Scattering characteristics of FSS comprised of L-shaped and one-turn helix shaped conductors for TE and TM excitation

The boundary value problem of doubly infinite periodic conductor arrays of L-shape and one-turn helix shape frequency selective surfaces (FSSs) backed by dielectric substrate are investigated by using modal expansion method. The moment method is employed by expressing the current induced on the metallic surfaces in terms of Piecewise Sinusoidal (PWS) functions. The variation of the reflection and transmission coefficients versus frequency for dielectric backed FSS is investigated for both transverse electric and transverse magnetic wave excitations at normal incidence. Reflection coefficients of dielectric backed FSS at normal and oblique incidence are plotted against frequency. The correctness of the algorithm is ensured by comparing the numerical results with the experimental results in the literature for an FSS composed of strips and proved to be as good. Tel.: +90-342-3601200 ext: 2131     

二维时变电磁场问题中涡流的约束

对于二维正弦电磁场问题,由于电源电流密度是一个未知的复常数,加上边界条件中向量磁位不易给定,因此需要对载流导体中的总电流进行约束,才能得到磁密和电密的唯一、正确解.本文对二维积分方程法和有限元法中涡流的约束方法进行了研究.对有限元法,根据问题的性质,又分成给定电流的多导体系统,串联约束和并联约束等三种情况,对每种情况都给出了定解方程和相应的离散格式.     

Ermittlung des elektromagnetischen Feldes von Mehrleiteranordnungen mit kreiszylindrischer Geometrie der Einzelleiter

Übersicht Das elektromagnetische Feld läßt sich im TEM-Fall in einer beliebigen Transversalebene aus einer Partikulärlösung der Poissongleichung, dem Coulomb-Integral, bestimmen. Im Falle kreiszylindrischer Leiter entsteht ein lineares Gleichungssystem zur Bestimmung der Fourierkoeffizienten der unbekannten Oberflächenstromdichteverteilungen bei gegebenen Leiterspannungen. Mit den Fourierkoeffizienten kann auch die Feldverteilung außerhalb der Leiter bestimmt werden. Die elektrischen und magnetischen Feldlinien werden mit Hilfe von Potentialfunktionen dargestellt. Als Beispiel werden die elektromagnetischen Felder von Grundanregungen der geschirmten symmetrischen Dreileiteranordnung in der Transversalebene betrachtet.

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Electromagnetic field investigation of multiconductor transmission lines by means of circular cylindrical conductors

Contents The TEM-field is determined by means of Coulombintegral, as a particular solution of Poisson's equation. After Fourier series expansion a linear equation system relates the Fourier coefficients of the surface current density on the circular cylindrical conductors to the applied voltage excitations on the conductors. The Fourier coefficients are required for determining the field distribution outside conductors. Then, by means of potential functions the electric and magnetic field distributions through flux lines are also obtained. For instance, the electromagnetic fields for some excitations of the shielded balanced three-conductor transmission line in transverse plane are considered.

     

Electromagnetic scattering from conductor-coated material bodies

A moment method solution is presented to compute electromagnetic scattering from material bodies. The bodies are supposed to be homogeneous, arbitrarily shaped and lossy; they can be coated with very thin perfect conductors in some parts. A formulation of the scattering problem is made in terms of the equivalent surface current densities for which mixed potentials are used. The equivalent currents are expanded in the space-domain by a triangular expansion function on the triangulated surfaces of the scatterer. The Galerkin procedure is carried out to test boundary integral equations and reduce the functional form of the equations to a partitioned matrix equation. The solution is applied to the scattering problem of a dielectric slab, a thin conductor coated by absorber material and a rectangular patch on a grounded dielectric slab. The computed backscattering radar cross-section and surface current densities of the structures are presented and some of the results are compared with experimental data.     

Modelling of electromagnetic wave penetration through loaded apertures

Calculation of the electromagnetic field diffracted by an aperture situated in a perfectly conducting ground plane can be made through the well-known theory of polarizabilities. However, simple expressions are only obtained under conditions which are not often fulfilled in electromagnetic compatibility problems since, for example, the disturbing field incident on the aperture must be considered as a uniform one. Furthermore, if the aperture is loaded by a low conducting material, available approximate formulas are only valid for a small circular hole. In this paper, we present a numerical approach based on the determination of the equivalent magnetic current distributed on the surface of the aperture. This distribution is the solution of an integral equation solved by the method of moments. This formulation allows us to take the surface impedance of a loading material and the contact resistance between this material and the rim into account. The validation of the computer code is shown by comparing computed and analytical results on some typical examples. Few applications are also described.     

