Buck Boost Converter
SECTION: G-2 (MECHANICAL ENGG.)
CAREER POINT UNIVERSITY
Prepared by Prepared for
Vinit Kumar Chauhan Mr.Somesh Sir
A study on the properties and control of a promising circuit topology for a DC-DC
buckboost power converter is presented. The circuit contains four transistors
operated synchronously in couples. We propose a set of mathematical models to
describe this circuit, and an approach to determine the behavior of the losses
occurring inside of it. These are then combined in order to achieve a control
scheme that drives the circuit while minimizing said losses. The control strategy
proposed here is based on a combined feedback (MPC) and feedforward action.
Control performance parameters such as disturbances rejection capability have
been investigated as well.
once provided by the diode - i.e. current rectification - is now undertaken by a
rectifying transistor, typically a MOSFET. Such rectification improves efficiency,
thermal performance, power densities, manufacturability, reliability as well as
having typically faster switching transients, and decreases the overall system cost
for power supplies (Selders 2003). These performance increases are mainly due to
the fact that the on-resistance of MOSFETs, RDS;on, can be reduced either by
increasing the size of the die or by paralleling discrete devices, while the forward
voltage-drop across diodes cannot be lowered under a certain (physically imposed)
limit; this motivates the choice of using synchronous rectifiers in the circuit
topology studied for this project.
The main objective of this project can now be stated as follows: by exploiting
these two degrees of freedom we will be able to affect the state of the circuit;
thus, many internal states will lead to the same output voltage, and the main task
will be to choose among all these possibilities the one that will lead to the least
possible power losses - i.e. to the most efficient way of driving the circuit.
This has been achieved as follows: first, different models of the circuit have been
developed for different purposes, see next Chapter. After that, a thorough study of
the losses inside the circuit has been conducted using some of these models. Based
on the study of the losses, the design of a control that drives the circuit while
accounting for losses has been done, and conclusive chapter, where possible
outlooks will be discussed and a summary of this project will be given.
Basic Analytical Models: Full-Buck
The circuit can be considered equivalent to a synchronous buck converter if the
third switch T3 is always turned on, i.e. if d2 = 1. Apreliminary study of the ”buck
mode” is useful to show the general approach which is going to be used for more
It turns out in fact that this version is the most attractive one as a starting point
for a study because the differential equations describing the states of the circuit
coming from the averaging method are linear by nature. This makes the successive
development of a control for this mode of the circuit straight-forward.
The procedure is the following: first, consider the case where T1 is on, and T2 is
off; applying Kirchhoff Voltage Law (KVL) and Kirchhoff Current Law (KCL) to
the circuit depicted in Figure 2.1 leads to the following equations for the states:
Then, consider the complementary case where T1 is off, and T2 is on; the same
equations hold basically, if vin is taken to be zero. Again, applying KCL and KVL
Our objective is to drive the circuit while minimizing the losses occurring inside
of it. In order to do this, models for the behavior of these losses are necessary;
There are two different types of losses occurring inside the circuit: Conduction
Losses (PConduction) and Switching Losses (PSwitching); in the following, these
two types of losses are going to be shortly described.
These are losses of resistive type, and, for the particular circuit that is investigated,
they are produced because of current flowing through the following resistive
MOSFETs’ channel resistance RDS;on
MOSFETs’ body diode
Capacitance’s ESR (Equivalent Series Resistance)
The mechanisms involved in the production of switching losses are more
complicated than the previous ones. They are produced by the action of turning on
and off active devices on the power’s path, therefore they only happen at discrete
times ”tj” (where j indexes all the times at which switchings of a given MOSFET
occur) and for a short period; they occur under the following circumstances
(Mohanet al. n.d.):
switching of power currents (”turning on and off currents in the presence of
parasitic drain capacitance charge and discharge
gate drive losses
body diode reverse recovery
MODELING POWER LOSSES
because of this, if the current iL is positive (flowing from the input stage to the
output stage), then switching losses will occur only at switches T1 and T4.
Conversely, if iL is negative, then switching losses will occur in switches T2 and
T3. On a side note, it can be noted that since these losses occur at switching times,
the more switchings there are, the higher the switching losses will be (if the same
MOSFETs are used), i.e. switching losses grow proportionally to the switching
Therefore, on one hand, switching frequency should not be chosen to be arbitrarily
high. But on the other hand, switching frequency should not be chosen too low
either because that would cause higher ripples on the output voltage.
