Hardware Reference
In-Depth Information
V
0
V
in
¼
R
4
ð
6
:
6
Þ
k
2
s
2
C
1
C
5
R
2
R
3
R
4
þ
s
4
C
5
R
2
R
4
þ
f
C
1
R
4
R
2
þ
ð
R
3
Þ
g þ
ð
R
2
þ
R
4
Þ
Figure
6.5c
also uses a CC
B
and can provide an inverting HPF response with the
transfer function given by
V
0
V
in
¼
s
2
C
2
C
3
R
1
R
4
R
5
2
R
4
ks
2
C
2
C
3
R
1
R
4
R
5
þ
sC
3
4
R
1
R
4
þ
f
ð
R
1
R
5
þ
R
4
R
5
Þ þ
C
2
R
4
R
5
g þ
ð
:
Þ
6
7
A generalized single-CC configuration was proposed by Metin et al. in [
6
] from
where a LPF/BPF, a HPF/BPF and Notch/APF/HPF were realizable as special
cases. Two specific configurations from [
6
] are shown in Fig.
6.6
.
For the circuit of Fig.
6.6a
, a straight forward analysis assuming CCI+ to be
characterized by i
y
¼
i
x,
v
x
¼
v
y
and i
z ¼
i
x
, gives the two transfer functions realiz-
able by the circuit as
s
2
C
3
C
4
R
1
R
4
þ
V
01
V
in
¼
sC
3
R
1
ð
R
4
Þ
ð
6
:
8
Þ
s
2
C
3
C
4
R
1
R
4
þ
sC
3
R
1
ð
R
4
Þ þ
2
sC
4
R
4
þ
2
V
02
V
in
¼
sC
3
R
4
ð
6
:
9
Þ
s
2
C
3
C
4
R
1
R
4
þ
sC
3
R
1
ð
R
4
Þ þ
2
sC
4
R
4
þ
2
Thus, for R
1
¼
R
4
,Eqs.(
6.8
) and (
6.9
) will provide HPF and BPF responses
respectively.
Similarly, for the circuit of Fig.
6.6b
, the two transfer functions are given as
2
s
2
C
1
C
2
R
3
R
4
þ
V
01
V
in
¼
sC
2
ð
C
1
Þ
R
4
þ
1
ð
6
:
10
Þ
2
s
2
C
1
C
2
R
3
R
4
þ
sC
2
ð
C
1
Þ
R
4
þ
2
sC
1
R
3
þ
1
2
s
2
C
1
C
2
R
3
R
4
þ
V
02
V
in
¼
sC
2
ð
C
1
Þ
R
4
ð
:
Þ
6
11
2
s
2
C
1
C
2
R
3
R
4
þ
sC
2
ð
C
1
Þ
R
4
þ
2
sC
1
R
3
þ
1
Thus, for C
1
¼
C
2
, the transfer functions in Eqs. (
6.10
) and (
6.11
) can realize notch
and HPF responses, respectively. Furthermore, if we select C
1
¼
2C
2
and R
4
¼
2R
3
,
Eq. (
6.10
) can provide an APF response also.
Using a CMOS CCI, pole frequencies of the order of 1.8 and 3.98 MHz have
been easily realised in practice.
6.2.3 Multiple-CC Multifunction Biquads
In this section, we present a number of multiple-CC biquads capable of realizing
three or more filter functions simultaneously under different conditions and/or at
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