Advanced Analog Technology, Inc.
Inductor selection
Power Stage Transfer Functions
The duty to output voltage transfer function Tp is:
VIN D
IL
= IIN +
, where D is duty cycle
( peak)
2Lfs
vo
d
(s + wesr )(s − wz2 )
Io
VIN
Tp (s) =
= Tp0
And IIN
=
, D = 1−
,
2
s2 + 2ξwn s + wn
1− D
Vo
The inductor current rating must be greater than
− rc
1
IL(peak)
.
WhereTp0 = VO
, wesr
=
(
1− D)(RL + rc
)
Crc
Loop Compensation Design
And
2
RL
1− D
)
− r
(
1− D
LC RL + rc
2 ] + L
)
2 RL + r
wz2 =
, wn =
L
(
)
C[r
RL + rc
)
+ RL rc
[r +
1− D
(
)
ξ =
,
2 LC RL + rc
(
)
1− D
)
2 RL ]
r = rL + DrDS + (1− D)RF
rL is the inductor equivalent series resistance, rc
is capacitor ESR, RL is the converter load
resistance, C is output filter capacitor, rDS is the
transistor on-resistance, and RF is the diode
Fig.1. Closed-current loop for boost with PCM
forward resistance.
The duty to inductor current transfer function Tpi is:
il
s + wzi
s2 + 2ξwn s + wn
Tpi (s) = = Tpi0
2
d
VO
RL + 2r
)
, wzi =
1
c
Where Tpi0
=
(
)
C
(
RL / 2 + r
)
L RL + r
c
c
Fig.2. Block diagram of boost converter with
PCM
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