Toroidal air-core reactors (TARs) exhibit significant advantages due to low leakage flux, making them suitable for compact applications, such as offshore wind power platsforms. Establishing a wideband equivalent circuit for TARs enables rapid calculation of transient voltage distribution, thereby assessing whether the existing structure meets insulation requirements. This paper proposes a modeling methodology for the transient voltage estimation of the TAR based on the concepts of equipotential conductor elements and terminal capacitance equivalence. The contributions lie in three aspects. First, wideband equivalent circuits are constructed at both the coil level and the TAR level. The capacitances in the model can all be explicitly defined by mathematical expressions, moving beyond behavioral equivalence and possessing clear physical meaning. Second, methods for extracting resistance, inductance, and capacitance parameters of the proposed models are presented, along with an analytical formula for the AC resistance of TARs. Finally, lightning impulse tests are conducted on a TAR prototype. The average errors between calculated and measured peak values of node-to-ground voltage, inter-coil voltage, and inter-turn voltage are 3.239%, 4.901%, and 8.603%, respectively, validating the accuracy of the proposed wideband equivalent circuit and parameter extraction methods.

Online shunt current loss estimation in alkaline water electrolyzers using a temperature-aware equivalent circuit method

Abstract This paper proposes a novel T-shaped periodic relativistic extended interaction oscillator (TSP-REIO) based on the T-shaped periodic slow-wave structure. The structure is analyzed using the equivalent circuit method, and the electron motion behavior is theoretically examined to derive the optimized configuration for efficient beam-wave interaction. Methodologically, the coupling section/cavity for the TSP-REIO equal inductance/capacitance; Kirchhoff’s law gives inter-cavity field distribution. Substituting this field into the 1D kinematic electron motion equation yields electron final velocity (varying initial phases) and energy conversion efficiency across periods. Four-period structure’s calculated efficiency: 43.78%. Parameters of the T-shaped four-period structure are optimized by Support Vector Regression (SVR) during modeling. The validity of the optimization is confirmed by the predicted efficiency (40.27%). Simulation results show that the T-shaped four-period structure achieves an efficiency of 40.44% when driven by a 450 kV and 400 A annular electron beam. The theoretical analysis method proposed herein effectively predicts the energy conversion efficiency of TSP-REIO, enabling rapid optimization of the T-shaped periodic resonant slow-wave structure. Its correctness is further validated by three-dimensional simulation results, providing an effective and viable scheme for the compact and efficient development of high-power microwave devices.

A hybrid wire with high bundle copper fill factor, enhanced thermal conductivity, and low AC losses is proposed for high-speed machines. Firstly, the topology of hybrid wire is presented, highlighting its advantages over conventional litz and solid wires in high-speed machine applications. Secondly, an analytical model for AC loss of the hybrid wire is developed based on the partial element equivalent circuit method. A loss-coupling iterative strategy is proposed to correct the cross-sectional impedance, enhancing the accuracy of AC losses calculations. Thirdly, comparison with finite element analysis results validates the analytical approach. Finally, experimental evaluation of different wire types, including solid, litz, and hybrid wires, demonstrates the superior AC loss suppression of hybrid wire and further confirms the validity of the analytical method for AC loss estimation.

Abstract In this paper, a dual-layer metamaterial structure which is composed of polytetrafluoroethylene (PTFE) substrate and copper was designed. The mechanism underlying the generation of multi-band analogous electromagnetically induced transparency (EIT) effect in the structure is analyzed by the finite integration time-domain (FITD) method and equivalent circuit method (ECM). Additionally, the influence of the structural parameters of the structure on transmission is also investigated. A detection approach utilizing the structure to detect the thickness and permittivity of solid plate structures is formulated, which can be employed in solid sensing. The results indicate that the structure holds potential applications in refractive index sensing and multi-band filter.

Modeling and analyzing multiphysics effects has become one of the most challenging issues in integrated circuit design. Equivalent thermal circuit method is one of the most commonly used method in circuit design to simulate the electrothermal coupling effects, since it is fast and compatible with SPICE. However, it is still difficult to realize electro-thermalmechanical coupling simulation based on equivalent circuit method due to a lack of equivalent mechanical circuit method, which brings difficulties to do electro-thermal-mechanical analysis by SPICE. The equivalent mechanical circuit method is proposed based on solid mechanics equilibrium equation by deriving the electro-mechanical equivalent relation, equivalent circuit elements, equivalent circuit structure, equivalent circuit boundary condition, and the solving algorithm. The equivalent multiphysics circuit of TSV and FinFET are then further constructed to simulate the electro-thermal-mechanical coupling effects and verified with simulation results obtained from the finite element method (FEM). The results show that our proposed equivalent multiphysics circuit framework is able to simulate the electro-thermal-mechanical coupling effects by SPICE in integrated circuits.

