AAT1415 Datasheet, PDF (29/32 Pages) Advanced Analog Technology, Inc. – FIVE-CHANNEL DC-DC CONVERTER WITH A 2.5V LDO

Advanced Analog Technology, Inc.
May 2008
AAT1415/AAT1415A
C_C
=
1.25V
0.25V / A
×
70µ A / V
2π ⋅ 35kHz
×
(1− 0.39)
250mA
≈
3.3nF
,
R_C
= 0.64 ×
0.25V / A
0.05 ×1.25 × 70µ A
/
V
≈ 36kΩ ,
equation:
R_C
= I_L(PK)
×
R_CS
TD% × V_{IN _}
× G_m
C_OUT
=
250mA
3.3V
× 36kΩ × 3.3nF ≈ 10µF
When the C_OUT value is two to three times greater than
what’s calculated above, better output voltage ripple
can be achieved.
Where I_L(PK) is the inductor peak current.
The output filter capacitor (typically ceramic capacitor)
is then chosen to cancel the R_CC_C zero:
C_OUT
=
I_LOAD
V_{OUT _}
× R_CC_C
C_U
=
1
2π ×164kΩ × 35kHz × (1.25V _3.3V)
≈ 100pF
Buck Converter Compensation
The buck converter employs current-mode control,
thereby simplifying the control-loop compensation.
When the buck converter operates with continuous
inductor current (typically the case), a R_LOAD C_OUT pole
appears in the loop-gain frequency response. To
ensure stability, set the compensation R_CC_C (Figure
9a) to zero to compensate for the R_LOAD C_OUT pole.
Then set the loop crossover frequency below 1/5 of the
switching frequency. The compensation resistor and
capacitor are then chosen to optimize control-loop
stability.
Choose the compensation capacitor C_C to set the
desired crossover frequency f_C . Determine the value
by the following equation:
C_C
=
V_{IN _}
I_LOAD × R_CS
×
G_m
2π ⋅ f_C
If the output filter capacitor (typically electrolytic
capacitor) has significant equivalent series resistance
(ESR), a zero occurs at the following:
Z_ESR
=
1
2π × C_OUT
× R_ESR
If Z_ESR >> f_C , it can be ignored. If Z_ESR is less than
f_C , it should be cancelled with a pole set by capacitor
C_P connected from EO_ to GND:
C_P
=
C_OUT × R_ESR
R_C
If the system wants better transient response, it can
parallel a capacitor C_U with R_{UPPER _} from IN_ to
V_{OUT _} :
C_U
=
2π × R_{UPPER _}
1
× f_C
×


V_IN
_

V_{OUT _}



where V_{IN_} is the feedback regulation voltage, 1.25V
(typ), R_CS is the current-sense amplifier transresistance,
0.5V/A (typ), G_m is the error amplifier transconductance,
70µS (typ). Select R_C based on the allowed
transient-droop ( TD% ) requirements by the following
If C_P or C_U is calculated to be less than 10pF, it can
be omitted.
So, for a 1.5V/250mA output with V_I = 3.0V, L = 10µH,
R_UPPER = 20 kΩ , f_SW = 500kHz and transient-droop
3%:
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Version 3.00
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