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1. 1
EE462L, Fall 2011
DC−DC Buck/Boost Converter

2. 2
Boost converter
+
Vout
–
Iout
C
Vin
iin
L1
+ v L1 –
Buck/Boost converter
+
v L2
–
C1
+ v C1 –
L2
Vin
iin
L1
+ v L1 –
+
v L2
–
C1
+ v C1 –
L2
+
Vout
–
Iout
C

3. 3
Buck/Boost 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

4. 4
+
Vout
–
Iout
C
Vin
Iin
L1
+ 0 –
+
0
–
KVL and KCL in the average sense
0
0
Iout
Iin
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. 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 open
Thus, 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.
C is discharging.
+ Vin –

6. 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
    0
1
1 





 out
in
avg
L V
D
V
D
V
in
out V
D
D
V 


 )
1
(
D
DV
V in
out


1
The input/output equation comes from recognizing that the average
voltage across L1 is zero
assume constant

7. 7
Inductor L1 current rating
in
rms
L I
I
3
2
1 
Use max
During the “on” state, L1 operates under the same conditions
as the boost converter L, so the results are the same

8. 8
Inductor L2 current rating
  2
2
2
2
2
3
4
2
12
1
out
out
out
rms
L I
I
I
I 



out
rms
L I
I
3
2
2 
2Iout
0
Iavg = Iout
ΔI
iL2
Use max
+
Vout
–
Iout
C
Vin
Iin
L1
+ 0 –
+
0
–
0
0
Iout
Iin
C1
L2
Iout
+ Vin –
Average values

9. 9
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
 
out
in
rms I
I
I 

3
2
Use max
switch
closed
switch
open
2(Iin + Iout)
iL1 + iL2

10. 10
Output capacitor C current and current rating
in
Crms I
I
3
2
 out
Crms I
I 
2Iin + Iout
−Iout
0
As D → 1, Iin >> Iout , so
iC = (iD – Iout)
As D → 0, Iin << Iout , so
 
D
I
D
I
D
DI
I in
out
out
in




1
,
1






 out
in
Crms I
I
I ,
3
2
max
switch
closed
switch
open

11. 11
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

12. 12
Series capacitor C1 current and current rating
in
rms
C I
I
3
2
1 
2Iin
−2Iout
0
As D → 1, Iin >> Iout , so
iC1
As D → 0, Iin << Iout , so






 out
in
rms
C I
I
I
3
2
,
3
2
max
1
switch
closed
switch
open
out
rms
C I
I
3
2
1 
Switch closed, IC1 = −IL2
Switch open, IC1 = IL1

13. 13
Worst-case load ripple voltage
Cf
I
C
T
I
C
Q
V out
out 





The worst case is where D → 1, where output capacitor C
provides Iout for most of the period. Then,
−Iout
0
iC = (iD – Iout)

14. 14
Worst case ripple voltage on series
capacitor C1
2Iin
−2Iout
0
iC1
f
C
I
V out



1
switch
closed
switch
open
 
1
1
1
1 C
T
D
I
C
DT
I
C
Q
V in
out 







Then, considering the worst case (i.e., D = 1)

15. 15
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

16. 16
Continuous current in L1
sec
/
1
A
L
Vout

   
f
L
D
V
T
D
L
D
DV
T
D
L
V
I
boundary
in
boundary
in
boundary
out
in
1
1
1
1
1
1
2 







f
I
D
V
L
in
in
boundary
2
1 
2Iin
0
Iavg = Iin
iL
(1 − D)T
f
I
V
L
in
in
2
1 guarantees continuous conduction
Then, considering the worst case (i.e., D → 1),
use max
use min

17. 17
Continuous current in L2
sec
/
2
A
L
Vout

f
L
D
V
T
D
L
V
I
boundary
out
boundary
out
out
2
)
1
(
)
1
(
2
2





2Iout
0
Iavg = Iout
iL
(1 − D)T
f
I
D
V
L
out
out
boundary
2
)
1
(
2


f
I
V
L
out
out
2
2  guarantees continuous conduction
Then, considering the worst case (i.e., D → 0),
use max
use min

18. 18
Impedance matching
out
out
load
I
V
R 
equiv
R
 
 
load
out
out
out
out
in
in
equiv R
D
D
I
V
D
D
D
DI
D
V
D
I
V
R
2
2
1
1
1
1





 







 





DC−DC Boost
Converter
+
Vin
−
+
−
Iin
+
Vin
−
Iin
Equivalent from
source perspective
Source D
DV
V in
out


1
 
D
D
I
I in
out


1

19. 19
Impedance matching
 
 
load
out
out
out
out
in
in
equiv R
D
D
I
V
D
D
D
DI
D
V
D
I
V
R
2
2
1
1
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 buck/boost converter can sweep the entire I-V
curve of a solar panel

20. 20
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
-
amps
D = 0.80
D = 0.50
D = 0.88
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

21. 21
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
-
amps
D = 0.47
D = 0.18
D = 0.61

22. 22
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
in
I
3
2 1.5 out
V






out
in I
I ,
3
2
max
)
(
2 out
in V
V 
 
out
in I
I 
3
2
5.66A p-p 200V, 250V 16A, 20A
Our components
9A 250V
10A, 5A
10A 90V 40V, 90V
Likely worst-case buck/boost 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
BUCK/BOOST DESIGN

23. 23
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
BUCK/BOOST DESIGN

24. 24
Minimum Inductance Values Needed to
Guarantee Continuous Current
Converter Type For Continuous
Current in the Input
Inductor
For Continuous
Current in L2
Buck/Boost
f
I
V
L
in
in
2
1 
f
I
V
L
out
out
2
2 
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
BUCK/BOOST DESIGN

25. 25
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 in
V








out
in I
I
3
2
,
3
2
max
f
C
Iout
1
out
I
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 5A
40V
Likely worst-case buck/boost situation
5A
5A
33µF 50kHz
3.0V
BUCK/BOOST DESIGN
Our components 9A
14A p-p
50V
Conclusion - 50kHz may be too low
for buck/boost converter

26. 26
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
out
I
3
2 1.5 out
V
out
I
3
1 2 in
V
out
I
3
2
Boost
in
I
3
2 1.5 out
V out
I 2 out
V
in
I
3
2
Buck/Boost
in
I
3
2 1.5 out
V








out
in I
I ,
3
2
max
 
out
in V
V 
2
 
out
in I
I 
3
2
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 in
V








out
in I
I
3
2
,
3
2
max
f
C
Iout
1
out
I
3
2

27. 27
Comparisons of Output Capacitor Ripple Voltage
Converter Type Volts (peak-to-peak)
Buck
Cf
Iout
4
Boost
Cf
Iout
Buck/Boost
Cf
Iout
Minimum Inductance Values Needed to Guarantee Continuous Current
Converter Type For Continuous Current
in the Input Inductor
For Continuous
Current in L2
Buck
f
I
V
L
out
out
2
 –
Boost
f
I
V
L
in
in
2
 –
Buck/Boost
f
I
V
L
in
in
2
1 
f
I
V
L
out
out
2
2 