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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