Datasheet

LT3757/LT3757A
22
3757afe
For more information www.linear.com/LT3757
applicaTions inForMaTion
Figure9. The Switch Current Waveform of the SEPIC Converter
3757 F08
∆I
SW = χ •
I
SW(MAX)
I
SW
t
DT
S
I
SW(MAX)
T
S
SEPIC Converter: Switch Duty Cycle and Frequency
For a SEPIC converter operating in CCM, the duty cycle
of the main switch can be calculated based on the output
voltage (V
OUT
), the input voltage (V
IN
) and the diode for-
ward voltage (V
D
).
The maximum duty cycle (D
MAX
) occurs when the con-
verter has the minimum input voltage:
D
MAX
=
V
OUT
+
V
D
V
IN(MIN)
+ V
OUT
+ V
D
SEPIC Converter: Inductor and Sense Resistor Selection
As shown in Figure1, the SEPIC converter contains two
inductors: L1 and L2. L1 and L2 can be independent, but
can also be wound on the same core, since identical volt
-
ages are applied to L1 and L2 throughout the switching
cycle.
For the SEPIC topology, the current through L1 is the
converter input current. Based on the fact that, ideally, the
output power is equal to the input power, the maximum
average inductor currents of L1 and L2 are:
I
L1(MAX)
=I
IN(MAX)
=I
O(MAX)
•
D
MAX
1−D
MAX
I
L2(MAX)
=I
O(MAX)
In a SEPIC converter, the switch current is equal to I
L1
+
I
L2
when the power switch is on, therefore, the maximum
average switch current is defined as:
I
SW(MAX)
=I
L1(MAX)
+I
L2(MAX)
=I
O(MAX)
•
1
1−D
MAX
and the peak switch current is:
I
SW(PEAK)
= 1+
c
2
⎛
⎝
⎜
⎞
⎠
⎟
• I
O(MAX)
•
1
1−D
MAX
The constant
c
in the preceding equations represents the
percentage peak-to-peak ripple current in the switch, rela-
tive to I
SW(MAX)
, as shown in Figure9. Then, the switch
ripple current ∆I
SW
can be calculated by:
∆I
SW
=
c
• I
SW(MAX)
The inductor ripple currents ∆I
L1
and ∆I
L2
are identical:
∆I
L1
= ∆I
L2
= 0.5 • ∆I
SW
The inductor ripple current has a direct effect on the
choice of the inductor value. Choosing smaller values of
∆I
L
requires large inductances and reduces the current
loop gain (the converter will approach voltage mode).
Accepting larger values of ∆I
L
allows the use of low induc-
tances, but results in higher input current ripple, greater
core losses, and in some cases, subharmonic oscillation.
A good starting point for
c
is 0.2 and careful evaluation
of system stability should be made to ensure adequate
design margin.
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