DC DC Power Supplies
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Transcript of DC DC Power Supplies
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Power Electronics
0 0.2 0.4 0.6 0.8 1.0
1
0.8
0.6
0.4
0.2
0
/o oI I
0 0.2 0.4 0.6 0.8 1.0
1
0.8
0.6
0.4
0.2
0
/o oI I
0 0.2 0.4 0.6 0.8 1.0
1
0.8
0.6
0.4
0.2
0
/o oI I
1o
i
o
i
v
E
v
E
=
discontinuous continuous
( )4 1oo
I
I
=
step-up
1
o
i
o
i
v
E
v
E
=
discontinuous continuous
( )4 1oo
I
I
=
o
o
o
i
I
I
vE
=
step-up/down
o
i
v
E =
discontinuous continuous
vo/Ei
45
35
25
1
5
5
2
231
1
-4
-1
- 23
-
( )4 1oo
I
I
=
1
o
oi
oo
i
v
EI
vI
E
=
1,
1,
1,
1o o
io
vI
EI
=
step-down
Figure 15.18. Characteristics for three dc-dc converters with respect to oI,
when the input voltage Eiis held constant. See table 15.4.
Switched mode dc dc Power Supplies
Table 15.4. Transfer functions with constant input voltage, Ei, with respect to Io
converterEi
constantstep-down step-up step-up/down
reference equation (15.4) (15.45) (15.75)
o
i
v
E=
1
1
o
i
v
E =
1
o
i
v
E
=
continuous inductorcurrent conduction
(and change of variable) o
i
v
E=
1o
i
o
i
v
E
v
E
= 1
=
o
i
o
i
v
E
v
E
reference equation (15.21) (15.60) (15.91)
discontinuous inductorcurrent conduction
2
1
21
o
i o
i
v
E LI
E
=
+
2
12
= +o i
i o
v E
E LI
2
2
o i
i o
v E
E LI
=
normalised
=o
i
v
E
where
8
iE
IL
=
o
2
1
11
4
o
i o
v
E I
I
=
+
o
2
1 4 /o o
i
v I
EI
= +
o
2
4 /o o
i
v I
EI
=
o
= =oo
I I 1pu @ = ; =o
i
v
E = ; 2=o
i
v
E = ; 1= o
i
v
E
change of variable
=o
o
I
I
2
1
4
=
o
io
o
o
i
v
EI
vI
E
2 14
1
=
o
oo
i
I
vI
E
2 1
4
= oo
o
i
I
vI
E
change of variable=
all with a boundary
1 = + o
o
I
I
1
=
o
io
o
i
v
EIv
IE
o
1oo
i
vI
EI
=
o
= ooi
vI
EIo
conduction boundary
1 = + o
o
I
I
( )
4 1
4 1
=
=
o oo
i io
v vI
E EI
( )
2
1
4
4 1
=
=
o
io
oo
i
v
EI
vIE
( )
24
1
4 1
=
=
o
io
oo
i
v
EI
vIE
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Figure 15.19. Characteristics for three dc-dc converters with respect to iI,
when the input voltage Eiis held constant. See table 15.5.
