[PDF] - 1 Prof. S. Ben-Yaakov , DC-DC Converters [2- 4] Buck t on In this PDF Document

SLIDE 1

1

Prof. S. Ben-Yaakov , DC-DC Converters

[2- 1]

2.1 Buck converter 2.1.1 Operation modes 2.1.2 Voltage transfer function 2.1.3 Current modes (CCM, DCM) 2.1.4 Capacitor current 2.2 Boost converter 2.2.1 Operation modes 2.2.2 Voltage transfer function 2.3 Buck-Boost converter 2.4 Comparison between topologies 2.5 Simulation of SMPS 2.5.1 The simulations problem 2.5.2 Basics of average model of SMPS 2.5.3 Example: Boost average model simulations

BUCK, BOOST, BUCK-BOOST, DCM

Prof. S. Ben-Yaakov , DC-DC Converters

[2- 2]

Buck Converter Constant Switching Frequency

t ON ON ON t ON ON ON control switch ton toff TS

s s

T 1 f = D

r

D T t

n

s

n

→ = D 1 D T t

ff

s

ff

− → = Switch frequency: Duty Cycle:

S Vin D L C R control

Prof. S. Ben-Yaakov , DC-DC Converters

[2- 3]

Operation modes

On Off

At steady state Ia=Ib

S Vin D L C R S Vin D L C R VL IL ts t Vin-Vo

Vo

Ia Ib t

Self commutation

VL IL ts t Vin-Vo Ia t

Commutation

SLIDE 2

2

Prof. S. Ben-Yaakov , DC-DC Converters

[2- 4]

In this case Inductor current waveform at steady state

L V V

in −

ton t IL toff L Vo − I ∆ S Vin D C R ton toff

Buck

Prof. S. Ben-Yaakov , DC-DC Converters

[2- 5]

Voltage transfer function

The ∆I method

Left triangle

n
in

t L V V I ⋅ − = ∆

Right triangle

ff
t

L V I ⋅ = ∆

ff
n
in

t L V t L V V =       −

n

s

n
ff
n
n

in

D

T t t t t V V = = + = Independent of L ! L V V

in −

ton t IL toff L Vo − I ∆

Prof. S. Ben-Yaakov , DC-DC Converters

[2- 6]

Vo

VL toff t Vin-Vo ton Ts +

At steady state, over one switching cycle:

; VL =

n

in

D

V V S S = ⇒ = +

− +

; t ) V V ( S

n
in

⋅ − =

+

; t ) V ( S

ff
⋅

− =

−

S Vin D C R ton toff Vo VL

Voltage transfer function

The average voltage method

SLIDE 3

3

Prof. S. Ben-Yaakov , DC-DC Converters

[2- 7]

Load Change with Fixed D

ton t IL toff Ts How will IL change if R is getting smaller?

S Vin D L C R control Vo

Prof. S. Ben-Yaakov , DC-DC Converters

[2- 8]

ton t IL toff Ts R2 R1 R3 L V V

in −

L Vo −

CCM - Continues Conductor Current Mode DCM - Discontinues Conductor Current Mode

3 2 1

R R R < <

Load Change

Prof. S. Ben-Yaakov , DC-DC Converters

[2- 9]

Discontinuous Inductor Current Mode (DCM)

S Vin D L C R Vx Vo control Different voltage transfer ratio ≠ Don Higher ripple current

t IL Ts R4 R3 t'off toff ton R4>R3

SLIDE 4

4

Prof. S. Ben-Yaakov , DC-DC Converters

[2- 10]

ton t IL t'

ff

Ts Ipk

Voltage transfer function (DCM)

The ∆I method

ff
n
in

pk

t L V t L V V I ′ = − =

ut
n
ut

in

ff

V D ) V V ( D − =       + ⋅ − = ) D D ( T T L V V 2 1 T 1 I

ff
n

S

n
in

S AV

R V I

AV =

) V V V 1 ( D T L V V 2 1 I

in
n
n
in

AV

− + ⋅ − =

2

in

S 2

n
in

LV 2 V T D ) V V ( R = −         − + = 1 T D R L 8 1 L 4 T D R V V

s 2

n

s 2

n

in

Prof. S. Ben-Yaakov , DC-DC Converters

[2- 11]

