Magnetic Core Research Articles

Hybrid Aerosol Jet Printing and Electrodeposition of Ferrite-Sandwiched Inductors

The additive manufacturing (AM) of inductors of suitable size to be integrated into packaged electronics is attractive to customize the device characteristics for the specific application. Magnetic ferrite cores are widely used in conventional inductors, however, wire wound inductors can be brittle, heavy, bulky. Planar spiral inductors in a sandwich configuration present a promising alternative. Aerosol jet printing, a direct write AM technology, can deposit metal inks at a resolution of < 10 µm. Metal nanoparticle inks have limited conductivity at < 40% bulk. Building a higher profile may result in loss of resolution. Electrodeposition offers the ability to plate thick layers of highly conductive metals, including copper and nickel which are normally hard to access as nanoparticle inks compatible with aerosol jetting. We have previously shown the construction of a multi-layer flyback transformer with this hybrid aerosol jet and electrodeposition method. [1]We present a three-layer planar inductor with the first layer being a 1.3mm stack of ferrite sheets (Fair-Rite) with a 9 mm x 9 mm footprint integrated onto a circuit board. The intermediate layer consists of a spiral inductor made by aerosol jet printing UTDots Ag40X silver nanoparticle ink as the seed layer. To achieve high accuracy, the inductor was printed with a rotary axis stage. Electrodeposition in an acidic CuSO4 plating bath on top of the Ag seed layer resulted in thicknesses of 50 µm. A submicron layer of Ni is added for oxidation protection by electrodeposition from a Ni-Sulfamate bath. Lastly, a top 1.3 mm ferrite stack, with laser cut holes, is added to provide pass throughs for wire bonding. Figure 1 shows a micrograph of an inductor as printed, after electrodeposition, and with the top ferrite layer. Electrical measurements including impedance characteristics will be presented.SNL is managed and operated by NTESS under DOE NNSA contract DE-NA0003525. The SAND No. is SAND2023-14571A.Figure 1. Construction of a ferrite-sandwiched inductor with (a) the aerosol jet printing of an Ag seed layer, (b) after electroplating of Cu and Ni.

Magnetic Field Mapping-Based Battery Management System (BMS) for Lead Acid Application

Lead Acid Batteries (LAB) are a widely used technology in Energy Storage Systems (ESS) due to their abundant and low-cost materials, non-flammable water-based electrolyte, and high recyclability rate. The main applications for LABs are in mobility, data centers, and telecommunications. According to the Consortium of Battery Innovation (CBI), the market for lead acid batteries is projected to increase 150 GWh between 2025 and 2030. Therefore, it is fundamental to identify emerging failure modes in LABs in ESS systems to reduce battery degradation and to extend the use life.An important failure mode in flooded LABs is acid stratification. This research explores H+ concentration changes in H2SO4 (sulfuric acid) electrolyte as a correlation of acid stratification. The objective is to develop a non-invasive, non-destructive, and accurate real-time battery monitoring system. The Magnetic Field Probing (MFP) technique, popular in the medical imaging field, shows a promising solution for ESS performance evaluation. This technique can measure induced magnetic field changes based on variation in H+ concentration in the cell during cycling. See Figure. 1 (a). MFP provides early onset notification of stratification in flooded LABs with capability to discern other failure modes in non-flooded lead batteries.A set of experimental trials measured pH and magnetic field variation of H2SO4 electrolyte. See Figure. 1 (a). The preliminary results demonstrated changes in electrolyte pH due to possible stratification. See Figure. 1 (b). A correlation between the output voltage resulting from the interaction of the induced magnetic field and the changes in the electrolyte concentration was found. See Figure 1(c) The optimal AC input frequency maximizes the induced magnetic field response. The value found for optimal AC input frequency was 32kHz, which depends on the physical properties of the magnetic field inductors (air core solenoid coils). The experimental results showed and concluded that the induced magnetic field across the tested cell is also inversely proportional to the distance between coils attached to the cell.Further research involves the use of magneto-resistors to establish a magnetic field mapping in lead acid cells as they are being cycled. Magnetic field response is measured while lead acid cells are cycled from 100% to 20% state of charge range. In the future, this study will provide insights and findings to model and predict cell stratification in lead acid cells with electrochemical computational simulations.Keywords: Energy storage systems, lead acid batteries, acid stratification, magnetic field, non-invasive method Figure 1

Experimental Investigations and MD Simulation on Nanoparticle-Enhanced CO2-Responsive Foam (NECRF): Implications on CO2-EOR.

