Nonlinear Impedances Research Articles

Analysis of faulted power system with fault current limiter using compensation current method

Fault current limiters (FCL) keep the fault current levels below equipment ratings in expanding power systems. Analyzing a faulted power system with FCL using symmetrical components becomes computationally intensive due to the coupling between FCL impedance and the need to recalculate the bus impedance matrix. This paper proposes a fault analysis method based on compensation currents to minimize the computation efforts. The paper presents the mathematical formulation for the compensation currents to model a fault and an FCL. This paper discusses the coupling between sequence networks for various FCL activation cases and identifies corresponding interconnections. The results of the proposed method for various fault types and FCL activation are validated with time-domain simulations. In addition, the computational efforts required by the proposed method are discussed with an application to a large power system. The results show that the proposed method requires minimum computations. The analysis of FCLs with non-linear impedances is beyond the scope of this paper.

Time-Domain Generalization of the Random-Coupling Model and Experimental Verification in a Complex Scattering System

Electromagnetic wave scattering in electrically large, irregularly shaped, environments is a common phenomenon. The deterministic, or first-principles, study of this process is usually computationally expensive and the results exhibit extreme sensitivity to scattering details. For this reason, the deterministic approach is often dropped in favor of a statistical one. The random coupling model (RCM) Hemmady et al. [Phys. Rev. Lett. 94, 014102 (2005).] is one such approach that has found great success in providing a statistical characterization for wave chaotic systems in the frequency domain. Here we aim to transform the RCM into the time domain and generalize it to alternative situations. The proposed time-domain RCM (TDRCM) method can treat a wave chaotic system with multiple ports and modes. Two features are now possible with the time-domain approach for chaotic resonators: the incorporation of early time short-orbit transmission path effects between the ports, and the inclusion of arbitrary nonlinear or time-varying port load impedances. We conduct short-pulse time-domain experiments in wave chaotic enclosures, and use the TDRCM to simulate the corresponding experimental setup. We also examine a diode-loaded port and compare experimental results with a numerical TDRCM treatment and find agreement.

Design and Experimental Validation of Linear and Nonlinear Digital Synthetic Impedances for Electromechanically Coupled Systems

Design and Experimental Validation of Linear and Nonlinear Digital Synthetic Impedances for Electromechanically Coupled Systems

Multi-conductor transmission line with nonlinear impedances: Application to 50Hz studies

This paper presents an algorithm for the evaluation of currents and voltages along a multi-conductor transmission line having non-linear impedances due to the presence of ferromagnetic conductors; we assume that these impedances are function of the current carried by the relevant conductor so that the equivalent circuit modelling the line is non-linear and has to be solved by means of an iterative procedure. The present paper can be considered as a generalization of our previous works successfully applied to single-conductor lines with earth return. Some examples of application to typical 50-60 Hz interference studies between power/railway lines on telecommunication cables and pipelines are shown.

Neural-Network Based Modeling of I/O Buffer Predriver under Power/Ground Supply Voltage Variations.

This paper presents a neural-network based nonlinear behavioral modelling of I/O buffer that accounts for timing distortion introduced by nonlinear switching behavior of the predriver electrical circuit under power and ground supply voltage (PGSV) variations. Model structure and I/O device characterization along with extraction procedure were described. The last stage of the I/O buffer is modelled as nonlinear current-voltage (I-V) and capacitance voltage (C-V) functions capturing the nonlinear dynamic impedances of the pull-up and pull-down transistors. The mathematical model structure of the predriver was derived from the analysis of the large-signal electrical circuit switching behavior. Accordingly, a generic and surrogate multilayer neural network (NN) structure was considered in this work. Timing series data which reflects the nonlinear switching behavior of the multistage predriver’s circuit PGSV variations, were used to train the NN model. The proposed model was implemented in the time-domain solver and validated against the reference transistor level (TL) model and the state-of-the-art input-output buffer information specification (IBIS) behavioral model under different scenarios. The analysis of jitter was performed using the eye diagrams plotted at different metrics values.

