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f
CO
+
f
LC
2
85 V
OUT
(7)
C
OUT
+
1
3357 L
OUT
f
CO
V
OUT
(8)
ESR
MAX
+
1
2p C
OUT
f
CO
(9)
V
PP
(MAX)=
()
ESR V V V
MAX OUT IN(MAX) OUT
´ ´ -
N
C IN(MAX) OUT SW
V L F 0.8´ ´ ´ ´
(10)
1
´
I
COUT(RMS)
=
Ö12
[ ]
V
OUT IN(MAX) OUT
V -V´
V
IN(MAX) OUT SW C
L F 0.8 N´ - ´ ´
( )-
(11)
TPS5420-EP
SLVS717 – DECEMBER 2006
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 ripple 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. Due to
the design of the internal compensation, it is recommended to keep the closed-loop crossover frequency in the
range 3 kHz to 30 kHz, as this frequency range has adequate phase boost to allow for stable operation. For this
design example, the intended closed-loop crossover frequency is between 2590 Hz and 24 kHz, and below the
ESR zero of the output capacitor. Under these conditions, the closed-loop crossover frequency is related to the
LC corner frequency as:
and the desired output capacitor value for the output filter to:
For a desired crossover of 18 kHz and a 33- µ H inductor, the calculated value for the output capacitor is 100 µ F.
The capacitor type should be chosen so that the ESR zero is above the loop crossover. The maximum ESR is:
The maximum ESR of the output capacitor also determines the amount of 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.
Check that the maximum specified ESR as listed in the capacitor data-sheet results in an acceptable output
ripple voltage:
Where:
∆ V
PP
= Desired peak-to-peak output ripple
N
C
= Number of parallel output capacitors
F
SW
= Switching frequency
The minimum ESR of the output capacitor should also be considered. For a good phase margin, if the ESR is
zero when the ESR is at its minimum, it should not be above the internal compensation poles at 24 kHz and
54 kHz.
The selected output capacitor must also be rated for a voltage greater than the desired output voltage, plus
one-half the ripple voltage. Any derating amount must also be included. The maximum RMS ripple current in the
output capacitor is given by Equation 11 :
Where:
N
C
= Number of output capacitors in parallel
F
SW
= Switching frequency
13
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