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An equivalent electrical circuit of a microstrip line (MSL) with a magnetic film was proposed. The estimation method of its circuit parameters was investigated in order to clarify a design guideline for noise suppression sheet (NSS) which was placed on the traces in electronic devices. Firstly, the effect of the complex permeability of the magnetic film on the circuit parameters was investigated by magnetic circuit analysis of the cross section of the line. Secondly, an MSL with a Co-Zr-Nb film was designed as a test bench considering the impedance matching in the signal frequency range (below 1 GHz). Then, its transmission coefficients and the conducted noise suppression was estimated. The result shows that impedance matching was successfully maintained below 1 GHz. The estimated transmission coefficients and the conducted noise suppression almost agreed with the measured ones below the effective FMR frequency of the Co-Zr-Nb film. The results indicate that the proposed equivalent circuit has the potential to estimate circuit parameters and transmission characteristics of the MSL with the magnetic film at the circuit design stage. It is also useful to clarify the design guidelines for NSS placed on the traces in electronic devices.

In this work, an analytical electromagnetic field coupling to transmission line model is proposed to efficiently evaluate the induced voltage/current responses of loads connected at the terminals. Specifically, an equivalent circuit is developed by combing the Lorentz reciprocity theorem with the classic passive transmission line model, it is found that active contribution by impinging field could be cast in analytic form, as a function of the far-field radiation pattern and input impedance of transmission line system in transmitting mode. Comparing to Agrawal’s model, the proposed method reports concise and physical formulations without degrading the accuracy. Moreover, it is demonstrated that defining impinging field in spherical coordinates aligning parallelly with line is advantageous in revealing the wave propagation process.

Switched reluctance machine (SRM) has progressed as a suitable contender in the family of electrical machines for its high starting torque and better performance in different operating conditions. The need for accurate modeling of this machine is therefore dependent on the accurate determination of losses of which iron loss is exigent. This paper aims to determine iron loss from the equivalent circuit parameters of the machine based on the input data tables that are directly obtained from the experiments performed on an existing 4-phase, bifilar wound switched reluctance machine. The procedure and necessary steps for the loss separation method are well defined and supported by the theoretical and practical results. The experimental determination of the iron losses has been compared with the predicted results under the same operating conditions.

A reaction sphere (RS) is a novel and promising actuator for microspacecraft attitude control systems (ACSs). However, the detection of the motor status, such as the rotating speed of the spherical rotor, is a difficult task. The equivalent circuit can be used to predict the motor status. This article presents an improved multi-layer transfer-matrix method for the equivalent circuit parameters’ calculation. Results compared with a finite element analysis (FEA) show that the proposed analytical model achieves an acceptable accuracy within the operating speed range. Meanwhile, its computation time is 0.072 s, on average, which is only 0.0003% of the FEA.

In this work, both planar and conformal novel electromagnetic interference (EMI) shielding structures with customized properties are developed using a unique coupling of frequency-selective surface (FSS) and magnetic substrate. A hybrid equivalent circuit model (ECM) blended whale optimization (WO) technique is offered in the quest of customized shielding of $L$ -, $S$ -, $C$ -, $X$ -, and $Ku$ -bands using a simple FSS geometry. The proposed structure is designed to shield $L$ -, $S$ -, $C$ -, $X$ -, and $Ku$ -bands with a fractional bandwidth of 66.67%, 66.67%, 66.67%, 50.2%, and 40.50%, respectively. The frequency-dependent complex dielectric permittivity ( $\epsilon '$ – $j\epsilon ''$ ) and complex magnetic permeability ( $\mu '$ – $j\mu ''$ ) of ferrite are measured using a waveguide measurement setup at $X$ -band. The measured electromagnetic parameters are utilized in the modeling of planar and conformal ferrite-based frequency-selective shielding structures. An optimal ferrite coupled FSS shielding structure is fabricated, and its performance is evaluated using a non-destructive free-space microwave measurement setup. The measured results are found in congruence with the full-wave simulation and WO results. Besides, the conformal configuration of the proposed shielding structure is peculiarly investigated for inward and outward curved shielding structures for different values of radius of curvature. The proposed technique is intended to achieve a customized, simple, wideband, polarization-insensitive, and angular stable structure in the desired frequency regime, thus verifying the potential of the aforementioned technique for shielding applications.

