Functionally Complete Elemental Basis of Mathematical Schemes of Electrical Circuits

2013 ◽  
Vol 448-453 ◽  
pp. 2120-2124
Author(s):  
Pivnev Vitaliy Viktorovich ◽  
Basan Sergey Nikolaevich
Keyword(s):  
Minimal Element ◽  
Electrical Energy ◽  
Electrical Circuit ◽  
Functional Element ◽  
Minimum Element ◽  
Electrical Circuits ◽  
Mathematical Diagrams ◽  
Definition Of ◽  
Extended Element

The paper gives the definition of the mathematical electrical circuit scheme, the extended element basis, the minimum and full functional element basis. The theorem about functionality of the full minimum element basis for the synthesis of mathematical diagrams of electrical circuits, which consists of: ideal conductor, ideal switch, one independent and one dependent source of electrical energy, capacitance or inductance, was convinced. There are a few variants of functionally complete minimal element bases.

scholarly journals Singular fractional linear systems and electrical circuits

2011 ◽  
Vol 21 (2) ◽  
pp. 379-384 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Fractional Derivative ◽  
Linear Systems ◽  
Laplace Transformation ◽  
State Equation ◽  
Electrical Circuit ◽  
The State ◽  
Electrical Circuits ◽  
New Class ◽  
Fractional System ◽  
Definition Of

Singular fractional linear systems and electrical circuitsA new class of singular fractional linear systems and electrical circuits is introduced. Using the Caputo definition of the fractional derivative, the Weierstrass regular pencil decomposition and the Laplace transformation, the solution to the state equation of singular fractional linear systems is derived. It is shown that every electrical circuit is a singular fractional system if it contains at least one mesh consisting of branches only with an ideal supercapacitor and voltage sources or at least one node with branches with supercoils.

Mathematical views of the fractional Chua's electrical circuit described by the Caputo-Liouville derivative

2021 ◽  
Vol 67 (1 Jan-Feb) ◽  
pp. 91
Author(s):  
N. Sene
Keyword(s):  
Caputo Derivative ◽  
Local Stability ◽  
Numerical Scheme ◽  
Equilibrium Points ◽  
Electrical Circuit ◽  
Maximal Lyapunov Exponent ◽  
Electrical Circuits ◽  
Adaptive Controls ◽  
Liouville Derivative

This paper revisits Chua's electrical circuit in the context of the Caputo derivative. We introduce the Caputo derivative into the modeling of the electrical circuit. The solutions of the new model are proposed using numerical discretizations. The discretizations use the numerical scheme of the Riemann-Liouville integral. We have determined the equilibrium points and study their local stability. The existence of the chaotic behaviors with the used fractional-order has been characterized by the determination of the maximal Lyapunov exponent value. The variations of the parameters of the model into the Chua's electrical circuit have been quantified using the bifurcation concept. We also propose adaptive controls under which the master and the slave fractional Chua's electrical circuits go in the same way. The graphical representations have supported all the main results of the paper.

scholarly journals Geometric Algebra Framework Applied to Symmetrical Balanced Three-Phase Systems for Sinusoidal and Non-Sinusoidal Voltage Supply

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1259
Author(s):  
Francisco G. Montoya ◽  
Raúl Baños ◽  
Alfredo Alcayde ◽  
Francisco Manuel Arrabal-Campos ◽  
Javier Roldán Roldán Pérez
Keyword(s):  
Geometric Algebra ◽  
Dimensional Euclidean Space ◽  
Active Components ◽  
Electrical Circuits ◽  
Current Harmonics ◽  
Operation Conditions ◽  
Multiple Phase ◽  
Three Phase ◽  
Phase Systems ◽  
Definition Of

