prof. s. ben-yaakov , dc-dc converters [2- 1] buck, boost ...dcdc/slides/dc-dc part 2_double.pdf ·...
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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
Prof. S. Ben-Yaakov , DC-DC Converters [2- 2]
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
2
Prof. S. Ben-Yaakov , DC-DC Converters [2- 3]
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
Prof. S. Ben-Yaakov , DC-DC Converters [2- 4]
In this case
Inductor current waveform at steady state
LVV oin −
ton
t
IL
toff
LVo−
I∆
S
VinD
C R
ton
toff
Buck
3
Prof. S. Ben-Yaakov , DC-DC Converters [2- 5]
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∆
Prof. S. Ben-Yaakov , DC-DC Converters [2- 6]
-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
4
Prof. S. Ben-Yaakov , DC-DC Converters [2- 7]
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
Prof. S. Ben-Yaakov , DC-DC Converters [2- 8]
tont
IL
toffTs
R2
R1
R3
LVV oin −
LVo−
CCM - Continues Conductor Current Mode
DCM - Discontinues Conductor Current Mode
321 RRR <<
Load Change
5
Prof. S. Ben-Yaakov , DC-DC Converters [2- 9]
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
Prof. S. Ben-Yaakov , DC-DC Converters [2- 10]
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
6
Prof. S. Ben-Yaakov , DC-DC Converters [2- 11]
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 ==
Prof. S. Ben-Yaakov , DC-DC Converters [2- 12]
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=⋅⋅
⋅==
=−= →==
7
Prof. S. Ben-Yaakov , DC-DC Converters [2- 13]
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
Prof. S. Ben-Yaakov , DC-DC Converters [2- 14]
BOOST Step-Up
Vo > Vin Why ??
SVin
DL
C R
VX Vo
8
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 modesVL
IL
ts
t
Vin
Ia t
VL
IL
ts
t
Vin
Vin-Vo
Ia Ib t
Boost
Prof. S. Ben-Yaakov , DC-DC Converters [2- 16]
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
9
Prof. S. Ben-Yaakov , DC-DC Converters [2- 17]
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
Prof. S. Ben-Yaakov , DC-DC Converters [2- 18]
BUCK-BOOSTStep-Up Step-Down
Find Vo/Vin
Hint: Average of Vx ?
S
Vin
D
LC R
Vo
VX
10
Prof. S. Ben-Yaakov , DC-DC Converters [2- 19]
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
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 componentDiscontinues current -> High ripple component
Input and Output Currents
11
Prof. S. Ben-Yaakov , DC-DC Converters [2- 21]
Modulator ControleVD
inV
AssemblySwitched
oV
+−
The simulation problem
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 equivalentcircuit which is SPICE compatible
Modulator ControleVD
inV
AssemblySwitched
oV
+−
The simulation problem
12
Prof. S. Ben-Yaakov , DC-DC Converters [2- 23]
+−
+−
−
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
Prof. S. Ben-Yaakov , DC-DC Converters [2- 24]
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
13
Prof. S. Ben-Yaakov , DC-DC Converters [2- 25]
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)
Prof. S. Ben-Yaakov , DC-DC Converters [2- 26]
⇓b
ca ?aI
cI
bI
b
ca L onT
offTaI
bI
cI
The SIM
Objective : To replace the switched part by a continuous network
14
Prof. S. Ben-Yaakov , DC-DC Converters [2- 27]
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
Prof. S. Ben-Yaakov , DC-DC Converters [2- 28]
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
15
Prof. S. Ben-Yaakov , DC-DC Converters [2- 29]
LIDeriving
LVt
LILI
V
LV
LV
LI
LI
LV
dtId
LV
dtdI LLLL =⇒=
Average inductor current
Prof. S. Ben-Yaakov , DC-DC Converters [2- 30]
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
16
Prof. S. Ben-Yaakov , DC-DC Converters [2- 31]
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)
Prof. S. Ben-Yaakov , DC-DC Converters [2- 32]
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
17
Prof. S. Ben-Yaakov , DC-DC Converters [2- 33]
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
Prof. S. Ben-Yaakov , DC-DC Converters [2- 34]
S
L
oC oRinV
DoV
L
oCoR
inV
oV
ooff VD ⋅
offL DI ⋅
• Emulate average voltage on inductor• sourcescurrentdependentICreate L
Boost
18
Prof. S. Ben-Yaakov , DC-DC Converters [2- 35]
L oC oRinV
D oV
L oCoRinV
oV
ooffonin VDDV ⋅+⋅
offL DI ⋅onL DI ⋅
Buck-Boost
Prof. S. Ben-Yaakov , DC-DC Converters [2- 36]
L
oCoRinV
oVLr
cr
dsonR
b ca
SIM
Partially accounting for parasitics
19
Prof. S. Ben-Yaakov , DC-DC Converters [2- 37]
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
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
onDLIbG L LI
Making the model SPICE compatible
20
Prof. S. Ben-Yaakov , DC-DC Converters [2- 39]
⇓
Don is coded into voltage
+− SourceonD
"D":nodeofName on
)L(I)D(V on ∗ L
Gvalue
In SPICE environment
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
21
Prof. S. Ben-Yaakov , DC-DC Converters [2- 41]
LI
b
ca L onT
offT
onT offT
offTsT
t
pkLILI
ons
onsoff D1
TTT'D −=
−=
onsoff TT'T −=
Discontinuous Model (DCM)
Prof. S. Ben-Yaakov , DC-DC Converters [2- 42]
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
22
Prof. S. Ben-Yaakov , DC-DC Converters [2- 43]
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
Prof. S. Ben-Yaakov , DC-DC Converters [2- 44]
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
23
Prof. S. Ben-Yaakov , DC-DC Converters [2- 45]
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
Prof. S. Ben-Yaakov , DC-DC Converters [2- 46]
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
24
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))
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
Prof. S. Ben-Yaakov , DC-DC Converters [2- 48]
Example: Boost average model simulation
25
Prof. S. Ben-Yaakov , DC-DC Converters [2- 49]
Example: Boost average model simulation
S
L
oC oRinV
DoV
Prof. S. Ben-Yaakov , DC-DC Converters [2- 50]
Example: Boost average model simulation
S
L
oC oRinV
DoV
26
Prof. S. Ben-Yaakov , DC-DC Converters [2- 51]
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
Prof. S. Ben-Yaakov , DC-DC Converters [2- 52]
Boost: Response to step of duty cycle
Don
Vout
Ti me
3 0 ms 3 5 ms 4 0 ms 45 ms 5 0 msV( OUT)
25 . 0 V
37 . 5 V
50 . 0 V
10 . 0 VSEL>>
V( Do n)40 0 mV
60 0 mV
80 0 mV
27
Prof. S. Ben-Yaakov , DC-DC Converters [2- 53]
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