Passive Electrical Circuit Research Articles

Auxetic enhancement of the shunted piezoelectric effect for vibration suppression

Shunted piezoelectric patches connected to passive electric circuits can be attached to a host structure for effective vibration attenuation. The effect of an auxetic layer to enhance the electromechanical coupling and subsequently the vibration suppression is studied here. Three different configurations are considered for the layer: a classical, a homogeneous auxetic and a layer with microstructure leading to auxetic behavior. First, is presented a modification of the “current-flowing” shunt circuit for multimode vibration control. Two finite element models have been validated, the frequency response graph of the system and the most suitable values of the electric parameters are calculated and a comparison is provided. Furthermore, it is shown that the vibration reduction of the second and third eigenmodes can be enhanced, provided that an auxetic of significant thickness is used. The results demonstrate the effect of the auxetic boosting on vibration suppression.

Electrorheological and magnetorheological properties of liquid composites based on polypyrrole nanotubes/magnetite nanoparticles

This research presents an in-depth exploration of the electrical and magnetic properties of a polypyrrole nanotubes/magnetite nanoparticles (PPyM) material embedded in a silicone oil matrix. A key finding of our study is the dual nature of the composite, i.e. it exhibits a behaviour akin to both electro- and magnetorheological suspensions. This unique duality is evident in its response to varying electric and magnetic field intensities. Our study focuses on examining the electrical properties of the composite, including its dielectric permittivity and dielectric loss factor. Additionally, we conduct an extensive analysis of its rheological behavior, with a particular emphasis on how its viscosity changes in response to electromagnetic stimuli. This property notably underscores the material’s dual-responsive nature. Employing a custom experimental design, we integrate the composite into a passive electrical circuit element subjected to alternating electric fields. This methodological approach allows us to precisely measure the material’s response in terms of resistance, capacitance, and charge under different field conditions. Our findings reveal substantial changes in the material’s electrical conductivity and rheological characteristics, which are significantly influenced by the intensity of the applied fields. These results enhance the understanding of electro-magnetorheological properties of PPyM-based magnetic composites, and also highlight their potential in applications involving smart materials. The distinct electrical, magnetic and rheological modulation capabilities demonstrated by this composite render it as promising candidate for advanced applications. These include sensory technology, actuation systems, and energy storage solutions.

An intelligent digital twinning approach for complex circuits

The digital twinning process is essential for transferring real-world objects to the Metaverse by creating accurate digital versions, known as digital twins. However, complex systems pose challenges in this process. With the increasing utilization of microwave components and circuits in telecommunication systems such as IoT, 5 G, and 6 G, the need for digital twins of these components arises. Nevertheless, high-frequency components exhibit intricate behavior, requiring advanced modeling techniques. Artificial intelligence (AI) provides a powerful tool for enhancing the reliability and accuracy of estimated models in such cases. In this study, a microstrip lowpass filter (LPF) is designed, fabricated, and measured as the physical twin. An intelligent digital twinning approach is employed using a machine learning method based on an adaptive neuro-fuzzy inference system (ANFIS), trained by a subtractive clustering algorithm. The resulting digital twin of the LPF proves valuable for communication networks and IoT applications. Moreover, this research showcases the applicability and accessibility of machine learning in creating digital twins of electromagnetic components for communication cyber-physical systems (CPSs) and the Metaverse. Furthermore, the proposed method exhibits adaptability to various passive and active electrical or electronic circuits. By harnessing the potential of AI and digital twinning, this study presents a robust and accurate approach for modeling and analyzing complex circuits, specifically in the context of communication systems and their integration into the Metaverse. The findings highlight the advantages of an intelligent digital twinning approach and its potential for advancing various domains involving complex circuitry.

Passive damping of vibrations of prestressed thin-walled structures using piezoelectric elements connected to electric circuits

In this paper we estimate the influence of static pressure on the efficiency of passive damping of vibrations of a circular cylindrical shell using an open piezoelectric ring connected to a passive electric circuit of different configurations. The mathematical formulation of the problem of the dynamic behavior of an electroelastic structure is based on the variational principle of virtual displacements, which is written in matrix form taking into account the prestressed non-deformed state caused by applied loads, and as well as the work done by external surface forces, inertial forces and external electric field to transfer the free charge. The resulting equation is supplemented by the equation for the electric circuit, which relates the voltage at the piezoelectric ring with the corresponding electric charge. The problem is solved in the framework of 3D formulation using the finite element method. As examples, we consider the serial RL- and resistive R-circuits. Their parameters providing the most effective damping of free vibrations in terms of their decay rate are determined by solving the optimization problem. The results obtained by numerical simulations are compared with the results calculated by the analytical formulas at different values of static pressure.

