Hardware Reference
In-Depth Information
thereby leading to D-R-mutators and M-R-mutators. More recently, mutators have
been defined even to convert memresistive elements into memcapacitive and
meminductive elements.
A type 1 C-R mutator is characterized by
v
1
¼
CR
di
2
v
2
and
i
1
¼
dt
while type
Cdv
2
dt
2 C-R mutator is characterized by
v
1
¼
i
2
R
,
i
1
¼
. Similarly, a type 1 L-R
CR
dv
2
mutator, is characterized by
v
1
¼
dt
,
i
1
¼
i
2
while type 2 L-R mutator is
CR
1
R
2
di
2
V
2
characterized by
v
1
¼
dt
,
i
1
¼
R
3
. Lastly, type 1 L-C- mutator is character-
V
2
R
3
ized by
v
1
¼
i
2
R
,
i
1
¼
while type 2 L-C mutator is characterized by
Z
C
2
R
2
dv
2
1
C
1
R
1
v
1
¼
i
2
dt
.
From a careful inspection of the above equations, it is not difficult to infer that it
should be possible to realize C-R mutators of both types, L-R mutator type 1 and
LC-mutator type 1 by using only two CCIIs while the remaining two mutators
namely, L-R mutator type 2 and L-C mutator type 2 may need at least three CCIIs.
Rotators
:R
dt
,
i
1
¼
,L
,orC
rotators are active 2-port elements which can rotate,
i
v
curve by a prescribed angle of rotation about the origin.
Reflectors
: A reflector is an active element which can reflect a given
i
v
,
ˆ
i
or
q
v
,
ˆ
i
or
q
v
curve with respect to a straight line (through the origin) having an angle
Ɵ
with the horizontal axis. Corresponding to the three curves under consideration, the
reflectors can be classified into three types, namely R
reflector.
Scalars: A scalar is a 2-port element which can scale the current, voltage or
power of a device or a nonlinear element. Thus, there are three basic types of scalars
namely, a voltage scalar, a current scalar and a power scalar. Scalars can also be
used to scale
,L
or C
ˆ
i
curve of a nonlinear inductor or
q
v
curve of a nonlinear
capacitor.
Since the introduction of the second generation CC by Sedra and Smith in 1970,
they were the first to demonstrate in [
28
] that CCII
appear to be very interesting
building blocks for realizing mutators, reflectors and rotators. Subsequently, the
problem of realizing mutators using current conveyors has been widely investigated
and a larger number of CC-based realisations of mutators are now known.
Some representative realisations of the four of the above mentioned six basic
mutator types are shown in Fig.
15.19
.
We have enumerated here only the CC-II based realisations proposed by Sedra
and Smith in [
28
] to give a glimpse of the type of circuits which make mutators. For
further studies the readers are referred to references [
29
-
35
] and those cited therein.
15.12 Memcapacitance and Meminductance Emulators
With the announcement of the practical realization of a memristive device by
Strukov et al. in 2008 [
36
] from Hevelett-Packard laboratories, the fourth funda-
mental element
Memristor
predicted by Chua in 1971 [
37
] became a very
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