Modelling of impedance‐loaded wire frequency‐selective surfaces with tunable reflection and transmission characteristics

In this paper an efficient means to control the reflection and transmission characteristics of wire‐based frequency‐selective surfaces (FSS) using linear‐lumped impedance loading is presented. We show that by varying the topology of the RLC loading circuits and the component values it is possible to control the resonance frequency of the array as well as its angular characteristics. We discuss several examples, particularly a switchable dual band bandpass filter and enhancement of FSS angle‐of‐arrival properties. The analysis is based on the self‐consistent solution of thin wire Hallen's type integral equation solved by Galerkin's method. The periodic Green's function in the kernel of integral equation has been accelerated using the Ewald transformation, which leads to a highly accurate and efficient numerical procedure. Copyright © 2008 John Wiley & Sons, Ltd.     

Numerical modelling of viscous flow in silicon thermal oxidation with the boundary element method

This paper describes the application of the boundary element method to solving two-dimensional steady slow viscous flow problems (creeping flow) in thermal silicon oxidation. The proposed method used the velocity–pressure formulation. The use of the incompressibility condition as a boundary condition and the application of the second Green's identity to transform the domain integral into a boundary integral result in a system of three boundary integral equations for velocity components and pressure. Solution of this system to be an ill-posed problem because of the presence of boundary conditions of the first kind. Two methods of regularization are employed. The numerical results for trench oxidation process are presented.     

Magnetic current loop as a source model for finite thin‐wire antennas

The paper deals with the concept of magnetic current loop as a source model for finite thin‐wire antennas. The formulation is based on the Pocklington integro‐differential equation with reduced kernel, which is handled by means of various numerical techniques, mostly using the Galerkin–Bubnov variant of Indirect Boundary Element Method. Extensive numerical experiments were carried out on various dipole and monopole antennas using different sources (delta gap, magnetic frill, and magnetic current loop), and results for input admittance are compared with measured data. The magnetic current loop source ensures accurate solution for input admittance. Copyright © 2014 John Wiley & Sons, Ltd.     

Modeling the superconducting effects on resonance and radiation characteristics of a cylindrical-rectangular microstrip antenna covered with a dielectric layer

In this work, the resonance and radiation characteristics of a superconducting cylindrical-rectangular microstrip antenna covered with a dielectric layer are studied using an electric field integral equation and the spectral-domain Green’s function. The effect of superconductivity of the patch is modeled by including surface complex impedance in the formulation. In order to validate the present method, numerical results for the cylindrical microstrip antenna with a perfectly conducting patch are presented and very good agreement has been demonstrated between our computed data and those found in the literature. Once the validity of the method is checked, the effect of the superconducting patch on resonance frequency, half-power bandwidth and radiation pattern of cylindrical rectangular microstrip patch is studied. It is found that the resonant frequency is affected significantly by the superconductivity property of the patch and the half-power bandwidth is considerably increased, which improves the narrow bandwidth characteristics of the microstrip structure. Further results show that a thin superconductor patch has a significant effect on the E-plane radiation pattern.     

Self and mutual impedances of a finite length gas-insulated transmission line (GIL)

Starting from three-dimensional integral Freedholm's equation of the second kind with weakly singular kernel we obtain two equations for the complex voltage drops in the phase conductor and the enclosure, respectively. Self and mutual impedances appearing in these equations are expressed in the form of integral relations for any current density distribution. In case of a single-phase GIL of finite length we introduce equations determining these impedances without taking into account skin and proximity effects as well as taking them into consideration. For the case of a three-phase GIL we work out an analytical numerical method of determination of self and mutual impedances of GIL, which takes into account also the so-called ‘outside proximity effect’. We also describe the research post consisting of a single-phase GIL with a return copper plate built in GTH&MT laboratory of GEC ALSTHOM T&D in Villeurbane.     

Novel numerical methods for measuring distributions of space charge and electric field in solid dielectrics with deconvolution algorithm

The deconvolution algorithm for measuring the distribution of space charge under DC by the pressure wave propagation (PWP) method is studied in this paper. A new Fredholm integral equation of the first kind, including a space charge distribution without a partial differential operator is presented. Numerical methods based on Tikhonov regularization for solving this integral equation and the original PWP equation are studied. Numerical simulation is studied for the effect of signal-to-noise ratio (SNR), and comparison with other algorithms is discussed. The numerical solution of an electric field distribution from measurements of a LDPE specimen is obtained successfully.     

Analysis and design of terahertz microstrip antenna on photonic bandgap material

In this paper, a dielectric slab with periodic implantation of the air gaps has been analyzed. An effective dielectric permittivity of the 1-D photonic bandgap substrate material (PBG material) with host material as Polytetrafluoroethylene (PTFE) has been computed at 600 GHz. Based on the extracted effective dielectric permittivity, a rectangular microstrip patch antennas on thin and thick 2-D PBG material as substrate have been designed. The electrical performances of the antennas have been simulated by using two different simulators, CST Microwave Studio based on the finite integral technique and Ansoft HFSS based on the finite element method. This proposed antenna on the PBG material as substrate shows the significant enhancement in the directivity. To validate the homogenized medium approximation, the effect of the antenna position on the substrate material has been observed. The response of antenna has been found to be independent of its position. Various electrical parameters of the proposed antennas have been compared with reported literature. In addition to this, the operating frequency of one of the antenna has been scaled down by the factor of 50 and its various results have been compared with the results obtained at 600 GHz.     