Theoretical investigation on skin effect factor of conductor in power cables

This paper describes a newly derived theoretical equation on the skin effect factor of power cables, and its application to large‐size OF and XLPE cables with segmental conductors, including insulated wires. The skin effect factors calculated with the new equation were fit very well to measurements in a wide range of conductor sizes. In the new equation, the important factor which characterizes the skin effect of segmental conductors is the “equivalent conductivity ratio” v defined by the ratio of longitudinal conductivity in axial direction of conductor to conductivity of conductor wires. Since the obtained ratio v in XLPE cable was three times greater than that in OF cable, the larger longitudinal eddy current passing from a wire to another increased the eddy current loss in conductor, which increased the conductor loss of XLPE cable. The new equation enables us to investigate quantitatively the dominant loss component affecting the skin effect factor. Then, the skin effect factors and coefficients for OF and XLPE cables were investigated with the new equation. It was revealed that the best number of separation, in which the skin effect reached a minimum, existed in OF and XLPE cables with segmental conductors. In addition, it was confirmed that the skin effect coefficients ks1 calculated with the new equation were very consistent with those used in JCS. © 2008 Wiley Periodicals, Inc. Electr Eng Jpn, 165(1): 18–34, 2008; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.20576     

On the Use of the Potential Integral for Determining the Fields of Physical Radiating Structures

It appears to be common practice in almost all introductory texts in electromagnetic theory to introduce radiation by means of "currents" in free space, rather than on a conducting structure. Then the assumption is made, often implicitly, that the results are applicable to currents on conductors. Two questions then arise: What justification is there for using a potential integral for inhomogeneous media? How can a metallic structure radiate energy (from what appears to be a distributed source along the antenna) when it has zero tangential electric field? In contrast to this unsatisfying approach, the authors develop in this paper a potential integral for the conductor problem which contains the unknown, but measurable, current on the conductor. The integral is identical in form to the one commonly used for currents in free space, but the meaning of all terms is now clear, and the assumption that the free-space potential integral is applicable to the conductor problem is shown to be unnecessary. Finally, the authors show that an appealing viewpoint on the concept of energy being radiated from each point on the antenna is that primary radiation is from the feed gap alone and that the antenna structure acts as a scatterer or reradiator.     

Modeling and optimization of radiation characteristics of triangular superconducting microstrip antenna array

This paper presents a mathematical model of array of equilateral triangular superconducting microstrips implanted in multilayered substrates. The full-wave method is used to calculate the radiation characteristics of equilateral triangular microstrip antennas. In this method, the electric field integral equation for a current element on a grounded dielectric slab of infinite extent is developed by basis functions. An improved analytical model is presented taking into account anisotropic substrates, superconducting material for the triangular patch and multilayered structure. The swarm particle optimization is used to determine an optimum set of excitation and position of the antenna element that provides a radiation pattern with maximal side lobe level reduction. The computed data are found to be in good agreement with results obtained using other methods.     

Efficient modelling of curved surfaces by planar patches and wire grids for electromagnetic scattering

The scattering of conducting regular polyhedrons of resonant size is studied by means of the electrical field integral equation (EFIE) and the method of moments (MoM). Two models are generated for each polyhedron, a wire grid model and a triangular patch model. Two numerical codes associated with those modelling techniques are used to obtain the radar cross section (RCS) of the polyhedrons. The calculated results are compared with the analytical results of the scattering of a perfectly conducting sphere. Practical criteria relating geometric properties of the sphere and the polyhedrons are investigated for the modelling of curved surfaces by facets in electromagnetic simulations.     

剪切波在周期裂纹界面上的反射和折射

研究了剪切波在周期裂纹界面上的反射和折射问题 ,根据问题的周期性 ,利用Fourier级数将该混合边值问题归结为一组Hilbert型的奇异积分方程 ,同时推导出散射波位移折射反射系数。通过数值求解奇异积分方程 ,计算了折反射系数 ,结果发现 :反射、折射系数受频率、入射角、裂纹周期、裂纹长度、材料组合等诸多因素影响 ,同时 ,折反射系数曲线在某些很窄的频率域内有陡升和陡降现象。     

Electromagnetic scattering from thin strips. I. Analytical solutions for wide and narrow strips

Electromagnetic scattering from thin resistive strips is formulated using an integral equation approach. Analytical expressions for the electric current density over wide and narrow strips are derived based on the physical optics and quasistatic approximation of the pertinent integral equations, respectively. The solutions are used to find closed form expressions for the echo width of the strip.     

A method for the design of MRI radiofrequency coils based on triangular and pulse basis functions

This paper presents a numerical technique for the design of an RF coil for asymmetric magnetic resonance imaging (MRI) systems. The formulation is based on an inverse approach where the cylindrical surface currents are expressed in terms of a combination of sub-domain basis functions: triangular and pulse functions. With the homogeneous transverse magnetic field specified in a spherical region, a functional method is applied to obtain the unknown current coefficients. The current distribution is then transformed to a conductor pattern by use of a stream function technique. Preliminary MR images acquired using a prototype RF coil are presented and validate the design method.     

