IEEE Circuits and Systems Magazine - Q2 2018 - 16
The type and the value of the energy storage element can be determined
by analyzing the frequency response of the small-signal admittance
function and by specifying the oscillation frequency.
G 0 is a scaling constant used to fit any desired memductance scale of the memristor. In this paper, we choose
G 0 = 1 for pedagogical reasons. In practice, the scaling
constant G 0 can be chosen such that the current will be
measured in mA, or such that the inductance value in
the small-signal circuit model will not be excessive. The
memristor state, current and voltage are denoted as x, i,
and v, respectively.
A. Dynamic Route and Pinched Hysteresis Loop
The dynamic route is a powerful tool valid for analyzing
the dynamics of nonlinear ordinary differential equations. It was invented by Chua [5], and has been applied
in numerous 1-st order nonlinear systems [6], [7]. The
dynamic route of (3) for v = 0 is shown in Fig. 2 by adding arrowheads indicating the direction of motion of the
state variable x, from any initial state x (0), when the
4-lobe Chua corsage memristor is short-circuited (v = 0) .
The direction of motion (to the right if dx/dt v = 0 2 0, and
to the left if dx/dt v = 0 1 0 ) is indicated by arrowheads on
the power-off-plot (POP) defined by:
dx
dt
v=0
= ft(x) = 59 - x + x - 20 - x - 40
+ x - 65 - x - 95 ,
(5)
as shown in Fig. 2. For any initial states x (0) which
specifies a point on the Power-off plot (POP) above the
x -axis where dx/dt > 0, the state variable x (t) increases with time and moves to the right as shown by the
blue arrowheads moving towards the right. In contrast,
for any x (0) which specifies a point on the POP below
the x -axis where dx/dt < 0, x (t) decreases with time
and moves to left as depicted by green arrowheads.
At dx/dt = 0, ft(x) intersects the x -axis at five points;
dx = f^(x )
30 dt v = 0
25
20
Red, blue, and purple circle denotes stable equilibrium points.
Green and magenta circle denotes unstable equilibrium points.
15
10
5
Q0
-20 -13 -6 0 1
-5
Q1
Q2
Q3
Q4
x
8 15 22 29 36 43 50 57 64 71 78 85 92 99 106 113 120
x = 31
x = 81
-10
-15
-20
Figure 2. dynamic route along the Power-off Plot (POP) of the 4-lobe chua corsage memristor.
16
IEEE cIrcuIts and systEms magazInE
sEcOnd quartEr 2018
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