In this article, a low-profile planar 1 bit non-diffractive vortex beam generator is proposed based on frequency selective surface (FSS) in microwave region. The characteristic of Bessel beam is introduced to control the divergence of the vortex beam. The proposed unit cell is analyzed through equivalent circuit model. The main resonance is provided by the coupling between the patches and the circular slot grid. A cross patch is embedded in the slot to form another resonance. Two elements with 0° and 180° transmission phase are designed to discretize the phase distribution of the metalens. The simulation results show that the metalens can generate fulfill non-diffracting transmission upon a distance of the $32\lambda _{\mathbf {0}}$ , verifying the effectiveness of the proposed method.

Many applications in communications and power electronics demand inductive components that operate at high frequency or a broad range of frequencies. For applications requiring miniature devices with large inductance values, most often the components are manufactured imprecisely in the traditional method where magnetic cores are wound with a fine gauge wire. To achieve the best high-frequency performance, there is a desire to use a practical manufacturing method that removes the imprecision of wire winding. In this article, a unique 3-D laser exposure system is used to direct-write conformal winding patterns on the surface of MnZn ferrite toroids. The toroidal helix windings were fabricated by both an additive laser direct structuring (LDS) process and a subtractive laser-written mask-and-etch process. Both methods were performed on both enamel-coated ferrites and bare ferrites. The performance and equivalent circuit model parameters of the transformers were measured up to 1.5 GHz and will be presented. The transformers fabricated on the enamel-coated cores were found to have comparable or better inductances and broadband coupling than wire-wound transformers of matching construction.

As an extension of the Cauer ladder network method, this article presents the equivalent circuit for an eddy current field including a translational mover. The speed voltages for the inductors in the equivalent circuit are obtained by using the directional derivatives of the inductors in the direction of mover displacement. These directional derivatives are determined by using the fact that the electromagnetic force can be represented in two forms, namely, Maxwell’s stress tensor and the virtual work principle. This result is also verified by using the theory of continuum mechanics. Finally, numerical examples of an electromagnet are presented.

In this article, a novel hybrid analysis method for spoke-type permanent magnet (PM) machines (STPMMs) is presented, which considers axial flux leakage using the machine’s lumped magnetic circuit. The STPMM can increase its air-gap flux density due to its effective flux concentration, but high flux leakage occurs in the axial end of its PMs. This results in a discrepancy between conventional 2-D finite-element analysis results and experimental data. To correct the discrepancy resulting from the unwanted axial flux leakage, a virtual residual flux density of the PM is proposed through equivalent circuits and a finite analysis model. The modified residual flux density is applied to 2-D numerical analyses, and the accuracy and usefulness of the proposed method are confirmed through 3-D numerical analyses.

Quantitative analysis of iron loss taking magnetic hysteresis behavior into account is essential to development of high-efficiency electric machines. In a previous article, a novel magnetic circuit model incorporating a play model was proposed. It was clear that the proposed model can calculate the hysteresis loop of the magnetic reactor with high accuracy and high speed. However, there is a possibility for further improvement in the calculation accuracy of the minor loop generated from carrier harmonics under PWM excitation because the influence of the skin effect cannot be considered. Therefore, this article describes that the Cauer’s equivalent circuit theory, which can represent dynamic hysteresis characteristics considering the influence of the skin effect, is applied to the magnetic circuit model, and indicates the validity of the proposed method experimentally.

Fast linear transformer driver (FLTD) is considered to be one of the most prospective technologies for the next generation Z-pinch driver. Our goal is to design a single-stage FLTD with compact construction and output current amplitude of 1 MA. Two different current return configurations of FLTDs are presented: the coaxial outer barrel and 24 separate columns. An equivalent circuit model for the single-stage FLTD with structure parameters obtained from finite-element analysis (FEA) is proposed. Moreover, 3-D numerical models of the single-stage FLTD have been constructed and computed based on the time-stepping finite-element method (TSFEM). However, the TSFEM is both time- and memory-consuming for even a single-stage FLTD. Therefore, the finite integration technique (FIT) in the time domain is implemented for solving the FLTD-related problem. It is demonstrated that output performance such as output current of the two configurations is in good agreement with an experimental prototype for both circuit simulation and electromagnetic (EM) computations. EM-field distribution and output performance of the two structures are also very similar.

