RLC Circuit Research Articles

Non-reflective Odd Harmonic Band Pass Filter

This article presents a non-reflective strip filter (NPF) with two passbands corresponding to the first and third harmonics of the received or transmitted signal. The NPF consists of connected strip lines (LPL) and RLC circuits included into the diagonal ports of the SPL. The solution of the inverse problem of obtaining the frequency dependence of the RLC circuits is presented. The obtained ratios provide the synthesis of the frequency characteristics of the RLC circuit and, ultimately, the characteristics of a non-reflective bandpass filter. Experimental results of the study of the single- stage NPF of odd harmonics with frequencies of 0.96 GHz and 2.9 GHz with return losses of at least –10 dB in the frequency range up to 4.8 GHz are presented.

Discrete Representation of Photovoltaic Modules

In order to develop a tool that facilitates the understanding of photovoltaic modules simulation, this work presents a methodology for representing these modules using only linear elements. Taking as a starting point the four-parameter representation of a photovoltaic module, a discrete equivalent is obtained based on the Newton-Raphson method for solving nonlinear equations. The characteristic curves, I-V and P-V, obtained with this methodology for a commercial module and its behavior when coupled to an RLC circuit are then presented.

Hidden attractors in Chua circuit: mathematical theory meets physical experiments

After the discovery in early 1960s by E. Lorenz and Y. Ueda of the first example of a chaotic attractor in numerical simulation of a real physical process, a new scientific direction of analysis of chaotic behavior in dynamical systems arose. Despite the key role of this first discovery, later on a number of works have appeared supposing that chaotic attractors of the considered dynamical models are rather artificial, computer-induced objects, i.e., they are generated not due to the physical nature of the process, but only by errors arising from the application of approximate numerical methods and finite-precision computations. Further justification for the possibility of a real existence of chaos in the study of a physical system developed in two directions. Within the first direction, effective analytic-numerical methods were invented providing the so-called computer-assisted proof of the existence of a chaotic attractor. In the framework of the second direction, attempts were made to detect chaotic behavior directly in a physical experiment, by designing a proper experimental setup. The first remarkable result in this direction is the experiment of L. Chua, in which he designed a simple RLC circuit (Chua circuit) containing a nonlinear element (Chua diode), and managed to demonstrate the real evidence of chaotic behavior in this circuit on the screen of oscilloscope. The mathematical model of the Chua circuit (further, Chua system) is also known to be the first example of a system in which the existence of a chaotic hidden attractor was discovered and the bifurcation scenario of its birth was described. Despite the nontriviality of this discovery and cogency of the procedure for hidden attractor localization, the question of detecting this type of attractor in a physical experiment remained open. This article aims to give an exhaustive answer to this question, demonstrating both a detailed formulation of a radiophysical experiment on the localization of a hidden attractor in the Chua circuit, as well as a thorough description of the relationship between a physical experiment, mathematical modeling, and computer simulation.

The radiation of RLC circuit with the longitudinal capacitor

The RLC circuit is generalized in such a way that the capacitor has longitudinal form and the components are all in series with the voltage source (R - L - C - v). The medium inside the capacitor is dielectric with the index of refraction n. The change of the amount of charges on the left and right side of the capacitor generate in dielectric medium special radiation which is not the Cerenkov radiation, no the Ginzburg transition radiation but the original radiation which must be confirmed in laboratories. We have calculated the spectral form of the radiation of RLC circuit with the longitudinal capacitor. It depends on the dielectric constant n of the capacitor medium. The defect in medium is involved in the spectral form and can be compared with the original medium. Such comparison is the analog of the Heyrovsky-Ilkovic procedure in the quantum electro-chemistry (Heyrovsky et al., 1965). The article is the preamble for the future investigation of electronic physics and can be integral part of such institutions as Bell Laboratories, NASA, CERN and so on.

