Datasheet

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
x
I
COUT(RMS)
=
√12
[ ]
V
OUT IN(MAX) OUT
×V – V
V
IN(MAX) OUT SW C
×L – F ×0.8×N
()
(11)
TPS5420-Q1
www.ti.com ................................................................................................................................................... SLVS752B – NOVEMBER 2007 – REVISED JUNE 2008
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 listed in the capacitor data sheet results in an acceptable output ripple
voltage:
Where:
Δ V
PP
is the desired peak-to-peak output ripple.
N
C
is the number of parallel output capacitors.
F
SW
is the 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
is the number of output capacitors in parallel.
F
SW
is the switching frequency.
For this design example, a single 100- µ F output capacitor is chosen for C3. The calculated RMS ripple current is
143 mA and the maximum ESR required is 88 m Ω . A capacitor that meets these requirements is a AVX
TPSD107M010R0080, rated at 10 V with a maximum ESR of 80 m Ω and a ripple current rating of 1.369 A. This
capacitor results in a peak-to-peak output ripple of 26 mV using equation 10. An additional small 0.1- µ F ceramic
bypass capacitor may also used, but is not included in this design.
Other capacitor types can be used with the TPS5420, depending on the needs of the application.
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