This article analyzes the flux characteristics of a novel tubular permanent magnet linear launcher (TPMLL) with short stroke and high-frequency motion characteristics, suitable for application in the electromagnetic launcher. In this article, the proposed TPMLL consists of the following parts: the outer stator, outer air gap, mover made of permanent magnets (PMs), inner air gap, and the inner stator. A magnetic equivalent circuit (MEC) method is established to analyze the electromagnetic characteristics and provide the basis for the structural design. To solve the MEC model, the Newton–Raphson method is adopted. By comparing the results of the finite element method (FEM) with the MEC model, it is found that the accuracy of MEC method has good accuracy in estimating the flux linkage of the proposed motor, which is very suitable to be used in the initial stage of the structural design.

This article presents the electromagnetic-thermal design and optimization of an Aluminum Ring Embedded Cylindrical (AREC) Magnetorheological Fluid (MRF) brake for high-speed, high-torque applications, particularly in the Fixed Canard Decoupled Dual-Spin Artillery Projectile (FCD-DSAP) system. An analytical model based on the magnetic equivalent circuit (MEC) method is developed to estimate the fluid gap magnetic field intensity. The Bingham fluid model is used to characterize the MRF-132DG fluid in its linear region, enabling an accurate evaluation of the braking torque. The brake is optimized by considering the total length of the brake, the excitation current, and the number of coil turns as decision variables. The optimized model is implemented in ANSYS Maxwell and the Bingham fluid model to obtain correlated speed, current, and torque data. These data are integrated into the dual-spin artillery projectile dynamic equation, where a zero angular-speed control for the canard is implemented using a PI controller, allowing for the estimation of net frictional power loss throughout the flight regime. The power loss data, combined with thermal boundary conditions, are then used in ANSYS transient thermal analysis to assess the thermal performance of the brake. The results confirm that the fluid temperature remains within the specified limits, ensuring the reliability and effectiveness of the brake in the underlying applications.

Twisted power cables are widely used in distribution networks due to their ease of installation and low maintenance requirements. As twisted power cables are typically composed of multi-stranded conductors, their complex structure poses challenges for impedance calculation, which increases the difficulty of optimizing systems involving twisted power cables and analyzing lightning surge transients. The common approaches for twisted power cable impedance analysis suffer from significant calculation errors and are time-consuming. This paper proposes an efficient method based on a multi-level partial element equivalent circuit (PEEC) method to address these challenges, an algorithm that effectively models the intricate structure of twisted power cables while maintaining computational efficiency. Experimental validation and verification with analytical methods and finite element methods (FEM) show that the proposed method achieves high accuracy, with calculated values closely matching measured results and significantly reducing errors in resistance and inductance computations, demonstrating the advantages of our proposed approach, particularly in largescale cable models and high-frequency applications. This work provides a valuable method for impedance assessment with broad application potential in cable design optimization and transient analysis.

An accurate circuit model of a two-port square-loop antenna is presented. The circuit consists of equivalent lumped elements based on the Quasi-Static (QS) Partial Element Equivalent Circuit (PEEC) method, under the thin-wire approximation. The introduced model is applied to calculate the transient port response for an impulsive electromagnetic (EM) plane-wave excitation, enabling separate electric and magnetic effects analysis. The presented results are validated with the aid of both state-of-the-art analytical solutions and PEEC method and with a commercial EM tool.

Accurate and efficient modeling and simulation of electro-thermal-mechanical field coupling is essential for evaluating multiphysics effects on devices/circuits’ performance and reliability, as the multiphysics coupling effects become severe in advanced integrated circuits. In our previous work, we developed the equivalent mechanical circuit (EMC) method, thereby constructing a SPICE-compatible equivalent multiphysics circuit framework to simulate electro-thermal-mechanical coupling processes in advanced integrated circuits. However, the computational efficiency of the previous EMC (pEMC) method remains limited compared with the finite element method (FEM), since the pEMC method requires multiple iterations to simulate thermal expansion, even in linear equation systems. In this article, we develop a novel EMC method by proposing voltage-controlled current sources (VCCSs) into the pEMC. Therefore, the novel EMC method can simulate thermal expansion without iteration in linear equation systems. The results demonstrate that the computational efficiency of the novel EMC method achieves a tenfold improvement compared to the pEMC method and exhibits computational efficiency comparable to the FEM under the same number of nodes.