This article introduces a new model order reduction method for a linear time-invariant system with symmetric positive-definite matrices. The proposed method allows the construction of a reduced model, represented by a Cauer-equivalent circuit, from the original system. The method is developed by extending the Cauer ladder network method for the quasi-static Maxwell's equations, which is shown to be regarded as the Lanczos algorithm with respect to a self-adjoint matrix. As a numerical example, a Cauer-equivalent circuit is generated from a simple mathematical model as well as the finite-element (FE) model of a magnetic reactor that is driven by a pulsewidth modulation voltage wave. The instantaneous power obtained from the circuit analysis is shown to be in good agreement with that obtained from the original FE model.

This article presents a method to synthesize the equivalent circuit of an induction heating (IH) machine used in the hot strip mill (HSM) process. The equivalent circuit not only allows to evaluate eddy current losses in different forms, such as iron plate and coils, but also compute the transient responses in online environments. The frequency characteristic of the IH machine is effectively computed by proper orthogonal decomposition. The equivalent circuit of the IH is synthesized through curve fitting to the computed characteristics in conjunction with Tikhonov's regularization. The equivalent circuit is shown to have good accuracy and works much faster than the finite-element method. The proposed equivalent circuit is expected to be used in online control of the HSM process.

Unlike three-phase induction motors, circular rotating fields cannot be inherently formed in single-phase induction motors (SPIMs). Backward rotating fields inevitably result in elliptical rotating fields and degradations of the performance (efficiency, torque). Therefore, the necessity for making rotating fields circular should be emphasized to maximize the effectiveness of design at an arbitrary operating point. In this article, the determination scheme of stator parameters based on circular rotating fields is introduced from equivalent circuits. The derived parameters of stator winding consider circular rotating fields and minimizing copper loss of stator windings, respectively. Then, examples of the design demonstrate the validation of the algorithm. Finally, the comparisons between reference and designed model illustrate that the proposed algorithm can provide insight into the design of high-performance capacitor-run SPIMs.

In this article, an unstructured–partial element equivalent circuit (PEEC) method for modeling electromagnetic thin regions is proposed. Two coupled circuits’ representations are used for solving both electric and/or magnetic effects in thin regions discretized by a finite-element surface mesh. Dynamic effects across the thickness of the sheet are modeled by equivalent complex conductivity and reluctivity. Nonsimply connected regions are treated with fundamental branch independent loop matrices coming from the circuit representation. The formulation enables the computation of eddy current losses and can be coupled with external circuits, PEEC cables or coils, thanks to the circuit representation.

An electromechanically coupled modeling framework for the simulation of electric current flow in ZnO varistors is developed. The model is based on an equivalent circuit representation of the varistor microstructure with grain boundaries represented by nonlinear resistor branches of the circuit. This approach extends on previous circuit models by including the effect of mechanical stress on grain boundary conductivity. In this article, we consider, in particular, the effect of residual thermal stress in polycrystalline structures on electrical conductivity. The distribution of this stress throughout the material is computed by finite element method (FEM) simulations. Then, each grain boundary conductivity is determined by applying a self-consistent model for the trapped interface charge induced by piezoelectric polarization. Finally, the electric current flow patterns and the bulk conductivity of the material are computed using the nonlinear circuit model. The simulated I–V characteristics reveal a significant sensitivity of the electrical conductivity to internal thermal stress within the material. Furthermore, for realistic ZnO microstructures, the simulations demonstrate the effect of current concentration along thin conducting paths depending on the mechanical stress condition of the material.

This paper presents a time-domain equivalent circuit approach for analyzing lightning-generated electromagnetic transients in modern buildings. The building is represented by a wire-plate structure and is modeled by the internal impedance and external inductance of current cells and the coefficients of potential cells. A vector-fitting technique is applied for modeling frequency-varying internal impedance for time-domain simulation. With this unique formulation, the number of unknown variables is reduced, and computational efficiency is improved significantly. Finally, lightning-generated impulse magnetic fields and voltages within a building are evaluated.

