26
LT3431
sn3431 3431fs
APPLICATIO S I FOR ATIO
WUUU
For a load current of 0.5A, this says that discontinuous
mode can be used and the minimum inductor needed is
found from:
LH
MIN
==µ
212 05
500 10 3
27
32
()(.)
(•)()
.
In practice, the inductor should be increased by about
30% over the calculated minimum to handle losses and
variations in value. This suggests a minimum inductor of
3.5µH for this application.
Ripple Current in the Input and Output Capacitors
Positive-to-negative converters have high ripple current in
the input capacitor. For long capacitor lifetime, the RMS
value of this current must be less than the high frequency
ripple current rating of the capacitor. The following for-
mula will give an
approximate
value for RMS ripple cur-
rent.
This formula assumes continuous mode and large
inductor value
. Small inductors will give somewhat higher
ripple current, especially in discontinuous mode. The
exact formulas are very complex and appear in Application
Note 44, pages 29 and 30. For our purposes here I have
simply added a fudge factor (ff). The value for ff is about
1.2 for higher load currents and L ≥15µH. It increases to
about 2.0 for smaller inductors at lower load currents.
Capacitor I ff I
V
V
RMS OUT
OUT
IN
= ()( )
ff = 1.2 to 2.0
The output capacitor ripple current for the positive-to-
negative converter is similar to that for a typical buck
regulator—it is a triangular waveform with peak-to-peak
value equal to the peak-to-peak triangular waveform of the
inductor. The low output ripple design in Figure 15 places
the input capacitor between V
IN
and the regulated negative
output. This placement of the input capacitor significantly
reduces the size required for the output capacitor (versus
placing the input capacitor between V
IN
and ground).
The peak-to-peak ripple current in both the inductor and
output capacitor (assuming continuous mode) is:
I
P-P
P-P
=
==
+
++
=
DC V
fL
DC Duty Cycle
VV
VVV
I RMS
I
IN
OUT F
OUT IN F
COUT
•
•
()
12
The output ripple voltage for this configuration is as low as
the typical buck regulator based predominantly on the
inductor’s triangular peak-to-peak ripple current and the
ESR of the chosen capacitor (see Output Ripple Voltage in
Applications Information).
Diode Current
Average
diode current is equal to load current.
Peak
diode
current will be considerably higher.
Peak diode current:
Continuous Mode
I
VV
V
VV
LfV V
Discontinuous Mode
IV
Lf
OUT
IN OUT
IN
IN OUT
IN OUT
OUT OUT
=
+
+
+
=
()()()
()()( )
()( )
()()
2
2
Keep in mind that during start-up and output overloads,
average diode current may be much higher than with
normal loads. Care should be used if diodes rated less than
1A are used, especially if continuous overload conditions
must be tolerated.
