The document presents an analysis of buck-boost and Cuk DC-DC converters. It discusses the operating principles, modes of operation, and circuit analyses of these converters. Key points include: - Buck-boost converters can step down or up voltage and have two operating modes depending on whether the switch is on or off. Circuit analyses include inductor current, capacitor voltage, and voltage conversion ratio. - Cuk converters also can step down or up voltage. Their two operating modes depend on the switch state and involve energy transfer between inductors and capacitors. Circuit analyses determine inductor currents and voltage conversion ratio. - Both converters can operate in continuous or discontinuous conduction mode depending on component values and duty cycle.

1. Presented by Won-yong Sung
Energy Mechatronics Lab.
School of Information and Communication Eng.
Sungkyunkwan University
http://seml.skku.ac.kr
DC-DC Converter(II)
(Buck-Boost & Cuk)
전기기기 컴퓨터제어
March. 24. 2011

2. Sungkyunkwan Univ., Energy Mechatronics Lab.
2
Buck-Boost Converter
𝑉𝑠 ≥ 𝑉𝑜
Buck
𝑉𝑠 ≤ 𝑉𝑜
Boost
𝑉𝑠 ≥ 𝑉𝑜
𝑉𝑠 ≤ 𝑉𝑜
Buck-Boost
Vi
Vs
VD
D
L VL C
is
iL
io
ic
iD
VOLoad
Step-Down Step-Up Step-Down/Up

3. Sungkyunkwan Univ., Energy Mechatronics Lab.
3
Vi
Vs
VD
D
L VL C
is
iL
io
ic
iD
VO
Mode Analysis - 1
0 ≤ 𝒕 < DT
 Switch on, Diode off
-
 Inductor current increases
-
 Diode Voltage
-
, 0s L Di i i 
D i Ov v v 
Buck-Boost Converter(CCM Analysis)
DT T
vS
t
Vi+Vo
vD
t
DT T
iD
t
Imax
Imin
DT T
iS
Imax
Imin
t
DT T
iL
t
Imax
Imin
DT T
vL
DT T
t
-Vo
Vi
Vi+Vo
min
0
1
)( IdtV
L
ti
t
iL  

4. Sungkyunkwan Univ., Energy Mechatronics Lab.
4
Vi
Vs
VD
D
L VL C
is
iL
io
ic
iD
VO
Mode Analysis - 2
DT ≤ 𝒕 < T
 Switch off, Diode on
-
 Inductor current decreases
-
 Switch Voltage
-
D Li i
s iv v
DT T
vS
t
Vi+Vo
vD
t
DT T
iD
t
Imax
Imin
DT T
iS
Imax
Imin
t
DT T
iL
t
Imax
Imin
DT T
vL
DT T
t
-Vo
Vi
Vi+Vo
max0 )(
1
)( Idtv
L
ti
t
DT
L  
Buck-Boost Converter(CCM Analysis)

5. Sungkyunkwan Univ., Energy Mechatronics Lab.
5
)1( DVDTV oi 
10
8
4
2
0
Gv
0.2 0.4
6
0.6 0.8 1
D
Buck Mode Boost Mode
0( ) (1 ) 0L i
Based on Inductor Volt Sec Balance
V V DT V D T

      
)1(
0
D
D
V
V
G
i
V


vL
DT T
-Vo
Vi
t
Buck-Boost Converter(CCM Analysis)

6. Sungkyunkwan Univ., Energy Mechatronics Lab.
6
Vi
Vs
VD
D
L VL C
is
iL
io
ic
iD
VO
Inductor Current Analysis
Vi
Vs
VD
D
L VL C
is
iL
io
ic
iD
VO
minmax ∫)( IdtV
L
DTtiI
DT
iL +
1
===
0
maxmin ∫ )-()( Idtv
L
TtiI
T
DT
L +
1
=== 0
DT
L
V
II i
 minmax
TD
L
V
II )-(- minmax 1•= 0
dt
di
Lv L
L 
L
V
dt
di iL

min
0
1
)( IdtV
L
ti
t
iL  
0vvL 
L
v
dt
diL 0

max0 )(
1
)( Idtv
L
ti
t
DT
L  
Buck-Boost Converter(CCM Analysis)

