prof r t kennedypower electronics 21 eet 423 power electronics -2

Prof R T KennedyProf R T Kennedy POWER ELECTRONICS 2POWER ELECTRONICS 2 11

EET 423 EET 423 POWER ELECTRONICS -2POWER ELECTRONICS -2


BUCK CONVERTER CIRCUIT BUCK CONVERTER CIRCUIT CURRENTSCURRENTS

Ifwd

Ids

Ei n

Ii n IL

Ids IC Ifwd

C R

L IL

Iout

a

b

Vout


BUCK CONVERTER CIRCUIT BUCK CONVERTER CIRCUIT VOLTAGESVOLTAGES

Ei n

Vout

Vds a

b

VL,a-b

C

R

L

Vfwd


SUB INTERVAL EQUIVALENT CIRCUITSSUB INTERVAL EQUIVALENT CIRCUITS

Vds = 0

a

b

VL,a-b= Ein-Vout

Ei n

C R

Vout

L MOSFET

ON

RECTIFIEROFF

Vfwd = -Ein

rds,on


SUB INTERVAL EQUIVALENT CIRCUITSSUB INTERVAL EQUIVALENT CIRCUITS

Ei n

C R

a

b

Vout Vfwd= 0

Vds = Ein

MOSFET OFF

RECTIFIERON

L

a

b

VL,a-b= -Vout VL,a-b= -Vout a

b

VL,a-b= -Vout


Ein =Vds +(- Vfwd)