This paper presents a new framework based on geometric algebra (GA) to solve and analyse three-phase balanced electrical circuits under sinusoidal and non-sinusoidal conditions. The proposed approach is an exploratory application of the geometric algebra power theory (GAPoT) to multiple-phase systems. A definition of geometric apparent power for three-phase systems, that complies with the energy conservation principle, is also introduced. Power calculations are performed in a multi-dimensional Euclidean space where cross effects between voltage and current harmonics are taken into consideration. By using the proposed framework, the current can be easily geometrically decomposed into active- and non-active components for current compensation purposes. The paper includes detailed examples in which electrical circuits are solved and the results are analysed. This work is a first step towards a more advanced polyphase proposal that can be applied to systems under real operation conditions, where unbalance and asymmetry is considered.

scholarly journals Signal Processing and Analysis of Electrical Circuit

Electronics ◽  
2019 ◽  
Vol 9 (1) ◽  
pp. 17
Author(s):  
Adam Glowacz ◽  
Jose Alfonso Antonino Daviu
Keyword(s):  
Signal Processing ◽  
Electrical Circuit ◽  
Electrical Circuits ◽  
Electrical Systems

The analysis of electrical circuits is an essential task in the evaluation of electrical systems [...]

Approximation and the point of flicker-noise formation

2021 ◽  
Author(s):  
A.S. Matsaev
Keyword(s):  
Spectral Density ◽  
Flicker Noise ◽  
Electronic Devices ◽  
Electrical Circuit ◽  
Maximum Magnitude ◽  
Noise Characteristics ◽  
Exponential Increase ◽  
Accurate Definition ◽  
Definition Of ◽  
Flat Section

The article refers to the field of research of noise fluctuations or flicker noise in electronic amplifiers and is devoted to the exact definition of the magnitude and shape of the spectral density of flicker-noise. The 1/f approximation of flicker noise is analyzed and the problem of its non-constructiveness in analyzing the noise characteristics of electronic amplifiers is shown. To eliminate this problem, the mechanism of physical formation of the envelope, a form of spectral density flicker-noise is defined. The physics of flicker-noise is detailed by accurate definition of the place of its formation. An accurate definition of the maximum difference of the amplifier flickernoise on the flat section of noise characteristics is given, using an explanation of the physics of flicker noise. The mechanism and conditions of the exponential increase of flicker noise and its subsequent exponential desire for maximum magnitude are explained. A simple physical approximation is given to determine the processes of forming the envelope form of the spectral density of flickernoise. The physical understanding of the formation of spectral density of flicker-noise tension in the internal structure of the transistor with the participation of external circuits of the amplifier electrical circuit is detailed. The results of the study will help developers to solve many problems of building electronic devices and optimizing their characteristics at a qualitatively new level.

scholarly journals Performance assessment of a small-size ocean wave energy harvester

2019 ◽  
Vol 283 ◽  
pp. 05006
Author(s):  
Yongjie Sang ◽  
Bertrand Dubus
Keyword(s):  
Electrical Power ◽  
Vertical Motion ◽  
Electrical Energy ◽  
Ocean Waves ◽  
Electrical Circuit ◽  
Optimal Choice ◽  
Ocean Wave ◽  
Unit Weight ◽  
Ocean Energy ◽  
Ocean Wave Energy

A lightweight electromechanical device is studied to harvest energy of ocean waves and supply electrical power to small-size ocean observation equipment such as sonobuoys. It is composed of a magnet fixed to the floating housing which follows the motion of the ocean surface and a moving coil connected to the case via a flexible spring. As the floating housing follows the vertical motion of water surface, a voltage is induced in the coil due to relative velocity between the coil and the magnet, and kinetic energy of the ocean wave is converted into electrical energy. Full bridge rectifying circuit and smoothing capacitor are used to convert AC voltage to constant voltage. Single degree of freedom electromechanical model of the prototype transducer (LGT-4.5 geophone) is developed and simulated with an electrical circuit software to predict energy harvesting performance. Vibration experiments are also performed with a shaker to validate transducer model and quantify output voltage. Parametric analysis is conducted to identify optimal choice of capacitance in terms of maximum stored energy and minimum charging time. This device is simple and small size relative to ocean wavelength compared to classical linear permanent magnetic generator used in offshore power plant. Its power generation per unit weight is compared to larger scale ocean energy converters.