Exploration of the Q factor for a parallel RLC circuit

An important property of oscillating systems like RLC circuits is the Q factor, which quantifies the strength of damping in the system. The Q factor is inversely proportional to the resistance for a series RLC circuit but increases with the resistance in a parallel RLC circuit. The surprising behavior of the parallel RLC circuit makes building and modeling this circuit an interesting project for a student laboratory. We describe an experiment that has been performed to explore this topic, share an example of the results that can be obtained, and suggest analyses that students might perform.

Mathematical Modeling of Electrical Circuits and Practical Works of Increasing Difficulty with Classical Spreadsheet Software

This paper presents a modeling practical works project of electrical engineering, proposed to the first-year students of the University Institute of Technology in France, during the COVID-19 pandemic. The objective of this paper is twofold. The first objective is to present to the students the opportunities of modeling and calculation development of a spreadsheet software in their professional lives. The second objective is to create a file that automatically calculates all the current and voltage values at each point of any alternative electrical circuit. The aim of this paper, geared toward students, is to bring them to build their own numerical remote lab, autonomously. Therefore, pedagogical keys are given along the reading of this document to help them to progress, both on electrical circuits conceptual understanding with series and parallel RLC circuits and on their computation in a spreadsheet software. As a conclusion, this paper can be used as a base to develop remote modeling practical works of many and different devices, as well as a database starting point of such analytical models.

ADAPTIVE TRACKING CONTROL FOR FRACTIONAL-ORDER NONLINEAR UNCERTAIN SYSTEMS WITH STATE CONSTRAINTS VIA COMMAND-FILTERING AND DISTURBANCE OBSERVER

In this paper, the state-constrained adaptive control problem for a class of uncertain fractional-order nonlinear systems with unknown external disturbances is studied. Using the fuzzy approximation and backstepping control layout, an adaptive disturbance-observer-based control method is proposed, which can effectively estimate the unknown external disturbances through the designed disturbance observers. As we know, the standard backstepping control has inherent computational complexity. Therefore, a design approach of fractional-order command filter is introduced, which takes advantage of fractional-order command filter to pre-estimate the virtual input signal and its fractional derivative. In addition, barrier Lyapunov functions are exploited to cope with the fractional states-constrained control problem. The combination of barrier Lyapunov function technique and backstepping design not only ensures excellent tracking performance, but also enhances the robustness of the system. Furthermore, based on the fractional Lyapunov approach, the relevant stability analysis is established, which demonstrates that all states of the system remain within their constrained scope, and all signals of the closed-loop system are bounded. Finally, the effectiveness of the proposed scheme is verified by numerical simulation examples of RLC circuit and horizontal platform system.

Haar Wavelet for Numeric Solution of Rlc Circuit Differential Equations

The wavelet transformation is a mathematical method developed over the past decades to be adapted for applications in the fields of science and engineering. The wavelet transform can be applied in the field of numerical analysis to solve the differential equation. This paper is concerned with applying Haar wavelet methods to solve an ordinary differential equation for an RLC series circuit with a known initial state. The matrix construction calculations are proposed in a simple way. Three numerical mathematical examples are shown that include second-order differential equations with variable and constant coefficients. The results showed that the proposed method is quite reasonable while comparing the solution of second order systems by Haar wavelet method with the exact solution in the context of serial RLC circuit. Moreover, the use of Haar waves is found to be simple, accurate, with flexible and appropriate arithmetic computational costs.

Adaptive Event-Triggered Control for Uncertain High-Order Fully Actuated System

In this brief, the adaptive event-triggered control problem is investigated for a class of uncertain high-order fully actuated (HOFA) systems. Different from the existing works on HOFA systems, this brief considers the unknown control matrix function, which only requires its maximum and minimum eigenvalues to be unknown a priori. To deal with the problem, the adaptive technique is applied to estimate the unknown parameters. To save the energy in signal transmission, the controller and its event-triggered mechanism are co-designed. By means of the Lyapunov stability theory, it is rigorously proved that the proposed controller can render that all signals of the closed-loop system are bounded. Finally, the effectiveness of the theoretical result is demonstrated on the basis of the numerical simulation on the RLC circuit.

