Datasheet

O
OFFMAX
OO
C
t
IV ´D<D
1
2
L
O
I
O
2
v
1
2
[C
O
(V
OS
2
* V
O
2
)]
TPS40200-EP
SGLS371A –JANUARY 2007–REVISED JANUARY 2013 www.ti.com
Output Capacitance
In order to satisfy the output voltage overshoot and undershoot specifications, there must be enough output
capacitance to keep the output voltage within the specified voltage limits during load current steps.
In a situation where a full load of 2.5 A within the specified voltage limits is suddenly removed, the output
capacitor must absorb energy stored in the output inductor. This condition may be described by realizing that the
energy stored in the inductor must be suddenly absorbed by the output capacitance. This energy relationship is
written as:
(15)
Where:
V
OS
= Allowed overshoot voltage above the output voltage
L
O
= Inductance
I
O
= Output current
C
O
= Output capacitance
V
O
= Output voltage
In this application, the worst-case load step is 2.25 A and the allowed overshoot is 100 mV. With a 33-μH output
inductor, this implies an output capacitance of 249 μF for a 3.3-V output and 165 μF for a 5-V output.
When the load increases from minimum to full load, the output capacitor must deliver current to the load. The
worst case is for a minimum on time that occurs at 16 V in and 3.3 V out and minimum load. This corresponds to
an off time of (1 – 0.2) times the period 3.3 μs, and is the worst-case time before the inductor can start supplying
current. This situation may be represented by:
(16)
Where:
ΔV
O
= Undershoot specification of 60 mV
ΔI
O
= Load current step
t
OFFMAX
= Maximum off time
This condition produces a requirement of 100 μf for the output capacitance. The larger of these two requirements
becomes the minimum value of output capacitance.
The ripple current develops a voltage across the ESR of the output capacitance, so another requirement on this
component is that its ESR be small relative to the ripple voltage specification.
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