AAT1168 Datasheet, PDF (17/22 Pages) Advanced Analog Technology, Inc. – TRIPLE-CHANNEL TFT LCD POWER SOLUTION WITH OPERATIONAL AMPLIFIERS

Advanced Analog Technology, Inc.
May 2008
Current Sampling Transfer Function
Error voltage to duty transfer function F_m is:
( ) _{Fm(s) =}
d
v_ei
=
2f_s2 s² + 2ξw_ns + w_n2
T_pi0R_CSs (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 = 2πf_s
AAT1168/1168A/1168B
Where β = ^VFB
V_O
The compensator transfer function
T_C(s) =
V_C
v _fb
= g_mR_C
s + w_c
s
Where
w_c
=
1
R_CC_C
Therefore, F_m depends on duty to inductor current
transfer function T_pi , and f_s is the clock switching
frequency; R_CS is the current-sense amplifier
transresistance.
For the boost converter, _M1= V_IN / L and _M2 =
( V_O − V_IN )/ L .
For AAT1168, R_CS = 0.24 V/A, M_a is slope
compensation, M_a = 0.8×10^6.
The closed-current loop transfer function T_icl is:
( ⁽ )( ⁾ ) ^Ticl(s)
=
12f_s2
R_CST_pi0
x
s² + 2ξw_ns + w_n2
s + w_zi s² + w_shs + 12f_s2
Figure 6. Voltage Loop Compensator
Compensator design guide:
1.
Crossover
frequency f_ci
<
1
2
f_s
2. Gain margin>10dB
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 + w_c
s
12f_s2T_p0
R _{C S} T_{p i0}
×
(s + w _z1)(s − w _z2 )
(s + w _zi )(s² + sw _sh + 12f_s2 )
∘ 3. Phase margin>45
4. The L_vi (s) = 1 at crossover frequency, Therefore,
the compensator resistance, R_C is determined by:
R_C
=
V_O
V_FB
2πf_ciCR_CS
g_mk
(R_L + 2r_C )

(1−

D ) R_L
−
r
(1−
D)



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