In this paper, analytical formulas for the electric field generated by currents, charges, and magnetization in conductive, dielectric, and magnetic media are presented in the framework of the partial element equivalent circuit (PEEC) method. Under the quasi-static hypothesis, assuming a Manhattan-type tessellation of the geometries and rectangular basis functions, the electric field is exploited in its contributions due to charges, currents, and magnetization. These different contributions require the computation of different type of integrals which are evaluated analytically. The mathematical derivations and the treatment of the singularities are described in detail. Two numerical examples are presented proving the accuracy of the proposed analytical formulas and their speed-up with respect to the numerical computation.

This paper deals with modeling and simulation of devices where current-carrying conductors are located close to magnetic bodies. These configurations typically occur in electromechanical energy converters such as in slots of electrical machines. Additional losses due to the inhomogeneous current density distribution (“current” or “field” diffusion) at high excitation frequency are a well-known phenomenon. However, classical approaches reach their limits as soon as field diffusion is influenced by ferromagnetic material with non-linear properties. An accurate but time-consuming computation can be achieved by using time-transient quasi-stationary finite-element analysis (FEA). Current diffusion can be described more efficiently by separating the conductor into parallel filaments, following the partial element equivalent circuit (PEEC) approach. As long as linear material characteristics are prevailing, the problem can, thus, be solved efficiently in the frequency domain. In this paper, a hybrid FEA-PEEC modeling approach is presented, where the magnetization of the ferromagnetic material is represented by equivalent currents obtained by 2-D FEA. It is suitable for complex multi-conductor configurations even including non-linear ferromagnetic material. For the proposed method, the resulting linear system is efficiently solvable in the frequency domain by direct solvers. A numerical example from the field of electric traction motors is presented to emphasize the accuracy and benefit of the proposed method for practical electromagnetic computations.

According to a rough estimation, a superconducting linear acceleration (SLA) system might be able to inject a fuel pellet into a core plasma. However, as the consequences of numerical simulations, it was found that the SLA system with only one electromagnet cannot inject the pellet into the core plasma. Therefore, the multiple electromagnets must be used in order to improve the acceleration performance of the SLA system. In this paper, the SLA system with the multiple electromagnets is numerically investigated by using an equivalent-circuit model (ECM). The ECM is composed of a set of ring-shaped electric wires and the multiple electromagnets. According to the numerical investigation, it was found that the ECM is a tool for investigating the SLA system instead of a finite-element method. In addition, the SLA system with the multiple electromagnets has the same acceleration performance as the conventional pellet injection system.

In this paper, the modeling process and transient performance analysis for induction heating system (IHS) are carried out, considering the frequency-dependent inductive load. First, the impedance of the inductive load at the frequency range of interest is computed by using the finite element method (FEM). Then the vector fitting (VF) and the passivity enforcement techniques are employed to obtain a stable, causal, and port passive rational approximation model for the considered impedance. Afterward, the circuit synthesis method is used to achieve a circuit representation in terms of the pole-residue rational model. Good agreements between the presented equivalent circuit and the results of the FEM are achieved both on the magnitude and on the phase. Finally, the transient performances of the IHS under the controls of open-loop and closed-loop are conducted. This transient model with the inclusion of frequency-dependent inductive load provides a reliable prediction method of energy efficiency at the early stages of design.

This paper proposes a novel dual stator solid rotor axial flux induction motor (DSSRAFIM) for a low-cost flywheel energy storage system. To simplify the analysis of its 3-D electromagnetic field distribution (EFD), a novel multi-slice and multi-layer method is applied. By this analytical method, DSSRAFIM is equivalent to a finite set of double primary steel secondary linear induction motors (DSSLIMs), and the steel secondary in each DSSLIM is divided into a finite set of layers with equal height. The EFD in each layer is obtained by solving Maxwell’s equations. The EFD calculated by this novel analytical method is in good agreement with those analyzed by the finite-element method (FEM). Compared with the FEM, this novel analytical method is time saving, resulting in that it is suitable for the optimized design. According to the EFD in DSSRAFIM, an equivalent circuit model (ECM) of DSSRAFIM is derived, which is an effective approach to predict the performance. The electromagnetic torque, efficiency, and power factor of a 5 kW, 7100 r/min prototype calculated by the ECM, FEM, and experimental test verify the validity of the ECM.

