Hardware Reference
In-Depth Information
V 0
V in ¼
R 4
ð
6
:
6
Þ
k 2 s 2 C 1 C 5 R 2 R 3 R 4 þ
s 4 C 5 R 2 R 4 þ
f
C 1 R 4 R 2 þ
ð
R 3
Þ
g þ
ð
R 2 þ
R 4
Þ
Figure 6.5c also uses a CC B and can provide an inverting HPF response with the
transfer function given by
V 0
V in ¼
s 2 C 2 C 3 R 1 R 4 R 5
2 R 4
ks 2 C 2 C 3 R 1 R 4 R 5 þ
sC 3 4 R 1 R 4 þ
f
ð
R 1 R 5 þ
R 4 R 5
Þ þ
C 2 R 4 R 5
g þ
ð
:
Þ
6
7
A generalized single-CC configuration was proposed by Metin et al. in [ 6 ] from
where a LPF/BPF, a HPF/BPF and Notch/APF/HPF were realizable as special
cases. Two specific configurations from [ 6 ] are shown in Fig. 6.6 .
For the circuit of Fig. 6.6a , a straight forward analysis assuming CCI+ to be
characterized by i y ¼
i x, v x ¼
v y and i z ¼ i x , gives the two transfer functions realiz-
able by the circuit as
s 2 C 3 C 4 R 1 R 4 þ
V 01
V in ¼
sC 3 R 1
ð
R 4
Þ
ð
6
:
8
Þ
s 2 C 3 C 4 R 1 R 4 þ
sC 3 R 1
ð
R 4
Þ þ
2 sC 4 R 4 þ
2
V 02
V in ¼
sC 3 R 4
ð
6
:
9
Þ
s 2 C 3 C 4 R 1 R 4 þ
sC 3 R 1
ð
R 4
Þ þ
2 sC 4 R 4 þ
2
Thus, for R 1 ¼
R 4 ,Eqs.( 6.8 ) and ( 6.9 ) will provide HPF and BPF responses
respectively.
Similarly, for the circuit of Fig. 6.6b , the two transfer functions are given as
2 s 2 C 1 C 2 R 3 R 4 þ
V 01
V in ¼
sC 2
ð
C 1
Þ
R 4 þ 1
ð
6
:
10
Þ
2 s 2 C 1 C 2 R 3 R 4 þ
sC 2
ð
C 1
Þ
R 4 þ
2 sC 1 R 3 þ
1
2 s 2 C 1 C 2 R 3 R 4 þ
V 02
V in ¼
sC 2
ð
C 1
Þ
R 4
ð
:
Þ
6
11
2 s 2 C 1 C 2 R 3 R 4 þ
sC 2
ð
C 1
Þ
R 4 þ
2 sC 1 R 3 þ
1
Thus, for C 1 ¼
C 2 , the transfer functions in Eqs. ( 6.10 ) and ( 6.11 ) can realize notch
and HPF responses, respectively. Furthermore, if we select C 1 ¼
2C 2 and R 4 ¼
2R 3 ,
Eq. ( 6.10 ) can provide an APF response also.
Using a CMOS CCI, pole frequencies of the order of 1.8 and 3.98 MHz have
been easily realised in practice.
6.2.3 Multiple-CC Multifunction Biquads
In this section, we present a number of multiple-CC biquads capable of realizing
three or more filter functions simultaneously under different conditions and/or at
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