Transcript Switch-Mode Power Supply DC-DC converters choppers Step Down DC-DC Converter (Buck Converter) vo Vd Vo ton Ts toff Id S L Vo iL Vd R vL Vd -Vo A -Vo ton Ts B toff t.

Switch-Mode Power Supply
DC-DC converters
choppers
Step Down DC-DC Converter (Buck Converter)
vo
Vd
Vo
ton
Ts
toff
Id
S
L
Vo
iL
Vd
R
vL
Vd -Vo
A
-Vo
ton
Ts
B
toff
t
TS
ton
TS
o
o
ton
 vL dt   vL dt   vL dt  0
VO

Vd
(Vd  VO ) ton  VO (TS  ton )
Pd  Po
Vd I d  Vo I o
iL,peak
ton
D
TS
I O Vd 1


I d VO D
iL
I LB  I oB
vL
Vd -Vo
-Vo
ton
Ts
toff
1
ton
DTS
I LB  I L, peak 
(Vd  Vo ) 
(Vd  Vo )  I oB
2
2L
2L
Discontinuous Conduction Mode with Constant Vd
TS Vd
I LB 
D(1  D )
2L
D  0 .5
TS Vd
I LB,max 
8L
I LB  4 I LB,max D(1  D)
iL,peak
iL
I L  Io
vL
Vd -Vo
-Vo
ton
Ts
1Ts  2Ts
Discontinuous Conduction Mode with Constant Vd (continue)
(Vd  Vo ) D TS  ( Vo ) 1 TS  0
Vo
D
V
D  1

 I L, peak  o 1TS
 I o  I L, peak
Vd D  1
L
2
Vo TS
Vd TS
 Io 
( D  1 ) 1 
D  4 I LB,max D 1
2L
2L
IO
Then  
1
4 I LB,max D
Vo

Vd
1
D  
4
2
D2
Io

I LB,max 
Discontinuous Conduction Mode with Constant Output Voltage
TS Vo
I LB 
(1  D )
2L
D0
 I LB  (1  D) I LB,max
V
 1  D d  D
Vo

V T
V V
 I o  o S D 2 d  d  1
2L
Vo  Vo 

2 Vd  Vd
 I o  I LB,max D
  1
Vo  Vo 
V
D  o
Vd
1/ 2
 I o I LB,max 
*

 1  Vo Vd  
T V
 I LB,max  S o
2L
Output Voltage Ripples
I LB  I OB
vL
Vd -Vo
-Vo
ton

Vo 

(1  D)
Vo
2

2
toff
Ts
fC 
iL,peak
iL
Q
I LB  I OB
Ts / 2
VO
VO
1
2 LC
fC 

fS 
2
In discontinuous conduction mode,

DTS (Vd  Vo )  L I O [ DTS (Vd  Vo )Vo  L I oVo  Vd  Vo DTS Vd  Vo   LIo ]
Vo 
i
2LCVo Vd  Vo 
L,peak
iL
I L  Io
vL
Vd -Vo
-Vo
1Ts  2Ts
ton
Ts
iL
iL,peak
Q
I L  Io
t 2  t1
t2
t1
Vo
Vo
Example 1 In buck converter, Vd=12 V to 40 V, Vo=5 V, Io=1 A, C=500 uF, and
fS=50 kHz. (a) Find the minimum inductance to keep the converter in
continuous conduction mode under all conditions.
(b) Calculate Vo in the output voltage at L=50 uH for Vd=12 and 40 V
(c) Calculate Vo in the output voltage at L=20 uH for Vd=12 and 40 V
Solution
Step Up (Boost) Converter
Io
IT + VL Vo
Vd
RL
vL
Vd
ton
Ts
toff
Vd -Vo
iL
IL
ton
Ts
toff
vL
Vd
ton
Ts
toff
Vd -Vo
iL
IL
ton
Ts
Vd ton  (Vd  VO ) toff  0
 Pd  PO
toff
Vo TS
1


Vd Toff 1  D
 Vd I d  Vo I o
I
 o  (1  D )
Id
Boundary Between Continuous And Discontinuous Conduction
1
1 Vd
TS Vo
I LB  I L, peak 
ton 
D(1  D )
2
2 L
2L
1
1 Vd
TS Vo
 I LB  I L, peak 
ton 
D(1  D )
2
2 L
2L
. D  0.5 maximum value at
TS VO
 I LB,max 
8L
TS Vo
 IOB 
D(1  D )2 has its maximum at D=1/3=0.3333. Then I OB
2L
2 TS Vo
TS Vo
IOB,max 
 0.074
27 L
L
I LB  4 D(1  D) I LB,max
27
I oB  D(1  D )2 I oB ,max
4
Discontinuous Conduction Mode
Vd DTS  (Vd  Vo ) 1TS  0
Vo 1  D
Io
1

And

Vd
1
I d 1  D
TSVd 

Io  
 D1
 2L 
Vd
Id 
DTS ( D  1 )
2L
1/ 2
 4 Vo  Vo
 Io 
D
  1

27
V
V
I
 oB ,max 
d d

Output Voltage Ripple For Continuous Conduction Mode
Q I O DTS VO DTS
VO 


C
C
RC
Output Voltage Ripple for Discontinuous Conduction Mode
Q
1 Vd DTs  LI o 2
 Vo 

Vo  Vd 
C 2 LC
Example 2