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I out
y
CCI+ z
x
y
z
CCII-
y
I 1
x
y
z
CCII-
I 2
I 3
z
x
CCI+
x
R 3
C 2
C 1
R 4
Fig. 6.39 Universal active CM filter proposed by Chang et al. [ 34 ]
From the above equation, the various filter responses can be obtained as follows:
HPF
:
I i3 ¼
I i2 ¼
0, I i1 ¼
I in ;
BPF
:
I i1 ¼
I i3 ¼
0, I i2 ¼
I in ;
LPF
:
I i1 ¼
I i2 ¼
0 and I i3 ¼
I in ;
Notch
:
I i2 ¼
0, I i1 ¼
I i3 ¼
I in and R 5 ¼
R 6 ;
and
APF
I i1 ¼
I i2 ¼
I i3 ¼
I in , and R 2 ¼
R 1 :
:
Chang, Chien and Wang CM Biquad The filter configuration shown in Fig. 6.39
was proposed by Chang et al. in [ 34 ] which uses two CCI+ and two CCII
with two
grounded resistors and two grounded capacitors. The circuit is capable of yielding
all the five generic filter responses without any component matching or sign
inversion of any input current(s).
Assuming ideal CCs, analysis of the circuit gives the following expression for
the output current in terms of the various input currents:
C 2 R 4 I 2 þ
I 1
s 2 I 3
1
1
C 1 C 2 R 3 R 4
s
I out ¼
C 2 R 6
ð 6 : 59 Þ
1
1
C 1 C 2 R 3 R 4
s 2
þ
s
þ
From Eq. ( 6.59 ), the following filter functions can be obtained: LPF: I 3 ¼
I 2 ¼
0,
I 1 ¼
I in ; BPF: I 1 ¼
I 3 ¼
0, I 2 ¼
I in ; HPF: I 1 ¼
I 2 ¼
0 and I 3 ¼
I in ; Notch: I 2 ¼
0,
I 1 ¼
I in .
This circuit offers several advantages such as: low sensitivities, use of grounded
capacitors and versatility to realize any type of active filter transfer function.
I 3 ¼
I in and R 5 ¼
R 6 ; and APF: I 1 ¼
I 2 ¼
I 3 ¼
6.2.4 Third Order Filters
Several authors have considered realization of third order Butterworth filters using
CCs [ 35 , 36 , 48 - 50 , 81 , 96 , 113 ]. Figure 6.40 shows two third order CM
Butterworth filter structures employing equal-valued capacitors and resistors with
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