Simple Equivalent Circuit Model Research Articles

Biological Cell Response to Electric Field: A Review of Equivalent Circuit Models and Future Challenges.

Biological cells, characterized by complex and dynamic structures, demand precise models for comprehensive understanding, especially when subjected to external factors such as electric fields (EF) for manipulation or treatment. This interaction is integral to technologies like pulsed electric fields (PEF), inducing reversible and irreversible structural variations. Our study explores both simplified and sophisticated equivalent circuit models for biological cells under the influence of an external EF, covering diverse cell structures from single- to double-shell configurations. The paper highlights challenges in circuit modeling, specifically addressing the incorporation of reversible or irreversible pores in the membrane during external EF interactions, emphasizing the need for further research to refine technical aspects in this field. Additionally, we review a comparative analysis of the performance and applicability of the proposed circuit models, providing insights into their strengths and limitations. This contributes to a deeper insight of the complexities associated with modeling biological cells under external EF influences, paving the way for enhanced applications in medical and technological domains in future.&#xD.

Impedimetric detection of chloride ions using two symmetric Ag/AgCl electrodes

The suitability of Ag/AgCl electrodes for specific detection of chloride ions in aqueous gels is investigated. In contrast to potentiometric sensors, we use an impedimetric approach and avoid the need for a separate reference electrode through a symmetric two-electrode configuration. As such, electrochemical impedance spectroscopy is employed to characterise the response of the Ag/AgCl electrodes in contact with gels at various hydration levels containing different types as well as concentrations of salt. In order to extract quantitative information related to e.g. the ion concentration and mobility from the impedance spectra, an equivalent circuit model is fitted to the data. Here, we develop a simple equivalent circuit model related to the physical parameters of the system, which can be reduced to a modified Randles circuit with only few circuit elements. Importantly, even though the equivalent circuit model contains the same elements as a Randles circuit, their physical origin is different. Systematic variations of ion mobility, ion concentration, and type of ions allow us to evaluate the relationship between those physical properties and the resulting fitting parameters of the modified Randles circuit. This finally enables us to determine chloride concentrations in complex liquids, containing other salts and long chain molecules.

Electrochemical Circuit Model Based State of Health Prognostics for Evaluation of Reusability of Lithium-Ion Batteries from Electric Vehicle.

For the purpose of predicting the state of health of already used lithium-ion batteries from 85 kWh electric vehicles, a simplified equivalent circuit model is utilized to estimate the electrochemical time constant from constant current discharge profiles. The grading process among as-obtained LIB cells is classified into three level types according to the remaining capacity and direct current resistance. Theoretically, the logarithmic equation describing cycling behavior is derived and utilized in the prediction of the state of health of the used cells. After the selection of the electrochemical time constant obtained from the best-fitting results in constant current discharge data, the suitable cycle number until the 20th cycle was selected for the prediction of the state of health after the 250th cycling data, which revealed that a narrow error range below 5% was for high and medium battery grades. Also, this error range became abruptly wider in lowest grade batteries, indicating that our proposed model for cycling behavior was highly useful in the prediction of the future state of health of the used batteries.

Impedance of nanocapacitors from molecular simulations to understand the dynamics of confined electrolytes

Nanoelectrochemical devices have become a promising candidate technology across various applications, including sensing and energy storage, and provide new platforms for studying fundamental properties of electrode/electrolyte interfaces. In this work, we employ constant-potential molecular dynamics simulations to investigate the impedance of gold-aqueous electrolyte nanocapacitors, exploiting a recently introduced fluctuation-dissipation relation. In particular, we relate the frequency-dependent impedance of these nanocapacitors to the complex conductivity of the bulk electrolyte in different regimes, and use this connection to design simple but accurate equivalent circuit models. We show that the electrode/electrolyte interfacial contribution is essentially capacitive and that the electrolyte response is bulk-like even when the interelectrode distance is only a few nanometers, provided that the latter is sufficiently large compared to the Debye screening length. We extensively compare our simulation results with spectroscopy experiments and predictions from analytical theories. In contrast to experiments, direct access in simulations to the ionic and solvent contributions to the polarization allows us to highlight their significant and persistent anticorrelation and to investigate the microscopic origin of the timescales observed in the impedance spectrum. This work opens avenues for the molecular interpretation of impedance measurements, and offers valuable contributions for future developments of accurate coarse-grained representations of confined electrolytes.

