Advanced Analog Technology, Inc
.
May 2008
AAT1168/1168A/1168B
VFB
VO
Current Sampling Transfer Function
Whereβ =
Error voltage to duty transfer function Fm is:
2
2
2
2f
s + 2ξw s + w
n n
s
pi0 CS
sh
The compensator transfer function
d
F (s) =
m
=
V
s + w
v
T
R
s s + w
(
s + w
)
(
)
C
c
ei
zi
T (s) =
C
= g R
m C
v
s
fb
3ws
M2 −Ma
M1 + Ma
1− α
1+ α
Where
Where wsh
=
, α =
π
1
w
=
c
R C
C
C
ws = 2πfs
Therefore, Fm depends on duty to inductor current
transfer function Tpi , and fs is the clock switching
frequency;
R
is the current-sense amplifier
CS
transresistance.
For the boost converter,
=
V
/
L
and
=
M2
M1
IN
(
VO
−
V )/L .
IN
For AAT1168,
R
= 0.24 V/A, Ma is slope
CS
compensation, Ma = 0.8×106.
The closed-current loop transfer function
T
is
:
Figure 6. Voltage Loop Compensator
Compensator design guide:
icl
2
s2 + 2
ξwns + wn
2
1
2
s+ w
12fs
1. Crossover frequencyfci
2. Gain margin>10dB
<
fs
T (s) =
x
icl
s2 + w s +12f
sh s
2
RCS pi0
T
(
)
(
)
zi
The Voltage-Loop Gain with Current Loop
Closed
3. Phase margin>45
The control to output voltage transfer function Td is
VO(s)
:
4. The Lvi(s)
=
1
at crossover frequency, Therefore,
is determined by:
the compensator resistance,
R
Td(s) =
= T (s)Tp(s)
icl
C
VC(s)
R + 2r
L
V
2πf CR
ci
The voltage-loop gain with current loop closed is:
C
O
CS
R
=
C
V
g k
m
r
FB
1−D R −
)
(
L
Lvi(s) =
β
TC(s)Td(s)
1−D
(
)
2
12f
R
T
p0
s + w
s
c
= βg R
m
×
C
s
T
CS pi0
s
+
s
−
wz2
2
(
s
+
wzi
)
(s2
+
sws
+
12fs )
h
–
–
–
Advanced Analog Technology, Inc
Version 1.00
. –
Page 17 of 22
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