Memory-Based Event-Triggered Output Regulation for Networked Switched Systems With Unstable Switching Dynamics.

This article studies an event-triggered asynchronous output regulation problem (EAORP) for networked switched systems (NSSs) with unstable switching dynamics (USDs) including all modes unstable and partial switching instants destabilization, which means that the Lyapunov function increases both on the activation intervals of all subsystems and at some switching instants. First, a memory-based mode-compared event-triggered mechanism for switched systems is proposed to effectively shorten asynchronous intervals, which employs historical sampled outputs and compares the mode of the current sampled instant and the adjacent sampled instant. Then, the maximum average dwell time for a novel switching signal is derived with a constraint on the ratio of total destabilizing switchings to total stabilizing switchings, which relaxes the requirement of the regular arrangement of destabilizing and stabilizing switchings. Moreover, with the help of different coordinate transformations in the EAORP, the discretized Lyapunov functions are no longer needed when synthesizing the NSSs with USDs, and the asynchronous switching situation is also discussed. Afterward, by designing a dynamic output feedback controller, sufficient conditions are given to solve the EAORP for NSSs with USDs subject to network-induced delays, packet disorders, and packet losses. Finally, the effectiveness of the proposed methods is verified via a switched RLC circuit.

Generalized Ulam–Hyers–Rassias Stability of Solution for the Caputo Fractional Non-instantaneous Impulsive Integro-differential Equation and Its Application to Fractional RLC Circuit

Generalized Ulam–Hyers–Rassias Stability of Solution for the Caputo Fractional Non-instantaneous Impulsive Integro-differential Equation and Its Application to Fractional RLC Circuit

A thermally activated VO2-based attenuator with SRR structure

To meet the requirement of blocking unwanted or interfering signals in modern communication systems, wideband phased-array antenna systems, and 5G mobile communications, we proposed a radio frequency (RF) attenuator based on a split ring resonator (SRR) that used a phase change material (PCM) vanadium dioxide (VO2). The SRR was transformed into a thermally activated attenuator by depositing a 120 nm VO2 thin film between the two gold rings of an SRR. We achieved an obvious attenuation (about 18 dB) at 3.55 GHz when the temperature increased from room temperature to 100 °C due to the dielectric constant drop and wide resistance variation of VO2 thin film during the phase change process. At the same time, we observed a hysteresis property on the S parameters due to the resistance hysteresis of VO2 during the heating and cooling process both in the theoretical and experimental results. Finally, considering the resistance of the VO2 thin film between two gold rings, we proposed a modified lumped RLC circuit model for the VO2-based RF attenuator.

Failure quantitative assessment approach to MOSFET power device by detecting parasitic parameters

With the emerging wide bandgap (WBG) semiconductor development, the increasing power density and efficiency of power electronic converters may cause more switching oscillation, electromagnetic interference noise, and additional power loss, further increasing the probability of device failure. Therefore, determining and quantifying the failure of a metal-oxide-semiconductor-field-effect transistor (MOSFET), which assembled using WBG semiconductor in some applications, is crucial to improving the reliability of a power converter. This study proposes a novel failure quantitative assessment approach based on MOSFET parasitic parameters. According to the two-port network theory, MOSFET is equivalent to some second-order RLC circuits composed of independent inductances, capacitances, and resistances in series. Then, the frequency-domain impedance associated with the physical failure of MOSFET is identified through frequency domain reflectometry. Accelerated aging and bond wires cut-off experiments are employed to obtain various quality states of the MOSFET device. Result shows that the MOSFET quality level and its number of bond wire lift-offs can be quantified effectively. Drain-to-source on-resistance (RDS(on)) that normally represents the MOSFET quality shows a positive linear function relationship on drain-to-source parasitic resistance (RD + RS) during the quality degradation proceeding. This finding matches with the correlation established between RDS (on) and RD + RS in theory. Meanwhile, source parasitic inductance (LS) increases with the severity of bond wires faults, and even the slight fault shows a high sensitivity. The proposed approach would be an effective quality screening technology for power semiconductor devices without power on treatment, which can effectively avoid the impact of junction temperature and test conditions (current and voltage) on test results, and does not need to design additional test circuits. The test frequency range we used in this approach was 10–300 MHz, which to some extent is suitable for providing an on-line quality monitoring technology for high-frequency WBG power devices manufacturing.

