Advanced Analog Technology, Inc.
April 2007
AAT1164/AAT1164B/AAT1164C
2
[r R + r + R r 1−D ] + L
2
s2 + 2ξωns +ωn
2
C
(
)
(
)
12fS
OUT
L
C
L C
ξ =
,
T (s) =
x
icl
2
R + r [r + 1−D R ]
2
s+ ωzi s2 +
ω
shs +12fS
RCS pi0
T
(
)
2 LC
(
)
(
)
(
)
OUT
L
C
L
r = r + Dr + (1− D)R
F
L
DS
The Voltage-Loop Gain with Current Loop
Closed
rL is the inductor equivalent series resistance, rC is
capacitor ESR, RL is the converter load resistance, COUT
is the output filter capacitor, rDS is the transistor turn on
resistance, and RF is the diode forward resistance.
The duty to inductor current transfer functionTpi is:
The control to output voltage transfer function Td is
:
VO(s)
Td(s) =
= T (s)Tp(s)
icl
VC(s)
The voltage-loop gain with current loop closed is:
LVI(s) = TC(s)Td(s)
i
T (s) = = T
s +ω
zi
l
pi
pi0
2
2
d
s + 2ξω s +ω
n
n
β
VO R + 2r
2
,
1
L
C
12fS Tp0
RCSTpi0
s + ωc
Where Tpi0
=
ωzi =
= βgmRC
×
L R +r
L
COUT R / 2+r
( )
(
)
C
L
C
s
s + ω
s − ω
z2
Current Sampling Transfer Function
z1
s + ω (s2 + sω +12fS
)
2
Error voltage to duty transfer function Fm(s) is:
(
)
zi
sh
2
2
2fS s2 + 2ξω s +ω
d
n
n
V
FB
Fm(s) =
=
Where β =
Vei
Tpi0RCSs s +ω s +ω
V
O
(
)
(
)
zi
sh
The compensator transfer function
3
ωs
M2 − Ma
M1 + Ma
1−
1+
α
α
Whereωsh
ωs = 2 fS
=
,
α
=
,
V
s + ω
c
C
π
T (s) =
C
= g R
m C
,
V
s
fb
π
Where
1
ω
=
c
R C
C
Therefore, Fm(s) depends on duty to inductor current
transfer function Tpi(s), and fS is the clock switching
frequency; RCS is the current-sense amplifier
transresistance.
C
For the boost converter M1 = VIN / L and
M2 = (VO–VIN) / L.
For AAT1164, RCS = 0.24 V/A, Ma is slope
compensation, Ma = 0.8×106.
The closed-current loop transfer function Tpi(s) is
:
Figure 6. Voltage Loop Compensator
–
–
–
Advanced Analog Technology, Inc
Version 1.00
. –
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