Complex Circuit Models Research Articles

Ecological network optimization of Jiuquan City, Gansu, China based on complex network theory and circuit model

Building a scientific and reasonable ecological network is the key for optimizing the pattern of territorial development and protection, and is of great significance for ensuring regional ecological security and promoting the virtuous cycle of ecosystems. In previous studies, nodal attack method (destruction of ecological source area) was often used in the "robustness" evaluation of ecological networks. Actually, the ecological corridor is more fragile than the source area, and thus the nodal attack method is not reasonable. In this study, taking Jiuquan City as the research area, based on the circuit model to construct the ecological network, we carried out the topology optimization of ecological network by using three strategies (random edge increase, node degree and priority edge increase with low node intermedium number) in complex network theory. We compared and analyzed the "robustness" of ecological network before and after optimization by constructing edge attack strategy, and selected the best network optimization strategy. The results showed that 65 ecological source areas were identified in Jiuquan City, with a total area of 20275.15 km2, and that grassland accounted for 89.5% of the source area. We identified 179 ecological corridors with a total length of 6387.16 km, 158 ecological barrier points with a total area of 1385.5 km2. The unused land accounted for 92.2% of the total barrier points area. We identified 63 ecological pinch points, mainly concentrated in the source edge and corridor intersection. Among them, the spatial distribution of 11 barrier points and pinch points was consistent, which was the key area to be repaired in ecological network optimization. The three optimization strategies had significantly improved the stability of ecological network in Jiuquan City. The relative size of the maximum connected subgraph and the edge connected rate of the ecological network of the optimization strategy of adding edges according to degree were all the most stable under random attack mode and deliberate attack mode, which was the best optimization scheme for ecological network in Jiuquan City.

Impedance Variation of All-Solid-State Battery Cell Using Li10GeP2S12; States-of-Charge Dependence Visualized by Distribution-of-Relaxation Time Analysis

Electrochemical impedance spectroscopy (EIS) will support understanding of electrochemical phenomena in emerging energy devices, including all-solid-state Li ion batteries (ASSLiBs), only when the results are analyzed in a consistent way without arbitrariness. This study1 aimed to establish such a robust analysis for ASSLiB cells using a fast lithium ion conductor Li10 +x Ge1+x P2 −x S12 (LGPS)2, by applying distribution-of-relaxation time (DRT) analysis3. The DRT method distinctively visualized impedance changes depending on states of charge (SOCs). Pellet-type cells were prepared with an In–Li anode, LGPS separator, cathode composite comprising LGPS and LiNbO3-coated LiCoO2 powders4. Figure 1a shows the discharge curve that was recorded for the cell at the current density of 13.2 μA cm−2 (1/40 C-rate) and with the cut-off voltage of 1.9–3.6 V vs. Li+/In–Li (2.55–4.25 V vs. Li+/Li). The EIS measurements were performed during discharge process at various SOCs from 100% to 20%. Nyquist diagrams obtained from the EIS data are shown in Figure 1b, where two broad semicircles are observed at low and high frequency sides. This result indicates at least two electrochemical processes exist in the cell. Both semicircles become large in size upon decreasing SOCs from 100 % down to 20%, indicating that the cell has SOC-dependent electrochemical processes. Figure 1c shows DRT transformation of the EIS data, which helps to separate impedance components in detail. Here horizonal and vertical axes respectively represent the measurement frequency and polarization contribution at each frequency. The center frequency of each distinct peak corresponds to time constant [τ =1/(2πf)] for the respective electrochemical process, and thus the number of peaks matches that of electrochemical processes in the cell. Meanwhile, the peak area represents polarization contribution of each process. Consistently in the whole SOC range, the above DRT analysis indicates the semicircle at high frequency side is divided into two impedance contributions and that at low frequency side cannot be separated any more. This result is consistent with the DRT spectra from additionally prepared symmetric cells; in total three DRT peaks were observed with two peaks from interphase and interface between In–Li/LGPS, and one from LiNbO3-coated LiCoO2/LGPS interface. Accordingly, DRT diagram in Figure 1c was interpreted as indicated by arrows for each peak. This study demonstrated that DRT analysis supports a consistent interpretation of EIS data from ASSLiB cells at various SOCs and with different electrode configurations, and thus implied that the method will also help subsequent equivalent circuit model analysis for reproducible parametrization of electrochemical processes.1. S. Hori et al., “Understanding the impedance spectra of all-solid-state lithium battery cells with sulfide superionic conductors,” J. Power Sources 556, 232450 (2023).2. N. Kamaya et al., “A lithium superionic conductor,” Nat. Mater. 10, 682–686 (2011).3. S. Dierickx, A. Weber, E. Ivers-Tiffée, “How the distribution of relaxation times enhances complex equivalent circuit models for fuel cells,” Electrochim. Acta 355, 136764 (2020).4. N. Ohta et al., “LiNbO3-coated LiCoO2 as cathode material for all solid-state lithium secondary batteries,” Electrochem. Commun. 9, 1486-1490 (2007). Figure 1