Natural vibration and aeroelastic stability of shallow shells with passive electric circuit

This article presents the results of study of natural vibration and aeroelastic stability of isotropic shallow cylindrical shells interacting with a supersonic gas flow. The examined systems are equipped with piezoelectric elements which are located on the inner surface of the structure, and can be connected to a passive electric circuit. The mathematical formulation of the problem is based on the variational principle of virtual displacements taking into account the work of inertia forces, aerodynamic pressure and electric field. The solution is developed in a three-dimensional formulation using the mode-superposition technique and finite element method. The non-classical problem on complex eigenvalues is solved using the Muller method. The validity of the obtained results is confirmed by solution convergence with increase of the nodal unknowns and by comparison with the literature. The influence of the piezoelectric element location on the frequency and critical pressure of the gas flow leading to the onset of flutter instability is analyzed at different combinations of kinematic boundary conditions. The applicability of shunt R and RL-circuits for controlling the aeroelastic stability boundary and the damping rate of free vibration in the subcritical region are evaluated. The methodology described in this paper allows obtaining higher damping ratios and provides the smallest difference between the natural vibration frequencies of the shell and the electric circuit, compared to solutions based on the known analytical expressions.

Observation of non-local impedance response in a passive electrical circuit

In media with only short-ranged couplings and interactions, it is natural to assume that physical responses must be local. Yet, we discover that this is not necessarily true, even in a system as commonplace as an electric circuit array. This work reports the experimental observation of non-local impedance response in a designed circuit network consisting exclusively of passive elements such as resistors, inductors and capacitors (RLC). Measurements reveal that the removal of boundary connections dramatically affects the two-point impedance between certain distant nodes, even in the absence of any amplification mechanism for the voltage signal. This non-local impedance response is distinct from the reciprocal non-Hermitian skin effect, affecting only selected pairs of nodes even as the circuit Laplacian exhibits universally broken spectral bulk-boundary correspondence. Surprisingly, not only are component parasitic resistances unable to erode the non-local response, but they in fact give rise to novel loss-induced topological modes at sufficiently large system sizes, constituting a new manifestation of the critical non-Hermitian skin effect. Our findings chart a new route towards attaining non-local responses in photonic or electrical metamaterials without involving non-linear, non-local, active or amplificative elements.

Computational Mathematics in Engineering Careers: Study of Electrical Circuits from the Perspective of Interdisciplinary Teaching

The new challenges of the educational engineering framework pretend to encourage the interdepartmental integration and interaction between basic sciences and the module of applied technology subjects. This paper presents a learning approach of interdisciplinary learning in the teaching of trigonometric functions, with special emphasis on the sinusoidal function, showing how the transformation of this function is related to fundamental concepts in the training of electrical energy engineers. The product of trigonometric functions makes it possible to analyze the instantaneous power of passive linear electric circuits and highlight the importance of studying the phase angle between voltage and current associated with the inductive or capacitive nature of the circuit. The development of the contents in the class contemplates the interdisciplinary and integrative aspect that must be implemented from the basic cycle as a bridge towards the applications of mathematics, articulating the problems of Engineering and the use of technologies in teaching.

Numerical and experimental investigation of the energy harvesting performance of electromechanically coupled piezoelectric prestressed beams subjected to nonlinear vibrations

Τhe piezoelectric energy harvesting from nonlinear vibrating structures has greatly attracted the attention of scientific community over the last decades, as it seems to provide one of the more promising ways for high electromechanical energy conversion. Current study deals with the development of a robust and accurate numerical tool capable of modelling and designing piezoelectric structures undergoing severe nonlinear vibrations. Specifically, a coupled multi-field generalized nonlinear mechanics framework for piezoelectric beams subjected to initial stresses and large rotations, extended to include passive external electric circuits in order to predict the dynamic response of the structure and the power generated at the external resistive load. An experimental setup was also developed providing great correlations with the numerical results in case of a vibrating axially prestressed composite beam under the prebuckling regime. At the end, a computational investigation was performed studying the complex dynamic behavior of the piezoelectric beam, in the postbuckling regime. The model successfully captures the measured energy harvesting response of the beam including additional effects induced by the asymmetric configuration of the piezoelectric film.

