AAT1102_5 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 F_m is:
( ) _{( )( ) Fm}
(s)
=
d
v_ei
= ^{2 f s 2 s 2 + 2ξwn s + wn 2}
T_pi0 R_cs s s + w_zi s + w_sh
Where w_sh
=
3w_s
π
⎜⎛
⎝
1
1
−
+
α
α
⎟⎞ ,α
⎠
=
M₂
M₁
− M_a
+ M_a
,
w_s = 2π . f _s
AAT1102 (BIN2)
=
βg_m R_c
s
+ w_c
s
12 f _s ²T _p0
R_cs T _{pi 0}
×
(s + w_z1 )(s − w_z2 )
(s + w_zi )(s ² + sw_{s h} + 12 f _s ² )
Where β = ^VFB ,
Vo
The compensator transfer function
Therefore, F_m depends on duty to inductor current
transfer functionT_pi , and f _s is the clock switching
T_c (s)
=
v_c
v _fb
=
g _m R_c
s + w_c
s
,
where
w_c
=
1
R_c C _c
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.
ν_c
ν_O
_^ν
+
The closed-current loop transfer functionT_icl is:
Comparator
( ₍ ) _{) ( ) Ticl (s)}
=
12 f _s ²
R_cs T _{pi 0}
×
s ² + 2ξw_n s + w_n ²
s + w_zi s ² + w_sh 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 T_d
is:
T_d
(s)
=
v_o (s)
v_c (s)
=
T_icl
(s)T_p (s)
The voltage-loop gain with current loop closed is:
Compensator design guide:
1.
Crossover
frequency
f _ci
<
1
2
f_s
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:
L_vi (s) = βT_c (s)T_d (s)
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V5.0