2.1 Ideal Memristor: Basic Properties and Signatures
35
Fig. 2.4 Waveforms of v(t), ϕ(t), q(t), and i(t). The example is adapted from [8]
The aim is to obtain the CR of D from electrical variables (voltage/flux and
current/charge) measured at the terminals of circuit elements. In particular, we use
a voltmeter to measure voltage v(t) on the memristor and an ammeter to measure
current i(t) through the memristor. By definition, the time integral 3 of the voltages
v s (t) and v(t) gives the fluxes ϕ s (t) and ϕ(t), respectively; the charge q(t) through
the circuit is derived from the time integral of i(t). Finally, for each one of the three
circuit elements in Fig. 2.6 the “admissible pairs” can be expressed in terms of either
current and voltage or charge and flux.
Let us consider the following case-studies (all variables are expressed in a
coherent system of units):
• v s (t) is a zero-mean triangular waveform with unitary amplitude and period T =
4. The corresponding flux ϕ s (t), assuming ϕ s (0) = 0, is reported in Fig. 2.7a. The
current i(t) and its time integral q(t), assuming q(0) = 0, are shown in Fig. 2.7b,
while Fig. 2.7c reports v(t) and ϕ(t), assuming ϕ(0) = 0. Let us focus on the
admissible pairs of D, namely (v, i) in the voltage-current domain and (ϕ, q) in
the flux-charge domain, respectively, whose representations in the corresponding
domain are shown in Fig. 2.8a, b. It turns out that (ϕ(t), q(t)) traces back and
forth a unique nonlinear (cubic) characteristic ϕ = q 3 /3 defining the CR of
an ideal (charge-controlled) memristor, whereas (v(t), i(t)) produces a pinched
hysteresis loop.
3 The time integral of electrical variables can be also measured via ballistic instruments (see
Sect. 1.1.2).
35
Fig. 2.4 Waveforms of v(t), ϕ(t), q(t), and i(t). The example is adapted from [8]
The aim is to obtain the CR of D from electrical variables (voltage/flux and
current/charge) measured at the terminals of circuit elements. In particular, we use
a voltmeter to measure voltage v(t) on the memristor and an ammeter to measure
current i(t) through the memristor. By definition, the time integral 3 of the voltages
v s (t) and v(t) gives the fluxes ϕ s (t) and ϕ(t), respectively; the charge q(t) through
the circuit is derived from the time integral of i(t). Finally, for each one of the three
circuit elements in Fig. 2.6 the “admissible pairs” can be expressed in terms of either
current and voltage or charge and flux.
Let us consider the following case-studies (all variables are expressed in a
coherent system of units):
• v s (t) is a zero-mean triangular waveform with unitary amplitude and period T =
4. The corresponding flux ϕ s (t), assuming ϕ s (0) = 0, is reported in Fig. 2.7a. The
current i(t) and its time integral q(t), assuming q(0) = 0, are shown in Fig. 2.7b,
while Fig. 2.7c reports v(t) and ϕ(t), assuming ϕ(0) = 0. Let us focus on the
admissible pairs of D, namely (v, i) in the voltage-current domain and (ϕ, q) in
the flux-charge domain, respectively, whose representations in the corresponding
domain are shown in Fig. 2.8a, b. It turns out that (ϕ(t), q(t)) traces back and
forth a unique nonlinear (cubic) characteristic ϕ = q 3 /3 defining the CR of
an ideal (charge-controlled) memristor, whereas (v(t), i(t)) produces a pinched
hysteresis loop.
3 The time integral of electrical variables can be also measured via ballistic instruments (see
Sect. 1.1.2).