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

2. Boost converter Buck/Boost converter
+ v L1 – i I in
out L1 C + V V in
out –
Buck/Boost converter V in i L1
+ v L1 – +
v L2 – C1
+ v C1 – L2 + V
out – I C +
v L2 – C1
+ v C1 – L2

3. Buck/Boost converter V in i L1
+ v L1 – +
v L2 – C1
+ v C1 – L2 + V
out – I C
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

4. KVL and KCL in the average sense
+ Vin –
+ 0 – I I I in
out
out L1 + – + C1 I V
out V in
out I C L2 in –
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 i I + L1 C1 V V C L2 – i I + L1 C1 V V C I L2 –
assume constant
+ Vin –
+ Vin –
+ v D – i + V
out – I C in L1 +
v L2 – C1 V in L2
KVL shows that vD = −(Vin + Vout),
so the diode is open
Thus, C is providing the load power when the switch is closed
+ Vin –
– (Vin + Vout) +
+ Vin – i I in
out L1 –
Vin + + C1 V V in
out C L2 I
out –
iL1 and iL2 are ramping up (charging). C1 is charging L2.
C is discharging.

6. Switch open (assume the diode is conducting because, otherwise, the circuit cannot work)
assume constant
+ Vin –
– Vout + i I in
out L1 + + C1 V V V in
out
out C L2 – –
C1 and C are charging. L1 and L2 are discharging.
KVL shows that VL1 = −Vout
The input/output equation comes from recognizing that the average voltage across L1 is zero

7. Inductor L1 current rating
During the “on” state, L1 operates under the same conditions as the boost converter L, so the results are the same
Use max

8. Inductor L2 current rating
Average values
+ Vin –
+ 0 – I I I in
out
out L1 + – + C1 I V
out V in
out I C in L2 –
iL2
2Iout
Iavg = Iout ΔI
Use max

9. MOSFET and diode currents and current ratings+
v L2 – C1
+ v C1 – L2
+ v L1 – i I in
out L1 + V V in
out C –
iL1 + iL2
MOSFET
Diode
iL1 + iL2
2(Iin + Iout)
2(Iin + Iout)
switch
closed
switch
open
Take worst case D for each
Use max

10. Output capacitor C current and current rating
iC = (iD – Iout)
2Iin + Iout
−Iout
switch closed
switch open
As D → 1, Iin >> Iout , so
As D → 0, Iin << Iout , so

11. Series capacitor C1 current and current rating
+ Vin –
– (Vin + Vout) +
+ Vin – i I in
out L1 –
Vin + + C1 V V in
out C L2 I
out –
+ Vin –
– Vout + i I in
out L1 + + C1 V V V in
out
out C L2 – –
Switch closed, IC1 = −IL2
Switch open, IC1 = IL1

12. Series capacitor C1 current and current rating
iC1
Switch closed, IC1 = −IL2
Switch open, IC1 = IL1
2Iin
switch closed
switch open
−2Iout
As D → 1, Iin >> Iout , so
As D → 0, Iin << Iout , so

13. Worst-case load ripple voltage
iC = (iD – Iout)
−Iout
The worst case is where D → 1, where output capacitor C provides Iout for most of the period. Then,

14. Worst case ripple voltage on series capacitor C1
iC1
switch open
2Iin
−2Iout
switch closed
Then, considering the worst case (i.e., D = 1)

15. Voltage ratings + L1 C1 V V C L2 – + L1 C1 V V C L2 – + Vin –
– (Vin + Vout) + L1 + C1 V V in
out C L2 –
MOSFET and diode see (Vin + Vout)
+ Vin –
– Vout + L1 + C1 V V in
out C L2 –
Diode and MOSFET, use 2(Vin + Vout)
Capacitor C1, use 1.5Vin
Capacitor C, use 1.5Vout

16. Continuous current in L1iL
2Iin
Iavg = Iin
(1 − D)T
Then, considering the worst case (i.e., D → 1),
use max
guarantees continuous conduction
use min

17. Continuous current in L2iL
2Iout
Iavg = Iout
(1 − D)T
Then, considering the worst case (i.e., D → 0),
use max
guarantees continuous conduction
use min

18. Impedance matching Iin DC−DC Boost Converter + + Vin − − Source Iin +
Equivalent from source perspective

19. Impedance matching
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. Example - connect a 100Ω load resistor
2Ω equiv.
6.44Ω equiv.
D = 0.50
100Ω equiv.
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. Example - connect a 5Ω load resistor
2Ω equiv.
6.44Ω equiv.
D = 0.18
100Ω equiv.

22. Likely worst-case buck/boost situation
BUCK/BOOST DESIGN
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

23. BUCK/BOOST DESIGN 5A 0.067V 1500µF 50kHz L1. 100µH, 9A L2. 100µH, 9A
C. 1500µF, 250V, 5.66A p-p
C1. 33µF, 50V, 14A p-p
Diode D. 200V, 16A
MOSFET M. 250V, 20A

24. BUCK/BOOST DESIGN 40V 90V 200µH 450µH 2A 50kHz 2A 50kHz L1. 100µH, 9A
C. 1500µF, 250V, 5.66A p-p
C1. 33µF, 50V, 14A p-p
Diode D. 200V, 16A
MOSFET M. 250V, 20A

25. Likely worst-case buck/boost situation
BUCK/BOOST DESIGN
Our components 9A
14A p-p
50V
10A A
40V
Likely worst-case buck/boost situation 5A
33µF
50kHz
3.0V
L1. 100µH, 9A
L2. 100µH, 9A
C. 1500µF, 250V, 5.66A p-p
C1. 33µF, 50V, 14A p-p
Diode D. 200V, 16A
Conclusion - 50kHz may be too low for buck/boost converter
MOSFET M. 250V, 20A