scholarly journals On the Electromagnetic Field of an Overhead Line Current Source

Electronics ◽  
2020 ◽  
Vol 9 (12) ◽  
pp. 2009
Author(s):  
Mauro Parise
Keyword(s):  
Electric Field ◽  
Line Source ◽  
Current Source ◽  
Form Solution ◽  
Complete Representation ◽  
Faraday’S Law ◽  
Sommerfeld Integral ◽  
Time Harmonic ◽  
Hankel Functions ◽  
Analytical Series

This work presents an analytical series-form solution for the time-harmonic electromagnetic (EM) field components produced by an overhead current line source. The solution arises from casting the integral term of the complete representation for the generated axial electric field into a form where the non-analytic part of the integrand is expanded into a power series of the vertical propagation coefficient in the air space. This makes it possible to express the electric field as a sum of derivatives of the Sommerfeld integral describing the primary field, whose explicit form is known. As a result, the electric field is given as a sum of cylindrical Hankel functions, with coefficients depending on the position of the field point relative to the line source and its ideal image. Analogous explicit expressions for the magnetic field components are obtained by applying Faraday’s law. The results from numerical simulations show that the derived analytical solution offers advantages in terms of time cost with respect to conventional numerical schemes used for computing Sommerfeld-type integrals.

scholarly journals On the Surface Fields of a Small Circular Loop Antenna Placed on Plane Stratified Earth

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Mauro Parise
Keyword(s):  
Analytical Method ◽  
Integral Formula ◽  
Integral Representations ◽  
Loop Antenna ◽  
Circular Loop ◽  
Time Harmonic ◽  
Hankel Functions ◽  
Cauchy’S Integral Formula ◽  
Em Field ◽  
Surface Fields

An analytical method is presented which makes it possible to derive exact explicit expressions for the time-harmonic surface fields excited by a small circular loop antenna placed on the top surface of plane layered earth. The developed procedure leads to casting the complete integral representations for the EM field components into forms suitable for application of Cauchy’s integral formula. As a result, the surface fields are expressed as sums of Hankel functions. Numerical simulations are performed to show the validity and accuracy of the proposed solution.

A reduced formulation for modelling time-harmonic electromagnetic field in the media with thin highly conductive inclusions

2018 ◽  
Author(s):  
Э.П. Шурина ◽  
Д.В. Добролюбова ◽  
Е.И. Штанько
Keyword(s):  
Electric Field ◽  
Variational Formulation ◽  
Computational Cost ◽  
Surface Current ◽  
Wide Frequency Range ◽  
Geometrical Shape ◽  
Frequency Range ◽  
Surface Current Density ◽  
Time Harmonic ◽  
The Media

При решении задач электромагнетизма в широком частотном диапазоне в областях с тонкими пластинами, оболочками и экранами численными методами возникает проблема резкого роста сеточной дискретизации вблизи внутренних структур с разномасштабными габаритными размерами. В работе предложена модификация вариационной постановки векторного метода конечных элементов, основанная на снижении размерности модели в окрестности тонких включений, которая позволяет преодолеть эту проблему за счет специфического учета таких структур на уровне вариационной постановки. Так как редуцирование модели обычно приводит к появлению ограничений на область ее применимости, выполнено исследование диапазона допустимых частот, контрастности электрофизических характеристик матрицы и включений, геометрических особенностей внутренней структуры, для которых предложенная модель позволяет получить корректные с точки зрения физики результаты. Purpose. In this paper, we propose a reduced variational formulation for the Helmholtz equation for the electric field, in which thin highly conductive objects are approximated by surfaces with the equivalent surface current density. We conduct a study aimed at defining the range of application for the reduced variational formulation, focusing on highly contrasting thin objects of various geometrical shape and arrangement in a wide frequency range. Methodology. The modelling is performed on unstructured tetrahedral meshes. Since the reduced variational formulation treats thin highly conductive objects as surfaces, no volume mesh is constructed inside of them.We compare the results obtained by the vector FEM using the proposed variational formulation with the results obtained using standard formulation. Findings. Due to the fact that the proposed variational formulation does not require volume meshing of the thin objects, its computational cost is significantly lower. However, the reduced formulation yields correct results in a restricted frequency range. It also imposes some limitations on the minimal contrast and maximal thickness of the thin highly conductive objects. Originality/value. The proposed reduced variational formulation can be applied to simulate the time-harmonic electric field in the media with thin highly conductive inclusions of either regular or chaotic arrangement, as well as thin shielding plates or casings of various geometrical forms.

On the boundary operator in electromagnetic scattering

1986 ◽  
Vol 103 (1-2) ◽  
pp. 91-98 ◽  
Author(s):  
Rainer Kress
Keyword(s):  
Magnetic Field ◽  
Electric Field ◽  
Electromagnetic Scattering ◽  
Maxwell Equations ◽  
Boundary Operator ◽  
Hölder Continuous ◽  
Operator Mapping ◽  
Time Harmonic ◽  
Continuous Surface ◽  
The Magnetic Field

SynopsisFor radiating solutions to the time-harmonic Maxwell equations, it is shown that the boundary operator mapping the tangential components of the electric field into the tangential components of the magnetic field is a bounded bijective operator from the space of Holder continuous tangential fields with Hölder continuous surface divergence onto itself.

scholarly journals Effect of Device Variables on Surface Potential and Threshold Voltage in DG-GNRFET

