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22 pages, 5460 KiB

Open AccessArticle

Are There an Infinite Number of Passive Circuit Elements in the World?

by Frank Zhigang Wang

Electronics 2024, 13(13), 2669; https://doi.org/10.3390/electronics13132669 - 7 Jul 2024

Viewed by 835

We found that a second-order ideal memristor [whose state is the charge, i.e.,

x = q

v = R (x, i, t) i

] degenerates into a negative nonlinear resistor with an internal power source. After extending analytically and geographically [...] Read more.

We found that a second-order ideal memristor [whose state is the charge, i.e.,

x = q

v = R (x, i, t) i

] degenerates into a negative nonlinear resistor with an internal power source. After extending analytically and geographically the above local activity (experimentally verified by the two active higher-integral-order memristors extracted from the famous Hodgkin–Huxley circuit) to other higher-order circuit elements, we concluded that all higher-order passive memory circuit elements do not exist in nature and that the periodic table of the two-terminal passive ideal circuit elements can be dramatically reduced to a reduced table comprising only six passive elements: a resistor, inductor, capacitor, memristor, mem-inductor, and mem-capacitor. Such a bounded table answered an open question asked by Chua 40 years ago: Are there an infinite number of passive circuit elements in the world? Full article

(This article belongs to the Special Issue Memristors beyond the Limitations: Novel Methods and Materials)

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15 pages, 3531 KiB

Open AccessArticle

Extended and Generic Higher-Order Elements for MEMS Modeling

by Zdeněk Biolek, Viera Biolková, Dalibor Biolek and Zdeněk Kolka

Sensors 2022, 22(20), 8007; https://doi.org/10.3390/s22208007 - 20 Oct 2022

Cited by 3 | Viewed by 1467

Abstract

State-dependent resistors, capacitors, and inductors are a common part of many smart engineering solutions, e.g., in MEMS (Micro-Electro-Mechanical Systems) sensors and actuators, Micro/NanoMachines, or biomimetic systems. These memory elements are today modeled as generic and extended memristors (MR), memcapacitors (MC), and meminductors (ML), which are more general versions of classical MR, MC, and ML from the infinite set of the fundamental elements of electrical engineering, known as Higher-Order Elements (HOEs). It turns out that models of many complex phenomena in MEMS cannot be constructed only from classical and state-dependent elements such as R, L, and C, but that other HOEs with generalized behavior should also be used. Thus, in this paper, generic and extended versions of HOEs are introduced, overcoming the existing limitation to MR, MC, and ML elements. The relevant circuit theorems are formulated, which generalize the well-known theorems of classical memory elements, and their application to model complex processes of various physical natures in MEMS is shown. Full article

(This article belongs to the Special Issue Advanced Sensors in MEMS)

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20 pages, 3404 KiB

Open AccessArticle

Higher-Order Hamiltonian for Circuits with (α,β) Elements

by Zdeněk Biolek, Dalibor Biolek, Viera Biolková and Zdeněk Kolka

Entropy 2020, 22(4), 412; https://doi.org/10.3390/e22040412 - 5 Apr 2020

Cited by 2 | Viewed by 2457

Abstract

The paper studies the construction of the Hamiltonian for circuits built from the (α,β) elements of Chua’s periodic table. It starts from the Lagrange function, whose existence is limited to Σ-circuits, i.e., circuits built exclusively from elements located on a common Σ-diagonal of the table. We show that the Hamiltonian can also be constructed via the generalized Tellegen’s theorem. According to the ideas of predictive modeling, the resulting Hamiltonian is made up exclusively of the constitutive relations of the elements in the circuit. Within the frame of Ostrogradsky’s formalism, the simulation scheme of Σ-circuits is designed and examined with the example of a nonlinear Pais–Uhlenbeck oscillator. Full article

(This article belongs to the Section Complexity)

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19 pages, 2830 KiB

Open AccessArticle

Lagrangian for Circuits with Higher-Order Elements

by Zdenek Biolek, Dalibor Biolek and Viera Biolkova

Entropy 2019, 21(11), 1059; https://doi.org/10.3390/e21111059 - 29 Oct 2019

Cited by 7 | Viewed by 3381

Abstract

The necessary and sufficient conditions of the validity of Hamilton’s variational principle for circuits consisting of (α,β) elements from Chua’s periodical table are derived. It is shown that the principle holds if and only if all the circuit elements lie on the so-called Σ-diagonal with a constant sum of the indices α and β. In this case, the Lagrangian is the sum of the state functions of the elements of the L or ⁺R types minus the sum of the state functions of the elements of the C or ⁻R types. The equations of motion generated by this Lagrangian are always of even-order. If all the elements are linear, the equations of motion contain only even-order derivatives of the independent variable. Conclusions are illustrated on an example of the synthesis of the Pais–Uhlenbeck oscillator via the elements from Chua’s table. Full article

(This article belongs to the Section Complexity)

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