Chapter 2
Fundamental Properties of
Mem-Elements
This chapter is devoted to discuss some basic properties of memristors, memcapacitors, and meminductors, a.k.a. mem-elements, that are both of theoretic and practical
interest. In the first part (Sects. 2.1 and 2.2), the main focus is on features of a
memristor as a (−1, −1)-element of the periodic table (cf. Chap. 1), hereinafter also
named ideal memristor. 1 Such properties include the passivity and the no energy
storage property. It is also shown why a memristor is able to store a continuum of
stable states and, as such, can implement a nonvolatile memory. In addition, the
chapter illustrates some basic signatures of memristors, as the pinched hysteresis
loop displayed in the voltage-current (v, i)-domain in response to a zero-mean
periodic input (e.g., a sinusoidal signal). In this regard it is however stressed that
Pinched hysteresis loops are not models (i.e., constitutive relations).
In other words, pinched hysteresis loops don’t have any predicting ability
because they represent just the device response to a specific input!
The second part of the chapter discusses the concept of memristive devices and
systems, introduced by Chua and Kang [1], as a generalization of an ideal memristor.
Memristive systems retain some properties that are analogous to those of an ideal
memristor. In particular, any memristive system still displays a pinched hysteresis
loop in the (v, i)-domain when subject to a zero-mean periodic input. However,
a memristive system may also feature basically different properties with respect
to an ideal memristor. For instance, a memristive device may be volatile, as it
happens for a thermistor. The concept of memristive devices and a classification
1 In classic Circuit Theory “ideal circuit elements” are defined by linear CRs characterized by
just one single parameter (e.g., the ideal resistor by the resistance R, the ideal capacitor by the
capacitance C, the ideal inductor by the inductance L, etc.). On the other hand, the term ideal is
also used for nonlinear circuit elements in which the parasitic effects are disregarded. According
to this point of view, the (α, β)-elements of the periodic table can be considered as ideal elements.
© 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_2
27
Fundamental Properties of
Mem-Elements
This chapter is devoted to discuss some basic properties of memristors, memcapacitors, and meminductors, a.k.a. mem-elements, that are both of theoretic and practical
interest. In the first part (Sects. 2.1 and 2.2), the main focus is on features of a
memristor as a (−1, −1)-element of the periodic table (cf. Chap. 1), hereinafter also
named ideal memristor. 1 Such properties include the passivity and the no energy
storage property. It is also shown why a memristor is able to store a continuum of
stable states and, as such, can implement a nonvolatile memory. In addition, the
chapter illustrates some basic signatures of memristors, as the pinched hysteresis
loop displayed in the voltage-current (v, i)-domain in response to a zero-mean
periodic input (e.g., a sinusoidal signal). In this regard it is however stressed that
Pinched hysteresis loops are not models (i.e., constitutive relations).
In other words, pinched hysteresis loops don’t have any predicting ability
because they represent just the device response to a specific input!
The second part of the chapter discusses the concept of memristive devices and
systems, introduced by Chua and Kang [1], as a generalization of an ideal memristor.
Memristive systems retain some properties that are analogous to those of an ideal
memristor. In particular, any memristive system still displays a pinched hysteresis
loop in the (v, i)-domain when subject to a zero-mean periodic input. However,
a memristive system may also feature basically different properties with respect
to an ideal memristor. For instance, a memristive device may be volatile, as it
happens for a thermistor. The concept of memristive devices and a classification
1 In classic Circuit Theory “ideal circuit elements” are defined by linear CRs characterized by
just one single parameter (e.g., the ideal resistor by the resistance R, the ideal capacitor by the
capacitance C, the ideal inductor by the inductance L, etc.). On the other hand, the term ideal is
also used for nonlinear circuit elements in which the parasitic effects are disregarded. According
to this point of view, the (α, β)-elements of the periodic table can be considered as ideal elements.
© 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_2
27