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y
2
V
02
DVCC
y
1
x
V
03
+
y
1
z+
z+
V
in
DVCC
C
y
2
-
x
V
01
R
Fig. 12.7 DVCCs-based first-order filters proposed by Horng [
8
]
two grounded passive elements and without any component matching condition.
Assuming ideal DVCCs, the three VM filter transfer functions obtained as:
V
01
V
in
¼
2
sCR
sCR
V
02
V
in
¼
2
sCR
V
03
V
in
HPF
1
LPF
1
and BPF
:
:
:
þ
þ
¼
sCR
þ
1
;
ð
12
:
29
Þ
sCR
þ
1
Khateb- Khatib-Koton biquad A SIMO-type VM multifunction filter configura-
tion based upon the idea of Akerberg-Mossberg [
203
] structure has been presented
by Khateb et al. [
11
] which employs three DVCCs and six grounded passive
elements.
A circuit analysis of Fig.
12.8
reveals the following transfer functions:
C
2
R
1
R
2
Ds
R
1
Ds
R
4
C
1
C
2
R
1
R
2
R
3
R
4
s
2
R
4
s
V
LP
V
IN
¼
V
BP
V
IN
¼
V
HP
V
IN
¼
ð
12
:
30
Þ
;
ðÞ
;
Ds
ðÞ
ðÞ
s
2
1
C
1
C
2
R
3
R
2
þ
V
BR
V
IN
¼
ð
12
:
31
Þ
Ds
ðÞ
where
R
4
C
2
R
1
R
2
þ
1
C
1
C
2
R
3
R
2
s
2
Ds
ðÞ¼
þ
ð
12
:
32
Þ
The filter parameters namely Q
0
and
ˉ
0
can be obtained as:
r
C
2
R
2
C
1
R
3
r
1
C
1
C
2
R
2
R
3
R
1
R
4
Q
0
¼
and
ω
0
¼
ð
12
:
33
Þ
Thus, for R
2
¼
ˉ
0
, and
ˉ
0
can also be tuned independently by simultaneously varying R
2
and R
3
(R
2
¼
R
3
,Q
0
can be controlled by R
1
and/or R
4
without disturbing
R
3
).
To confirm the workability of the proposed structure, simulation results using
0.18
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