Numerical higher-order Runge-Kutta methods in transient and damping analysis

Transient analysis of an RLC circuit (or LCR circuit) comprising of a resistor, an inductor, and a capacitor are analyzed. Kirchhoff’s voltage and current laws were used to generate equations for voltages and currents across the elements in an RLC circuit. From Kirchhoff’s law, the resulting first-order and second-order differential equations, The different higher-order Runge-Kutta methods are applied with MATLAB simulations to check how changes in resistance affect transient which is transitory bursts of energy induced upon power, data, or communication lines; characterized by extremely high voltages that drive tremendous amounts of current into an electrical circuit for a few millionths, up to a few thousandths, of a second, and are very sensitive as well important their critical and careful analysis is also very important. The Runge-Kutta 5th and Runge-Kutta 8th order methods are applied to get nearer exact solutions and the numerical results are presented to illustrate the robustness and competency of the different higher-order Runge-Kutta methods in terms of accuracy.

High-Frequency Modeling of Delta- and Star-Connected Induction Motors

In this article, a high-frequency (HF) six-port delta- and star-connected three-phase induction motor model is proposed. The model consists of multistage RLC circuits, which include the mutual inductances between the phases. The three-phase HF motor model is derived from common-mode (CM) and differential-mode (DM) equivalent circuits, which are extracted from CM and DM measurements on the motor. A methodology is developed to consider the nonlinear DM inductance effect in the low-frequency (LF) range. The per-phase circuit is symmetric concerning the begin and end points. This symmetry allows us to connect a star configuration into a delta configuration by simply changing the phase connections of the proposed three-phase circuit without recalculating the parameters and vice versa. The three-phase motor model is eventually combined with external circuitry and simulated by a standard circuit solver. The proposed model allows impedance predictions with good accuracy up to 100 MHz. The method is verified with two induction machines, which have 3- and 11-kW rated powers. The proposed HF six-port three-phase motor model can be used for decoupled CM and DM noise predictions as well as for six-port mixed-mode noise prediction.

Application of Differential Transform Method with Adomian Polynomial for solving RLC Circuits Problems and Higher Order differential equations

. The differential transform method (DTM) for solving linear and nonlinear higher order differential equations especially which arising in the field of electric circuit problems is used. In almost cases, DTM gives the series of solutions which can be easily converted to exact ones. In nonlinear problems it is useful to use the Adomian polynomial to overheads the nonlinear terms. Also, this method is useful in both initial and boundary value problems.This method introduces a semi-analytic solution for differential equations, in polynomial form, it differs from the regular high order Taylor series technique, which necessitates the symbolic calculation of the necessary derivatives for the data functions. Comparison is made between numerical solutions obtained using DTM and other numerical methods, which trusses up the efficiency of the DTM method. Some illustrative examples are presented with some RLC circuit problems to show the simplicity and efficiency of the used method. All calculations are made with the help of computer algebra software Mathematica 11.2.

Imaginary axis eigenvalues of Hamiltonian matrix: controllability, defectiveness and the ϵ-characteristic

