The field of power electronics is concerned with the processing and control of electrical power using high efficiency electronic circuits The key functional element in power electronics is called a switching converter. This lecture describes the basic functions performed by switching converters and it introduces how high efficincy electronic circuits can be constructed that realize these functions. The switching converter generally includes two input terminals. One is the power input. Where the, where a source is connected. The second input is a control input that tells the converter how to process the input power to produce the output. Dc to Dc conversion is a common function performed by converters. In which the voltage of the DC is changed and possibly regulated. So we may change a, say a high-input voltage into a low DC output voltage. Rectification is the converstion of AC to DC. And in the process we may want to control the output voltage, the DC output voltage. And, and maybe also the AC input current waveform. The inverse of rectification is called inversion, in which we have a DC input, and we produce an AC output of a controllable frequency and magnitude. AC to AC cycloconversion. Involves changing the frequency and the amplitude of, of the AC voltage. In each of these, the switching converter is the key electronic power processing element, and it is composed of electronic devices as well as reactive elements and we attempt to, to build this with very high efficiency. Control is invariably required. [COUGH] we usually want to regulate the output voltage. We may, although, we may want to control currents or other quantities, so we're generally also building some kind of control system. That adjusts the control input to the converter, for example, to regulate the output. We can do this with either traditional analog feedback or nowadays it's economically feasible to use quite sophisticated control using digital micro-controllers. High efficiency is essential in any application that involves very much power. We want high efficiency nowadays, of course, because we want to conserve energy. But in addition to that it's simply not possible and not economically feasible. To process large amounts of power with low efficiency because our convertor will, will not be able to handle the heat from the power lost. So here's the equation for efficiency. It's the ratio of output power to input power. And the loss is the difference between the input and output power, which we can express in terms of the output power and the efficiency in this way. Now, our switching converters are loss limited. They're limited by the amount of heat sinking that we have and the size of the enclosure. And so for a loss limited converter with a given an efficiency, this limits the amount of output power that, that the converter can produce. So, if we can build a converter with higher efficiency, then we can either reduce the the loss and build a smaller converter, with smaller heat sinks, or for the same amount of heat sinking, we can get more output power. And build a converter that produces more power. So a measure of how good the converter technology is really is the ratio of the output power to the efficiency. And here it's expressed in terms of efficiency. We can solve for this quantity and it turns out to be efficienty divided by 1 minus efficiency. And it's plotted here, and so you can see that even increasing the efficiency by a few percent can increase the amount of output power or reduce or increase the ratio of output power to loss substantially, and so our goal is to produce efficiencies that approach one which, which makes the ratio of output power to loss approach infinity. So, the higher we can get on this curve, the smaller our converter can be, and the more input and output power it can produce. So this drawing here is meant to, to represent a very small size converter with very large input and output converters. So we have a very small converter with very high efficiency. The processes is a very large amount of electric power. How do we build a, a circuit that changes the voltage with high efficiency? Here's a, diagram of general, the different categories of electrical circuit elements that we have. Resistors, capacitors, magnetics, inc, including transformers and inductors, and semiconductor devices that here are generally grouped into two, two categories. The first is linear-mode transistors, such as class A amplifiers or off-amp circuits, and the second is switched-mode, which is transistors that are operated. As on-off devices, such as in a digital circuit, where they're either all the way on or all the way off. In signal processing, such as you probably learned in undergraduate electronics and circuits courses, we usually avoid magnetics well, we don't have to, but magnetics generally are more expensive. Their hard to integrate on integrated circuits, and most engineers don't know how to design them and so for a variety of reasons, we usually ignore or, avoid magnetics. But resistors and capacitors are fine, linear and switch mode semiconductors are also common. In power processing by contrast what we want to do is avoid using elements that consume power. So for that reason we don't want to use resistors. However, capacitors and magnetics are fine, and in fact. It may be easier in a high power application to build a good inductor than it is to build a good capacitor. But, we commonly use inductors, capacitors, transformers and other elements because although they store energy, they don't, ideally they don't consume power. And we can get that stored energy back at some later time. We avoid linear mode transistors for the same reason that we avoid resistors with a class A amplifier for example operates with a transistor having voltage across it and current through it at the same time and so it consumes power. On the other hand, switched mode. Transistors or transistors that are operated as on-off switches are, are good. they don't consume power. The reason for that is if we can get them to operate close to the behavior of an ideal switch, then what happens is when the switch is closed, there's no voltage across the switch. And when the switch is open, there's no current through the switch and in either state the power consumed by the switch which is the product of origin current is zero. So to the extent that we can make a semi-conductor device operate as an ideal switch, like this