Hardware Reference
In-Depth Information
þ
1
R
2
C
2
1
C
1
C
2
R
1
R
2
s
2
Ds
ðÞ¼
þ
s
ð
12
:
186
Þ
On the other hand, I
01
and I
03
in terms of input currents have been obtained as:
n
C
2
R
2
o
C
2
R
2
I
1
s
2
1
1
C
1
C
2
R
1
R
2
1
1
C
1
C
2
R
1
R
2
þ
s
þ
I
2
s
I
3
I
01
¼
ð
12
:
187
Þ
Ds
ðÞ
C
2
R
2
1
1
C
1
C
2
R
1
R
2
I
2
s
I
3
I
03
¼
ð
:
Þ
12
188
Ds
ðÞ
From the above equations, the following five generic filter responses can be
derived: LPF: I
1
¼
I
2
¼
0, I
3
¼
I
in
and I
out
¼
I
01
¼
I
03
; BPF: I
1
¼
I
3
¼
0, I
2
¼
I
in
and
I
out
¼
I
01
¼
I
03
;I
1
¼
I
2
¼
0, HPF: I
1
¼
I
2
¼
I
3
¼
I
in
and I
out
¼
I
01
; Notch: I
2
¼
0,
I
1
¼
I
3
¼
I
in
and I
out
¼
I
01
; and APF: I
1
¼
I
2
¼
I
in
,I
3
¼
0 and I
out
¼
I
01
+I
03
. The
expression for D(s) remains same as equation (
12.190
).
Abuelma
'
atti-Bentrcia mixed-mode biquad The biquads described so far
attempt to realize all the five basic functions either in VM (where both input and
output variables are voltages) or in CM (where the operating variables are currents).
Apart from VM and CM biquads a number of authors have also described universal
biquads in which input variable is current but output variable is voltage (the
resulting circuits being called transimpedance type biquads) or circuits in which
input is voltage but outputs are currents (the resulting circuits are called as trans
admittance biquads). There have been several attempts in evolving universal
biquads using CCs which realize all the basic five filtering functions in two or
more of the four possible modes namely, VM, CM transimpedance mode (TIM),
and trans admittance mode(TAM) such circuits are referred to as mixed mode
universal biquads. In the following we describe number of prominent circuit
configurations of this type.
Figure
12.53
shows a novel mixed-mode filter proposed by Abuelma
atti and
Bentrcia [
134
] employing five CCIIs, seven resistors and two grounded capacitors.
All standard second-order filter responses can be obtained in both CM and VM from
the same topology. The bandwidth and angular frequency can be controlled elec-
tronically independently. Assuming ideal CCIIs, a routine circuit analysis gives:
'
N
r
s
and
C
1
C
2
R
1
R
5
R
6
R
4
R
7
R
2
ðÞ
D
r
s
V
out
¼
ðÞ
N
r
s
ð
12
:
189
Þ
C
1
C
2
R
1
R
5
R
6
R
4
R
2
ðÞ
D
r
s
I
out
¼
ðÞ
where
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