Advanced Analog Technology, Inc.
AAT1102 (BIN2)
Current Sampling Transfer
Function
Error voltage to duty transfer function
F
m
is:
2
f
s
s
2
+
2
ξ
w
n
s
+
w
n
d
F
m
(
s
)
=
=
v
ei
T
pi
0
R
cs
s
(
s
+
w
zi
)(
s
+
w
sh
)
2
2
s
+
w
c
12
f
s
T
p
0
=
β
g
m
R
c
×
s
R
cs
T
pi
0
2
(
)
(
s
+
w
z
1
)(
s
−
w
z
2
)
(
s
+
w
zi
)
(
s
2
+
sw
s h
+
12
f
s
2
)
Where
β
=
V
FB
,
Vo
Where
w
sh
=
3
w
s
⎛
1
−
α
⎞
M
−
M
a
,
⎜
⎟
,
α
=
2
π
⎝
1
+
α
⎠
M
1
+
M
a
w
s
=
2
π
.
f
s
The compensator transfer function
Therefore,
F
m
depends on duty to inductor current
T
(
s
)
=
v
c
=
g R s
+
w
c
, where
w
=
1
c
m c
c
R
c
C
c
s
v
fb
transfer function
T
pi
, and
f
s
is the clock switching
frequency;
R
cs
is the current-sense amplifier
transresistance. For the boost converter
M
1
=
V
IN
/
L
and
M
2
= (
V
O
-
V
IN
)/
L
For AAT1102 ,
R
cs
= 0.275 V/A,
M
a
is slope
compensation,
M
a
=0.8
×
10
6.
The closed-current loop transfer function
T
icl
12
f
s
s
2
+
2
ξ
w
n
s
+
w
n
T
icl
(
s
)
=
×
R
cs
T
pi
0
(
s
+
w
zi
)
s
2
+
w
sh
s
+
12
f
s
2
2
2
�½
O
�½
c
_
+
Comparator
�½
is
:
(
(
)
)
Fig.3. Voltage loop compensator
Compensator design guide:
1
f
s
2
The Voltage-Loop Gain With
Current Loop Closed
The control to output voltage transfer function
T
d
is
:
v
(
s
)
T
d
(
s
)
=
o
=
T
icl
(
s
)
T
p
(
s
)
v
c
(
s
)
The voltage-loop gain with current loop closed is:
L
vi
(
s
)
=
β
T
c
(
s
)
T
d
(
s
)
1. Crossover frequency
f
ci
<
2. Gain margin>10dB
3. Phase margin>40
∘
4. The
L
vi
(
s
)
=
1
at crossover frequency, Therefore,
the compensator resistance,
R
c
is determined
by:
–
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–
–
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.
–
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