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 t on t off T S s s T 1 f = D or D T t on s on → = D 1 D T t off s off − → = Switch frequency: Duty Cycle: S V in D L C R control
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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