Datasheet

ú
û
ù
ê
ë
é
+
´´
-
=
E S R
OSW
LP PO P P
R
CF
D
IV
4
)5.0(
)2/(1
max_min_ COOO
FRC ´´´= p
LPP
L(PK) OUT(MAX)
I
I = I +
2
2 2
OUT(MAX) LPP
L(RMS)
1
I = I + × I
12
( )
( )
OUT IN(MAX) - OUT
LPP
IN MAX OUT SW
V × V V
I =
V × L F 0.8´ ´
( )
OUT(MAX) IN(MAX) OUT
MIN
IN(MAX) IND OUT SW
V V V
L =
V K I F
´ -
´ ´ ´
TPS54231
www.ti.com SLUS851C –OCTOBER 2008–REVISED JULY 2012
(8)
K
IND
is a coefficient that represents the amount of inductor ripple current relative to the maximum output current.
This value is at the discretion of the designer; however, the following guidelines may be used. For designs using
low ESR output capacitors such as ceramics, a value as high as K
IND
= 0.3 may be used. When using higher
ESR output capacitors, K
IND
= 0.2 yields better results.
For this design example, use K
IND
= 0.3 and the minimum inductor value is calculated to be 8.5 μH. For this
design, a large value was chosen: 10 μH.
For the output filter inductor, it is important that the RMS current and saturation current ratings not be exceeded.
The peak-to-peak inductor current is calculated using Equation 9
(9)
The RMS inductor current can be found from Equation 10
(10)
and the peak inductor current can be determined with Equation 11
(11)
For this design, the RMS inductor current is 2.008 A and the peak inductor current is 2.32 A. The chosen
inductor is a Coilcraft MSS1038-103NL 10 μH. It has a saturation current rating of 3.04 A and an RMS current
rating of 2.90 A, meeting these requirements. Smaller or larger inductor values can be used depending on the
amount of ripple current the designer wishes to allow so long as the other design requirements are met. Larger
value inductors will have lower ac current and result in lower output voltage ripple, while smaller inductor values
will increase ac current and output voltage ripple. In general, inductor values for use with the TPS54231 are in
the range of 6.8 μH to 47μH.
Capacitor Selection
The important design factors for the output capacitor are dc voltage rating, ripple current rating, and equivalent
series resistance (ESR). The dc voltage and ripple current ratings cannot be exceeded. The ESR is important
because along with the inductor current it determines the amount of output ripple voltage. The actual value of the
output capacitor is not critical, but some practical limits do exist. Consider the relationship between the desired
closed loop crossover frequency of the design and LC corner frequency of the output filter. In general, it is
desirable to keep the closed loop crossover frequency at less than 1/5 of the switching frequency. With high
switching frequencies such as the 570-kHz frequency of this design, internal circuit limitations of the TPS54231
limit the practical maximum crossover frequency to about 25 kHz. In general, the closed loop crossover
frequency should be higher than the corner frequency determined by the load impedance and the output
capacitor. This limits the minimum capacitor value for the output filter to:
(12)
Where R
O
is the output load impedance (V
O
/I
O
) and f
CO
is the desired crossover frequency. For a desired
maximum crossover of 25 kHz the minimum value for the output capacitor is around 3.6μF. This may not satisfy
the output ripple voltage requirement. The output ripple voltage can be estimated by Equation 13:
(13)
Where:
D = Duty cycle (V
OUT
/V
IN
)
C
O
= Output Capacitance
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