Purpose This paper aims to develop a new 3D electromagnetic analytical model in cylindrical coordinates to study the transient and steady-state dynamic performance of radial flux permanent magnet couplers. Design/methodology/approach The magneto-dynamic problem is addressed by coupling the proposed 3D electromagnetic model with the equations of motion and the circuit model of the drive motor. The electromagnetic model is developed by solving Maxwell’s equations in three-dimensional cylindrical coordinates using a magnetic scalar potential approach. The static torque expression is then derived from the Lorentz force, based on the electrostatic-magnetostatic analogy. Findings The obtained results demonstrate the accuracy of the proposed method, which accounts for magnetic edge effects without the need for correction factors. The magneto-dynamic model accurately predicts transient and steady-state performance while ensuring a good compromise between accuracy and computation time. Practical implications The 3D analytical model significantly reduces computation time compared to 3D finite element simulations, making it an efficient and accurate tool for designing and optimizing radial flux permanent magnet couplers. Originality/value A new 3D analytical model in cylindrical coordinates has been developed to compute the electromagnetic torque in radial flux permanent magnet couplers. This model inherently accounts for 3D magnetic edge and curvature effects without requiring correction factors. The 3D electromagnetic model is coupled with the dynamic equations to analyze both transient and steady-state performance.

Purpose This study aims to understand the physical processes that occurs at the contact of conductivity-contrasting media responsible for the distortion of the measured magnetotelluric response. Design/methodology/approach A two-dimensional (2D) model of a resistive half-space and an adjacent conductive layer embedded therein was first investigated. It was theoretically shown that at their vertical contact, an incident electromagnetic wave activates processes that lead to disturbances of the original fields – Coulomb action and current induction. To generalise this knowledge, a three-dimensional (3D) model of a layered half-space with several different interfaces was designed. Key to its construction was the mathematical demonstration that the undisturbed apparent resistivity is the result of the convolution of the electric field and the inverse function of the magnetic field passing through the individual layers. Findings Theoretical analysis led to the creation of computational programs for calculating transfer functions in 2D and 3D situations for a wide frequency range. The distortion of the synthetic response thus obtained was discussed mainly in connection with the undesirable phenomenon of static shift in the measured data. It was shown that the static shift is a manifestation of the asymptotic behaviour of solutions at large periods, which is consistent with observations. Originality/value Understanding the patterns of behaviour of disturbance quantities and their expressibility in the form of standard mathematical functions gives the prospect of developing a method for eliminating their manifestations, first from synthetic and later from real field data.

Purpose The most used numerical method in electrical engineering resources is the finite element method (FEM). This paper aims to present the use of the finite volume method to solve differential systems that contain the curl-curl operator. Design/methodology/approach Two discretization approaches have been implemented and tested. In the first one, the authors present the approximation of the curl operator using the diamond scheme. The second approach, called the split-diamond scheme, is a dual version of the first for heterogeneous media. A comparison with FEM software is performed to validate the proposed approaches and highlight the advantages of the second method. Findings The authors validate the adaptation of the curl-curl operator on both schemes. The expected second-order spatial accuracy is obtained. For steep discontinuous media, the authors show that the split-diamond scheme greatly reduces the approximation errors. Originality/value Edge FEMs are usually used for the curl-curl operator because their basis functions naturally provide the continuity of the tangential component. The authors propose a finite volume method to solve the H-formulation obtained from Maxwell equations. The curl-curl operator is rewritten as div-grad to respect the requirements of the finite volume method. Inspired by an approximation of grad, the authors propose an approximation of curl operator. The flux expressions considered here to connect neighboring cells provide the continuity of the tangential component.

Purpose The purpose of this paper is to introduce a fast and resource-efficient method for modeling litz wires with complex structures. The method is also capable of taking into account nonlinear materials in the configuration (e.g. ferrite-core coil). Design/methodology/approach The modeling of litz wires is performed in two-dimensional (2D), with the key being the proper consideration of three dimension (3D) phenomena (twisting, constraints resulting from braiding, winding and the circuit constraints) in 2D. These phenomena can be taken into account through specific constraint conditions, which, when incorporated into the boundary value problem equations, enable the system of equations to be solved in a single step. Findings With the developed method, 3D problems related to wire modeling can be solved in 2D by eliminating superposition. As a result, the model can handle nonlinearities such as a magnitude-dependent complex permeability, allowing for the modeling of ferrite-core coils as well. A comparison between a simple 2D-3D model example demonstrates significant time savings, while the 2D model reproduces the results of the 3D model fairly well. The 2D model can also be extended to wires with more complex structures, the modeling of which in 3D would require extremely high computational power, if feasible at all. Originality/value This paper shows the applicability of the 2D model as a substitute for the 3D model by showing the agreement of the results, as well as the savings in computation time and performance.

Purpose The purpose of this paper is to propose an exact and effective method for calculating the armature reaction field distribution of slotted permanent magnet pseudo direct drive (PDD) machines with surface mounted magnets. Design/methodology/approach Based on the Helmholtz’s theorem and using the Maxwell’s equations, two-dimensional analytical expressions are used to calculate the radial and tangential components of the inner and outer air-gap magnetic flux density. Neumann and continuous boundary condition between adjacent regions are used to calculate integration constants. Findings Comparing the results obtained from the proposed method with the results of the finite element method shows that despite the geometrical complexities due to the presence of the modulator openings and slots, the boundary value problem formulation is well implemented with negligible assumptions. Originality/value Effectiveness and accuracy of the proposed approach is assessed on two different sizes slotted PDD machines. Combining the presented analytical method with meta-heuristic methods can be simply used for the optimal design of PDD machines.

