Page 227 - Rashid, Power Electronics Handbook

216 D. Czarkowski

The boost converter operates in the CCM for L > L where
b
2
ð1 ÿ DÞ DR
L ¼ ð13:15Þ
b
2f
For D ¼ 0:5, R ¼ 10 O, and f ¼ 100 kHz, the boundary value
of the inductance is L ¼ 6:25 mH.
b
As shown in Fig. 13.9b, the current supplied to the output
RC circuit is discontinuous. Thus, a larger ®lter capacitor is
required in comparison to that in the buck-derived converters
to limit the output voltage ripple. The ®lter capacitor must
provide the output dc current to the load when the diode D is
off. The minimum value of the ®lter capacitance that results in
the voltage ripple V is given by
r
DV O
C ¼ ð13:16Þ
min
V Rf
r
At D ¼ 0:5, V =V ¼ 1%, R ¼ 10 O, and f ¼ 100 kHz, the
O
r
minimum capacitance for the boost converter is C min ¼ 50 mF.
The boost converter does not have a popular transformer
(isolated) version.

13.5 Buck-Boost Converter

13.5.1 Basic Converter
A nonisolated (transformerless) topology of the buck-boost
converter is shown in Fig. 13.10a. The converter consists of dc
input voltage source V , controlled switch S, inductor L, diode
S
D, ®lter capacitor C, and load resistance R. With the switch on,
FIGURE 13.9 Boost converter: (a) circuit diagram; (b) waveforms. the inductor current increases while the diode is maintained
off. When the switch is turned off, the diode provides a path
for the inductor current. Note the polarity of the diode that
presented in Fig. 13.9b. When the switch S is in the on state,
results in its current being drawn from the output.
the current in the boost inductor increases linearly and the
The buck-boost converter waveforms are depicted in Fig.
diode D is off at that time. When the switch S is turned off, the
13.10b. The condition of a zero volt-second product for the
energy stored in the inductor is released through the diode to
inductor in steady state yields
the output RC circuit.
Using Faraday's law for the boost inductor
V DT ¼ÿV ð1 ÿ DÞT ð13:17Þ
S O
V DT ¼ðV ÿ V Þð1 ÿ DÞT ð13:13Þ
S O S Hence, the dc voltage transfer function of the buck-boost
converter is
from which the dc voltage transfer function turns out to be
V O D
M ¼ÿ ð13:18Þ
V V 1 ÿ D
V O 1 S
M ¼ ð13:14Þ
V
V S 1 ÿ D
The output voltage V is negative with respect to the ground.
O
Its magnitude can be either greater or smaller (equal at
As the name of the converter suggests, the output voltage is D ¼ 0:5) than the input voltage as the name of the converter
always greater than the input voltage. implies.