Linear Inductor Research Articles

Solving dynamic electric circuit with nonlinear hysteretic inductor using harmonics interpolation method

SummaryThe aim of this paper is to present a methodology for solving а dynamic electric circuit with nonlinear hysteretic inductor without the use of hysteresis model or equivalent circuits. A consideration of nonlinear and hysteretic behaviour of the magnetic core under quasistatic conditions is based on applying harmonics interpolation method (HIM) to the measured magnetising field strength waveforms. A dynamic behaviour of the magnetic core is considered through the application of the statistical theory of losses (STL). A considered electric circuit consists of AC voltage source connected in series with shunt resistor, additional linear resistor and inductor, as well as a nonlinear hysteretic inductor. The solution for electric current of the circuit is obtained by solving equation derived from Kirchhoff's laws through a series of successive iterations. Coupling of electric and magnetic part of the circuit is obtained from fundamental laws of electromagnetism. Methodology is validated for four cases of the considered electric circuit — without additional elements, with one additional or both additional elements, for sinusoidal voltage source amplitudes of 2, 4, 6, 8 and 9 V and frequency of 50 Hz. Validation is repeated for frequencies of 100, 200 and 300 Hz while keeping the ratio of the amplitude to frequency constant. Detailed theoretical approach and methodology, comparisons between measured and calculated results, as well as adequate discussion are presented.

Exact Analytical Solutions for the Kinks, the Solitons and the Shocks in Discrete Nonlinear Transmission Line with Nonlinear Capacitance

Discrete transmission lines constructed from ideal linear inductors and nonlinear capacitors (and possibly resistors) are studied. The localized travelling waves in the lossless transmission lines are the kinks and the solitons, the localized travelling waves in the lossy transmission lines are the dissipative kinks and the shocks. The speeds and profiles of all these waves are calculated.

Математическая модель для проектирования линейных асинхронных электродвигателей и ее программная реализация

Mathematical models are the main tool for the layout design of linear asynchronous electric motors. Existing design models of linear asynchronous electric motors assume that the device is powered from a source of multiphase symmetrical positive sequence current, which excludes from consideration the asymmetry of the inductor phase currents and the associated reduction in traction force. This approach is not flexible enough, since the operation of linear asynchronous electric motors in a wide range of movement speeds assumes a functional relationship between the current asymmetry coefficient and the movement speed. The study developed a mathematical model for design purposes that implements the functional relationship between the current asymmetry coefficient and the speed of movement. The mathematical model represents 13 linear equations linking geometric dimensions, current loads, electromagnetic field characteristics and mechanical forces with the speed of the secondary element of the electric motor. The current load of an electric motor has a variable degree of ellipticity depending on the speed of movement. An algorithmic study of the mathematical model was carried out and corresponding software modeling tools were developed. The proposed program algorithm, containing two subroutines, is implemented using the Maple symbolic computing software package. In order to expand the range of users, the software model is additionally implemented in C++. In this case, the functional dependence of the asymmetry coefficient of the exciting current wave on the speed of movement is implemented in the form of an iterative procedure for the case of connecting the winding of the linear asynchronous electric motors inductor to a source of symmetrical three-phase voltage according to the “triangle” circuit. Using the example of a three-phase linear asynchronous electric motors, the electromagnetic and mechanical characteristics of the electric motor were simulated. It was stated that the influence of current asymmetry on the mechanical characteristics of the linear asynchronous electric motors is small and is expressed in the region of high speeds. This makes it possible, in design tasks for the layout of an electric motor, to use models that involve powering the linear asynchronous electric motors from a symmetrical current source or to introduce a fixed asymmetry coefficient into them.

