Slides PECh3 July03

8/18/2019 Slides PECh3 July03

1/39

© Ned Mohan, 2003

3- 1

3-1 DC-DC Converters

3-2 Switching Power-Pole in DC Steady State

3-3 Simplifying Assumptions

3-4 Common Operating Principles

3-5 Buck Converter Switching Analysis in DC Steady State

3-6 Boost Converter Switching Analysis in DC Steady State

3-7 Buck-Boost Converter Switching Analysis in DC Steady State

3-8 Topology Selection

3-9 Worst-Case Design

3-10 Synchronous-Rectified Buck Converter for Very Low Output Voltages

3-11 Interleaving of Converters

3-12 Regulation of DC-DC Converters by PWM

3-13 Dynamic Average Representation of Converters in CCM

3-14 Bi-Directional Switching Power-Pole

3-15 Discontinuous-Conduction Mode (DCM)

ReferencesProblems

Appendix 3A Discontinuous-Conduction Mode (DCM) in DC-DC Converters

Chapter 3

SWITCH-MODE DC-DC CONVERTERS:

SWITCHING ANALYSIS, TOPOLOGY

SELECTION AND DESIGN


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© Ned Mohan, 2003

3- 2

Regulated switch-mode dc power supplies

Figure 3-1 Regulated switch-mode dc power supplies.

inV oV

,o ref V controller

dc-dcconverter topology

,in oV V

,in o I I

(a) (b)

inV oV

,o ref V controller

dc-dcconverter topology

,in oV V

,in o I I

(a) (b)


3/39

© Ned Mohan, 2003

3- 3

Switching power-pole as the building block of dc-dc converters

( ) ( ) L L si t i t T = −

0

area area

10

s s

s

DT T

L L L

s DT

A B

V v d v d T

τ τ

= ⋅ + ⋅ =

∫ ∫

( ) ( )C C sv t v t T = −

Figure 3-2 Switching power-pole as the building block of dc-dc converters.

inV

Lv

Li

q

A Lv

Li

t

t

B

0

0

s DT

sT

( )b( )a

inV

Lv

Li

q

inV

Lv

Li

q

A Lv

Li

t

t

B

0

0

s DT

sT

Lv

Li

t

t

B

0

0

s DT

sT

( )b( )a


4/39

© Ned Mohan, 2003

3- 4

• Simplifying Assumptions

• Two-Step Process

• Common Operating Principles


5/39

© Ned Mohan, 2003

3- 5

BUCK CONVERTER SWITCHING ANALYSIS IN DC STEADY STATE

o A inV V DV = =

(1 )in o o L s sV V V

i DT D T L L

−∆ = = −

o L o

V I I = =

,( ) ( )C L ripplei t i t

in L o DI DI = =

in in o oV I V I =

Figure 3-3 Buck dc-dc converter.

inV

Li

Av

L in ov V V = −

Lv

oV

1q =

inV

Li Av

L ov V = −

oV

0q =

0 Av =

inV

ini

Li

Av Lv

oV

q

C i o I

(a)

(b)

q

Av

Lv

, L ripplei

Li

ini

inV A oV V =

( )in o

V V −

( )oV −

Li∆

L o I I =

in I

A

B

t

t

t

t

t

t 0

0

0

0

0

0

1

(c)(d)

inV

Li

Av

L in ov V V = −

Lv

oV

1q =

Li

Av

L in ov V V = −

Lv

oV

1q =

inV

Li

Av

L ov V = −

oV

0q =

0 Av =

inV

Li

Av

L ov V = −

oV

0q =

0 Av =

inV

ini

Li

Av Lv

oV

q

C i o I

(a)

(b)

q

Av

Lv

, L ripplei

Li

ini

inV A oV V =

( )in o

V V −

( )oV −

Li∆

L o I I =

in I

A

B

t

t

t

t

t

t 0

0

0

0

0

0

1q

Av

Lv

, L ripplei

Li

ini

inV A oV V =

( )in o

V V −

( )oV −

Li∆

L o I I =

in I

A

B

t

t

t

t

t

t 0

0

0

0

0

0

1

(c)(d)


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© Ned Mohan, 2003

3- 6

PSpice Modeling: C:\FirstCourse_PE_Book03\Buckconv.sch


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© Ned Mohan, 2003

3- 7

Simulation Results

Time

450us 455us 460us 465us 470us 475us 480us 485us 490us 495us 500us

I(C1) I(L1) V(L1:1,L1:2)

