AAT1415 Datasheet, PDF (28/32 Pages) Advanced Analog Technology, Inc. – FIVE-CHANNEL DC-DC CONVERTER WITH A 2.5V LDO

Advanced Analog Technology, Inc.
May 2008
AAT1415/AAT1415A
Where V_RIPPLE is the output ripple voltage, ∆I_L is the
inductor ripple current, f_SW is the switching frequency
and COUT is the output capacitance. In the case of
tantalum or low- ESR electrolytic capacitors, the ESR
dominates the impedance at the switching frequency,
and so the output ripple is calculated as:
V_RIPPLE ≈ ∆I_L × R_ESR
Where V_RIPPLE is the output voltage ripple, ∆I_L is the
inductor ripple current, and R_ESR is the equivalent
series resistance of the output capacitors.
Boost Converter Compensation
The compensation resistor and capacitor (Figure 9a)
are chosen to optimize control-loop stability. The boost
converter employs current-mode control, thereby
simplifying the control-loop compensation. When the
converter operates with continuous conduction mode
(typically the case), a right-half-plane zero appears in
the loop-gain frequency response. To ensure stability,
the cross over frequency ( f_C ) should be much less
than that of the right-half-plane zero.
For CCM, the right-half-plane zero frequency ( f_RHPZ )
is given by the following:
following equation:
R_C
= I_L(PK)
×
R_CS
TD% × V_{IN _}
× G_m
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
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:
f_RHPZ
=
V_{OUT _} × (1− D)²
2π × L × I_LOAD
Typically target cross over frequency ( f_C ) is the value
for 1/6 of the RHPZ. Choose f_C , and then calculate
compensation capacitor ( C_C ) as follows:
C_C
=
V_{IN _}
R_CS
×
G_m
2π ⋅ f_C
×
(1− D)
I_LOAD
Where V_{IN _} is the feedback regulation voltage, 1.25V
(typ), R_CS is the current-sense amplifier transresistance,
0.25V/A (typ), G_M is the error amplifier
transconductance, 70µS (typ). Select R_C based on the
allowed transient-droop ( TD% ) requirements by the
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 _}
V_{OUT _} :
C_U
=
2π × R_{UPPER _}
1
× f_C
×


V_IN
_

V_{OUT _}



from IN_ to
If C_P or C_U is calculated to be less than 10pF, it can
be omitted. Additionally, C_P or C_U can suppress the
inrush current.
So, for a 3.3V/250mA output with V_I = 2.0V, L = 3.5µH,
R_UPPER = 164k, f_SW = 500kHz and transient-droop
5%:
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