scholarly journals Fractional derivatives in electrical circuit theory – critical remarks

2017 ◽  
Vol 66 (1) ◽  
pp. 155-163 ◽  
Author(s):  
Ryszard Sikora
Keyword(s):  
Maxwell Equations ◽  
Fractional Derivatives ◽  
Circuit Theory ◽  
Electrical Circuit ◽  
Physical Equation ◽  
Dimensional Uniformity ◽  
Potential Impact

Abstract A number of critical remarks related to the application of fractional derivatives in electrical circuit theory have been presented in this paper. Few cases have been pointed out that refer to observed in selected publications violations of dimensional uniformity of physical equation rules as well as to a potential impact on the Maxwell equations.

scholarly journals Time-Domain Analysis of Fractional Electrical Circuit Containing Two Ladder Elements

Electronics ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 475
Author(s):  
Ewa Piotrowska ◽  
Krzysztof Rogowski
Keyword(s):  
Fractional Derivative ◽  
Fractional Derivatives ◽  
Electric Circuit ◽  
Theoretical Models ◽  
Time Domain Analysis ◽  
Electrical Circuit ◽  
State Variable ◽  
State Space System ◽  
Derivatives Of ◽  
Different Order

The paper is devoted to the theoretical and experimental analysis of an electric circuit consisting of two elements that are described by fractional derivatives of different orders. These elements are designed and performed as RC ladders with properly selected values of resistances and capacitances. Different orders of differentiation lead to the state-space system model, in which each state variable has a different order of fractional derivative. Solutions for such models are presented for three cases of derivative operators: Classical (first-order differentiation), Caputo definition, and Conformable Fractional Derivative (CFD). Using theoretical models, the step responses of the fractional electrical circuit were computed and compared with the measurements of a real electrical system.

The Logical Basis of Electrical Circuit Theory

1978 ◽  
Vol 15 (1) ◽  
pp. 87-89 ◽  
Author(s):  
Z. L. Budrikis
Keyword(s):  
Circuit Theory ◽  
Electrical Circuit ◽  
Poisson’S Equation ◽  
Poisson's Equation ◽  
Logical Basis ◽  
Circuit Components ◽  
Speed Of Propagation ◽  
Infinite Speed Of Propagation

Two assumptions underlie circuit theory: infinite speed of propagation of force and existence at all times of equilibrium in matter. The theory is therefore essentially of static states. Voltages across all circuit components, including inductors, transformers, generators and others, are differences in potential, traceable to Coulomb forces and obeying Poisson's equation.

scholarly journals Possessive Relational Process Clauses in Scientific Text: Implication on ESP Teaching

2019 ◽  
Vol 4 (2) ◽  
pp. 61-76
Author(s):  
Mulyati Khorina
Keyword(s):  
Engineering Students ◽  
Systemic Functional Linguistics ◽  
Circuit Theory ◽  
Electrical Circuit ◽  
Scientific Texts ◽  
Dominant Type ◽  
Scientific Text ◽  
Functional Linguistics ◽  
Relational Processes ◽  
Relational Process

This paper focuses of this paper aimsis possessive relational process clauses which is a type of relational process clauses in which relational processes work. Threepoints concerning possessive relational process clauses are discussed in this paper. First, the relational process type which is dominant possessed by possessive relational process clauses. Second, the lexical verbs which realize the dominant type of relational process. The last, the roles played by possessive relational process clauses. The data for this study were taken from Electrical Circuit Theory and Technology, Fundamentals of Electronics Circuits, Electronics Devices, Flow Version, and A Textbook of Electrical Technology, all of which are used as references by  Electronics Engineering students of PoliteknikNegeri Bandung. To analyse the data, Systemic Functional Linguistics (SFL) was employed. The results showed that possessive relational process clauses in scientific texts operate solely on attributive relational process. The attributive relational process is realized by lexical verbs have, consist, include, make which represent the possessive relational process clauses as Classification, Composition and Feature.

scholarly journals On Applications of Elements Modelled by Fractional Derivatives in Circuit Theory

Energies ◽  
2020 ◽  
Vol 13 (21) ◽  
pp. 5768 ◽  
Author(s):  
Jacek Gulgowski ◽  
Tomasz P. Stefański ◽  
Damian Trofimowicz
Keyword(s):  
Transmission Line ◽  
Fractional Order ◽  
Fractional Derivatives ◽  
Circuit Theory ◽  
Base Point ◽  
Semigroup Property ◽  
Caputo Derivatives ◽  
Potential Problems ◽  
Limited Applicability

In this paper, concepts of fractional-order (FO) derivatives are reviewed and discussed with regard to element models applied in the circuit theory. The properties of FO derivatives required for the circuit-level modeling are formulated. Potential problems related to the generalization of transmission-line equations with the use of FO derivatives are presented. It is demonstrated that some formulations of FO derivatives have limited applicability in the circuit theory. Out of the most popular approaches considered in this paper, only the Grünwald–Letnikov and Marchaud definitions (which are actually equivalent) satisfy the semigroup property and are naturally representable in the phasor domain. The generalization of this concept, i.e., the two-sided fractional Ortigueira–Machado derivative, satisfies the semigroup property, but its phasor representation is less natural. Other ideas (including the Riemann–Liouville and Caputo derivatives—with a finite or an infinite base point) seem to have limited applicability.

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