Boundary of CCM and DCM

t on t toff Ts L Vo − L V V

in −

IL L2 L min Iav

For CCM L > Lmin In Buck

av pk

ff

min

I

2 I t L V = =

s

ff

s av

ff
min

f 2 D R f I 2 D V L = =

Prof. S. Ben-Yaakov , DC-DC Converters

[2- 12]

Example

A BUCK converter has a following characteristics: Output voltage: Output current: Input voltage: Frequency: Current mode: CCM Find: V 5 Vo = A 10 I I

av

ut

= = V 10 Vin = kHz 100 fs =

min

L H 2 . 1 10 10 2 5 . 5 f I 2 D V L 5 . D 1 D CCM 5 . D V V

5 s av

ff
min
n
ff
n

in

µ

= ⋅ ⋅ ⋅ = = = − =    →  = =

SLIDE 5

5

Prof. S. Ben-Yaakov , DC-DC Converters

[2- 13]

IL t Iav t Iav IR IC t AC DC Capacitor current

Capacitor current

S Vin D L C R IL IC IR control Vo R L C

I I I − =

Assumption:

V0 has small ripple

Prof. S. Ben-Yaakov , DC-DC Converters

[2- 14]

BOOST Step-Up

Vo > Vin

Why ?? S Vin D L C R VX Vo

Prof. S. Ben-Yaakov , DC-DC Converters

[2- 15]

ON

VL=Vin

OFF

VL=Vin-Vo

Vin L C R Vo Vin L C R Vo

Operation modes

VL IL ts t Vin Ia t VL IL ts t Vin Vin-Vo Ia Ib t

Boost

SLIDE 6

6

Prof. S. Ben-Yaakov , DC-DC Converters

[2- 16]

toff TS Vo Vx t

ff

in

ff
in

D 1 V V D V V = → =

S Vin D L C R VX Vo

The average voltage method ; D V T t V V ; V V ; V V ; V V ; V

ff
s
ff
x

in in x in x in L

= = = = = − =

Voltage transfer function

Prof. S. Ben-Yaakov , DC-DC Converters

[2- 17]

Voltage transfer function

The ∆I method

ton IL toff Ts t L V V

in

−

− L Vin

I ∆

ff

in

n

in

t L V V t L V ⋅ − = ⋅

ff
ff
n

in

t V ) t t ( V ⋅ = + ⋅

ff

in

D

1 V V =

S Vin D L C R VX Vo

Prof. S. Ben-Yaakov , DC-DC Converters

[2- 18]

BUCK-BOOST Step-Up Step-Down

Find Vo/Vin

Hint: Average of Vx ? S Vin D L C R Vo VX

SLIDE 7

7

Prof. S. Ben-Yaakov , DC-DC Converters

[2- 19]

Comparison between basic topologies CCM

S Vin D L C R Vo S Vin D L C R Vo S Vin D L C R Vo S D L Basic Cell L a b c Switched inductor

Prof. S. Ben-Yaakov , DC-DC Converters

[2- 20]

Iin t Iin t Iin t Io t Io t Io t

Source current Load current Buck Boost Buck Boost Continues current -> Low ripple component Discontinues current -> High ripple component Input and Output Currents

Prof. S. Ben-Yaakov , DC-DC Converters

[2- 21]

Modulator Control

e

V D

in

V Assembly Switched

V

+ −

The simulation problem

SLIDE 8

8

Prof. S. Ben-Yaakov , DC-DC Converters

[2- 22]

The problematic part : Switched Assembly
Rest of the circuit continuous - SPICE compatible
Only possible simulation :