Linear generator for power supply to on-board consumers of high-speed magnetically levitated carriages

Background: Maglev transport is a promising mode of transport that can provide passenger and freight transportation at speeds of up to 400-500 km/h, and in the longer term – up to 1000 km/h. Active research in this area is being conducted in China, Japan, and the USA. Currently, in China and Japan, speeds of 450-500 km/h have been achieved for commercial transportation, and promising programs have been adopted for the construction of high-speed maglev tracks and the creation of rolling stock. At such speeds, one of the pressing problems is the problem of contactless energy transfer for on-board consumers located on the carriage, because it is very difficult to ensure reliable contact current collection at speeds of 450-500 km/h and above.
 Aim: development of the design, calculation and analysis of the characteristics of a linear generator of electrical energy for contactless power transfer to the moving crew of high-speed magnetically levitated transport.
 Materials and methods: to calculate the external magnetic field of the linear generator inductor and the EMF induced in the receiving coil of the crew, methods of electromagnetic field theory and electrical circuit theory were used; calculation algorithms are implemented in the Visual Basic for Applications software environment.
 Results: a design was proposed and the calculation of the external magnetic field of an inductor with transposition of conductors was performed; to increase the EMF induced in the receiving coil of the crew, it is proposed to give the receiving coil a double 8-shape; the most rational inter-circuit distance of the linear generator inductor has been established; the nature of the change in the magnetic flux penetrating the receiving coil when the vehicle moves, and the magnitude of the emf induced in the receiving coil are determined.
 Conclusion: the results can be used in the development of rolling stock for promising high-speed maglev transport systems.

Solitonic rogue waves induced by the modulation instability in a split-ring-resonator-based left-handed coplanar waveguide

Modulation instability and nonlinear excitation modes in lower and upper frequency bands are investigated in the nonlinear left-handed coplanar waveguide, where nonlinear capacitance (voltage-dependent) is used. The multi-scale method is employed to derive a system of two coupled nonlinear Schödinger equations governing the evolution of the kink and bright solitons of these modes. A modulation instability is investigated to show the effects of the left-handed and right-handed influences on the modulation instability gain and the intensity of the plane wave. In the lower and upper frequency modes, the breathing structures have strong values for the left-handed component. At the end, the numerical simulation of the continuous wave is used to show the development of the modulated waves and localized objects. Another relevant localized structure has been obtained to display the second-order breathers and Akhmediev breathers of types A and B under the variation of the perturbed wave number. Both linear inductances and perturbed wave numbers are tools for controlling the amplitude of the localized structures, and modulation instability is sensitive to these parameters.

Arnold Tongue-Like Structures and Coexisting Attractors in the Memristive Muthuswamy–Chua–Ginoux Circuit Model

The three-dimensional Muthuswamy–Chua–Ginoux (MCG) circuit model is a generalization of the paradigmatic canonical Muthuswamy–Chua circuit, where a physical memristor assumes the role of a thermistor, and it is connected in series with a linear passive capacitor, a linear passive inductor, and a nonlinear resistor. The physical memristor presents an electrical resistance which is a function of temperature. Nowadays, the MCG circuit model has gained considerable attention due to the lack of extensive numerical explorations and their distinct dynamical properties, exemplified by phenomena such as the transition from torus breakdown to chaos, giving rise to a double spiral attractor associated to independent period-doubling cascades. In this contribution, the complex dynamics of the MCG circuit model is studied in terms of the Lyapunov exponents spectra, Kaplan–Yorke (KY) dimension, and the number of local maxima (LM) computed in one period of oscillation, as two parameters are simultaneously varied. Using the Lyapunov spectra to distinguish different dynamical regimes, KY dimension to estimate the attractors’ dimension, and the number of LM to characterize different periodic attractors, we construct high-resolution two-dimensional stability diagrams considering specific ranges of the parameter pairs [Formula: see text]. These parameters are associated with the inverse of the capacitance in the passive capacitor, and the heat capacitance and dissipation constant of the thermistor, respectively. Unexpectedly, we identify sequences of infinite self-organized generic stable periodic structures (SPSs) and Arnold tongues-like structures (ATSs) merged into chaotic dynamics domains, and the coexistence of different attracting sets (attractors) for the same parameter combinations and different initial conditions (multistability). We explore the multistable dynamics using the stability analysis and computation of Lyapunov coefficients, the inspection of the coexisting attractors, bifurcations diagrams, and basins of attraction. The periods of the ATSs and a particular sequence of shrimp-shaped SPSs obey specific generating and recurrence rules responsible for the bifurcation cascades. As the MCG circuit model has the crucial properties presented by the usual Muthuswamy–Chua circuit model, specific properties explored in our study should be helpful in real problems involving circuits with the presence of physical memristor playing the role of thermistors.

