Page 162 - Rashid, Power Electronics Handbook

10 Diode Recti®ers 151

FIGURE 10.21 Inductive-input dc ®lters. (a) Simplest inductive-input
dc ®lter; (b) L-section ®lter.

For the simple inductive-input dc ®lter shown in Fig.
10.21a, the ripple is reduced by the factor

v R
o
¼ q  ð10:64Þ
v L 2 2
R þð2pf L Þ
r f
where v is the ripple voltage before ®ltering, v is the ripple
L o FIGURE 10.23 Voltage and current waveforms of full-wave recti®er
voltage after ®ltering, and f is the ripple frequency.
r with inductor-input dc ®lter.
For the inductive-input dc ®lter shown in Fig. 10.21b, the
amount of reduction in the ripple voltage can be estimated as
10.5.1.2 Critical Inductance L C

v o ¼ 1 ð10:65Þ In the case of single-phase full-wave recti®ers, the critical
2
v 1 ÿð2pf Þ L C inductance can be found as
L r f f
R
where f is the ripple frequency, if R 1=2pf C : Full-wave L ¼ ð10:66Þ
C
f
r
r
6pf i
10.5.1.1 Voltage and Current Waveforms for a Full- where f is the input mains frequency.
Wave Rectifier with Inductor-Input dc Filter i
In the case of polyphase recti®ers, the critical inductance
Figure 10.22 shows a single-phase full-wave recti®er with an can be found as
inductor-input dc ®lter. The voltage and current waveforms
are illustrated in Fig. 10.23. R
When the inductance of L is in®nite, the current through Polyphase L ¼ 3pmðm ÿ 1Þf ð10:67Þ
C
2
f
the inductor and the output voltage are constant. When i
inductor L is ®nite, the current through the inductor has a where m is the ratio of the lowest ripple frequency to the input
f
ripple component, as shown by the dotted lines in Fig. 10.23.
frequency, for example, m ¼ 6 for a three-phase bridge recti-
If the input inductance is too small, the current decreases to
®er.
zero (becoming discontinuous) during a portion of the time
between the peaks of the recti®er output voltage. The mini-
mum value of inductance required to maintain a continuous 10.5.1.3 Determining the Input Inductance for a
current is known as the critical inductance L . Given Ripple Factor
C
In practice, the choice of the input inductance depends on the
required ripple factor of the output voltage. The ripple voltage
of a recti®er without ®ltering can be found by means of
Fourier analysis. For example, the coef®cient of the nth
harmonic component of the recti®ed voltage v shown in
L
Fig. 10.22 can be expressed as
ÿ4V m
v ¼ ð10:68Þ
L n 2
pðn ÿ 1Þ
FIGURE 10.22 A full-wave recti®er with inductor-input dc ®lter. where n ¼ 2; 4; 8; ... , etc.