Closed Form Resonance Solution in Metallic Nanoparticles With Cubic Nonlinearity

Higher order intensity of light introduces third order nonlinear susceptibility in metallic nanostructures. Circuit theory is often used to represent complex phenomena and adequately models the frequency dependent linear resonance in metallic nanostructures with great accuracy. In this article, we use the linear circuit approach and propose a compact impedance model to represent resonance in metallic nanoparticle with cubic nonlinearity. The model uses full-wave dipole equation by employing all time-dependent fields and introduces the concept of nonlinear radiation impedances. Analytical expressions for the nonlinear radiation (internal and external) impedances are derived and used for the first time to get the close-form expression of nonlinear (NL) scattering cross-sectional area using voltages, currents and circuit elements. The effects of nanoparticle parameters i.e. radius, intensity and dielectric function of surrounding medium on cubic nonlinearity are analyzed using impedance model. The validated close-form impedance model preserves the macroscopic properties to give intuitive understanding of NL behavior necessary in facilitating next-generation nanophotonics applications.

Role of Quasiparticles in an Electric Circuit with Josephson Junctions.

Although Josephson junctions can be viewed as highly nonlinear impedances for superconducting quantum technologies, they also possess internal dynamics that may strongly affect their behavior. Here, we construct a computational framework that includes a microscopic description of the junction (full fledged treatment of both the superconducting condensate and the quasiparticles) in the presence of a surrounding electrical circuit. Our approach generalizes the standard resistor capacitor Josephson model to arbitrary junctions (including, e.g., multiterminal geometries and/or junctions that embed topological or magnetic elements) and arbitrary electric circuits treated at the classical level. By treating the superconducting condensate and quasiparticles on equal footings, we capture nonequilibrium phenomena such as multiple Andreev reflection. We show that the interplay between the quasiparticle dynamics and the electrical environment leads to the emergence of new phenomena. In a RC circuit connected to single channel Josephson junction, we find out-of-equilibrium current-phase relations that are strongly distorted with respect to the (almost sinusoidal) equilibrium one, revealing the presence of the high harmonic ac Josephson effect. In an RLC circuit connected to a junction, we find that the shape of the resonance is strongly modified by the quasiparticle dynamics: close to resonance, the current can be smaller than without the resonator. Our approach provides a route for the quantitative modeling of superconducting-based circuits.

Large-Signal Modeling and Experimental Design Automation of Self-Isolated Harmonic Oscillator for Pulling Effect Reduction

A class of self-isolated harmonic oscillator (SIHO) with a feedback-loop structure is able to significantly reduce the pulling effect without involving extra circuit complexity such as a buffer amplifier. In the first part of this paper, the operation principle of the SIHO is theoretically studied through equivalent circuit models and X-parameter techniques. Closed-form expressions are derived to represent the respective linear and nonlinear equivalent impedances of SIHO subnetworks perturbed by varied load and injected signals. A conventional feedback-loop oscillator structure delivering the fundamental tone is used for comparative study. Such a modeling technique reveals the physical principle and behavior parameters that have an impact on the pulling effect. The experimental verification of the SIHO operation principle and modeling is presented as the second part of this paper. To this end, a harmonic measurement and design system is proposed and implemented for the design of an exemplary SIHO, which delivers a 4-GHz signal with 16.6-dBm power, 28% dc-RF efficiency, and −136.5-dBc/Hz phase noise at 1-MHz offset. The design process does not rely on circuit simulation software packages or a prior knowledge of the large-signal model of transistors, thus demonstrating the concept of a model-free nonlinear circuit design automation based on the experimental optimization. The SIHO circuit model is validated with the measured X-parameters of its nonlinear subnetwork.

Thermodynamic Effects on Nonlinear Electrochemical Impedance Spectra in Lithium NMC | Graphite Cells