CO2-responsive foam (CRF) is a highly promising candidate for CO2-enhanced oil recovery (CO2-EOR) because it displays higher stability than the surfactant-stabilized foam owing to the formation of robust wormlike micelles (WLMs) upon exposure to CO2. In this work, the nanoparticle-enhanced CO2-responsive foam (NECRF) was properly prepared using lauryl ether sulfate sodium (LES)/diethylenetriamine/nano-SiO2, and its interfacial properties and EOR potential were experimentally and numerically assessed, aiming to explore the feasibility and effectiveness of NECRF as a novel CO2-EOR technique. It was found that the interfacial expansion elastic modulus increased 6-fold after CO2 stimulation. The modulus continued to increase with the introduction of nano-SiO2 owing to the pronounced synergistic effect of WLMs and nanoparticles. In addition to increasing the viscosity of the foaming liquid, WLMs and nano-SiO2 enhanced the shearing resistance of the NECRF as well. Calculations demonstrated that both the coarsening rate and the size distribution uniformity coefficient of NECRF were markedly lower than that of the LES foam, which subsequently inhibited NECRF decay and greatly improved its dynamic stability. Besides, molecular dynamics simulation revealed that adding inorganic salts to NECRF could notably enhance the foaming performance due to the intensified hydration of surfactant head groups and reduced binding energy of neighboring molecules. Nuclear magnetic resonance-assisted core flooding experiments validated the exceptional capacity of NECRF to sweep the low-permeability region and improve the conformance profile. Overall, these findings may provide valuable insights into the development and application of novel materials and strategies for the CO2-EOR.

Modeling Methodology of Magnetic Toroidal Cores for 3-D FEM Full-Wave Simulation up to 100 MHz

Modeling Methodology of Magnetic Toroidal Cores for 3-D FEM Full-Wave Simulation up to 100 MHz

Research on multi-objective optimization method in the design of high-power nanocrystalline alloy high-frequency transformer

The optimization design of high-frequency transformer (HFT) is a multi-objective optimization problem owing to the mutual constraints between design parameters such as power density, efficiency and temperature rise, and traditional design methods often face difficulties in balancing and selecting multiple design parameters. Therefore, this paper derives the structural parameters of HFT, calculates the magnetic core losses and winding losses considering temperature effects, and establishes a 7-node thermal network model. Selecting power density and efficiency as optimization objectives, the HFT is optimized based on multi-objective particle swarm optimization algorithm and non-dominated genetic algorithm, and compared with traditional free parameter scanning method to analyze the advantages of intelligent optimization algorithm. Further, the influence of temperature rise calculation methods on the optimization design results of HFT is compared and analyzed. Finally, a nanocrystalline HFT with 17 MW/m3 power density and 99 % efficiency and an optimization scheme of HFT with 26 MW/m3 power density and 99.2 % efficiency are designed based on the proposed optimization design processes. The effectiveness of the calculation model and optimization method is verified through experimental measurement, and the essential principle of improving the HFT performance through optimization methods is explored through finite element simulation, providing theoretical reference and data support for the optimization design of nanocrystalline HFT.

Optimization of Magnetic Core Structures for Enhanced Magnetic Coupling in Helical Coil Inductive Power Transmission

Inductive power transfer (IPT) systems often encounter limitations in efficiency and transmission distance due to near-field magnetic coupling characteristics. Increasing the inductance can enhance the transmission distance, but it also raises the system’s Q factor, leading to several issues. This study aimed to optimize the magnetic core design of helical coils to enhance magnetic coupling in IPT systems while minimizing the increase in self-inductance. Through finite element analysis, various core placements were evaluated, leading to a proposed core design process that integrates inner and lower cores at optimal angles. The proposed design was compared with conventional cores, and its performance was validated in an IPT system. The results demonstrate that the proposed core design significantly enhances the coupling coefficient (k) and extends power transmission distance compared with conventional planar and U-shaped core structures without substantially increasing self-inductance (L). This design effectively balances the trade-off between increasing inductance and maintaining system stability, thereby improving transmission efficiency while minimizing frequency instability and voltage stress.

