Advanced Analog Technology, Inc.
2
Current Sampling Transfer
Function
12 fs Tp0
s + wc
= βgm Rc
×
s
RcsTpi 0
Error voltage to duty transfer function Fm is:
)
2
2
2 fs
s2 + 2ξwn s + wn
d
2
(
s + wzi
)
(s2 + sws +12 fs )
Fm (s) =
=
h
vei Tpi0 Rcs s
(
s + wzi )(s + wsh
)
VFB
Vo
Where β =
,
3ws
M 2 − M a
M1 + M a
1−α
1+α
⎛
⎜
⎞
⎟
Where wsh =
ws = 2π. fs
,α =
,
π
⎝
⎠
The compensator transfer function
vc
s + wc
1
Therefore, Fm depends on duty to inductor current
transfer functionTpi , and fs is the clock switching
frequency; Rcs is the current-sense amplifier
Tc (s) =
= gm Rc
, where wc =
vfb
s
RcCc
νO
transresistance. For the boost converter
=VIN / L
M1
and
= (VO -VIN )/ L
M 2
For AAT1102 , Rcs = 0.275 V/A, M a is slope
compensation, M a =0.8×106.
ν
_
νc
+
The closed-current loop transfer functionTicl is:
Comparator
2
2
12 fs
s2 + 2ξwn s + wn
Ticl (s) =
×
2
RcsTpi0
(
s + wzi
)
(
s2 + wsh s +12 fs
)
Fig.3. Voltage loop compensator
Compensator design guide:
1
1. Crossover frequency fci < fs
The Voltage-Loop Gain With
Current Loop Closed
2
2. Gain margin>10dB
The control to output voltage transfer function Td
3. Phase margin>40∘
is:
vo (s)
4. The Lvi (s) = 1 at crossover frequency, Therefore,
Td (s) =
= Ticl (s)Tp (s)
vc (s)
the compensator resistance, Rc is determined
by:
The voltage-loop gain with current loop closed is:
Lvi (s) = βTc (s)Td (s)
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