1
EE462L, Spring 2014DC−DC SEPIC (Converter)
2
Boost converter
+ Vout
–
Iout
CVin
iin
L1
+ v L1 –
SEPIC converter
+
v L2
–
C1
+ v C1 –
L2
Vin
iin
L1
+ v L1 –
+
v L2
–
C1
+ v C1 –
L2
+ Vout
–
Iout
C
!
3
SEPIC converter
This circuit is more unforgiving than the boost converter, because the MOSFET and diode voltages and currents are higher
• Before applying power, make sure that your D is at the minimum, and that a load is solidly connected
• Limit your output voltage to 90V
Vin
iin
L1
+ v L1 –
+
v L2
–
C1
+ v C1 –
L2
+ Vout
–
Iout
C
!
SEPIC = single ended primary inductor converter
4
+ Vout
–
Iout
CVin
I in
L1
+ 0 –
+ 0
–
KVL and KCL in the average sense
0
0
Iout
I in
C1
L2
Iout
+ Vin –
KVL shows that VC1 = Vin
Interestingly, no average current passes from the source side, through C1, to the load side, and yet this is a “DC - DC” converter
5
Switch closed
Vin
iin
L1
+ Vin –
+
v L2
–
C1
+ Vin –
L2
+ Vout
–
Iout
C
assume constant
+ v D –
KVL shows that vD = −(Vin + Vout),
so the diode is openThus, C is providing the load power when the switch is closed
Vin
iin
L1 –
Vin
+
C1 + Vin –
L2
+ Vout
–
Iout
C
– (Vin + Vout) +
Iout
iL1 and iL2 are ramping up (charging). C1 is charging L2
(so C1 is discharging). C is also discharging.
+ Vin –
6
Switch open (assume the diode is conducting because, otherwise, the circuit cannot work)
Vin
iin
L1
– Vout +
C1
+ Vin –
L2
+ Vout
–
Iout
C
C1 and C are charging. L1 and L2 are discharging.
+ Vout
–
KVL shows that VL1 = −Vout
011 outinavgL VDVDV
inout VDDV )1(
D
DVV inout
1
The input/output equation comes from recognizing that the average voltage across L1 is zero
assume constant
Voltage can be stepped-up or stepped-down
!
7
+ Vin –
–
Vout +
iL L C iC
Iout
id iin
D
DVV inout
1
Voltage can be stepped-up or stepped-down
The buck-boost converterInverse polarity with respect to input
Compared with SEPIC:
+ Fewer energy storage components
+ Capacitor does not carry load current
+ In both converters isolation can be easily implemented
- Polarity is reversed
!
8
Inductor L1 current rating
inrmsL II3
21
Use max
During the “on” state, L1 operates under the same conditions as the boost converter L, so the results are the same
9
Inductor L2 current rating
22222 3
42
12
1outoutoutrmsL IIII
outrmsL II3
22
2Iout
0Iavg = Iout ΔI
iL2
Use max
+ Vout
–
Iout
CVin
I in
L1
+ 0 –
+ 0
–
0
0
Iout
I in
C1
L2
Iout
+ Vin –
Average values
10
MOSFET and diode currents and current ratings
0
2(Iin + Iout)
0
Take worst case D for each
Vin
iin
L1
+ v L1 –
+
v L2
–
C1
+ v C1 –
L2
+ Vout
–
Iout
C
MOSFET Diode iL1 + iL2
outinrms III 3
2
Use max
switchclosed
switchopen
2(Iin + Iout)
iL1 + iL2
11
Output capacitor C current and current rating
inCrms II3
2 outCrms II
2Iin + Iout
−Iout
0
As D → 1, Iin >> Iout , so
iC = (iD – Iout)
As D → 0, Iin << Iout , so
D
IDI
D
DII in
outout
in
1
,1
outinCrms III ,3
2max
switch closed
switch open
12
Series capacitor C1 current and current rating
Switch closed, IC1 = −IL2
Vin
iin
L1 –
Vin
+
C1
+ Vin –
L2
+ Vout
–
Iout
C
– (Vin + Vout) +
Iout
+ Vin –
Vin
iin
L1
– Vout +
C1
+ Vin –
L2
+ Vout
–
Iout
C
+ Vout
–
Switch open, IC1 = IL1
13
Series capacitor C1 current and current rating
inrmsC II3
21
2Iin
−2Iout
0
As D → 1, Iin >> Iout , so
iC1
As D → 0, Iin << Iout , so
outinrmsC III3
2,
3
2max1
switch closed
switch open
outrmsC II3
21
Switch closed, IC1 = −IL2
Switch open, IC1 = IL1
The high capacitor current rating is a disadvantage of this converter
!
