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V
04
R
3
R
4
DVCC
V
02
DVCC
y
2
V
01
DVCC
y
1
1
z+
x
y
1
2
z+
C
2
z+
V
05
3
x
C
1
x
y
2
V
in
y
1
y
2
V
03
R
1
R
2
Fig. 12.13 VM universal filter proposed by Horng et al. (Adapted from [
16
]
2006 Birkhauser
©
Boston)
can be obtained by adding I
HP
and I
LP
(for R
1
¼
R
2
). Further, if we connect I
HP
,I
LP
and I
BP,
an APF can be realized for R
1
¼
R
3
.
Since the circuit employs grounded resistors, this enables simulation of the
electronic resistor as shown in Fig.
12.12b
. Assuming saturation region operation
of diode connected matched MOSFETs, MR
1
and MR
2
in Fig.
12.12b
, its equiva-
lent resistance is obtain
e
d as:
R
2
¼
V
in
I
in
¼
L
R
eq
¼
forV
B
¼
V
A
ð
12
:
51
Þ
Þ
;
2
ʼ
n
C
ox
WV
A
ð
V
T
where symbols have their usual meanings.
Horng- Hou-Chang-Chou-Lin biquad A high input impedance voltage-mode
universal biquadratic filter using DVCCs as shown in Fig.
12.13
was proposed by
Horng et al. [
16
] which can realize all five standard second-order filters with
grounded capacitors.
By a routine circuit analysis,
the various filter responses (assuming ideal
DVCCs) are given by:
1
C
2
R
1
s
1
C
1
C
2
R
1
R
2
s
2
Ds
V
02
V
in
¼
V
03
V
in
¼
V
04
V
in
V
01
V
in
¼
;
;
ðÞ
;
Ds
ðÞ
Ds
ðÞ
1
C
1
C
2
R
1
R
2
s
2
þ
and
V
05
V
in
¼
Ds
ðÞ
R
3
C
2
R
1
R
2
1
C
1
C
2
R
1
R
2
s
2
s
þ
¼
for
R
3
¼
R
4
Ds
ðÞ
ð
12
:
52
Þ
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