prof. s. ben-yaakov , dc-dc converters [2- 1] buck ... - bgudcdc/slides/dc-dc part 2 _triple.pdf ·...

1

Prof. S. Ben-Yaakov , DC-DC Converters [2- 1]

2.1 Buck converter2.1.1 Operation modes2.1.2 Voltage transfer function2.1.3 Current modes (CCM, DCM)2.1.4 Capacitor current

2.2 Boost converter2.2.1 Operation modes2.2.2 Voltage transfer function

2.3 Buck-Boost converter2.4 Comparison between topologies 2.5 Simulation of SMPS

2.5.1 The simulations problem2.5.2 Basics of average model of SMPS2.5.3 Example: Boost average model simulations

BUCK, BOOST, BUCK-BOOST, DCM


Buck Converter Constant Switching Frequency

tON ON ON

tON ON ON

control

switch

ton toff

TS

ss T

1f =

DorDTt

ons

on →=

D1DTt

offs

off −→=

Switch frequency:

Duty Cycle:

S

Vin D

L

C Rcontrol


Operation modesOn

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

2


In this case

Inductor current waveform at steady state

LVV oin −

ton

t

IL

toff

LVo−

I∆

S

VinD

C R

ton

toff

Buck


Voltage transfer functionThe ∆I method

Left triangle

onoin t

LVVI ⋅

−=∆

Right triangle

offo t

LVI ⋅=∆

offo

onoin t

LVt

LVV =

−

ons

on

offon

on

in

o DTt

ttt

VV

==+

= Independent of L !

LVV oin −

ton

t

IL

toff

LVo−

I∆


-Vo

VL

toff t

Vin-Vo

ton

Ts

+-

At steady state, over one switching cycle: ;0VL =

onin

o DVV0SS =⇒=+ −+

;t)VV(S onoin ⋅−=+

;t)V(S offo ⋅−=−

S

VinD C

R

ton

toff

Vo

VL

Voltage transfer functionThe average voltage method

3


Load Change with Fixed D

ton

t

IL

toffTs

How will IL change if R is getting smaller?

S

Vin D

L

C Rcontrol

Vo


tont

IL

toffTs

R2

R1

R3

LVV oin −

LVo−

CCM - Continues Conductor Current Mode

DCM - Discontinues Conductor Current Mode

321 RRR <<

Load Change


Discontinuous Inductor Current Mode (DCM)

SVin

D

L

C R

Vx Vo

control

Different voltage transfer ratio ≠ Don

Higher ripple current

t

IL

Ts

R4

R3

t'off

toffton

R4>R3

4


tont

IL

t'offTs

Ipk

Voltage transfer function (DCM)The ∆I method

offo

onoin

pk tLVt

LVVI ′=

−=

out

onoutinoff V

D)VV(D −=

+⋅

−= )DD(TT

LVV

21

T1I offonSon

oin

SAV

RVI o

AV =

)V

VV1(DTL

VV21I

o

oinonon

oinAV

−+⋅

−=

2oinS

2onoin LV2VTD)VV(R =−

−+= 1

TDRL81

L4TDR

VV

s2on

s2on

in

o


Boundary of CCM and DCM

t onttoff

Ts

LVo−

LVV oin −

IL

L2

Lmin

Iav

For CCM L > Lmin

In Buck avpkoffmin

o I2ItLV

==s

off

sav

offomin f2

DRfI2

DVL ==


ExampleA BUCK converter has a following characteristics:

Output voltage: Output current:

Input voltage: Frequency:

Current mode: CCM

Find:

V5Vo = A10II avout ==

V10Vin = kHz100fs =

minL

H2.1101025.05

fI2DVL

5.0D1DCCM5.0DVV

5sav

offomin

onoffonin

o

µ=⋅⋅

⋅==

=−= →==

5


IL

t

Iav

t

IavIR

IC

tAC

DC

Capacitor current

Capacitor currentS

Vin D

L

C RIL IC IRcontrol

Vo

RLC III −=

Assumption: V0 has small ripple


BOOST Step-Up

Vo > Vin Why ??

