Nonlinear Electrical Circuit Research Articles

Solving Nonlinear Circuits With Pulsed Excitation by Multirate Partial Differential Equations

In this paper the concept of Multirate Partial Differential Equations (MPDEs) is applied to obtain an efficient solution for nonlinear low-frequency electrical circuits with pulsed excitation. The MPDEs are solved by a Galerkin approach and a conventional time discretization. Nonlinearities are efficiently accounted for by neglecting the high-frequency components (ripples) of the state variables and using only their envelope for the evaluation. It is shown that the impact of this approximation on the solution becomes increasingly negligible for rising frequency and leads to significant performance gains.

Experimental and Analytical Studies on Highly Efficient Regenerative Characteristics of a 20-kW Class HTS Induction/Synchronous Motor

This paper presents regeneration characteristics of a 20-kW class high-temperature superconductor induction /synchronous motor (HTS-ISM). It has experimentally been demonstrated that the HTS-ISM generates synchronous electric power at about rated condition (20 kW), and the corresponding efficiency is more than 90%. The tested characteristics have also been reproduced based on the nonlinear electrical equivalent circuit. These results clearly show the possibility of highly efficient synchronous regeneration performance.

A new approach to steady state analysis of nonlinear electrical circuits

PurposeThe purpose of this study is to identify a novel methodology for direct calculation of steady-state periodic solutions for electrical circuits described by nonlinear differential equations, in the time domain.Design/methodology/approachAn iterative algorithm was created to determine periodic steady-state solutions for circuits with nonlinear elements in a chosen set of time instants.FindingsThis study found a novel differential operator for periodic functions and its application in the steady-state analysis.Research limitations/implicationsThis approach can be extended to the determination of two- or multi-periodic solutions of nonlinear dynamic systems.Practical implicationsThe complexity of the steady-state analysis can be reduced in comparison with the frequency-domain approach.Originality/valueThis study identified novel difference equations for direct steady-state analysis of nonlinear electrical circuits.

Limits on the power available to harvest from broadband random excitation

With the large diversity in energy harvesters aiming to extract maximum power from broadband excitations, it is important to know what the maximum power achievable is. This paper derives new upper bounds on the available power for a harvester with general nonlinear stiffness coupled to a nonlinear electrical circuit. White noise base excitations are known to input power proportional to the total oscillating mass of the system and the magnitude of the spectral density of the noise regardless of the details of the oscillating system. This power is split between undesirable mechanical damping and useful electrical dissipation with the form of the stiffness profile and device parameters determining the relative proportions in each dissipation mechanism. An upper bound on electrical power is sought and, provided certain conditions are met, shown to be a simple function of relatively few system parameters and, importantly, independent of the stiffness profile or electrical nonlinearity.The benefits of knowing the upper limits on power are threefold: to guide optimal harvester design, to assess how close to optimal current devices are and to provide a preliminary estimation of the harvester mass necessary in a given operating environment for a given power requirement.

Structured Identification of Reduced-Order Models of Power Systems in a Differential-Algebraic Form

In a recent paper, we proposed a system identification method for constructing reduced-order models for the electro-mechanical dynamics of large power systems, divided into multiple coherent clusters, using Synchrophasors. Every cluster in the actual model was represented as an aggregate generator in the reduced-order model. An aggregate network graph connected one aggregate generator to another. In this paper, we extend this identification approach to differential-algebraic (DAE) models. First, every cluster is associated with a unique terminal bus, referred to as the pilot bus, that couples its internal network to the rest of the system. The proposed algorithm uses Synchrophasor measurements from the pilot buses to identify the dynamic model of the aggregate generator for each cluster using nonlinear least squares while retaining the identity of all the pilot buses. The resulting reduced-order model is in the form of a nonlinear electric circuit described by aggregate differential and algebraic equations. We illustrate our results using two case studies, one for the IEEE 9-bus power system and another for the IEEE 39-bus power system. We also discuss how these reduced-order DAE models may be useful for designing shunt controllers at the pilot buses by using Synchrophasor feedback.

Analysis of spatial chaos appearance in cascade connected nonlinear electrical circuits

The system consisting of several cascade connected electrical circuits is presented in this paper. Considering the system structure and the fact that the tunnel diodes have nonlinear characteristics, one of the properties of this system is the possibility of the chaos appearance. Necessary conditions and sufficient condition for the chaos appearance in the nonlinear cascade connected systems are given and analyzed, too. The results are confirmed by bifurcation and escape-time diagrams simulation.

