2.3 Memristive Devices and Systems
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2.3.2 Memory Memristive Devices and Power-Off-Plot (POP)
Let us discuss in more detail memristor devices behaving as a volatile or a
nonvolatile memory memristor. Consider a voltage-controlled memristive device
i = G(x, v)v
where
dx(t)
dt
= g(x(t), v(t))
and suppose for simplicity there is a single internal state variable x ∈ R.
A memristive device acts as a:
• nonvolatile memory if and only if it exhibits at least two stable states when power
is switched off
• volatile memory if and only if there is only one stable state when power is
switched off.
Namely, set v = 0 and consider the scalar differential equation
dx
dt
= g(x, 0).
(2.17)
The memristor is nonvolatile if and only if Eq. (2.17) has at least two different stable
EPs x A and x B , i.e., g(x A , 0) = 0 and g(x B , 0) = 0, with x A = x B , whereas is
volatile if there is only one stable EP (e.g., x A ).
A graphical approach based on the dynamic route (cf. Chap. 4) permits to
understand if the memristive device is volatile or nonvolatile. The dynamic route
corresponds to the plot of g(x, 0) in (2.17) in the plane (x, ˙
x); such dynamic route
goes under the name Power-Off-Plot (POP). The POP is an extremely useful concept
to understand the qualitative behavior of the scalar state variable x and to locate EPs.
Let us show the concept of POP in an ideal memristor.
Example 2.13 (POP in Ideal Memristor) The POP of an ideal flux-controlled
memristor q = ˆ
q(ϕ), i.e.,
i = ˆ
q
(ϕ)v
˙
ϕ = v
(2.18)
corresponds to the equation ˙
ϕ = 0, that is, the ϕ-axis in the plane (ϕ, ˙
ϕ). Hence, the
POP makes clear the existence of a continuum of stable EPs (i.e., any value of ϕ).
The next example illustrates how to use the POP to characterize volatile and
nonvolatile memristive devices.
51
2.3.2 Memory Memristive Devices and Power-Off-Plot (POP)
Let us discuss in more detail memristor devices behaving as a volatile or a
nonvolatile memory memristor. Consider a voltage-controlled memristive device
i = G(x, v)v
where
dx(t)
dt
= g(x(t), v(t))
and suppose for simplicity there is a single internal state variable x ∈ R.
A memristive device acts as a:
• nonvolatile memory if and only if it exhibits at least two stable states when power
is switched off
• volatile memory if and only if there is only one stable state when power is
switched off.
Namely, set v = 0 and consider the scalar differential equation
dx
dt
= g(x, 0).
(2.17)
The memristor is nonvolatile if and only if Eq. (2.17) has at least two different stable
EPs x A and x B , i.e., g(x A , 0) = 0 and g(x B , 0) = 0, with x A = x B , whereas is
volatile if there is only one stable EP (e.g., x A ).
A graphical approach based on the dynamic route (cf. Chap. 4) permits to
understand if the memristive device is volatile or nonvolatile. The dynamic route
corresponds to the plot of g(x, 0) in (2.17) in the plane (x, ˙
x); such dynamic route
goes under the name Power-Off-Plot (POP). The POP is an extremely useful concept
to understand the qualitative behavior of the scalar state variable x and to locate EPs.
Let us show the concept of POP in an ideal memristor.
Example 2.13 (POP in Ideal Memristor) The POP of an ideal flux-controlled
memristor q = ˆ
q(ϕ), i.e.,
i = ˆ
q
(ϕ)v
˙
ϕ = v
(2.18)
corresponds to the equation ˙
ϕ = 0, that is, the ϕ-axis in the plane (ϕ, ˙
ϕ). Hence, the
POP makes clear the existence of a continuum of stable EPs (i.e., any value of ϕ).
The next example illustrates how to use the POP to characterize volatile and
nonvolatile memristive devices.