SVin

DL

C R

VX Vo


ON VL=Vin

OFF VL=Vin-Vo

Vin

L

C R

Vo

Vin

L

C R

Vo

Operation modesVL

IL

ts

t

Vin

Ia t

VL

IL

ts

t

Vin

Vin-Vo

Ia Ib t

Boost

6


toffTS

VoVx

t

offin

ooffoin D

1VVDVV =→=

SVin

DL

C R

VX Vo

The average voltage method

;DVTtVV

;VV;VV;0VV;0V

offos

offox

inin

xinxinL

==

=

==−=

Voltage transfer function


Voltage transfer functionThe ∆I method

ton

IL

toffTs

t

LVV ino −

−LVin

I∆

offino

onin t

LVVt

LV ⋅

−=⋅

offooffonin tV)tt(V ⋅=+⋅

offin

o

D1

VV

=

SVin

DL

C R

VX Vo


BUCK-BOOSTStep-Up Step-Down

Find Vo/Vin

Hint: Average of Vx ?

S

Vin

D

LC R

Vo

VX

7


Comparison between basic topologies CCM

SVin

DL

CR

Vo

SVin

DL

C R

Vo

SVin D

LC

R

Vo

S

DLBasic Cell

La

b

c

Switched inductor


Iin

t

Iin

t

Iin

t

Io

t

Io

t

Io

t

Source current Load current

Buck

Boost

Buck Boost

Continues current -> Low ripple componentDiscontinues current -> High ripple component

Input and Output Currents


Modulator ControleVD

inV

AssemblySwitched

oV

+−

The simulation problem

8


•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 equivalentcircuit which is SPICE compatible

Modulator ControleVD

inV

AssemblySwitched

oV

+−

The simulation problem


+−

+−

−

b d c

afC LoadR

outV

inVLI

bI CI

outV outV

LoadR LoadRfCfC

L

a d c

b

CILIbI

inVinV

b onT L

bI LI

CI

d

c

L

Buck Boost

BoostBuck −

onT

+−

Average Simulation of PWM Converters


Ton - switch conduction time Toff - diode conduction timeTDCM - no current time (in DCM)

L ab

c

b onT

DCMToffT

L

c

a

The Switched Inductor Model

9


The concept of average signals

t

t

t

aI

bI

cI

bI

aI

cI

b

ca L onT

offTaI

bI

cI

The Switched Inductor Model (SIM) (CCM)


⇓b

ca ?aI

cI

bI

b

ca L onT

offTaI

bI

cI

The SIM

Objective : To replace the switched part by a continuous network


IbI

LI

bI

ONTST

onLS

onLb DI

TTI

I ==

S

ONon T

TD =

offLS

offLc DI

TTI

I ==

La II =

Similarly :

b

ca L onT

offTaI

bI

cI

Average current

10


b

c

bI

cI

a aGbG

cG

aI

b

caLa II =

onLb DII ⋅=

offLc DII ⋅=

⇓Ga, Gb,Cc - currentdependent sources

offLc

onLb

La

DIG

DIG

IG

⋅≡

⋅≡

≡

Toward a continuous model


LIDeriving

LVt

LILI

V

LV

LV

LI

LI

LV

dtId

LV

dtdI LLLL =⇒=

Average inductor current


b

ca L

)b,a(V

)c,a(V

LV ( )b,aV

( )c,aV

onT offT

sT

offon

S

offonL

D)c,a(VD)b,a(V

TT)c,a(VT)b,a(VV

⋅+⋅=

=⋅+⋅

=

Average inductor current

11


b

c

aaG bG

cG

L

Lr

LI

LE LV

Topology independent !

offonL D)c,a(VD)b,a(VE ⋅+⋅=offLc DIG ⋅=onLb DIG ⋅=

La IG =

b

ca L onT

offT

The Generalized Switched Inductor Model(GSIM)