Response of a resonant tunnelling diode optoelectronic oscillator coupled to a non‐linear electrical circuit

In this study, the authors present a numerical study of the dynamics of a non-linear optoelectronic oscillator (OEO) based on the resonant tunnelling diode (RTD) oscillator incorporating a photo-detector and coupled to a non-linear electrical circuit. In the first part, it is found that the RTD-OEO oscillator presents periodic and quasiperiodic behaviours depending on the values of the parameters of a pulse-like optical signal. In the second part where the RTD-OEO is coupled to the Van der Pol oscillator, the dynamics present a variety of states including bursting, relaxation and sinusoidal oscillations.

Equations and Stable Modes of Parametron

This work is devoted to investigation of nonlinear electric circuit—the resonance scheme with nonlinear reactive element. The role of this non-linearity plays the saturation of magnetic transformed coupling. The stationary mode in this scheme is supported by generator of alternating current. The idea of work of parametron is an opportunity of two stationary modes of current corresponded to borders of the main zone of parametrical resonance. These modes are used as binary logical states with high-frequency ability of switching. The efficiency of this scheme increases with growth of frequency and simultaneously decreasing of scale. The aim of this article is a summarizing of the method of study for scheme of this type for this and some analogous devices.

Integration of a torsion-based shear-mode energy harvester and energy management electronics for a sensor module

This work demonstrates the ability of a torsion-based shear-mode energy harvester to power a sensor module by integrating a temperature sensor circuit with a purpose developed piezoelectric energy harvester. A 10-cm3 energy harvester was developed for this application and was found to produce over 200 µW of maximum power through an optimal load resistance under 0.25 gpk acceleration excitation at its resonant frequency of 237 Hz. This harvester was then tested with two interface circuits: a standard interface diode bridge rectifier and a nonlinear synchronous electrical charge extraction circuit that were compared for their suitability in powering the sensor module. Through this, the synchronous electrical charge extraction nonlinear conditioning circuit was found to have superior performance when charging a capacitor and with DC loads at low voltages and was capable of providing a maximum power output of 37 µW under 0.25 gpk acceleration at 237 Hz. This output power was then used to successfully power a temperature sensor module consisting of a temperature sensor, a microcontroller, and a radio-frequency identification memory chip at a sensing frequency of 0.5 Hz.

Application of Input–State of the System Transformation for Linearization of Selected Electrical Circuits

Abstract The paper presents a transformation of nonlinear electric circuit into linear one through changing coordinates (local diffeomorphism) with the use of closed feedback loop. The necessary conditions that must be fulfilled by nonlinear system to enable carrying out linearizing procedures are presented. Numerical solutions of state equations for the nonlinear system and equivalent linearized system are included.

Saddle-Node Bifurcations in Classical and Memristive Circuits

This paper addresses a systematic characterization of saddle-node bifurcations in nonlinear electrical and electronic circuits. Our approach is a circuit-theoretic one, meaning that the bifurcation is analyzed in terms of the devices’ characteristics and the graph-theoretic properties of the digraph underlying the circuit. The analysis is based on a reformulation of independent interest of the saddle-node theorem of Sotomayor for semiexplicit index one differential-algebraic equations (DAEs), which define the natural context to set up nonlinear circuit models. The bifurcation is addressed not only for classical circuits, but also for circuits with memristors. The presence of this device systematically leads to nonisolated equilibria, and in this context the saddle-node bifurcation is shown to yield a bifurcation of manifolds of equilibria; in cases with a single memristor, this phenomenon describes the splitting of a line of equilibria into two, with different stability properties.

高温超電導誘導同期モータの駆動温度特性に関する解析的検討

This paper presents an analytical study on the temperature dependency of rotating characteristics in hightemperature superconducting induction/synchronous motors based upon the application of a nonlinear electrical equivalent circuit. The nonlinear current transport property of a superconducting BSCCO rotor bar is firstly characterized for different temperatures, and then introduced to the equivalent circuit. The cooling efficiency of a cryocooler is also considered for calculating motor performance. It is shown that the subject motor shows high efficiency for variable rotation speed and torque even when considering cryocooler consumption power.

Simulation and initial experiments of a high power pulsed TEA CO2 laser

In this paper, the output characteristics of a UV pin array pre-ionized TEA CO2 laser have been simulated and compared with the associated experimental data. In our simulation, a new theoretical model has been improved for transient behavior analysis of the discharge current pulse. The laser discharge tube was modeled by a nonlinear RLC electric circuit as a real model for electron density calculation. This model was coupled with a six-temperature model (6TM) in order to simulation dynamic emission processes of the TEA CO2 laser. The equations were solved numerically by the fourth order Runge–Kutta numerical method and some important variables such as current and voltage of the main discharge, resistance of the plasma column and electron density in the main discharge region, were calculated as functions of time. The effects of non-dissociation factor, rotational quantum number and output coupler reflectivity were also studied theoretically. The experimental and simulation results are in good agreement.

