TPS54231
SLUS851–OCTOBER 2008.............................................................................................................................................................................................. www.ti.com
VOUT(MAX)
´
VIN(MAX) - VOUT
(
´ KIND ´IOUT ´FSW
)
LMIN
=
V
IN(MAX)
(8)
KIND is a coefficient that represents the amount of inductor ripple current relative to the maximum output current.
In general, 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 KIND = 0.3 may be used. When
using higher ESR output capacitors, KIND = 0.2 yields better results.
For this design example, use KIND = 0.3 and the minimum inductor value is calculated to be 8.5µH. 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 RMS inductor current can be found from Equation 9
æ
ç
ç
è
ö2
÷
÷
ø
VOUT
×
V
- VOUT
(
)
× LOUT × FSW × 0.8
IN(MAX)
1
IL(RMS)
=
IO2 UT(MAX)
+
×
12
V
IN(MAX)
(9)
and the peak inductor current can be determined with Equation 10
VOUT - VOUT
1.6 ´ V
×
V
IN(MAX)
(
)
IL(PK) = IOUT(MAX)
+
× LOUT × FSW
IN(MAX)
(10)
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:
CO _ min =1/(2´p ´ RO ´ FCO _ max
)
(11)
Where RO is the output load impedance (VO/IO) and fCO 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:
é
ê
ë
ù
ú
û
(D - 0.5)
VOPP = I LPP
+ RESR
4 ´ FSW ´ CO
(12)
Where NC is the number of output capacitors in parallel.
The maximum ESR of the output capacitor is determined by the amount of allowable output ripple as specified in
the initial design parameters. The output ripple voltage is the inductor ripple current times the ESR of the output
filter, so the maximum specified ESR as listed in the capacitor data sheet is given by Equation 13
12
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