VL + Vout = -Vfwd

0

0

0

0

0

0

Ein

VL

Vout

Vfwd

Vds

0

Vgs


Ein = Vds + (-Vfwd)0

0

0

0

0

0

Ein

VL

Vout

Vfwd

Vds

0

Vgs

-Vfwd


SMPS OPERATIONSMPS OPERATION

QUANTIZED POWER/ENERGY TRANSFERQUANTIZED POWER/ENERGY TRANSFER

VOLTAGE REGULATIONVOLTAGE REGULATION


VOLTAGE TRANSFER FUNCTION ANALYSISVOLTAGE TRANSFER FUNCTION ANALYSIS

• ENERGY BALANCEENERGY BALANCE

• POWER BALANCEPOWER BALANCE

• VOLT-TIME INTEGRALVOLT-TIME INTEGRAL


‘‘IDEAL’ IDEAL’ BUCK ANALYSIS CCMBUCK ANALYSIS CCM ENERGY BALANCE APPROACH ENERGY BALANCE APPROACH

INDUCTOR CURRENT

IL,M

IL,m

IL,av = Iout

0

LoutmLML

outLmLML

outmLML

loutmL

LoutML

IIII

IIII

III

III

III

2

2

2

2

2,

2,

,,

,,

,

,

2LI

2LI

outL II

t


SUB INTERVAL -1: MOSFET ONSUB INTERVAL -1: MOSFET ON

Ei n

C R

L

OFF

a

b

ON ENERG

YSTORE

D

LoutmLMLL IILIILJ )(21 2

,2

,

INPUTENERG

Y

TDIEtPJ swoutinoninin

LOAD ENERGYfrom source

TDIVtPJ swoutoutonoutsload ,


SUB INTERVAL -2: RECTIFIER ONSUB INTERVAL -2: RECTIFIER ON

Ei n

C R

L

ON

a

b

OFF

ENERGYDischarge

NO INPUTENERGY

LOAD ENERGYfrom inductor

LoutLload IILJ ,

TDIVTDIVJ swoutoutfwdoutoutLload )1(,


Lloadsload JJenergyloadtotal ,,

))1(()( TDIVTDIV swoutoutswoutout

)(,, TIVJJ outoutLloadsload

swin

out

swoutinoutout

DEV

TDIETIV

energyinputenergyloadtotal

Dsw Ein Vout


‘‘IDEAL’ IDEAL’ BUCK ANALYSIS CCMBUCK ANALYSIS CCMPOWER BALANCE APPROACHPOWER BALANCE APPROACH

INPUT CURRENT = MOSFET CURRENT

Iin,av = Ids,av IL,m

IL,M Iout

0

Dsw T

Dfwd T

Iin

t

swin

out

outswinoutout

avininoutout

inout

DEV

IDEIV

IEIV

PP

,


FARADAY’S VOLT-TIME INTEGRALFARADAY’S VOLT-TIME INTEGRAL

0

1

1

0,

0,

0,

0,

TavL

TavL

TavL

TavL

IITLV

ITLV

diLT

V

dtdtdiL

TV

INDUCTOR VOLTAGE

V1

t1

0

INDUCTOR CURRENT

t2

V2

0

t

t

I m

I M

T

current start and finish at same value

2211

00)(

tVtV

dttvT

EQUAL AREAS


‘‘IDEAL’ IDEAL’ BUCK ANALYSIS CCMBUCK ANALYSIS CCMVOLT-TIME INTEGRAL APPROACHVOLT-TIME INTEGRAL APPROACH

INDUCTOR VOLTAGE

Dsw T

Dfwd T

0

IL

VL

0

Ein -Vout

-Vout t

area B

area A


‘‘IDEAL’ IDEAL’ BUCK ANALYSIS CCMBUCK ANALYSIS CCMVOLT-TIME INTEGRAL APPROACHVOLT-TIME INTEGRAL APPROACH

INDUCTOR VOLTAGE

swin

out

swoutswoutin

swoutswoutin

DEV

TDVTDVE

TDVTDVE

BareaAarea

)1()(

0)1()(

0


‘‘ideal’ideal’ BUCK CONVERTER CCM BUCK CONVERTER CCMvoltage & current waveformsvoltage & current waveforms

• refer to msw noteletrefer to msw notelet


ka

d s

a

k

d s

Vout

0

0

DswT

DfwdT

REDI insw

out

sw

swinswML fL

RDREDI

2)1(1,

sw

swinswmL fL

RDREDI

2)1(1,

inE

outI

outin VE

inE

inswout EDV

Csw

swoutinL I

fLDVEI

)(

LDE

dtI swinriseL )1(,

LED

dtI inswfallL

,

Dfwd = 1-Dsw

0

0

0

0

0

0

0

0

0

Vgs

Iout

Ic

IL

Ids

Ifwd

Ein

Vds

Vfwd

VL

Vout

outI

outI

outswavds IDI ,

2

, 1211

out

Lswoutrmsds I

IDII

inE

outV

outfwdavfwd IDI ,

12,L

rmsCII

2

, 1211

out

Lfwdoutrmsfwd I

IDII

sw

outinswrmsL fL

VEDI12

)(,

Ei n R

Iout

IC

L

C

Ids ILVds

Iout

Ifwd

VfwdVgsfsw

VL


INDUCTOR CURRENT WAVEFORMSINDUCTOR CURRENT WAVEFORMS

• CCM or DCM operational modeCCM or DCM operational mode• component current stresscomponent current stress• capacitor ripple currentcapacitor ripple current• output voltage rippleoutput voltage ripple• converter efficiencyconverter efficiency• closed loop regulation performanceclosed loop regulation performance


