28
2 Fundamental Properties of Mem-Elements
of memristive devices and systems are discussed in Sects. 2.3 and 2.4, respectively.
A brief discussion on fundamental properties of memcapacitors and meminductors
is provided in Sect. 2.5.
Finally, Appendix 1 of this chapter is concerned with the technological realization of real passive electronic devices (HP memristor, Resistive RAM, PhaseChange Memories—PCMs, Magnetic RAM) whose behavior can be described in
terms of a memristor. Materials and physical phenomena underlying the memristor
behavior and the historical links between memristor and resistive switching devices
are briefly discussed. The appendix ends with a discussion on the applications of
memristor devices in nonlinear complex circuits and systems, including neuromorphic architectures and nonlinear oscillators.
2.1 Ideal Memristor: Basic Properties and Signatures
In this section, and in the next one, we refer to ideal memristors only. In Chap. 1 an
ideal memristor has been defined by the CR f M (ϕ, q) = 0 in the flux-charge (ϕ, q)domain. In the charge-controlled case, the nonlinear characteristic can be explicitly
written as
ϕ = ˆ
ϕ(q).
(2.1)
In the (v, i)-domain a charge-controlled ideal memristor is characterized by the
state-dependent Ohm’s Law
v = ˆ
ϕ
(q)i
(2.2)
where
dq
dt
= i.
(2.3)
Dually, in the flux-controlled case we have q = ˆ
q(ϕ) and the ideal memristor obeys
i = ˆ
q
(ϕ)v
(2.4)
where
dϕ
dt
= v.
(2.5)
Recall that M(q) = ˆ
ϕ (q) and W (q) = ˆ
q (ϕ) are named memristance and
memductance, respectively.
Next, chief properties and peculiar signatures of ideal memristors are summarized. Readers interested in further details can also refer to [1–6].
2 Fundamental Properties of Mem-Elements
of memristive devices and systems are discussed in Sects. 2.3 and 2.4, respectively.
A brief discussion on fundamental properties of memcapacitors and meminductors
is provided in Sect. 2.5.
Finally, Appendix 1 of this chapter is concerned with the technological realization of real passive electronic devices (HP memristor, Resistive RAM, PhaseChange Memories—PCMs, Magnetic RAM) whose behavior can be described in
terms of a memristor. Materials and physical phenomena underlying the memristor
behavior and the historical links between memristor and resistive switching devices
are briefly discussed. The appendix ends with a discussion on the applications of
memristor devices in nonlinear complex circuits and systems, including neuromorphic architectures and nonlinear oscillators.
2.1 Ideal Memristor: Basic Properties and Signatures
In this section, and in the next one, we refer to ideal memristors only. In Chap. 1 an
ideal memristor has been defined by the CR f M (ϕ, q) = 0 in the flux-charge (ϕ, q)domain. In the charge-controlled case, the nonlinear characteristic can be explicitly
written as
ϕ = ˆ
ϕ(q).
(2.1)
In the (v, i)-domain a charge-controlled ideal memristor is characterized by the
state-dependent Ohm’s Law
v = ˆ
ϕ
(q)i
(2.2)
where
dq
dt
= i.
(2.3)
Dually, in the flux-controlled case we have q = ˆ
q(ϕ) and the ideal memristor obeys
i = ˆ
q
(ϕ)v
(2.4)
where
dϕ
dt
= v.
(2.5)
Recall that M(q) = ˆ
ϕ (q) and W (q) = ˆ
q (ϕ) are named memristance and
memductance, respectively.
Next, chief properties and peculiar signatures of ideal memristors are summarized. Readers interested in further details can also refer to [1–6].