Series RLC Circuit Research Articles

Measuring the Q-factor of a series RLC circuit with a smartphone as a function generator

Abstract The use of smartphones as tools for teaching circuits has revolutionized the educational practice in this field. Free applications allow to measure the acoustic intensity with a smartphone and to generate an acoustic signal with a specific frequency. In this way, students turn their mobile devices into function generators and oscilloscopes, respectively, through the audio port. This innovation facilitates the implementation of hands-on experiments with basic circuits. This work implements a smartphone as a function generator connected to a series RLC circuit to obtain the average dissipated power and the corresponding Q-factor. A very good agreement is obtained between theoretical and experimental results.

Study of the interdigital electrode sensor at resonance frequency during water transition

This paper uses the co-planar interdigital electrode (IDE) sensor to measure water level. The researchers generally characterize the interdigital electrode sensor as a fringe field capacitor sensor developed on the printed circuit board and utilize the capacitor sensor's properties for liquid-level measurement. The interdigital electrode sensors illustrate more than one resonance at the higher frequencies, and in this study, the first resonance frequency fr -has been utilized for the water level measurement. Three water types are examined here: distilled, tap, and river. The study assesses that with the transition of water, the permittivity between the electrodes is changed and, it leads to a change in capacitance hence, the change in resonance frequency was observed. The proposed sensor can be represented by the lumped element equivalent series RLC circuit. The developed IDE sensor has good repeatability, small variability, and small hysteresis error. The maximum standard error for distilled, tap, and river water are 0.02833, 0.02503, and 0.02618, respectively, and the hysteresis error is less than 1.903% of full-scale output variation. The maximum error for the fr estimation is about ±2 Hz.

Smartphone Fast Charger Analysis Based on RLC Circuit Transient Process

In today's era, the widespread adoption of mobile terminals, particularly smartphones, has been facilitated by the rapid advancements in information and communication technology. However, a notable drawback of smartphones is their high-power consumption, necessitating faster charging solutions to enhance user convenience. This paper focuses on the RLC circuit of fast chargers. Initially, it introduces the fundamental principles and associated protocols of fast charging technology, elucidating the operation of integrated circuits within fast chargers and highlighting the advantages of fast charging compared to conventional slow charging methods. Moreover, the paper conducts an in-depth analysis of the transient processes within the pivotal series RLC circuit in fast chargers, encompassing zero-input responses and sinusoidal AC excitation responses. The transient processes are categorized into overdamped, critically damped, or underdamped states based on circuit element parameters, with initial conditions and power supply phase determining whether the circuit transitions directly into a steady-state process when stimulated by sinusoidal AC. This research contributes to a deeper understanding of the RLC circuit within smartphone fast chargers and serves as a valuable reference for advancing the development of fast charging solutions.

Electrically-tunable active metamaterials for damped elastic wave propagation control

An electrically-tunable metamaterial is herein designed for the active control of damped elastic waves. The periodic device is conceived including both elastic phases and a piezoelectric phase, shunted by a dissipative electric circuit whose impedance/admittance can be adjusted on demand. As a consequence, the frequency band structure of the metamaterial can be modified to meet design requirements, possibly changing over time. A significant issue is that in the presence of a dissipative circuit, the frequency spectra are obtained by solving eigen-problems with rational terms. This circumstance makes the problem particularly difficult to treat, either resorting to analytical or numerical techniques. In this context, a new derationalization strategy is proposed to overcome some limitations of standard approaches. The starting point is an infinite-dimensional rational eigen-problem, obtained by expanding in their Fourier series the periodic terms involved in the governing dynamic equations. A special derationalization is then applied to the truncated eigen-problem. The key idea is exploiting a LU factorization of the matrix collecting the rational terms. The method allows to considerably reduce the size of the problem to solve with respect to available techniques in literature. This strategy is successfully applied to the case of a three-phase metamaterial shunted by a series RLC circuit with rational admittance.

