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Boost Converter

3-2-1 Circuit diagram and key waveforms

C

Vg

D

+

Vo

-

Vg

+ VL -

(b)

+ VL -

R

L

(a)

+

Vo

-

L

C

(c)

L

Vg

R

RC

IRF150

+

Vo

-

+ VL -

iDiL

io

vL

C

A

B

iL,min

iL,maxiD

t

t

vo

vo

t

(1-D)TDT

iL,min

iL,maxiL

-Vo/R

iL

t

Vg

Vg

- Vo

(d)

ic

t

Figure 3-2 (a) Boost converter (b) switch on for a time durationDT(c) switch off for a timeduration (1-D)T(d) key waveforms.

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3-2-2 Circuit description and operation

Circuit description. The three basic dc-dc converters use a pair of switches, usually one

controlled (eg. MOSFET) and one uncontrolled (ie. diode), to achieve unidirectional power

flow from input to output. The converters also use one capacitor and one inductor to store

and transfer energy from input to output. They also filter or smooth voltage and current.

The dc-dc coverters can have two distinct modes of operation: Continuous

conduction mode (CCM) and discontinuous conduction mode (DCM). In practice, a

converter may operate in both modes, which have significantly different characteristics.

Therefore, a converter and its control should be designed based on both modes of operation.

However, for this course we only consider the dc-dc converters operated in CCM.

Circuit Operation. When the switch is on for a time duration DT, the switch conducts theinductor current and the diode becomes reverse biased. This results in a positive voltage vL =

Vg across the inductor. This voltage causes a linear increase in the inductor current iL. When

the switch is turned off, because of the inductive energy storage, iLcontinues to flow. Thiscurrent now flows through the diode, and vL = Vg-Vo for a time duration (1-D)T until the

switch is turned on again.

3-2-3 Analytical expressions forg

o

V

V, iL, and vo

Assumptions made about the operation of the converter are as follows:

The circuit is operating in the steady state The circuit is operating in the CCM

The capacitor is large enough to assume a constant output voltage The component are ideal.

Equating the integral of the inductor voltage over one time period to zero yields

0)1()(

0000

=+

=+= TDVVDTV

dtvdtvdtv

ogg

t

L

t

L

T

L

offon

go VD

V= 11

or

DV

V

g

o

=

1

1

Assuming a lossless circuit,Pg=Po,

Therefore

oogg IVIV =

And

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DV

V

I

I

o

g

g

o == 1

For a boost converter, it is obvious that

Lg II =

]A)(AreawaveformunderareaShaded[1

1

0

L

DT

LL

vL

dtvL

i

=

=

DTVL

g=1

From iL we can obtain iL,min and iL, max

2min,

LLL

iIi

=

2max,

LLL

iIi

+=

To obtain the average inductor current, we can use the relationship

LoD IDII )1( ==

Therefore

RD

V

D

II ooL

)1()1( =

=

The peak-peak output voltage ripple, vo. From the information of the capacitorcurrent, ic we can obtain vo.

DTR

V

C

iL

dtiC

vv

o

c

cco

=

=

==

1

]waveformunderareaShaded[1

1

therefore

DTR

V

Cv oo =

1

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3-2-4 CCM/DCM boundary condition

Being at the boundary between the continuous and the discontinuous mode, by definition, the

inductor current iLgoes to zero at the end of the off period. At this boundary, the averageinductor current is

2

LL

iI =

the minimum inductor current, iL, min = 0 and the maximum inductor curren iL, max= iL.

(1-D)TDT

iL

vL

t

Vg

Vg- Vo

We know that for buck convertersR

VII ooD == and TDVV

LDTV

Li oggL )1)((

11== .

Equation at the CCM/DCM boundary,2

LL

iI

= , can be used to determine the combination

ofL, fandR that will result in CCM. The minimum load current required for CCM operation

is:

TDDVL

TDDVL

I

DTVL

i

D

I

IDI

DTVL

iI

o

go

g

Lo

Lo

g

LL

2

min,

)1(2

1

)1(2

1

21

21

)1(but

2

1

2

=

=

=

=

=

=

=

If the desired switching frequency f and load resistance R are established, the minimum

inductor current required for CCM is:

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f

RDD

RTDDL

DTDVL

DTVLDR

V

iI

ogo

LL

2

)1(

2)1(

)1(2

1

2

1

)1(

2

2

2

min

=

=

==

=

If the desired value of the inductorL and the load resistanceR are established, the minimum

switching frequency required for CCM is

L

RDDf

2

)1( 2

min

=

If the desired switching frequency and the value of the inductor L are established, the

minimum load resistance required for CCM is

2min )1(

2

DD

fLR

=

-tammat-