Texas Instruments TPA2013D1, User Manual

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I
L
+
I
CC
ǒ
V
CC
V
DD
0.8
Ǔ
(2)
L
+
V
DD
ǒ
V
CC
*
V
DD
Ǔ
D I
L
f
boost
V
CC
(3)
2.2.4 Changing the Boost Capacitor
C
+
2
I
CC
ǒ
V
CC
*
V
DD
Ǔ
D V f
boost
V
CC
(4)
C
+
I
CC
ǒ
V
CC
*
V
DD
Ǔ
D V f
boost
V
CC
(5)
Operation
Use Equation 2 to determine the required current rating. Equation 2 shows the approximate relationship
between the average inductor current, I
L
, to the load current, load voltage, and input voltage (I
CC
, V
CC
, and
V
DD
, respectively.) Insert I
CC
, V
CC
, and V
DD
into Equation 2 to solve for I
L
. The inductor must maintain at
least 90% of its initial inductance value at this current.
The minimum working inductance is 2.2 μ H. A lower value may cause instability.
Ripple current,
Δ
I
L
, is peak-to-peak variation in inductor current. Smaller ripple current reduces core losses
in the inductor as well as the potential for EMI. Use Equation 3 to determine the value of the inductor, L.
Equation 3 shows the relationships among inductance L, V
DD
, V
CC
, the switching frequency, f
boost
, and
Δ
I
L
.
Insert the maximum acceptable ripple current into Equation 3 to solve for L.
Δ
I
L
is inversely proportional to L. Minimize
Δ
I
L
as much as is necessary for a specific application. Increase
the inductance to reduce the ripple current. Note that making the inductance too large prevents the boost
converter from responding to fast load changes properly. Typical inductor values for the TPA2013D1 are
4.7
μ H to 6.8 μ H.
Select an inductor with a small dc resistance, DCR. DCR reduces the output power due to the voltage
drop across the inductor.
The value of the boost capacitor is determined by the minimum value of working capacitance required for
stability and the maximum voltage ripple allowed on V
CC
in the application. The minimum value of working
capacitance is 10 μ F. Do not use any component with a working capacitance less than 10 μ F.
For X5R or X7R ceramic capacitors, Equation 4 shows the relationships among the boost capacitance, C,
to load current, load voltage, ripple voltage, input voltage, and switching frequency (I
CC
, V
CC
, Δ V, V
DD
,
f
boost
respectively). Insert the maximum allowed ripple voltage into Equation 4 to solve for C. A factor of
about 2 is included to implement the rules and specifications listed in the "Surface Mount Capacitors"
section of the TPA2013D1 data sheet (
SLOS520 ).
For aluminum or tantalum capacitors, Equation 5 shows the relationships among the boost capacitance,
C, to load current, load voltage, ripple voltage, input voltage, and switching frequency (I
CC
, V
CC
, Δ V, V
DD
,
f
boost
respectively). Insert the maximum allowed ripple voltage into Equation 5 to solve for C. Solve this
equation assuming ESR is zero.
Capacitance of aluminum and tantalum capacitors is normally insensitive to applied voltage, so there is no
factor of 2 included in
Equation 5 . However, the ESR in aluminum and tantalum capacitors can be
significant. Choose an aluminum or tantalum capacitor with an ESR around 30 m
Ω
. For best performance
with tantalum capacitors, use at least a 10-V rating. Note that tantalum capacitors must generally be used
at voltages of half their ratings or less.
TPA2013D1EVM 4 SLOU194 – August 2007
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