2015 ◽  
Vol 5 (5) ◽  
pp. 1003
Author(s):  
Baharak Mehrdel ◽  
Azlan Abdul Aziz ◽  
Mahdiar Hossein Ghadiri
Keyword(s):  
Electric Field ◽  
Surface Potential ◽  
Threshold Voltage ◽  
Structural Parameters ◽  
Closed Form Solution ◽  
Form Solution ◽  
Electric Field Effect ◽  
Short Channel ◽  
Lateral Electric Field ◽  
Saturation Velocity

<p><em>In this paper we present four simple analytical threshold voltage model for short- channel and length of saturation velocity region (LVSR) effect that takes into account the built – in potential of the source and drain channel junction, the surface potential and the surface electric field effect on double – gate graphene nanoribbon transistors. Four established models for surface potential, lateral electric field, LVSR and threshold voltage are presented. These models are based on the easy analytical solution of the two dimensional potential distribution in the graphene and Poisson equation which can be used to obtain surface potential, lateral electric field, LVSR and threshold voltage. These models give a closed form solution of the surface potential and electrical field distribution as a function of structural parameters and drain bias. Most of analytical outcomes are shown to correlate with outcomes acquired by Matlab simulation and the end model applicability to the published silicon base devices is demonstrated.</em></p>

Alternative current source based Schottky contact with additional electric field

2017 ◽  
Vol 107 ◽  
pp. 28-37 ◽  
Author(s):  
R.K. Mamedov ◽  
A.R. Aslanova
Keyword(s):  
Electric Field ◽  
Current Source ◽  
Schottky Contact ◽  
Alternative Current

Dynamic Response of Kirchhoff Plate on a Viscoelastic Foundation to Harmonic Circular Loads

2003 ◽  
Vol 70 (4) ◽  
pp. 595-600 ◽  
Author(s):  
L. Sun
Keyword(s):  
Frequency Response ◽  
Response Function ◽  
Frequency Response Function ◽  
Closed Form Solution ◽  
Static Solution ◽  
Form Solution ◽  
Kirchhoff Plate ◽  
Viscoelastic Foundation ◽  
Hankel Functions ◽  
Circular Load

In this paper Fourier transform is used to derive the analytical solution of a Kirchhoff plate on a viscoelastic foundation subjected to harmonic circular loads. The solution is first given as a convolution of the Green’s function of the plate. Poles of the integrand in the integral representation of the solution are identified for different cases of the foundation damping and the load frequency. The theorem of residue is then utilized to evaluate the generalized integral of the frequency response function. A closed-form solution is obtained in terms of the Bessel and Hankel functions corresponding to the frequency response function of the plate under a harmonic circular load. The result is partially verified by comparing the static solution of a point source obtained in this paper to a well-known result. This analytical representation permits one to construct fast algorithms for parameter identification in pavement nondestructive test.

scholarly journals Analysis of an Underground Vertical Electrically Small Wire Antenna

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Shuwei Dong ◽  
Aiguo Yao ◽  
Fanhe Meng
Keyword(s):  
Electric Field ◽  
Green's Function ◽  
Method Of Moments ◽  
Current Distribution ◽  
Radial Distance ◽  
Wire Antenna ◽  
Sommerfeld Integral ◽  
Antenna Surface ◽  
Electromagnetic Signals ◽  
Easy Solution

The problem considered is a vertical electrically small wire antenna located underground, which transmits electromagnetic signals to the ground. Getting Green’s function of the vertical dipole underground was the first step to calculate this issue. A quasistatic situation was considered to make an approximation on Sommerfeld integral for easy solution. The method of moments was used to solve the current distribution on the antenna surface at different frequencies, which laid a good foundation for obtaining the electric field of the antenna. Then the axial and radial components of the electric field with the radial distance on the ground were investigated, as well as the voltage received on the ground. Furthermore, the influence of the frequency and stratum parameters on current and electric field was studied to understand the variation clearly.

ON THE MATHIEU EQUATION DESCRIBING ULTRA-RELATIVISTIC FERMIONS EVOLVING IN A TIME-HARMONIC ELECTRIC FIELD PARALLEL TO A STATIC MAGNETIC INDUCTION

2013 ◽  
Vol 28 (35) ◽  
pp. 1350157 ◽  
Author(s):  
MARINA-AURA DARIESCU ◽  
CIPRIAN DARIESCU
Keyword(s):  
Electric Field ◽  
Mathieu Equation ◽  
Type Equation ◽  
Static Field ◽  
Parabolic Cylinder ◽  
Longitudinal Momentum ◽  
Temporal Part ◽  
Time Harmonic ◽  
Electric And Magnetic Fields ◽  
Parabolic Cylinder Functions

The present work is studying the behavior of relativistic fermions in parallel electric and magnetic fields, oriented along Oz. As expected, in the particular case of static field intensities, the temporal part of the wave function is expressed in terms of the parabolic cylinder functions. When the static electric field is replaced by a time-harmonic one, the ultra-relativistic particles are described by a Mathieu-type equation, of purely imaginary parameter. Below the first branching point, which imposes a maximum value for the electric intensity, one may use a series expansion of the Mathieu's functions to derive the corresponding wave functions and the conserved current density components. Finally, we obtain a nontrivial quantization law of the longitudinal momentum, pz.

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