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AAT1102 Datasheet, PDF (11/18 Pages) Advanced Analog Technology, Inc. – ADVANCED PWM DC-DC CONVERTER WITH INTERNAL SWITCH AND SOFT-START
Advanced Analog Technology, Inc.
Current Sampling Transfer
Function
Error voltage to duty transfer function Fm is:
( ) ( )( ) Fm (s) =
d
vei
= 2 f s 2 s 2 + 2ξwn s + wn 2
Tpi0 Rcs s s + wzi s + wsh
Where wsh
=
3ws
π


1
1
−
+
α
α
 ,α

=
M2
M1
− Ma
+ Ma
,
ws = 2π . f s
=
βgm Rc
s + wc
s
12 f s 2T p0
Rcs T pi 0
×
(s + wz1 )(s − wz2 )
(s + wzi )(s 2 + sws h + 12 f s 2 )
Where β = VFB ,
Vo
AAT1102
The compensator transfer function
Therefore, Fm depends on duty to inductor current
transfer functionTpi , and f s is the clock switching
Tc (s) =
vc
v fb
=
g m Rc
s + wc
s
,
where
wc
=
1
RcCc
frequency; Rcs is the current-sense amplifier
transresistance. For the boost converter M 1 =VIN / L
and M 2 = (VO -VIN )/ L
For AAT1102 , Rcs = 0.275 V/A, M a is slope
compensation, M a =0.8ͪ106.
The closed-current loop transfer functionTicl is:
( ( ) ) ( ) Ticl (s)
=
12 f s 2
RcsT pi 0
×
s 2 + 2ξwn s + wn 2
s + wzi s 2 + wsh s + 12 f s 2
Fig.3. Voltage loop compensator
The Voltage-Loop Gain With
Current Loop Closed
The control to output voltage transfer function Td
is:
Td
(s)
=
vo (s)
vc (s)
=
Ticl
(s)Tp (s)
The voltage-loop gain with current loop closed is:
Compensator design guide:
1.
Crossover
frequency
f ci
<
1
2
fs
2. Gain margin>10dB
3. Phase margin>40ш
4. The Lvi (s) = 1 at crossover frequency, Therefore,
the compensator resistance, Rc is determined
by:
Lvi (s) = βTc (s)Td (s) ʳ
؀ –᨜ᣊֺઝैݾٝૻڶֆ– ׹
– Advanced Analog Technology, Inc. –
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