Event-triggered integral sliding mode control of Takagi-Sugeno fuzzy stochastic systems

This article analyzes the integral sliding mode control (ISMC) problem for the nonlinear stochastic system by employing the fuzzy approach. Firstly, the Takagi-Sugeno (T-S) fuzzy stochastic model with unknown nonlinear function and external disturbance has been developed. Based on the fuzzy model, an observer-based integral sliding mode fuzzy controller is derived under the event-triggered scheme (ETS). The Lyapunov-Krasovskii functionals (LKFs) involving double and triple integral terms are considered and evaluated by applying Writinger inequality lemma and reciprocally convex combination lemma. With the help of matrix's singular value decomposition lemma, the stability conditions have been derived which is in terms of linear matrix inequalities (LMIs) and this can be solved by MATLAB LMI toolbox. Two numerical examples are provided to demonstrate the usefulness of our theoretical conclusions.     

A comparison of numerical methods for the full‐wave analysis of flange mounted rectangular apertures

The analysis and design of small‐ and medium‐sized aperture antenna arrays is an important task in the development of many microwave systems, and is computationally heavy due to the typical requirements for efficiency and accuracy. Several approaches have already been proposed in the literature, but they have not been compared so far in terms of their computational efficiency. In this paper, we compare different methods, either based on rectangular waveguide modes to expand the field over the aperture, or based on Gegenbauer's polynomials for singular fields representation. Their numerical properties are studied, and their performance compared. It is concluded that similar accuracies are achieved, whilst the approach using the spectral‐domain rectangular waveguide mode formulation is the more robust, and should be considered for the development of general purpose software packages. Copyright © 2000 John Wiley & Sons, Ltd.     

Symbolic approach to inverse problems in method of moments

Symbolic computational systems introduce some unique features in computational engineering. There have been several papers published on the solution of differential equations under given boundary conditions by symbolic systems. The finite element formalism has received prime attention in the course of development of symbolic computation in engineering. The main idea has been to develop a symbolic FEM package to reduce the burden of manual algebra, eliminate errors introduced by numerical quadrature, and improve the efficiency of element generation. This work discusses a symbolic solution to electromagnetic linear antenna problems. The solution is a method of moments that transforms Pocklington's integral equation to a matrix equation. The symbolic system is used to produce (1) analytical integration, (2) the parametric expression for the input impedance and (3) computational code for forward and reverse problem of the input impedance.     

热脉冲法数据处理的反问题求解研究

应用热脉冲法测量聚合物薄膜电介质内空间电荷分布的数据分析过程涉及第一类Fredholm积分方程,过往先求解电场分布后微分的传统做法,会使反问题求解的不适定性带来的误差进一步放大。该文提出一种用于热脉冲法数据分析中反问题求解的直接计算空间电荷分布方法。结合一维热传导方程,推导得到了能够直接求解获取空间电荷分布的热响应电流方程。以Tikhonov正则化与尺度变换法2种数值求解算法为例,研究了不同信噪比对热脉冲法测量方法中直接计算电荷分布结果的影响,并讨论了2种数值算法直接进行空间电荷分布计算的优缺点。仿真结果表明,应用2种数值方法对含有一定噪声的数据处理时,直接计算空间电荷分布的方式相较于传统对电场分布微分的方式而言,能够很好地克服第一类Fredholm积分方程的不适定性,使解分布曲线中的振荡减少,且对仿真电流信号的噪声敏感程度更低,能更好地契合预设分布曲线,提高了空间电荷计算结果的准确性。     

A new polynomial approach to the numerical solution of thin cylindrical antenna problem

Contents This paper is aimed at providing a new method of the numerical solution of the Hallén's equation for the thin cylindrical antenna. Essentially, the method is a combination of the well known polynomial approximation for the current distribution along the antenna and a semi-polynomial approximation for the kernel in the Hallén's equation which leads to integrals in closed form suitable for the rapid and accurate numerical calculations.

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Übersicht Dieser Aufsatz setzt sich das Ziel, eine neue Methode zur numerischen Lösung der Hallén'schen Gleichung für die dünne zylindrische Antenne zu geben. Im Wesentlichen ist die Methode eine Kombination der wohl bekannten Polynom-Approximation für die Stromverteilung entlang der Antenne und einer teilweisen Polynom-Approximation für den Kern der Hallén'schen Gleichung, welche auf Integrale in geschlossener Form und damit rasch zur genauen zahlenmäßigen Lösung führt.