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Worst-case load ripple voltage
Cf
I
C
TI
C
QV outout
The worst case is where D → 1, where output capacitor C
provides Iout for most of the period. Then,
−Iout
0
iC = (iD – Iout)
15
Worst case ripple voltage on series capacitor C1
2Iin
−2Iout
0
iC1
fC
IV out
1
switch closed
switch open
1
1
11 C
TDI
C
DTI
C
QV inout
Then, considering the worst case (i.e., D = 1)
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Voltage ratings
MOSFET and diode see (Vin + Vout)
• Diode and MOSFET, use 2(Vin + Vout)
• Capacitor C1, use 1.5Vin
• Capacitor C, use 1.5Vout
Vin
L1 C1
+ Vin –
L2
+ Vout
–
C
– (Vin + Vout) +
Vin
L1
– Vout +
C1
+ Vin –
L2
+ Vout
–
C
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Continuous current in L1sec/
1A
L
Vout
fL
DVTD
LD
DV
TDL
VI
boundary
in
boundary
in
boundary
outin 1
11
111
2
fI
DVL
in
inboundary 2
1
2Iin
0Iavg = Iin
iL
(1 − D)T
fI
VL
in
in
21 guarantees continuous conduction
Then, considering the worst case (i.e., D → 1),
use max
use min
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Continuous current in L2
sec/ 2A
L
Vout
fL
DVTD
L
VI
boundary
out
boundary
outout 2
)1()1(
22
2Iout
0
Iavg = Iout
iL
(1 − D)T
fI
DVL
out
outboundary 2
)1(2
fI
VL
out
out
22 guarantees continuous conduction
Then, considering the worst case (i.e., D → 0),
use max
use min
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Impedance matching
out
outload I
VR
equivR
load
out
out
out
out
in
inequiv R
D
D
I
V
D
D
D
DID
VD
I
VR
22 11
1
1
DC−DC Boost Converter
+
Vin
−
+
−
Iin
+
Vin
−
Iin
Equivalent from source perspective
Source D
DVV inout
1
D
DII inout
1
20
Impedance matching
load
out
out
out
out
in
inequiv R
D
D
I
V
D
D
D
DID
VD
I
VR
22 11
1
1
For any Rload, as D → 0, then Requiv → ∞ (i.e., an open circuit)
For any Rload, as D → 1, then Requiv → 0 (i.e., a short circuit)
Thus, the SEPIC converter can sweep the entire I-V curve of a solar panel
!
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Example - connect a 100Ω load resistor
PV Station 13, Bright Sun, Dec. 6, 2002
0
1
2
3
4
5
6
0 5 10 15 20 25 30 35 40 45
V(panel) - volts
I - a
mp
s
D = 0.80
6.44Ω equiv.
100Ω equiv.
D = 0.50
D = 0.88
2Ω e
quiv
.
With a 100Ω load resistor attached, raising D from 0 to 1 moves the solar panel load from the open circuit condition to the short circuit condition
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Example - connect a 5Ω load resistor
PV Station 13, Bright Sun, Dec. 6, 2002
0
1
2
3
4
5
6
0 5 10 15 20 25 30 35 40 45
V(panel) - volts
I - a
mp
s
D = 0.47
6.44Ω equiv.
100Ω equiv.
D = 0.18
D = 0.61
2Ω e
quiv
.
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Worst-Case Component Ratings Comparisons for DC-DC Converters
Converter Type
Input Inductor
Current (Arms)
Output Capacitor Voltage
Output Capacitor Current (Arms)
Diode and MOSFET Voltage
Diode and MOSFET Current (Arms)
Buck/Boost inI
3
2
1.5 outV
outin II ,
3
2max
)(2 outin VV outin II 3
2
5.66A p-p 200V, 250V 16A, 20A
Our components
9A 250V
10A, 5A10A 90V 40V, 90V
Likely worst-case SEPIC situation
10A, 5A
MOSFET M. 250V, 20A
L1. 100µH, 9A
C. 1500µF, 250V, 5.66A p-p
Diode D. 200V, 16A
L2. 100µH, 9A
C1. 33µF, 50V, 14A p-p
SEPIC DESIGN
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Comparisons of Output Capacitor Ripple Voltage
Converter Type Volts (peak-to-peak) Buck/Boost
Cf
Iout
5A
1500µF 50kHz
0.067V
MOSFET M. 250V, 20A
L1. 100µH, 9A
C. 1500µF, 250V, 5.66A p-p
Diode D. 200V, 16A
L2. 100µH, 9A
C1. 33µF, 50V, 14A p-p
SEPIC DESIGN
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Minimum Inductance Values Needed to Guarantee Continuous Current
Converter Type For Continuous
Current in the Input Inductor
For Continuous Current in L2
Buck/Boost
fI
VL
in
in
21 fI
VL
out
out
22
40V
2A 50kHz
200µH
90V
2A 50kHz
450µH
MOSFET M. 250V, 20A
L1. 100µH, 9A
C. 1500µF, 250V, 5.66A p-p
Diode D. 200V, 16A
L2. 100µH, 9A
C1. 33µF, 50V, 14A p-p
SEPIC DESIGN
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Additional Components for Buck/Boost Converter
Series Capacitor
Voltage
Series Capacitor (C1)
Current (Arms)
Series Capacitor (C1)
Ripple Voltage (peak-to-peak)
Second Inductor (L2)
Current (Arms)
1.5 inV
outin II
3
2,
3
2max
fC
Iout
1 outI
3
2
MOSFET M. 250V, 20A
L1. 100µH, 9A
C. 1500µF, 250V, 5.66A p-p
Diode D. 200V, 16A
L2. 100µH, 9A
C1. 33µF, 50V, 14A p-p
10A 5A40V
Likely worst-case SEPIC situation
5A
5A
33µF 50kHz3.0V
SEPIC DESIGN
Our components 9A14A p-p50V
Conclusion - 50kHz may be too low for SEPIC converter
SEPIC converter
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