Parallel RLC Circuit Research Articles

On the Impact of Some Fixed Point Theorems on Dynamic Programming and RLC Circuit Models in R-Modular b-Metric-like Spaces

In this study, we significantly extend the concept of modular metric-like spaces to introduce the notion of b-metric-like spaces. Furthermore, by incorporating a binary relation R, we develop the framework of R-modular b-metric-like spaces. We establish a groundbreaking fixed point theorem for certain extensions of Geraghty-type contraction mappings, incorporating both 𝒵 simulation function and E-type contraction within this innovative structure. Moreover, we present several novel outcomes that stem from our newly defined notations. Afterwards, we introduce an unprecedented concept, the graphical modular b-metric-like space, which is derived from the binary relation R. Finally, we examine the existence of solutions for a class of functional equations that are pivotal in dynamic programming and in solving initial value problems related to the electric current in an RLC parallel circuit.

A wide-band high gain beamsteerable variable patch reflectarray antenna for THz applications

This article proposed a compact size, high gain, wideband reflectarray antenna for THz and 6 G applications. To enhance the aperture efficiency and gain, a single layer L-shape delay line-based unit cell with a size of 0.45λ0 is adopted. The λ0 is the free space wavelength at 1.35 THz. The SiO2 substrate is sandwiched between L- shape delay line and the ground plane of gold. The unit cell, equivalent parallel RLC circuit modelled with gap coupled capacitance is also presented which is validated through the Ansys-High Frequency Structure Simulator (HFSS) and Advanced Design System (ADS). The dimension of the RA is 3 mm having 610 elements. It is excited by the pyramidal horn antenna at an optimum distance (F/D =1.21). The optimum ratio (F/D) is calculated with the help of the cosq model at −10 dB edge taper. The operating bandwidth is obtained 46.15 % from 1 to 1.6 THz. The reflection phase and magnitude are 500° and 3.93 dB at 1.35 THz. It is adjusted by varying the length of the delay line. The maximum aperture efficiency and realized gain are 35 % and 28 dBi respectively. The Side lobe level is −15.5 dB and the Co-Cross polarization level is below −30 dB.

Litar Setara Dwi Jalur Antena Dwikutub Bersepadu untuk Aplikasi RFID

This paper presents dual band antenna by designing basic dipole antenna integrated with C-shaped patches structure for RFID applications. This C-shaped patch is inspired by E-shapes patch antenna that able to perform multiband frequency. The design of the equivalent circuit started with the fundamental circuit of impedance Zo and Z1 which functioned as a dipole antenna in single band. The parallel RLC circuit of impedance Z2 is added in the circuit as loaded patch has affected the resonating frequency. Variations of C1 and L1 on impedance Z1 effect a gap between the two resonance frequencies without changing the bandwidth by shifting the lower frequency. In addition, the variation of C2 and L2 on the impedance Z2 also affects the ratio between the two resonance frequencies but both frequencies are shifted and the bandwidth changes. Consequently, the dual band is presented at 0.915 GHz (UHF RFID) and 2.4 GHz (ISM RFID) by calculating the value of the resistance, inductance and capacitance. The data from electromagnetic simulation are compared with the data predicted by the antenna circuit modeling. The frequency sampled measurement data may be represented in the form of S-parameter in order to represent dependent data in a time domain simulator in P-SPICE software. The C-shaped design can be independently controlled to perform lower band and upper band by adjusting the width and length of the patch. The performance of the proposed antenna demonstrates the dual band antenna for RFID application with good agreements between measured and simulated results.

Electrothermal Analyses of Bandpass NGD RLC-Network Topologies

This paper develops an original study of temperature effect on the unfamiliar bandpass (BP) negative group delay (NGD) lumped passive circuits. The paper presents the first study of electrothermal analysis of electronic circuits classified as BP-NGD topologies. The considered BP-NGD passive cells are mainly constituted by RLC-resonant networks. The equivalence between two basic BP-NGD topologies constituted by RLC-series and RLC-parallel networks is elaborated via the voltage transfer function (VTF) analogy. Then, the theoretical demonstrations are introduced to define the main specifications as the NGD center frequency, NGD value, attenuation and NGD bandwidth. The electrothermal innovative study is developed based on the temperature coefficient resistor (TCR) of elements constituting the BP-NGD circuits. With proofs of concept of RLC-series and RLC-parallel circuits operating with -500 ns NGD value at 13.56 MHz, calculated and simulated results showing are in excellent agreement. The sensitivity analyses of BP-NGD specifications in function of ambient temperature variation from 0°C to 100°C are investigated. The BP-NGD response variations versus frequency and temperature are characterized with thermo-frequency cartographies and discussed.

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.

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.