Electrochemical impedance spectroscopy (EIS) is widely used to diagnose and characterize physicochemical processes in lithium-ion batteries.1 EIS relies on a low magnitude sinusoidal modulation of either current or voltage so that the battery has a linear response, allowing subsequent analyses to be done through either equivalent circuit methods or linearized physics-based models.2 The analysis can provide qualitative and quantitative information about charge-transfer, mass transport, and thermodynamics processes occurring in the cell.3,4 Linearization of an inherently nonlinear system, like a battery, intrinsically limits the information content of an impedance spectrum. Nonlinear electrochemical impedance spectroscopy (NLEIS) provides all of the information of EIS—e.g. generates the familiar linear spectrum that satisfies Kramers-Kronig relationships—while also revealing additional physics. The key to NLEIS is modestly increasing the magnitude of the input sinusoidal modulation, thereby driving the system into the weakly nonlinear regime, while measuring output signal at twice the input modulation frequency (the second-harmonic). Volterra series analysis (common in the study of weak nonlinearity in electronics) produces a second-harmonic impedance (Z2(w)) spectrum that probes physicochemical processes in new ways, and that are often invisible to linearized EIS.5 From prior work, we know that EIS and NLEIS depend on different thermodynamic traits of a battery, locally, at different states of charge. Samsung 18650 LiNMC | C batteries (1500 mAh) were cycled under aggressive conditions to promote aging and degradation. The open-circuit potentials of these batteries were determined through extremely low rate cycling with high-precision coulometry, and the first and second order derivatives of the open-circuit potential with respect to the capacity were calculated. These calculated derivatives from the full cells are related to the low-frequency harmonic responses in a nontrivial, but consequential manner. Prior works have shown that the first derivatives of each individual electrode affects both the linear and nonlinear impedance response, while the second derivatives only affects the nonlinear response.6 In this work, we have performed NLEIS at voltages of interest in the first and second order derivatives of the full cells to understand their impact on the linear and the second harmonic impedance Z2(w) spectra. Here, we look at how the magnitude of both full-cell derivatives and the sign (+/-) of the second derivative impact the magnitude and the direction of the low-frequency nonlinear response. Although the nonlinear responses are collected from full cells, we can use an extension of the pseudo-2D model of lithium-ion batteries, that also computes the higher order harmonic responses, to gain insight into thermodynamics of the individual electrodes.6 These measurements can be collected with more ease and in shorter time frames than traditional half-cell experiments and differential voltage analyses, which are time-intensive and can be difficult to properly control.7,8 Using both the linear and nonlinear impedances simultaneously can provide fundamental insight into the impacts of the system thermodynamics and can then be used to determine, in shorter measurement times and with more sensitivity, the state of health of lithium-ion batteries. C. Ho, I. D. Raistrick, and R. A. Huggins, J. Electrochem. Soc., 127, 343–350 (1980).M. E. Orazem and B. Tribollet, in Electrochemical Impedance Spectroscopy,, p. 107–128, John Wiley & Sons, Inc. (2008) C.-F. Chen and P. P. Mukherjee, Phys. Chem. Chem. Phys., 17, 9812–9827 (2015).T. Osaka, D. Mukoyama, and H. Nara, J. Electrochem. Soc. 162, 2529-2537 (2015)J. R. Wilson, D. T. Schwartz, and S. B. Adler, Electrochimica Acta, 51, 1389–1402 (2006).M. D. Murbach and D. T. Schwartz, J. Electrochem. Soc., 164, E3311–E3320 (2017).M. Verbrugge, D. Baker, B. Koch, X. Xiao, and W. Gu, J. Electrochem. Soc., 164, E3243–E3253 (2017).M. Ecker, N. Nieto, S. Käbitz, J. Schmalstieg, H. Blanke, A. Warnecke, D. U. Sauer, Journal of Power Sources, 248, 839–851 (2014).

Measurement of Non-Linear Impedances and Zero Free Parameter Modeling Approach for Predicting Battery Voltages

