2.2 Ideal Memristors and Non-volatile Memories
45
q = ˆ
q(ϕ)
v s (t)
i(t)
v(t)
(a)
(b)
(c)
(d)
Q(t 0 )
Q(t 0 + ΔT )
ϕ Q = EΔT
q Q
ϕ
q
t 0
t 0 + ΔT
ΔT
E
t
v s (t)
t 0
t 0 + ΔT
EΔT
t
ϕ(t)
Fig. 2.17 An experiment to show that an ideal memristor acts as a nonvolatile memory. (a)
Elementary circuit with memristor and voltage source. (b) Characteristic of the memristor. (c)
Pulse applied via a voltage source and (d) time-domain behavior of memristor flux
Example 2.10 (Memristor as an Analog Memory) Suppose that the CR of a passive
flux-controlled memristor is given by a monotonically increasing cubic function
ˆ
q(ϕ) =
1
3
ϕ
3 .
The corresponding memductance
ˆ
q
(ϕ) = ϕ
2
assumes a continuum of values in the interval [0, +∞). The memristance ˆ
q (ϕ)
vs. state ϕ map is shown in Fig. 2.18; this allows one to tune the memductance
continuously by using short voltage impulses (cf. Example 2.11). In conclusion,
such an ideal memristor is nonvolatile and continuously tunable via pulses and
basically corresponds to an analogue, variable, and programmable resistor.