Datasheet

L
RIPPLE P P
V
1.2
I di dt 3.05 4.88 A
L 0.75
-
= = ´ = m ´ =
m
( ) ( )
( )
2
2 2
2
RMS DC AC RMS
4.88
I I I 20 20.05 A
12
æ ö
= + = + =
ç ÷
è ø
P P
PEAK DC PEAK
I
4.88
I I 20 22.44 A
2 2
-
= + = + =
( )
( )
2
2
2
RMS
P I R I DCR 20.05 1.2m 0.482 W= ´ = ´ = ´ W =
( )
2
OUT O
OUT OUT OUT O
OVERSHOOT
OUT OUT OUT OUT OUT
I L
I I I L
V t
C C V V C
D ´
D D D ´
< ´ D = ´ =
´
( )
( )
( )
2
OUT O
OUT OUT OUT O
UNDERSHOOT
OUT OUT
IN OUT IN OUT OUT
I L
I I I L
V t
C C
V V V V C
D ´
D D D ´
< ´ D = ´ =
- - ´
( ) ( )
2
2
OUT OUT
OUT
OUT OVERSHOOT
I L
10 750nH
C 520 F
V V 1.2 120mV
D ´
´
= = = m
´ ´
( )
RIPPLE
SPEC
SPEC
RIPPLE cap
OUT SW
MAX
RIPPLE RIPPLE
I
4.88
V
50mV
V V
8 C f
8 521 F 300kHz
ESR 9.45m
I I 4.88
æ ö
æ ö
-
-
ç ÷
ç ÷
-
´ ´
´ m ´
è ø è ø
= = = = W
TPS40400
SLUS930B –APRIL 2011– REVISED OCTOBER 2011 www.ti.com
For this design a 750-nH inductor from Pulse (PG0077.801) was selected. The actual ripple current should now
be recalculated using the actual inductance value.
(37)
With this ripple current, the inductor RMS and peak current values can be calculated.
The RMS value of a zero-average triangular wave is given by Equation 38.
(38)
At maximum load and maximum line, the peak inductor current is given by Equation 39.
(39)
The DCR of the selected inductor (from the data sheet) is 1.2 mΩ. Inductor conduction losses are described in
Equation 40.
(40)
Output Capacitance, C
OUT
The selection of the output capacitor is typically affected by the output transient response requirement.
Equation 41 and Equation 42 can be used to over-estimate the voltage deviation to account for delays in the loop
bandwidth and can be used to determine the required output capacitance. The estimate of C
OUT
based on
overshoot is shown in Equation 41.
(41)
The estimate of C
OUT
based on undershoot is shown in Equation 42.
(42)
When V
IN(min)
> 2 x V
OUT
, use the overshoot equation (V
Overshoot)
to calculate minimum output capacitance.
When V
IN(min)
< 2 x V
OUT
use the undershoot equation (V
Undershoot
). In this design example, V
IN(min)
is much larger
than 2 x V
OUT
so Equation 43 is used to determine the required minimum output capacitance.
(43)
The Resistive Component of Output Ripple
With a minimum capacitance, the maximum allowable ESR is determined by the maximum ripple voltage and is
approximated by Equation 44.
(44)
The factor of 8 in the equation above results from the calculation of capacitor voltage resulting from a triangular
current. For this design, a 680-µF, 45-mΩ ESR, 5-nH ESL tantalum and two, 47-µF, 3-mΩ ESR, 0.9-nH ESL
ceramic capacitors were selected for a total capacitance of 780 µF.
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