Datasheet
C
O
+
L
ƪ
ǒ
I
OH
Ǔ
2
*
ǒ
I
OL
Ǔ
2
ƫ
ƪ
ǒ
V
f
Ǔ
2
*
ǒ
V
i
Ǔ
2
ƫ
(Farads)
V
2
+
ƪ
ǒ
V
f
Ǔ
2
*
ǒ
V
i
Ǔ
2
ƫ
ǒ
Volts
2
Ǔ
E
C
+
1
2
C V
2
(Joules)
I
2
+
ƪ
ǒ
I
OH
Ǔ
2
*
ǒ
I
OL
Ǔ
2
ƫ
ǒ
(
Amperes
)
2
Ǔ
E
L
+
1
2
L I
2
(Joules)
O SW
1
V I ESR
8 C f
æ ö
æ ö
D = D ´ +
ç ÷
ç ÷
ç ÷
´ ´
è ø
è ø
TPS40054
TPS40055
TPS40057
SLUS593H –DECEMBER 2003–REVISED JULY 2012
www.ti.com
CALCULATING THE OUTPUT CAPACITANCE
The output capacitance depends on the output ripple voltage requirement, output ripple current, as well as any
output voltage deviation requirement during a load transient.
The output ripple voltage is a function of both the output capacitance and capacitor ESR. The worst-case output
ripple is described in Equation 6.
where
• C
O
is the output capacitance
• ESR is the equivalent series resistance of the output capacitance (6)
The output ripple voltage is typically between 90% and 95% due to the ESR component.
The output capacitance requirement typically increases in the presence of a load transient requirement. During a
step load, the output capacitance must provide energy to the load (light to heavy load step) or absorb excess
inductor energy (heavy to light load step) while maintaining the output voltage within acceptable limits. The
amount of capacitance depends on the magnitude of the load step, the speed of the loop and the size of the
inductor.
Stepping the load from a heavy load to a light load results in an output overshoot. Excess energy stored in the
inductor must be absorbed by the output capacitance. The energy stored in the inductor is described in
Equation 7.
(7)
where
• I
OH
is the output current under heavy load conditions
• I
OL
is the output current under light load conditions (8)
Energy in the capacitor is described in Equation 9.
(9)
where
where
• V
f
is the final peak capacitor voltage
• V
i
is the initial capacitor voltage (10)
Substituting Equation 8 into Equation 7, then substituting Equation 10 into Equation 9, then setting Equation 9
equal to Equation 7, and then solving for C
O
yields the capacitance described in Equation 11.
(11)
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