Datasheet

( )
IN(max) OUT OUT
LRIPPLE
IN(max) OUT SW
V V V
I
V L f
- ´
=
´ ´
( )
2
( )
2
IN(max) OUT OUT
L(RMS) OUT
IN(max) OUT SW
V V V
1
I I
12 V L f
æ ö
- ´
= + ´
ç ÷
ç ÷
´ ´
è ø
RIPPLE
L(peak) OUT
I
I I
2
= +
( )
OUT
OUT
SW OUT OUT ESR
2 I
C
f V I R
´ D
>
´ D - D ´
TPS5401
SLVSAB0 –DECEMBER 2010 www.ti.com
(17)
(18)
(19)
As the equation set demonstrates, lower ripple currents reduce the output voltage ripple of the regulator but
require a larger value of inductance. Selecting higher ripple currents increases the output voltage ripple of the
regulator but allows for a lower inductance value. The current flowing through the inductor is the inductor ripple
current plus the output current. During power up, faults or transient load conditions, the inductor current can
increase above the calculated peak inductor current level. In transient conditions, the inductor current can
increase up to the switch current limit of the device. For this reason, the most conservative approach is to specify
an inductor with a saturation current rating equal to or greater than the switch current limit rather than the peak
inductor current. For this design, I
LRIPPLE
= 0.1303 A, I
L(RMS)
= 0.501 A and I
L(peak)
= 0.565 A. The inductor used is
a Coilcraft MSS1048-473ML type, with a saturation current rating of 1.44 A and an rms current rating of 1.83 A.
Output Capacitor
There are three primary considerations for selecting the value of the output capacitor. The output capacitor
determines the modulator pole, the output voltage ripple, and how the regulator responds to a large change in
load current. The output capacitance must be selected based on the most-stringent of these three criteria.
The desired response to a large change in the load current is the first criterion. The output capacitor must supply
the load with current when the regulator cannot. This situation occurs if there are desired hold-up times for the
regulator where the output capacitor must hold the output voltage above a certain level for a specified amount of
time after the input power is removed. The regulator also is temporarily unable to supply sufficient output current
if there is a large, fast increase in the current needs of the load, such as when transitioning from no load to a full
load. The regulator usually requires two or more clock cycles for the control loop to see the change in load
current and output voltage and adjust the duty cycle to react to the change. The output capacitor must be sized
to supply the extra current to the load until the control loop responds to the load change. The output capacitance
must be large enough to supply the difference in current for two clock cycles while only allowing a tolerable
amount of droop in the output voltage. Equation 20 shows the minimum output capacitance necessary to
accomplish this.
(20)
Where:
• ΔI
OUT
is the change in output current
• f
SW
is the regulator switching frequency
• ΔV
OUT
is the allowable change in the output voltage
• R
ESR
is the equivalent series resistance (ESR) of the output capacitor.
Equation 20 indicates the ESR must be less than ΔV
OUT
/ΔI
OUT
. For this example, the transient load response is
specified as a 4% change in V
OUT
for a load step from 0 A (no load) to 0.5 A (full load). For this example, ΔI
OUT
=
0.5A and ΔV
OUT
= 0.04 × 5 V = 0.2 V. For ceramic capacitors, the ESR is usually small enough to ignore in this
calculation. Aluminum electrolytic and tantalum capacitors have higher ESR that should be taken into account.
Using these numbers gives a minimum capacitance of 7.14 mF for ceramic capacitor and 20.4 µF for electrolytic
capacitor with 260 mΩ ESR.
The catch diode of the regulator cannot sink current, so any stored energy in the inductor produces an output
voltage overshoot when the load current rapidly decreases. The output capacitor must also be sized to absorb
energy stored in the inductor when transitioning from a high load current to a lower load current. The excess
energy that gets stored in the output capacitor increases the voltage on the capacitor. The capacitor must be
sized to maintain the desired output voltage during these transient periods. Equation 21 is used to calculate the
minimum capacitance to keep the output voltage overshoot to a desired value, where L
OUT
is the value of the
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