Analysis of the Charging Current in Cyclic Voltammetry and Supercapacitor's Galvanostatic Charging Profile Based on a Constant-Phase Element.

We investigated the charging current in cyclic voltammetry and the galvanostatic charging/discharging behavior of a controversial constant-phase element (CPE) to describe an electrical double layer used only in electrochemical impedance spectroscopy. The linear potential sweep in the time domain was transformed into the frequency domain using a Fourier transform. The current phasor was estimated by Ohm’s law with the voltage phasor and a frequency-dependent CPE, followed by an inverse Fourier transform to determine the current in the time domain. For galvanostatic charging/discharging, the same procedure, apart from swapping the voltage signal with the current signal, was applied. The obtained cyclic voltammetry (CV) shows (1) a gradual increase in the charging current, (2) a higher charging current at a low scan rate, and (3) a deviation from the linear relationship between the charging current and the scan rate. For galvanostatic charging/discharging, the results demonstrate (1) curved charging/discharging behavior, (2) a higher voltage in the early stage, and (3) a lower voltage during longer charging periods. In contrast to a previous approach based on solving a differential equation with a simple RC circuit, our Fourier transform-based approach enables an analysis of electrochemical data with an arbitrary and complex circuit model such as a Randles equivalent circuit. The CPE model is more consistent with previous experimental results than a simple ideal capacitor, indicating a ubiquitous CPE in electrochemistry and a fair figure of merit for supercapacitors.

A Novel Battery State of Charge Estimation Based on the Joint Unscented Kalman Filter and Support Vector Machine Algorithms

With the development of new energy sources becoming the mainstream of energy development strategies, the role of electric vehicle-powered lithium-ion batteries in the field of automobile transportation is becoming more and more obvious. An efficient the Battery Management System is necessary for the real-time usage monitor of each battery cell, which analyzes the battery status to ensure its safe operation. A complex equivalent circuit model is proposed and established. The Improved Equivalent Circuit Model is used to realize the precise mathematical expression of the power lithiumion battery packs under special conditions. The State of Charge estimation method which is based on Unscented Kalman Filter has a good filtering effect on the nonlinear systems. Based on the State of Charge estimation of Support Vector Machine, the samples in the nonlinear space of lithium-ion battery are mapped to the linear space. It can be seen from the experimental analysis that a joint Unscented Kalman Filter and Support Vector Machine algorithms for State of Charge estimation has higher accuracy. The experimental results show that the tracking error is less than 1.00%.

How the distribution of relaxation times enhances complex equivalent circuit models for fuel cells

Distribution of relaxation times (DRT) is a well-established method for deconvoluting electrochemical impedance spectroscopy (EIS) data from fuel cells. DRT-analysis provides a deeper insight into electrode reactions and supports identification of the most accurate equivalent circuit models. This established method has undergone much change in recent decades and has been applied to many sub-fields. Contemporary studies are highly specialized and produce specialist literature: to further a comprehensive view, this paper provides an overview and retrospective. EIS measurement and subsequent interpretation by DRT are challenging because (i) high-performance electrodes have very low impedances (10–100 mΩ), (ii) the concept of one rate-limiting step is usually not applicable, and (iii) the charge transfer and transport processes in anode and cathode are often coupled; overlapping in the frequency domain. In this paper selected results from advanced EIS and DRT analyses are discussed. We demonstrate the importance of EIS data quality, introduce the use of the Kramers-Kronig transformation, explain the impacts of statistically distributed noise and single errors in EIS spectra, and the selection of the regularization parameter lambda for improved interpretation of DRT curves. Finally, well-selected examples of DRT approaches lead to adequate models with different complexity. As a result, this paper deepens the understanding of how to assess electrochemical measurements of fuel cells based on the DRT. It, therefore, represents a vital guide for DRT analysis.

