Hardware Reference
In-Depth Information
The various design equations are given by:
R
n
r
n
;
R
n
1
r
n
1
¼
a
1
b
1
;
R
n
2
r
n
2
¼
a
2
b
2
;
:::::
;
a
n
1
b
n
1
¼
R
1
r
1
;
a
n
b
n
¼
a
0
¼
1
ð
12
:
150
Þ
C
n
R
n
b
2
b
n
1
b
n
2
¼
b
n
b
n
1
¼
b
0
¼
1
;
b
1
¼
b
1
¼
C
n
1
R
n
1
;...
:
;
C
2
R
2
;
C
1
R
1
ð
12
:
151
Þ
2
I
ABCn
V
T
2
I
abcn
where
R
n
¼
V
T
are the resistances on port-X of nth translinear CFCCII
p
,
I
ABCn
and I
abcn
are the auxiliary bias currents of the nth translinear CFCCII
p
and V
T
is the thermal voltage. An interesting feature of this structure is that the coefficients
of numerator and denominator of nth order transfer function are independently
controllable of each other.
,
r
n
¼
12.2.10 Filter Design Using OFCC
Like a CCII and a CFOA, an operational floating CC (OFCC) is yet another
building block which was proposed by Toumazou, Payne and Lidgey with the
objective of creating alternative building blocks which overcome the well-known
bandwidth conflict of the traditional VM op-amp. It has been demonstrated in an
earlier chapter of this monograph that OFCCs indeed make it possible to realize all
the basic controlled sources with a minimum number of active and passive elements
without requiring any component matching and within the assured property of
maintaining same constant bandwidth even under the variability of the gain.
An ideal OFCC can be characterized by the following matrix:
2
4
3
5
2
4
3
5
2
4
3
5
i
y
v
x
v
w
i
zþ
i
z
00000
10000
0
Z
t
000
00100
00
v
y
i
x
i
w
v
z
þ
v
z
¼
ð
12
:
152
Þ
100
where Z
t
is the impedance between X and W ports.
In this section, we outline another application of the OFCCs in realizing a
universal biquad employing OFCCs.
Ghallab, Badawy, El-Ela and El-Said biquad Figure
12.43
shows a universal
MISO-type VM fitter configuration proposed by Ghallab and Badawy in [
122
]
using two OFCCs, two capacitors and five resistors.
Assuming ideal OFCCs, a straight forward circuit analysis of Fig.
12.43
yields
the following relation between the inputs and the output of the circuit:
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