scholarly journals Minimum energy control of fractional positive electrical circuits

2016 ◽  
Vol 65 (2) ◽  
pp. 191-201 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Control Problem ◽  
Minimum Energy ◽  
Sufficient Conditions ◽  
Electrical Circuit ◽  
Existence Of Solution ◽  
Energy Control ◽  
Electrical Circuits ◽  
Minimum Energy Control

Abstract Minimum energy control problem for the fractional positive electrical circuits is formulated and solved. Sufficient conditions for the existence of solution to the problem are established. A procedure for solving of the problem is proposed and illustrated by an example of fractional positive electrical circuit.

Optimizing Energy Output of Piezoelectric Microcantilevers

2011 ◽  
Author(s):  
Mehdi Rezaeisaray ◽  
Don Raboud ◽  
Walied Moussa
Keyword(s):  
Output Voltage ◽  
Proof Mass ◽  
Geometry Optimization ◽  
Electrical Energy ◽  
Electrical Circuit ◽  
Energy Output ◽  
Test Cases ◽  
New Methods ◽  
Piezoelectric Cantilever ◽  
Piezoelectric Cantilevers

This work presents some new methods in optimizing electrical energy, harvested using a micro piezoelectric cantilever. Both mechanical and electrical aspects have been considered. Mechanically, two items have been considered to maximize the generated voltage: geometry of the cantilever and placement of the electrodes. It has been shown that for given sizes of length and width of the harvester and for a given natural frequency, the output voltage can be increased by adjusting the thickness of the beam and the proof mass and consequently increasing the amplitude of vibration. As well, the placement of the electrodes plays a very important role in optimizing output voltage. It has also been shown that piezoelectric cantilevers with shorter top electrodes induce higher voltage than cantilevers with longer top electrodes. Overall results agree with the analytical equations reported in literature so far. Moreover, distribution of top electrodes along the width of the cantilever has been taken into consideration. It has been shown how output voltage can be approximately doubled by using two narrower top electrodes along the width of the cantilever. All analysis in this work was carried out in ANSYS. In this research, to improve the electrical efficiency, diodes have been considered in the circuit to reduce electrical losses in comparison to rectifiers which have been used in conventional harvesters. Applying these methods to particular test cases, a 71% increase in output voltage was observed for the case of geometry optimization, a 116% increase was observed for the case of shortening the top electrode and losses in the electrical circuit were reduced by approximately 50% by using diodes comparing to using rectifiers. While these results focused on cantilever based harvesters, the ideas contained are equally applicable to other structures.

Study of an electromechanical nonlinear vibration absorber: Design via analytical approach

2020 ◽  
pp. 1045389X2095710
Author(s):  
Vinciane Guillot ◽  
Alireza Ture Savadkoohi ◽  
Claude-Henri Lamarque
Keyword(s):  
Degrees Of Freedom ◽  
Mechanical Response ◽  
Electrical Circuit ◽  
Vibration Absorber ◽  
Cubic Nonlinearity ◽  
Analytical Treatment ◽  
Nonlinear Absorber ◽  
Definition Of ◽  
Direct Numerical Integration ◽  
Two Degree Of Freedom

This article deals with the behavior and design of a homogeneous beam linked to an electrical absorber, via a piezoelectric material patched on the beam. The beam presents a cubic nonlinearity, which is consistent with geometrical nonlinearities for clamped-free beams. A cubic nonlinearity is added to the electrical circuit for similarity purposes. The coupled electromechanical equations are reduced to a two degrees of freedom system. The equation representing the mechanical response of the system is seen as the main system, whereas the equation coming from the electrical circuit would represent a nonlinear absorber. An analytical treatment at different time scales is endowed to identify electrical coefficients allowing the design of the electromechanical vibration absorber behavior. The equilibrium and singular points are identified, allowing the definition of ranges of forcing amplitudes leading to periodic and modulated regimes. The analytical results are compared with those obtained from direct numerical integration of the two degree of freedom system.

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