1. The formal approach

b

c

a

aGbG

cG

oRoC

inV

oV

LE LIL

)b,a(V

)c,a(VLr

off0onin0L D]V0[D]VV[E ⋅−+⋅−=

offconba D)L(IGD)L(IG)L(IG ⋅=⋅==

Example Implementation in Buck TopologyS

Vin D

L Vo

RoCo

b

c

a


2. The intuitive approach - by inspection

L

oCoRinV

oV

LIinE

bG

S L

oC oRinV D

oV

Polarity: (voltage and current sources) selected by inspection

Loin VVE →−

oninin DVE ⋅=

onLb DIG ⋅=

Implementation in Buck Topology

12


S

L

oC oRinV

DoV

L

oCoR

inV

oV

ooff VD ⋅

offL DI ⋅

• Emulate average voltage on inductor• sourcescurrentdependentICreate L

Boost


L oC oRinV

D oV

L oCoRinV

oV

ooffonin VDDV ⋅+⋅

offL DI ⋅onL DI ⋅

Buck-Boost


L

oCoRinV

oVLr

cr

dsonR

b ca

SIM

Partially accounting for parasitics

13


inV

dsonR b

c

aGbG

cG

oC

oRcr

a

L

Lr

LI

LE LV

offcaonbaL D)VV(D)VV(E ⋅−+⋅−=offLc DIG ⋅=onLb DIG ⋅=

La IG =

Modified Average Model


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

onDLIbG L LI

Making the model SPICE compatible


⇓

Don is coded into voltage

+− SourceonD

"D":nodeofName on

)L(I)D(V on ∗ L

Gvalue

In SPICE environment

14


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


LI

b

ca L onT

offT

onT offT

offTsT

t

pkLILI

ons

onsoff D1

TTT'D −=

−=

onsoff TT'T −=

Discontinuous Model (DCM)


1.The average inductor current in DCM

LV )b,a(V

)c,a(V

sT

onT offT

off'T

t b

ca L

)b,a(V

)c,a(V

onT

CCMinasD)c,a(VD)b,a(VV offonL +=

Combining CCM / DCM

15


b

c

aaG bG

cG

aI

bI

cI tonT offT

LSILI

sT

LI

offon

L

offon

sLLs DD

ITT

TII+

=+

=

La IisI∗

Lscb IsamplingareIisI∗offc TduringsampledisI∗onb TduringsampledisI∗

Combining CCM / DCM


b

c

aaG bG

cG

aI

bI

cI

La IG =

offon

onLb DD

DIG+

=

offon

offLc DD

DIG+

=

1)DD(:CCMin offon =+

tonT offT

LSILI

sT

LI

Combining CCM / DCM


onT offT

LI

off'T

LVab

t

LVac

pkILI

LT)b,a(VI on

pk =

S

offononL T

)TT(L

T)b,a(V21I +

=

)DD(Lf2

D)b,a(VI offons

onL +=

onon

sLoff D

D)b,a(VLfI2D −=

onoff D1D −=′

onoff D1D −≤

Doff in DCM

16


b

ca

L

b

c

aaG bG

cG

La IG ≡

offon

onLb DD

DIG+

≡offon

offLc DD

DIG+

≡

offonL D)c,a(VD)b,a(VE ⋅+⋅=

−−= on

on

sLonoff D

D)b,a(VLfI2),D1(minD

L

Lr

LI

LE LV

The combined DCM / CCM mode


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))

GVALUEOUT+OUT-

IN+IN-

PARAMETERS:LMAIN = 75uCOUT = 220uRLOAD = 10

Doff

Gb

V(Don)*I(Lmain)/(V(Don)+V(Doff))

GVALUEOUT+OUT-

IN+IN-

0

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

0

PARAMETERS:FS = 100kTS = {1/fs}

b

Vin_DC

{Vin_DC}

+

-

aCout{Cout}

PARAMETERS:RESR = 0.07RINDUCTOR = 0.1RSW = 0.1

PARAMETERS:VIN_DC = 10vVDON = 0.5

outc

Ga

I(Lmain)GVALUE

OUT+OUT-

IN+IN-

Don

S

L

oC oRinV

DoV



17



S

L

oC oRinV

DoV



S

L

oC oRinV

DoV


Boost: Response to step of input voltage

Ti me

3 0 ms 3 5 ms 4 0 ms 4 5 ms 5 0 msV( o u t )

1 8 V

1 9 V

2 0 V

2 1 V

SEL>>

V( a )9 V

1 0 V

1 1 V

1 2 V

(average model simulation)

Vin

Vout

18


Boost: Response to step of duty cycle

Don

Vout

Ti me

3 0 ms 3 5 ms 4 0 ms 4 5 ms 5 0 msV( OUT)

2 5 . 0 V

3 7 . 5 V

5 0 . 0 V

1 0 . 0 VSEL>>

V( Do n )4 0 0 mV

6 0 0 mV

8 0 0 mV


VDo n

0 V 0 . 1 V 0 . 2 V 0 . 3 V 0 . 4 V 0 . 5 V 0 . 6 V 0 . 7 V 0 . 8 V 0 . 9 V 1 . 0 VV( OUT) / V( a ) V( i d e a l )

0

5

1 0

1 5

Boost transfer function (CCM)

onin

o

D11

VV

−=

DC Sweep simulation

ideal case

real caseParasitic resistances are taken into account

prof. s. ben-yaakov , dc-dc converters [2- 1] buck ... - bgudcdc/slides/dc-dc part 2 _triple.pdf ·...

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