[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.