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Keywords = Tellegen’s theorem

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25 pages, 6775 KB  
Article
Cyclostationary Approach to the Analysis of the Power in Electric Circuits under Periodic Excitations
by Timofey Shevgunov, Oksana Guschina and Yury Kuznetsov
Appl. Sci. 2021, 11(20), 9711; https://doi.org/10.3390/app11209711 - 18 Oct 2021
Cited by 17 | Viewed by 2693
Abstract
This paper proposes a cyclostationary based approach to power analysis carried out for electric circuits under arbitrary periodic excitation. Instantaneous power is considered to be a particular case of the two-dimensional cross correlation function (CCF) of the voltage across, and current through, an [...] Read more.
This paper proposes a cyclostationary based approach to power analysis carried out for electric circuits under arbitrary periodic excitation. Instantaneous power is considered to be a particular case of the two-dimensional cross correlation function (CCF) of the voltage across, and current through, an element in the electric circuit. The cyclostationary notation is used for deriving the frequency domain counterpart of CCF—voltage–current cross spectrum correlation function (CSCF). Not only does the latter exhibit the complete representation of voltage–current interaction in the element, but it can be systematically exploited for evaluating all commonly used power measures, including instantaneous power, in the form of Fourier series expansion. Simulation examples, which are given for the parallel resonant circuit excited by the periodic currents expressed as a finite sum of sinusoids and periodic train of pulses with distorted edges, numerically illustrate the components of voltage–current CSCF and the characteristics derived from it. In addition, the generalization of Tellegen’s theorem, suggested in the paper, leads to the immediate formulation of the power conservation law for each CSCF component separately. Full article
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20 pages, 3404 KB  
Article
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 3 | Viewed by 3319
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 [...] Read more.
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
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