Appendix 2: Memristor Modeling and Simulation
87
augmented with an additive state-dependent linear term to resolve the “terminalstate problem.”
One of the finest circuit emulators of memristor behavior is credited to Shin and
Kang [62], which proposed a general model where the control waveform may be
in either current or voltage form and the state is defined as the memristance. Their
model, from which the charge-flux relationship of the memristor under modeling
may be easily extracted, may be suitably tuned through the introduction of a window
function depending on the memristor charge.
Kavehei [63] proposed a memristor model based on the specification of a
piecewise-linear charge q-flux ϕ relationship. In such model the state and output
equations are not specified. Its PSpice implementation is based on Chua’s [2] first
circuit realization of a memristor through a type-1 memristor-resistor mutator.
An interesting model was presented in [64] to explain the memristor behavior of
nanoparticle assemblies.
The nonlinear dependence of the time derivative of the state on the input signal
is taken into account in Lehtonen’s model [65], inspired by the experimental work
from [66], where the current is related to the voltage by means of a rectifying
exponential function in the off state (as in a diode) and of a sinh function in the on
state (typical of electron tunneling). This model, where the control waveform is in
voltage form, was implemented in PSpice to describe the neighborhood connections
among cells in cellular neural networks (CNNs) [67, 68].
An even more highly nonlinear function of the input governs the state equation
in the voltage-controlled model from Poikonen [69], which studied the transition
between non-programming and programming phases in memristor devices.
In the memristor emulator circuit from [70], used as basic building block of a 4memristor bridge synapse for neuromorphic applications, the memristance, modeled
by the input impedance of an active circuit, is made proportional to the time integral
of the memristor current by constraining the voltage at one of the input terminals
of an operational amplifier to be the analogue multiplication between the voltage
across a resistor, proportional to the memristor current, and the voltage across a
capacitor, proportional to the time integral of the memristor current.
In [71] Strukov and Williams demonstrated the exponential relationship between
drift velocity and local electric field. Since this discovery a number of models have
been introduced to support threshold-activated state dynamics. Among them, one
which merits mention is the physics-based Pickett’s model from [72], in which
the dependency of the rate of change of the state on the current-form input is
strongly nonlinear. In such model the memristor is seen as the series between a
low resistance associated with the conductive layer of the nano-film and Simmons’
electron tunneling barrier [73], whose width is chosen as the system state. A PSpice
version of the latter was presented in [74].
More recently Kvatinski developed a simplified version of the Pickett’s model
[72] and named it as ThrEshold Adaptive Memristor (TEAM) model [34]. In
such model for input current magnitude below a certain adaptable threshold no
state change occurs, otherwise the state evolution rule may be tuned to the
memristor element under modeling through specification of an appropriate set of
87
augmented with an additive state-dependent linear term to resolve the “terminalstate problem.”
One of the finest circuit emulators of memristor behavior is credited to Shin and
Kang [62], which proposed a general model where the control waveform may be
in either current or voltage form and the state is defined as the memristance. Their
model, from which the charge-flux relationship of the memristor under modeling
may be easily extracted, may be suitably tuned through the introduction of a window
function depending on the memristor charge.
Kavehei [63] proposed a memristor model based on the specification of a
piecewise-linear charge q-flux ϕ relationship. In such model the state and output
equations are not specified. Its PSpice implementation is based on Chua’s [2] first
circuit realization of a memristor through a type-1 memristor-resistor mutator.
An interesting model was presented in [64] to explain the memristor behavior of
nanoparticle assemblies.
The nonlinear dependence of the time derivative of the state on the input signal
is taken into account in Lehtonen’s model [65], inspired by the experimental work
from [66], where the current is related to the voltage by means of a rectifying
exponential function in the off state (as in a diode) and of a sinh function in the on
state (typical of electron tunneling). This model, where the control waveform is in
voltage form, was implemented in PSpice to describe the neighborhood connections
among cells in cellular neural networks (CNNs) [67, 68].
An even more highly nonlinear function of the input governs the state equation
in the voltage-controlled model from Poikonen [69], which studied the transition
between non-programming and programming phases in memristor devices.
In the memristor emulator circuit from [70], used as basic building block of a 4memristor bridge synapse for neuromorphic applications, the memristance, modeled
by the input impedance of an active circuit, is made proportional to the time integral
of the memristor current by constraining the voltage at one of the input terminals
of an operational amplifier to be the analogue multiplication between the voltage
across a resistor, proportional to the memristor current, and the voltage across a
capacitor, proportional to the time integral of the memristor current.
In [71] Strukov and Williams demonstrated the exponential relationship between
drift velocity and local electric field. Since this discovery a number of models have
been introduced to support threshold-activated state dynamics. Among them, one
which merits mention is the physics-based Pickett’s model from [72], in which
the dependency of the rate of change of the state on the current-form input is
strongly nonlinear. In such model the memristor is seen as the series between a
low resistance associated with the conductive layer of the nano-film and Simmons’
electron tunneling barrier [73], whose width is chosen as the system state. A PSpice
version of the latter was presented in [74].
More recently Kvatinski developed a simplified version of the Pickett’s model
[72] and named it as ThrEshold Adaptive Memristor (TEAM) model [34]. In
such model for input current magnitude below a certain adaptable threshold no
state change occurs, otherwise the state evolution rule may be tuned to the
memristor element under modeling through specification of an appropriate set of