Hardware Reference
In-Depth Information
many as possible of the following desirable features: (i) employment of a minimum
possible number of capacitors preferably grounded as desirable for integrated
circuit implementation (ii) availability of sequential/independent tunability of as
many characteristic parameters (namely, radian frequency
ω
0
, quality factor Q
0
and
gain H
0
) as possible (iii) ease of cascadability-which can be attained by infinite
input impedance and/or zero output impedance in case of the voltage-mode con-
figurations and by infinite output impedance and/or zero input impedance in case of
the current-mode configurations (iv) employment of a canonic number of resistors
for the realization of the intended functions and (v) availability of multifunction
capability wherever feasible.
6.2.1 Single-CC First Order All Pass Filters
For an economic and efficient design, it is often necessary to keep the number of
passive as well as active elements as small as possible to reduce the power
consumption, noise, space and cost. For this purpose, therefore, active filter circuits
realizable with a single CC are of interest. In the literature on CCs, there exist a
wide variety of single-CC filters, for instance, see [
1
-
6
,
11
,
30
,
42
-
46
,
53
,
56
-
60
,
62
,
64
,
68
,
69
,
73
,
74
,
139
,
151
,
153
,
154
,
166
].
A lot of attention has been given in the CC literature on realizing all pass filters
for instance, see [
2
,
3
,
5
,
12
,
16
,
22
,
52
,
60
,
83
,
87
,
100
,
129
,
134
,
148
,
149
,
156
]
because of their utility as phase shifters and their use in the design of oscillators.
Higashimura and Fukui [
1
] demonstrated that a first order all pass network can
be realized by a single CCII
along with only three resistors and a single capacitor.
Two of their prepositions are shown in Fig.
6.1
. Assuming CCII
to be character-
ized by i
y
¼
0, v
x
¼
v
y
and i
z
¼
i
x
, the open circuit voltage ratio transfer function
for these circuits is given by
V
out
V
in
¼
1
sCR
Ts
ðÞ
¼
ð
6
:
1
Þ
þ
sCR
1
where the + sign corresponds to the circuit of Fig.
6.1a
and the
sign corresponds to
the circuit of Fig.
6.1b
. The circuit of Fig.
6.1a
can provide a phase shift from 0
to
180
whereas that of Fig.
6.1b
can provide a phase shift from +180
to 0
. Both
the circuits have ideally infinite input impedance which is helpful for easy cascad-
ing without requiring any impedance-matching device.
The same authors presented in 1990 [
2
] two equally simple configurations for
realizing first order all pass functions in current-mode with the feature of the
availability of ideally infinite output impedance and thereby, facilitating easy
cascadability. These circuits from [
2
] are shown in Fig.
6.2
.
Assuming CCII
to be characterized by i
y
¼
0, v
x
¼
v
y
and i
z
¼
i
x
, the current
transfer functions for the two circuits are given by
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