Programmable hardening and softening cubic inductive shunts for piezoelectric structures: Harmonic balance analysis and experiments

It has been well explored in the literature that intentionally introduced (designed) nonlinearities offer significant advantages in vibration absorption and isolation problems. In the context of using piezoelectric shunt damping for vibration attenuation in flexible structures, synthetic impedance circuits with digital control enable precise tuning capabilities and eliminate the need for bulky analog circuit components when targeting low frequencies, and they have been studied mostly for linear circuits. In this work, we explore nonlinear synthetic impedance-based Duffing shunts with hardening and softening nonlinearities, connected to a cantilever under base excitation in its geometrically and materially linear regime. We demonstrate a shunt of nonlinear impedance equivalent to a positive or negative cubic inductor connected in parallel to a linear inductor and a linear resistor. This shunt, along with the inherent piezoelectric capacitance, provides digital analog of a hardening- or softening-type nonlinear stiffness, linear stiffness, linear damping, and mass, as a synthetic Duffing circuit. Electromechanical modeling of a piezoelectric cantilevered beam shunted to the Duffing oscillator with hardening or softening inductance is performed. Numerical simulations for single-term and multi-term harmonic balance solutions are performed for periodic response. These approximate analytical predictions are compared against time-domain numerical simulations and are experimentally validated for various mechanical excitation amplitudes and nonlinear coefficients. Overall, a very good agreement is obtained between the model simulations and experimental results, in addition to demonstrating the unique digital programming capabilities of this nonlinear shunt.

All-JJ Logic Based on Bistable JJs

The all-JJ logic family is a promising area and power efficient, scalable single flux quantum (SFQ) technology for application to exascale supercomputers. All-JJ superconductive logic is based on a superconductor-ferromagnet-superconductor (SFS) bistable JJ, enabling nanometer feature sizes in VLSI complexity superconductive systems. In this paper, a mechanical analogy is proposed to describe the dynamic behavior of these bistable JJs. Novel all-JJ logic gates, such as TFF, DFF, OR, AND, and NOT gates, are presented here. All-JJ circuits are composed of bistable JJs, standard JJs, and bias currents, requiring no large inductors within the storage loops. All-JJ logic cells exhibit less delay and power than standard SFQ cells with the same critical current density. All-JJ systems can operate at high frequencies due to the small capacitance of the SFS JJ. A complex all-JJ circuit from the suite of ISCAS'85 benchmark circuits is also characterized. This complex all-JJ circuit exhibits less delay and power as compared to standard SFQ logic. The bias current in a conventional benchmark circuit and all-JJ benchmark circuit is, respectively, 22 mA and 13 mA. The delay of each cell within the conventional benchmark circuit and all-JJ benchmark circuit is, respectively, approximately 20 and 8 ps. A parasitic inductance in series with the JJs disturbs the current distribution within the all-JJ circuits while degrading the margins. To suppress the effects of this parasitic inductance on SFS JJs, small linear inductors are added to manage the current distribution and improve parameter margins.

EXCITATION MAGNETIC FIELD IN THE GAP OF A LINEAR INDUCTOR MOTOR

In high-speed land transport (HSLT), asynchronous, synchronous and inductor linear motors can be used to drive the crew. Asynchronous linear motors are simple in design, but have relatively low energy performance (efficiency of 0.8; cosφ = 0.5). Synchronous linear motors have higher energy indices (efficiency of 0,9; cosφ = 0,95), but require large material expenses. The intermediate variant is the linear inductor motors, the construction of which is a little more complicated than the linear induction motors, but these motors, as well as synchronous motors, have high energy indicators.