Towards low-temperature anodic bonding for RbN3-filled MEMS atomic vapor cells and defect inspection by OCT

From the different methodologies to fill microfabricated alkali-metal vapor cells, the rubidium azide (RbN3) decomposition by UV radiation is a cost-effective solution to produce rubidium (Rb) and nitrogen (N2). The typical fabrication of the vapor cells is based on silicon and glass bonding, in which the substrates are heated to temperatures between 300 and 450 ºC along with a high electrostatic field (400 – 1000 V) to establish the solid-state connection. However, the RbN3 compound has been reported to undergo thermal decomposition within the temperature range of 355–395 ºC. In this work, a systematic variation of the bonding temperature (from 200 to 300 ºC) in silicon cavity-based vapor cells is presented to prevent the RbN3 decomposition during the cell fabrication. Considering that the anodic bonding process can be well represented by a simplified equivalent electrical circuit model, we report a maximum bond strength of 6.05 MPa and a lowest time constant τ of 180.03 s for 300 ºC with a simple electrode configuration. A total transferred charge of ≥0.250 mC.mm−2 for temperatures above 225 ºC are indicative of a good quality bond. Interestingly, distinct differences in the failure mode of bonding are observed, in which undamaged bonded interfaces are only observed for temperatures of 275 ºC and above. As a result, a 3 mm diameter vapor cell was successfully fabricated using anodic bonding at 275 ºC. Moreover, and for the first time, optical coherence tomography (OCT) was implemented as an effective and novel technique to investigate the glass-silicon-glass bonding in a MEMS vapor cell, providing a cross-sectional image of the device, in a non-destructive and contactless manner, to ensure the production of reliable and defect-free devices.

Analysis of Impedance Based Sensor to Discover the Invasive Nature of A549 Lung Cancer Cell

Numerous studies have been conducted to investigate the effectiveness of impedance-based sensors in detecting the invasive behavior of cancer cells, specifically through the use of Electric Cell-substrate Impedance Sensing (ECIS) methodology. However, the current equivalent circuit models used to represent the invasive nature of cancer cells have limitations and inaccuracies, and there has been a lack of utilization of mathematical and data analysis software to better understand the growth and invasive behavior of these cells. To address these gaps, this research aims to measure the impedance of A549 lung cancer cells, develop a simplified equivalent circuit model, and analyze the results using mathematical and data analysis software. The invasive behavior of A549 cells will first be studied through impedance measurements, and then a circuit model will be designed and simulated using software tools to reveal the true invasive nature of these cells. Finally, rigorous mathematical analysis and the use of suitable data analysis software (such as Matlab Powergui and Simulink, EIS Spectrum Analyzer, and Plotly) will be applied to gain a comprehensive understanding of the morphological behavior of the cells. The experimental results of this research are expected to align with previous findings, and a quadratic equation will be derived to predict the body's resistance of the A549 lung cancer cell using mathematical and data analysis approaches.

Simplified Current-Equivalent Circuit Models of Synchronous Reluctance Machines and Salient Pole Synchronous Machines Considering the Reluctance Torque

This paper describes a simplified one-phase equivalent circuit model of three-phase salient pole synchronous machines and synchronous reluctance machines. The model represents the pole saliency as a susceptance, with a magnitude based on the pole saliency and a phase angle based on twice the load angle. The reluctance torque itself is then modeled equivalent to a conductance. The model is made as an extension to Norton equivalents, where the internal inductance is connected as a shunt. This approach shares similarities to the magnetization shunt branch in circuit models of transformers and induction motors. The model is derived using the rotating dq-frame, using Park transform and two-reaction theory. The model is then rewritten to better fit one-phase equivalent circuit models, with the terminal voltage as the angular reference. The resulting two-pole model can then more easily be combined with basic circuit theory, thereby synthesizing dq-theory and phasor circuit models.

