We saw in the last lecture how to apply transformation such as inversion of source and load or cascade connection of converters. To take a DC-DC converter and generate a new DC-DC converter, that has different, possibly desirable properties. The approaches that were considered in that lecture will, will not generate an inverter. So, suppose we have DC-DC converters, but we want to make a DC to AC or AC to DC type converter. we need to be able to change the polarity of the voltage, and so far in the previous lecture none of those approaches would accomplish that. So in this lecture, we'll talk briefly about one of the widely used ways to to produce AC. And it's, called the differential connection of the load. So, if we have two DC DC converters. What we can do is connect the load differentially between their outputs. So, for example, suppose these converters are buck converters. 'Kay. So, the first buck produces an output voltage that is the duty cycle times Vg, and it's a DC voltage. The second buck produces an output voltage that is its duty cycle times the input voltage, which is also DC. But we connect the load differentially between the outputs. So that the voltage across the load is, voltage1 minus voltage2. Now, if we have, if both buck converters produce the same output voltage. Then we will get zero volts, differentially, across the load. But if we make one of the converters produce a higher voltage than the other, then we can get either positive or negative voltage across the load depending on which output, which buck converter makes the higher voltage. And in fact if we control the duty cycles of the two buck converters in a skillful way, then we could make, for example, a sinusoidal voltage. That appears differentially across the load. So, here, we'll draw out the circuit. Here's buck converter number one, with its switch and lc filter. Here's buck converter number two with its switch and lc filter. And what we're going to do is drive buck converter number two. With the compliment of the duty cycle of convertor one. So if we drive the transistor at buck convertor one with, say, the duty cycle d, then buck convertor two will have its transistor driven with d prime. Okay? So then the voltage across the load will be V1 minus V2. Or DVg minus D prime Vg. And we can combine the D and D prime together to get this. 2D minus 1 is actually D minus D prime. Or D minus the quantity 1 minus D. It, [COUGH], so we get 2D minus 1. [SOUND] Okay? Here's a plot of that conversion ratio. 2D minus one versus D. At D of a half of a conversion ratio is zero. And when D is greater than a half, we get a positive voltage. And when D is less than a half, we get a negative voltage. Now this circuit can be considerably simplified. We have a lot of LC filters, and we can again, like in the last lecture, simplify this filtering. And the first thing we might want to do is, if you look at this, you see we have capacitors that are connected from the individual outputs to ground. Where what we might really want to do instead is directly put a capacitor across our load and filter the load voltage. So here what I've done is remove these two capacitors and replace them with a single capacitor across the load. Once we do that, you can see that now effectively we have our two inductors in series. So we could take those two inductors, and combine them into a single inductor, like this, and this value would be the sum of the two individual inductor values. And now, you can see, we have simply an lc low pass filter that's taking the differential voltage coming out of the two switch networks. And putting that through a two pole low pas filter to provide the load voltage. Okay? this is the way we most often build this circuit. And on the right side here, is exactly the same circuit, it's just re-drawn in the way it's normally drawn, where we have our two switch networks, and the load, and LC low-pass filters connected differentially across the outputs. this is often called the H Bridge, or Fall bridge, circuit, or a bridge inverter circuit, it's very commonly used in single phase inverter applications. But we have a DC input Vg, that we want to produce a sinusoidal output across the load V. its also used in DC, DC applications. for example in DC motor drives or server line amplifiers in control systems, where we want to drive a DC motor in either direction. So to drive the motor in one direction, we apply a positive voltage, that's DC, to drive it in the opposite direction, we apply a negative DC voltage. And so we can do that with a circuit like this as well. We might, in that, case actually replace the whole rlc network simply with a DC motor, connected differentially between these terminals. The self inductance of the motor winding takes the place of this inductor, and the inertia of the shaft replaces the capacitor. If we want to make three phase AC, we can do the same trick with three converters. So here, we might have three different buck converters, one for each phase. Each buck converter produces an output voltage that is, its duty cycle times the DC input voltage Vg. And we connect our three phase load differentially across the outputs the three, of the three converters. Okay? So the line to line voltage from phase A to phase B, will be V1 minus V2. The line to line voltage from B, phase B to phase C, will be V2 minus V3, and so on. like this. So what we do then, is we control the duty cycles of the three converters to make the three individual AC output voltages be the desired sinusoids. with no offset, or no DC bias. So here is that circuit. Here again, we have three buck converters, with their individual filters. As before, we can change the filtering, and again, instead of filtering the voltage from one phase to ground, we might instead want to filter the AC voltage. So we can move these capacitors across the AC load. Here, the circuit is drawn with the capacitors omitted altogether, and we simply have the three inductors of the three buck converters, and the three switch networks. One for each phase. If desired, we can put three phase capacitor filters as well. For example, we could connect them in what's called a delta connection, and make them filter each line-to-line voltage. Or in some applications, we might omit those capacitors. if we want to build a motor drive. We might replace this whole network with, say, a three phase induction motor. The inductors become the inductances of the windings, and there will, there will be also filtering from the inertia of the load. But, effectively, we have a three phase AC load that is connected differentially across the outputs of three buck converters. Here's another similar kind of circuit, that has a boost type characteristic, there's a single inductor on the input, there are switches for each of the three phases, and we have capacitor filters on the output. this is the current source inverter It has a boost type conversion characteristic. But, it has a similar three phase bridge in it. In each of these circuits, I've drawn ideal switches, but of course we have to realize the switches carefully, according to the procedures we discussed in chapter four. So, for for this circuit, with the buck converters, our buck switches, need to be current bi-directional switches, because they conduct the AC output currents. And in the current source inverter, we need voltage bi-directional switches, because they block the output voltages. But we've now already discussed how to do this, and we know how. 'Kay? So we've seen the, the differential connections of DC-DC converters can lead to inverter type characteristics. And gives us a way to really synthesize and understand where some of these inverter circuits come from. Now there are other ways to do it as well, but this differential connection is in fact the most widely used approach.