1o
i
o
i
v
E
v
E
=
discontinuous continuous
1 o
i i
oi
i
v
EI
vI
E
=
i
i
I
I=
step-up
1
o
i
o
i
v
E
v
E
=
discontinuous continuous
i
i
I
I
=
2i
i
I
I=
step-up/down
vo/Ei
4
5
35
2
5
1
5
5
2
231
1
-4
-1
- 23
-
o
i
v
E
=
2 31,
discontinuous continuous1
i
i
o
i
I
I
v
E
=
4
27
( ) 21ii
I
I =
427 step-down
0 0.2 0.4 0.6 0.8 1.0
1
0.8
0.6
0.4
0.2
0
/i iI I
0 0.2 0.4 0.6 0.8 1.0
1
0.8
0.6
0.4
0.2
0
/i iI I
0 0.2 0.4 0.6 0.8 1.0
1
0.8
0.6
0.4
0.2
0
/i iI I
+
pp
Table 15.5. Transfer functions with constant input voltage,Ei, with respect to Ii
converterEi
constantstep-down step-up step-up/down
reference equation (15.4) (15.45) (15.75)
o
i
v
E=
1
1
o
i
v
E =
1
o
i
v
E
=
continuous inductorcurrent conduction
(and change of variable) o
i
v
E=
1o
i
o
i
v
E
v
E
= 1
=
o
i
o
i
v
E
v
E
reference equation (15.20) (15.61) (15.91)
discontinuous inductorcurrent conduction 2
21o i
i i
v LI
E E = 21
12
=
o
ii
i
vEE
LI
2
2
o o
i i
v v
E LI
=
normalised
=o
i
v
E
2
41
27
o i
i
v I
EI
=
i
where
4
27 2
iE
IL
=
i
2
1
1 /
o
ii
v
EI
I
=
i
where
2
iE
IL
=
i
21 / i
I
I
=
i
where
2
iE
IL
=
i
= =i iI I 1pu @ = ;23=
o
i
v
E = 1; o
i
v
E = 1; o
i
v
E
change of variable
=i
i
I
I
227
4 1
=
oi
i
vI
EI
i
2
1
=
o
ii
o
i
v
EI
vIE
i
2
=iI
Ii
change of variable
=
427
1
1
=
i
o
i
Iv
IEi
1o
i i
o
i
v
I E
vIE
=
i
i
I
I
=
i
conduction boundary
( )
2
2
274
274
1
1
=
=
o oi
i i
v vI
E EI
i
1
=
=
o
ii
o
i
vEI
vI
Ei
2
2
1
=
=
o
ii
o
i
vEI
vI
Ei
conduction boundary ( )2274 1 = iI
Ii
= iI
Ii
= iI
Ii
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Figure 15.20. Characteristics for three dc-dc converters with respect to oI,
when the output voltage vois held constant. See table 15.6.
0 0.2 0.4 0.6 0.8 1.0
1
0.8
0.6
0.4
0.2
0
/o oI I
0 0.2 0.4 0.6 0.8 1.0
1
0.8
0.6
0.4
0.2
0
/o oI I
0 0.2 0.4 0.6 0.8 1.0
1
0.8
0.6
0.4
0.2
0
/o oI I
o
i
v
E =
discontinuous continuous1
o
o o
oi
i
I
v I
vE
E
=
1o
o
I
I=
step-down
131,
1o
i
o
i
v
E
v
E
=
discontinuous continuous
1o o o
i io
v vI
E EI
=
427
step-up
1
o
i
o
i
v
E
v
E
=
discontinuous continuous
oo
i o
v I
E I
=
( )2
1o
o
I
I=
step-up/down
( )2
1o
o
I
I =
427
vo/Ei
4
5
3
5
25
1
5
5
2
231
1
-4
-1
- 23
-
Table 15.6. Transfer functions with constant output voltage, vo, with respect to Io
convertervo
constantstep-down step-up step-up/down
reference equation (15.4) (15.45) (15.75)
o
i
v
E=
1
1
o
i
v
E =
1
o
i
v
E
=
continuous inductorcurrent conduction
(and change of variable) o
i
v
E=
1o
i
o
i
v
E
v
E
= 1
=
o
i
o
i
v
E
v
E
reference equation (15.20) (15.61) (15.91)
discontinuous inductorcurrent conduction
2
21o i
i i
v LI
E E = 2
1
12
=
o
ii
i
v
EE
LI
2
2
o o
i i
v v
E LI
=
normalised
=o
i
v
E
2
2
11
4
o oo
i i
v vI
E EI
=
o
where
2
ov
I
L
=
o
2
2274
1
1 /
=
o
ioo
i
v
E vI
EIo
where
4
27 2
ov
I L
=
o
2/o oo
i i
v vI
E EI
= o
where
2
= o
vI
L
o
= =oo
I I 1pu @ = 0; 0=o
i
v
E = ; 1=o
i
v
E = 0; 0=o
i
v
E
change of variable
=o
o
I
I
2
2
1
=
o
io
oo
i
v
EI
vIE
2274
1
1
=
o
o oo
i i
I
v vI
E E
2
2
1
=
o
oo
i
I
vIE
change of variable
=
1
1
=
o o
oi
i
v IvE IE
o
427 1
=
o oo
i i
v vI
E EIo
= o o
i
v I
EIo
conduction boundary
1
1
=
=
oo
io
vI
EI
( )
3
2
274
274
1
1
=
=
o
io
oo
i
v
EI
vIE
( )
2
2
1
1
1
=
=
o
oo
i
I
vIE
conduction boundary 1 oI
I
=
o
( )2
274 1
oI
I
=
o
1 oI
I
=
o
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Figure 15.22. Characteristics for three dc-dc converters, when the input voltage Eiis held constant.