-8

-4

0

4

8

12

16


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© Ned Mohan, 2003

3- 8

BOOST CONVERTER SWITCHING ANALYSIS IN DC STEADY STATE

Figure 3-4 Boost dc-dc converter.

oV

inV

q p

C Lv

Li

inV

oV

p

C Lv

q

Li

(a) (b)

oV

inV

q p

C Lv

Li

oV

inV

q p

C Lv

Li

inV

oV

p

C Lv

q

Li

inV

oV

p

C Lv

q

Li

(a) (b)


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© Ned Mohan, 2003

3- 9

Boost converter: operation and waveforms

1

1

o

in

V

V D=

− ( )o inV V >

(1 )in o in L s sV V V

i DT D T L L

−∆ = = −

in in o oV I V I = 11 1

o o o L in o

in

V I V I I I

V D D R= = = =

− −

,( ) ( )C diode ripple diode oi t i t i I = −

Figure 3-5 Boost converter: operation and waveforms.

inV oV

L inv V =

Li 0 Av =

1q =

inV

oV

L in ov V V = −

Li

0q =

A ov V =

Lv

Av

q

, L ripplei

Li

diodei

C i

t

t

t

t

t

t

t 0

0

0

0

0

0

0

oV

A inv V =

A

B( )o inV V − −

Li∆

L I

( )diode o

I I =

inV

(a)

(b) (c)

inV oV

L inv V =

Li 0 Av =

1q =

inV oV

L inv V =

Li 0 Av =

1q =

inV

oV

L in ov V V = −

Li

0q =

A ov V =

Lv

Av

q

, L ripplei

Li

diodei

C i

t

t

t

t

t

t

t 0

0

0

0

0

0

0

oV

A inv V =

A

B( )o inV V − −

Li∆

L I

( )diode o

I I =

inV L

v

Av

q

, L ripplei

Li

diodei

C i

t

t

t

t

t

t

t 0

0

0

0

0

0

0

oV

A inv V =

A

B( )o inV V − −

Li∆

L I

( )diode o

I I =

inV

(a)

(b) (c)


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© Ned Mohan, 2003

3- 10

PSpice Modeling: C:\FirstCourse_PE_Book03\Boost.sch


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© Ned Mohan, 2003

3- 11

Time

1.950ms 1.955ms 1.960ms 1.965ms 1.970ms 1.975ms 1.980ms 1.985ms 1.990ms 1.995ms 2.000ms

I(L1) V(L1:1,L1:2)

-15

-10

-5

0

5

10

15

Simulation Results


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© Ned Mohan, 2003

3- 12

Boost converter: voltage transfer ratio

Figure 3-6 Boost converter: voltage transfer ratio.

0

1

1 D−

, L crit I DCM CCM

L I

o

in

V

V

1

0

1

1 D−

, L crit I DCM CCM

L I

o

in

V

V

1


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© Ned Mohan, 2003

3- 13

BUCK-BOOST CONVERTER ANALYSIS IN DC

STEADY STATE

Figure 3-7 Buck-Boost dc-dc converter.

q

A

Av

Lv

Li inV

oV

diodei

o I Lv

Av

oV inV o

I

(a) (b)

Li

q

A

Av

Lv

Li inV

oV

diodei

o I

q

A

Av

Lv

Li inV

oV

diodei

o I Lv

Av

oV inV o

I

(a) (b)

Li


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© Ned Mohan, 2003

3- 14

Figure 3-8 Buck-Boost converter: operation and waveforms.

ini

L inv V =

A in ov V V = +

oV inV Li

inV Li L ov V = −

0 Av =

oV

(a)

(b)

Lv

Av

q

, L ripplei

Li

diodei

C i

t

t

t

t

t

t

t 0

0

0

0

0

0

0

oV −

A oV V =

A

B

( )in oV V +

Li∆

L I

( )diode o I I =

inV

(c)

inio I

o I

ini

L inv V =

A in ov V V = +

oV inV Li

L inv V =

A in ov V V = +

oV inV Li

inV Li L ov V = −

0 Av =

oV

(a)

(b)