we, the, the semi-conductor device will be lossless. So let's do a simple example of how to build a DC-DC converter with high efficiency and using just inductors, capacitors, and switches. Okay, so I'm going to take simple examples, some round numbers here. We have an input voltage I've labeled V g. That is a power source. And it has, it's a 100 volts. And what we would like to do is change this 100 volts into 50 volts to supply a resistive load. And just for some round numbers, let's suppose the resistance is five ohms. So that we have ten amps flowing through our load. Okay? So how can this converter be realized? First of all, let's ask how you, you know beginning circuits class, what ciricuits do you know that could change 100 volts into 50 volts. Okay, well the resisted voltage divider is one of the first circuits taught usually in a beginning circuits class. And we learned that the, the output voltage of the divider is equal to this voltage divider ratio of the load resistance over the sum of the two resistances times the input voltage, so if we adjust this added resistor, to be the same value as our load resistor, we get a divider ratio of a half And the output voltage will be half of the input. Okay? The problem with this is that the same current flowing to the load also flows through this resistor and the same power in the load then is equal to the power in this resistor. And so we will have our ten amps flowing through the resistor. That has 50 volts across it, so they'll be 500 watts of loss in this resistor. There's 500 watts going to the load and we draw 1000 watts out of each E, so the efficiency is only 50%. At low power levels, it's common to build a series pass regulator circuit, that operates almost in the same way as the resist voltage divider, except, instead of resistor we put a transistor that operates in the active region, And it has the same voltage across it that the resistor on the previous slide had, so it dissipates the same 500 Watts. When the series pass regulator with the transistor allows us to do is to build a feedback loop that adjusts the control or the drive of the transistor to regulate the output voltage. but in this example, the series pass regular is approximately 50% efficient. So, we need, a very large transistor that can take 500 watts, and that has enough heat sinking to dissipate that 500 watts, which is not an easy thing to do. Let's consider instead how to do this function e, with switches. So, instead of an active region transistor we will use a semi-conductors that are operated like on-off switches. And here I'm going to draw an ideal switch, but we will realize this switch in practice with transistors and diodes that turn on and off. So, let's suppose we have such a switch. We switch it quickly between positions one and two, so that the voltage coming out of the switch network from here to here, Vs sub-t, has this waveform. So when the switch is in position one, the voltage, Vs, is equal to the input voltage, Vg, of 100 volts. When the switch is in position two the output voltage is zero, and we will operate the switch so half of the time it's in position one, and the other half it's in position two. Okay, what do we accomplish with this? While a switch changes the DC voltage level, [COUGH]. So here's the, this actual waveform coming out of the switch. We can use Fourier analysis to find its DC component. And you may recall from Fourier analysis that the DC component of a waveform. Is found by integrating the wave form over one period, and then dividing by the period. So if you integrate this wave form, the integral is the area under this curve, which is, what, this width? Dts times the height, Vg, so we get an area. Of DTsVg and if you divide by the ts then what we find for the dc component is that it, it is d times Vg or d is the duty cycle or the fraction of time that the switch is in position one. Okay, so if the switch is in position one for half of the time, the duty cycle is a half and the out, the output voltage of the switch has a dc component that is half of the input. So the switch succeeds, then, in changing the DC component of the voltage from 100 volts down to 50 volts. Generally, we don't like to have that switched voltage appear across our load, so we will put a low-pass filter, and here's an L C low-pass filter that can be put in that If we design this filter correctly, so the cutoff frequency is much lower than the switching frequency, this filter will pass the DC component, but it will reject the switching frequency in its harmonics and not let them pass through to the load, so that the output voltage is smooth and essentially is just the DC component. Of 50 volts, so this a circuit that, can change the DC voltage and it does it with components that are ideally lossless, only switches, inductors and capacitors, so it can have effeciences that approach 100%. this is known as the Buck converter. Here is one way to realize the switch using transistors and diodes. We have an, a power mosfet and a power diode that's switched together. and I've also shown here a feedback circuit, say a simple analog feedback circuit, that adjusts the duty cycle. It, it actually turns the transistor on and off and adjusts it's duty cycle. To regulate the output voltage. So this is a buck regulator. It's possible to build converters that will change any voltage into any other voltage. Here's an example of a boost converter. that can increase the voltage. So we can build circuits that contain inductors, capacitors and switches connected in different ways that can actually change any voltage into any other voltage, as desired. Here's another example of a single phase inverter. Here we have two single pole double throw switches. With the load and filter connected differentially between their outputs, so that the voltage, differentially, between the two switch outputs, looks like this, can switch between plus Vg when the switches are in position one, or minus V, Vg when the switches are in position two, and by changing the duty cycle, we can change the average value. And we can actually modulate the duty cycle sinusoidally and make a sine wave of output voltage. If we like, if we want to produce say a dc to ac inverter. Okay. So, in this course you are going to learn how to build these converter circuits, how to analyze them and model them. To, for example, predict their efficiencies and also how to design and model their control systems.