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.