TPS40042_16 Datasheet, PDF (19/36 Pages) Texas Instruments – LOW PIN COUNT, LOW VIN (3.0 V TO 5.5 V) SYNCHRONOUS BUCK DC-TO-DC CONTROLLER WITH EXTERNAL REFERENCE INPUT

TPS40042
www.ti.com
SLUS777 – NOVEMBER 2007
L
+
V_IN(max)
0.3
* V_OUT
I_OUT
V_OUT
V_IN(max)
1
F _SW
(4)
Solving with V_IN(max) = 5.5 V, an inductor value of 0.69 µH is obtained. A standard value of 0.8 µH is selected,
resulting in 1.56-A peak-peak ripple. The RMS current through the inductor is approximated by the equation:
Ǹǒ Ǔ Ǹ _{IL(rms) +}
I_L(avg)
2
)
1
12
ǒ_IRIPPLEǓ²
+
ǒ_IOUTǓ²
)
1
12
ǒ_I
Ǔ²
RIPPLE
(5)
Using Equation 5, the maximum RMS current in the inductor is about 6 A.
Output Capacitor Selection (C8 & C9)
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.
( ) ^{COUT(min) =}
I_T
2
R A N(m a x)
´
L
V_IN(min) - V_OUT ´ V_TRAN ´ 2
when
V_{IN(m in )}
<
2 ´ V_OUT
(6)
C_OUT(min)
=
I_TRAN(max)2 ´ L
V_OUT ´ V_TRAN ´ 2
when
V_IN(min)
>
2 ´ V_OUT
(7)
For this example, Equation 7 is used in calculating the minimum output capacitance.
Based on a 4-A load transient with a maximum 40-mV deviation, a minimum of 177-µF 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:
ǒ Ǔ _ESRMAX
+
V_{RIPPLE(total)} * V_RIPPLE(cap)
I _RIPPLE
+
V_{RIPPLE(total)} *
I _RIPPLE
C_OUT F_SW
I _RIPPLE
(8)
Based on 177 µF of capacitance, 1.56-A ripple current, 600-kHz switching frequency and a design goal of 36-mV
ripple voltage, we calculate a maximum ESR of 13.6 mΩ. Two 1206, 100-µF, 6.3-V, X5R ceramic capacitors are
selected to provide significantly less than 13.6 mΩ of ESR.
Peak Current Rating of Inductor
With output capacitance known, it is now possible to calculate the charging current during start-up and determine
the minimum saturation current rating for the inductor. The start-up charging current is approximated by:
I _CHARGE
+
V_OUT C_OUT
T_SS
(9)
Using the TPS40042’s soft-start time of 5-ms, C_OUT = 200 µF and V_OUT = 0.9 V, I_CHARGE is found to be 40 mA.
The peak current rating of the inductor is now found by:
L_L(peak)
+
I_OUT(max)
)
1
2
ǒ_IRIPPLEǓ
)
I_CHARGE
(10)
The inductor requirements are summarized in the table below.
Copyright © 2007, Texas Instruments Incorporated
19
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