Comparative investigation of magneto-fluorescent core@shell nanostructures prepared using hard and soft ferrite as core

The paper focuses on the potential of magneto-fluorescent nanostructures intended to join simultaneously several functions of dissimilar core and shell material into a single entity. Two different types of magneto-fluorescent nanostructures with a broad array of physicochemical properties are premeditated and collated here. Strontium hexaferrite (Hard ferrite) core with CdS shell and Nickel Zinc ferrite (Soft ferrite) core with CdS shell are the two sets of magneto fluorescent nanostructures that were designed. Magnetic and optical analysis of both sets provides divergent outcomes. The shape of the derivative hysteresis curve gives a direct indication of the dissimilar nature (superparamagnetic & Permanent magnetic) of magnetic cores respectively. Optical results depict that both sets of magneto-fluorescent nanostructures are highly stable showing emission only in the position of the CdS shell only.

A new single magnetic core coupled-inductor based active switched Quasi Z-source inverter

This paper presents a novel topology for Z-source inverters (ZSI). The new Z-Source network is based on the coupled-inductors and active switched boost. Features of the topology include high voltage boost ability, single magnetic-core, low voltage stress on the active switch, and capacitors. The principles of operation, analysis, voltage and current equations of each component, and the converter voltage gain in the steady-state are presented. A comparison with other topologies has also been performed to determine the advantages and disadvantages of the proposed ZSI. Finally, experimental results of the laboratory prototype are presented to confirm the performance of the proposed topology.

Dynamic model of magnetic transmission

In the work, a non-contact electromechanical energy converter with permanent magnets, which is known as magnetic transmission, is studied. Magnetic transmissions have certain structural advantages compared to mechanical transmissions, namely: high reliability, efficiency, lower losses, non-contact transmission of mechanical power, no maintenance costs, and simplicity of construction. The use of magnetic transmissions for systems of conversion of low-potential mechanical energy into electrical energy is especially relevant: wind energy, water energy, energy of mechanical vibrations, etc. The use of magnetic gearboxes in autonomous wind power plants can be more promising from an economic and technical point of view compared to traditional mechanical transmissions. A numerical simulation mathematical model of magnetic transmission with permanent magnets has been developed. The use of magnetic transmission, for example, for autonomous wind power systems allows to increase the reliability of the operation of such installations, reduce operating costs and increase the efficiency of their operation. In emergency modes of operation, the use of magnetic transmission allows to avoid destruction or emergency shutdowns of electrical equipment. The developed simulation model of magnetic transmission takes into account the pulsations of the electromagnetic moment due to the discrete structure of the magnetic transmission and the change of the model parameters when the input moment changes: pulsations, losses in the magnetic core and permanent magnets, the change of the load angle and the transmitted electromagnetic moment. A feature of the developed model of the magnetic transmission system is that a change in the load of the electric power source leads to a change in the operating point on the mechanical characteristics of the rotor of the wind turbine. Conversely, when the wind parameters change, the output parameters of the source of electrical energy change: power, voltage, current and electromagnetic moment.

Superparamagnetic hydrophilic molecularly imprinted nanoparticles for an efficient and selective removal of tetracycline from water

In this work, a novel superparamagnetic hydrophilic molecularly imprinted nanomaterial for the removal of tetracycline (TC) was synthesized utilizing magnetite (Fe3O4) as the magnetic core, TC as the template molecule, 3-aminopropyltriethoxysilane (APTES) as the functional monomer, and tetraethoxysilane (TEOS) as the cross-linker. Initially, Fe3O4 magnetic nanoparticles (MNP) coated with SiO2 (MNP@SiO2) were synthesized, followed by TC molecular imprinting on the nanoparticles. Initially, Fe3O4 MNP coated with SiO2 (MNP@SiO2) were synthesized, followed by TC molecular imprinting on the nanoparticles. The synthesis method for MNP@SiO2 was optimized, and DLS analysis of 10 replicates showed a nanoparticle size of 70.1 ± 5.8 nm, indicating high method reproducibility. The MNP@SiO2, as well as the imprinted (MNP@SiO2-MIP) and non-imprinted (MNP@SiO2–NIP) nanomaterials, were characterized by FTIR, TEM, VSM, XRD, DLS, Z potential, and BET analysis. The saturation magnetization (Ms) values were 43 emu/g for MNP@SiO2 and 32 emu/g for both MNP@SiO2-MIP and MNP@SiO2–NIP, confirming suitability for magnetic separation using external magnets. Batch binding experiments conducted in water and methanol assessed adsorption isotherms and binding kinetics, with data fitting the Langmuir isotherm model better than the Freundlich model. The developed MIP exhibited significant selectivity against other molecules with similar functional groups and size. In water, the adsorption capacity of the MNP@SiO2-MIP was 23 mg/g, with an imprinting factor of 2.2. Furthermore, the MIP demonstrated good regeneration performance. The material was tested on TC-spiked tap water samples, achieving 80.1 % TC removal with high reproducibility (3.2 %, n = 3). Combining hydrophilic superparamagnetic nanoparticles with molecular imprinting enhances their potential applications in environmental remediation, antibiotic purification, and drug delivery.

