Datasheet

LTC1871-7
25
18717fd
applicaTions inForMaTion
The maximum output voltage for a SEPIC converter is:
V
O(MAX)
= V
IN
+ V
D
( )
D
MAX
1– D
MAX
– V
D
1
1– D
MAX
The maximum duty cycle of the LTC1871-7 is typically 92%.
SEPIC Converter: The Peak and Average
Input Currents
The control circuit in the LTC1871-7 is measuring the input
current (using a sense resistor in the MOSFET source),
so the output current needs to be reflected back to the
input in order to dimension the power MOSFET properly.
Based on the fact that, ideally, the output power is equal
to the input power, the maximum input current for a SEPIC
converter is:
I
IN(MAX)
= I
O(MAX)
•
D
MAX
1– D
MAX
The peak input current is :
I
IN(PEAK)
= 1+
χ
2






• I
O(MAX)
•
D
MAX
1– D
MAX
The maximum duty cycle, D
MAX
, should be calculated at
minimum V
IN
.
The constant ‘
χ
’ represents the fraction of ripple current in
the inductor relative to its maximum value. For example, if
30% ripple current is chosen, then
χ
= 0.30 and the peak
current is 15% greater than the average.
It is worth noting here that SEPIC converters that operate
at high duty cycles (i.e., that develop a high output voltage
from a low input voltage) can have very high input currents,
relative to the output current. Be sure to check that the
maximum load current will not overload the input supply.
SEPIC Converter: Inductor Selection
For most SEPIC applications the equal inductor values
will fall in the range of 10µH to 100µH. Higher values will
reduce the input ripple voltage and reduce the core loss.
Lower inductor values are chosen to reduce physical size
and improve transient response.
Like the boost converter, the input current of the SEPIC
converter is calculated at full load current and minimum
input voltage. The peak inductor current can be significantly
higher than the output current, especially with smaller in-
ductors and lighter loads. The following formulas assume
CCM operation and calculate the maximum peak inductor
currents at minimum V
IN
:
I
L1(PEAK)
= 1+
χ
2






•I
O(MAX)
•
V
O
+ V
D
V
IN(MIN)
I
L2(PEAK)
= 1+
χ
2






•I
O(MAX)
•
V
IN(MIN)
+ V
D
V
IN(MIN)
The ripple current in the inductor is typically 20% to 40%
(i.e., a range of ‘
χ
’ from 0.20 to 0.40) of the maximum
average input current occurring at V
IN(MIN)
and I
O(MAX)
and
∆I
L1
= ∆I
L2
. Expressing this ripple current as a function of
the output current results in the following equations for
calculating the inductor value:
L =
V
IN(MIN)
∆I
L
• f
•D
MAX
where
∆I
L
= χ •I
O(MAX)
•
D
MAX
1– D
MAX
By making L1 = L2 and winding them on the same core,
the value of inductance in the equation above is replace
by 2L due to mutual inductance. Doing this maintains the
same ripple current and energy storage in the inductors. For
example, a Coiltronix CTX10-4 is a 10µH inductor with two
windings. With the windings in parallel, 10µH inductance
is obtained with a current rating of 4A (the number of
turns hasn’t changed, but the wire diameter has doubled).
Splitting the two windings creates two 10µH inductors
with a current rating of 2A each. Therefore, substituting
2L yields the following equation for coupled inductors:
L1= L2 =
V
IN(MIN)
2 • ∆I
L
• f
•D
MAX
Specify the maximum inductor current to safely handle
I
L(PK)
specified in the equation above. The saturation current