Hardware Reference
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CCII
CCII
y
1
+
z
y
-
x
z
C
x
CR
1
R
2
R
2
CCII
z
2
1
2
R
1
x
+
y
Fig. 5.37 Lossless FI circuit proposed by Senani [
28
]
5.3.7 A Family of Three-CC Floating Inductor/FDNR
Simulators
There is an important result in circuit theory [
163
,
164
] related to gyrators realiz-
able using nullors and resistors, which states that if only two nullors are permitted
then the realization of a gyrator requires at least five resistors (impedances) and if
only three resistors are allowed then at least three nullors will be required for the
same purpose.
There is another old but less well known theory [
168
] as per which an impedance
converter, with respect to some port, can be looked upon as an impedance converter
with respect to some other port and vice versa.
In view of the above mentioned results, the FGPIC/FGPII circuits of the previ-
ous section can be looked upon as two nullor five impedance circuits recalling that
each CCII
is, in fact, a three-terminal nullor. It is, therefore, apparent that there
should be a class of three-nullor three impedances, converters and inverters. More
specifically, this means that a floating GPIC/GPII network should also be realizable
by three CCs and no more than three passive elements. This section presents a
variety of such three-CC based FGPIC/FGPII configurations or special cases
thereof, which have been presented in the literature as lossless floating inductors
or lossless floating FDNRs.
A floating lossless inductance using only three CCs and only three passive
elements was first proposed by Senani in 1980 [
28
] which is shown in Fig.
5.37
.
The circuit realizes a lossless floating inductance of value L
eq
¼
CR
1
R
2
between
ports 1 and 2.
A floating ideal FDNR was reported by Nandi et al. [
37
] in 1983. Assuming
CCIIs to be characterized by i
y
¼
0, v
x
¼
v
y
and i
z
¼
h
k
i
x
(k
¼
1, 2, 3) where,
ideally, h
¼
1 and the sign associated with h determines the polarity of the CCII
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