Series RLC Circuit Research Articles

RLC circuits: Obtaining the current graph using a mobile application

In this document we simulate the response (current value for t≥0) for a series RLC circuit through the solution of a second order differential equation. A mobile application is developed for the Android Operating System that obtains the graph of this current using the ANDROID STUDIO development environment and the GRAPHVIEW library. With the choice of the mathematical expression that defines the voltage in the circuit and the values of the resistance, the inductance, capacitance, the initial current and the initial voltage in the capacitor or initial charge, this graph is obtained, which when compared with what is obtained using a CAS, no difference is perceived, which shows the validity of the results of the app. This application can help engineering students to understand in an easy and simple way the concepts related to this type of circuits, thus promoting the use of mobile devices in teaching-learning environments.

Inductive excitation of a series RLC-circuit by rectangular voltage pulses. Analysis, numerical estimates

Inductive excitation of a series RLC-circuit by rectangular voltage pulses. Analysis, numerical estimates

Continuum Modeling of Inductor Magnetic Hysteresis and Eddy Currents in Resonant Circuits

This paper presents a high-fidelity finite-element modeling technique for magnetic hysteresis and eddy current losses in toroid inductors. The method is based on the separation of ferromagnetic loss characteristics into two components: a quasi-static hysteresis component and a dynamic eddy current component. The Preisach model is used to describe the quasi-static magnetic hysteresis behavior of the core, providing strong guarantees on the reproducibility of the experimentally measured characteristics. This model is used to represent the magnetic field constitutive relationships within a finite-element framework combining the effects of hysteresis and eddy currents in a unified dynamic simulation. The finite-element model of the toroid is used as a high-order inductor model coupled to a resonant circuit simulation. The modeling technique is validated through experimental measurements on two different series RLC circuits. The first circuit is based on an M19 electrical steel toroid having resonant frequency near 200 Hz. The second circuit is based on a T38 ferrite toroid having a resonant frequency near 10 kHz. The models agree closely with the measured voltages, currents, and losses. The models also successfully predict discontinuities in the measured frequency responses due to the existence of bistable operating regimes.

Periodic Event-Triggered Dynamic Output Feedback Dissipative Control With Stochastic Detection

This brief is concerned with the problem of periodic event-triggered dynamic output feedback (DOF) dissipative control with a probabilistic detection of event-triggering conditions. By employing the input-delay approach, the stochastically periodic event-triggered control (SPETC) system is modeled as a probabilistic delay closed-loop system. Then by utilizing tools from Lyapunov functional and stochastic system theory, sufficient conditions are derived in terms of linear matrix inequalities to guarantee the closed-loop system to be strictly $(\mathcal {Q}, \mathcal {S}, \mathcal {R})$ - $\alpha $ -dissipative. The effectiveness of the design procedure is illustrated numerically by conducting simulations on a second order series RLC circuit example.

Improved model of streamer propagation in liquid dielectrics

Breakdown and pre‐breakdown cause extensive damage in dielectric oils used in power systems subjected to high voltages. Consequently, several research works are devoted to these phenomena. Related investigations are made very difficult by the numerous influencing parameters and the large number of characteristics of these phenomena. The main goal of the present work was to establish a new electrical model that describes the propagation of streamers in liquid dielectrics for a point‐plane configuration subjected to high‐voltage fields. The novelty consists in the presence of an inductance in the equivalent electrical circuit, which represents the dielectric during the partial discharges characterized by fast variations of current. Criticisms were first made concerning previous electrical models that show some disadvantages. The developed model consists of a series RLC circuit whose element values change during propagation. In particular, the value of the resistance decreases in anticipation of breakdown. The simulation of the developed model gave satisfactory results, similar to experimental ones. For instance, the influence of electrical and geometrical parameters on the current pulses amplitude as well as on the streamers propagation velocity and the quantity of charge and the energy injected were studied. Good agreement was also obtained between the obtained results and experimental ones, which reinforces the validity of the model.

