not optimized to be a good, fast recovery diode. We'll talk about that in a few a few lectures from now. and in fact the diode is slow enough and you switch it off quickly you can actually get such high currents flowing through that diode that it will make the device fail. So there are failure mechanisms associated with turning off the slow body diode. So, we have to be careful if we want to operate the MOSFET in the reverse direction. But there are significant applications today where we do that, and there are MOSFETs that are designed to have fast body diodes that can work in that direc, can work like that. So, the MOSFET is widely used as a single-quadrant switch just like the BJT and IGBT. And also there are some applications where it is used as a current bidirectional switch. So, here's an example. Here's our buck converter again. And, what I've done here is draw the switch in the buck converter as two single-pole, single-throw switches. And what I want to do is illustrate now, by example, how to go through the analysis of those switches, to decide how they must be realized with transistors and diodes. So what I've done is I've labelled them. We have a switch A and a switch B. And I've arbitrarily defined voltages across the switches. So VA I've just defined and taken as a reference direction that is plus on the left and minus on the right. I could just as well choose at the other direction at this point, but this is how I've chosen it. Having chosen that, we. I define the direction of the switch current iA, is flowing from the reference depositor terminal to the reference negative terminal. Likewise, for switch B, I'm going to arbitrarily define the voltage across switch B is having a reference direction of plus on the bottom and minus on the top And so the reference direction for the current IB will flow from plus to minus through switch B. Now, what we have to do is figure out what is the on-state voltage, or on-state current imposed on each switch by the converter and also what is the off-state voltage. That the switches have to block. So let's do switch A first. Okay, so when a switch is on, we have A is on, and B is off, then you can see the current that switch A conducts is the inductor current. So iA equals iL. Now we've all ready solved this converter previously, and we know that the inductor current iL is the low current. So iL is the load current over R, and I mean the load voltage over R which is the load current. And V is D times Vg. So we get DVg over R, is the current that the switch has to conduct. Now all of these are positive quantities. We'll assume Vg is positive. The duty cycle is positive. And R is positive, it's a passive load. So that the on-state current iA is positive. Okay. So here's the on-state current of iA as a positive current. when A is off, it has to, what voltage does it have to block? But when we turn A off, we turn switch B on. And when A off and B on, the voltage VA is equal to Vg. And that's a positive quantity. So when the switch is off, it blocks a voltage Vg. So the on-state current and the off-state voltage are both positive. Wherein. Quadrant one, and therefore in quadrant one we can realize this switch with a transistor. Say an IGBT. [COUGH] [SOUND] Okay? So with an IGBT there it will block positive voltage and conduct positive currant which is how it's designed to operate. Okay let's consider switch B next. When switch B is turned on, and switch A is off, what current does it have to conduct? Well, with switch B on and switch A off, you can see that iB equals iL. [NOISE] And, the defined polarities of iB and iL are the same in this case, and so this is a positive quantity, and we're conducting positive current. When switch B is off, then we have switch A is on and switch B has to block Vg. But be careful. The way we define the direction of VB VB is actually minus Vg. Which is a negative quantity. So I have to block negative voltage. Okay. So, in this case. We have a, a positive current, on-state current, a negative off-state voltage, we're in the second quadrant, and that's a diode. [SOUND]. 'Kay. So switch B must be realized with a diode. Now you could see here also that the choice of switch isn't arbitrary. I couldn't put a diode at switch A or a, a transistor at switch B, at least not an IGBT or a BJT. so we have to realize these switches correctly. But by doing this simple exercise we can see, we can follow in a systematic way to see exactly how to realize the devices. So here's the summary then. I put at a BJT for switch A and a diode for switch B. Okay, in the next lecture we're going to consider, two quadrants, which is. And see some examples where they're needed.