prof r t kennedy 1 eet 423 power electronics -2. prof r t kennedy2 buck converter circuit currents i...
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Prof R T KennedyProf R T Kennedy 11
EET 423 EET 423 POWER ELECTRONICS -2POWER ELECTRONICS -2
Prof R T KennedyProf R T Kennedy 22
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
Prof R T KennedyProf R T Kennedy 33
BUCK CONVERTER CIRCUIT BUCK CONVERTER CIRCUIT VOLTAGESVOLTAGES
Ei n
Vout
Vds a
b
VL,a-b
C
R
L
Vfwd
Prof R T KennedyProf R T Kennedy 44
SUB INTERVAL EQUIVALENT CIRCUITSSUB INTERVAL EQUIVALENT CIRCUITS
Vds = 0
a
b
VL,a-b= Ein-Vout
Ei n
C R
Vout
L MOSFET
ON
RECTIFIER
OFF
Vfwd = -Ein
rds,on
Prof R T KennedyProf R T Kennedy 55
SUB INTERVAL EQUIVALENT CIRCUITSSUB INTERVAL EQUIVALENT CIRCUITS
Ei n
C R
a
b
Vout
Vfwd= 0
Vds = Ein
MOSFET
OFF
RECTIFIER
ON
L
a
b
VL,a-b= -Vout VL,a-b= -Vout a
b
VL,a-b= -Vout
Prof R T KennedyProf R T Kennedy 66
Ein =Vds +(- Vfwd)
VL + Vout = -Vfwd
0
0
0
0
0
0
Ein
VL
Vout
Vfwd
Vds
0
Vgs
Prof R T KennedyProf R T Kennedy 77
Ein = Vds + (-Vfwd)0
0
0
0
0
0
Ein
VL
Vout
Vfwd
Vds
0
Vgs
-Vfwd
Prof R T KennedyProf R T Kennedy 88
SMPS OPERATIONSMPS OPERATION
QUANTIZED POWER/ENERGY TRANSFERQUANTIZED POWER/ENERGY TRANSFER
VOLTAGE REGULATIONVOLTAGE REGULATION
Prof R T KennedyProf R T Kennedy 99
VOLTAGE TRANSFER FUNCTION ANALYSISVOLTAGE TRANSFER FUNCTION ANALYSIS
• ENERGY BALANCEENERGY BALANCE
• POWER BALANCEPOWER BALANCE
• VOLT-TIME INTEGRALVOLT-TIME INTEGRAL
Prof R T KennedyProf R T Kennedy 1010
‘‘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
Prof R T KennedyProf R T Kennedy 1111
SUB INTERVAL -1: MOSFET ONSUB INTERVAL -1: MOSFET ON
Ei n
C
R
L
OFF
a
b
ON
ENERGY
STORED
LoutmLMLL IILIILJ )(2
1 2,
2,
INPUTENERG
Y
TDIEtPJ swoutinoninin
LOAD ENERGYfrom source
TDIVtPJ swoutoutonoutsload ,
Prof R T KennedyProf R T Kennedy 1212
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(,
Prof R T KennedyProf R T Kennedy 1313
Lloadsload JJenergyloadtotal ,,
))1(()( TDIVTDIV swoutoutswoutout
)(,, TIVJJ outoutLloadsload
swin
out
swoutinoutout
DE
V
TDIETIV
energyinputenergyloadtotal
Dsw Ein Vout
Prof R T KennedyProf R T Kennedy 1414
‘‘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
DE
V
IDEIV
IEIV
PP
,
Prof R T KennedyProf R T Kennedy 1515
FARADAY’S VOLT-TIME INTEGRALFARADAY’S VOLT-TIME INTEGRAL
0
1
1
0,
0,
0,
0,
TavL
TavL
TavL
TavL
IIT
LV
IT
LV
diLT
V
dtdt
diL
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
Prof R T KennedyProf R T Kennedy 1616
‘‘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
Prof R T KennedyProf R T Kennedy 1717
‘‘IDEAL’ IDEAL’ BUCK ANALYSIS CCMBUCK ANALYSIS CCMVOLT-TIME INTEGRAL APPROACHVOLT-TIME INTEGRAL APPROACH
INDUCTOR VOLTAGE
swin
out
swoutswoutin
swoutswoutin
DE
V
TDVTDVE
TDVTDVE
BareaAarea
)1()(
0)1()(
0
Prof R T KennedyProf R T Kennedy 1818
‘‘ideal’ideal’ BUCK CONVERTER CCM BUCK CONVERTER CCMvoltage & current waveformsvoltage & current waveforms
• refer to msw noteletrefer to msw notelet
Prof R T KennedyProf R T Kennedy 1919
ka
d s
a
k
d s
Vout
0
0
Dsw
TDfwdT
R
EDI inswout
sw
swinswML fL
RD
R
EDI
2
)1(1,
sw
swinswmL fL
RD
R
EDI
2
)1(1,
inE
outI
outin VE
inE
inswout EDV
Csw
swoutinL I
fL
DVEI
)(
L
DE
dt
I swinriseL )1(,
L
ED
dt
I 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
, 12
11
out
Lswoutrmsds I
IDII
inE
outV
outfwdavfwd IDI ,
12,
LrmsC
II
2
, 12
11
out
Lfwdoutrmsfwd I
IDII
sw
outinswrmsL
fL
VEDI
12
)(,
Ei n R
Iout
IC
L
C
Ids ILVds
Iout
Ifwd
VfwdVgs
fsw
VL
Prof R T KennedyProf R T Kennedy 2020
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
Prof R T KennedyProf R T Kennedy 2121
INDUCTOR CURRENT INDUCTOR CURRENT v v INDUCTANCEINDUCTANCE