Lv

Av

q

, L ripplei

Li

diodei

C i

t

t

t

t

t

t

t 0

0

0

0

0

0

0

oV −

A oV V =

A

B

( )in oV V +

Li∆

L I

( )diode o I I =

inV

(c)

inio I

o I

Buck-Boost converter: operation and waveforms

1

o

in

V D

V D

=

−

(1 )in o L s sV V

i DT D T L L

∆ = = −

L in o I I = +

in in o oV I V I =

1

oin o o

in

V D

I I I V D= = −1 1

1 1

o L in o o

V I I I I

D D R= + = =

− −

,( ) ( )C diode ripplei t i t


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© Ned Mohan, 2003

3- 15

PSpice Modeling: C:\FirstCourse_PE_Book03\Buck-Boost_Switching.sch


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© Ned Mohan, 2003

3- 16

Simulation Results

Time

2.950ms 2.955ms 2.960ms 2.965ms 2.970ms 2.975ms 2.980ms 2.985ms 2.990ms 2.995ms 3.000ms

I(L1) V(L1:1,L1:2)

-30

-20

-10

0

10

20


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© Ned Mohan, 2003

3- 17

Buck-Boost converter: voltage transfer ratio

Figure 3-9 Buck-Boost converter: voltage transfer ratio.

0

1

D

D−

, L crit I DCM CCM

L I

o

in

V

V

1

0

1

D

D−

, L crit I DCM CCM

L I

o

in

V

V

1


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© Ned Mohan, 2003

3- 18

Other Buck-Boost Topologies

• SEPIC Converters (Single-Ended Primary Inductor Converters)

• Cuk Converters


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© Ned Mohan, 2003

3- 19

SEPIC Converters (Single-Ended Primary Inductor Converters)

(1 )in oV D V = −1

o

in

V D

V D

=

−

Figure 3-10 SEPIC converter.

inV

2 Li

q

C v

oV

Li diodei

2 Lv(a)

inV

C v

oV

2 L C v v=1q =

2 LvoV

inV

0q =

C v2 Lv

2 L ov V = −

(b) (c)

inV

2 Li

q

C v

oV

Li diodei

2 Lv(a) inV

2 Li

q

C v

oV

Li diodei

2 LvinV

2 Li

q

C v

oV

Li diodei

2 Lv(a)

inV

C v

oV

2 L C v v=1q =

2 LvoV

inV

0q =

C v2 Lv

2 L ov V = −

(b) (c)inV

C v

oV

2 L C v v=1q =

2 LvinV

C v

oV

2 L C v v=1q =

2 LvoV

inV

0q =

C v2 Lv

2 L ov V = −

oV inV

0q =

C v2 Lv

2 L ov V = −

(b) (c)


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© Ned Mohan, 2003

3- 20

Cuk Converter

(1 )o in I D I = − 1in

o

I D

I D=

− 1o

in

V D

V D=

−

Figure 3-11 Cuk converter.

inV

q

C v

oV

Li oi

o I

C 1 L 2 L

(a)

inV

1q =

C v

oV ini

oi

inV

0q =

C v

oV ini oi

(b) (c)

inV

q

C v

oV

Li oi

o I

C 1 L 2 L

(a) inV

q

C v

oV

Li oi

o I

C 1 L 2 L

inV

q

C v

oV

Li oi

o I

C 1 L 2 L

(a)

inV

1q =

C v

oV ini

oi

inV

0q =

C v

oV ini oi

(b) (c)


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© Ned Mohan, 2003

3- 21

TOPOLOGY SELECTION

Criterion Buck Boost Buck-Boost

Transistor

ˆ

V inV oV ( )in oV V +

Transistor ˆ I o I in I in o I I +

rms I Transistor o DI in DI ( )in o D I I +

Transistoro DI in DI ( )in o D I I + avg I

Diode (1 ) o D I − (1 ) in D I − ( )(1 ) in o D I I − +

L I o I in I in o I I +

Effect of L on C significant little little

Pulsating Current input output both


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© Ned Mohan, 2003

3- 22

WORST-CASE DESIGN

The worst-case design should consider the ranges in which the input voltage and the

output load vary. As mentioned earlier, often converters above a few tens of watts are

designed to operate in CCM. To ensure CCM even under very light load conditions

would require prohibitively large inductance. Hence, the inductance value chosen is

often no larger than three times the critical inductance ( )3 c L L< , where, as discussed in

section 3-15, the critical inductance c L is the value of the inductor that will make the

converter operate at the border of CCM and DCM at full-load.


