Quasi-Analytical Calculation of Frequency-Dependent Resistance of Rectangular Conductors Considering the Edge Effect

This paper presents an accurate quasi-analytical approximation of frequency-dependent ac resistance of single rectangular conductors. In this work, first, a two-dimensional analytical ac resistance of rectangular conductors is derived. Unlike circular conductors, where current density distributes evenly in each layer of the conductor’s cross-section, the edge effect is involved for rectangular conductors. Due to the edge effect, one cannot define an accurate boundary condition for solving the two-dimensional partial differential equation of magnetic field or current density of rectangular conductors. Hence, the calculated two-dimensional analytical current density result is not accurate and is modified and fitted on FEM simulation, taking the conductor’s thickness into account using the least-square problem to improve its accuracy. Unlike numerical approaches, the proposed method yields an easy-to-use formula applicable to industrial applications in different fields. Contrary to the one-dimensional approach, which is only valid for very thin rectangular conductors, this method takes edge effect into account and can be used for any thickness (from square to very thin rectangular conductors). The proposed method can be used in applications where an accurate ac resistance of rectangular conductors over a wide frequency range is required, such as white-box modeling of power transformers and interpreting its frequency response analysis (FRA), and calculating the resistance of electric machine winding, busbars, and printed circuit board traces.

Low-temperature induction heating of flat metal objects in a traveling electromagnetic field

The article discusses possible options for a low-temperature induction heating system (LTIHS) of flat metal products in a traveling electromagnetic field. The problem of calculating eddy currents, active and reactive powers induced in a heated flat object, as well as electromagnetic forces acting on the object moving it in a given direction, is posed and solved. A mathematical model has been developed that takes into account the dependence of the influence on the main parameters of the electromagnetic field of the following factors: geometric dimensions of the air gap between the poles of the magnetic circuit and the heated flat body; the longitudinal edge effect caused by the open circuit of the magnetic circuit of the inductor, as well as the transverse edge effect associated with the appearance of the longitudinal components of eddy currents in a heated flat object. The solution of particular problems of LTIHS in one- and two-dimensional formulation allows them to be simplified and to perform calculations for various design variants of induction heating devices with a traveling electromagnetic field, using a one-dimensional model that explicitly takes into account the features of electromagnetic processes in the systems under study.

Edge Effect in Electronic and Transport Properties of 1D Fluorinated Graphene Materials

A systematic examination of the electronic and transport properties of 1D fluorine-saturated zigzag graphene nanoribbons (ZGNRs) is presented in this article. One publication (Withers et al., Nano Lett., 2011, 11, 3912–3916.) reported a controlled synthesis of fluorinated graphene via an electron beam, where the correlation between the conductivity of the resulting materials and the width of the fluorinated area is revealed. In order to understand the detailed transport mechanism, edge-fluorinated ZGNRs with different widths and fluorination degrees are investigated. Periodic density functional theory (DFT) is employed to determine their thermodynamic stabilities and electronic structures. The associated transport models of the selected structures are subsequently constructed. The combination of a non-equilibrium Green’s function (NEGF) and a standard Landauer equation is applied to investigate the global transport properties, such as the total current-bias voltage dependence. By projecting the corresponding lesser Green’s function on the atomic orbital basis and their spatial derivatives, the local current density maps of the selected systems are calculated. Our results suggest that specific fluorination patterns and fluorination degrees have significant impacts on conductivity. The conjugated π system is the dominate electron flux migration pathway, and the edge effect of the ZGNRs can be well observed in the local transport properties. In addition, with an asymmetric fluorination pattern, one can trigger spin-dependent transport properties, which shows its great potential for spintronics applications.

Extraordinary optical transmission from a thin microcavity by macroscopic quantum effect

The macroscopic quantum effect is revealed to elaborate the extraordinary optical transmission (EOT) from a subwavelength thin microcavity based on the uncertainty property of the transmitted electromagnetic fields after the aperture. A critical radius is found in the thin microcavity under a certain incident electromagnetic wavelength. With the aperture radius varying, the transmitted field can be divided into three regimes: I. the macroscopic quantum regime when the aperture radius is less than the critical radius, in which the field edge effect occurs and EOT phenomenon is perfectly manifested; II. The wave-particle duality regime in the vicinity of the critical radius, in which the edge effect and diffraction phenomenon exist simultaneously; III. The wave regime when the aperture radius is greater than the critical radius, in which the near-field diffraction emerges. In addition, the influences of incident wavelength and microcavity thickness on EOT are also investigated. Our research have potential applications in advanced optical devices, such as light switch and optical manipulations.