REDUCTION in L
DswT Dfwd T
0
0
Iout
Ein-Vout
-Vout
VL
IL
t
Prof R T KennedyProf R T Kennedy 2222
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
dt
dI riseL,
dt
dI fallL,
Prof R T KennedyProf R T Kennedy 2323
INDUCTOR CURRENTINDUCTOR CURRENT
sw
swinswML
sw
swoutML
sw
swoutoutML
LoutML
fL
RD
R
EDI
fL
RD
R
VI
fL
DV
R
VI
III
2
)1(1
2
)1(1
2
)1(
2
,
,
,
,
L
outML
M
R
VI
2
11,
R
fL
TR
L sw
swL
in
out
E
VM
sw
swinswmL fL
RD
R
EDI
2
)1(1,
L
outmL
M
R
VI
2
11,
sw
swswin
sw
swoutL fL
DDE
fL
DVI
)1()1(
L
outL
M
R
VI
1
Prof R T KennedyProf R T Kennedy 2424
INDUCTOR CURRENTINDUCTOR CURRENT
0
LI
IL
t
LI
LI
Iout
Dsw = 0.2Dsw = 0.5
Dsw = 0.8
Dsw > 0.5
Dsw < 0.5
Dsw= 0.5
Prof R T KennedyProf R T Kennedy 2525
INDUCTOR CURRENTINDUCTOR CURRENT
0
LIIL
t
LI
LI
L
DE
dt
dI swinriseL )1(,
UPSLOPE
L
DE
dt
dI swinfallL ,
DOWNSLOPE
Prof R T KennedyProf R T Kennedy 2626
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
Prof R T KennedyProf R T Kennedy 2727
CCM-DCM BOUNDARYCCM-DCM BOUNDARY
sw
swcritical
sw
swoutout
Lout
f
RDLL
fL
DV
R
V
II
2
)1(
2
)1(
2
2
1 swsw D
R
fL
outL II
2
outL II
2LI
0t
TDsw
outI
Prof R T KennedyProf R T Kennedy 2828
CCM-DCM BOUNDARYCCM-DCM BOUNDARY
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
R
fL sw
swD
2
1 swsw D
R
fL
boundary
2
1: swsw D
R
fLCCM
2
1: swsw D
R
fLDCM
R
fL
tconstimeinductornormalisedT
sw
sw
L
tan
Prof R T KennedyProf R T Kennedy 2929
CCM-DCM BOUNDARYCCM-DCM BOUNDARY
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
R
fL sw
swD
boundary
CCM
CCM
DCM
Prof R T KennedyProf R T Kennedy 3030
CCM / DCM determined by
R
CCM-DCM BOUNDARYCCM-DCM BOUNDARY
L 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
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
R
fL sw
swD
CCM
DCM
INCREASE R
‘light loading’
Prof R T KennedyProf R T Kennedy 3131
CCM / DCM determined by
L
CCM-DCM BOUNDARYCCM-DCM BOUNDARY
R Dsw fsw
constant
to ensure a desired CCM
does not transfer to DCM
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
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
R
fL sw
swD
CCM
DCM
DECREASE L
Prof R T KennedyProf R T Kennedy 3232
CCM / DCM determined by
fsw
CCM-DCM BOUNDARYCCM-DCM BOUNDARY
R Dsw fsw
constant
to ensure a desired CCM
does not transfer to DCM
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
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
R
fL sw
swD
CCM
DCM
DECREASE fsw
Prof R T KennedyProf R T Kennedy 3333
CCM / DCM determined by
Dsw
CCM-DCM BOUNDARYCCM-DCM BOUNDARY
L R fsw
constant
to ensure a desired CCM
does not transfer to DCM
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
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
R
fL sw
swD
CCM
DCM
DECREASE Dsw
Prof R T KennedyProf R T Kennedy 3434
LINE & LOAD LINE & LOAD REGULATIONREGULATION
R
fL 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
out
E
VM
swD
DCM
CCMM
DCMM
swD
CCM
DCMM
Prof R T KennedyProf R T Kennedy 3535
LINE & LOAD LINE & LOAD REGULATIONREGULATION
R
fL 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
out
E
VM
swD
DCM
CCM
ccmswD ,dcmswD ,
M
Prof R T KennedyProf R T Kennedy 3636
IL
IL
IL
t0
0
0
t
t
Prof R T KennedyProf R T Kennedy 3737
IL
IL
IL
t0
0
0
t
t
Prof R T KennedyProf R T Kennedy 3838
IL
IL
IL
t0
0
0
t
t
Prof R T KennedyProf R T Kennedy 3939
OUTPUT EFFECTSOUTPUT EFFECTS
Ei n
C
L
Vout= 0
s/c
Iin
t0
L
E
dt
dI inin
Prof R T KennedyProf R T Kennedy 4040
OUTPUT EFFECTSOUTPUT EFFECTS
Ei n
C
L
VoutEin
o/c
Prof R T KennedyProf R T Kennedy 4141
POWER - UP EFFECTPOWER - UP EFFECT
Ei n
C
R
Vout
Vc= 0
L
Prof R T KennedyProf R T Kennedy 4242
POWER - DOWN EFFECTPOWER - DOWN EFFECT
Ei n
C
R
Vout
L