A Unified Approach to the Analysis of DC/AC Converters, Based on the Study of Electromagnetic Processes in a Series RLC Circuit

This paper presents a unified approach to the analysis of DC/AC converters based on an equivalent representation of their AC circuit as a series RLC circuit. The resonant DC/AC converter with reverse diodes was chosen as the basis of the examination, and the obtained ratios for this device were used to derive the main ratios describing the operation of the other types of DC/AC converters—voltage source inverters (VSI) and current source inverters (CSI). Based on the commonality of electromagnetic processes in power circuits, the expressions for the current through the inductance and the voltage of the capacitor are found in a compact form with their initial phases. The base ratios found through the analysis are normalized to the control frequency, thereby summarizing all possible operating modes. In this way, electromagnetic processes in a whole class of power electronic devices are described from general positions, which is convenient from a methodical point of view with a view to improving power electronics education. The proposed analysis approach is also applicable to three-phase DC/AC inverters, taking into account the specifics related to the presence of three phases and, accordingly, their mutual influence in the formation of the output currents and voltages. On the other hand, the basic ratios determined through the application of the unified analysis approach are also useful with a view to creating engineering design methodologies, in which the values of all circuit elements are determined with comparatively simplified calculation procedures.

Comprehensive Analysis of Capacitance and Inductance Effect in the RLC Circuit Toward the Cut-off Frequency and Bandwidth

Electronics filter design is essential for signal processing tasks in electronics, biomedical engineering, and control systems. Filter design in the frequency domain is based on the foundation laid by the theory of Fourier transform developed by Joseph Fourier in 1807, where the filter is intended to remove unwanted frequency components from the input signal. Lumped electronic filters are constructed by components of resistor (R), capacitor (C), and inductor (L). In this study, we comprehensively explored how different values of capacitors and inductors impact the cut-off or center frequency in the series LC or RLC circuit. Analytical solutions of the magnitude of the ratio between output and input voltage are provided and the results from simulations are used to compare with the derivations from the analytical solutions. The simulation result is within the range of +-0.65% of the theoretical value due to numerical precision from the simulation tool LT-Spice.

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.

Frequency Characteristics of Dissipative and Generative Fractional RLC Circuits

Equations governing the transient- and steady-state regimes of the fractional series RLC circuits containing dissipative and/or generative capacitor and inductor are posed by considering the electric current as a response to electromotive force. Further, fractional RLC circuits are analyzed in the steady-state regime and their energy consumption/production properties are established depending on the angular frequency of electromotive force. Frequency characteristics of the modulus and argument of transfer function, i.e., of circuit’s equivalent admittance, are analyzed through the Bode diagrams for the whole frequency range, as well as for low and high frequencies employing the asymptotic expansions of transfer function modulus and argument.

Using Impedance to explore resonance in mechanical, acoustical, and electrical analog systems

Resonance is usually defined as the frequency at which a measured quantity reaches a maximum value with any change in frequency resulting in a decrease in the amplitude of the measured quantity. Sometimes, but not always, this resonance frequency corresponds to the undamped natural frequency, ωo, of the system. This paper explores the responses of analogous mechanical, acoustic, and electrical oscillating systems, comparing the typical measured response curves (displacement, pressure, and current, respectively) used to showcase the concept of resonance for each. Driving point impedance (real, imaginary, magnitude, and phase) is used to compare the three types of systems. Frequency dependence of the input mechanical impedance (measured with an impedance head) for three mechanical systems (damped mass-spring, tuning fork, wineglass) reveals differences depending on where the system is driven. Measurements of the input acoustic impedance (measured with a microflown p-u probe) for a Helmholtz resonator allows for extraction of the undamped natural frequency in the presence of damping which cannot otherwise be ignored. The electrical impedance of series and parallel RLC circuits and a loudspeaker illustrate differences in the definition of “resonance” when compared with analogous mechanical and acoustic systems.

Electric trapping and circuit cooling of charged nanorotors

The motion of charged particles can be interfaced with electric circuitry via the current induced in nearby pick-up electrodes. Here we show how the rotational and translational dynamics of levitated objects with arbitrary charge distributions can be coupled to a circuit and how the latter acts back on the particle motion. The ensuing cooling rates in series and parallel RLC circuits are determined, demonstrating that quadrupole ion traps are well suited for implementing all-electric cooling. We derive the effective macromotion potential for general trap geometries and illustrate how consecutive rotational and translational resistive cooling of a microscale particle can be achieved in linear Paul traps.

