Datasheet

V
DROOP
= 'I
OUTSTEP
x R
ESR
+
L x 'I
OUTSTEP
2
C
OUT
x (V
IN
- V
OUT
)
'V
OUT
 'I
L
x
1
8 x f
SW
x C
OUT
R
ESR
+
L =
(V
IN
± V
OUT
)
D
üI
L
f
SW
V
IN
I
L AVG
= I
OUT
'I
L
Time
Time
I
L
V
SW
LM21212-1
SNVS671E –FEBRUARY 2011–REVISED MARCH 2013 www.ti.com
Figure 32. Switch and Inductor Current Waveforms
Once the ripple current has been determined, the appropriate inductor size can be calculated using the following
equation:
(5)
OUTPUT CAPACITOR SELECTION
The output capacitor, C
OUT
, filters the inductor ripple current and provides a source of charge for transient load
conditions. A wide range of output capacitors may be used with the LM21212-1 that provide various advantages.
The best performance is typically obtained using ceramic, SP or OSCON type chemistries. Typical trade-offs are
that the ceramic capacitor provides extremely low ESR to reduce the output ripple voltage and noise spikes,
while the SP and OSCON capacitors provide a large bulk capacitance in a small volume for transient loading
conditions.
When selecting the value for the output capacitor, the two performance characteristics to consider are the output
voltage ripple and transient response. The output voltage ripple can be approximated by using the following
formula:
(6)
where ΔV
OUT
(V) is the amount of peak to peak voltage ripple at the power supply output, R
ESR
(Ω) is the series
resistance of the output capacitor, f
SW
(Hz) is the switching frequency, and C
OUT
(F) is the output capacitance
used in the design. The amount of output ripple that can be tolerated is application specific; however a general
recommendation is to keep the output ripple less than 1% of the rated output voltage. Keep in mind ceramic
capacitors are sometimes preferred because they have very low ESR; however, depending on package and
voltage rating of the capacitor the value of the capacitance can drop significantly with applied voltage. The output
capacitor selection will also affect the output voltage droop during a load transient. The peak droop on the output
voltage during a load transient is dependent on many factors; however, an approximation of the transient droop
ignoring loop bandwidth can be obtained using the following equation:
(7)
where, C
OUT
(F) is the minimum required output capacitance, L (H) is the value of the inductor, V
DROOP
(V) is the
output voltage drop ignoring loop bandwidth considerations, ΔI
OUTSTEP
(A) is the load step change, R
ESR
(Ω) is
the output capacitor ESR, V
IN
(V) is the input voltage, and V
OUT
(V) is the set regulator output voltage. Both the
tolerance and voltage coefficient of the capacitor should be examined when designing for a specific output ripple
or transient droop target.
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