discontinuous
discontinuous
discontinuous
continuous
/i i
I I
24
o
i
v
E
( )2
4
1
o
i
o
i
v
E
v
E
4 1v vo o
E Ei i
24 1
voEi
voEi
( )( )
2
4 1oi
o
i
vE
vE
1
1
o
i
v
E =
o
i
v
E =
1
o
i
v
E
=
2
1
o
i
o
i
v
E
v
E
1o
i
o
i
v
E
v E
1
1
o
i
v
E =
1
o
i
v
E
=
o
i
v
E =
( )2274 1 oi
v
E
2
/i i
I I
=
2
1
o
i
o
i
v
E
vE
227
4 1 o o
i i
v vE E
/o oI I
o
i
v
E
24
1o
i
v
E
2
1
=
=
=
=
=
=
=
=
=
=
=
=
0
= 0
= 1
1
= 0
= 1
=
=
= 0= 0
2
-2
-1
1
-
01
0
00
1
Eiconstant Eiconstant
Figure 15.23. Characteristics for three dc-dc converters, when the output voltage vois held constant.
/i iI I
/ ooI I
o
i
v
E
o
i
v-E
=
=
=
=
=
=
=
=
=
=
=
=
0
= 0
= 1
1
= 0
= 1
=
=
= 0= 0
2
-2
-1
1
-
1
24
o
i
vE
( )2
4
1
o
i
o
i
v
E
vE
4 1v vo o
E Ei i
24 1 vo
Eivo
Ei
24
1oi
vE
( )( )
2
4 1oi
o
i
v
E
vE
1
1o
i
vE
=
o
i
vE
=
1
o
i
v
E
=
( )
2
2
o
i
v
E
21
2
voEi
voEi
( )
2274
1o o
i i
v v
E E
( )3
274 1
o
i
o
i
vE
v
E
1 oi
vE
( )2
1
1
oi
vE
1
o
i
v
E
=
voEi
=
1
1
o
i
vE
=
voconstant voconstant
0 0
00
discontinuous
discontinuous
continuous
0
0
551
1 /
o i
v E
k
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PowerElectronics
Table25
.8.
Converterparametersfordiscontinuousandcontinuousinductorc
onductionregionsandboundaries.
Converter
Forwa
rd
step-do
wn
Flyback
step-up
Flyback
step-
up/down
;
0
1
=
=
Tt
R
k
L
discontinuous
continuous
disconti
nuous
continuous
discontinuous
continuous
(
)
(
)
21
=
critical
o i
k v
k
E
2
1
2
1
k
k
2
1
2
1
k
k
(
)2
272
2
1
>
k
k
27
2
k
(
)2
2
1
2
1
k
k
(
)2
2
1
2
1
k
k
(
)
,
=
=
i
o
o
i
i
o
v
I
R
k
I
E
E
I
2
2
8
1
1
+
+
k
k
2
1
1
2
+
+
k
1
1
k
1
=
D
D
t
1
o i
o iv Ev E
1
1
1
o i
v E
1
1 o i
v E
1
(
)
1
= =
+
x
x
D
t
1
1
o i
v E
0
1-
1
o i
o iv E
v E
0
1
1
o i
o iv Ev E
+
0
,
L
L
i
i
R
R
I
I
E
E
1
,0
o i
v
k
E
(
)
1
o i
v
k
E
,0
k
1
1
o i
v
k
E
,0
k
1
1
o i
v
k
E
(
)
=
L
i
L
L
L
D
R
I
E
I
i
i
+
+
2
1
o i
o iv E
k
v E
o i
v E
2
1
o i
o iv E
k
v E
1
1
o i
v E
2
1
o i
o iv E
k
v E
+
1
1
o i
v E
/
T
t
t
D
t
k