Time domain (cycle-by-cycle) -Transient

The objective : translate the

Switched Assembly into an equivalent circuit which is SPICE compatible

Modulator Control

e

V D

in

V Assembly Switched

V

+ −

The simulation problem

Prof. S. Ben-Yaakov , DC-DC Converters

[2- 23]

in

V b

n

T

L

b

I

L

I

C

I d c L Buck Boost Boost Buck −

n

T

+ −

Average Simulation of PWM Converters

Prof. S. Ben-Yaakov , DC-DC Converters

[2- 24]

Ton - switch conduction time Toff - diode conduction time TDCM - no current time (in DCM) L a b c b

n

T

DCM

T

ff

T L c a

The Switched Inductor Model

SLIDE 9

9

Prof. S. Ben-Yaakov , DC-DC Converters

[2- 25]

The concept of average signals

t t t

a

I

b

I

c

I

b

I

a

I

c

I b c a L

n

T

ff

T

a

I

b

I

c

I

The Switched Inductor Model (SIM) (CCM)

Prof. S. Ben-Yaakov , DC-DC Converters

[2- 26]

⇓

b c a

?

a

I

c

I

b

I

b c a L

n

T

ff

T

a

I

b

I

c

I

The SIM Objective : To replace the switched part by a continuous network

Prof. S. Ben-Yaakov , DC-DC Converters

[2- 27]

I

b

I

L

I

b

I

ON

T

S

T

n

L S

n

L b

D I T T I I = =

S ON

n

T T D =

ff

L S

ff

L c

D I T T I I = =

L a

I I =

Similarly : b c a L

n

T

ff

T

a

I

b

I

c

I

Average current

SLIDE 10

10

Prof. S. Ben-Yaakov , DC-DC Converters

[2- 28]

b c

b

I

c

I a

a

G

b

G

c

G

a

I b c a

L a

I I =

n

L b

D I I ⋅ =

ff

L c

D I I ⋅ =

⇓

Ga, Gb,Cc - current dependent sources

ff

L c

n

L b L a

D I G D I G I G ⋅ ≡ ⋅ ≡ ≡

Toward a continuous model

Prof. S. Ben-Yaakov , DC-DC Converters

[2- 29]

L

I Deriving

L

V t

L

I

L

I V

L

V

L

V

L

I

L

I

L V dt I d L V dt dI

L L L L

= ⇒ =

Average inductor current

Prof. S. Ben-Yaakov , DC-DC Converters

[2- 30]

b c a L ) b , a ( V ) c , a ( V

L

V

( )

b , a V

( )

c , a V

n

T

ff

T

s

T

ff
n

S

ff
n

L

D ) c , a ( V D ) b , a ( V T T ) c , a ( V T ) b , a ( V V ⋅ + ⋅ = = ⋅ + ⋅ =

Average inductor current

SLIDE 11

11

Prof. S. Ben-Yaakov , DC-DC Converters

[2- 31]

b c a

a

G

b

G

c

G

L

r

L

I

L

E

L

V Topology independent !

ff
n

L

D ) c , a ( V D ) b , a ( V E ⋅ + ⋅ =

ff

L c

D I G ⋅ =

n

L b

D I G ⋅ =

L a

I G = b c a L

n

T

ff

T

The Generalized Switched Inductor Model (GSIM)

Prof. S. Ben-Yaakov , DC-DC Converters

[2- 32]

1. The formal approach

b c a

a

G

b

G

c

G

R
C

in

V

V

L

E

L

I

L ) b , a ( V ) c , a ( V

L

r

ff
n

in L

D ] V [ D ] V V [ E ⋅ − + ⋅ − =

ff

c

n

b a

D ) L ( I G D ) L ( I G ) L ( I G ⋅ = ⋅ = =

Example Implementation in Buck Topology

S Vin D L Vo Ro Co b c a

Prof. S. Ben-Yaakov , DC-DC Converters

[2- 33]