Luminescence coupling in 28.4%-efficient tandem solar cell utilizing 20.8%-efficient perovskite minimodule stacked on silicon cell

The total power conversion efficiency (PCE) of 28.4% with an aperture area of 64 cm2 on a four-terminal (4T) tandem solar cell with a 20.8% efficiency-semitransparent perovskite module (SPM) with a series interconnection structure and a conventional passivated emitter and rear cell type crystalline silicon solar cell is independently confirmed. This is the independently confirmed record PCE of a 4T perovskite and crystalline silicon tandem solar cell with a structure having the same active area for both top and bottom cells. The impact of the luminescence coupling monitored by the silicon solar cell in the 4T tandem solar cell was investigated based on electrical properties of the top SPM analyzed by a simple one-diode equivalent circuit model.

A Conformable Organic Electronic Device for Monitoring Epithelial Integrity at the Air Liquid Interface.

Air liquid interfaced (ALI) epithelial barriers are essential for homeostatic functions such as nutrient transport and immunological protection. Dysfunction of such barriers are implicated in a variety of autoimmune and inflammatory disorders and, as such, sensors capable of monitoring barrier health are integral for disease modelling, diagnostics and drug screening applications. To date, gold-standard electrical methods for detecting barrier resistance require rigid electrodes bathed in an electrolyte, which limits compatibility with biological architectures and is non-physiological for ALI. This work presents a flexible all-planar electronic device capable of monitoring barrier formation and perturbations in human respiratory and intestinal cells at ALI. By interrogating patient samples with electrochemical impedance spectroscopy and simple equivalent circuit models, disease-specific and patient-specific signatures are uncovered. Device readouts are validated against commercially available chopstick electrodes and show greater conformability, sensitivity and biocompatibility. The effect of electrode size on sensing efficiency is investigated and a cut-off sensing area is established, which is one order of magnitude smaller than previously reported. This work provides the first steps in creating a physiologically relevant sensor capable of mapping local and real-time changes of epithelial barrier function at ALI, which will have broad applications in toxicology and drug screening applications.

A Simplified Equivalent Circuit Model for the Photo-Charging Process of Carbon-Based Quasi-Solid Photosupercapacitors

Solar irradiation can be converted into electrical current by a solar cell, which in turn can be stored in a supercapacitor. The coupling of a solar cell and a supercapacitor, called photosupercapacitor, shows promising applications that demand multidisciplinary studies to understand its functionality and potential. Normally, supercapacitors are characterized with potentiostats or power sources that provide a constant current or voltage, however, we find that the photocurrent provided by a solar cell in a photosupercapacitor configuration largely depends on the voltage stored in the supercapacitor connected in parallel to the solar cell. Therefore, we use a simplified equivalent circuit model to demonstrate that the charging time of a photosupercapacitor depends mainly on its capacitance, and to a lesser extent, on its resistance. At the same time, the maximum output voltage of the photosupercapacitor depends on the saturation and short circuit currents of the solar cell. The numerical results confirm qualitatively the experimental behavior of the photo-charging curves of quasi-solid supercapacitors, which consist of polyvinyl alcohol (PVA)-H2SO4 electrolyte for both activated carbon or reduced graphene oxide-based electrodes. The latter presents better electrochemical characteristics that optimize the operation of the photosupercapacitor. The electrical circuit analysis is a useful tool to guide further improvements in the photosupercapacitor design and fabrication.

Effects of operational parameters on plasma characteristics and liquid treatment of a DBD-based unipolar microsecond-pulsed helium atmospheric pressure plasma jet

A dielectric-barrier-discharge-based square unipolar microsecond-pulsed helium atmospheric pressure plasma jet (APPJ) was characterized by combining a simplified equivalent circuit model with a transferred charge (Q) measured by introducing an additional capacitance in series with the reactor. From Q-V plots, Cd and Ccell for DBD reactors under pulsed excitation were determined. Q-V plots were drawn for varying operational parameters, and the dissipated energy per cycle was evaluated. Operational parameters, such as the gas flow rate and pulse frequency, were varied, and the resulting changes in the plasma plume length, gas temperature, excitation temperature, discharge current, dissipated power, and optical emission spectra were examined. As an example of the application of the plasma jet, liquid media, including de-ionized water, were exposed to the APPJ, and their properties (pH and electrical conductivity) and concentrations of reactive species generated in the media were measured as functions of the operational parameters. Furthermore, changes in the plasma-activated media after storage for different durations and under different conditions were examined. The correlation between plasma characteristics and properties of plasma-treated liquid is discussed.

