Hardware Reference
In-Depth Information
Fig. 12.17 (a) A general
scheme of realizing an
all-pass filter (b)A
canonical VM APF
proposed by Ibrahim
et al. (Adapted from [
32
]
©
2003 Birkhauser Boston)
a
−1
V
0
Unity gain
first order
LPF/HPF
+2
V
i
b
DDCC+
V
i
y
1
y
2
V
0
z
C
y
3
x
R
Fig. 12.18 APF proposed
by Horng et al. [
37
]
DDCC
y
2
R
x
y
1
+
+
y
3
V
i
z
V
0
-
C
-
Chen
'
s SIMO-type VM biquad Figure
12.19
shows a SIMO-type VM universal
filter employing two DDCCs and five passive elements proposed by Chen.
Assuming ideal DDCCs, a routine circuit analysis of Fig.
12.19
gives the
following VM transfer functions:
1
C
2
R
2
1
C
1
C
2
R
1
R
2
s
2
1
C
1
C
2
R
1
R
2
s
þ
V
02
V
in
¼
V
03
V
in
¼
V
01
V
in
¼
;
;
;
Ds
ðÞ
Ds
ðÞ
Ds
ðÞ
ð
12
:
74
Þ
þ
1
C
2
R
2
1
R
1
R
2
C
1
C
2
s
2
s
s
2
Ds
V
04
V
in
¼
V
05
V
in
¼
and
ðÞ
Ds
ðÞ
where
R
3
C
2
R
1
R
2
1
C
1
C
2
R
1
R
2
s
2
Ds
ðÞ¼
þ
s
þ
ð
:
Þ
12
75
From the above expressions, it can be seen that an APF can be realized with
R
3
¼
R
1
. The component matching conditions can be eliminated if capacitor C
1
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