AAT1164 Datasheet, PDF (18/24 Pages) Advanced Analog Technology, Inc. – TRIPLE-CHANNEL TFT LCD POWER SOLUTION

Advanced Analog Technology, Inc.
April 2007
AAT1164/AAT1164B/AAT1164C
ξ = ^{COUT [r (RL + rC ) + RLrC (1− D)2 ] + L} ,
2 LC_OUT (R_L + r_C )[r + (1− D)² R_L ]
r = r_L + Dr_DS + (1 − D)R_F
r_L is the inductor equivalent series resistance, r_C is
capacitor ESR, R_L is the converter load resistance, C_OUT
is the output filter capacitor, r_DS is the transistor turn on
resistance, and R_F is the diode forward resistance.
The duty to inductor current transfer functionT_pi is:
T_pi (s)
=
i_l
d
=
T_pi0
s²
+
s + ω_zi
2ξω_ns +
ω_n2
(( ) ⁾ ( ) ^Where
T_pi0
=
V_O
L
R_L + 2r_C
R_L + r_C
, ω_zi = _COUT
1
R_L / 2 + r_C
( ⁽ )( ⁾ ) ^Ticl(s)
=
12f_S2
R_CST_pi0
x
s² + 2ξω_ns + ω_n2
s + ω_zi s² + ω_shs + 12f_S2
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:
L_VI(s) = βT_C(s)T_d(s)
= βg_mR_C
s + ω_c
s
1 2 f_S ² T_{p 0}
R_CS T_pi0
×
Current Sampling Transfer Function
Error voltage to duty transfer function F_m(s) is:
d
( ) ^2f_S2 ^{s2 + 2ξω}_n^{s + ω}_n2
( )( ) ^{Fm(s) = V}ei ⁼ T_pi0R_CSs s + ω_zi s + ω_sh
Where ω_sh
=
3ω_s
π


1−
1+
α
α


,
α
=
M₂
M₁
− M_a
+ M_a
,
ω_s = 2πf_S
Therefore, F_m(s) depends on duty to inductor current
transfer function T_pi(s), and f_S is the clock switching
frequency; R_CS is the current-sense amplifier
transresistance.
(s + ω_z1)(s − ω_z2 )
(s + ω_zi )(s² + sω_sh + 12f_S2 )
Where β = ^VFB
V_O
The compensator transfer function
T_C(s) =
V_C
V_fb
= g_mR_C
s + ω_c
s
,
Where
ω_c
=
1
R_CC_C
For the boost converter M₁ = V_IN / L and
M₂ = (V_O–V_IN) / L.
For AAT1164, R_CS = 0.24 V/A, Ma is slope
compensation, Ma = 0.8×10^6.
The closed-current loop transfer function T_pi(s) is:
Figure 6. Voltage Loop Compensator
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