Ferroelectricity‐Induced Surface Ferromagnetism in Core–Shell Magnetoelectric Nanoparticles

Magnetoelectric nanoparticles (NPs) present an important class of nanomaterials with a wide interest in piezocatalytic and biomedical applications. Herein, the results of magnetoelectric and magnetization measurements performed on core–shell NPs having magnetic core (MnFe2O4, MFO) and ferroelectric shell (Ba0.85Ca0.15Ti0.5Zr0.5O3, BCZT) synthesized by the microwave hydrothermal method are reported. Magnetic results are compared with the measurements on reference MFO NPs prepared under identical conditions. Detailed SQUID magnetometer measurements of the magnetization hysteresis loops M(H) down to 2 K reveal the existence of a clear exchange bias effect in pure MFO NPs attributed to the coexistence of ferromagnetic and antiferromagnetic short‐range interactions. When the magnetic core is covered by the thin ferroelectric BCZT shell, it is observed that 1) the shell suppresses the apparent bias effect and 2) induces an “extra” ferromagnetic magnetization at T &lt; 20 K. The results indicate that this “extra” ferromagnetism has a 2D character and it is most likely related to the interface interactions between the MFO core and BCZT shell. Ferroelectric properties and strong magnetoelectric effect in core–shell NPs are revealed via piezoresponse force microscopy under magnetic field. The mechanisms of the observed effects are discussed.

BBB-penetrating magnetoelectric nanoparticles with sustainable Gel formulation for enhanced chemotherapy and reduced postoperative glioma recurrence

Overcoming blood–brain barrier (BBB), reducing drug resistance and inhibiting postoperative recurrence are the huge challenges of glioma treatment. Herein, a magnetoelectric nanoparticle, applying CoFe2O4 as magnetic core, BaTiO3 as piezoelectric shell and polyethylene glycol-connected I6P8 peptide as surface coating (CBPI), was used for glioma-targeted treatment. This nanoparticle could down-regulate tight junction proteins of BBB via magnetoelectric effect, synergized with I6P8 peptide, to achieve the enhanced BBB permeability and glioma targeting. Under magnetic field activation, this nanoparticle, after doxorubicin loading to formulate CBPID, could accomplish magnetoelectricity and pH-responsive drug release, and generate mild reactive oxygen species to sensitize the chemotherapy through c-Jun N-terminal kinase phosphorylation pathway. Importantly, CBPID facilitated intraoperative cavity administration with magnetic immobilization after easy doping to Surgiflo filler, benefiting the repeated magnetoelectric-activated therapy to inhibit glioma postoperative recurrence. Moreover, CBPID could be mostly excreted through feces after intravenous injection, which did not cause obvious blood and organ abnormalities and even improved the behavioral abnormalities caused by glioma.

Sustainable Electromagnetic Prototype for Detecting Internal Deterioration in Building Walls.

The aim of this study was to develop a sustainable electromagnetic prototype to detect the interior deterioration of walls in buildings in order to mitigate uncertainty as it is a challenge to observe the interior state of walls without utilising destructive procedures. The method used was experimental, developmental and quantitative in its approach. The inductance, electric current, modulated frequency and power of the electromagnetic field were used to penetrate the constructed specimens, which were built of materials such as concrete, brick, adobe, plaster and fine sand and had walls with a thickness of less than 300 millimetres. The results show that the optimum value of the magnetic field was 0.18 µT, which was sufficient to penetrate 150 mm with densities between 1.0 and 2.4 g/cm3 and porosities between 11 and 60%. The current and wave each had a coefficient of determination R2 = 0.8914, and the average inductance value was 184 µH, which was established with an air core of radius 9.75 cm and with 19 turns with AWG-25 wire. The frequency-modulated signal ranged in the audible zone between 10 and 22 kHz. The presented prototype detects the interior deterioration of the walls of the building, and the signal is reflected on a metallic guide on the opposite side of the wall with a reading error of 5%. The use of this prototype does not represent a risk to the operator or the environment.

