[BLANK_AUDIO] This week, we're going to discuss converter circuits. First, we're going to talk about where all these converters come from. And, what are the relationships between them. So, I have you know, just brought up, kind of out of the blue, introduced some different converters. Such as the boost, or the buck boost, or some others, that we've done in problems. so I want to talk, just a little bit, about what the relationships are between these, and how you can derive one from the other. Then, second we're going to talk about transformer isolated converters which, so far, in the course have not been covered [COUGH]. So, we will talk about the important topic, of how to introduce a physical magnetic isolation transformer into a power convertor. And, discuss some of the well known, and widely used isolated converter circuits. So, we'll begin with section 6.1 called Circuit Manipulations. And, what we're going to discuss here, is how to take a converter, we already know, and manipulate it to generate a new one. And to perform some, you know, new function that we want. So, what we're going to do, is, start with a buck converter, as the you know, the original rudimentary converter. And, at the beginning of the course, I introduced this converter from first principles, that we have a switch network. That changes the DC component of the voltage. And then, this is followed by a filter that removes the switching harmonics, and passes this changed DC component to the load. And we know, now, from all of the analysis and basic arguments we've given. That the conversion ratio of the buck converter M, is equal to the duty cycle, where this conversion ratio, is the ratio of the output to the input voltages. Okay now, something that we can do to a converter, is first we can consider changing the positions of the power source, and the load. So, here I've drawn, kind of a box around the buck converter, where we have input terminals labeled voltage V1, where there is a source of power connected. And, we have output terminals are labeled V2 here where we've connected a load with a filter capacitor. So, power flows from the source to the load, and we know, since this is a buck converter, that V2 is equal to the duty cycle times V1. Now, one thing that we could do is, connect our power source to port 2 and our load to port 1. And, here's an example of that. so here I've connected the power source here as V2. The load is V1. But the relationship between V1 and V2 is the same. In fact, if you apply volt second balance to this inductor, you find, you get exactly the same relationship, that V2 is still D V1. But now, V2 is the power source, and V1 is the load. So, if we solve for V1, we find that V1 is equal to V2, divided by the duty cycle. And since, the duty cycle is less than 1, the load voltage, V1, is greater than the source voltage, V2. So, this performs the function, actually, of boosting the voltage. And in fact, if you look at this carefully, you might recognize that this looks like a boost converter, just drawn from right to left, instead of from left to right. by interchanging the source in the load, what we've done is reverse the direction of powerflow. So, this actually makes current flow the other direction, through the inductor. And, as a result, we have to look at, carefully, at how we realize the switches. So, back in chapter four, we introduced a formal way to realize the switches. And, if we apply that process here, what we find is that we have to put a transistor from the switching node to ground. And, we have to put a diode from the switching node to port one. which is quite different than what we had to do in the buck converter, when the current flowed the other direction. And, something this does, is that, it actually changes the definition of the duty cycle. We can define the duty cycle as being, the fraction of the time, the switch is in position 1. Or, we could define it as the fraction of time, the switch is in position 2. It's really just semantics. We typically define the duty cycle according to the transistor duty cycle. And here, when this transistor is on, the switch, now, is in position two, not one. In fact, we can just define switch position one, as when the transistor's on. And, if we do that we have to interchange D and D prime. So, V1, we then write as 1 over D prime, times V2, instead of 1 over D. And this then, is in fact, the the traditional equation for the boost converter. That the output voltage, which is now V1, is 1 over D prime, times the input voltage. So, the D prime comes, simply, because power is flowing in the opposite direction, and we have to realize the switches in a different way. So, the boost literally is, simply, a buck converter connected backwards. Okay, a second thing we can do, is we can connect converters and cascade. So, take your favorite converter and make, call it converter number 1. And we know, if we know it's conversion ratio, so, the output voltage of converter 1, V1 is equal to this conversion ratio M1 of D. Times the input voltage Vg. And, we can take that voltage V1, and use it as the input voltage of a second converter. So, take, say, your second most favorite converter, and put it there as converter number 2, and its output voltage that. here we will apply to the load, is the conversion ratio in 2, for the second converter times V1. Okay? So, the overall conversion ratio of this cascade connection, then, is, V is equal to M1, times M2, times Vg. So, we get a conversion ratio of M1 times M2. Okay? Well, that's fine. But let's, let's try it. So, I think a straightforward thing to do, might be to take a buck converter, and put it as converter 1. And let's put a boost converter, as converter 2. So, this combination is capable of making an output voltage, that is either less than, or greater than Vg. Depending on the duty cycles of the individual buck and boost converters. Okay, and