Hardware Reference
In-Depth Information
b
3
summer
b
1
-
V
02
V
03
-1
ST
1
-1
ST
2
V
in
V
01
+
b
2
Fig. 6.9 State variable representation of the classical KHN-biquad
152
,
157
,
163
]. In this section, we present some prominent configurations belonging
to this class.
The first KHN-equivalent biquad using CCIIs was presented by Soliman in [
78
]
which was capable of realizing exactly the same transfer functions as the op-amp-
based KHN-biquad. Several alternative KHN equivalent biquads were subse-
quently reported independently by Soliman in [
83
] and one by Senani and Singh
in [
9
]. Since the latter circuit offers a number of advantages over the circuit
proposed by Soliman in [
78
], in the following, we describe the genesis of the
quoted circuit from [
167
].
The original KHN-biquad was derived from the state variable block diagram
shown in Fig.
6.9
.
The three transfer functions realized by this block diagram are given by:
T
LP
s
ðÞ
¼
ð
b
1
=
T
1
T
2
Þ=
Ds
ðÞ
;
T
BP
s
ðÞ
¼
ð
sb
1
=
T
1
Þ=
Ds
ðÞ
and T
HP
s
ðÞ
s
2
b
1
=
¼
Ds
ðÞ
s
2
where D s
ðÞ
¼
þ
sb
2
=
ð
T
1
Þþ
ð
b
3
=
T
1
T
2
Þ
ð
6
:
14
Þ
The various transfer functions of the Senani-Singh circuit [
9
] of Fig.
6.10
, with
CCIIs characterized by i
y
¼
0, v
x
¼
v
y
,i
z
¼
i
x
, are given by
R
6
=
V
01
V
in
¼
R
4
R
5
R
4
R
1
R
2
C
1
C
2
H
0
ω
0
2
T
1
s
ðÞ
¼
=
Ds
ðÞ
¼
=
Ds
ðÞ
ð
6
:
15
Þ
R
6
R
1
R
3
C
1
s
=
V
02
V
in
¼
R
3
R
5
H
0
ω
0
Q
0
T
2
s
ðÞ
¼
=
Ds
ðÞ
¼
Ds
ðÞ
ð
6
:
16
Þ
and
s
2
V
03
V
in
¼
R
6
R
5
H
0
s
2
T
3
s
ðÞ
¼
=
Ds
ðÞ
¼
=
Ds
ðÞ
ð
6
:
17
Þ
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