Choosing the appropriate energy storage system for a given application is one of the most important and deciding issues that need to be tackled in designing electric powered equipment. In particular, for electric vehicles, a plethora of power consumption regimes are described by regulatory bodies. These power consumption profiles can be easily transformed to current requirements of the energy storage system which results in countless such current profiles. The problem is further complicated with the vast variety of available energy storage systems, that all need to be tested for a given application specified by the required current profile. Therefore, rather than testing every single combination, modelling approaches are utilized to predict various combinations. Models in the literature usually employ impedance measurements as their basis, either to obtain relevant parameters for a first principles model or to fit an equivalent circuit which is subsequently taken to the time domain. In our modelling approach[1], the current profile to be modeled is converted to the frequency domain via a Fourier Transform. This frequency domain profile is multiplied by the impedance at each frequency, yielding a voltage response again in the frequency domain. This frequency domain voltage is then inverse Fourier transformed to obtain the time domain voltage response. After correcting for the state of charge with a simple DC discharge map, the voltage response of any electrochemical storage system can be obtained with errors less than 1%[1,2]. The developed modelling approach does not fit any models to the impedance data, thus has no free parameters. Thus, modeling battery systems require the accurate measurement of impedance in both our method [1,2]and others. In order to acquire an accurate impedance spectrum, the system needs to be stable throughout the measurement and the sine wave applied needs to lead to a linear response. The impedance spectrum measured can either have non-linearities due to the high amplitude used, or due to the chemistry of the system being irreversible. In either case, the measured impedance and/or the response of the battery would have contributions due to non-linearities. EIS assumes linearity which is usually valid for small amplitudes (of both voltage and current) for energy storage systems. In real applications, however, larger amplitudes are required from these systems which is not easily modeled using equivalent circuit models. In our approach, however, the non-linearities can be accounted for by simply adding the relevant harmonics to the otherwise linear impedance data. We will show the applicability of our model for nonlinear systems using a supercapacitor under high current loads. For the latter case, a primary chemistry, SOCl2 is investigated. In the literature the impedance of SOCl2 batteries is ill-characterized where the reports either have obvious non-linearities[3] or omit data [4]. If the following half reactions and the resulting total reaction is considered for the chemistry, a cell potential that is independent of any concentration is seen, which causes the cell voltage to stay constant at around 3.6V (minus a small decrease due to i.R) as shown in Figure a. Li(s) --> Li+(dis.) + e- (Anode) 4Li+(dis.)+ 4e- + 2SOCl2 (l)--> 4LiCl(s) + SO2 (g)+ S(s) (Cathode) Even a small perturbation such as the small amplitude voltage signal of a potentiostatic impedance measurement is not viable, where in the discharge region the cell potential drops below 3.6V only at full discharge and in the charge region, the reaction is not defined. Utilizing a galvanostatic measurement with a DC offset and dynamic adjustment of the measurement parameters, we will show Kramers-Kronig transformable impedance data for SOCl2 batteries as shown in Figure b.

A New GaN HEMT Equivalent Circuit Modeling Technique Based on X-Parameters

In this paper, a new accurate small- and large-signal equivalent-circuit-based modeling technique for gallium nitride (GaN) HEMT transistors grown on silicon substrate is presented. Despite X-parameters are developed as tools for the development of black-box modeling, they are used for equivalent-circuit-based model extraction. Unlike traditional modeling that uses the small-signal data to build with an indirect manner a nonlinear model, the proposed model is extracted from X-parameter measurements directly. However, similar to the equivalent-circuit-based models discussed in the literature, the new model is subdivided into extrinsic and intrinsic parts. The extrinsic part consists of linear elements and is related to the physical layout of the transistor. The intrinsic part can be extracted with the proposed analytical de-embedding technique. The nonlinear intrinsic elements are represented by new nonlinear lumped impedances and admittances whose extraction is carried out using a newly proposed technique. This new technique uses nonlinear network parameters, various X-parameter conversion rules, and basic analysis techniques of interconnected nonlinear networks. It is accurate and more advantageous than traditional transistor modeling techniques. The modeling procedure was applied to a 10 $\mu \text{m} \times $ 200 $\mu \text{m}$ GaN HEMT with a gate length of $0.25~\mu \text{m}$ . A very good accordance between model simulations and measurements was obtained, validating the modeling approach.

Nonlinear impedances of thermoacoustic stacks with ordered and disordered structures

Nonlinear impedances of two thermoacoustic stacks with ordered structures (plate-type and pipe-type) and one with a disordered structure (copper mesh) are studied. The linear resistances, nonlinear coefficients and effective acoustic masses of the stacks are extracted from the experimental results based on an analogical model of nonlinear impedances of porous materials. The resistance and nonlinear coefficient of the disordered stack are found to be much larger than those of the ordered stacks, which have similar volume porosities. In the ordered stacks, the resistance is only marginally influenced by the length of the stack, while in the disordered stack, the resistance increases significantly with the length. These characteristics of the impedances of ordered and disordered stacks are explained with the minor loss theory and the tortuosity of a stack.

