1

EE362L, Fall 2008DC−DC Buck/Boost Converter

2

Boost converter

+ Vout

–

Iout

CVin

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

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

+ 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.

C is discharging.

+ Vin –

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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

7

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

8

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

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

( )outinrms III +=3

2

Use max

switchclosed

switchopen

2(Iin + Iout)

iL1 + iL2

10

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

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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

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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 III

3

2,

3

2max1

switch closed

switch open

outrmsC II3

21 =

Switch closed, IC1 = −IL2

Switch open, IC1 = IL1

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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)

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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

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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 buck/boost 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 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

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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

BUCK/BOOST 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

BUCK/BOOST 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 II3

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 buck/boost situation

5A

5A

33µF 50kHz3.0V

BUCK/BOOST DESIGN

Our components 9A14A p-p50V

Conclusion - 50kHz may be too low for buck/boost converter