# Lecture 13 - DC-DC Boost Converter 13 - DC-DC Boost... · PDF fileELEC4614 Power Electronics Lecture 13 DC-DC (Boost) Converter 13-3 F. Rahman Boundary between continuous/discontinuous

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• ELEC4614 Power Electronics

Lecture 13 DC-DC (Boost) Converter 13-1 F. Rahman

Lecture 13 - Boost DC-DC Converters

Step-Up or Boost converters deliver DC power from a lower voltage DC level (Vd) to a higher load voltage Vo.

(a)

Circuit during ton Circuit during toff

Figure 13.1. (a) The basic boost converter during ton & toff

+ Vd

iL L + vL - C RVo

+Vd

iLL

+ vL - C RVo

+

iD

+ vL

iL

Vo CVd ic

D

Io

id

T

Vd

Vd V0 iL

0L

VIR 1 D

0

on

s

tDT

toff = (1-D)Ts

Ts

ton toff

vL

Io

• ELEC4614 Power Electronics

Lecture 13 DC-DC (Boost) Converter 13-2 F. Rahman

Analysis of the boost converter with continuous conduction mode of inductor current (CCM)

From T i( Ts s )

L0 i( 0 )

v dt L di 0 (13.1)

Vd ton + (Vd V0)toff = 0 (13.2)

o

d

V 1V 1 D

(13.3)

so that Vo > Vd for this converter. Theoretically, Vo when D = 1.

Assuming the converter to be lossless

Pd = VdId = VoIo

0

d

I 1 DI

(13.4)

0 0 d

L d 2I V V

I I1 D R(1 D) R(1 D)

(13.5)

Note that for the boost converter, the average inductor current IL and the average input current Id (not the average output current as in the buck converter) are the same.

• ELEC4614 Power Electronics

Lecture 13 DC-DC (Boost) Converter 13-3 F. Rahman

Boundary between continuous/discontinuous conduction

Figure 13.2 Inductor current and voltage waveforms with continuous conduction (CCM) of inductor current.

When conduction is just continuous,

d

LB L max on1 1 VI i t2 2 L

ds

os

V1 D T2 L

V D( 1 D )T2L

(13.6)

The inductor current for operation at the boundary of CCM and DCM as a function of D is plotted in figure 13.3.

Vd

d oV V

ton toff t

vL iLmax

iL

sT

• ELEC4614 Power Electronics

Lecture 13 DC-DC (Boost) Converter 13-4 F. Rahman

Figure 13.3. Continuous-discontinuous boundary for the boost converter.

From (13.4) IOB = 2o sV T D(1 D )

2L (13.7)

It can be shown that ILB and IoB become maximum for D = 12 and

13 . The corresponding maximum values are:

s o

LB maxT VI8L

(13.8)

and s o

oB maxT V2I

27 L (13.9)

I L B m a xI o B m a x

0 .5 0 .3 3

D 1 .0

0 .7 5

0 .2 5

• ELEC4614 Power Electronics

Lecture 13 DC-DC (Boost) Converter 13-5 F. Rahman

From 13.5

d d sL

L max L 2V V DTi

i I2 2LR( 1 D )

(13.10)

d d sL

L min L 2V V DTi

i I2 2LR( 1 D )

(13.11)

At the boundary of continuous and discontinuous conduction,

Lmini 0

d d s d

2s

V V DT V D2L 2LfR( 1 D )

(13.12)

2

sD(1 D ) RLf

2

for operation at the boundary of CCM and DCM operation of inductor current.

• ELEC4614 Power Electronics

Lecture 13 DC-DC (Boost) Converter 13-6 F. Rahman

DCM operation with constant Vd

Figure 13.4 Inductor current and voltage waveforms with

discontinuous conduction.

From T i( Ts s )

L0 i( 0 )

v dt L di 0 d s d o 1 sV DT V V T 0

o 1

d 1

V DV

(13.13) Because Pd = Po,

0 1

d 1

II D

(13.14)

The average inductor current IL is also the average input current Id, thus

Vd iL

Ts ton 1 sT

vL

Vd Vo

• ELEC4614 Power Electronics

Lecture 13 DC-DC (Boost) Converter 13-7 F. Rahman

d

d s 1VI DT ( D )2L

(13.15)

From (13.14), d s

0 1V TI D2L

(13.15a) Using (13.13), (13.15a) and (13.9)

12

o o 0

d d oB max

V V I4D 127 V V I

(13.16)

The range of required variation in D to keep Vo constant at a specified level when the inductor current is discontinuous is indicated in figure 13.5.

Figure 13.5 Vo D characteristic with load; for constant Vo and variable Vd.

