Environmental Engineering Reference
In-Depth Information
The inductor and the capacitor act as a filter to improve the quality of the output voltage and
the load current.
The switch
Q
is turned on and off periodically. Assume that the switching period is
T
and the duty cycle is
k
. Then, the OFF time in one period is (1
k
)
T
. The circuit has two
operation modes: Mode 1 when the switch
Q
is turned ON and Mode 2 when the switch
Q
is
turned OFF. The equivalent circuits in both modes are shown in Figures 1.14(b) and 1.14(c),
respectively. During Mode 1, the inductor current
i
L
increases linearly because
−
L
d
i
L
d
t
=
v
s
−
v
o
,
where
v
s
−
v
o
is almost constant and positive. During Mode 2, the inductor current freewheels
through the diode and decreases linearly because
L
d
i
L
d
t
=
0
−
v
o
,
where
−
v
o
is almost constant and negative. The corresponding inductor current waveform is
shown in Figure 1.14(d). Ideally, the ripple current should flow through the capacitor and the
corresponding voltage waveform is shown in Figure 1.14(e).
In the steady state, the net energy changed in the inductor should be zero during one period,
which means the current increased in Mode 1 should be equal to the current decreased in
Mode 2. That is,
kT
L
(
(1
−
k
)
T
L
v
s
−
v
o
)
=
v
o
.
Hence, the output voltage is
v
o
=
k
v
s
.
Indeed, this is a buck converter because
α
=
k
.
1.2.2.2 Boost Converters
Figure 1.15(a) shows a typical boost converter. A boost converter is also called a step-up
converter because the output voltage is higher than the input voltage. As a result, the output
current is lower than the input current because of the power balance. Similarly, there are also
two operation modes when the switch
Q
is turned ON and OFF. The equivalent circuits in
these two modes are shown in Figures 1.15(b) and 1.15(c), respectively.
During Mode 1, the inductor current increases linearly because
L
d
i
L
d
t
=
v
s
−
0
,
and the inductor stores energy from the power source while the capacitor discharges to
supply the load. During Mode 2, both the energy stored in the inductor and from the power
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