A new AC motor driven by travelling magnetic field excited on LC ladder circuit without its nonlinearity

In three-phase AC motors, three-phase AC voltage system is essential to generate a rotating magnetic field. Three- phase AC motors also require a three-phase inverter for variable speed and torque operation. In general, the number of switching devices used in three-phase inverter is not less than six and decreasing its number is difficult. This paper focuses on an LC ladder circuit consisting of linear inductors and capacitors. This paper presents a new operating method of the AC motor based on a propagating magnetic field. It is successfully excited by connecting one single-phase AC power supply to the end of the LC ladder circuit. The induction motor operated by the presented method produces torque as in general induction motors.

The Dynamic Model of a Linear Electromagnetic Motor for a Laboratory Shaker

For setting up linear movement (translational or reciprocating) with a specified frequency, rack, screw or more complex gears are most often used. The presence of an additional kinematic link results in increased losses, degraded reliability, increased noise, and pooper weight and dimension indicators. An alternative option is to use a linear electromechanical converter. The article presents the results of numerical simulation of a linear electromagnetic motor (also known as a linear inductor motor) based on the finite element method. An linear inductor motor is designed to drive a laboratory shaker applied in medicine. A mathematical model of the physical processes of linear inductor motor operation is presented. A term for considering the viscous friction force is introduced into the equation of motion, which makes it possible to improve the accuracy of the calculations. Three-dimensional models of an linear inductor motor are considered: a single-sided one (for the action of a one-sided electromagnetic force and a two-sided one (for the case of alternately acting oppositely directed electromagnetic forces). Various design options are analyzed, and the most suitable one is proposed based on the analysis results. Temporal dynamic characteristics of the linear inductor motor model for the case of operation in the regions of resonant and off-resonant frequencies are obtained, their analysis is performed, and recommendations for further improvement of the design are given. The possibility of using the considered motor for driving a laboratory shaker is qualitatively assessed.

Nanoscale on-chip inductors using a linearized meminductive circuit

This work presents a novel RF on-chip inductor that overcomes the problems with conventional large-sized inductors, which cannot be placed in an integrated circuit (IC) for large inductance values. The proposed inductor depends mainly on the meminductor, a new passive circuit element that has memory properties. This new circuit element is argued to be common in the nanoscale, where the dynamical properties of electrons and ions are likely to depend on the history of the system. Being nonlinear, it is shown that, by a suitable arrangement of meminductors and through appropriate initial values for their inductances, we can achieve a linear nanoscale inductor.

Floating Interleaved Boost Converter with Zero-Ripple Input Current Using Variable Inductor

A zero-ripple input current is known to improve the lifetime of battery sets and fuel cells and to assure maximum power point tracking in PV panels. To perform current ripple elimination in a floating interleaved boost converter (FIBC), one of the typical linear inductors is substituted by a variable inductor, and phases of the converter have complementary duty cycles. This variable inductor is controlled using a switched current-source converter, which adjusts the input current ripple. An equivalent model for the variable inductor is presented, including uncertainties in the component description. To achieve current stabilization, a variable inductor controller was designed using the sliding modes approach via fixed frequency. An experimental prototype is implemented and tested with an output voltage controller to compare with the conventional FIBC. The results demonstrate that the input current ripple of the proposed converter is eliminated without significantly decreasing the efficiency.

Assessment of the Current for a Non-Linear Power Inductor Including Temperature in DC-DC Converters

A method for estimating the current flowing through a non-linear power inductor operating in a DC/DC converter is proposed. The knowledge of such current, that cannot be calculated in closed form as for the linear inductor, is crucial for the design of the converter. The proposed method is based on a third-order polynomial model of the inductor, already developed by the authors; it is exploited to solve the differential equation of the inductor and to implement a flux model in a circuit simulator. The method allows the estimation of the current up to saturation, intended as the point at which the differential inductance is reduced to half of its maximum value. The current profile depends also on the inductor temperature. Based on this, the influence of core temperature on the conduction time of the power switch was determined. This study shows that the exploitation of saturation requires a proper value of the conduction time value that depends on the temperature. The theoretical analysis has been experimentally verified on a boost converter and is valid for the entire class of DC-DC converters in which the power inductor is subjected to a constant voltage for a given time. The simulations agree with the experimental data from a case study concerning conduction time and temperature.