IoBmax

0.5

D

1.0

0.75

0.25

Io, Amps

Vo = constantd

o

V 0.25V

d

o

V0.5

V

d

o

V 0.75V

• ELEC4614 Power Electronics

Lecture 13 DC-DC (Boost) Converter 13-8 F. Rahman

Note that during discontinuous conduction, the energy

stored in the inductor at the end of each ton, i.e., 2L max

1 Li2 ,

is transferred to the load circuit which includes the capacitor C. If the load is not able to absorb this energy, the capacitor voltage must rise, leading possibly to too high capacitor voltage. This can be avoided if Vo is controlled (i.e., regulated) during every switching cycle (Ts). Output Voltage Ripple

During ton, the diode current is zero. The load current is maintained by the capacitor. Assuming continuous conduction of load current and also assuming that the average load current is Io, which is also the average diode current, the change in the load voltage, Vo, during ton is given by

o s o s

oI DT V DTQV

C C RC

(13.17)

o s

o

V DTV RC

(13.18) The above analysis is valid only for continuous conduction mode and when D min oi I or ID

• ELEC4614 Power Electronics

Lecture 13 DC-DC (Boost) Converter 13-9 F. Rahman

iDID = Io

DTs (1-D)Ts

VoVo

t

ton toff

Ts

Q Q

0

Figure 13.6 Waveforms of output voltage, capacitor current and diode current ripple.

• ELEC4614 Power Electronics

Lecture 13 DC-DC (Boost) Converter 13-10 F. Rahman

Example: design of a boost converter Given, Vd = 12 V; Vo = 30 V; R = 50 ; fs = 25 kHz

(i) Find L so that operation is in CCM for the load specified. What L would you choose for DCM operation up to the maximum (specified) load?

(ii) Find iL

(iii) Find C for Vo/Vo < 10% (iv) Sketch the voltage and current waveforms of the

switch and the diode.

on

s

tDT

toff = (1-D)Ts

+

iD

T

+ vL

iL

ic

D

Io

Vd

Vd V0 iL0

0VIR

0

Tston toff

• ELEC4614 Power Electronics

Lecture 13 DC-DC (Boost) Converter 13-11 F. Rahman

Solution:

o

d

V 1V 1 D

; D = 0.6

6

ss 1040f1T s.

At the continuous /discontinuous boundary,

2

s minD( 1 D ) RLf

2

Lmax = 96 H Alternatively, the DC output current IoB = 30/50 = 0.6A.

s2ooB TD1DL2VI ; from 13.7.

L

106.57 6 A

For operation in CCM with Io IoB = 0.6A, L = 96H

Normally, we choose L < 96 H, say, 85 H, to ensure DCM for the maximum (50 in this example) load. With L = 96H,

(ii) A3DTL

VI sdL

(iii) s

3o o

so o

DT D 0.6C 48 FV V 25 10 50 0.01R f R

V V

• ELEC4614 Power Electronics

Lecture 13 DC-DC (Boost) Converter 13-12 F. Rahman

(vi)

A5.1D1R

VD1R

VD1

II 2doo

L

d s

L maxV DTI 1.5 3 A

2L

d s

LminV DT& I 1.5 0 A

2L

Sketch of iT , vT, iD and vD are left for you as an exercise. Boost Converter Gain Note that for a boost converter,

o

d

V 1V 1 D

With continuous conduction, Vo approaches as D 1. This does not happen in practice because parasitic elements, such as the switch, diode and inductor resistances and the capacitor ESR, prevent the rise of Vo when D approaches unity. Note also that as D 1, iL approaches .

• ELEC4614 Power Electronics

Lecture 13 DC-DC (Boost) Converter 13-13 F. Rahman

o

d

VV

D 1.0

11 D

0

With cont. conduction

With disc. conduction

Figure 13.7 Boost converter gain characteristic. The sign of practical boost converter gain becomes negative as D approaches unity. Because of this and the other problems mentioned above, the boost converter is normally operated with duty cycle less than 0.85 or so. Also, the small-signal transfer function of the boost converter in CCM exhibits a zero in the right-half s-plane. This makes it difficult to obtain good closed-loop performance and stability. Because of these reasons, the boost converter is often operated in DCM to ensure stable operation and fast dynamics of control.

• ELEC4614 Power Electronics

Lecture 13 DC-DC (Boost) Converter 13-14 F. Rahman

Buck-Boost Converter

The output DC voltage of a buck-boost converter can be lower or higher than the input DC voltage, with reversed polarity with respect to the input DC voltage.

D

C R L

T

Vd iL Vo

+ Io id

iD

Figure 13.8 Buck-boost converter circuit

Operation with continuous inductor current

during ton during toff

Figure 13.8 Buck-boost converter operating modes

RC L Vd

iL

+ vL _ io

Vo

+RC L

Vd

iL+vL_ io

Vo

+

Vd Li

0V

sT

ton = DTs toff

t

vL IL= Id + Io

0

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