Analysis of a Fractional-Order Wireless Power Transfer System

This brief presents a fractional coupled model of fractional-order wireless power transfer (FOWPT) system based on the fractional calculus. By applying coupled-mode theory (CMT), dynamic characteristics of fractional systems can be described clearly while avoiding complex circuit models. The theoretical simulation results indicate that the FOWPT system has better characteristics and greater design freedom. Furthermore, the fractional coupled model is in good agreement with the circuit model and experiment, which proves the correctness of the generalized fractional coupled mode equations. Therefore, the fractional coupled model provides a valuable tool for the further analysis of FOWPT systems and may be used in other fractional-order resonant circuits.

Material parameters from frequency dispersion simulation of floating gate memory with Ge nanocrystals in HfO2

Abstract Trilayer memory capacitors with Ge nanocrystals (NCs) floating gate in HfO 2 were obtained by magnetron sputtering deposition on p-type Si substrate followed by rapid thermal annealing at relatively low temperature of 600 °C. The frequency dispersion of capacitance and resistance was measured in accumulation regime of Al/HfO 2 gate oxide/Ge NCs in HfO 2 floating gate/HfO 2 tunnel oxide/SiO x /p-Si/Al memory capacitors. For simulation of the frequency dispersion a complex circuit model was used considering an equivalent parallel RC circuit for each layer of the trilayer structure. A series resistance due to metallic contacts and Si substrate was necessary to be included in the model. A very good fit to the experimental data was obtained and the parameters of each layer in the memory capacitor, i.e. capacitances and resistances were determined and in turn the intrinsic material parameters, i.e. dielectric constants and resistivities of layers were evaluated. The results are very important for the study and optimization of the hysteresis behaviour of floating gate memories based on NCs embedded in oxide.

Optimization of current waveform tailoring for magnetically driven isentropic compression experiments.

The Thor pulsed power generator is being developed at Sandia National Laboratories. The design consists of up to 288 decoupled and transit time isolated capacitor-switch units, called "bricks," that can be individually triggered to achieve a high degree of pulse tailoring for magnetically driven isentropic compression experiments (ICE) [D. B. Reisman et al., Phys. Rev. Spec. Top.-Accel. Beams 18, 090401 (2015)]. The connecting transmission lines are impedance matched to the bricks, allowing the capacitor energy to be efficiently delivered to an ICE strip-line load with peak pressures of over 100 GPa. Thor will drive experiments to explore equation of state, material strength, and phase transition properties of a wide variety of materials. We present an optimization process for producing tailored current pulses, a requirement for many material studies, on the Thor generator. This technique, which is unique to the novel "current-adder" architecture used by Thor, entirely avoids the iterative use of complex circuit models to converge to the desired electrical pulse. We begin with magnetohydrodynamic simulations for a given material to determine its time dependent pressure and thus the desired strip-line load current and voltage. Because the bricks are connected to a central power flow section through transit-time isolated coaxial cables of constant impedance, the brick forward-going pulses are independent of each other. We observe that the desired equivalent forward-going current driving the pulse must be equal to the sum of the individual brick forward-going currents. We find a set of optimal brick delay times by requiring that the L2 norm of the difference between the brick-sum current and the desired forward-going current be a minimum. We describe the optimization procedure for the Thor design and show results for various materials of interest.