Purpose This work aims to develop a method that balances computational efficiency and accuracy for evaluating the performance of linear electromagnetic actuators (LEAs) in the presence of stray magnetic fields (SMFs). Design/methodology/approach This paper presents a loop-equation-based magnetic equivalent circuit network (MECN) model for evaluating the electromagnetic characteristics of LEAs in the presence of SMFs. By using magnetic flux as the state variable, the proposed model enables analysis of leakage flux in windings. In this approach, SMFs are introduced as boundary conditions, thus reducing computational complexity. A solenoid-type LEA is used as a case study, and the accuracy of the proposed MECN is validated through comparison with finite element analysis (FEA) results. Findings The results demonstrate that the loop-equation-based MECN achieves good agreement with FEA simulations while significantly improving computational efficiency. This indicates that the proposed approach provides both reliable accuracy and reduced computational cost for analysing LEAs under SMFs. Originality/value This study proposes a loop-equation-based MECN method that introduces magnetic flux as a state variable, enabling analysis of magnetic fields in current-carrying regions. By incorporating SMFs as boundary conditions, the model is simplified, thus enhancing computational efficiency.

Purpose This paper aims to enhance the performance of the cascaded single-stage distributed amplifier (CSSDA) by proposing a novel architecture that simultaneously improves gain, bandwidth and ripple rate control. The objective is to address the trade-off between gain enhancement and bandwidth reduction typically encountered in distributed amplifiers (DAs). Design/methodology/approach A new structure, referred to as the Chebyshev CSSDA (Ccssda), is introduced. In this architecture, the input and output artificial transmission lines are left open-circuited, which doubles the gate-source voltage and increases the output current, resulting in a 12-dB gain improvement at low frequencies. However, this introduces impedance mismatches that affect bandwidth. To overcome this, the amplifier’s transfer function is analytically derived and approximated using Chebyshev polynomials, enabling ripple control and gain flattening. A cascode configuration is also integrated to mitigate nonideal transistor behavior. Findings The proposed Ccssda design achieves a significant gain enhancement of approximately 12 dB compared to the conventional CSSDA. Moreover, the Chebyshev-based approximation ensures gain uniformity and bandwidth stability up to the desired cutoff frequency. Simulation results confirm the effectiveness of the method and demonstrate the feasibility of ripple rate control through impedance tuning. Originality/value The novelty of this work lies in the combination of an open-circuited artificial line structure with a Chebyshev approximation method to improve amplifier performance. The proposed methodology offers flexibility and can be applied to any transistor technology using normalized design parameters. This work contributes to the development of high-performance DAs for broadband RF and mm-wave applications.

Purpose The purpose of the paper is to analyze and compare a novel three-stage macromeso-micro (M3) modeling framework for simulating phrenic nerve stimulation. This stimulation might be used to improve ventilation in intensive care unit patients. The focus is on a detailed finite element analysis of the first two M3 steps using a realistic neck model. Design/methodology/approach A finite element method for stationary electric current flow was used to compute extracellular electric potential distributions along intra-fascicular pathways of the phrenic nerve, essential for nerve activation prediction. A 14-tissue, electrically isotropic realistic neck model was used in the first stage (macro model). Subsequently, in the meso stage, a geometric phrenic nerve model with three electrically anisotropic fascicles representing bundles of axon fibers was analyzed. In this step, the electric potential values calculated in the macro stage were used to define Dirichlet boundary conditions on the nerve surface. The pathways along which the extracellular electric potential was calculated run centrally within the fascicles. To assess the accuracy of the extracellular electric potential calculations, a full macro model including electrically anisotropic fascicles was additionally developed. The potential values calculated based on this model are used for validation and error calculations. Findings The results demonstrate changes in the courses of the extracellular electric potential with implemented anisotropic electrical conductivity. Specifically, these changes are larger at the boundaries of the fascicles compared to the center of the fascicles. The use of separate macro- and meso-geometric models can significantly increase computation time. Therefore, it is recommended to use (if computational resources allow) only one, full macro-geometric model that accounts for the electrical anisotropy of fascicles. Originality/value Development and comparison of modeling approaches for simulating phrenic nerve stimulation.

Purpose This study aims to introduce an effective material to efficiently and accurately solve the eddy current problem in laminated iron cores considering circuit coupling. Design/methodology/approach In the first step, a representative cell problem is solved to obtain the complex-valued non-linear magnetic reluctivity. In the second step, this effective material is then used in a homogenised static magnetic field formulation and accurately approximates the eddy current losses and the reactive power as well as the corresponding distributions. Findings As a representative numerical example, a voltage-driven single-phase transformer is simulated with great success. The eddy current losses and the reactive power of the simulation using the standard finite element method and the simulation using the effective material agree very well and the required simulation time is tremendously reduced. Originality/value The presented approach uses an A-formulation with circuit coupling of voltage-driven excitation coils for an effective material to homogenise the core.