so, in fact, if we drive the switches of the, the two converters with the same duty cycle, then what we get for the cascade connection is D over 1, minus D. Which sounds like a buck boost type conversion ratio. And here, literally, is the circuit then. Here's our buck converter, the switch, and LC filter. The output of the buck, becomes the input to the boost converter, that has its switch, and its L and C, driving the load. Okay, well that's all fine however, I would say that there are some things we can do to simplify this circuit. And for one thing, if you look at the, this inner part of this circuit, we have a three pole low-pass filter. So, there's an inductor, then a capacitor, and then another inductor, that are filtering the ripple. Now, you, you can do this if you want, but we don't really have to. We can reduce the order of this low-pass filter, and the basic DC waveforms will be unchanged. Changing the order of the filter, merely changes how it filters the ripple. So, for example, we could remove C1, if we like. And once we've done that, we have two inductors in series, and we can combine the series connection of inductors, into one inductor. So, here's that. We have the two inductors in series, we combined them into a single effective inductor, that's the sum of the two inductances. And, we get this circuit. Okay. This is called the noninverting buck-boost converter. And, it's actually a popular converter. It's widely used in applications such as mobile computing, and cell phones. where we need an output voltage, that is either greater than, or less than the input voltage. And, we, actually, don't have to control the two switch networks with the same duty cycle. You can switch, for example, just one and not the other, if you want. And, that turns out to be a good way to control them. So, if you want to boost, we make the buck switches, just always connected in position 1. And, we operate the boost switches with some duty cycle, to control the boost ratio. And conversely, if we want to buck, we just leave the boost switches in position 2. And, we control the buck switches, with some duty cycle to control the buck ratio of the converter. this is a very efficient converter, and especially, if the output voltage is near the input voltage. we have a low switching loss and low conduction loss, in this converter, and it can operate with very high efficiency. Okay there's something else we can do to this non-inverting, but boost converter. if we just look at what this circuit is, with a switch in the two different positions. And let's assume now, that we operate both switch networks with the same duty cycle, then with the switches in position 1, the inductors connected to the Vg. And, I put a dot here to to follow the polarity, in which the inductors connected. So the dot is connected to Vg. And, the non dot side of the inductor is connected to ground. So, we have this circuit for subinterval 1. In subinterval 2, we have the dot side of the inductor connected to the ground, and the non dot side connected to the output, like this. Okay, So, this is what I just described, and this is this noninverting buck-boost converter. Now, one simple thing that we can do, is change the polarity of the inductor during one of the intervals. So, for example, during subinterval 2, if we just reverse the direction of the inductor. And, connect the dot side to the output voltage, instead of to ground, like this. Then, that will change the polarity of the output voltage. Our inductor current, instead of flowing, in this way to the output, will flow the other direction, and cause a negative output voltage. otherwise, this is the same circuit, as before [COUGH]. So, this is called the inverting buck-boost converter, and it turns out to reduce the number of switches necessary. Because, if you look at this the non dot side of the inductor now, is always connected to ground. And, all you have to do, is connect the dot side, either to Vg in position 1. Or to the output voltage in position 2. Okay? So here are the 2 sub intervals. And, we connect a switch like this, as I just mentioned. And, what we get then, is the inverting buck boost converter, which is what we have talked about previously in this course. So, the inverting buck boost converter, can be derived from the cascade connection, of a buck converter and a boost converter. And then, by reversing the polarity of the inductor, during one of the intervals, we simplify the number of switches needed. And, we get a minus sign, so, that it's a inverting converter. Okay, so cascade connections of converters, then, can actually lead to new converters as well. We cascade two converters, and then simplify the result. And, we can generate a new converter with properties that combine the properties of the two individual original converters. if you construct the equivalent circuit model of the buck-boost converter, what you find is that you actually get two DC transformer models in it. There's a buck transformer and later there's a boost transformer in the equivalent circuit model. And this actually reflects it, the origin of the buck loose converter that it is, in fact, the cascade of a buck followed by a boost. there's other cascade connections possible. I just took one arbitrary one. another well known cascade connection, starts with a boost and, is followed by a buck. So we have boost first, then buck instead of buck followed by boost. And, if we do that connection and follow the same arguments, that I applied to the buck boost converter, what we get in this case is a Cuk converter. which is named after its inventor. And, he actually derived this converter, by cascading a boost followed by a buck. Now you can plug other converters in, and follow them. We're not going to do that. But, as an exercise it's an interesting thing to try to do. And see what other kinds of converter circuits you can generate.