Application of Numerical Methods for the Analysis of Damped Parallel RLC Circuit

A sudden application of sources results in time-varying currents and voltages in the circuit known as transients. This phenomenon occurs frequently during switching. A simple circuit constituting a resistor, an inductor, and a capacitor is termed an RLC circuit. It may be in parallel or series configuration or both. Different values of damping factors determine the different nature of the transient response. We applied different numerical solution methods such as explicit (forward) Euler method, third-order Runge-Kutta (RK3) method, and Butcher's fifth-order Runge-Kutta (BRK5) method to approximate the solution of second-order differential equation with initial value problem (IVP). We thoroughly compared the numerical solutions obtained by these methods with the necessary visualization and analysis of error. We also examined the superiority of these methods over one another and the appropriateness of numerical methods for different damping conditions is explored. With high accuracy of the approximation and thorough analysis of the observation, we found Butcher's fifth-order Runge-Kutta (BRK5) method to be the best numerical technique. Regarding the different values of damping factors, we considered the further possibility of discussion and analysis of this iterative method.

Electric circuit model of microwave optomechanics

We report on the generic classical electric circuit modeling that describes standard single-tone microwave optomechanics. Based on a parallel RLC circuit in which a mechanical oscillator acts as a movable capacitor, derivations of analytical expressions are presented, including key features such as the back-action force, the input–output expressions, and the spectral densities associated, all in the classical regime. These expressions coincide with the standard quantum treatment performed in optomechanics when the occupation number of both cavity and mechanical oscillator are large. Besides, the derived analytics transposes optical elements and properties into electronics terms, which is mandatory for quantitative measurement and design purposes. Finally, the direct comparison between the standard quantum treatment and the classical model addresses the bounds between quantum and classical regimes, highlighting the features which are truly quantum, and those which are not.

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.

Nonlinear distortion of angle modulation signal in output power amplifiers

The output power amplifier is operated in nonlinear mode to increase its efficiency, at which the signal is distorted more. The goal is to analyze effects of nonlinearity on the modulating signal of angle-modulated signal distortions for single-ended and push-pull output power amplifiers with memory and without it. The amplifier characteristic ic(vBE) is preset by the cubic polynomial. The output voltage of memoryless amplifier uout(t) is found by Ohm's law. And in case with amplifier with memory, the output voltage uout(t) is found by Complex amplitude method with a Fourier series of function ic(t). The output voltage uout(t) is represented as the narrowband process with envelope of the waveform U1(t) and initial phase Ф1(t) to determine the angular modulation law Ф1(t) at the amplifier output. The function U1(t) is defined as combination of in-phase А(t) and quadrature В(t) components. The distortion estimate based on Total Harmonic Distortion (THD). The measurement of THD is defined as the ratio of the RMS amplitude of a set of higher harmonic frequencies to the RMS amplitude of the first harmonic. The spectrum of function Ф1(t) is represented a Fourier series. In single-ended memoryless amplifier and non-cutoff mode, the THD decreases as m increases and THD of modulating signal is {37.6; 18.8; 6.3%} at m {0.5; 1; 3}. In cutoff mode, the smallest THD is {15.18; 5.13%} at m {1; 3} as θ = 140o. In push-pull memoryless amplifier and θ = 90o, the THD is {22.2; 11.1; 3.7%} at m {0.5; 1; 3} which is 1.7 times less than in a single-ended amplifier without cutoff. This is due to compensation even-order harmonic of amplified signal at the output of a pushpull amplifier. In this case of memoryless amplifier, the transistor load is a parallel RLC circuit. The distortion decreases under m increases at first (up m is 1.5), but then rapidly increases (from m is 1.7). This is due to increase of the parasitic harmonics level caused by the nonlinearity of the phase-frequency characteristic of RLC circuit. The calculations show that THD of modulating signal is 3.35, 9.02 and 22.88 % at Q = 10 and m {0.5; 1; 3}, respectively. In cutoff mode, the smallest THD is at θ = 90o and it does not depend on θ at large values of m. In push-pull amplifier with memory, the THD is 2.8, 2.5 and 3.0 times less than for a singleended amplifier without cutoff at Q {2.5; 5; 10}, respectively. The results of this paper can be used for the design of signal processing systems.

Design and miniaturization of dual-band Wilkinson power dividers

Abstract In this paper, four differently shaped Wilkinson power dividers are presented by selecting the same physical length of two-section transmission lines, dual arbitrary frequency band Wilkinson power dividers can be achieved. The 2.4 GHz (WLAN) and 5.9 GHz (DSRC IEEE 802.11p) frequency bands are selected to complement the future development of multi-band, multi-standard transceivers. To improve physical separation and electrical isolation between the two output ports a parallel RLC circuit is employed. For verification, the simulated and measured performance results of dual-band Wilkinson power dividers implemented on the Rogers 4003C laminate are presented. The measurement results for the fabricated Wilkinson power dividers were in good agreement with theoretical simulation results and show dual-band characteristics.