Accurate Microwave Circuit Co-Simulation Method Based on Simplified Equivalent Circuit Modeling.

A new co-simulation method is proposed for active devices and electromagnetic resonant circuits at microwave frequency range. For the measured and extracted device parameters, three steps of equivalent circuit models are processed of the general, simplified, and EM RLC models. To overcome the limited lumped element simulation in an electromagnetic simulator, the simplified equivalent circuit model is established by mathematical computation. The co-simulation procedures are described and experimentally verified for commercial diodes. The application circuit is designed and implemented using the proposed co-simulation method. The experimental results verify that design using the proposed co-simulated method presented excellent agreement for a wideband frequency range of 0-4 GHz, compared with that using a conventional design method. The proposed co-simulation method can be applied to any commercial EM simulation tools without active model error.

Performance evaluation of a high flow rate annular linear induction pump using a simple equivalent circuit model taking into account dynamic end effects

ElectroMagnetic Induction Pumps are a relevant technical solution for the transportation of alkali metals in applications where safety and reliability are fundamental. Especially, Annular Linear Induction Pumps (ALIPs) are preferred when high flow rates are required. In the early stage design of an ALIP, simple analytical models are convenient to get an estimate of performances. Equivalent circuit models are often used to this purpose. Their accuracy has been found variable, depending on pumps configuration and operating conditions. To assess the relevance for high flow rate applications, circuit models are applied to the ALIP of PEMDyn facility, in CEA Cadarache research centre. The simplest equivalent circuit model for a LIM is tested. Then, a modification to account for dynamic end effects is added. Results are compared to experimental measurements. The correction for dynamic end effects allows a significant reduction of the relative error, especially for the range of highest flow rates.

Current Pulse-Based Measurement Technique for Zinc–Air Battery Parameters

Zinc–air batteries possess advantages such as high energy density, low operational costs, and abundant reserves of raw materials, demonstrating broad prospects for applications in areas like stationary power supplies and emergency power sources. However, despite significant advancements in zinc–air battery technology, a comprehensive measurement model for zinc–air battery parameters is still lacking. This paper utilizes a gas diffusion model to separately calculate the concentration polarization of zinc–air batteries, decoupling it from electrochemical polarization and ohmic polarization, simplifying the equivalent circuit model of zinc–air batteries into a first-order RC circuit. Subsequently, based on the simplified equivalent circuit model and gas diffusion model, a zinc–air battery parameter measurement technique utilizing current pulse methods is proposed, with predictions made for the dynamic voltage response during current pulse discharges. Validation of this method was conducted through single current pulses and step current pulses. Experimental results demonstrate the method’s capability to accurately measure zinc–air battery parameters and predict the dynamic voltage response.

Generalized Inversion of Electrochemical Impedance Data for Battery Systems

Electrochemical Impedance Spectroscopy (EIS) is a key technique for taking a snapshot of an electrochemical system near equilibrium conditions. Due to the richness of the complex-valued dataset and its simple experimental operation, it is currently being investigated as a test to diagnosis battery health and degradation details. Nevertheless, challenges with use of EIS is in interpreting the measured impedance. Current methods for analysis involving either fitting simplified equivalent circuit models or inverting distribution of relaxation times with a singular basis function. Because of these methods' simplifications, their results sometime fail to capture both the complex and heterogeneous underlying physics.Here, we present a novel algorithm for the inversion of EIS data for battery systems, which generalizes the inversion problem to any given linear equivalent circuit model, allowing for the analysis of complicated electrochemical systems. Importantly, this algorithm provides two clear benefits. First, it allows for the analysis of both bounded and unbounded processes, something quite common to battery systems and is vital in understanding non-obvious relationships in degraded batteries. Second, the distribution of independent processes, which can correspond to different physical phenomena, are also inverted by this algorithm. These distributions contain vital features in the identification and prediction of battery state-of-health. Overall, this tool will be indispensable in the analysis of degradation extent over battery aging, and provide an algorithmic framework for interpreting EIS measurements of complicated electrochemical systems.