     

Hybrid spatial‐spectral MoM analysis of microstrip structures

In this paper, a new hybrid method formulation to resolve the mixed potential integral equation in an efficient and a fast approach, which is based on a simultaneous formulation in both spatial and spectral domains, is proposed. The entries of the method of moments matrix are then given by the sum of two integrals. The first one is expressed in the spatial domain. This part is analytically evaluated after a development in Taylor series of the exponential terms in the function to integrate. The integrals expressed in the spectral domain have a finite range, and they are calculated using numerical integration. Then the convergence problem is avoided in this approach. A good agreement between the simulated and measured results has been achieved. Copyright © 2015 John Wiley & Sons, Ltd.     

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.     

涡流无损检测中的广义索末菲尔德积分快速计算

广义索末菲尔德(Sommerfeld)积分的快速准确计算是涡流无损检测数值仿真的重要研究内容之一。对于积分核中含有2个贝塞尔(Bessel)函数乘积的广义Sommerfeld积分,给出一种高效准确的数值算法。通过将原积分核中远谱渐近分量抽出,广义Sommerfeld积分核可表示为具有快速收敛的积分核和渐近积分核2项之和的形式。对于渐近积分核部分,推导了其闭式指数积分表达式;对于快速收敛积分核部分,确定了数值积分的积分上限和对应的积分误差限。数值算例表明,与直接采用数值积分的算法相比,在同等计算精度情况下,该文的方法可提高计算效率10~100倍,该快速算法可应用于了涡流无损检测数值仿真中。     

A constant recursive convolution technique for frequency dependent scalar wave equation based FDTD algorithm

A scalar wave equation based recursive convolution finite-difference time-domain algorithm is developed for a frequency-dependent Debye medium in this paper. This algorithm is based on a recursive evaluation of a convolution integral in the time domain. A numerical example is presented for a problem of wide-band reflection from an air-water interface. The obtained results are compared with an analytical solution. The excellent agreement is observed between the numerical results. Memory and computational time advantages of the proposed method over Maxwell’s equations based solution are also shown.     

双相介质空间含有偏心裂纹的界面圆柱夹杂对SH 波的散射

采用Green函数和“裂纹切割”方法,对全空间双相介质界面上含有偏心径向裂纹的圆柱形弹性夹杂,在入射SH 波作用下的散射情况进行动应力分析。首先,构造所需的 Green 函数表达式;其次,采用“裂纹切割”方法及“界面契合”技术构造理论模型裂纹,然后,根据连续性条件建立第一类Fredholm积分方程组,考虑弱奇异积分方程组可以直接离散及散射波的衰减特性求解此方程组;最后,通过算例,分析裂纹长度、入射波数及介质参数等对裂纹尖端动应力强度因子的影响。     

High Frequency LIMM - A Powerful Tool for Ferroelectric Thin Film Characterization

In this work, the laser intensity modulation method (LIMM) is applied to the investigation of sputtered self-polarized PZT thin films. A previous analytic solution of the LIMM Fredholm integral equation of the first kind by use of the Mellin transform is generalized and limitations of this approach are discussed. The numerically reconstruction of the pyroelectric coefficient profile is based on a eight-layer thermal model. The profile reconstruction was performed using MATLAB software containing algorithms for the inverse solution of the appropriate Fredholm integral equation and a Tikhonov regularization method for stable numerical solutions. Optimized algorithms for thermal parameter determination from the low frequency part of the pyroelectric current spectrum are presented. The impact of thermal parameters on the reconstructed profile was investigated. Monte-Carlo simulations were used for a comparison of different approaches for the regularization parameter estimation.     

Two approaches to transient stability-constrained optimal power flow

Formulation of transient stability-constrained optimal power flow (TSC-OPF) and finding a practical solution for the problem have gained much attention recently. In this paper, two approaches to include transient stability constraints in the OPF problem considering detailed dynamic models for generators and their controls are introduced. The first method is based on the maximum relative rotor angle deviation (MRRAD) of generators which suits systems that have specific requirements on MRRAD. The second method represents the transient stability margin of the system based on generators output power (GOP) and hence does not rely on MRRADs. The transient stability boundary can be represented by a nonlinear function of GOP. The Artificial Neural Network (ANN) curve-fitting tool is used to derive a mathematical formulation for the transient stability boundary (TSB). The closed form representation of the TSB is then inserted in the OPF problem as a new constraint. The proposed method is examined using the WSCC 9-bus, the New England 39-bus and the IEEE 300-bus test systems. The results indicate that the proposed methods lead to lower computational time in solving TSC-OPF which has been a serious challenge for this problem.     

AN ADVANCED BOUNDARY INTEGRAL EQUATION METHOD FOR TWO-DIMENSIONAL ELECTROMAGNETIC FIELD PROBLEMS*

ABSTRACT

The features of an advanced numerical solution capability for two-dimensional electromagnetic field problems governed by Laplace's Equation or, under certain conditions, by Poisson's Equation are outlined. Specifically, the relevant Boundary Integral Equation (BIE) formulation is presented, and a process for numerical solution is given based on assumed piecewise-quadratic variation of the boundary functions over boundary segments which, in turn, are assumed to be piecewise-quadratic curves between nodes. This numerical process based on quadratic assumptions is contrasted with the piecewise-constant or piecewise-linear assumptions which appear more commonly in the literature. A problem involving the forces on the windings in the “window” of a simple core-type transformer is solved for illustration