Nonlinear acoustic impedances of thermoacoustic stacks with different structures in resonance pipes

The acoustic impedances of thermoacoustic stacks in the resonance pipes are measured by the method for measuring the nonlinear fluid resistances of porous materials. The thermoacoustic stacks with different structures of plate-type, pipe-type and meshed copper stacks are studied, in which the influences of the porosity and thickness of the stack and the operating frequency are evaluated experimentally. In the evaluations, the velocity variations in the stacks are neglected, so the thicknesses of the stacks must be much shorter than the acoustic wavelengths in the resonance pipe. The measured results show that the resistance of the stack keeps constant when the acoustic pressure level is low, but it increases rapidly with the tendency of quadratic function when the acoustic pressure level increases more than about 130 dB. Furthermore, both the linear and nonlinear acoustic resistances of the stacks increase with the thicknesses, while decrease with the increase of the porosity and/or the operating frequency. Finally, it is believed that the results of the influences of the structures and parameters of stacks on the acoustic impedances can be used in the nonlinear model of the thermoacoustic refrigerator.

전력증폭기 트랜지스터 파라미터의 능동 주파수 체배기 성능 영향에 대한 분석

본 논문은 RF 전력증폭기용 트랜지스터의 주파수 체배기 활용을 위한 최대 효율 조건에 대해 분석하고, 고효율 달성을 위한 출력 정합 회로에서의 고조파 임피던스와 기생 성분에 의한 부정합 영향에 대해 고찰하였다. 이를 바탕으로 능동 주파수 체배기의 설계에 있어 입력 바이어스 제어를 통해 고조파 전류를 발생시키는 경우의 이론적인 고조파 전력을 예상하였으며, class-F 구조를 기반으로 하여 주파수 3체배기를 설계하고, 트랜지스터의 비선형 파라미터로써 정규화된 3차 고조파 전력을 예상하였다. 위의 분석 결과를 바탕으로 2.475 GHz에서 주파수 3체배기를 설계하였으며, 시뮬레이션 효율 약 19.5 % 및 측정 효율 22.9 %, 최대 변환 이득 9.5 dB의 결과를 얻을 수 있었다. In this paper, the optimal condition for efficient active frequency multipliers is analyzed. This analysis is based on the effects from transistor nonlinear coefficients, harmonic impedances, and output parasitic components. From the analysis, normalized harmonic power is estimated with the clipping condition of a commercial transistor, and the condition for high conversion efficiency is suggested. From the analysis, a class-F frequency tripler was implemented for the output at 2.475 GHz, showing the maximum efficiency of 22.9 % and the maximum conversion gain of 9.5 dB.

Modeling of Human Voice Box in VLSI for Low Power Biomedical Applications

Communication is heavily dependent on ideas expressed through speech. The ideas and tonal qualities during vocal expression give voice an idea about person characteristics and personality. The estimation of vocal tract configuration from speech sound to represent speech events with robust and compact signals that describe the salient features of speech is an important area of speech communication. The Human Voice Box (Glottis) is the source of voice production and an important part of human body. Recent techniques of speech processing, such as speech recognition and speech synthesis, use the glottal closure and opening instants. Current models of the glottal waves derive their shape from approximate information rather than from exactly measured data. In this work, an electrical model of Human Voice Box is presented by exploiting fluid volume velocity to current and fluid pressure to voltage. The glottis modeled as current source includes linear and nonlinear impedances to represent laminar and turbulent flow, respectively, in the vocal tract. The complete model of glottis runs at power supply of 1.8 volt and the design is verified in a standard TSMC 0.18 micrometer technology on BSIM 3v3 model using ELDO Simulator.

Measurements of Nonlinear Electrical Impedances by Virtue of Induced Conformational Changes in DNAs

A method for label-free electrical impedance sensing of DNA is proposed, and experimentally demonstrated using a micro Electrical Impedance Spectroscopy (µ- EIS) device. The method features not only the detection of DNA without any labelling, but also the control of the conformation that would enhance the electrical impedance signal. In order to conduct semiautomated measurements controlled by an external PC, a microfluidic chip made of a silicone elastomer of polydimethylsiloxane (PDMS), a measurement chip embedded with micro-electrodes, and a micropump chip are fully integrated in the µ-EIS device. The µ-EIS device is capable of detecting DNA concentrations of a few nM in aqueous solution of a few pL in volume by virtue of the conformation-enhanced nonlinear impedance response. As a first demonstration of conformational-change-induced DNA analysis, the frequency and the electric field strength dependence of various lengths of DNA are evaluated.