МОДЕЛИРОВАНИЕ ВОЗВРАТНО-ПОСТУПАТЕЛЬНО-ВРАЩАТЕЛЬНОГО ЭЛЕКТРОПРИВОДА ВИБРОЦЕНТРОБЕЖНОГО СЕПАРАТОРА

The article considers a computer model of a reciprocating-rotational electric drive based on rotational and linear motion electric motors implemented in the Matlab (Simulink). Giving the working body of a centrifugal separator with a vertical axis of rotation of axial vibrations loosens the grain mixture and cleans the main grain crop from weed impurities. In addition, the superimposition of vertical inertia forces to the centrifugal inertia force makes it possible to ensure the maximum possible value of the coefficient of the living section of the sieve. In addition, the superimposition of vertical inertia forces to the centrifugal inertia force makes it possible to ensure the maximum possible value of the coefficient of the living section of the sieve. The use of a linear inductor motor (LIM) paired with an elastic element for the implementation of axial oscillatory movements of the working body makes it possible to simplify the design of the drive mechanism of the separator. According to the results of the conducted studies of the simulation model of a reciprocating-rotational electric drive, it was determined that with a decrease in the length of the hole l relative to the circumference of the ring (secondary element of the LIM), the magnitude of the displacement of the center of the oscillation of the working organ from the point of the beginning of its movement increases and the amplitude of the oscillation increases.

A Cubic Memristive System with Two Twin Rössler-Type Chaotic Attractors Symmetrical About an Invariant Plane

Memristive circuits and systems have been widely studied in the last years due to their potential applications in several technological areas. They are capable of producing nonlinear periodic and chaotic oscillations, due to their locally-active characteristics. In this paper, we consider a cubic four-parameter differential system which models a memristive circuit consisting of three elements: a passive linear inductor, a passive linear capacitor and a locally-active current-controlled generic memristor. This system has a saddle-focus equilibrium point at the origin, whose global stable and unstable manifolds are, respectively, the [Formula: see text]-axis and the plane [Formula: see text], which are invariant sets where the dynamic is linear. We show that this structure can generate two twin Rössler-type chaotic attractors symmetrical with respect to the plane [Formula: see text]. We describe the mechanism of creation of these chaotic attractors, showing that, although being similar to the Rössler attractor, the twin attractors presented here have simpler structural mechanism of formation, since the system has no homoclinic or heteroclinic orbits to the saddle-focus, as presented by the Rössler system. The studied memristive system has the rare property of having chaotic dynamics and an invariant plane with linear dynamic, which is quite different from other chaotic systems presented in the literature that have invariant surfaces filled by equilibrium points. We also present and discuss the electronic circuit implementation of the considered system and study its dynamics at infinity, via the Poincaré compactification, showing that all the solutions, except the ones contained in the plane [Formula: see text], are bounded and cannot escape to infinity.

Nonlinear wave transmission in a two-dimensional nonlinear electric transmission network with dissipative elements

A two-dimensional nonlinear discrete electric transmission network made of several well-known anharmonic modified Noguchi lines coupled transversely to one another with a linear inductor is considered and the dynamics of modulated waves are investigated. The linear analysis shows that increasing either the dispersive elements of the network, the coupling elements of the network, or the transverse wavenumber increases the propagating frequencies. Employing the reductive perturbation method, we establish that the dynamics of modulated waves in the network system are governed by a two-dimensional dissipative nonlinear Schrödinger (NLS) equation having, depending on both the longitudinal and transverse wavenumbers as well as on the network parameters, either the hyperbolic or the elliptic character. Through the derived dissipative NLS equation, the phenomenon of the baseband modulational instability (MI) of the electric system under consideration is investigated and the analytical expression for the baseband MI growth rate is presented. We show that the dispersive elements of the network system softens the baseband MI and enhances the baseband MI domain. Under the condition of the baseband MI, we find approximate modulated wave solutions of the governing equations which are then used for analytical investigation of the transmission of super rogue wave voltage, Peregrine soliton voltage, and bright solitary wave signals through the network system under consideration. The effects of the network and solution parameters such as the dispersive, coupling parameters, the carrier wavenumber, and the wavenumbers in both the longitudinal and transverse directions on the dissipative wave signals are presented.