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© Ned Mohan, 2003

3- 23

SYNCHRONOUS-RECTIFIED BUCK CONVERTER FOR

VERY LOW OUTPUT VOLTAGES

Figure 3-12 Buck converter: synchronous rectified.

inV

oV Av

T +

T −

q+

q−

Li

( )a

q+ q−

Av

Li

t

t

t

0t =

s DT sT

inV

oV 0

0

0

0 L I

( )b

inV

oV Av

T +

T −

q+

q−

Li

( )a

inV

oV Av

T +

T −

q+

q−

Li

( )a

q+ q−

Av

Li

t

t

t

0t =

s DT sT

inV

oV 0

0

0

0 L I

( )b

q+ q−

Av

Li

t

t

t

0t =

s DT sT

inV

oV 0

0

0

0 L I

( )b

3 24


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© Ned Mohan, 2003

3- 24

INTERLEAVING OF CONVERTERS

Figure 3-13 Interleaving of converters.

1q2q

1

q

2q

0

0

t

t

(a) (b)

inV

+

−

−

+

oV

1 Li

2 Li

1q2q

1

q

2q

0

0

t

t

(a) (b)

inV

+

−

−

+

oV

1 Li

2 Li

3 25


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© Ned Mohan, 2003

3- 25

REGULATION OF DC-DC CONVERTERS BY PWM

( )( )

ˆc

r

v t d t

V =

Figure 3-14 Regulation of output by PWM.

inV oV

,o ref V controller

dc-dcconverter

topology

(a) (b)

0 sd T

sT t

ˆr V

( )cv t

t

r v

( )q t

0

1

inV oV

,o ref V controller

dc-dcconverter

topology

(a) (b)

0 sd T

sT t

ˆr V

( )cv t

t

r v

( )q t

0

1

3 26


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© Ned Mohan, 2003

3- 26

Figure 3-15 Average dynamic model of a switching power-pole.

( )q t

( )r v t

( )cv t

vpv

cpv

cpi

vpi

vpV

cpV

cp I

vp I

1: D

cpv

1: ( )d t

( )cv t ^

1

r V

(c)(a) (b)

vpi

vpv

cpi

( )q t

( )r v t

( )cv t

vpv

cpv

cpi

vpi

vpV

cpV

cp I

vp I

1: D

cpv

1: ( )d t

( )cv t ^

1

r V

(c)(a) (b)

vpi

vpv

cpi

DYNAMIC AVERAGE REPRESENTATION OF

CONVERTERS IN CCM

( ) ( ) ( )cp vpv t d t v t =

( ) ( ) ( )vp cpi t d t i t =

cp vpV DV =

vp o I D I =

3 27


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© Ned Mohan, 2003

3- 27

Average dynamic models of three converters

Figure 3-16 Average dynamic models of three converters.

q

inV

ov Lv

Li

oV

inV

q p

A A

qoV

inV

inV

1: ( )d t

inV

1: (1 ( ))d t −

p 1: ( )d t

inV

(a)

(b)

Li Li

L

i

Li Li

ov ov

ov

⇓ ⇓ ⇓q

inV

ov Lv

Li

oV

inV

q p

A A

qoV

inV

inV

1: ( )d t

inV

1: (1 ( ))d t −

p 1: ( )d t

inV

(a)

(b)

Li Li

L

i

Li Li

ov ov

ov

⇓ ⇓ ⇓

3 28


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© Ned Mohan, 2003

3- 30

Simulation Results

Time

0s 0.5ms 1.0ms 1.5ms 2.0ms 2.5ms 3.0ms 3.5ms 4.0ms 4.5ms 5.0ms

I(L1) V(L1:1,L1:2)

-40

-20

0

20

40


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3- 32


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© Ned Mohan, 2003

3- 32

Average dynamic model of the switching power-pole with

bi-directional power flow

Figure 3-18 Average dynamic model of the switching power-pole with bi-directional power

flow.

q

inV

Li

Buck Boost

(1 )q q−

= − 1: d

Li

inV

(a) (b)q

inV

Li

Buck Boost

(1 )q q−

= − 1: d

Li

inV

(a) (b)

3- 33


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© Ned Mohan, 2003

3- 33

DISCONTINUOUS-CONDUCTION MODE (DCM)

Figure 3-19 Inductor current at various loads; duty-ratio is kept constant.

1 Li

2 Li, L crii

1 L I

2 L I

, L crit I

t

Li

0

1 Li

2 Li, L crii

1 L I

2 L I

, L crit I

t

Li

0

3- 34


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© Ned Mohan, 2003

3 34

Figure 3-20 Waveforms for the three converters at the border of CCM/DCM.

