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LT3757EDD#PBF

P1-P3P4-P6P7-P9P10-P12P13-P15P16-P18P19-P21P22-P24P25-P27P28-P30P31-P33P34-P36
LT3757/LT3757A
22
3757afd
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
forward voltage (V
D
).
The maximum duty cycle (D
MAX
) occurs when the converter
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 voltages
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 in-
ductances, but results in higher input current ripple and
greater core losses. It is recommended that
c
falls in the
range of 0.2 to 0.4.
LT3757/LT3757A
23
3757afd
Given an operating input voltage range, and having chosen
the operating frequency and ripple current in the inductor,
the inductor value (L1 and L2 are independent) of the SEPIC
converter can be determined using the following equation:
L1= L2 =
V
IN(MIN)
0.5 • ∆I
SW
• f
• D
MAX
For most SEPIC applications, the equal inductor values
will fall in the range of 1µH to 100µH.
By making L1 = L2, and winding them on the same core, the
value of inductance in the preceding equation is replaced
by 2L, due to mutual inductance:
L =
V
IN(MIN)
∆I
SW
• f
• D
MAX
This maintains the same ripple current and energy storage
in the inductors. The peak inductor currents are:
I
L1(PEAK)
= I
L1(MAX)
+ 0.5 • ∆I
L1
I
L2(PEAK)
= I
L2(MAX)
+ 0.5 • ∆I
L2
The RMS inductor currents are:
I
L1(RMS)
=I
L1(MAX)
• 1+
c
2
L1
12
where:
c
L1
=
∆I
L1
I
L1(MAX)
I
L2(RMS)
=I
L2(MAX)
• 1+
c
2
L2
12
where:
c
L2
=
∆I
L2
I
L2 (MAX)
Based on the preceding equations, the user should choose
the inductors having sufficient saturation and RMS cur-
rent ratings.
In a SEPIC converter, when the power switch is turned on,
the current flowing through the sense resistor (I
SENSE
) is
the switch current.
Set the sense voltage at I
SENSE(PEAK)
to be the minimum
of the SENSE current limit threshold with a 20% margin.
The sense resistor value can then be calculated to be:
R
SENSE
=
80 mV
I
SW(PEAK)
SEPIC Converter: Power MOSFET Selection
For the SEPIC configuration, choose a MOSFET with a
V
DC
rating higher than the sum of the output voltage and
input voltage by a safety margin (a 10V safety margin is
usually sufficient).
The power dissipated by the MOSFET in a SEPIC con-
verter is:
P
FET
= I
2
SW(MAX)
• R
DS(ON)
• D
MAX
+ 2 • (V
IN(MIN)
+ V
OUT
)
2
• I
L(MAX)
• C
RSS
• f /1A
The first term in this equation represents the conduction
losses in the device, and the second term, the switching
loss. C
RSS
is the reverse transfer capacitance, which is
usually specified in the MOSFET characteristics.
For maximum efficiency, R
DS(ON)
and C
RSS
should be
minimized. From a known power dissipated in the power
MOSFET, its junction temperature can be obtained using
the following equation:
T
J
= T
A
+ P
FET
• θ
JA
= T
A
+ P
FET
• (θ
JC
+ θ
CA
)
T
J
must not exceed the MOSFET maximum junction
temperature rating. It is recommended to measure the
MOSFET temperature in steady state to ensure that absolute
maximum ratings are not exceeded.
applicaTions inForMaTion
LT3757/LT3757A
24
3757afd
applicaTions inForMaTion
Figure 10. A Simplified Inverting Converter
R
SENSE
C
DC
V
IN
C
IN
L1
D1
C
OUT
V
OUT
3757 F09
+
GATE
GND
LT3757
SENSE
L2
M1
+
–
+
–
+
SEPIC Converter: Output Diode Selection
To maximize efficiency, a fast switching diode with a low
forward drop and low reverse leakage is desirable. The
average forward current in normal operation is equal to
the output current, and the peak current is equal to:
I
D(PEAK)
= 1+
c
2
• I
O(MAX)
•
1
1− D
MAX
It is recommended that the peak repetitive reverse voltage
rating V
RRM
is higher than V
OUT
+ V
IN(MAX)
by a safety
margin (a 10V safety margin is usually sufficient).
The power dissipated by the diode is:
P
D
= I
O(MAX)
• V
D
and the diode junction temperature is:
T
J
= T
A
+ P
D
• R
θJA
The R
θJA
used in this equation normally includes the R
θJC
for the device, plus the thermal resistance from the board,
to the ambient temperature in the enclosure. T
J
must not
exceed the diode maximum junction temperature rating.
SEPIC Converter: Output and Input Capacitor Selection
The selections of the output and input capacitors of the
SEPIC converter are similar to those of the boost converter.
Please refer to the Boost Converter, Output Capacitor
Selection and Boost Converter, Input Capacitor Selection
sections.
SEPIC Converter: Selecting the DC Coupling Capacitor
The DC voltage rating of the DC coupling capacitor (C
DC
,
as shown in Figure 1) should be larger than the maximum
input voltage:
V
CDC
> V
IN(MAX)
C
DC
has nearly a rectangular current waveform. During
the switch off-time, the current through C
DC
is I
IN
, while
approximately –I
O
flows during the on-time. The RMS
rating of the coupling capacitor is determined by the fol-
lowing equation:
I
RMS(CDC)
> I
O(MAX)
•
V
OUT
+ V
D
V
IN(MIN)
A low ESR and ESL, X5R or X7R ceramic capacitor works
well for C
DC
.
INVERTING CONVERTER APPLICATIONS
The LT3757 can be configured as a dual-inductor inverting
topology, as shown in Figure 10. The V
OUT
to V
IN
ratio is:
V
OUT
− V
D
V
IN
= −
D
1− D
in continuous conduction mode (CCM).
P1-P3P4-P6P7-P9P10-P12P13-P15P16-P18P19-P21P22-P24P25-P27P28-P30P31-P33P34-P36

LT3757EDD#PBF

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Manufacturer:
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Description:
Switching Voltage Regulators Boost, Fly, SEPIC & Inv Cntr
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