Hardware Reference
In-Depth Information
1
V
M
I
M
¼
R
M
x
ð
;
V
M
;
t
Þ
ð
:
Þ
½
15
65
dx
dt
¼
fx
ð
;
V
M
;
t
Þ
ð
:
Þ
15
66
where I
M
and V
M
are the current through and the voltage across the memristive
system respectively, R
M
is the memristance (time-dependent resistance), x is a
vector of internal state variables, f is a device-specific function and t denotes
implicit and explicit time dependence of corresponding elements. It is assumed
that a memristor realized by a physical material/system is available from which
meminductive and memcapacitive systems are to be created.
The first circuit of Fig.
15.20
(Fig.
15.20a
) transforms the time-dependent
response of a memristive system into that of a meminductive response while the
circuit of Fig.
15.20b
converts the same into time response of a memcapacitive
system. By a straight forward analysis using CCII + characterization, it turns out
that the first circuit, between ports 1 and 2 is characterized by the following
equation:
1
1
I
¼
Þ
˕
½
Lx
ð
; ˕;
t
Þ
˕
ð
:
Þ
15
67
CRR
M
x
,
ð
˕
,
=
ðÞ
RC
,
t
dx
dt
¼
fx
,
ð
˕
,
=
ðÞ
RC
,
t
Þ
ð
15
:
68
Þ
¼
R
t
0
(
V
1
(
t
0
)
V
2
(
t
0
))
dt
0
. Thus, the above equations
describe a
floating
flux-controlled meminductive system.
In a similar way, the circuit of Fig.
15.20b
is characterized by the following
equations:
where flux
˕
is given by
˕
(
t
)
L
Q
¼
ð
V
1
V
2
Þ
Cx
ð
;
ð
V
1
V
2
Þ;
t
Þ
ð
V
1
V
2
Þ
ð
15
:
69
Þ
RR
M
x
ð
;
ð
V
1
V
2
Þ;
t
Þ
dx
dt
¼
fx
ð
;
ð
V
1
V
2
Þ;
t
Þ
ð
15
:
70
Þ
The above equations imply a floating voltage-controlled meminductive system.
If dual output CCIIs are employed the number of active elements can be reduced
to two in each case to realize the same elements. Two such circuits are shown in
Fig.
15.21a
and
b
respectively. Note that while the circuits of Fig.
15.21
cannot be
realized practically those of Fig.
15.20
due to the use of only CCII + s can be
practically implemented using AD844AN ICs. The above examples demonstrate
that CCII + s have potential applications in realizing circuits involving memristive,
meminductive and memcapacitive elements.
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