7. Sungkyunkwan Univ., Energy Mechatronics Lab.
7
iD
t
Imax
Imin
DT T
iS
Imax
Imin
t
DT T
iL
t
Imax
Imin
DT T
iD
t
Imax
Imin
DT T
iS
Imax
Imin
t
DT T
iL
t
Imax
Imin
DT T
2
minmax II
IL


LiLi
siin
IVD
T
DT
IV
IVP








RD
VD
R
V
IVP
i




2
22
0
000
)1(
)(
)1(
)1()1(
0
0
2
D
I
DR
V
DR
VD
I i
L







T
L
VD
I
DT
L
V
II
L
i
L




2
)1(
2
0
max
T
L
VD
I
DT
L
V
II
L
i
L




2
)1(
2
0
min
siin iVp 
Inductor Current Analysis
Buck-Boost Converter(CCM Analysis)

8. Sungkyunkwan Univ., Energy Mechatronics Lab.
8
iD
t
Imax
Imin
DT T
Io=Vo/R
DT T
iC
t
-Io
Io
t
DT T
vC-Vo
Δvo
)
1
1
0
00
/R(VDT
C
IDT
C
Δv


R
V
Ii 0
00 
R
V
ii DC
0

Capacitor Voltage Analysis
Buck-Boost Converter(CCM Analysis)
𝐶 =
𝐷𝑇
𝑅
𝑉𝑜
∆𝑣 𝑜
=
𝐷
𝑅𝑓𝑠𝑤
1
𝑅𝐹

9. Sungkyunkwan Univ., Energy Mechatronics Lab.
9
𝐼𝐿,𝑚𝑖𝑛 = 𝐼𝐿 −
𝑉𝑜 𝑇
2𝐿
1 − 𝐷 = 0
𝐼 𝑜
1 − 𝐷
=
𝑉𝑜 𝑇
2𝐿
1 − 𝐷
𝐿 ≥
𝑅
2𝑓𝑠𝑤
1 − 𝐷 2
: CCM
Buck-Boost Converter
Boundary Conduction Mode
20
00
0
max
)1(
2
)1(
)1(
2
2
2
)1(
D
L
TV
I
D
I
D
L
TV
I
I
L
TVD
II
oB
LB
LL






L
TV
I
L
TV
I
oB
LB
2
2
0
max,
0
max,



10. Sungkyunkwan Univ., Energy Mechatronics Lab.
10
Buck-Boost Converter
DD
D
V
V
G
Ai
V

 0
 
TD
DT
AL
A
Idtv
L
TDti 0)(
1
)( max0
0
max
TV
LI
DDA  )(
2
max
0 DD
I
I A 
0
02
TV
LI
DDA 
Discontinuous Conduction Mode
Based on Inductor Volt Sec Balance
𝑉𝑖 𝐷𝑇 + 𝑉𝑜 𝐷𝐴 − 𝐷 𝑇 = 0

11. Sungkyunkwan Univ., Energy Mechatronics Lab.
11
Buck-Boost Converter
Simulation
𝐿 ≥
𝑅
2𝑓𝑠𝑤
1 − 𝐷 2
=
10
2 × 5000
0.8 2
= 640𝑢𝐹

12. Sungkyunkwan Univ., Energy Mechatronics Lab.
12
Buck-Boost Converter
Simulation
L=1280uF>640uF
=> CCM
L=640uF=640uF
=> BCM
L=320uF<640uF
=> DCM

13. Sungkyunkwan Univ., Energy Mechatronics Lab.
13
Cuk Converter
 Buck-Boost와 마찬가지로 출력전압의 승압과 강압이 모
두 가능
+ v L1 -
i C1
-
Vo
+
S
L1 C1
C2
+
vs
-
+ v C1 -
i L2i L1
i D1
- vL2 +
D
L2
Vi
i o
i c-
Vd
+
i s