Li

ˆ L I

t

t

Av

in oV V −

0

0

0

S DT (1 ) S D T −

S T

(a)

Liˆ L I

t

t

AvoV

0

0

0

S DT (1 ) S D T −

S T

(b) (c)

Li

ˆ L I

t

t

Av

in oV V +

0

0

0

S DT (1 ) S D T −

S T

Li

ˆ L I

t

t

Av

in oV V −

0

0

0

S DT (1 ) S D T −

S T

(a)

Li

ˆ L I

t

t

Av

in oV V −

0

0

0

S DT (1 ) S D T −

S T

Li

ˆ L I

t

t

Av

in oV V −

0

0

0

S DT (1 ) S D T −

S T

(a)

Liˆ L I

t

t

AvoV

0

0

0

S DT (1 ) S D T −

S T

(b)

Liˆ L I

t

t

AvoV

0

0

0

S DT (1 ) S D T −

S T

(b) (c)

Li

ˆ L I

t

t

Av

in oV V +

0

0

0

S DT (1 ) S D T −

S T

(c)

Li

ˆ L I

t

t

Av

in oV V +

0

0

0

S DT (1 ) S D T −

S T

Li

ˆ L I

t

t

Av

in oV V +

0

0

0

S DT (1 ) S D T −

S T

, , , , -2

in L crit Boost L crit Buck Boost

V I I D f

= =, , (1 )2

in L crit Buck

V I D D Lf

= −

Critical Inductor Currents

3- 35


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© Ned Mohan, 2003

3 35

Buck converter in DCM

Figure 3A-1 Buck converter in DCM.

Liˆ L I s

t

T

Av

oV inV

0

0

D ,1off D ,2off D

1

o

in

V

V

, L crit I DCM CCM

L I

(a)

0

D

1

s

t T

(b)

Liˆ L I s

t

T

Av

oV inV

0

0

D ,1off D ,2off D

1

o

in

V

V

, L crit I DCM CCM

L I

(a)

0

D

1

s

t T

(b)

3- 36


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© Ned Mohan, 2003

3 36

Boost Converters in DCM

Figure 3A-2 Boost converter in DCM.

Liˆ L I

s

t

T

AvoV

inV

0

0

D ,1off D ,2off D

1(a)

0

1

1 D−

, L crit

I DCM CCM L I

o

in

V

V

1

(b)

s

t

T

Liˆ L I

s

t

T

AvoV

inV

0

0

D ,1off D ,2off D

1(a)

0

1

1 D−

, L crit

I DCM CCM L I

o

in

V

V

1

(b)

s

t

T

3- 37


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© Ned Mohan, 2003

3 37

Buck-Boost converter in DCM

Figure 3A-3 Buck-Boost converter in DCM.

Li

ˆ L I s

t

T

Av

oV in oV V +

0

0

D ,1off D ,2off D

1

(a)

0

1

D

D−

, L crit I DCM CCM L

I

o

in

V

V

(b)

1

s

t

T

Li

ˆ L I s

t

T

Av

oV in oV V +

0

0

D ,1off D ,2off D

1

(a)

0

1

D

D−

, L crit I DCM CCM L

I

o

in

V

V

(b)

1

s

t

T

3- 38


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© Ned Mohan, 2003

AVERAGE REPRESENTATION OF DC-DC

CONVERTERS IN DCM

, 0

2[1 ]

( )

s Lk Buck

in o

Lf iv v

V v d = −

−

2

, 0( )2

k Buck in Ld i V v di Lf

= − −

• Dependent Sources in Buck and Buck-Boost Converters in DCM

,

21 s Lk Buck Boost o

in

Lf iv v

V d −

= −

2

,2

k Buck Boost in Ld i V di Lf

− = −

Figure 3A-4 Average dynamic model for Buck and Buck-Boost converters.

vpv cpv

vpicpi

k v

k i

1: ( )d t

vpv cpv

vpicpi

k v

k i

1: ( )d t

3- 39


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© N d M h 2003

• Dependent Sources in Boost Converters in DCM

( ), 02

1 s Lk Boost inin

Lf iv V vV d

= − −

2

,

2k Boost in L

d i V di

Lf

= −

Figure 3A-5 Average dynamic model for Boost converters.

(1 ) :1d −

cpv

cpi k v

k i

vpi

vpv

(1 ) :1d −

cpv

cpi k v

k i

vpi

vpv

Documents

Slides PECh3 July03