Based on the established equivalent circuit model of a magnetostrictive vibration generator, the low ac voltage and low power produced by the generator under low acceleration are calculated. Comparisons between the calculated and measured results show that the model can provide reasonable data trends of the generator under different loads. To boost the low ac voltage to a high dc voltage required by electronic devices in low power consumption, two energy extraction circuits (EECs) (i.e., a proportion integration-based EEC and an improved EEC) are studied. The corresponding two harvesting systems, which include the generator and the proposed EECs, are designed and simulated in LTspice for system-level evaluation. It is found that the two harvesting systems can effectively boost a few hundred millivolts of ac voltage to the steady dc voltage under low acceleration and varying load conditions. Moreover, the system with the improved EEC can be powered by the harvested energy to maintain self-sustaining operation, and the batteries in the system can be charged for future start-up operations; thus, the system has strong practicability in the dc supply for the electronic devices.

© 1965-2012 IEEE. Soft magnetic composite (SMC) materials and SMC electromagnetic devices have attracted strong research interest in the past decades. However, SMC devices have large core loss that needs to be put into consideration even at the design stage. Effective and accurate prediction of the core loss becomes crucial for the design and optimization of high-performance motors with these materials. Equivalent circuit model is a widely used method for machine analysis, due to the advantages in the fast calculation with a clear physical mechanism. This paper presents an equivalent circuit model to predict the core loss of a claw-pole permanent magnet motor with SMC stator core. All the parameters including the equivalent core-loss resistance in the equivalent circuit model are identified based on the finite-element method to achieve high accuracy, and the effectiveness of the parameters identification methods is experimentally verified. The proposed equivalent circuit model can predict the core loss and motor's performance efficiently both under no-load and loading conditions.

DC bias in power transformers leads to strong core saturation and thus nonlinearly inferior operation. This paper analyzes the ability of power transformers to withstand the dc bias by novel analytical criteria. The proposed criteria are obtained from the nonlinear equivalent circuit, which considers the effects of nonlinear inductances. The validity of the proposed analytical criteria is verified by the finite-element analysis results and experimental results, which indicates that the proposed analytical criteria are effective to evaluate the ability to withstand the dc bias of power transformers.

This paper discusses $R$ , $L$ , $G$ , and $C$ parameters of an on-chip transmission line with a magnetic film for developing the design rule of a film-type electromagnetic noise suppressor. A microstrip line (MSL) is fabricated using a regular silicon process, and a Co85Zr3Nb12(Co–Zr–Nb) film is deposited on the MSL. The target frequency of the noise suppression and the passband are set to 5 GHz and a several hundred MHz range, respectively. The T-type equivalent circuit model is converted from the measured S-parameter. In the passband frequency range, the resistance value of the MSL with the magnetic film is almost the same as that without the film. The measured resistance successfully peaks at $34~\Omega $ around the 5.4 GHz target frequency based on the ferromagnetic resonance and Joule losses. Furthermore, the inductance and the capacitance with the magnetic film are 1.3 and 2.5 times higher, respectively, than without the film because of the high permeability and metallic boundary of the magnetic film. Therefore, these results demonstrate the great usefulness of the approach for developing a standardized design method for a magnetic film-type noise suppressor.

A new analytical model of axial-flux eddy current device is proposed in this paper, which is based on the equivalent circuit model. In order to simplify analysis, linearization at the mean radius is assumed in the 3-D model of eddy current device. In the equivalent circuit model, copper plate can be seen as a sum of coils in different volume elements. The equivalent circuit of coil is characterized by induced voltage, resistance, and inductance, which are calculated with the electromotive force, reaction flux, and linkage current in the copper plate frame of reference. To obtain these field solutions, the 3-D analytical computation method is employed to solve the Maxwell equations in Cartesian coordinate. The flux linkage equation, voltage equation, and torque equation are set up to depict the reaction field produced by eddy current and the function between the torque and slip speed in steady-state condition. With the equivalent resistance and inductance, the expression of torque becomes much simpler, and the inverse of which can also be obtained. Then, magnetic flux density, torque, and slip speed calculated by the proposed analytical model are compared with the 3-D analytical model and 3-D finite-element method.

