IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308
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Volume: 02 Issue: 08 | Aug-2013, Available http:www.ijret.org 38
+ −
+ +
−
+
+ −
− +
− =
R r
C R
r C
R C
R r
L R
R r
R r
r L
L r
r L
A
C C
C C
C L
L C
2 2
2 2
1 2
2 2
2 2
2 1
1 1
1 2
1 1
1 1
1
+ −
+ =
R r
C R
R r
L R
r B
C C
C
2 2
2 2
2 2
+ +
= R
r R
R r
R r
C
C C
C 2
2 2
2
+ −
= R
r R
r E
C C
2 2
2
Equation 8 is revisited and the state-space matrices derived previously for ON and OFF-state are used, the weighted
average matrices are:
D A
D A
A −
+ =
1
2 1
+ −
+ −
− +
− +
+ +
+ −
− −
+ −
− =
R r
C R
r C
R C
D C
D R
r L
R L
D R
r L
R r
Dr r
R r
L D
L r
D r
A
C C
C C
C C
L C
L C
2 2
2 2
1 1
2 2
2 2
2 2
1 2
2 1
1 1
1
1 1
1 1
+ −
+ =
− +
= R
r C
R R
r L
R r
L D
L D
D B
D B
B
C C
C
2 2
2 2
2 2
1 2
1
1
+ +
= −
+ =
R r
R R
r R
r D
C D
C C
C C
C 2
2 2
2 1
1
+
− =
− +
= R
r R
r D
E D
E E
C C
2 2
2 1
1
3.2 Zeta Converter Steady-state
U is consisted of two input variables which are VS and IZ. However, for the steady-state output equation, the goal is to
find the relationship between output and input voltage. Thus only variable VS is used for the derivation. However for IZ
multiplication, matrices B and E are included. For this reason, B and E matrices need to be separated into two matrices; BS,
ES for input variable VS and BZ, EZ for input variable IZ which are presented as follow:
[ ]
+ −
+ =
= R
r C
R R
r L
R r
L D
L D
B B
B
C C
C Z
S 2
2 2
2 2
2 1
Thus,
=
2 1
L D
L D
B
S
+ −
+ =
R r
C R
R r
L R
r B
C C
C Z
2 2
2 2
2
Also,
[ ]
+ −
= =
R r
R r
E E
E
C C
Z S
2 2
Thus,
[ ]
=
S
E
+
− =
R r
R r
E
C C
Z 2
2
Equation 7 is revisited, EU
BU CA
V
O
+ −
=
− 1
To get an equation that relates the output and input voltage, the above equation needs to be modified by replacing U=VS,
B=BS and E=ES=0:
S S
O
V B
CA V
1 −
− =
Or in circuit parameters form [1]:
− +
− +
+
−
=
2 1
1 2
1 1
1 1
1 D
D R
r D
D R
r R
r D
D V
V
L C
L S
O
3.3 Zeta Converter Small-signal
Equation 6 is substituted into 9, thus the small signal state- space equation can be written as:
21
22
IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308
__________________________________________________________________________________________
Volume: 02 Issue: 08 | Aug-2013, Available http:www.ijret.org 39
[ ]
d U
B B
BU A
A A
u B
x A
x ~
~ ~
~
2 1
1 2
1
− +
− −
+ +
= ′
−
Or d
B u
B x
A x
d
~ ~
~ ~
+ +
= ′
Where, U
B B
BU A
A A
B
d 2
1 1
2 1
− +
− −
=
−
in circuit parameters form [4]:
[ ]
[ ]
[ ]
− +
− +
− −
+ −
− +
+ −
− +
− +
+ −
= 1
1 1
1 1
1 1
1 1
1 1
1
1 1
1 2
1 1
1 2
1 2
1 1
2 2
Z S
Z L
C S
L Z
L S
C L
L C
L d
I D
R DV
C RI
Dr D
r V
r R
D L
RI Dr
V Dr
r R
D L
D D
R r
D D
R r
R r
D R
B
24 Equation 10 is recalled, the small signal output equation is
written as
[ ]
d U
E E
X C
C u
E x
C v
O
~ ~
~ ~
2 1
2 1
− +
− +
+ =
Since C1=C2 and E1=E2, the equation above is simplified as: u
E x
C v
O
~ ~
~ +
=
4. CONTROL OF ZETA CONVERTER USING FULL-STATE