2. The intuitive approach - by inspection

L

C
R

in

V

V

L

I

in

E

b

G S L

C
R

in

V D

V

Polarity: (voltage and current sources) selected by inspection

L

in

V V E → −

n

in in

D V E ⋅ =

n

L b

D I G ⋅ =

Implementation in Buck Topology

SLIDE 12

12

Prof. S. Ben-Yaakov , DC-DC Converters

[2- 34]

S L

C
R

in

V D

V

L

C
R

in

V

V
ff V

D ⋅

ff

L D

I ⋅

Emulate average voltage on inductor
sources

current dependent I Create

L

Boost

Prof. S. Ben-Yaakov , DC-DC Converters

[2- 35]

L

C
R

in

V D

V

L

C
R

in

V

V
ff
n

in

V D D V ⋅ + ⋅

ff

L D

I ⋅

n

L D

I ⋅

Buck-Boost

Prof. S. Ben-Yaakov , DC-DC Converters

[2- 36]

L

C
R

in

V

V

L

r

c

r

dson

R b c a SIM

Partially accounting for parasitics

SLIDE 13

13

Prof. S. Ben-Yaakov , DC-DC Converters

[2- 37]

in

V

dson

R b c

a

G

b

G

c

G

C
R

c

r a L

L

r

L

I

L

E

L

V

ff

c a

n

b a L

D ) V V ( D ) V V ( E ⋅ − + ⋅ − =

ff

L c

D I G ⋅ =

n

L b

D I G ⋅ =

L a

I G =

Modified Average Model

Prof. S. Ben-Yaakov , DC-DC Converters

[2- 38]

IL and Don are time dependent variables {IL(t), Don (t) } Don is not an electrical variable

n

D

L

I

b

G

L

I

Making the model SPICE compatible

Prof. S. Ben-Yaakov , DC-DC Converters

[2- 39]

⇓

Don is coded into voltage

+ − Source

n

D " D " : node

f

Name

n

) L ( I ) D ( V

n ∗

L Gvalue

In SPICE environment

SLIDE 14

14

Prof. S. Ben-Yaakov , DC-DC Converters

[2- 40]

Running SPICE simulation DC (steady state points) - as is TRAN (time domain) - as is AC ( small signal) - as is * Linearization is done by simulator !

Simulation

Prof. S. Ben-Yaakov , DC-DC Converters

[2- 41]

L

I b c a L

n

T

ff

T

n

T

ff

T

ff

T

s

T t

pk L

I

L

I

n

s

n

s

ff

D 1 T T T ' D − = − =

n

s

ff

T T ' T − =

Discontinuous Model (DCM)

Prof. S. Ben-Yaakov , DC-DC Converters

[2- 42]

1.The average inductor current in DCM

L

V

) b , a ( V ) c , a ( V

s

T

n

T

ff

T

ff

' T t b c a L ) b , a ( V ) c , a ( V

n

T

CCM in as D ) c , a ( V D ) b , a ( V V

ff
n

L

+ =

Combining CCM / DCM

SLIDE 15

15

Prof. S. Ben-Yaakov , DC-DC Converters

[2- 43]

b c a

a

L

ff
n

s L Ls

D D I T T T I I + = + =

L a

I is I ∗

Ls c b

I sampling are I is I ∗

ff

c

T during sampled is I ∗

n

b

T during sampled is I ∗

Combining CCM / DCM

Prof. S. Ben-Yaakov , DC-DC Converters

[2- 44]

b c a

a

G

b

G

c

G

a

I

b

I

c

I

L a

I G =

ff
n
n

L b

D D D I G + =

ff
n
ff

L c

D D D I G + = 1 ) D D ( : CCM in

ff
n

= + t

n

T

ff

T

LS

I

L

I

s

T

L

I

Combining CCM / DCM

Prof. S. Ben-Yaakov , DC-DC Converters

[2- 45]