Refinement and Generalization of Maxwell's Thermal Theorem

In the famous treatise on electricity and magnetism, J.K. Maxwell led to the conclusion that in a passive system of conductors, the current increases sharply in order to approach an increase in heating power. In such cases, Maxwell's thermal gain is valid only for passive electrical circuits when there are no electromotive forces (EMFs). We proposed to change the formulation of the theorem to the statement that the current is distributed in such a way as to minimize the loss of one second of the power for heating. This refinement allows, as shown in the article, to extend such a thermal theorem to active electrical circuits in which there may be sources of E.D.S. This allows us to make physically interpretable Lagrange multipliers of constraints expressing the first Kirchhoff law. The Lagrange multipliers under restrictions in this case coincide with the potentials in the nodes of the electric circuit. This refinement also leads to new interesting formulations of the thermal theorem including the distribution of voltages over the nodes of the electrical circuit.

Computationally efficient memristor model based on Hann window function

Memristor is a fourth fundamental passive electric circuit element. A great deal of effort is devoted to the mathematical modeling of a memristor to figure out its complex and dynamic behavior. This research aims to address the demerits of existing mathematical models of the memristor such as computational inefficiency and inaccuracy. A novel model of the memristor with a Hann window function is developed for a Pt–TiO2–Pt based memristive devices. The threshold values for voltage, frequency and device length are identified. Unlike the existing models, the proposed model has the capability to work with a frequency between 0.5 to 100 Hz. The threshold for a voltage range varies between 0.02 to 3 V. The memristance was observed only if a device length of the proposed model varies between 5 to 250 nm. It is inferred that a memory window skews with an increase in applied voltage frequency and device length. Whereas memory window increases with the increase in applied voltage. The scaling parameter (j) is incorporated in the proposed model to make it more scalable and flexible. Results depict that the proposed model simulation runtime and elapsed time improved by 36% and 33% respectively. The accuracy of the presented model is 1.748 in terms of relative root mean square error. The proposed model exhibits low complexity with sufficient accuracy in simple, intuitive and closed-form.

Effective modes of operation of radio-bombing devices for covert information gathering in the field of noise interference

The information security of modern society is in constant counteraction and constant improvement of technical means used for unauthorized information pickup, and technical means that prevent it. The paper analyzes examples of methods of applying noise interference to counteract the unauthorized pickup. The possibility of unauthorized pickup by passive radio devices using noise interferences is shown and analyzed using noise interferences, which are used to suppress the eavesdropping devices. The transfer of picked up information is possible both by radio wave and low-frequency channels using metal structures or water pipes. As a model of noise interference, a random narrow-band signal with a Gaussian distribution was used. The electrical model of the device was simulated by a transmission line with a high-frequency diode at its end. The idealized exponential dependence of the diode current on the voltage was used. The reflected wave spectra are obtained for different ratios of the transmission line resistance, the differential resistance of diode, and the external offset voltage at the diode. The modes and features of analog and digital information transmission by the radio tab device using energy of radio noises are analyzed. In the radio tab device, the information is transmitted by reflected wave, the spectrum of which is distorted at a nonlinear element placed at the end of transmission line. An analysis of the device operation was carried out along the full possible frequency range associated with the spectrum of the incident noise interference. The optimal elements parameters for the passive electrical circuit are calculated: the resistance of the transmission line, the differential resistance of the diode, the offset voltage, and the modulation mode, depending on the frequency range in which the leak is possible.

Numerical algorithm for searching for layouts of electroelastic bodies with external electric circuits for obtaining the best damping properties

This paper presents an algorithm which allows finding such layouts of electromechanical systems that provide the best vibration damping whether for one mode or a set of vibration modes within some continuous frequency ranges. The basis for the algorithm is the problem solution about natural vibrations. An elastic structure with a piezoelectric element located on its surfaces, which electrodes are connected to a passive external electric circuit, is treated as an electromechanical system. The piezoelectric elements shunted with an electric circuit are the devices where energy dissipation occurs, thus leads to damping of vibrations. A change in damping properties of such systems can be reached by a proper choice of parameters of the electric circuits and corresponding location of the piezoelectric element, which provides the highest energy withdrawal into the electric circuit. The paper presents the mathematical formulation of the natural vibrations problem for piecewise-homogeneous electroelastic bodies shunted with passive external electric circuits. Within the proposed mathematical statement, the problem solution of natural vibrations for such objects is based on values of complex natural vibration frequencies. Real parts of the complex natural vibration frequencies are the circular frequency of vibrations, and the imaginary parts are the damping indices of vibrations. We proposed techniques aimed at determining the location of the piezoelectric element and selecting parameters of shunting the external electric circuit. These approaches are based on values of the complex natural vibration frequencies obtained as results of solving the natural vibrations problem. The proposed approach is demonstrated using a specimen of a thin-walled shell in the semi-cylinder form. The piezoelectric element has a form of a segment of a ring made of PZT-4 piezoceramics. Electrodes of the piezoelectric element are connected to the series resonant RL -circuit. The formulated problem is solved numerically using the finite element method and ANSYS commercial package.

