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.