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V
04
V
05
R
1
y
1
R
3
V
01
2
z+
V
in
y
1
x
x
V
03
y
2
z-
1
C
2
y
2
V
02
R
2
C
1
Fig. 12.16 VM SIMO-type universal biquad filter proposed by Horng (Adapted from [
18
]
©
2010
Springer Science + Buisiness Media)
Horng
'
s universal SIMO VM biquad In 2010, Horng proposed a universal VM
SIMO-type biquad employing only two DVCCs, two grounded capacitors and three
resistors [
18
] which is shown in Fig.
12.16
.
In this circuit, the filter parameters
ω
0
and Q
0
are orthogonally controllable. The
various transfer functions realized by this circuit (Fig.
12.16
), assuming ideal
DVCCs are given by:
C
1
R
2
Ds
s
1
C
1
C
2
R
1
R
2
s
2
Ds
V
02
V
in
¼
V
03
V
in
¼
V
01
V
in
¼
;
ðÞ
;
ðÞ
;
Ds
ðÞ
ð
:
Þ
12
66
s
2
1
C
1
C
2
R
1
R
2
s
2
s
1
C
1
C
2
R
1
R
2
þ
C
1
R
2
þ
V
04
V
in
¼
V
05
V
in
¼
;
Ds
ðÞ
Ds
ðÞ
where
R
3
C
1
R
1
R
2
1
C
1
C
2
R
1
R
2
s
2
Ds
ðÞ¼
þ
s
þ
ð
12
:
67
Þ
From the above equations it may be seen that a LPF, BPF, HPF, notch can be realized
at V
01
,V
02
,V
03
,V
04
respectively simultaneously and an APF at V
05
for R
1
¼
R
3
can
also be obtained. The filter parameters namely,
ω
0
and Q
0
can be given as:
r
1
C
1
C
2
R
2
R
1
r
C
1
R
1
R
2
C
2
1
R
3
ω
0
¼
andQ
0
¼
ð
12
:
68
Þ
Thus, Q
0
can be controlled independently by R
3
.
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