Datasheet

1
x
I
COUT(RMS)
=
Ö12
[ ]
V
OUT IN(MAX) OUT
xV -V
V
IN(MAX) OUT SW
xL -F x0.8xN
C
()
V
PP
(MAX)=
()
ESR xV V V
MAX OUT IN(MAX) OUT
x -
N
C IN(MAX) OUT SW
xV xL xF x0.8
ESR
MAX
+
1
2p C
OUT
f
CO
C
OUT
+
1
3357 L
OUT
f
CO
V
OUT
f
CO
+
f
LC
2
85 V
OUT
TPS5410
www.ti.com SLVS675C –AUGUST 2006–REVISED SEPTEMBER 2013
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:
(7)
and the desired output capacitor value for the output filter to:
(8)
For a desired crossover of 10 kHz and a 68-μH inductor, the calculated value for the output capacitor is 36.5 μF.
The capacitor type should be chosen so that the ESR zero is above the loop crossover. The maximum ESR is:
(9)
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:
(10)
Where:
ΔV
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:
(11)
Where:
N
C
is the number of output capacitors in parallel.
F
SW
is the switching frequency.
For this design example, a single 47-μF output capacitor is chosen for C3. This value is close to the calculated
value of 36.5 μF and yields an actual closed loop cross over frequency of 10.05 kHz. The calculated RMS ripple
current is 84.9 mA and the maximum ESR required is 339 mΩ. A capacitor that meets these requirements is a
AVX TPSE476M020R0150, rated at 20 V with a maximum ESR of 150 mΩ and a ripple current rating of 1.369 A.
This capacitor results in a peak-to-peak output ripple of 44 mV using equation 10. An additional small 0.1-μF
ceramic bypass capacitor may also used, but is not included in this design.
Other capacitor types can be used with the TPS5410, depending on the needs of the application.
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