2.4 Genealogy of Memristor Devices
69
where σ 0 , A, k B , ω, d are parameters and k B is the Boltzmann constant. The state
variable is given by the temperature T which obeys Newton’s law of cooling
dT
dt
=
iv
C th
−
T − T amb
C th R th (T )
where T amb = 300 K is the ambient temperature, C th is the thermal capacitance,
and R th (T ) is the temperature-dependent effective thermal resistance of the device
modeled by
R th (T ) =
1.4 × 10 6 , T ≤ T C
2.0 × 10 6 , T > T C
where T C = 1, 070 K is the Mott metal-insulator transition temperature.
By turning off power, i.e., letting v = 0, we have
dT
dt
= −
T − T amb
C th R th (T )
which has a unique EP T = T amb attracting all solutions. We conclude that, as it
happens for PTC and NTC thermistors in Example 2.16, the NbO 2 -Mott memristor
device is volatile.
Example 2.25 (The First Example of Extended Memristor Made of Passive Electronic Components) The first and unique example of extended memristor made of
passive electronic components is reported in [36]. Consider the circuit of Fig. 2.26.
A voltage source v g is applied across a full-wave rectifier cascaded with a RLC
series filter. The two-terminal RLC filter connected to the output terminal of the
diode bridge can be substituted by any linear dynamical bipole [37]. The relation
between the voltage across and the current through diode D k , named as v k and i k
respectively (k = {1, 2, 3, 4}), is modeled as
Fig. 2.26 Extended memristor based on a four diode-bridge and standard passive components
69
where σ 0 , A, k B , ω, d are parameters and k B is the Boltzmann constant. The state
variable is given by the temperature T which obeys Newton’s law of cooling
dT
dt
=
iv
C th
−
T − T amb
C th R th (T )
where T amb = 300 K is the ambient temperature, C th is the thermal capacitance,
and R th (T ) is the temperature-dependent effective thermal resistance of the device
modeled by
R th (T ) =
1.4 × 10 6 , T ≤ T C
2.0 × 10 6 , T > T C
where T C = 1, 070 K is the Mott metal-insulator transition temperature.
By turning off power, i.e., letting v = 0, we have
dT
dt
= −
T − T amb
C th R th (T )
which has a unique EP T = T amb attracting all solutions. We conclude that, as it
happens for PTC and NTC thermistors in Example 2.16, the NbO 2 -Mott memristor
device is volatile.
Example 2.25 (The First Example of Extended Memristor Made of Passive Electronic Components) The first and unique example of extended memristor made of
passive electronic components is reported in [36]. Consider the circuit of Fig. 2.26.
A voltage source v g is applied across a full-wave rectifier cascaded with a RLC
series filter. The two-terminal RLC filter connected to the output terminal of the
diode bridge can be substituted by any linear dynamical bipole [37]. The relation
between the voltage across and the current through diode D k , named as v k and i k
respectively (k = {1, 2, 3, 4}), is modeled as
Fig. 2.26 Extended memristor based on a four diode-bridge and standard passive components