Anti-OTC antibody-conjugated fluorescent magnetic/silica and fluorescent hybrid silica nanoparticles for oxytetracycline detection

Abstract This study presents two alternative fluorescent nanoparticle-based oxytetracycline (OTC) detection methods in milk samples. Rhodamine 6G-coated fluorescent hybrid silica nanoparticles and fluorescent magnetic/silica nanoparticles functionalized with anti-OTC antibodies were used in this test. The sandwich test format was utilized to compare anti-OTC antibody-conjugated fluorescent magnetic/silica nanoparticles with OTC/OTC antibody-conjugated fluorescent hybrid silica nanoparticles in an Eppendorf tube with magnetic separators. The magnetic separator helps to quickly retain all of the OTC captured by fluorescent magnetic core–shell nanoparticles in the milk sample. As a result, the assay time was dramatically shortened. The obtained linear range was 1.34 × 10−6 to 2.10 × 10−8 (M) (R 2 = 0.9954), the detection limit was 4.76 ng/mL, and the total assay time was 90 min. This approach was used to determine the OTC concentration in milk samples, and the maximum percentage (%) of interference was less than 3.0%, with a recovery rate of greater than 97.0%. This approach offers a high potential for residue detection in milk samples. With a total analysis period of less than 90 min, this approach provided the best way to determine the capture and detector nanoparticles’ response.

Hierarchical Magnetic Carbon Nanoflowers for Ultra-Efficient Electromagnetic Wave Absorption.

Porous carbon nanomaterials are widely applied in the electromagnetic wave absorption (EMWA) field. Among them, an emerging flower-like carbon nanomaterial, termed carbon nanoflowers (CNFs), has attracted tremendous research attention due to their unique hierarchical flower-like structure. However, the design of flower-like carbon nanomaterials with different magnetic cores for EMWA has rarely been reported. Herein, a general template method is proposed to achieve a set of high-quality magnetic CNFs, namely Co@Void@CNFs, CoNi@CNFs, and Ni@CNFs. The prepared magnetic CNFs have highly accessible surface area and internal space, rich heteroatom content, multi-scale pore system, and uniform and highly dispersed magnetic nanoparticles, as a result, deliver superior EMWA performance. Specifically, when the thickness is 2.6mm, the Co@Void@CNFs exhibit a maximum refection loss (RLmax) of -56.6dB and an effective absorption bandwidth (EAB) from 8.0 to 12.1GHz covering the whole X band. The CoNi@CNFs have an RLmax of up to -57.6dB and a wide EAB of 5.6GHz at just 1.9mm. For the Ni@CNFs, possess an ultra-broad EAB of 6.1GHz, covering the entire Ku band at 2.0mm. Overall, the hierarchical magnetic carbon nanoflowers proposed here offer new insights toward realizing multifunctional integrated carbon nanomaterials for EMWA.

Magnetic heterogenization of supramolecular carbohydrates for the efficient adsorption of heavy metals removal from wastewater

BackgroundAs the high impact of heavy metals hazards for humans and the environment, providing a suitable method to remove heavy metals is of great importance. Recently, magnetic adsorbents have been developed for their ease of separation, high absorption efficiency, and cost-effectiveness has been expanding. On the other hand, hybridism adsorbents composed of a magnetic core and an organic branch amended with different functional groups such as –OH, –NH2, −SH, and –COOH have suitable potentials for heavy metal removals. MethodsIn this, a simple procedure for the preparation of β-cyclodextrin bonded Fe3O4@SiO2 (β-CD-SiO2@Fe3O4) was reported. The morphological, structural, and thermal stability characteristics were investigated by the XRD, SEM, EDS, FT-IR, and TGA-DTA techniques. Next, the potential of β-CD-SiO2@Fe3O4 in the absorption of Cd2+ and Pb2+ ions from wastewaters was investigated. The effect of various parameters such as pH, adsorbent dosage, Pb/Cd concentration, and the temperature was investigated on the absorption of Cd2+ and Pb2+ heavy metal ions. Significant findingsThe maximum adsorption was achieved when pH = 6.5, heavy metal ion concentration (250 mg/L), and adsorbent dosage (0.075 g) at room temperature was used. The adsorption process could be described by kinetic models and the pseudo-second-order model was well-matched. The maximum adsorption capacities of Pb2+ and Cd2+ were obtained at 160 and 159.33 mg/g respectively. The negative value of ΔG indicates the spontaneity of the absorption process. The negative values of ΔH and ΔS show the exothermic nature of the absorption reaction.