An approach to the analysis of hydroelastic vibrations of electromechanical systems, based on the solution of the non-classical eigenvalue problem

In this paper we introduce an approach to solution of the problem of natural vibrations of piecewise homogeneous electroelastic bodies connected to external passive electric circuits and interacting with a quiescent fluid. A mathematical formulation of the problem, and a variant of its numerical implementation based on the finite element method are presented. Based on the obtained results we extend the previously developed approach to the selection of optimal parameters of shunt circuits for damping of vibrations of electroelastic structures in the case of their interaction with a fluid.

Algorithm for Indirect Measurement of the Parameters of the Passive Complex Conductivity of a Two-Terminal Circuit in a Multipole Electrical Circuit

An algorithm is proposed for indirect measurement of the parameters of the passive complex conductivity as a separate two-terminal circuit and also as a two-terminal device located in one of the branches of a multipole passive triangle-type electrical circuit without needing to separate it into separate two-terminal circuits. A structural diagram is presented for a microprocessor device to measure the parameters of the passive complex conductivity of a two-terminal device located in one of the branches of a multipole passive triangle-type electrical circuit. The algorithm for the indirect method of measuring the parameters of the passive complex conductivity of the two-terminal circuit is based on the theory of matrices and nondirectional graphs. Equations are obtained for calculating the modulus and components of the passive complex conductivity of a two-terminal circuit located in a multipole triangle-type electrical circuit. The proposed algorithm avoids the methodological error owing to the influence of parasitic parameters. Results are presented from an experimental test of the algorithm for indirect measurement of the conductivity of a two-terminal circuit.

Realization of Weyl semimetal phases in topoelectrical circuits

In this work, we demonstrate a simple and effective method to design and realize various Weyl semimetal (WSM) states in a three-dimensional periodic circuit lattice composed of passive electric circuit elements such as inductors and capacitors (LC). The experimental accessibility of such LC circuits offers a ready platform for the realization of not only various WSM phases but also for exploring transport properties in topological systems. The characteristics of such LC circuits are described by the circuit admittance matrices, which are mathematically related to the Hamiltonian of the quantum tight-binding model. The system can be switched between the Type-I and Type-II WSM phases simply by an appropriate choice of inductive or capacitive coupling between certain nodes. A peculiar phase with a flat admittance band emerges at the transition between the Type-I and Type-II Weyl phases. Impedance resonances occur in the LC circuits at certain frequencies associated with vanishing eigenvalues of the admittance matrix. The impedance readout can be used to classify the Type-I and Type-II WSM states. A Type-I WSM shows impedance peaks only at the Weyl points (WPs) whereas a Type-II WSM exhibits multiple secondary peaks near the WPs. This impedance behaviour reflects the vanishing and non-vanishing density of states at the Weyl nodes in the Type-I and Type-II WSM phases, respectively.

S-Parameter-Based Theoretical Analysis of a Matching Network for Generic Multiport Antennas

This article describes a general method for finding an S-parameter of a matching network converting between arbitrary passive reciprocal multiport electrical circuits with the same amount of ports. In particular, the application to multiport antennas is explored. A quality of the matching is shown on a simulated 73 GHz 16-element $0.4\lambda $ -spaced bow-tie linear array, with its matched optimum realized gain achieving the theoretical maximum of the optimal gain over the $[-\pi /2,\pi /2]$ scanning arc and showing a 5 dB improvement over the unmatched case. Degrees of freedom describing different matching network’s realizations with the proposed method are enumerated, and their utilization for the transmitter amplifiers back-off reduction are presented. A fitness of the obtained matching network S-parameter for the conversion into a physical design is explored, and a practical method of obtaining a robust, feasibly realizable solution is given. The proposed network is estimated to require a quality factor 100 or better and demonstrates the useful bandwidth of 2 GHz and a good performance even with the coupling compensation reduced only to the neighboring ports.