This paper proposes a novel eddy current retarder (NECR) and thermal management method, aiming to solve the problems of low electromagnetic utilization rate, serious thermal decay of braking torque, and waste of braking energy in traditional eddy current retarder. The structure characteristics and working principle of NECR are introduced. The braking model is analyzed and calculated by using the equivalent magnetic circuit method. The transient magnetic field and temperature field of NECR are numerically simulated by finite element method. A thermal management method of NECR is proposed. And the braking force distribution strategy based on fuzzy control system is designed. And the braking force distribution strategy based on fuzzy control system is designed. The simulation results show that the heat generated by NECR can heat the electric bus cabin temperature to 19 °C. And the energy consumption of the vehicle is reduced by 28.8% compared to the use of electric energy to heat the cabin. The experimental results show that the average error between the experimental value and the simulation analysis value of braking torque is <5.8%. When the excitation current is 100 A and the rotating speed is 1500 rpm, the braking torque can reach a maximum of 2410 N·m. After continuous braking for 10 min, the braking torque decreases by only 13.7% and the temperature is stable within 100 °C.

Previous studies on reconfigurable intelligent metasurface (RIS) design have primarily relied on full-wave electromagnetic simulation software, which often incurs high computational costs and lacks clear design direction. The design of multi-bit RIS remains challenging and there is currently no suitable systematic method for selecting the corresponding tuning devices. To overcome these limitations, this article proposes a novel equivalent circuit-based approach to RIS design. In contrast to the conventional approach, where the equivalent circuit model is derived from post-design evaluation of the scattering properties of RIS, our work is entirely driven by the equivalent circuit model from the outset to accomplish the unit cell design. A complete workflow as well as details of each constituent step are presented for the topology design of RIS based on equivalent circuit topology. Building on this circuit topology, a 3-bit reflective phase reconfigurable unit cell is developed based on a tunable band-stop filter circuit. We conducted adjustable phase verification experiments and beam deflection experiments. The consistency between the experimental results and circuit theory demonstrates the feasibility and practicality of the equivalent circuit method of RIS design. This circuit-to-structure methodology provides a physically interpretable and systematic framework for designing RIS with arbitrary electromagnetic responses, offering new insights into RIS design.

Equivalent circuit parameter extraction can reflect the electrical characteristics of actual components or systems, but there are problems such as parameter correlation at different scales, balance between calculation accuracy and efficiency in the process of circuit extraction. A new method for extracting circuit parameters is proposed. This method combines the volume integral equation algorithm and the method of moments to handle both dielectric and conductor regions. Classical surface-based and edge-based basis functions are used to discretize the conductor structure, ensuring numerical stability and convergence. In addition, multi-branch basis functions are introduced for port excitation modeling, which improves the simulation accuracy for complex port geometries. The experimental results show that the voltage pressure test results and time differences are 0.01, 0.02, 0.02, 0.03 in 697 to 1650000 grids, with the maximum being 0.03 and the minimum being 0.01. The small difference between the voltage pressure test calculation results and the reference values proves that the partial element equivalent circuit method of the volume integral equation algorithm and the moment algorithm has good computational accuracy and precision in large-scale grid computing. The above results indicate that the method proposed by the research institute has good accuracy and multi-layer interconnectivity in extracting circuit parameters, providing theoretical support for the subsequent development of circuit parameter extraction.

Time-varying (TV) materials have recently gained considerable attention for their ability to manipulate electromagnetic (EM) waves and improve the performance beyond the limits of conventional time-invariant materials. In addition, distributed TV capacitors are becoming more attractive to achieve particular effects. This work presents a systematic approach to modeling TV dielectrics by incorporating TV capacitors in the framework of the partial element equivalent circuit (PEEC) method. Thus, the standard formulation of the PEEC method is modified to include TV dielectrics and lumped elements for general 3D geometries directly in the time domain (TD). It is shown that this is possible through TV capacitances and voltage-controlled current sources. Four numerical examples validate the proposed approach.

This article addresses the limitations of standard chips in processing large-scale datasets by leveraging neuromorphic architectures, particularly spike neural networks (SNNs), to simulate the pulsed signals of biological brains for enhanced power efficiency and performance. Initially, we developed a complementary metal-oxide–semiconductor (CMOS) circuit based on the integrate-and-fire (IF) neuron model, which generates spike signals with the spatiotemporal dynamics typical of neurons. This approach provides a novel perspective for neuromorphic chip design. Next, we introduce the partial element equivalent circuit (PEEC) method to establish a unit circuit model for the memristor crossbar array, accounting for all resistance-inductance–capacitance (RLC) parasitic couplings. This model enables precise signal integrity (SI) analysis, offering deeper insights into the signal transmission mechanisms within memristor crossbar arrays and serving as a foundation for optimizing neuromorphic chip performance. Building upon this model, we designed a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$24\times 24$ </tex-math></inline-formula> crossbar array hardware prototype, experimentally validating the reliability and feasibility of the circuit. Finally, we perform SI analysis to demonstrate that the performance of the memristor crossbar array can be enhanced by optimizing the rise time, adjusting the memristor’s resistance state, and adding inductance at the output. These findings provide both a theoretical foundation and a technical pathway for improving the performance of neuromorphic chips in practical applications.

