2.4. BOOST CONVERTER 59
[VG_ rg_rds_ rD_ VD_ rL_ L_ rC_ C_ R_ D_ 0])));
disp('VC ')
disp(eval(subs(VC ,[vg rg rds rD vD rL L rC C R d io],
[VG_ rg_rds_ rD_ VD_ rL_ L_ rC_ C_ R_ D_ 0])));
e program gives the following results:
v
o
.s/
d.s/
D 0:94123
s C 1:267 10
5
.s 1:168 10
5
/
s
2
C 7560s C 2:332 10
8
(2.23)
Z
in
.s/ D
v
g
.
s
/
i
g
.
s
/
D 0:000125
s
2
C 7560s C 2:332 10
8
s C 2475
(2.24)
Z
o
.s/ D
v
o
.
s
/
i
o
.
s
/
D 0:049505
s C 2:5 10
5
.
s C 4194
/
s
2
C 7560s C 2:332 10
8
: (2.25)
Bode diagram of control-to-output transfer function, open-loop input impedance, and
open-loop output impedance is shown in Figs. 2.15, 2.16, and 2.17, respectively.
2.4 BOOST CONVERTER
Schematic of the boost converter is shown in Fig. 2.18. When the MOSFET is closed, the diode
is reverse biased and Fig. 2.19 is an equivalent circuit.
According to Fig. 2.19, the circuit differential equations can be written as:
d i
L
.t/
dt
D
1
L
r
g
C r
ds
C r
L
i
L
C v
g
(2.26)
dv
C
.t/
dt
D
1
C
1
R C r
C
v
C
C
R
R C r
C
i
O
(2.27)
i
g
D i
L
(2.28)
v
o
D
R
R C r
C
v
C
C
R r
C
R C r
C
i
O
: (2.29)
When the MOSFET switch is opened, the diode becomes forward-biased. Figure 2.20
shows the equivalent circuit for this case.
60 2. ON THE EXTRACTION OF INPUT AND OUTPUT IMPEDANCE OF PWM DC-DC
60
40
20
0
-20
360
270
180
90
10
3
10
4
10
6
10
5
Frequency (rad/s)
Phases (deg) Magnitude (dB)
Figure 2.15: Control-to-output transfer function of the studied buck-boost converter.
2.4. BOOST CONVERTER 61
60
40
20
0
-20
90
45
0
-45
-90
10
2
10
3
10
4
10
6
10
5
Frequency (rad/s)
Phases (deg) Magnitude (dB)
Figure 2.16: Open-loop input impedance of buck-boost converter.
62 2. ON THE EXTRACTION OF INPUT AND OUTPUT IMPEDANCE OF PWM DC-DC
10
0
-10
-20
-30
45
0
-45
-90
10
2
10
3
10
4
10
7
10
6
10
5
Frequency (rad/s)
Phases (deg) Magnitude (dB)
Figure 2.17: Open-loop output impedance of buck-boost converter.
–
+
Vg
rg
i
?
R
C
+
rL
rC
D
L
Figure 2.18: Schematic of PWM boost converter.
2.4. BOOST CONVERTER 63
–
+
Vg
rg
i
?
R io
C
+
rL
rC
rds
L
Z
in
(s)
Z
0
(s)
Figure 2.19: Equivalent circuit of boost converter with closed MOSFET.
–
–
+
+
Vg
VD
rg
i
?
R io
C
+
rL rL
rC
L
Z
in
(s)
Z
0
(s)
Figure 2.20: Equivalent circuit of boost converter with open MOSFET.
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