Conveniently Revealing Lithium-Ion Battery Reaction Kinetics Using Nonlinear Frequency Response Analysis

Nonlinear Frequency Response Analysis (NFRA) can be considered a nonlinear modification of galvanostatic EIS. Due to an increased AC excitation, higher harmonics are additionally present in the voltage response of the cell [1]. Here, a single particle model (SPM) [2] in the frequency domain is used for the simulation of the NFR of lithium-ion batteries (LiB). The time-dependent processes (double-layer charging, solid diffusion) are linear in currently available SPMs. Hence, they can be described algebraically as impedances in the frequency domain. From the nonlinear, time-independent equations (Butler-Volmer, Nernst), for the case of sinusoidal excitations, a system of algebraic equations for the fundamental and higher harmonics up to a freely selectable order N is derived. By combining these systems with the impedances, we obtain a still nonlinear SPM in the frequency domain, which can be solved in a purely algebraic way for the higher harmonics. The proposed model enables researchers to conveniently analyze the NFR of LiBs. This is especially beneficial for investigations of the reaction kinetics since charge transfer coefficients can be obtained directly by parameterizing the model with NFR measurements.The abilities of the model are shown with two exemplary cell setups. At first, a symmetric cell built from metallic lithium is analyzed. The measured impedance is used to parameterize a simple equivalent circuit model (ECM), including transport through the solid electrolyte interphase (SEI). The resulting exchange current densities are used within the frequency domain SPM, which represents a nonlinear version of the ECM. Subsequently, the charge transfer coefficients of the plating/stripping reaction can be obtained conveniently by comparing the NFR measurements with the SPM response. Since the sum of obtained charge transfer coefficients is smaller than one, they are interpreted in the sense of Marcus-Hush-Chidsey kinetics [3], which is possible within a certain range of overpotential. This leads to a distinct value for the solvent reorganization energy. The calculated value is in coincidence with literature values, which are relying on high scan rate CVs with ultramicroelectrodes [4].Secondly, a full pouch cell (NMC622/Graphite) was analyzed in a similar manner. Even though the SPM cannot capture microstructural effects of the porous electrode, a sufficient fit for the EIS measurement was found. After a subsequent parameterization of the charge transfer coefficients, the NFR measurement and simulation again agree well. The resulting values for intercalation reorganization energies at the graphite anode and NMC cathode are even lower than for the plating/stripping reaction. The reorganization energies could not be validated due to the lack of literature values. However, available values for LFP [5] and a value based on unpublished data for graphite [6], are also lower compared to the plating/stripping reaction.The proposed method is very promising since it can directly capture the complete nonlinear kinetics of an electrode. Due to the frequency dependence of LiBs, the separation of kinetic and diffusive effects remains as convenient as it is for EIS.If reorganization energies are considered as given, two persistent challenges in EIS analysis could be tackled: The separation of SEI resistance and charge transfer resistance since the latter is considered as nonlinear. In addition, the ionic transport resistance and charge transfer resistance could be separated for the same reason.In the future, microstructural effects should be integrated into the model. Vidaković-Koch, T.; Miličić, T.; Živković, L. A.; Chan, H. S.; Krewer, U.; Petkovska, M. Nonlinear Frequency Response Analysis: A Recent Review and Perspectives. Opin. Electrochem. 2021, 30, 100851. https://doi.org/10.1016/J.COELEC.2021.100851.Ning, G.; Popov, B. N. Cycle Life Modeling of Lithium-Ion Batteries. Electrochem. Soc. 2004, 151 (10), A1584. https://doi.org/10.1149/1.1787631/XML.Henstridge, M. C.; Laborda, E.; Rees, N. V.; Compton, R. G. Marcus–Hush–Chidsey Theory of Electron Transfer Applied to Voltammetry: A Review. Acta 2012, 84, 12–20. https://doi.org/10.1016/J.ELECTACTA.2011.10.026.Boyle, D. T.; Kong, X.; Pei, A.; Rudnicki, P. E.; Shi, F.; Huang, W.; Bao, Z.; Qin, J.; Cui, Y. Transient Voltammetry with Ultramicroelectrodes Reveals the Electron Transfer Kinetics of Lithium Metal Anodes. ACS Energy Lett. 2020, 5 (3), 701–709. https://doi.org/10.1021/acsenergylett.0c00031.Bai, P.; Bazant, M. Z. Charge Transfer Kinetics at the Solid-Solid Interface in Porous Electrodes. Commun. 2014, 5 (1), 1–7. https://doi.org/10.1038/ncomms4585.Gao, T.; Han, Y.; Fraggedakis, D.; Das, S.; Zhou, T.; Yeh, C. N.; Xu, S.; Chueh, W. C.; Li, J.; Bazant, M. Z. Interplay of Lithium Intercalation and Plating on a Single Graphite Particle. Joule 2021, 5 (2), 393–414. https://doi.org/10.1016/J.JOULE.2020.12.020. Figure 1