Also, it is of critical importance to note at this point that during the simulations
described further in this chapter, the magnitude of the losses is estimated using
these very equations. But since these equations only give results that are
proportional to the exact values, their shape will describe the general behavior of
the losses properly, but their magnitude will need to be corrected by an adequate
multiplicative correction constant. This constant will strongly depend on the choice
of components that is going to be made. This aspect is discussed more in detail in
the next Section.
Based on the research done on the models in Chapter 2 and the Losses in Chapter3,
it is now possible to start developing an efficient control for the plant. As a
reminder, our task is to control the duty cycles of each pair of transistors and their
phase, so as to ensure:
First and most important: reaching of and stabilizing around a given output
reaching the target steady state should happen in the desired manner, i.e.
The controller needs to handle transients properly;
The controller also needs to be able to reject disturbances (usually
encountered on the load and on the input voltage source vin);
while doing all this, the controller (in the full buck-boost mode) needs to
choose among the infinite possibilities of inputs, that would satisfy the
above conditions, those that will cause the least losses.
Basic Control Strategies
Buck, the Simplest Mode
As discussed in Chapter 2.3.1, the model obtained with the averaging technique
is linear. There is only one variable being controlled (d1) and there is no
optimization of controls towards least losses. This is why a simple feedback
approach (as opposed to a combined feedforward and feedback approach, as
discussed later) is enough to control this scheme.
The buck-boost implementation is similar to the boost one in that non-linearity is
still present. Other than that, it turns out that exploiting the possibilities given by
the full buck-boost operation requires additional care because:
There are now multiple inputs
Control actions also need to drive the plant while ensuring least possible
It can be argued that if this precalculated lookup table does indeed contain the best
values the plant (circuit) can be driven at steady state, then the contribution from
the MPC feedback can be avoided. This is of course not the case: first, it is clear
that the contribution from the MPC boosts the performance during the initial
transient. Furthermore, a feedback action is always desired in any control scheme,
in order to ensure the ability to reject disturbances and model uncertainties.
The two contributions to the u signal coming from the feedback and from the
feedfoward part can be seen in Figure 4.10. As it can be seen, the MPC supplies
the plant with a contribution different than zero only during the transient. As soon
as the transient has settled, it contribution goes to zero and stays there; this is
always the case as long as no disturbances or other external influences affect the
circuit; if disturbances are indeed applied, then the MPC control is going to counter
those and its contribution is going to be different than zero.
A typical disturbance rejection done by the controller can be seen in the blue
bottom curve depicts the perturbation (in percentage) affecting the input voltage
vin, while in the upper graph, the red curve shows how this perturbation affects the
output voltage if no feedback action is taken, and the green one shows the output if
rejections are countered by the MPC.
The resulting output start-up performance for a set of different output references
can be seen in notice that the controller is indeed able to drive the circuit both in its
”buck” mode and ”boost” mode, as specified in the objectives for this project.
Further, notice that the control is indeed able to properly drive the plant also
towards steady states different than those around which the models were
linearized, thus showing its ”well” behavior.
The present work is a study on the circuit depicted in Figure 1.2 which is used to
achieve DC-DC power conversion. In the first part of the work (Chapters 1-3),
different models for its behavior have been developed, including a state-space
averaged model and an hybrid one.
Based on these models simulations have been conducted in order to assess the
losses occurring inside of it. These simulations reveal that it is in general not
possible to drive the circuit while minimizing simultaneously both conduction and
switching losses. Rather, in order to drive the circuit in the most efficent way, an
optimizedbalance between these two losses needs to be made. Further, this balance
depends on the specific choice of components used.
In the second part of the work (Chapter 4), for a specific choice of components,
the implementation of a controller for this circuit is discussed. The controller has
been designed as working on the combined action of a precalculated look-up table
(feedforward action) and a Model Predictive Control (MPC) based feedback
The abilty to drive the circuit both in its boost as well its buck modes and its noise
rejection capabilty are the performance benchmarks for this controller which have
been studied. Recommended extensions to this work include the refinement of the
models to account for parasitics and non-ideal behaviours, so as to enable a
subsequent controller implementation based solely on MPC, and a more accurate
evaluation of thecontroller’s stabilization capabilties.
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