8
Fig. 3. Equivalent zeta converter circuit when Q turns off
Fig. 4. i
L1
left and i
L2
right waveform in CCM [3]
2.2.1 State-space Description of Zeta Converter
ON-state Q turns on
Z S
C C
C C
C L
L
C C
C C
C C
L L
C C
L L
i v
R r
C R
R r
L R
r L
L
v v
i i
R r
C R
r C
R C
R r
L R
L R
r R
r r
r L
L r
dt dv
dt dv
dt di
dt di
2 2
2 2
2 2
1
2 1
2 1
2 2
2 2
1 2
2 2
2 2
1 2
2 1
1
2 1
2 1
1 1
1 1
1 1
9
OFF-state Q turns off
Output voltage equation for both states:
The weighted average matrices for ON-state and OFF-state are:
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
B
C C
C
2 2
2 2
2 2
1
R
r R
R r
R r
C
C C
C 2
2 2
R
r R
r E
C C
2 2
Z S
C C
C C
C L
L
C C
C C
C L
L C
C C
L L
i v
R r
C R
R r
L R
r L
L
v v
i i
R r
C R
r C
R C
R r
L R
R r
R r
r L
L r
r L
dt dv
dt dv
dt di
dt di
2 2
2 2
2 2
1
2 1
2 1
2 2
2 2
1 2
2 2
2 2
2 1
1 1
1
2 1
2 1
1 1
1 1
1 1
1
Z S
C C
C C
L L
C C
C O
i v
R r
R r
v v
i i
R r
R R
r R
r v
2 2
2 1
2 1
2 2
2
10
2.2.2 Zeta Converter Steady-state
U is consisted of two input variables which are V
S
and I
Z
. However, for the steady-state output equation, the goal is to find the relationship between output and input voltage. Thus only
variable V
S
is used for the derivation. However for I
Z
multiplication, matrices B and E are included. For this reason, B and E matrices need to be separated into two matrices; B
S
, E
S
for input variable V
S
and B
Z
, E
Z
for input variable I
Z
which are presented as follow:
To get an equation that relates the output and input voltage, the above equation 7 needs to be modified by replacing U=V
S
, B=B
S
and E=E
S
=0:
or in circuit parameters form [1]:
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
R r
R r
E E
E
C C
Z S
2 2
S S
O
V B
CA V
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
11
2.2.3 Zeta Converter Small-signal