A DECOUPLED MAGNETIC INTEGRATION TECHNIQUE FOR DUAL-FREQUENCY TOPOLOGIES

The dual-frequency converter comprises a high-frequency buck unit and a low-frequency buck unit, which has the advantages of high efficiency and fast dynamic response. But also, the increase of magnetic parts leads to the power density of the converter being greatly reduced; for this problem, this paper proposes a three-section winding method to decouple the two inductors in the converter integrated into a magnetic core, given the integrated magnetic parts structure and establish its gyrator-capacitor model to derive the decoupling conditions. The flux density distribution of the magnetic components is analyzed by finite element simulation software and compared with the existing integration method; this decoupling integration method can make the flux distribution more uniform and improve the core utilization. The results show that the volume and weight are reduced by 31.2 % and 25.3 % compared with those of the separated magnetic parts, and the efficiency is also consistent with that of the separated magnetic parts, which verifies the correctness and feasibility of the theoretical analysis.

Optimising miniaturised hydrocyclones for enhanced separation of microplastics

Microplastics, particularly those in the 5–20µm range, pose substantial risks in aquatic environments, yet effective removal techniques are limited. This study assesses two critical geometric parameters of a 10 mm mini-hydrocyclone: inlet radius and insertion angle. Along with the inlet velocity, they are optimised collectively to enhance the MPs’ removal. Computational Fluid Dynamics (CFD) simulations using the Mixture model and Reynolds stress model were employed to track the particle–water–air interactions, revealing the flow dynamics and absence of an air core. The Response Surface Methodology (RSM) using a Box-Behnken design of experiments was adopted to assess the impact of the geometric and operational parameters and determine the optimal design. Recovery efficiency, concentration efficiency, and split rate were recorded during experiments and compared with CFD results, showing a good agreement between experiments and CFD simulations. The resulting novel design achieved an 88.53% MPs recovery and a concentration efficiency of 1.83, which represents an obvious improvement over the commercial design’s MPs recovery efficiency of 79.97% and concentration efficiency of 1.68. Simulations reveal that the novel design shortens the path for MPs through the forced turbulence region and modifies the velocity and turbulence fields, enhancing the concentration gradient of MPs within the mini-hydrocyclone’s chamber. Moreover, the novel design exhibits a more robust response to inlet velocity variations, a crucial advantage for its application in arrays. Experiments further confirm that a matrix composed of 10 novel mini-hydrocyclones achieves 10 percentage points higher recovery efficiency than the matrix with 10 commercial mini-hydrocyclones. These findings mark a significant step towards effective MP removal, addressing a critical environmental issue.

Magnetic vortex polarity reversal induced gyrotropic motion spectrum splitting in a ferromagnetic disk

We investigate the gyrotropic motion of the magnetic vortex core in a chain of a few micron-sized Permalloy disks by electrical resistance measurement with amplitude-modulated magnetic field. We observe a distinctive splitting of the resistance peak due to the resonant vortex-core motion under heightened radio frequency (RF) magnetic field excitation. Our micromagnetic simulation identifies the splitting of the resonant peak as an outcome of vortex polarity reversal under substantial RF amplitudes. This study enhances our understanding of nonlinear magnetic vortex dynamics amidst large RF amplitudes and proposes a potential pathway for spintronic neural computing thanks to their unique and controllable magnetization dynamics.

Solving dynamic electric circuit with nonlinear hysteretic inductor using harmonics interpolation method

SummaryThe aim of this paper is to present a methodology for solving а dynamic electric circuit with nonlinear hysteretic inductor without the use of hysteresis model or equivalent circuits. A consideration of nonlinear and hysteretic behaviour of the magnetic core under quasistatic conditions is based on applying harmonics interpolation method (HIM) to the measured magnetising field strength waveforms. A dynamic behaviour of the magnetic core is considered through the application of the statistical theory of losses (STL). A considered electric circuit consists of AC voltage source connected in series with shunt resistor, additional linear resistor and inductor, as well as a nonlinear hysteretic inductor. The solution for electric current of the circuit is obtained by solving equation derived from Kirchhoff's laws through a series of successive iterations. Coupling of electric and magnetic part of the circuit is obtained from fundamental laws of electromagnetism. Methodology is validated for four cases of the considered electric circuit — without additional elements, with one additional or both additional elements, for sinusoidal voltage source amplitudes of 2, 4, 6, 8 and 9 V and frequency of 50 Hz. Validation is repeated for frequencies of 100, 200 and 300 Hz while keeping the ratio of the amplitude to frequency constant. Detailed theoretical approach and methodology, comparisons between measured and calculated results, as well as adequate discussion are presented.