This paper presents the methodology and computation results for the torque and iron losses in a bearingless synchronous reluctance machine. The aim is to compute the hysteresis torque related to the asynchronous operation of the machine under the effect of the levitation field rotating at twice the synchronous speed. For this purpose, and because it is impossible to compute the hysteresis torque with a single-valued B-H characteristic, a magneto-dynamic vector hysteresis model is used. The computations show that the hysteresis-related shaft power is considerable under no-load operation of the machine. It is also shown that the asynchronous torque can be approximated by the classical equivalent circuit of an induction machine. acceptedVersion

In this paper, the multi-turn coil used in a wireless power transfer (WPT) device is modeled as a uniform material using the homogenization method to consider the proximity effect. By fitting the coil impedance to the numerical results, the Cauer equivalent circuit of the multi-turn coil is synthesized for the design and optimization of the power circuits in the WPT device. It is shown that the results obtained from the equivalent circuit and measurement are in good agreement. Moreover, the impedance of a flat WPT coil composed of a Litz wire is shown to be accurately evaluated by the proposed method when the contribution of capacitance is negligible.

This paper presents a composite solid rotor designed to improve starting performance of the line-start permanent-magnet synchronous motor (LSPMSM). The rotor is mainly constituted by the solid steel which can inherently generate high starting torque. Moreover, the axial slots milled on the rotor surface deepen the flux penetration into core and a brass made cage attached to the rotor enlarges the eddy current density. With above promotions, the induction torque increases, and hence drives the motor to startup and synchronize under heavy load conditions. The enhanced starting capability by applying the proposed rotor for an LSPMSM is validated by the 2-D time-stepping finite-element method (FEM). To guarantee a well match with the 3-D construction where end effects occur, an equivalent circuit is built in the 2-D method to represent the uneven ring fractions. Simultaneously, considering the non-axial currents in core ends, conductivity of the solid-rotor segments in 2-D field is corrected by a multistep optimum-seeking technique. Calculation precision of the 2-D FEM covering end effects is certificated by the corresponding 3-D FEM with good results agreement.

Thermal analysis is an important issue in machine design which allows to have a knowledge of the machine temperature rise. This paper presents the thermal analysis, modeling, and experiments of a linear-switched reluctance machine (LSRM) with toroidally wound mover and segmental structure. First, a 3-D heat flow model with the homogenized region for the presented LSRM is established using the thermal equivalent circuit. The equivalent thermal resistance of the model is developed together with the nodes forming of the thermal resistance network. The thermal identification to each component such as windings and core steel is performed. Then both the numerical 2-D and 3-D heat flow model for the presented LSRM are established by finite-element analysis which can give the detailed temperature distribution of the entire machine. At last, the actual experiment on a prototype is carried out, validating the accuracy, and feasibility of the thermal equivalent model above.

This paper used a finite-element magnetic field analysis (FEA) to investigate the instantaneous and average power in a single phase transformer and a three-phase rotating machine. We examined the influence of the hysteretic properties of the magnetic materials on the instantaneous power in FEA using the isotropic vector play model. We applied post-correction to estimate the accuracy of the average power from their equivalent circuits.

As a reliable and non-destructive technique, frequency response analysis (FRA) has been widely recognized for transformer winding deformation detection and assessment. In this paper, frequency response functions (FRFs) are obtained by two different FRA measurement connection ways, namely, end-to-end voltage ratio (EE) and transfer voltage (TF) ratio measurements. At the same time, according to the two ways, sensitivities of the FRFs to electrical parameters of the equivalent circuit model of the transformer winding are investigated. Based on Tellegen theorem, adjoint network method is derived to calculate the values of the sensitivities of FRFs to electrical parameters. Meanwhile, the sensitivity characteristics of circuit parameters are studied. In addition, by comparing the sensitivity results of the two ways, the variation laws of the sensitivities under the two different connection approaches are determined. Besides, this paper can provide a new and objective method to interpret the FRA results and give us a better understanding how much the parameter variations can influence the FRA measurement results.