Chapter 1
Device Modeling and Circuit Elements
This chapter discusses a device-independent black-box approach to model a broad
variety of physical devices. For the purpose of network theory, a circuit element
can be considered as a black-box, whose electrical behavior is defined in terms
of a mathematical model (i.e., a set of algebraic and/or differential and/or integral
equations), relating currents and voltages at various terminals of the device. The
physical means required to implement the black-box are irrelevant. The circuit
element is therefore an ideal entity, corresponding to the best abstraction and to
the most suited description of a physical device.
1.1 Axiomatic Approach to Device Modeling
Device modeling is more of an “art” than science. Since the aim of any model is
to “mimic” as accurately as possible a physical device D, it is crucial to identify
all important properties and behaviors of D. Most existing models of physical
devices have been derived via two basic approaches: the physical approach and
the black-box approach. The physical approach relies on a careful study of physics
and operating mechanisms of the device (e.g., solid-state devices as Gunn diode,
Josephson junction, etc.). On the other hand, the black-box approach is fundamental
when the device physics and operating mechanisms are so complex that the physical
approach results to be impractical (e.g., bio-physical systems as membranes, nerves,
etc.). In either approach, a mathematical description (e.g., a system of nonlinear
algebraic and differential equations) which is capable of simulating most of the
observed properties of a device is essential. This crucial step is where most of the
“art” is involved.
Once the mathematical description of D is obtained, a unified theory of device
modeling can be developed by an axiomatic approach based on the concept of basic
© Springer Nature Switzerland AG 2021
F. Corinto et al., Nonlinear Circuits and Systems with Memristors,
https://doi.org/10.1007/978-3-030-55651-8_1
3
Device Modeling and Circuit Elements
This chapter discusses a device-independent black-box approach to model a broad
variety of physical devices. For the purpose of network theory, a circuit element
can be considered as a black-box, whose electrical behavior is defined in terms
of a mathematical model (i.e., a set of algebraic and/or differential and/or integral
equations), relating currents and voltages at various terminals of the device. The
physical means required to implement the black-box are irrelevant. The circuit
element is therefore an ideal entity, corresponding to the best abstraction and to
the most suited description of a physical device.
1.1 Axiomatic Approach to Device Modeling
Device modeling is more of an “art” than science. Since the aim of any model is
to “mimic” as accurately as possible a physical device D, it is crucial to identify
all important properties and behaviors of D. Most existing models of physical
devices have been derived via two basic approaches: the physical approach and
the black-box approach. The physical approach relies on a careful study of physics
and operating mechanisms of the device (e.g., solid-state devices as Gunn diode,
Josephson junction, etc.). On the other hand, the black-box approach is fundamental
when the device physics and operating mechanisms are so complex that the physical
approach results to be impractical (e.g., bio-physical systems as membranes, nerves,
etc.). In either approach, a mathematical description (e.g., a system of nonlinear
algebraic and differential equations) which is capable of simulating most of the
observed properties of a device is essential. This crucial step is where most of the
“art” is involved.
Once the mathematical description of D is obtained, a unified theory of device
modeling can be developed by an axiomatic approach based on the concept of basic
© Springer Nature Switzerland AG 2021
F. Corinto et al., Nonlinear Circuits and Systems with Memristors,
https://doi.org/10.1007/978-3-030-55651-8_1
3