IEEE Circuits and Systems Magazine - Q2 2018 - 60

0.8
x

0.6
0.4
0.2
0
10-10

dx -1
/s
dt

x0 = 1
x0 = 0.9
x0 = 0.8
x0 = 0.7
x0 = 0.6
x0 = 0.5
x0 = 0.4
x0 = 0.3

10-5

100

7,000
6,000
5,000
4,000
3,000
2,000
1,000
0

200
100

-200
-300

8

im /mA

4

4

2
0

3
7
6

vm /V

-4
-0.5

0

-0.5

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
t /s
(a)

1
x0 = 0.9

0.8

x0 = 0.7

x

0.6

x0 = 0.5

0.4
x0 = 0.3

0.2
0

x0 = 0.1
0

0.1

0.2

0.3

0.4

0.5

t /s
(b)

im /mA

10

0

-10

x0 = 0.9
x0 = 0.7
x0 = 0.5
x0 = 0.3
x0 = 0.1

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
t /s
(c)

Figure 14. time waveforms of the two-tone voltage applied
across the nano-device (a), and of the resulting memory
state (b), and memristor current (c) for a number of initial
conditions.
60

IEEE cIrcuIts and systEms magazInE

0.1 0.2 0.3 0.4 0.5
x

6

-2
0.5

0

-100

0.1 0.15 0.5 0.25 0.3 0.35 0.4 0.45 0.5
x
(a)

105

t /s
Figure 13. memristor state response to the application of a dc negative voltage of value Vm = - 0.55 V directly across the tantalum oxide nanodevice from HP
Labs for all initial conditions in the set expressed by
x 0 ! " 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1 , .

300
dx -1
/s
dt

1

2

5
-0.25

1
0
vm /V
(b)

0.25

0.5

Figure 15. unique initial condition-independent steady-state
loci emerging in the x-xo plane (a)-where an inset provides
a detailed view of the lower left part of the xo versus x loci-
and in the v m -i m plane (b) under device stimulation with the
ac periodic voltage waveform shown in Fig. 14(a).

with a numerical example in Fig. 13, illustrating the fading memory of the tantalum oxide memristor induced
by the DC input voltage Vm = - 0.55 V for the set of initial states x 0 ! " 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1 , .
The tantalum oxide memristor nano-device from
HP Labs is subject to memory loss also under AC periodic stimulation, as reported elsewhere in the literature
([33], [42]). Here we show a new AC simulation result
revealing the formation of initial condition-independent
loci with peculiar shape on the memristor voltage-memristor current plane at steady state. A periodic signal
of the form v m = vt (m1) · sin (2 · r · f1 · t) + vt (m2) · sin (2 · r · f2 · t),
with vt (m1) = 0.3 V, f1 = 25 Hz, vt (m2) = 0.2 V, and f1 = 20 Hz,
was applied directly across the memristor, and the
Strachan's model was integrated for initial conditions
over the set x 0 ! " 0.1, 0.3, 0.5, 0.7, 0.9 , . Plots (a), (b),
and (c) of Fig. 14 respectively show the input voltage
applied across the memristor, and the nano-device
state and current response for all the aforementioned
initial conditions. It is evident that the initial condition has no influence on the steady-state oscillatory
behaviour of memristor state and current. Figs. 15(a)
and (b) illustrate the unique steady-state loci of the
state rate of change versus the state itself and of the
device current versus the device voltage, respectively.
sEcOnd quartEr 2018



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