Boost converter

A boost converter (step-up converter) is a DC-to-DC power converter with an output voltage greater than its
input voltage. It is a class of s w i t c h e d - m o d e p o w e r s u p p l y (SMPS) containing at least two
s e m i c o n d u c t o r switches (a diode and a transistor) and at least one energy storage element, a capacitor, inductor,
or the two in combination. Filters made of capacitors (sometimes in combination with inductors) are normally
added to the output of the
converter to reduce output voltage ripple.

Overview
Power for the boost converter can
come from any suitable DC sources,
such as batteries, solar panels,
rectifiers and DC generators. A process
that changes one DC voltage to a
different DC voltage is called DC to
DC conversion. A boost converter is a
The basic schematic of a boost converter. The switch is typically a MOSFET, IGBT, or
DC to DC converter with an BJT.
output
voltage greater than the source voltage.
A boost converter is sometimes called a step-up converter since it “steps up” the source voltage. Since power (
) must be conserved, the output current is lower than the source current.

History
For high efficiency, the SMPS switch must turn on and off quickly and have low losses. The advent of a commercial
semiconductor switch in the 1950s represented a major milestone that made SMPSs such as the boost converter
possible. The major DC to DC converters were developed in the early 1960s when semiconductor switches had
become available. The aerospace industry’s need for small, lightweight, and efficient power converters led to the
converter’s rapid development.
Switched systems such as SMPS are a challenge to design since its model depends on whether a switch is opened or
closed. R. D. Middlebrook from Caltech in 1977 published the models for DC to DC converters used today.
Middlebrook averaged the circuit configurations for each switch state in a technique called state-space averaging.
This simplification reduced two systems into one. The new model led to insightful design equations which helped
SMPS growth.

Applications
Battery power systems often stack cells in series to achieve higher voltage. However, sufficient stacking of cells is
not possible in many high voltage applications due to lack of space. Boost converters can increase the voltage and
reduce the number of cells. Two battery-powered applications that use boost converters are hybrid electric vehicles
(HEV) and lighting systems.
The NHW20 model Toyota Prius HEV uses a 500 V motor. Without a boost converter, the Prius would need
nearly
417 cells to power the motor. However, a Prius actually uses only 168 cells and boosts the battery voltage from 202
V to 500 V. Boost converters also power devices at smaller scale applications, such as portable lighting systems. A
white LED typically requires 3.3 V to emit light, and a boost converter can step up the voltage from a single 1.5 V
alkaline cell to power the lamp. Boost converters can also produce higher voltages to operate cold cathode
fluorescent tubes (CCFL) in devices such as LCD backlights and some flashlights.
A boost converter is used as the voltage increase mechanism in the circuit known as the 'Joule thief'. This circuit
topology is used with low power battery applications, and is aimed at the ability of a boost converter to 'steal' the
remaining energy in a battery. This energy would otherwise be wasted since the low voltage of a nearly depleted
battery makes it unusable for a normal load. This energy would otherwise remain untapped because many
applications do not allow enough current to flow through a load when voltage decreases. This voltage decrease
occurs as batteries become depleted, and is a characteristic of the ubiquitous alkaline battery. Since ( ) as well, and R

tends to be stable, power available to the load goes down significantly as voltage decreases.

Circuit analysis

Operating principle
The key principle that drives the boost converter is the tendency of an i n d u c t o r to resist changes in current
by creating and destroying a magnetic field. In a boost converter, the output voltage is always higher than the input
voltage. A schematic of a boost power stage is shown in Figure 1.
(a) When the switch is closed, current flows through the inductor in clockwise direction and the inductor stores some
energy by generating a magnetic field. Polarity of the left side of the inductor is positive.
(b) When the switch is opened, current will be reduced as the impedance is higher. The magnetic field previously
created will be destroyed to maintain the current flow towards the load. Thus the polarity will be reversed (means
left side of inductor will be negative now). As a result two sources will be in series causing a higher voltage to
charge the capacitor through the diode D.
If the switch is cycled fast enough, the inductor will not discharge fully in between charging stages, and the load will
always see a voltage greater than that of the input source alone when the switch is opened. Also while the switch is
opened, the capacitor in parallel with the load is charged to this combined voltage. When the switch is then closed
and the right hand side is shorted out from the left hand side, the capacitor is therefore able to provide the voltage
and energy to the load. During this time, the blocking diode prevents the capacitor from discharging through the
switch. The switch must of course be opened again fast enough to prevent the capacitor from discharging too much.
The basic principle of a Boost converter consists of 2
distinct states (see figure 2):
• in the On-state, the switch S (see figure 1) is closed,
resulting in an increase in the inductor current;
• in the Off-state, the switch is open and the only path
offered to inductor current is through the flyback
diode D, the capacitor C and the load R. This results Fig. 1: Boost converter schematic
in transferring the energy accumulated during the
On-state into the capacitor.
• The input current is the same as the inductor current as can be seen in figure 2. So it is not discontinuous as in the
buck converter and the requirements on the input filter are relaxed compared to a buck converter.
 Fig. 2: The two configurations of a boost
converter,depending on the state of the switch S.

Continuous mode

When a boost converter operates in

continuous mode, the current through
the inductor ( ) never falls to zero.
Figure 3 shows the typical waveforms
of currents and voltages in a converter
operating in this mode. The output
voltage can be calculated as follows, in
the case of an ideal converter (i.e.
using components with an ideal
behaviour) operating in steady
[1]
conditions:
During the On-state, the switch S is
closed, which makes the input voltage
( ) appear across the inductor,
Fig. 3: Waveforms of current and voltage in a boost converter operating in continuous
mode. which causes a change in current (
) flowing through the inductor during a
time period (t) by the formula:

At the end of the On-state, the increase of IL is therefore:

D is the duty cycle. It represents the fraction of the commutation period T during which the switch is On. Therefore
D ranges between 0 (S is never on) and 1 (S is always on).
During the Off-state, the switch S is open, so the inductor current flows through the load. If we consider zero voltage
drop in the diode, and a capacitor large enough for its voltage to remain constant, the evolution of I is:
L

Therefore, the variation of I during the Off-period is:

L

As we consider that the converter operates in steady-state conditions, the amount of energy stored in each of its
components has to be the same at the beginning and at the end of a commutation cycle. In particular, the energy
stored in the inductor is given by:

So, the inductor current has to be the same at the start and end of the commutation cycle. This means the overall
change in the current (the sum of the changes) is zero:

Substituting and by their expressions yields:

This can be written as:

Which in turn reveals the duty cycle to be:

The above expression shows that the output voltage is always higher than the input voltage (as the duty cycle goes
from 0 to 1), and that it increases with D, theoretically to infinity as D approaches 1. This is why this converter is
sometimes referred to as astep-upconverter.

Discontinuous mode
If the ripple amplitude of the current is
too high, the inductor may be
completely discharged before the end
of a whole commutation cycle. This
commonly occurs under light loads. In
this case, the current through the
inductor falls to zero during part of the
period (see waveforms in figure 4).
Although slight, the difference has a
strong effect on the output voltage
equation. It can be calculated as
follows:
As the inductor current at the
beginning of the cycle is zero, its

maximum value (at

) is Fig. 4:Waveforms of current and voltage in a boost converter operating in discontinuous
mode.
 falls to zero after :
During the off-period, IL

Using the two previous equations, δ is:

The load current Io is equal to the average diode current (I ).

D