14. Sungkyunkwan Univ., Energy Mechatronics Lab.
14
C
+ v L1 -
-
Vo
+
L1 C1
+
vs
-
+ v C1 -
i L2i L1
i D1
- vL2 +
D
L2
i C1=i L1
SVi
i o
i c-
Vd
+
i s
Switch off, Diode on
Inductor current 𝑖 𝐿1, 𝑖 𝐿2 decrease
Capacitor is discharged electricity
Cuk Converter
① Switch OFF / Diode ON
0
off
on
Vin
t
vL1
0
off
on
t
vL2
(Vin-VC1=-Vo)
VC1-Vo
-Vo
0 t
iL1
IL1
0 t
iL2
IL2
(1-D)Ts
(=toff)
DTs
(=ton)
Mode Analysis - 1

15. Sungkyunkwan Univ., Energy Mechatronics Lab.
15
CS
+ v L1 -
i C1=-i L2
-
Vo
+
L1 C
+
vs
-
+ v C1 -
i L2i L1
- vL2 +
L2
DVi
i o
i c
i D1
-
Vd
+
i s
Cuk Converter
② Switch ON / Diode OFF
Switch on, Diode off
Inductor current 𝑖 𝐿1, 𝑖 𝐿2 increase
Capacitor charges electricity
0
off
on
Vin
t
vL1
0
off
on
t
vL2
(Vin-VC1=-Vo)
VC1-Vo
-Vo
0 t
iL1
IL1
0 t
iL2
IL2
(1-D)Ts
(=toff)
DTs
(=ton)
Mode Analysis - 2

16. Sungkyunkwan Univ., Energy Mechatronics Lab.
16
10
8
4
2
0
Gv
0.2 0.4
6
0.6 0.8 1
D
Buck Mode Boost Mode
Cuk Converter
Based on Inductor Volt Sec Balance
𝑉𝐿1 ∶ 𝑉𝑖 𝐷𝑇 + 𝑉𝑖 − 𝑉𝐶1 1 − 𝐷 𝑇=0
𝑉𝐿2 ∶ 𝑉𝐶1 − 𝑉𝑜 𝐷𝑇 + −𝑉𝑜 1 − 𝐷 𝑇=0
𝑉𝐶1 =
𝑉𝑖
1 − 𝐷
𝑉𝑜 = 𝐷𝑉𝐶1 =
𝐷
1 − 𝐷
𝑉𝑖
0
off
on
Vin
0
off
on
vL2
(Vin-VC1=-Vo)
VC1-Vo
-Vo
t
vL1
t
(1-D)Ts
(=toff)
DTs
(=ton)
(1-D)Ts
(=toff)
DTs
(=ton)
01 VVV iC 
iC V
D
D
DVV 


1
10

17. Sungkyunkwan Univ., Energy Mechatronics Lab.
17
Inductor Current 𝒊 𝑳𝟏
Cuk Converter
CS
+ v L1 -
i C1=-i L2
-
Vo
+
L1 C
+
vs
-
+ v C1 -
i L2i L1
- vL2 +
L2
DVi
i o
i c
i D1
-
Vd
+
i s
DTt 0
dt
di
Lv L
L
1
11 
1
1
L
V
dt
di iL

1min
01
1
1
)( IdtV
L
ti
t
iL  
1min
01
11max
1
)( IdtV
L
DTtii
DT
iL  
DT
L
V
II i

1
1min1max
0 t
iL1
IL1
0
off
on
Vin
vL1
(Vin-VC=-Vo)
(1-D)Ts
(=toff)
DTs
(=ton)
t

18. Sungkyunkwan Univ., Energy Mechatronics Lab.
18
Inductor Current 𝒊 𝑳𝟏
Cuk Converter
C
+ v L1 -
-
Vo
+
L1 C1
+
vs
-
+ v C1 -
i L2i L1
i D1
- vL2 +
D
L2
i C1=i L1
SVi
i o
i c-
Vd
+
i s
TtDT 
11 CiL vVv 
1
11
L
vV
dt
di CiL 

 
t
DT
ciL IdtvV
L
ti 1max1
1
1 )(
1
)(
1max1
1
11min )(
1
)( IdtvV
L
TtiI
T
DT
CiL  
TD
L
VV
II Ci
)1(
1
1
1max1min 


