Hardware Reference
In-Depth Information
Fig. 12.44 Universal
biquad filter configuration
proposed by Chen [
205
]
R
3
R
2
x+
y
1
y
2
z
+
V
0
C
2
BDI-
+
z
-
x-
V
2
-
+
R
1
V
3
+
-
C
1
V
1
-
12.2.11 Filter Design Using Balanced-dual-input Dual-
output-CC (BDI-DOCC)
In this section, we present an interesting biquad filter configuration using yet
another variety of CCs called balanced dual input-dual output CC (BDI-DOCC)
which is shown here in Fig.
12.44
.
A BDI-DOCC is characterized by the following terminal equations:
V
X
þ
¼
V
Y
1
,
V
X
¼
V
Y
2
,
I
Z
þ
¼
I
X
þ
and
I
Z
¼
I
X
ð
12
:
155
Þ
Chen biquad using BDI-DOCC The VM MISO-type filter configuration shown
in Fig.
12.44
employs one BDI-DOCC, two capacitors and three resistors. This
circuit which was proposed by Chen in [
205
] offers (i) realization of all standard
second-order filters from the same topology (ii) no requirement of matching
condition(s) of components
(iii)
low active and passive sensitivities and
(iv) orthogonal control of
ω
0
and Q
0
.
Assuming ideal BDI-DOCC, a routine circuit analysis yields the following VM
transfer function:
V
2
þ
V
3
s
2
V
1
þ
s
C
1
1
1
R
3
1
C
1
C
2
R
1
R
2
R
2
þ
V
0
¼
ð
:
Þ
12
156
s
C
1
1
1
R
3
1
C
1
C
2
R
2
R
1
s
2
þ
R
2
þ
þ
Using the equation (
12.156
) all standard second-order filter responses can be found
as follows:
HPF: if
V
2
¼
V
3
¼
0 (grounded) and
V
1
¼
V
in
(input signal); BPF: if
V
1
¼
V
3
¼
0
and
V
2
¼
V
in
; LPF: if
V
1
¼
V
2
¼
0 and
V
3
¼
V
in
; Notch: if
V
2
¼
0 and
V
1
¼
V
3
¼
V
in
and APF: if
V
1
¼
V
2
¼
V
3
¼
V
in
.
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