The eigenstructure of imaginary axis eigenvalues of a Hamiltonian matrix is of importance in many fields of control systems, for example, in stability analysis of linear Hamiltonian systems, computation of the solutions of an algebraic Riccati equation (ARE), existence of a Lyapunov function for LTI systems, etc. The dynamical system consisting of all stationary trajectories for an optimal control problem – often called the Hamiltonian system – is known to admit, in its state space dynamical equation, a Hamiltonian matrix for the system matrix. In each of these cases, defectiveness of imaginary axis eigenvalues of a Hamiltonian matrix turns out to be of crucial importance. For example, defectiveness causes unboundedness of the oscillatory stationary trajectories in the Hamiltonian system. A characterisation of the ARE solutions in terms of Lagrangian invariant subspaces of the Hamiltonian matrix when the imaginary axis eigenvalues are defective has been addressed in the literature for the controllable case. This paper focuses on the general case of uncontrollable systems; we formulate conditions under which the imaginary axis eigenvalues of the Hamiltonian matrix are non-defective: this is central for solutions corresponding to imaginary axis eigenvalues to not become unbounded. We provide conditions on the so-called -characteristic of the non-defective imaginary axis eigenvalue: this helps in the characterisation of Lagrangian invariant subspaces. We formulate conditions under which a passivity-based Hamiltonian matrix is normal (i.e. it commutes with its transpose), and we link normality of such Hamiltonian matrices with all-pass behaviour. In summary, this paper formulates results that link defectiveness of imaginary axis eigenvalues of Hamiltonian matrix to solvabilities of Lyapunov and Algebraic Riccati equations, controllability/observability, -characteristic and sign-controllability. We consider examples in the area of bounded-real transfer functions and RLC circuits, both controllable and uncontrollable, to study applicability of the results of this paper.

Intelligent Control of Performance Constrained Switched Nonlinear Systems With Random Noises and Its Application: An Event-Driven Approach

In this paper, the adaptive fuzzy control of switched stochastic nonlinear systems with set-time prescribed performance based on event-driven mechanism is studied. The creative part of this paper is that based on the set-time performance function, a modified event-triggered strategy that considers asynchronous switching to deteriorate system performance without strict assumptions is presented, which avoids Zeno behavior and saves communication resources. Then, by using backstepping recursive design technique, It <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\hat {o}$ </tex-math></inline-formula> ’s differential lemma and mode-dependent average dwell time (MDADT) method, a novel adaptive performance control scheme is proposed, which can ensure that all the variables in the system are semiglobally uniformly ultimately bounded (SGUUB) in probability and the tracking error gets into prescribed boundary no later than an arbitrarily adjusted setting time. Finally, the proposed algorithm is applied to a RLC circuit and its practicability is verified via simulation results.

Numerical Solutions of Fractional-Order Electrical RLC Circuit Equations via Three Numerical Techniques

In this article, three different techniques, the Fractional Perturbation Iteration Method (FPIA), Fractional Successive Differentiation Method (FSDM), and Fractional Novel Analytical Method (FNAM), have been introduced. These three iterative methods are applied on different types of Electrical RLC-Circuit Equations of fractional-order. The fractional series approximation of the derived solutions can be established by using the obtained coefficients. These three algorithms handle the problems in a direct manner without any need for restrictive assumptions. The comparison displays an agreement between the obtained results. The beauty of this paper lies in the error analysis between the exact solution and approximate solutions obtained by these three methods which prove that the Approximate Solution obtained by FNAM converge very rapidly to the exact solution.

Electronic transport in doped and dielectric inserted MLGNR interconnects: Crosstalk induced delay and stability analyses at sub-threshold regime

A simplified equivalent distributed temperature-dependent RLC circuit model of coupled multilayer graphene nanoribbon (MLGNR) interconnects has been discussed by considering the relaxation time induced mean free path (MFP), and its impact on line resistance (R) has been examined in detail. Further, the performance of copper, undoped, doped and dielectric inserted MLGNRs has been compared in terms of crosstalk induced delay and frequency response at sub-threshold operating conditions. It is revealed that the various scattering mechanisms (acoustic scatterings, edge roughness etc.) control the overall MFP in undoped and doped MLGNRs, however, the electron MFP in dielectric inserted MLGNRs depends on surrounding dielectric environment. Out of the five different cases of dielectric inserted MLGNRs, the insertion of hafnium oxide (HfO2) between GNR layers, along with silicon dioxide (SiO2) provides the best performance characteristics. To obtain minimum crosstalk delay at the subthreshold operating mode, copper, undoped, doped, and dielectric inserted MLGNRs have been optimized for thicknesses of 36, 38.25, 41.4, and 43.65 nm.