Development and study of a microprocessor automatic control system for a mono-switch tie type with a linear inductive electric motor and a discrete speed controller

Introduction. The article is devoted to the development of the microprocessor automatic control system for a gearless controlled electric drive of a mono-switch tie based on a linear inductor electric motor. This solution provides control the position of the switch point, to carry out the transfer process with a smooth drive of shanks to the frame rail, to protect electric motor elements from overloads. Goal. development and study of the behavior of microprocessor automatic control system for mono-switch tie type with linear inductive electric motor and discrete PID speed controller which coefficients are adjusted according to Chin-Hrons-Reswick method to meet modern traffic safety requirements and improve operational reliability factors. Methodology. On the basis of electric drive theory, a kinematic line of a mono-switch tie type with nonlinear friction characteristic is presented. Using differential equation theory and Laplace transformation, a mathematic description of a linear inductor electric motor has been made. Using the z-transform method, a difference equation for describing a discrete PID speed controller is obtained, the coefficients of which are derived using the Chin-Hrons-Reswick method. A simulation mathematical model of the electric drive mono-switch tie type as the microprocessor automatic control system with linear inductive electric motor and discrete PID speed controller and nonlinear friction characteristic was built in MATLAB. Results. Simulation modelling of a mathematical model of the microprocessor automatic control system of the electric drive mono-switch tie type with the linear inductive electric motor and discrete PID speed controller and nonlinear friction characteristic have been developed and performed. Studies of dynamics of switch point movement have shown that, a drive time of less than 0.7 s at a constant speed motor armature of 0.2 and 0.3 m/s provides to meet modern requirements for railway switch points. The application of discrete PID speed controller has shown improved dynamics of switch point. Originality. First for the electric drive of the mono-switch tie type with linear inductive electric motor a mathematical model of the discrete PID speed controller and nonlinear friction characteristic as an object of speed control of switch point movement, has been developed. Practical value. Mathematical model of a railway track switch of the mono-switch tie type with linear inductive electric motor and discrete PID speed controller has been developed to carry out the control of the position of the switch point, process with a smooth drive them to the frame rail, to protect electric motor elements from overloads.

EMI Worsening in a SMPS with Non-linear Inductor

This paper is focused on the input current in a Switched Mode Power Supply (SMPS) in which the power inductor is exploited up to the saturation showing a non-linear behaviour. The input current exhibits a distortion due to the nonlinearity. The electromagnetic interference (EMI) caused by the ripple at switching frequency, superimposed to the DC value of the input current, requires a suitable design of the input differential mode (DM) filter. The input current is analyzed both in the time and frequency domain for different operating conditions, and it is compared to a SMPS equipped with a traditional linear inductor.

Analysis of an Oscillation Circuit with a Linear Time-invariant Inductor and a Capacitor Modelled with Conformal Fractional Order Derivative

Fractional order circuit elements are being examined by researchers unremittingly. They are ever becoming more popular in the literature. The Conformable Fractional Derivative has been proposed and gained importance in the last decade. Examination of an LC tank circuit or an LC oscillator can be found in almost all undergrad physics books. There’s a considerable number of studies on fractional-order capacitor circuits but, to the best of our knowledge, examination of an oscillator made of a linear time-invariant inductor and a supercapacitor modeled with Conformable Fractional Derivative has not been found in literature. In this paper, a lossless oscillator circuit containing a linear time-invariant inductor and a supercapacitor modeled with Conformable Fractional Derivative is examined for the first time in the literature. Natural response of the circuit has been found analytically. Its behavior has been illustrated with simulations for different initial conditions.