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In-Depth Information
DXCCII
DXCCII
I
HP
z
p
x
p
z
p
Y
M
2
V
c4
M
1
V
c2
x
p
2
z
p
x
n
M
4
1
I
BP
z
n
z
n
V
c1
x
n
Y
I
in
C
2
C
1
DXCCII
I
LP
x
p
z
p
M
3
V
c3
3
x
n
z
n
Y
Fig. 12.39 CM universal biquad filter proposed by Minaei [
111
]
, where V
Tn
is the threshold voltage,
K
ni
¼ ʼ
n
C
ox
L
i
is
the transconductance parameter of the ith NMOS transistor and V
Ci
is the
D.C. control voltage through which resistance value of transistors can be controlled.
The circuit of Fig.
12.39
contains two integrators and a summer/subtractor hence
the circuit is an equivalent of KHN-biquad.
A straight forward circuit analysis of Fig.
12.39
yields the following CM filter
responses:
1
K
ni
V
Ci
V
Tn
obtained as:
R
i
¼
ð
Þ
R
1
s
2
Ds
R
4
4
R
1
þRð Þ
C
1
C
2
R
1
R
2
R
3
Ds
2
R
1
þR
4
ð
Þ
I
in
¼
s
I
LP
I
in
¼
I
BP
and
I
HP
C
1
R
1
R
2
I
in
¼
ð
12
:
139
Þ
ðÞ
;
Ds
ðÞ
ðÞ
where
s
2
R
1
þ
Rð Þ
C
1
R
1
R
2
þ
Rð Þ
C
1
C
2
R
1
R
2
R
3
4
R
1
þ
s
2
Ds
ðÞ¼
þ
ð
12
:
140
Þ
Notch and APF can also be realized by adding relevant output currents for the
condition R
1
¼
ω
0
,Q
0
and bandwidth (
ω
0
/Q
0
) can be
R
4
. The filter parameters
obtained as:
s
C
1
R
1
R
2
C
2
R
3
R
1
þ
r
R
1
þ
R
4
C
1
C
2
R
1
R
2
R
3
,
ω
0
2
R
1
þ
ð
R
4
Þ
ω
0
¼
2
,
Q
0
¼
Q
0
¼
;
ð
12
:
141
Þ
ð
R
4
Þ
C
1
R
1
R
2
From the above equation (
12.141
),
ω
0
can be controlled by R
3
without disturbing
bandwidth, also
ω
0
can be tuned without changing Q
0
through R
2
xR
3
keeping the
ratio of R
2
/R
3
constant and Q
0
can be varied through R
2
/R3 without keeping R
2
xR
3
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