The Experts below are selected from a list of 44721 Experts worldwide ranked by ideXlab platform
Jacek Gulgowski - One of the best experts on this subject based on the ideXlab platform.
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On Applications of Elements Modelled by Fractional Derivatives in Circuit Theory
Energies, 2020Co-Authors: Jacek Gulgowski, Tomasz P. Stefanski, Damian TrofimowiczAbstract: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 Grunwald–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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MIXDES - On Applications of Fractional Derivatives in Circuit Theory
2020Co-Authors: Jacek Gulgowski, Tomasz P. Stefanski, Damian TrofimowiczAbstract:In this paper, concepts of fractional-order (FO) derivatives are discussed from the point of view of applications in the Circuit Theory. The properties of FO derivatives required for the Circuit-level modelling 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 of formulations of the FO derivatives have limited applicability in the Circuit Theory. That is, the Riemann-Liouville and Caputo derivatives with finite base point have a limited applicability whereas the Grunwald-Letnikov and Marchaud derivatives lead to reasonable results of the Circuit-level modelling.
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Electromagnetic-based derivation of fractional-order Circuit Theory
Communications in Nonlinear Science and Numerical Simulation, 2019Co-Authors: Tomasz P. Stefanski, Jacek GulgowskiAbstract:Abstract In this paper, foundations of the fractional-order Circuit Theory are revisited. Although many papers have been devoted to fractional-order modelling of electrical Circuits, there are relatively few foundations for such an approach. Therefore, we derive fractional-order lumped-element equations for capacitors, inductors and resistors, as well as Kirchhoff’s voltage and current laws using quasi-static approximations of fractional-order Maxwell’s equations. The proposed approach is not limited by the geometry of the considered lumped elements and employs the concepts of voltage and current known from the Circuit Theory. Finally, the proposed Theory of Circuit elements is applied to interpretation of Poynting’s theorem in fractional-order electromagnetism.
D F Williams - One of the best experts on this subject based on the ideXlab platform.
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Causality and waveguide Circuit Theory
IEEE Transactions on Microwave Theory and Techniques, 2001Co-Authors: D F Williams, B.k. AlpertAbstract:We develop a new causal power-normalized waveguide equivalent-Circuit Theory that, unlike its predecessors, results in network parameters usable in both the frequency and time domains in a broad class of waveguides. Enforcing simultaneity of the voltages, currents, and fields and a power normalization fixes all of the parameters of the new Theory within a single normalization factor, including both the magnitude and phase of the characteristic impedance of the waveguide. Enforcing simultaneity also ensures that the Theory's voltages and currents do not start before their excitation, and that the network parameters of passive devices are causal, a necessary condition for stable time-domain simulations.
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Characteristic impedance, power, and causality [waveguide Circuit Theory]
IEEE Microwave and Guided Wave Letters, 1999Co-Authors: D F Williams, B.k. AlpertAbstract:A new causal power-normalized waveguide equivalent-Circuit Theory determines uniquely both the magnitude and phase of the characteristic impedance of a waveguide.
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A general waveguide Circuit Theory
Journal of Research of the National Institute of Standards and Technology, 1992Co-Authors: R.b. Marks, D F WilliamsAbstract:This work generalizes and extends the classical Circuit Theory of electromagnetic waveguides. Unlike the conventional Theory, the present formulation applies to all waveguides composed of linear, isotropic material, even those involving lossy conductors and hybrid mode fields, in a fully rigorous way. Special attention is given to distinguishing the traveling waves, constructed with respect to a well-defined characteristic impedance, from a set of pseudo-waves, defined with respect to an arbitrary reference impedance. Matrices characterizing a linear Circuit are defined, and relationships among them, some newly discovered, are derived. New ramifications of reciprocity are developed. Measurement of various network parameters is given extensive treatment.
B.k. Alpert - One of the best experts on this subject based on the ideXlab platform.