Second-Order Analytic Extension of Eigenvalues for Fast Frequency Sweep Analysis of RF Circuits

A second-order analytic extension of eigenvalue (AEE) method is presented and investigated for efficiently computing the Z- parameters of passive RF circuits over a wide frequency band with full-wave accuracy. The Z- parameters of an RF circuit are first extracted based on a full-wave simulation on sampling frequencies and then decomposed into eigenmodes, whose eigenvalues are analytically extended to all other frequencies within the frequency band of interest based on functional equations constructed from second-order series and parallel RLC circuits. An eigenvector-eigenvalue identity is adopted to compute the frequency-dependent eigenvectors from the eigenvalues of the submatrices, which are used in the expansion of the Z- parameters. A comparison with full-wave solutions is given for the second-order AEE where four frequencies are employed to accurately approximate the Z- parameters and predict the frequency response over the entire band of interest that goes to much higher frequencies than the first-order AEE. With this, the previously developed first-order AEE for a quasi-static analysis is successfully extended to much higher frequencies. Numerical examples are provided to validate the accuracy and demonstrate the capability of the second-order AEE. It is found that the second-order AEE is very accurate for modeling RF circuits with electrical sizes up to one wavelength that possibly contains resonances, as compared to the first-order AEE, which is applicable only to RF circuits with electrical sizes smaller than one-tenth to one-fifth of a wavelength that contains no resonance.

Visualization, formulation and intuitive explanation of iterative methods for transient analysis of series RLC circuit

The time varying currents and voltages resulting from the sudden application of sources usually due to switching are transients. An RLC circuit is an electrical circuit consisting of a resistor, an inductor, and a capacitor, connected in series or in parallel. The transient response is dependent on the value of the different characteristics of damping factor (i.e., over damped, critically damped and under damped). We have computed the numerical solutions of second order differential equation with initial value problem (IVP) by using Explicit (Forward) Euler method, Third order Runge-Kutta (RK3) methods and Butchers fifth order Runge-Kutta (BRK5). The observation compares this numerical solution of ODEs obtained by above-mentioned methods among them with necessary visualization and analysis of the error. These iterative methods will be extended and implement to analyze the transient analysis of an RLC circuit. We have examined the superiority of those methods over one another. The Butchers fifth order Runge-Kutta (BRK5) method is found to be the best numerical technique to solve the transient analysis due to its high accuracy of approximations. Moreover, we consider the possibility of discussion and analyze above mentioned iterative methods in the cases of different characteristics of damping factor.
 BIBECHANA 18 (2) (2021) 9-17

Fractional [formula omitted] circuit in transient and steady state regimes

Assuming accumulated charge being dependent on capacitor voltage memory as well as by expressing magnetic flux in inductor in terms of current memory, generalized capacitor and inductor are constitutively modeled by the sum of terms containing instantaneous and power type hereditary contributions. Constitutive models are further used in analyzing transient and steady state responses of series RLC circuit subject to electromotive force. Depending on model parameters, the character of transfer function changes the behavior of fractional RLC circuit’s impulse response in transient regime from aperiodic, over critically aperiodic, to damped oscillatory. Transition from transient to steady state regime is also analyzed, so as its predominant type depending on element’s fractional order.

The Lagrangian and Hamiltonian for RLC Circuit: Simple Case

The Lagrangian and Hamiltonian for series RLC circuit has been formulated. We use the analogical concept of classical mechanics with electrical quantity. The analogy is as follow mass, position, spring constant, velocity, and damping constant corresponding with inductance, charge, the reciprocal of capacitance, electric current, and resistance respectively. We find the Lagrangian for the LC, RL, RC, and RLC circuit by using the analogy and find the kinetic and potential energy. First, we formulate the Lagrangian of the system. Second, we construct the Hamiltonian of the system by using the Legendre transformation of the Lagrangian. The results indicate that the Hamiltonian is the total energy of the system which means the equation of constraints is time independent. In addition, the Hamiltonian of overdamping and critical damping oscillation is distinguished by a certain factor.

