AAT1102 Datasheet, PDF (10/18 Pages) Advanced Analog Technology, Inc. – ADVANCED PWM DC-DC CONVERTER WITH INTERNAL SWITCH AND SOFT-START

Advanced Analog Technology, Inc.
Inductor selection
I _{L( peak)}
=
I _IN
+
V_IN D
2Lf_s
,
where
D
is
duty
cycle
And I _IN
= ^Io
1− D
, D = 1 − ^VIN ,
V_o
The inductor current rating must be greater than
I _{L(peak) .}
AAT1102
Power Stage Transfer Functions
The duty to output voltage transfer function T_p is:
T_p (s) =
v_o
d
=
T_p0
(s + w_esr )(s − w_z2 )
s ² + 2ξw_n s + w_n ²
Where T_p0
= V_O
− r_c
(1 − D)(R_L
) + r_c ^{, wesr}
=
1
Cr_c
Loop Compensation Design
And
w_z2
=
R_L (1 − D)²
L
−r
, w_n
=
(1 − D)² R_L + r
LC(R_L + r_c )
ξ = ^{C[r(RL + rc ) + RLrc (1 − D)2 ] + L} ,
2 LC(R_L + r_c )[r + (1 − D)² R_L ]
r = r_L + Dr_DS + (1 − D)R_F
Fig.1. Closed-current loop for boost with PCM
r_L is the inductor equivalent series resistance, r_c
is capacitor ESR, R_L is the converter load
resistance, C is output filter capacitor, r_DS is the
transistor on-resistance, and R_F is the diode
forward resistance.
The duty to inductor current transfer function T_pi is:
T_pi (s) =
i_l
d
= T_pi0
s²
s + w_zi
+ 2ξw_n s + w_n ²
Where
T_pi0
=
V_O (R_L
L(R_L
+
+
2r_c
r_c )
)
,
w_zi
=
C(R_L
1
/2+
r_c )
Fig.2. Block diagram of boost converter with
PCM
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