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Causality and waveguide Circuit Theory
IEEE Transactions on Microwave Theory and Techniques, 2001Co-Authors: D F Williams, B.k. AlpertAbstract:We develop a new causal power-normalized waveguide equivalent-Circuit Theory that, unlike its predecessors, results in network parameters usable in both the frequency and time domains in a broad class of waveguides. Enforcing simultaneity of the voltages, currents, and fields and a power normalization fixes all of the parameters of the new Theory within a single normalization factor, including both the magnitude and phase of the characteristic impedance of the waveguide. Enforcing simultaneity also ensures that the Theory's voltages and currents do not start before their excitation, and that the network parameters of passive devices are causal, a necessary condition for stable time-domain simulations.
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Characteristic impedance, power, and causality [waveguide Circuit Theory]
IEEE Microwave and Guided Wave Letters, 1999Co-Authors: D F Williams, B.k. AlpertAbstract:A new causal power-normalized waveguide equivalent-Circuit Theory determines uniquely both the magnitude and phase of the characteristic impedance of a waveguide.
Tomasz P. Stefanski - One of the best experts on this subject based on the ideXlab platform.
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On Applications of Elements Modelled by Fractional Derivatives in Circuit Theory
Energies, 2020Co-Authors: Jacek Gulgowski, Tomasz P. Stefanski, Damian TrofimowiczAbstract: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 Grunwald–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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MIXDES - On Applications of Fractional Derivatives in Circuit Theory
2020Co-Authors: Jacek Gulgowski, Tomasz P. Stefanski, Damian TrofimowiczAbstract:In this paper, concepts of fractional-order (FO) derivatives are discussed from the point of view of applications in the Circuit Theory. The properties of FO derivatives required for the Circuit-level modelling 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 of formulations of the FO derivatives have limited applicability in the Circuit Theory. That is, the Riemann-Liouville and Caputo derivatives with finite base point have a limited applicability whereas the Grunwald-Letnikov and Marchaud derivatives lead to reasonable results of the Circuit-level modelling.
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Electromagnetic-based derivation of fractional-order Circuit Theory
Communications in Nonlinear Science and Numerical Simulation, 2019Co-Authors: Tomasz P. Stefanski, Jacek GulgowskiAbstract:Abstract In this paper, foundations of the fractional-order Circuit Theory are revisited. Although many papers have been devoted to fractional-order modelling of electrical Circuits, there are relatively few foundations for such an approach. Therefore, we derive fractional-order lumped-element equations for capacitors, inductors and resistors, as well as Kirchhoff’s voltage and current laws using quasi-static approximations of fractional-order Maxwell’s equations. The proposed approach is not limited by the geometry of the considered lumped elements and employs the concepts of voltage and current known from the Circuit Theory. Finally, the proposed Theory of Circuit elements is applied to interpretation of Poynting’s theorem in fractional-order electromagnetism.
Yuli V. Nazarov - One of the best experts on this subject based on the ideXlab platform.
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Circuit Theory of non-equilibrium superconductivity
Physica C-superconductivity and Its Applications, 2001Co-Authors: Yuli V. NazarovAbstract:We give here a short account of a recently developed Circuit Theory of superconductivity. The Theory accounts for decoherence between electrons and holes, twofold nature of the distribution function in the superconducting state and includes arbitrary connectors. We give a simple example and discuss numerical implementation of the Theory.
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Novel Circuit Theory of Andreev reflection
Superlattices and Microstructures, 1999Co-Authors: Yuli V. NazarovAbstract:We review here a novel Circuit Theory of superconductivity. The existing Circuit Theory of Andreev reflection has been revised to account for decoherence between electrons and holes and the twofold nature of the distribution function. The description of arbitrary connectors has been elaborated on. In this way one can cope with most of the factors that limited the applicability of the old Circuit Theory. We give a simple example and discuss numerical implementation of the Theory.
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Circuit Theory of Andreev conductance.
Physical review letters, 1994Co-Authors: Yuli V. NazarovAbstract:Conductance of small normal metal structures adjacent to a superconductor is determined by coherent Andreev reflection. We show that under certain limitations the conductance can be found by means of an extended Circuit Theory. The Theory deals with two types of elements: tunnel junctions and diffusive conductors and provides the basis for practical calculations. A new device proposed illustrates the advantages of the Theory.