The Effect of Capacitance on the Power Factor Value of Parallel RLC Circuits

The power factor of the circuit is determined by the amount of pure resistance (R), self-inductance of the coil (L) and the capacitance of the capacitor (C). In this study, the measurement of the power factor value in a parallel RLC circuit was carried out through experimental testing and simulation with the value of C as the independent variable, while the values of R and L were fixed conditioned quantities. The purpose of this study was to determine the effect of capacitance on a parallel RLC circuit. One of the ways to improve the power factor value in a circuit is to install capacitive compensation using a capacitor. The relation between the power factor value and the capacitance and inductive reactance based on the experimental results and the simulation calculation results in the parallel RLC circuit both shows the same pattern with a relative uncertainty below 8%. The experimental results and simulation results both show that the power factor can be improved by using a right capacitance which is around the capacitance value when there is resonance in the circuit.

Unveiling Stimulation Secrets of Electrical Excitation of Neural Tissue Using a Circuit Probability Theory.

Electrical excitation of neural tissue has wide applications, but how electrical stimulation interacts with neural tissue remains to be elucidated. Here, we propose a new theory, named the Circuit-Probability theory, to reveal how this physical interaction happen. The relation between the electrical stimulation input and the neural response can be theoretically calculated. We show that many empirical models, including strength-duration relationship and linear-non-linear-Poisson model, can be theoretically explained, derived, and amended using our theory. Furthermore, this theory can explain the complex non-linear and resonant phenomena and fit in vivo experiment data. In this letter, we validated an entirely new framework to study electrical stimulation on neural tissue, which is to simulate voltage waveforms using a parallel RLC circuit first, and then calculate the excitation probability stochastically.

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.

Increasing signal amplitude in electrical impedance tomography of neural activity using a parallel resistor inductor capacitor (RLC) circuit

Objective. To increase the impedance signal amplitude produced during neural activity using a novel approach of implementing a parallel resistor inductor capacitor (RLC) circuit across the current source used in electrical impedance tomography (EIT) of peripheral nerve. Approach. The frequency response of the impedance signal was characterized in the range 4–18 kHz, then a frequency range with significant capacitive charge transfer was selected for experiment with the RLC circuit. Design of the RLC circuit was aided by in vitro impedance measurements on nerve and nerve cuff in the range 5 Hz to 50 kHz. Main results. The frequency response of the impedance signal across 4–18 kHz showed maximum amplitude at 6–8 kHz, and steady decline in amplitude between 8 and 18 kHz with −6 dB reduction at 14 kHz. The frequency range 17 ± 1 kHz was selected for the RLC experiment. The RLC experiment was performed on four subjects using an RLC circuit designed to produce a resonant frequency of 17 kHz with a bandwidth of 3.6 kHz, and containing a 22 mH inductive element and a 3.45 nF capacitive element with +0.8/− 3.45 nF manual tuning range. With the RLC circuit connected, relative increases in the impedance signal (±3σ noise) of 44% (±15%), 33% (±30%), 37% (±8.6%), and 16% (±19%) were produced. Significance. The increase in impedance signal amplitude at high frequencies, generated by the novel implementation of a parallel RLC circuit across the drive current, improves spatial resolution by increasing the number of parallel drive currents which can be implemented in a frequency division multiplexed (FDM) EIT system, and aids the long term goal of a real-time FDM EIT system by reducing the need for ensemble averaging.

Coupling Electromagnetic Waves to Spin Waves: A Physics-Based Nonlinear Circuit Model for Frequency-Selective Limiters

A physics-based nonlinear circuit model is developed for frequency-selective limiters (FSLs) based on thin-film magnetic materials. The equivalent circuit model is structured and its parameters are determined rigorously from the fundamental physics of electromagnetic waves and spin waves. The spin motions as well as the ferromagnetic resonance (FMR) are modeled by RLC parallel circuits with parameters derived from Polder’s tensor and Kittel’s equations. The exchange coupling between spins is modeled by an inductor added between adjacent RLC circuits based on quantum spin theory. The nonlinear cross-frequency coupling from signal at $\omega $ to spin waves at $\omega $ /2 is represented by a nonlinear coupled inductor model that follows the mathematics of a pendulum motion to represent the parametric oscillations of spins. The circuit units are cascaded to describe the spin-wave propagation inside the magnetic material, and transmission line parameters are added finally to describe the electromagnetic wave propagation. An FSL device described in the literature is used as an example to validate the circuit model, and the model successfully predicts the power-dependent insertion loss as well as the threshold power level, time delay, and frequency selectivity of the power limiting effect.

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.

Krasovskii’s Passivity

In this paper we introduce a new notion of passivity which we call Krasovskii’s passivity and provide a sufficient condition for a system to be Krasovskii’s passive. Based on this condition, we investigate classes of port-Hamiltonian and gradient systems which are Krasovskii’s passive. Moreover, we provide a new interconnection based control technique based on Krasovskii’s passivity. Our proposed control technique can be used even in the case when it is not clear how to construct the standard passivity based controller, which is demonstrated by examples of a Boost converter and a parallel RLC circuit.