Datasheet
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Inductor Selection
L +
V
IN(max)
* V
OUT
0.3 I
OUT
V
OUT
V
IN(max)
1
F
SW
(4)
I
L(rms)
+
ǒ
I
L(avg)
Ǔ
2
)
1
12
ǒ
I
RIPPLE
Ǔ
2
Ǹ
+
ǒ
I
OUT
Ǔ
2
)
1
12
ǒ
I
RIPPLE
Ǔ
2
Ǹ
(5)
Output Capacitor Selection (C8 & C9)
C
OUT(min)
+
I
TRAN(max)
2
L
ǒ
V
IN(min)
* V
OUT
Ǔ
V
TRAN
when V
IN(min)
t 2 V
OUT
(6)
C
OUT(min)
+
I
TRAN(max)
2
L
ǒ
V
OUT
Ǔ
V
TRAN
when V
IN(min)
u 2 V
OUT
(7)
ESR
MAX
+
V
RIPPLE(total)
* V
RIPPLE(cap)
I
RIPPLE
+
V
RIPPLE(total)
*
ǒ
I
RIPPLE
C
OUT
F
SW
Ǔ
I
RIPPLE
(8)
TPS40040 , TPS40041
SLUS700D – MARCH 2006 – REVISED DECEMBER 2007
The inductor is typically sized for 30% peak-to-peak ripple current (I
RIPPLE
) Given this target ripple current, the
required inductor size is calculated by:
Solving with V
IN(max)
= 5.5 V, an inductor value of 1.12 µ H is obtained. A standard value of 1.0 µ H is selected,
resulting in 2-A peak-peak ripple. The RMS current through the inductor is approximated by the equation:
Using Equation 5 , the maximum RMS current in the inductor is about 6.03 A.
The selection of the output capacitor is typically driven by the output load transient response requirement.
Equation 6 and Equation 7 estimate the output capacitance required for a given output voltage transient
deviation.
For this example, Equation 7 is used in calculating the minimum output capacitance.
Based on a 4-A load transient with a maximum 50-mV deviation, a minimum of 178- µ F output of capacitance is
required.
The output ripple is divided into two components. The first is the ripple voltage generated by inductor ripple
current flowing through the output capacitor's capacitance, and the second is the voltage generated by the ripple
current flowing in the output capacitor's ESR. The maximum allowable ESR is then determined by the maximum
ripple voltage and is approximated by:
Based on 178 µ F of capacitance, 2-A ripple current, 600-kHz switching frequency and a design goal of 36-mV
ripple voltage, we calculate a capacitive ripple component of 18.7 mV and a maximum ESR of 8.6 m Ω . Two
1206, 100- µ F, 6.3-V, X5R ceramic capacitors are selected to provide significantly less than 8.6 m Ω of ESR.
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