FPGA Implementation of Self-Testing Logic Gates, Adders and Multipliers

This study presents self-checking designs for arithmetic and logic circuits using Field Programmable Gate Array (FPGA) design. At present, we are implementing every circuit using VLSI technology because of its excellent features like low power, less area, wide implementation. Since finding error manually is a tedious process, self-checking method would be most wanted. Self-checking circuits are preferable to Automatic Testing Equipment (ATE) because they demand less hardware, low cost and takes very less test application time. The replica construction and pattern recognition are the two methods presented for self-checking logic gates. Self-checking single-bit full adder, 4-bit adder and 2-bit multiplier circuits are implemented and tested on EP2C20F484C7 Altera Cyclone-II FPGA device using Very High-Speed Integrated Circuits Hardware Description Language (VHDL) script. The test data input samples are applied through input switches and the Error/No Error results are obtained on the 7-segment display device. This study discuss in detail about basic self-checking methods with a experimental way. If the complexity of the circuit increases, the components used and the number of connections between the components increases. As a result, the probability of error occurrence increases for complex designs. But this error occurrence can be avoided to the maximum by using self-checking circuits at different build stages in the complex circuit model. The reliability of any system becomes very important especially in the area of applications such space technology, medical image analysis, military communications, etc.

Reduced Order PEEC Modeling for EMC Problems via Mixed Arnoldi Algorithm and Padé Approximation

The Partial Element Equivalent Circuit (PEEC) method is a 3-D full-wave modeling method suitable for combined electromagnetic and circuit analysis, and now is one of the promising numerical methods for Electromagnetic Compatibility (EMC) modeling. Model order reduction (MOR) techniques provide a feasibility to approximate complex circuit models with compact reduced-order models, and have great potentials to improve the computational efficiency for complex modeling problems. An effective MOR technique basing on mixed Arnoldi algorithm and Padé approximation for the PEEC modeling is introduced in this paper. Numerical simulations of a typical coupled micro-strip line EMC problem indicate the effectiveness of the proposed methods.

Research on Impedance Characterization of Triple-Layer Piezoelectric Bender

The use of piezoelectric material as transducer is prevalent. Piezoelectric bending mode element can be used for vibration energy harvesting because it can convert mechanical energy into electrical energy. In this article, electrical impedance characterization and equivalent circuit of triple-layer piezoelectric bender are discussed. Triple-layer piezoelectric bending device is fabricated, measured and modeled. This paper is aimed to explore simple but practical equivalent circuit models, expressed using electrical parameters of triple-layer piezoelectric bender and investigate the applicability of the Van Dyke circuit model and the complex circuit model in modeling the specimen’s equivalent circuit. The models produced impedance curves that closely matched the impedance measured for piezoelectric sample. The impedance characterization can provide a good understanding on the electrical behaviors of the triple layer piezoelectric bender when analyzing the performance of piezoelectric device.

MODEL ORDER REDUCTION FOR PEEC MODELING BASED ON MOMENT MATCHING

Accurate and efiective system-level modeling has become necessary to address electromagnetic compatibility (EMC) issues in modern circuit and system design. Model order reduction (MOR) techniques provide a feasibility to approximate complex circuit models with compact reduced-order models. In this paper, an efiective MOR technique entitled multi-point moment matching (MMM) is implemented for the partial element equivalent circuit (PEEC) modeling. Moment information at multiple frequency points is used in this method in order to accurately estimate a given system over an entire frequency range of interest, and for each frequency an enhanced asymptotic waveform evaluation (AWE) is applied to obtain a reduced-order model by constructing a pole-residue representation of the original transfer function. The improvements of conventional AWE in aspects of both moment computation and moment matching can avoid ill-conditioned moment matrices and unstable dominant poles. The complex frequency hopping (CFH) technique is employed to select the multiple expansion points by using a newly developed upward- search algorithm. Numerical simulations of coupled microstrip lines in both frequency and time domain indicate the efiectiveness of the proposed method.

