Alpha Omega Electromagnetics (United States)

In this article we highlight an Elemental Modelling Method, as an alternative to the standard Harmonic (or Fourier) Model, that can include variable permeability and non-periodic 3D geometry with superposition of boundary-free analytic magnetic field solutions. The methodology is demonstrated with an exhaustive parametric search to optimise a set of tubular double-sided Halbach slotless permanent magnet linear synchronous motor topologies, within a fixed volume constraint. The modelling method is computationally efficient, facilitating the search of close to 900,000 topologies with an axisymmetric-2D assumption, subsequently converted to a full 3D design. The aim of this study is to investigate the effect of strategic addition of iron within the topologies, against the trade-off of reducing permanent magnet volume – such an analysis is not simple, or possible, within the Harmonic Model. The elements of the model include coil filaments, permanent magnets, and iron segments inclusive of saturation effects from nonlinear permeability. A design with inset permanent magnets and surface iron found in the parametric search is shown to outperform the optimal Halbach topologies, with improved figures of merit for force and force ripple with low phase currents. Results are compared with Finite Element Analysis and performance of a design with non-unity relative permeability of the permanent magnets is assessed. • A new elemental modelling method for linear motor design. • Uses analytic magnetic field equations for semi-analytic forces. • Includes non-periodic arrays and nonlinear materials. • Parametric and comparative optimisation studies. • Validated against finite element analysis.

The Maxwell Stress Tensor is a computationally efficient method for calculating the force and torque between two arbitrary collections of rigidly-connected permanent magnets, coils, and/or iron (soft magnet) segments, when using exact analytic magnetic field solutions. However, use of the tensor exacerbates numerical errors present in the closed-surface free space mesh of a region, whether that be from an approximate field solution such as a finite sum, or discretisation errors that create a numeric non-zero divergence. Using a specialised identity of the divergence theorem, this article derives a generalised Maxwell Stress Tensor, which is interchangeable with the standard form and significantly reduces or removes numerical error sources from the meshing. The application focus of this work is modelling of non-periodic permanent magnet machines without geometrical assumptions through superposition of analytic magnetic field solutions ( B and H ) from a large number of elements. The influence of relative permeability can be included in these elements through varying the volumetric magnetic charge or current densities. Case studies with analytic or finite element force solutions are used to verify the result and compare the accuracy and computational efficiency with traditional semi-analytic methods. The proposed tensor enables parametric studies with accuracy not previously possible using an elemental modelling method, and can be applied to existing multiphysics models. • Electromagnetic stress tensor that is a function of two arbitrary vector fields. • Improved numerical accuracy of force density with discretisation of analytic fields. • Semi-analytic application in 2D/3D linear or nonlinear actuator models. • Validation with comparison to exact analytic solutions and/or finite element models. • The tensor can be extended to multiphysics applications.

The present formulation of quantum electrodynamics inevitably leads to mathematical infinities when considering the self interaction of fields, in particular, the electromagnetic fields of a charged particle (electron) interacting with itself to produce infinite energy. Nonetheless, if these infinities are simply removed to obtain finite values that conform to measurements, a process called “renormalization”, quantum electrodynamics is a remarkably successful theory for predicting the interactions of photons with atomic electrons.

By tuning with dispersive permittivity or permeability, the quality factors and thus the Chu lower bound for lossy magnetic- or electric-dipole antennas at isolated resonances or antiresonances can be reduced by a factor of one half (bandwidth doubled) for input-impedance bandwidth power-drops of about −24 dB with radiation efficiencies of about 50%. Further reductions in quality factor (greater increases in bandwidth) for less restrictive power drops can be obtained with lower efficiencies.

This article addresses the problem of efficiently and accurately evaluating the singular or near-singular double volume (6-D) reaction integrals fundamental to the solution of volume integral equations (VIEs) using the method of moments (MoM). VIE techniques based on the MoM are used to obtain accurate solutions for electromagnetic (EM) problems of all types, and the accurate computation of the singular and near-singular reaction integrals that occur in the resulting system matrices is crucial for accurate EM modeling. Here we propose a scheme to treat, as a whole, the 6-D reaction integrals appearing in the MoM. The divergence theorem is directly applied twice in the physical space domain, not a transformed domain, thus eliminating restrictions to well-shaped elements. With appropriate integration reordering, the 6-D volume integrals are expressed as two radial integrals followed by two surface integrals over source and observation domain boundaries. We further smooth the integral by removing the static form of the kernel and evaluating it separately using a semi-analytical approach. The method is numerically validated for static and dynamic kernels arising in the electric field VIEs (i.e., for kernels having <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$1/R$ </tex-math></inline-formula> singularities) and for linear basis functions.

This article proposes a jitter-aware decoupling capacitors placement optimization method that uses the genetic algorithm (GA). A novel method for defining the optimization target function in regard to power delivery network (PDN) and power source-induced jitter (PSIJ) optimization based on the GA-based tool is proposed. The proposed method can provide an optimum and economic solution for the number of decoupling capacitors to use in a PDN to reach the target impedance. Then, by modifying the optimization target function with our proposed method, an optimum solution of the number of decoupling capacitors regarding the PSIJ can be obtained. The PSIJ analytical expressions are derived in conjunction with a resonant cavity model that includes the coordinates of the decoupling capacitors and the PSIJ transfer function. The GA-based optimization algorithm with the proposed target function is first applied to optimize the number of decoupling capacitors regarding the PSIJ. Finally, the measured jitters from HSPICE simulation results are used to verify our optimization method such that both the simulated results and analytically calculated results support the efficiency of our proposed optimization method.