n

T

ff

T

L

I

ff

' T L Vab

t

L Vac

pk

I

L

I

L T ) b , a ( V I

n

pk = S

ff
n
n

L

T ) T T ( L T ) b , a ( V 2 1 I +       = ) D D ( Lf 2 D ) b , a ( V I

ff
n

s

n

L

+ =

n
n

s L

ff

D D ) b , a ( V Lf I 2 D − =

n
ff

D 1 D − = ′

n
ff

D 1 D − ≤

Doff in DCM

SLIDE 16

16

Prof. S. Ben-Yaakov , DC-DC Converters

[2- 46]

b c a L b c a

a

G

b

G

c

G

L a

I G ≡

ff
n
n

L b

D D D I G + ≡

ff
n
ff

L c

D D D I G + ≡

ff
n

L

D ) c , a ( V D ) b , a ( V E ⋅ + ⋅ =               − − =

n
n

s L

n
ff

D D ) b , a ( V Lf I 2 ), D 1 ( min D L

L

r

L

I

L

E

L

V

The combined DCM / CCM mode

Prof. S. Ben-Yaakov , DC-DC Converters

[2- 47]

Example: Boost average model simulation

Rsw {Rsw} EDoff min(2*I(Lmain)*Lmain/(Ts*v(a,b)*V(Don))-V(Don),1-V(Don)) etable

OUT+ OUT- IN+ IN-

Resr {Resr} Gc V(Doff)*I(Lmain)/(V(Don)+V(Doff)) GVALUE

OUT+ OUT- IN+ IN-

PARAMETERS: LMAIN = 75u COUT = 220u RLOAD = 10 Doff Gb V(Don)*I(Lmain)/(V(Don)+V(Doff)) GVALUE

OUT+ OUT- IN+ IN-

Lmain {Lmain} RLoad {RLoad} Dbreak Dmain VDon {VDon}

+

Rinductor

{Rinductor} EL (V(Don)*V(a,b)+V(Doff)*V(a,c)) EVALUE

OUT+ OUT- IN+ IN-

1 PARAMETERS: FS = 100k TS = {1/fs} b Vin_DC {Vin_DC}

+

a

Cout {Cout} PARAMETERS: RESR = 0.07 RINDUCTOR = 0.1 RSW = 0.1 PARAMETERS: VIN_DC = 10v VDON = 0.5

ut

c Ga I(Lmain) GVALUE

OUT+ OUT- IN+ IN-

Don

S L

C
R

in

V D

V
Prof. S. Ben-Yaakov , DC-DC Converters

[2- 48]

Example: Boost average model simulation

SLIDE 17

17

Prof. S. Ben-Yaakov , DC-DC Converters

[2- 49]

Example: Boost average model simulation

S L

C
R

in

V D

V
Prof. S. Ben-Yaakov , DC-DC Converters

[2- 50]

Example: Boost average model simulation

S L

C
R

in

V D

V
Prof. S. Ben-Yaakov , DC-DC Converters

[2- 51]

Boost: Response to step of input voltage

Ti me 30ms 35ms 40ms 45ms 50ms V( out ) 18V 19V 20V 21V SEL>> V( a ) 9V 10V 11V 12V

(average model simulation) Vin Vout

SLIDE 18

18

Prof. S. Ben-Yaakov , DC-DC Converters

[2- 52]

Boost: Response to step of duty cycle

Don Vout

Ti me 30m s 35ms 40ms 45ms 50ms V( OUT)

25. 0V
37. 5V
50. 0V
10. 0V

SEL>> V( Don) 400mV 600mV 800mV

Prof. S. Ben-Yaakov , DC-DC Converters

[2- 53]

VDon 0V

0. 1V
0. 2 V
0. 3 V
0. 4V
0. 5V

0 . 6V 0 . 7V 0 . 8V

0. 9V
1. 0V

V( OUT) / V( a ) V( i de a l ) 5 10 15

Boost transfer function (CCM)

n

in

D

1 1 V V − = DC Sweep simulation ideal case real case

Parasitic resistances are taken into account