A Method for Interfacing Lumped-Circuit Models and Transmission-Line System Models With Application to Railways

Transient analysis of lossy multiconductor transmission lines (MTLs) has been studied using the finite-difference time-domain (FDTD) method with lumped loads/devices connected at line terminations. In electrified railway networks, series and shunt devices (whose circuit models are derived either from experiments/borrowed off the shelf), e.g., transformers, converters, switchgear, signal equipments, etc., are found distributed along the MTL system. To simulate such railway systems involving both transmission lines (TLs) and lumped circuits, an interface technique between TL systems, which is solved using FDTD, and all the lumped circuits, which are solved using alternative transients program/electromagnetic transients program software (circuit solver), is proposed. This sufficiently accurate method is simple to apply as only instantaneous voltages and currents are transmitted between the stand-alone FDTD routine and circuit solver. Moreover, the user avoids coding complex circuit models within the FDTD, while at the same time, efficiently uses the potential of accurate frequency-dependent loss models (nonexistent in circuit software) coded in FDTD. The technique is applied on typical electrified railway systems to demonstrate how traction transformers, track circuits, and line interconnections affect the propagating voltages and currents. The method could be beneficial for transient protection and insulation coordination studies in electrified railway systems.

MOS Capacitor Evaluation of Deep States at the Interfacial Grain Boundary in (110/100) Bonded Silicon

Three different characterization structures of MOS capacitor: Homo orientation, Hybrid orientation and hybrid orientation with shallow grain boundary were applied to evaluate the deep states at (110/100) grain boundary. With multiple frequency C-V and G-V measurements from our unique HOMO and HOT structures, a complex equivalent circuit model of MOS capacitor on bonded wafer was proposed and fitted. With this non-destructive characterization approach, charge density at deep grain boundary became accessible. Moreover, the Continuum of interface trap density at grain boundary, ranged from 0.3 eV below mid-gap to 0.16 eV above mid-gap was completed by applying designed HOT MOS capacitor with shallow grain boundary. This accomplishment is leading us toward further studies on deep state of grain boundaries playing key roles in real device.

Impedance spectroscopic studies of cement-based piezoelectric ceramic composites

A complex equivalent circuit model for cement-based piezoelectric ceramic composite in the thickness mode is presented. The losses of the composites have been taken into account by considering the elements of the circuit as complex quantities; one factor causing the losses is the electrical leaking of cement matrix. The simulated curves derived from the complex circuit model match the experimental results closely. The calculation of the equivalent circuit parameters from the material properties is straightforward. Conversely, the material constants of composites can be derived when the complex circuit parameters are known. A reciprocal relationship exists between the material constants and equivalent circuit parameters have been proved in this study both in theoretically and experimentally.

Evaluation of electrochemical impedance by means of a coulostatic method

Purpose – Aims to evaluate the impedance of a rapidly‐evolving corrosion cell by developing an alternative method to the traditional frequency domain method, and to present a new method to analyze the coulostatically‐induced transient (CIT).Design/methodology/approach – The coulostatic impulse signal was used to obtain the CIT. By transforming the CIT from the time domain into the frequency domain, the coulostatically induced impedance spectrum (CIS) can be obtained, which contributes to the evaluation of the impedance of the electrode and of its corrosion processes. The equations for the coulostatic response also can be obtained by using network analysis in the Laplace domain.Findings – Obtaining the CIS of an electrode in the time domain can facilitate accurate evaluation of metal corrosion rate in a rapidly evolving system. Compared with the traditional method for deriving CIT equations, the proposed method based on network analysis is convenient for more complex circuit models to obtain the CIT equati...

Complex circuit model for RF inductors

AbstractIn this paper, a complex circuit model is introduced for an RF choke by considering the magnetic, dielectric, and eddy current effect in ferrite. By calculating the active power and reactive power in an RF inductor, the resistive components and capacitive, inductive components in the circuit model are extracted. The circuit model is useful to determine the total loss and loss components with different magnetization levels at different frequencies. © 2002 John Wiley & Sons, Inc. Microwave Opt Technol Lett 32: 159–162, 2002.

Gradient approximation method for circuit optimisation

In the paper a new optimisation method, gradient approximation and descent control (GADC), is presented in two parts. The first part is an algorithm based on a data processing technique to approximate the performance gradients, which permits a fast convergence rate. The second is an iterative algorithm which allows an improvement in the approximation, and consequently a solution of the problem in reduced computation time. It is particularly suited to solve the ‘FIT’ problems, to applications related to numerous complex circuit models, and to multipleobjective problems having double-sided specifications (e.g. limited satisfaction intervals). Examples given include model parameters fitting with a very competitive overall computation time and satisfying very tight specifications.