One-port nonlinear electric circuit for simulating grounding systems under impulse current

A one-port nonlinear electric circuit to simulate grounding systems behaviors under high impulse currents is presented. The circuit is based on Loboda's and Pochanke's equations, which describe nonlinear behaviors of soil ionization phenomena. One of the major features of this nonlinear circuit is the possibility to simulate both ionization regions (linear and nonlinear) as a complete grounding system, in commercial simulation software such as Pspice, WorkBench®, ATP or EMTP. In order to determine the linear and nonlinear circuit parameters, two known impulse current curves i(t) were applied on scale models and the corresponding impulse voltages U(t) were measured. From these circuit parameters, the U(t)×i(t) experimental curves were compared with one-port simulated results and the similarities, evaluated using the Area Under Curve (AUC) method, varied in the range 92–99%. In order to compare simulations with experimental data, a field circuit was elaborated to test three experimental scale models using single rods of different lengths.

Experimental active spike responses of analog electrical neuron: beyond “integrate-and-fire” transmission

Using an analog electrical FitzHugh–Nagumo neuron including complex threshold excitation (CTE) properties, we analyze its spiking responses on pulse stimulation. The system is subjected to external pulse stimulus and can generate nonlinear integrate-and-fire and resonant responses which are typical for excitable neuronal cells. Following earlier theoretical predictions, we found that for certain parameters range, there is a possibility to trigger a spiking sequence with a finite number of spikes in response to a single short stimulus pulse. Hence, active transformation of N incoming pulses to M outgoing spikes is possible. We also show that the nonlinear electrical circuit with the CTE feature can be effectively synchronized by a periodic pulse train with 1 to M spike frequency ratio.

Electromechanical Modeling of <inline-formula> <tex-math notation="TeX">$\hbox{Nb}_{3}\hbox{Sn} $</tex-math></inline-formula> Superconducting Wires Subjected to Periodic Bending Strain

The transport performance of Nb <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> Sn cable-inconduit conductors (CICCs) depends on the strain distribution along the superconducting filaments determined by the combination of electromagnetic and mechanical forces applied to the strands. Experimental studies on the effect of bending strain were performed at the University of Twente by means of the Test Arrangement for Strain Influence on Strands (TARSIS) facility. The aim of this paper is to verify the agreement between a detailed electromechanical model of the wire and the experimental results obtained in TARSIS. A numerical model of two Nb <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> Sn internal tin strands was developed, which describes the wire through a distributed parameter nonlinear electrical circuit. The model requires a single strand to be discretized into a number of elements, connected by transverse conductances and subjected to a given strain distribution. The strain distribution maps were computed at the École Centrale Paris by means of the MULTIFIL code at different experimental conditions in the TARSIS facility. The simulation results show good agreement with the experimental ones in terms of both critical current and n-value degradation.

Modelling and computation of nonlinear magnetic and electric circuits

Modelling and computation of nonlinear magnetic and electric circuits

Computation of intermodulation distortion in RF MEMS variable capacitor circuits using moments

This paper introduces a new technique for the efficient computation of intermodulation distortion in radio frequency circuits that contain microelectromechanical system (MEMS) variable capacitors using moments analysis. This method is applied to an extended harmonic balance formulation, which contains the nonlinear equations that describe the dynamic mechanical behavior of MEMS variable capacitors, in addition to the nonlinear electric circuit equations. As a result, the moments method becomes a general multi-domain simulation method for quantifying nonlinear intermodulation distortion, while presenting significant computational cost reduction over harmonic balance-based methods.

Chaos modelling and simulation of cascade connected nonlinear electrical systems using MATLAB/Bondsim

In this paper, a system consisting of several cascade connected nonlinear electrical circuits is presented with tunnel diodes situated in each cascade. Tunnel diodes have nonlinear characteristics, enabling the possibility of chaos appearance in a system with several cascade connected electrical circuits. In this paper, Bondsim library and tools used to simplify modelling and simulation of cascade connected electrical circuits will be presented. This library enables direct drawing of the MATLAB/Simulink block diagrams from bond graphs. MATLAB M-files were also used for escape-time diagrams simulation and defining values of bifurcation amplification.

Controlling networks of nonlinearly-coupled nodes using response surfaces.

Control of complex processes is a major goal of network analyses. Most approaches to control nonlinearly coupled systems require the network topology and/or network dynamics. Unfortunately, neither the full set of participating nodes nor the network topology is known for many important systems. On the other hand, system responses to perturbations are often easily measured. We show how the collection of such responses –a response surface– can be used for network control. Analyses of model systems show that response surfaces are smooth and hence can be approximated using low order polynomials. Importantly, these approximations are largely insensitive to stochastic fluctuations in data or measurement errors. They can be used to compute how a small set of nodes need to be altered in order to direct the network close to a pre-specified target state. These ideas, illustrated on a nonlinear electrical circuit, can prove useful in many contexts including in reprogramming cellular states.