On the self‐resonant frequency reduction of closed‐ and open‐bifilar coils

SummaryIn this work we present the electrical characterization of closed‐ and open‐bifilar solenoid coils by comparing their self‐capacitance, self‐inductance, and self‐resonant frequency (SRF). The analysis is done by relating these parameters with those of a conventional solenoid coil with same dimensions and number of turns. It is shown that bifilar coils have a greater self‐capacitance and lower SRF when compared with the respective conventional coil and that this relation can be expressed only in terms of the number of turns of the coils. Therefore, these components have a potential use in applications that need to avoid the use of a real capacitor and need to operate in a smaller resonant frequency, such as in wireless power transfer systems, for example. In a similar way, the self‐inductances of closed‐ and open‐bifilar coils are also compared with those of conventional coils with the same dimensions. It is also shown that the SRF of closed‐ and open‐bifilar coils are approximately the same for practical values of the quality factor and that their impedance behaves as series and parallel RLC circuits. Practical experiments are conducted validating the developed theory.

Extraction of hysteresis parameters in foil magnetostrictive composites

The work discusses the extraction of the uncommon hysteresis parameters as a function of the magnetization, M and magnetic field, H using low-field resonance principles to characterize foil magnetostrictive composites. Linear magnetizing process is derived as hysteresis lag, because the magnetic field lines generated by current flowing on the inductive winding are vector deviated. A series RLC circuit is employed here to evaluate hysteresis lag, where its equivalent voltage signals are inputs to a XY graph to obtain the hysteresis cycle as M-H loop in an oscilloscope screen. To validate the feasibility of the extraction of such those hysteresis parameters, bulk Mn-Zn ferrites were cut in foils to be evaluated by physical equations defined here. Hence, the conduction parameters estimated using M-H loops show as structure ordering of magnetostrictive composites is dependent on magnetic properties in the small-scale structures.

Studying a physics problem with the help of open source software

Tools for drawing, computing, and graphical representation of data can be exploited by students and educators for studying efficiently different physical systems, and for simulating their behaviour. This could lead to a deeper understanding of the model and help preparing laboratory activities. Some open source software packages make such tools readily available and accessible also to users without advanced programming skills. A few examples are considered in this work: the study of transient phenomena in the series RLC circuit; the dispersion of light through a prism; the free fall of an oil droplet in air, as used in Millikan’s experiment. Similar codes might be suitably developed and adapted for study of simple physics problems.

Wavelet analysis of near-resonant series RLC circuit with time-dependent forcing frequency

In this work, the results of an analysis of the response of a near-resonant series resistance−inductance−capacitance (RLC) electric circuit with time-dependent forcing frequency by means of a wavelet cross-correlation approach are reported. In particular, it is shown how the wavelet approach enables frequency and time analysis of the circuit response to be carried out simultaneously—this procedure not being possible by Fourier transform, since the frequency is not stationary in time. A series RLC circuit simulation is performed by using the Simulation Program with Integrated Circuits Emphasis (SPICE), in which an oscillatory sinusoidal voltage drive signal of constant amplitude is swept through the resonant condition by progressively increasing the frequency over a 20-second time window, linearly, from 0.32 Hz to 6.69 Hz. It is shown that the wavelet cross-correlation procedure quantifies the common power between the input signal (represented by the electromotive force) and the output signal, which in the present case is a current, highlighting not only which frequencies are present but also when they occur, i.e. providing a simultaneous time-frequency analysis. The work is directed toward graduate Physics, Engineering and Mathematics students, with the main intention of introducing wavelet analysis into their data analysis toolkit.

Dual of Defected Ground Structure for Coplanar Stripline

Defected ground structures (DGS) have been used with microstrip and coplanar waveguide (CPW), but until now no comparable structure has been demonstrated for coplanar stripline (CPS), probably because there is no “ground plane.” This letter introduces a dual of DGS for CPS with dual properties, or it acts as a shunt, series RLC circuit that creates an equivalent shunt short circuit at the resonant frequency, which is the dual of the DGS in microstrip or CPW.

A Method for Controlling Parallel and Series RLC Circuits with Time-Varying Resistance, Inductance and Capacitance

Parallel and series RLC circuits are widely encountered in numerous electrical and electronic applications. Accurate control of the voltage/current in parallel/series RLC circuits with time-varying resistance, inductance and capacitance is a challenge. In this work, an approach is proposed for control of voltage in time-varying parallel RLC circuits and of current in time-varying series RLC circuits. The proposed controller is described by an algebraic equation and forces the tracking error to quickly converge to zero. Illustrative results verify the proposed method for forcing the voltage/current in time-varying parallel/series RLC circuits to follow the targeted voltage/current trajectories efficiently. Compared with the conventional approach based on the gradient method, the proposed method demonstrates higher accuracy in controlling time-varying parallel and series RLC circuits.