Electrochemical Impedance Spectroscopy‐Based Dynamic Modeling of Lithium‐Ion Batteries Using a Simple Equivalent Circuit Model

As one of the most commonly used models for describing the dynamic voltage response of lithium‐ion batteries (LIBs), the equivalent circuit model (ECM) is routinely parameterized using the time–domain experimental data from some dynamic tests. One downside of this time–domain approach is a lack of credible physical interpretation about the model parameters. In this article, a genuine electrochemical impedance spectroscopy (EIS)‐based dynamic modeling approach for LIBs is developed, which only uses low‐frequency EIS data in parameterization of the ECM. The EIS‐based modeling method combines simplicity, high accuracy, and clear physical interpretation. With the EIS‐based modeling method, a simple ECM, namely, a serial connection of a resistance (), describing Ohmic polarization and interfacial reactions, and an resistance–capacitance parallel branch (), describing diffusion polarization, suffice to accurately capture LIB dynamics in most applications.

The Retrieval and Effect of Core Parameters for Near-Field Inter-Body Coupling Communication

The potential of the Internet of Body (IoB) to support healthcare systems in the future lies in its ability to enable proactive wellness screening through the early detection and prevention of diseases. One promising technology for facilitating IoB applications is near-field inter-body coupling communication (NF-IBCC), which features lower power consumption and higher data security when compared to conventional radio frequency (RF) communication. However, designing efficient transceivers requires a profound understanding of the channel characteristics of NF-IBCC, which remain unclear due to significant differences in the magnitude and passband characteristics of existing research. In response to this problem, this paper clarifies the physical mechanisms of the differences in the magnitude and passband characteristics of NF-IBCC channel characteristics in existing research work through the core parameters that determine the gain of the NF-IBCC system. The core parameters of NF-IBCC are extracted through the combination of transfer functions, finite element simulations, and physical experiments. The core parameters include the inter-body coupling capacitance (CH), the load impedance (ZL), and the capacitance (Cair), coupled by two floating transceiver grounds. The results illustrate that CH, and particularly Cair, primarily determine the gain magnitude. Moreover, ZL mainly determines the passband characteristics of the NF-IBCC system gain. Based on these findings, we propose a simplified equivalent circuit model containing only core parameters, which can accurately capture the gain characteristics of the NF-IBCC system and help to concisely describe the channel characteristics of the system. This work lays a theoretical foundation for developing efficient and reliable NF-IBCC systems that can support IoB for early disease detection and prevention in healthcare applications. The potential benefits of IoB and NF-IBCC technology can, thus, be fully realized by developing optimized transceiver designs based on a comprehensive understanding of the channel characteristics.

Simplified exponential equivalent circuit models for prediction of printed supercapacitor's discharge behavior - Simulations and experiments

Simplified exponential equivalent circuit models for prediction of printed supercapacitor's discharge behavior - Simulations and experiments

A Current Saturation Strategy for Enhancing the Low Voltage Ride-Through Capability of Grid-Forming Inverters

This brief proposes a new current saturation strategy (CSS) for grid-forming (GFM) inverters to comply with the existing low-voltage ride-through (LVRT) capability requirements. The proposed control philosophy enables the GFM inverters to follow one of the standardized grid codes by limiting the output current during LVRT via a new control parameter, the power factor angle (PFA). First, a nonlinear mathematical model capturing the full-order averaged dynamics of a GFM inverter embedded with current limiting control has been developed. Following this, the proposed CSS has been analytically evaluated by developing a simplified equivalent circuit model. Finally, numerical and experimental results are presented to verify the accuracy of the CSS for assessing the large-signal stability of a GFM inverter subjected to severe symmetrical grid faults.