Energy dissipation and efficiency of exploding stainless steel wires of various lengths and diameters

Electrical exploding wires have found many applications in industry and research. Some of the most promising applications include high-speed sheet metal forming and explosive welding. Most research to date has been conducted using thin highly conductive, pure metal wires at relatively low energies. In contrast, experimental trials are performed in air, on relatively thick AISI 304 stainless steel wires with diameters 600–800 µm and lengths ranging from 40 to 160 mm. The test wire produces circuit damping in a series RLC circuit with C = 150 µF and L = 4.36 µH, which yields a maximum theoretical discharge energy of 2.7 kJ at 6 kV. The energy absorbed in the wire and the wire plasma respectively, is calculated to determine the fraction of absorbed energy, i.e. the energy transfer efficiency, for each case and the optimum wire dimensions for the circuit. Longer wires attain a lower action integral and absorb more energy with respect to short wires resulting in a higher energy transfer efficiency to the wire. Thicker wires attain a lower final action integral despite lower initial resistance and absorb more energy with respect to thin wires resulting in a higher energy transfer efficiency to the wire. The total efficiency of dissipated energy in the wire is analysed depending on the wire length and diameter, together with an introduction of the time-averaged wire resistance.

Modern Tesla Coil as a Multidisciplinary Example in STEM Teaching

A modern Tesla coil is an excellent multidisciplinary example in undergraduate STEM teaching. It incorporates several concepts from physics and electrical engineering. For example, Ampere’s law and Faraday’s law are concepts in physics while an LC circuit, an RLC circuit, and the properties of a transistor are concepts in electrical engineering. A Tesla coil shows the intimate relationship between electricity and magnetism. Ampere’s law states that a current induces a magnetic field and Faraday’s law states that a changing magnetic flux induces a voltage. In a classical Tesla coil, a spark gap switches the current on and off flowing through the primary coil. Meanwhile, in many modern Tesla coils, a transistor is used instead of a spark gap, since it can switch on and off very quickly using a lower voltage. Several papers described how modern tesla coils work. However, the designs of modern Tesla coils were complicated and the mathematical descriptions for Tesla coils were beyond undergraduate students’ level. This paper describes a modern Tesla coil by providing mathematical details that are appropriate for undergraduate students’ level. To satisfy the educational purpose of this paper, we also choose the simplest design for a modern Tesla coil. The primary circuit in a modern Tesla coil used here is a parallel RLC circuit. We show that it can play the same role as the series RLC circuit of the primary circuit in the classical Tesla coil.

Driven Series RLC Circuit and Resonance: A Graphic Approach to Energy

Resonance is an important, and rather dramatic, phenomenon in physics. The mechanical case of a mass-spring oscillator is generally the first example that students encounter in introductory courses. In electromagnetism, the resonance in driven RLC circuits is presented in analogy with mechanics, since the mathematical equations describing them are similar. In this work, the resonance phenomenon is approached by means of the graphs of the power as a function of time, something unusual in textbooks on electricity. The maximum absorption of energy by the circuit at resonance is emphasized, using the mathematical solutions for this oscillation. The meanings of power delivered by the external source and energy absorbed by the system are highlighted by means of both the physical interpretation of the equation for P(t) and the graphs of the power vs. time.

Pulse Tube Cryocooler: Phasor Analysis and One-Dimensional Numerical Simulation

An analysis of the detailed operation for the tube element is proposed for an orifice pulse tube cryocooler. This is achieved through phasor analysis using basic thermodynamic relations to estimate the approximated cooling power associated with this machine. Moreover, the effect of the phase shift angle is illustrated by forming an analogy between the phase shift mechanism and a series RLC circuit model. Next, a one-dimensional model based on the conservation equations of mass and energy is presented; the reduced model is solved numerically, for the temperature and velocity of the gas along the tube, to determine the mass flow and time-averaged enthalpy flows at the cold and hot ends of the tube. The findings from the one-dimensional analysis are compared with the phasor analysis results and validated by comparison with similar studies in the literature.

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.