Digital lock-in amplifier based on soundcard interface for physics laboratory

The purpose of this paper is to develop a digital lock-in amplifier based on soundcard interface for undergraduate physics laboratory. Both series and parallel RLC circuit laboratory are tested because of its well-known, easy to understand and simple confirm. The sinusoidal signal at the frequency of 10 Hz – 15 kHz is generated to the circuits. The amplitude and phase of the voltage drop across the resistor, R are measured in 10 step decade. The signals from soundcard interface and lock-in amplifier are compared. The results give a good correlation. It indicates that the design digital lock-in amplifier is promising for undergraduate physic laboratory.

The effect of annealing on induction like properties of (FeCoZr)x(CaF2)(100−x) nanocomposite films produced by ion-beam sputtering in the vacuum environment

The paper presents frequency f and temperature T dependences of the phase angle θ, conductivity σ, capacity Cp and tgδ for (FeCoZr)x(CaF2)(100−x) nanocomposite films deposited with the application of ion-beam sputtering of a complex target in the gas atmosphere of mixed argon and oxygen. The examined films are composed of metallic FeCoZr “cores” covered with FeCo-based oxide “shells” embedded in an oxygen-free dielectric matrix (fluorite).It has been found that in nanocomposites (FeCoZr)62.7(CaF2)37.3 produced with ion-beam sputtering using combined argon–oxygen ions, the phase angle values change from the negative, through zero, up to the positive ones. It means that the phase angle changes from the capacitive to the inductive type of conduction.Thermo-gravimetric analyses show that nanogranules have metallic phase cores covered by oxides of metallic-phase atoms. The inductive type of nanocomposites conductivity is related to the presence of the oxide cover. Annealing of the nanocomposites at the temperature of 398 K and higher causes an extension of the phase angle change range to an area exceeding +90°. This is due to the fact that during the sputtering of the dielectric CaF2 with argon and oxygen ion beam, some fluorine ions get released and participate in the chemical reaction with surface atoms of nanogranules during the annealing. Such reactions produce a coating composed of oxides and fluorides of the metallic phase on the surface of metallic nanogranules, which results in the extended range of the phase angle changes beyond the area of +90°. In the annealed nanocomposites, frequency dependences of capacity exhibit a sharp minimum which is related to the phase angle transition through zero, as with the voltage resonance phenomena in series RLC circuits. Frequency vs. conductivity characteristics show strong minima, which are related to the phase angle passing through the values of θ = +90°. They correspond to the current resonances in parallel RLC circuits.Relaxation times of the capacity τC and conductivity τσ correspond to the phase angle transition through zero 0° and through +90°. Relaxation time dependences of activation energy on annealing temperature have been determined with the use of the Arrhenius dependences for capacity and conductivity.It has been found that for annealing temperatures higher than 573 K an increase of activation energy occurs, which is related to the oxidation of metal atoms in the core of metallic-phase nanoparticles.

Analysis of the Soft-Start Circuit of the High Voltage Power Supply Based on PSM Technology

The power supply based on pulse step modulation technology has been widely used as the high-voltage power supply (HVPS) for additional heating systems. The topology contains numbers of converters and multisecondary transformers. For the magnetizing inrush of the transformer and charging current of the converters connecting with the secondary windings of transformer, the power up of the power supply system is quite complex. There are resistor branches series with the transformer and each converter is used to limit the inrush current. A lot of resister branches and parallel contactors in the converter modules are required, and as a result the dissipation and electromagnetic interference inside the module are serious. In this paper, the soft-start circuit is simplified to only one resistor branch. The precharge circuits of the converters, which are connected to the secondary, are diverted from the inside of the modules to the primary winding of transformer. Since the multisecondary transformer powers up at the same time as converters, the capacitors in all converters will limit the ramp up rate of the transformer voltage, and the magnetic inrush current can be ignored. To analyze the characters of the precharge branches, all converters can be equaled as parallel during the soft-start process. The equivalent circuit, a series RLC circuit, is proposed in this paper. A 1.2-kV power supply, contains 12 converters, with soft start has been built up in laboratory. Simulation and experiment results are shown to verify the theoretical analysis. A new soft-start circuit of 100-kV HVPS system was designed.

