We previously discussed some circuit manipulations.
To ex, expose the relationships between the different
converters and to derive some new ones. There's another way to do this. We can actually derive all possible
converters that have a given set of constraints. Such as having, say, two switching
intervals and one inductor. I'm not going to derive all the possible
converters. It turns out that there are an infinite
number of them. And they do some pretty interesting and
diverse things. But I do want to briefly summarize some of the basic results.
so, what's shown here is I think the most rudimentary
class of converters, where we have one inductor
that is switched between the input source VG and the output load V in two
different ways. One way during interval one, and another
way during interval two. Now, there's only a limited number of
possible ways to connect in, an inductor between two voltages and pick one for the
first interval and one for the second. And we can write down all the possible ways to do that and see what converters
occur. And the answer is right here, there are
eight converters that are interesting. in addition to a few degenerate or
redundant cases that don't add anything new. And we can group these converters,
actually, into three different groups. the first group are converters that I
would call dc-dc. Namely that if you have a positive input
voltage then the output voltage is always of the same polarity
regardless of the duty cycle. there's also two converters where when you vary the duty cycle from zero to
one, the output voltage changes polarity in such a way that these are
useful as dc to ac type inverters. And then the the last two are the
inversion of the inverters. So, they're more suitable for ac to dc
type applications or rectifiers. So here they are.
the first two are the buck and the boost, which we
already know about. the next two, we've also discussed. We have the buck-boost and the
noninverting buck-boost. so these are the four converters in this
class. they're all you can make with a single inductor and two intervals that are dc/dc
type converters. Okay?
Converters five and six are ones that you might say are suitable as
inverters. And we've already discussed the H bridge
in the last lecture. This is converter number five. Converter number six is a pretty strange
one. It was invented, actually, the transformer
isolated version of this was invented at the
Watkins-Johnson company. And we call this the Watkins-Johnson
converter. It has this conversion ratio 2d minus 1
divided by d. It looks like this. but it passes through 0 at d of a half and
it can make either positive or negative output voltages,
although the m of d function is a non-linear one. and then the last two in this class are
the inverse of numbers five and six. So converter number seven is what you get
if you swap the source and the load of the H bridge and this one is sometimes called
the current-fed bridge. So its conversion ratio is 1 over 2D minus
1. And at d of a half, the ideal conversion
ratio goes to infinity. So here's a plot of its conversion ratio.
This is a pretty strange conversion ratio. But, in fact, if the input is a sinusoid,
and you want the output to be dc, this is the conversion ratio that you need to,
to perform this rectification function. So, when the sinusoid at the input passes
through zero, and the output voltage is non-zero, then
the ratio, or the conversion ratio, goes to infinity. But in fact, we're not making infinite
output voltage, we're just holding up the output voltage when the
input is going through zero. So, if you vary the duty cycle
sinusoidally about a half, then you can convert an ac input voltage
to a dc output. And then the last one is what we get from inversion of source and load with the
Watkins-Johnson converter and its conversion ratio is the inverse, which
also goes to infinity at d of a half. So those are all the converters that are
possible if you only have one inductor and you have
two switching intervals. we can think of other classes of
converters, and the next most logical class might be the class of
two inductor type converters. So we have two inductors and we switch
them in one way between the source and load for the first interval, and a different way for the second
interval. There are many more than eight members of
this class of converters and they can do some pretty
interesting different things. here's just a couple of them.
The Cuk converter, we've previously mentioned derived this by cascade of a
boost followed by a buck converter. it's an inverting buck-boost type
converter. The SEPIC is another converter in this
class. the transformer isolated version of the
SEPIC was invented at Bell Labs in the 1970's. And they called it a single ended primary inductance converter, whose
initials are SEPIC. this turns out to be a noninverting
buck-boost converter. And it's interesting, actually finds quite
a few applications. It's interesting, for one, because it can, its transistor has its source connected to
ground. And you realize the switch is with
transistor and diode like this. so it's easy to drive this transistor with
a low side driver and get this noninverting
buck-boost type characteristic. Here's another converter, is the inverse
of the SEPIC. It's also a noninverting buck-boost type
converter. some people call this the zeta converter. then there's a lot of other very different
converters. So some of them have what we call
quadratic conversion ratios that are functions of
the duty cycle, squared. Here's one of those that was in an earlier
homework assignment that has a conversion ratio equal to D squared.
and it's interesting that you can get such a conversion ratio in a converter that has
three diodes and only one transistor. We can get quadratic conversion ratios
that have other functions also like buck-boost
squared or other types of conversion ratios by
some of the members of this class. So there are some very interesting and exotic conversion ratios that are
possible. In general you know, if you have an
arbitrary number of inductors and switches, we can build there are an infinite number of converters that are
possible. And in this universe of converters, there
are many different and unusual functions of duty cycle and some of these
can can have practical applications.