2
1min1max
1
II
IL


DT
L
V
II i
L 
1
11max
2
DT
L
V
II i
L 
1
11min
2
0 t
iL1
IL1
0
off
on
Vin
vL1
(Vin-VC=-Vo)
(1-D)Ts
(=toff)
DTs
(=ton)
t

19. Sungkyunkwan Univ., Energy Mechatronics Lab.
19
Inductor Current 𝒊 𝑳𝟐
Cuk Converter
CS
+ v L1 -
i C1=-i L2
-
Vo
+
L1 C
+
vs
-
+ v C1 -
i L2i L1
- vL2 +
L2
DVi
i o
i c
i D1
-
Vd
+
i s
DTt 0
dt
di
Lv L
L
2
22 
2
012
L
vv
dt
di CL 

 
t
CL Idtvv
L
ti
0
2min01
2
2 )(
1
)(
2min
0
01
2
22max
)(
1
)(
IdtVV
L
DTtiI
DT
C
L



DT
L
VV
II C



2
01
2min2max
0
off
on
vL2 VC1-Vo
0 t
iL2
IL2
(1-D)Ts
(=toff)
DTs
(=ton)
t
-Vo

20. Sungkyunkwan Univ., Energy Mechatronics Lab.
20
Inductor Current 𝒊 𝑳𝟏
Cuk Converter
C
+ v L1 -
-
Vo
+
L1 C1
+
vs
-
+ v C1 -
i L2i L1
i D1
- vL2 +
D
L2
i C1=i L1
SVi
i o
i c-
Vd
+
i s
0
off
on
vL2 VC1-Vo
0 t
iL2
IL2
(1-D)Ts
(=toff)
DTs
(=ton)
t
-Vo
TtDT 
2
2min2max
2
II
IL


R
V
D
D
R
V
II
i
L




1
0
02
DT
L
V
I
TD
L
V
II
i
L
L


2
2
2
0
22max
2
)1(
2
DT
L
V
I
TD
L
V
II
i
L
L


2
2
2
0
22min
2
)1(
2

21. Sungkyunkwan Univ., Energy Mechatronics Lab.
21
Capacitor Voltage 𝒗 𝑪𝟏
+ v L1 -
i C1
-
Vo
+
S
L1 C1
C2
+
vs
-
+ v C1 -
i L2i L1
i D1
- vL2 +
D
L2
Vi
i o
i c-
Vd
+
i s
iC1
t
Imax1
Imin1
- Imax2
- Imin2
DT T
vC1 – VC1
ΔvC1 t
t
1
1
1 )1(
1
LC ITD
C
v 
Cuk Converter

22. Sungkyunkwan Univ., Energy Mechatronics Lab.
22
Capacitor Voltage 𝒗 𝑪𝟐
+ v L1 -
i C1
-
Vo
+
S
L1 C1
C2
+
vs
-
+ v C1 -
i L2i L1
i D1
- vL2 +
D
L2
Vi
i o
i c-
Vd
+
i s
t
iC2
(Imax2 – Imin2)
1
2
(Imax2 – Imin2)
1
2
t
vC2 - Vo
Δvo
DT
DT
T
T
R
v
i 0
0 
R
V
Ii 0
00 
dt
dv
CiC
0
22 
8
1
222
11
2
2min2max
2
2min2max
2
0
T
)I(I
C
TII
C
Δv






 

22
2
2
2
0
2
0
8
8
)1(
1
CL
TDV
T
D
L
V
C
v
i


Cuk Converter

23. Sungkyunkwan Univ., Energy Mechatronics Lab.
23
Simulation
Cuk Converter

24. Sungkyunkwan Univ., Energy Mechatronics Lab.
24
Simulation
Cuk Converter