Wilkinson Power Divider With Complex Isolation Component and Its Miniaturization

By adding a complex isolation component between two 90 ° transmission lines at an arbitrary phase angle from the input terminal, a small Wilkinson power divider provides physical separation and electrical isolation between two output ports. General design equations for the complex isolation component are derived from even- and odd-mode analysis. Parallel and series RLC circuits are chosen to realize complex isolation components, respectively. Considering the bandwidths of S <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">22</sub> , S <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">33</sub> , and S <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">32</sub> , inductors in both parallel and series RLC components are omitted to get the widest bandwidths; mathematical proof and design examples are also presented in this paper. A coupled line section with a compensating capacitor is introduced to reduce the circuit size, where characteristic impedances between even and odd mode are different in the coupled line section, and their electrical lengths are also different in inhomogeneous medium. Mathematical equations and simulation examples prove that the compensating capacitor compensates the characteristic impedance difference in the homogeneous medium and the electrical length difference in the inhomogeneous medium. Finally, an experimental circuit shows good agreement with the theoretical simulation.

On Resonance and Frequency Response Characteristics of Electrical Circuits

While teaching network analysis to undergraduate students, the frequency response of electrical circuits consisting of passive elements such as resistors, capacitors and inductors are commonly analysed. Students are familiar with the sharp amplitude peak or trough normally occurring at resonance. This observation is not only intuitively pleasing, but also consistent with the concept of resonance in many physical systems. In the well-known series and parallel RLC circuits, the maximum and minimum currents, respectively, occur at resonance. Because of this, many students and even instructors (sometimes) may erroneously assume that the resonance in general RLC circuits implies maximum or minimum current. In this paper, it will be shown that this is generally untrue. The theoretical analyses and experimental validation of series, parallel and series-parallel RLC circuits are presented to address this common misconception.

A circuit to demonstrate phase relationships in RLC circuits

We have developed a circuit to demonstrate the phase relationships between resistive and reactive elements in series RLC circuits. We utilize a differential amplifier to allow the phases of the three elements and the current to be simultaneously displayed on an inexpensive four channel oscilloscope. We have included a novel circuit that provides a visual indication of the magnitude and direction of the voltage or current using LEDs. This allows the phase relationships to be demonstrated directly using the very intuitive measurement of the brightness of a light.

Nonlinear dielectric response in the mixed K0.91(NH4)0.09H2PO4 crystal

The influence of bias and variable electric fields on the dielectric response of the K0.91(NH4)0.09H2PO4 single crystal has been studied in the vicinity of the ferroelectric phase transition temperature T C. Below T C, the nonlinear response is caused mainly by the domain mechanism. This is confirmed, in particular, by observations of chaotic oscillations in a series RLC-circuit containing the studied sample as a capacitor C and excited by a sinusoidal voltage. Peculiarities of the behavior of the dielectric nonlinearity are found near the Curie temperature, which are explained by the emergence of an intermediate heterophase state.

Interrupting Short-Circuit Direct Current Using an AC Circuit Breaker in Series with a Reactor

This paper describes and demonstrates the principle and efficacy of a novel direct current fault interruption scheme using a reactor in series with a controlled rectifier and a conventional AC circuit breaker. The presence of the series reactor limits the capacitive discharge current from the DC filter capacitor at the output terminals of the phase-controlled rectifier. In addition, the series reactor along with the filter capacitor forms an underdamped series RLC circuit which forces the fault current to oscillate about zero. This synthetic alternating current can then be interrupted using a conventional AC circuit breaker. The selection criteria for the series reactor and overcurrent protection are presented as well. Using the proposed scheme for an example case, a DC fault current magnitude is reduced from 56 kA to 14 kA, while the interruption time is reduced from 44 ms to 25 ms.

Low noise measurement system for determination of the critical currents in superconducting tapes by a pulse method

Steady state measurements of the high critical currents in superconducting composite wires and tapes might be burdened with some errors. The origin of the errors is mainly associated with the Joule heat generated at current leads contacts, which at high transport currents can considerably increase temperature of an investigated sample wire. To avoid this unwanted heating phenomenon pulsed current methods are widely used. A waveform of the current pulse is usually shaped by means of a series RLC circuit with the subcritical dumping condition. Measurement results (i.e., a value of current peak, its time derivative, and a voltage drop along a superconducting sample) are recorded by means of a 4-channels, 12-bit resolution, 50 ns sampling time, digital recorder. Very low noise, broadband, voltage preamplifiers, based on rf bipolar transistors, were designed and fabricated. From the data, current-voltage characteristics are plotted and then the critical currents of investigated tapes are determined. Presented in the work our home-made, low noise, measurement setup allows to obtain a current pulse of about 4000 A at duration time of several milliseconds.