Due to direct shaft connection to induction motors, centrifugal pumps can only run at a limited number of speeds. Impeller trimming is normally applied to fine tune the pump operating point to match the demanded design performance with degraded pump efficiency. Due to dynamic water flow, motors are often powered by variable frequency drives (VFDs). The question is whether the VFD can replace impeller trimming to achieve the design performance without degrading pump efficiency. The objective of this paper is to investigate the overall efficiency of motor-driven pump systems powered by a VFD with and without impeller trimming through simulations. First, potential approaches to obtain pump efficiency and the equivalent circuit method to obtain motor efficiency are discussed. Second, an approach to obtain pump efficiency is identified using manufacturer data. Finally, the overall efficiency with and without impeller trimming is simulated for a 4 × 5×13.5 pump on the right and left boundaries of the preferred operation region as well as the best efficiency points. The simulation results reveal that the utilization of VFDs can provide an absolute improvement of 10% in the efficiency if the impeller is trimmed below 12.5 inch but risk of overloaded motors exists with incorrect VFD settings.

For the direct-driven wave energy converters (WEC) with time-varying disturbance and uncertain parameters of model, a maximum wave energy capture strategy based on input saturation L 1 adaptive control is proposed. By analyzing the hydrodynamic model of a direct-drive WEC and the mathematical model of permanent magnet linear synchronous generator (PMLSG), a state-space model of the direct-drive WEC is established; the maximum power capture condition is obtained by using the equivalent circuit method; the input saturation L 1 adaptive controller with µ-modification is designed considering the controller limited case, which can effectively suppress the effects of time-varying disturbances and uncertain parameters of model to make the system track the desired current, and then achieve the maximum power tracking control. The convergence proof of the observation and reference errors is given. Simulations verify the effectiveness of the proposed control strategy, and the system has good steady state tracking performance and transient performance.

In the case of highly conductive dielectric materials such as water and other aqueous liquids, semi-conductive stress grading materials, etc., there are some difficulties and limitations in measuring their electro-physical parameters using the measurement methods and conventional metal electrodes. This paper describes the development of an experimental device capable of measuring dielectric permittivity and dielectric loss tangent of the above-mentioned highly conductive dielectric materials in the comparatively wide frequency range of power frequencies to 1 MHz, the principle of which is based on the three-voltage method; and also, it has been dealt with how to design the hardware and software. The operating characteristic and reliability of the designed and manufactured experimental device were verified through the simulation by using electrical equivalent circuit method and comparing with the measurement data for the standard experiment device.

Concerns over the health risks, flammability, and limited low-frequency efficiency of fiber absorbers have encouraged the use of micro-perforated panels (MPPs). However, their performance is often limited by narrow absorption bandwidths. This study developed a heterogeneous parallel MPP absorber and evaluated its acoustic performance using impedance tube measurements, finite element method (FEM), and equivalent circuit method (ECM) models. Response surface methodology (RSM) was employed to optimize design parameters. Optimization results revealed a strong correlation between resonance frequency and perforation ratio. A configuration with perforation ratios of P1 = 2% and P2 = 0.6% provided the most favorable half-absorption bandwidth (α ≥ 0.5). Increasing hole diameter at lower perforation ratios broadened the absorption region and enhanced peak intensities; at 430 Hz, an enlarged d2 led to both higher absorption and wider bandwidth. Larger depth differences between the two MPP layers further expanded the absorption range. The final fabricated design incorporated hole diameters of 0.35 mm and 0.7 mm, perforation ratios of 1.8% and 0.8%, and cavity depths of 20 mm and 40 mm. This configuration achieved an average sound absorption coefficient of 0.618. Impedance tube tests showed absorption peaks of 0.96, 0.84, and 0.95 at 596 Hz, 1184 Hz, and 1440 Hz, respectively. Half-bandwidth absorption (α ≥ 0.5) was consistently observed across 400–1600 Hz, with experimental, FEM, and ECM results in close agreement. In conclusion, this MPP offer a safer and more robust alternative to fiber absorbers, the proposed heterogeneous parallel design expanded the half-absorption bandwidth up to threefold, significantly enhancing low-frequency and broadband performance.