IEEE Circuits and Systems Magazine - Q2 2018 - 45
by the derivative of voltage. Since not only the voltage but
consequently also the current increase when the frequency
increases, the homothety fingerprint also holds for this case.
Note that the above situation constitutes in fact a violation of the fingerprints from [19]. When the frequency
increases and the amplitude of the driving voltage remains fixed, the flux tends to zero, but the resistance
is still periodically switched between Ron and R off. As a
result, the pinched hysteresis loop remains unchanged
for f " 3. This mode thus violates the Fingerprint No. 2
i
Resistor
q
from [19] (Hysteresis lobe area decreases as frequency increases) and also the Fingerprint No. 3 from [19]
(Pinched hysteresis loop shrinks to a single-valued
function at infinite frequency). This conforms to the fact
that the given element is not a memristor.
III. Fingerprint of Preserving the
Constitutive Relation
The analyzed element is a memristor, if it preserves the
flux-charge constitutive relation in all circumstances.
i
q
Memristor
σ
σ
ρ
ϕ
i
ν
ρ
ϕ
ν
ϕ
ν
i
Inductor
Meminductor
q
q
σ
σ
ρ
ϕ
ν
i
ρ
i
Capacitor
q
q
σ
σ
Memcapacitor
ρ
ϕ
ν
ρ
ϕ
ν
Figure 8. Waveforms of voltages (v), currents (i), integrals of voltages-fluxes ({), integrals of currents-charges (q), integrals of
fluxes - tIF ( t), and integrals of charges -tIq (v), sensed on all the elements in the circuit in Fig. 7. the left side contains the
characteristics of classical r, L, C elements, the right side the characteristics of their memory versions. the unambiguous constitutive relations, which identify the corresponding fundamental element, are highlighted in color.
SECOND quartEr 2018
IEEE CIrCuItS aND SyStEmS magazINE
45
Table of Contents for the Digital Edition of IEEE Circuits and Systems Magazine - Q2 2018
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