A method for the design of MRI radiofrequency coils based on triangular and pulse basis functions.

This paper presents a numerical technique for the design of an RF coil for asymmetric magnetic resonance imaging (MRI) systems. The formulation is based on an inverse approach where the cylindrical surface currents are expressed in terms of a combination of sub-domain basis functions: triangular and pulse functions. With the homogeneous transverse magnetic field specified in a spherical region, a functional method is applied to obtain the unknown current coefficients. The current distribution is then transformed to a conductor pattern by use of a stream function technique. Preliminary MR images acquired using a prototype RF coil are presented and validate the design method.     

干式变压器箔绕导体三维涡流场与附加损耗的数值仿真研究

针对干式变压器箔绕导体具有面积大、厚度薄和激励与感应电流共存的特点分析,建立了绕组三维涡流场与等效电路计算模型,并利用场—路耦合方法对铜箔和铝箔两个方案的绕组涡流场、短路阻抗与附加损耗等性能参数进行了数值验证和优化分析.计算结果表明了方法的合理性,并由此获得了绕组漏磁场、导体涡流损耗分布规律和优化设计方案,为干式变压器设计和预防局部过热提供了一种有效的分析方法.     

神经网络预测应用于横向磁通感应加热中涡流场与温度场的有限元分析

利用神经网络预测横向磁通感应加热中连续运动金属薄板表面涡流分布和温度分布。所采用的两条神经网络中，一条对涡流场分布进行预测，另一条对温度场分布进行预测。在抽取的检测样本中，预测温度分布的相对误差平均值为1．6～3．2％，以神经网络预测结果作为非线性有限元离散方程组迭代求解的初值，比薄板初始温度作为初值的情况节省55．6～67．6％的迭代次数。     

变压器导体中涡流损耗的数值计算

导体中的涡流损耗可以用求解二维正弦涡流方程的办法来算出。本文通过数值计算,给出工程上常用的一些不同尺寸比的导体在均匀磁场和直线分布的磁场内的涡流损耗曲线;并且探讨了处于实际变压器漏磁场中导体涡流损耗的算法,得出了需加电流约束的导体范围,为实际工程计算提供了依据。     

地面上方水平载流导体空间辐射场的快速计算

地面上方水平载流导体产生的空间辐射电磁场的计算是电磁兼容研究的基础问题之一,其本质是广义索末菲尔德积分的计算.提出一种由抽取积分函数渐近项的方法快速求解广义索末菲尔德积分的计算方案,借助指数积分得到了广义索末菲尔德积分渐近项的闭式解.通过数值算例验证了该计算方案的正确性,而且该方案相比直接积分方法,可提高计算效率达3倍以上.文章最后计算了一段水平载流导体产生的空间辐射场,并且通过和Bannister近似公式比较,说明了该方法对索末菲尔德积分的参数无特殊要求,是一种通用的计算方法.     

复镜像法在平板导体涡流场计算中的应用

为了根据涡流检测中积分方程法(IEM)的理想裂缝模型,用矢量磁位推导出平板导体涡流场的并矢格林函数,将复镜像法用于涡流场并矢格林函数的计算,用Prony方法对矢量磁位中广义Sommerfeld积分(GSI)的被积函数进行指数逼近,使GSI转化为有限项级数之和,加速了无穷积分的计算,提高了涡流场的求解速度和计算精度。用涡流无损检测中的两组典型数据比较用复镜像法和直接数值积分法计算广义Sommerfeld积分的计算精度和求解速度,结果表明复镜像法在涡流场GSI积分计算中准确且高效。用复镜像法计算平板导体中含有平行裂缝和十字型裂缝的涡流场,其结果与有限元一边界元耦合法的计算结果对比表明求解方法正确和高效。     

积分方程与解析法组合计算薄钢板的涡流损耗

介绍了采用将数值与解析联合起来计算矩形导电媒质涡流损耗的方法。首先利用积分方程法求出磁介质表面网格点的入射磁密,然后对这些任意分布的离散磁密点用双重傅立叶级数进行逼近,最后计算涡流损耗。通过验证,计算值与测量值吻合很好,证明了该方法的可行性。     

Comparison of zeroth-order and harmonic expansion calculation of the electrostatic parameters of three-conductor bundles

An electrostatic field analysis of three-conductor bundles in triangular and flat (coplanar) configurations above ground is presented. The two configurations are compared from the viewpoint of bundle-to-ground capacitance, geometric mean radius, surface charge distributions, and electric field strength. Approximate results, neglecting proximity effects are firstly obtained considering a zeroth-order approach for the potential coefficient matrix. Accurate results are determined by application of the harmonic expansion method in order to correctly deal with proximity effects between individual conductors of the bundle. The latter approach yields significantly increased values for the electric field strength at certain points along the circumference of the individual conductors of the bundle. It is shown that the triangular configuration is more effective as far as corona problems are concerned.