Hardware Reference
In-Depth Information
Fig. 6.28 The method of
derivation of a CM biquad
filter from a passive RLC
prototype, proposed by
Senani [
24
]
CCII-
R
0
I
R0
x
z
y
CCII-
C
0
I
C0
x
z
y
I
in
L
0
CCII-
I
L0
x
y
z
1
L
0
C
0
Ds
s
1
R
0
C
0
Ds
s
2
1
L
0
C
0
Ds
s
2
Ds
þ
I
L
0
I
IN
¼
I
R
0
I
IN
¼
I
L
0
I
IN
¼
I
01
I
IN
¼
and
ðÞ
;
ðÞ
;
ðÞ
;
ðÞ
s
2
1
1
L
0
C
0
s
C
0
R
0
þ
I
02
I
IN
¼
1
C
0
R
0
þ
1
L
0
C
0
s
2
where
Ds
ðÞ
¼
þ
s
ð
6
:
41
Þ
Ds
ðÞ
It is interesting to note that depending upon the type of simulated inductor
employed, this basic scheme can give rise to a variety if CC-based universal
biquads. An exemplary circuit is shown in Fig.
6.29
which realizes all the five
functions mentioned above with L
o
¼
C
1
R
1
R
2
.
Another exemplary CM biquad realizable with only four CCIIs is shown in
Fig.
6.30
.
The various transfer functions realized by this circuit are given by:
I
IN
¼
s
1
R
2
C
1
Ds
s
þ
1
R
1
C
1
Ds
s
2
Ds
I
01
I
IN
¼
I
03
I
02
I
IN
¼
ðÞ
;
ðÞ
;
ðÞ
1
C
1
R
1
þ
1
C
1
R
1
C
2
R
2
s
2
where
Ds
ðÞ
¼
þ
s
ð
:
Þ
6
42
A LPF can be realized by adding currents I
02
and I
03
(with R
1
¼
R
2
); Notch can be
realized by obtaining I
notch
¼
I
01
+I
02
+I
03
(with R
1
¼
R
2
) and finally, an APF can
be realized by adding I
01
,I
02
, and I
03
(with R
1
¼
2R
2
)
Senani
'
s CM Universal Biquad The CM filter structure shown in Fig.
6.31
was
proposed by Senani [
25
] and offers the realization of all generic filter functions
without requiring critical matching conditions/ cancellation constraints using all
grounded passive elements.
This configuration also provides (i) availability of non-interacting controllability
of the parameters of the realized filters through grounded resistors (advantageous
for obtaining voltage control
through incorporation of FET-based voltage
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