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DV
+ DI
ESR
)
1
8
C
OUT
f
SW
(V)
(3)
C
O(under) +
L
I
STEP
2
V
UNDER
D
MAX
V
IN * VOUT
(F)
(4)
C
O(over) +
L
I
STEP
2
V
OVER
V
OUT
(F)
(5)
SLUS726 – SEPTEMBER 2006
APPLICATION INFORMATION (continued)
where
V is the peak to peak output ripple voltage (V)
I is the peak-to-peak ripple current in the inductor (A)
f
SW is the switching frequency chosen for the converter (Hz)
C
OUT is the capacitance value of the output capacitor (F)
ESR is the equivalent series resistance of the capacitor, C
OUT ()
For electrolytic capacitors, the output ripple voltage is almost entirely (90% or more) due to the ESR of the
capacitor. When using ceramic output capacitors, the output ripple contribution from ESR is much smaller and
the capacitance value itself becomes more significant. Paralleling output capacitors to achieve a desired output
capacitance generally lowers the effective ESR more effectively than using a single larger capacitor. This
increases performance at the expense of board area.
If there are load transient requirements that must be met, the overshoot and undershoot of the output voltage
must be considered. If the load suddenly increases, the output voltage momentarily dips until the current in the
inductor can ramp up to match the new load requirement. If the feedback loop is designed aggressively, this
undershoot can be minimized. For a given undershoot specification, the required output capacitance can be
found by:
where
C
O(under) is the output capacitance required to meet the undershoot specification (F)
L is the inductor value (H)
I
STEP is the change in load current (A)
V
UNDER is the maximum allowable output voltage undershoot
D
MAX is the maximum duty cycle for the converter
V
IN is the input voltage
V
OUT is the output voltage
Similarly, if the load current suddenly goes from a high value to a low value, the output voltage overshoots. The
ouput voltage rises until the current in the inductor drops to the new load current. The required capacitance for a
given amount of overshoot can be found by:
where
C
O(over) is the output capacitance required to meet the undershoot specification (F)
L in the inductor value (H)
I
STEP is the change in load current (A)
V
OVER is the maximum allowable output voltage overshoot
V
OUT is the output voltage
The required value of output capacitance is the maximum of CO(under) and CO(over).
Knowing the inductor ripple current, the switching frequency, the required load step and the allowable output
voltage excursion allows calculation of the required output capacitance from a transient response perspective.
The actual value and type of output capacitance is the one that satisfies both the ripple and transient
specifications.
16