Algorithm for indirect measurement method of parameters of passive complex conductance of a two-pole in a multi-pole electrical circuit

An algorithm is proposed for indirectly measuring the parameters of the passive complex conductivity of a two-terminal circuit, both separate and located in one of the branches of a multi-pole passive electric circuit of the triangle-type. A block diagram of a microprocessor measurement unit is presented. The algorithm of the indirect method for measuring the parameters of the passive complex conductivity of a two-terminal circuit, the rationale of which is given on the basis of the theory of matrices and undirected graphs, is considered. Equations for calculating the modulus and components of the studied passive complex conductivity of a two-terminal device located in a multi-pole electric circuit of the triangle-type are obtained. The revealed features of the proposed algorithm exclude a methodological error due to the influence of spurious parameters. Parasitic parameters include: input complex conductivities and transmission coefficients of voltage converters; complex conductivity of a harmonic signal source; passive complex conductivity of two-terminal circuits located in other branches of the studied passive multipolar electric circuit. The results of an experimental verification of the developed algorithm of the indirect method for measuring the module of the complex conductivity of a two-terminal device are presented. The developed algorithm can be used to measure the parameters of passive complex conductivity of both an individual two-terminal circuit and a two-terminal circuit located in one of the branches of a multi-pole passive electric circuit of the triangle-type, without the need for its separation into separate two-terminal devices.

Design and evaluation of a shunted flexible piezoelectric damper for vibration control of cable structures

In this work a shunted flexible piezoelectric damping system is designed and numerically evaluated for the purpose of vibration attenuation of large deployable space cable structures. We propose a design of a tube-shaped flexible piezoelectric energy absorber consisting of multilayered PVDF sectors, which could be shunted with two types of passive electric circuits, i.e. the series resistance-inductance (LR) shunt and the series resistance-negative capacitance (NC-R) shunt. The compatible stiffness of the PVDF tube ensures an effective transformation of deformation from the vibrating cable to the energy absorber. For best performance we carried out optimization on the geometric parameters of the PVDF tube. By analysis we found that the optimal thickness of the PVDF tube is roughly 0.4 times of the inner tube radius. We optimized the shunt circuits and selected the appropriate distribution position of the damper in the flexible cable structures. The performance of the design was numerically evaluated based on three problems, namely the longitudinal vibration of a single-cable structure, the transverse vibration of a single-cable structure and the vibration of a cross-cable structure. Based on the results, we confirm the remarkable performance of the design. Being highly frequency dependent, the design with the LR shunt only works for one deformation mode at a time, e.g. bending or stretching. In contrast, the design with the NC-R shunt works for both modes as it has a much wider frequency band. The design with the LR shunt has better performance than the NC-R shunt when dealing with the stretching deformation mode only. For vibration with combined stretching and bending, however, the performance of both designs is equally good. This is because the NC-R shunt can work for both deformation modes simultaneously, and hence it shows great adaptability and application potential in vibration control of complex flexible space structures.

A finite element algorithm for solution of the natural vibration problem of electroelastic bodies with passive external electric circuits, interacting with a quiescent fluid

In this paper we consider a mathematical statement of the problem on natural vibrations of piecewise-homogeneous electroelastic bodies with passive external electric circuits (shunting circuits) of arbitrary configuration and interacting with a quiescent fluid. The behavior of the piezoelectric body is described using the equations of electrodynamics of deformable electroelastic media in the quasi-static approximation. The motion of an ideal fluid in the case of small perturbations is considered within the framework of the acoustic approximation. Small strains in a thin plate are determined using the Reissner – Mindlin theory. The numerical solution is developed using the finite element method. The proposed algorithm is based on the approach, in which the global stiffness matrix generated with the aid of the ANSYS software package is decomposed into required constituents. The system of governing equations is constructed using the developed algorithm, which is realized in the FORTRAN language. Complex eigenvalues of the examined system are defined from the solution of the non-classic modal problem using the Mueller method. A thin plate with piezoelectric element located on the free surface of a layer of a quiescent fluid of finite size is considered as an example.

Electrodynamic resonance of surface conduction and THz transmission through arrays of rectangular apertures in opaque metallic thin films.

A modal method is developed analytically to investigate the THz optical transmission and reflection of a metallic thin film perforated by a 2D array of rectangular apertures. For subwavelength apertures, this optical model is interpreted in terms of passive electrical circuits, with interface admittances accounting for the THz surface conduction properties of the metallic film. The reactive component of the admittance of the evanescent diffraction cloud is shown to exhibit resonant behavior governed by the shape factors of the array. Interaction of such an electrodynamic resonance with the Rayleigh diffraction orders may alter their standard Fano profiles. Experimental evidence of the resonance is obtained owing to lineshape analysis of transmittance measurements in the THz range on metallic thin films deposited on a dielectric substrate, both above and below the first Wood-Rayleigh anomaly.