Effect of DC-DC Converter Topologies and Operation on the Electrical Performance of Fuel Cells

An analysis of DC-DC converter-driven direct ethanol fuel cell systems is presented. The output voltage characteristics of two systems—boost-driven and buck-boost-driven systems—are compared. Experimental results show that direct ethanol fuel cells exhibit variable non-linear impedances as a function of frequency. It is shown that DC-DC converter-driven direct ethanol fuel cell systems do not exhibit a predictable output as a function of duty cycle alone, in both boost and buck-boost configurations. The analysis shows that Ni-foam anode direct ethanol fuel cell and Ni-mesh anode direct ethanol fuel cell output voltage characteristics become nearly identical at switching frequencies beyond 6 kHz.

Circuit-Level Design of Human Voice Source

Communication is heavily dependent on ideas expressed through speech. The ideas and tonal qualities during vocal expression give voice an idea about person characteristics and personality. The problem of representing speech events with robust and compact signals that describe the salient features of speech is an important area of speech communication. The Glottal Source is an important component of voice as it can be considered as the excitation signal to the voice apparatus. Nowadays, new techniques of speech processing such as speech recognition and speech synthesis use the glottal closure and opening instants. The pitch synchronous analysis that is used in several area of speech processing often requires robust detection of the instants of glottal closure and opening. Current models of the glottal waves derive their shape from approximate information rather than from exactly measured data. General method concentrate on assessment of the glottis opening using optical, acoustical methods, or on visualization of the larynx position using ultrasound, computer tomography or magnetic resonance imaging techniques. In this work, an experimental integrated circuit of human glottis using MOS is presented by exploiting fluid volume velocity to current, fluid pressure to voltage, and linear and nonlinear mechanical impedances to linear and nonlinear electrical impedances. The glottis modeled as current source includes linear, non-linear impedances to represent laminar and turbulent flow respectively, in vocal tract. The MOS modeling and simulation of glottis were carried out on TSMC 0.18 micrometer technology.

An Analog Integrated-Circuit Vocal Tract

We present the first experimental integrated-circuit vocal tract by mapping fluid volume velocity to current, fluid pressure to voltage, and linear and nonlinear mechanical impedances to linear and nonlinear electrical impedances. The 275 muW analog vocal tract chip includes a 16-stage cascade of two-port pi-elements that forms a tunable transmission line, electronically variable impedances, and a current source as the glottal source. A nonlinear resistor models laminar and turbulent flow in the vocal tract. The measured SNR at the output of the analog vocal tract is 64, 66, and 63 dB for the first three formant resonances of a vocal tract with uniform cross-sectional area. The analog vocal tract can be used with auditory processors in a feedback speech locked loop-analogous to a phase locked loop-to implement speech recognition that is potentially robust in noise. Our use of a physiological model of the human vocal tract enables the analog vocal tract chip to synthesize speech signals of interest, using articulatory parameters that are intrinsically compact and linearly interpolatable.

A Probabilistic Approach for Optimal Passive Harmonic Filter Planning

This paper presents a new approach based on the linear approximation method and chance-constrained programming model for the optimal planning of single-tuned harmonic passive filters in an industrial power system. In the problem, the effects of the probabilistic characteristics of the nonlinear load currents and harmonic impedances of the system and linear loads are considered in the filter planning. The objective is to minimize the total filter installation cost, while the harmonic currents limits and filter component constraints are satisfied with predetermined confidence levels. The formulated probability-constrained problem is then transformed into a deterministic nonlinear programming problem and is solved by a sequential quadratic programming (SQP) solver. The proposed solution procedure is tested with an actual industrial power system and is verified by the conventional deterministic approach and by the Monte Carlo simulation. Numerical experiences show that the proposed method yields favorable results for the filter planning.