INDUCTOR CURRENT INDUCTOR CURRENT v v INDUCTANCEINDUCTANCE

REDUCTION in L

DswT Dfwd T

0

0

Iout

Ein-Vout

-Vout

VL

IL

t


INDUCTOR CURRENT INDUCTOR CURRENT v v INDUCTANCEINDUCTANCE

REDUCTION in L

DswT Dfwd T

0

0

Iout

Ein-Vout

-Vout

VL

IL

t

increased

Isw,max

Ifwd,max

IC,ripple

Vout,ripple

dtdI riseL,

dt

dI fallL,


INDUCTOR CURRENTINDUCTOR CURRENT

sw

swinswML

sw

swoutML

sw

swoutoutML

LoutML

fLRD

REDI

fLRD

RVI

fLDV

RVI

III

2)1(1

2)1(1

2)1(

2

,

,

,

,

L

outML

MRVI

211,

RfL

TRL sw

swL

in

outEVM

sw

swinswmL fL

RDRED

I2

)1(1,

L

outmL

MRVI

211,

sw

swswin

sw

swoutL fL

DDEfLDVI

)1()1(

L

outL

MRV

I

1



0

LI

IL

t

LI

LI

Iout

Dsw = 0.2Dsw = 0.5Dsw = 0.8

Dsw > 0.5

Dsw < 0.5

Dsw= 0.5



0

LIIL

t

LI

LI

LDE

dtdI swinriseL )1(,

UPSLOPELDE

dtdI swinfallL ,

DOWNSLOPE


INDUCTOR INDUCTOR PEAK-PEAK RIPPLE CURRENTPEAK-PEAK RIPPLE CURRENT

)1( swswn

L DDfI

5.00 1

swD

LI

sw

swswinL fL

DDEI

)1(

max,LI


IL

IL

IL

t0

0

0

t

t


LI

swI

fwdI

outI

MswI ,

rmsswI ,

avswI ,

MfwdI ,rmsfwdI ,

avfwdI ,

swD fwdD

‘‘IDEAL’ BUCK CCM DEVICE CURRENTIDEAL’ BUCK CCM DEVICE CURRENT


‘‘IDEAL’ BUCK CCM DEVICE CURRENTIDEAL’ BUCK CCM DEVICE CURRENT

LI

swI

fwdI

outI

MswI ,

rmsswI ,

avswI ,

MfwdI ,rmsfwdI ,

avfwdI ,

swD fwdD


‘‘IDEAL’ BUCK CCM TRANSISTOR CURRENTIDEAL’ BUCK CCM TRANSISTOR CURRENT

CCM TRANSISTOR CURRENT IM

sw

swoutfLRD

RV

21

1

L

out MR

V2

11

Iav swout DRV M

RVout

Irms sw

out

sw

swswsw

out DR

VfLRDD

DR

V

22

12)1( M

RVMM

RV out

L

out

2

21

1211

IL

swsw

outfLRD

RV 1

L

out MRV

1

in

outEVM

RfL sw

L


‘‘IDEAL’ BUCK CCM RECTIFIER CURRENTIDEAL’ BUCK CCM RECTIFIER CURRENT CCM RECTIFIER CURRENT

IM

sw

fwdoutfLRD

RV

21

L

out MR

V2

11

Iav fwdout DRV M

RVout 1

Irms fwd

out

sw

fwdfwd

out DR

VfLRD

DR

V

23

12

)( MR

VMMR

V out

L

out

2

21

1211

IL

swfwd

outfLR

DRV

L

out MRV

1

avrmsffi

fwdsw

fwd

fwd DfLRD

D1

121

2

M

M1

in

outEV

M RfL sw

L


OUTPUT EFFECTSOUTPUT EFFECTS

Ei n

C

L

Vout= 0

s/c

Iin

t0

LE

dtdI inin


OUTPUT EFFECTSOUTPUT EFFECTS

Ei n

C

L

VoutEin

o/c


POWER - UP EFFECTPOWER - UP EFFECT

Ei n

C

R

Vout

Vc= 0

L


POWER - DOWN EFFECTPOWER - DOWN EFFECT

Ei n

C

R

Vout

L


CCM-DCM BOUNDARYCCM-DCM BOUNDARY

sw

swcritical

sw

swoutout

Lout

fRDLL

fLDV

RV

II

2)1(

2)1(

2

21 swsw D

RfL

outL II

2out

L II

2

LI

0t

TDsw

outI



0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.050.1

0.150.2

0.250.3

0.350.4

0.450.5

RfL sw

swD

21 swsw D

RfL

boundary

21: swsw D

RfLCCM

21: swsw D

RfLDCM

RfL

tconstimeinductornormalisedT

sw

sw

L

tan



0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.050.1

0.150.2

0.250.3

0.350.4

0.450.5

RfL sw

swD

boundary

CCM

CCM

DCM


CCM / DCM determined by

R

CCM-DCM BOUNDARYCCM-DCM BOUNDARYL Dsw fsw

constant

to ensure a desired CCM does not transfer to DCM

specify a minimum load current (maximum R)

avoid open circuit operation

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.050.1

0.150.2

0.250.3

0.350.4

0.450.5

RfL sw

swD

CCM

DCM

INCREASE R‘light loading’



L

CCM-DCM BOUNDARYCCM-DCM BOUNDARYR Dsw fsw

constant


design for CMM at lowest inductance

including L v I

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.050.1

0.150.2

0.250.3

0.350.4

0.450.5

RfL sw

swD

CCM

DCM

DECREASE L



fsw

CCM-DCM BOUNDARYCCM-DCM BOUNDARYR Dsw fsw

constant


design for CMM at lowest frequency

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.050.1

0.150.2

0.250.3

0.350.4

0.450.5

RfL sw

swD

CCM

DCM

DECREASE fsw



Dsw

CCM-DCM BOUNDARYCCM-DCM BOUNDARYL R fsw

constant


design for CMM at lowest duty cycle

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.050.1

0.150.2

0.250.3

0.350.4

0.450.5

RfL sw

swD

CCM

DCM

DECREASE Dsw


LINE & LOAD LINE & LOAD REGULATIONREGULATION

RfL sw

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

in

outEVM

swD

DCM

CCMM

DCMM

swD

CCM

DCMM


LINE & LOAD LINE & LOAD REGULATIONREGULATION

RfL sw

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

in

outEVM

swD

DCM

CCM

ccmswD ,dcmswD ,

M

prof r t kennedypower electronics 21 eet 423 power electronics -2

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