A robust method for the computation of new closed‐form Green's functions for microstrip structures

A robust approach for the computation of new closed‐form Green's functions is considered to calculate the symmetrical microstrip Green's functions. In this method, the surface‐wave poles are first extracted using a recursive contour integration method. Then, the remainder is approximated by a series of complex exponentials using the Prony's method or the generalized pencil‐of‐function method (GPOF) along the extended rooftop shaped path in k_ρ‐plane. Subsequently, an analytical identity is employed to obtain the new spatial‐domain Green's functions. It is observed that this method can evaluate the spatial‐domain Green's functions accurately and efficiently for both near and far fields. In addition, there is no erroneous results in the near‐field region when z ≠ z′ and ρ → 0. © 2011 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2011.     

An efficient multilayered shielded microwave circuit analysis method based on neural networks

In previous works, a neural network based technique to analyze multilayered shielded microwave circuits was developed. The method is based on the approximation of the shielded media Green's functions by radial‐basis‐function neural networks (RBFNNs). The trained neural networks, substitute the original Green's functions during the application of the integral equation approach, allowing a faster analysis than the direct solution. In this article, new and important improvements are applied to the training of the RBFNNs, which permit a reduction in the approximation error introduced by the neural networks. Furthermore, outstanding time reductions in the analysis of printed circuits are achieved, clearly outperforming the former technique. The main improvement consists on a better processing of the Green's function singularity near the source. The singularity produces rapid variations near the source that makes difficult the neural network training. In this work, the singularity is extracted in a more suitable fashion than in previous works. The functions resulting from the singularity extraction present a smooth behavior, so they can be easily approximated by neural networks. In addition, a new subdivision strategy for the input space is proposed to efficiently train the neural networks. Two practical microwave filters are analyzed using the new techniques. Comparisons with measured results are also presented for validation. © 2010 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2010.     

A new algorithm for the extraction of the surface waves for the Green’s function in layered dielectrics

There exist the complicated waveguide modes as well as the surface waves in the electromagnetic field induced by a horizontal electric dipole in layered lossless dielectrics between two ground planes. In spectral domain, all these modes can be characterized by the rational parts with the real poles of the vector and scalar potentials. The accurate extraction of these modes plays an important role in the evaluation of the Green’s function in spatial domain. In this paper, a new algorithm based on rational approximation is presented, which can accurately extract all the real poles and the residues of each pole simultaneously. Thus, we can get all the surface wave modes and waveguide modes, which is of great help to the calculation of the spatial domain Green’s function. The numerical results demonstrated the accuracy and efficiency of the proposed method.     

A closed‐form analysis of printed wide‐slot antennas

A mixed‐potential integral equation is formulated for the wide‐slot antenna, fed by a microstrip line, and solved using the method of moments (MoM). Our MoM implementation makes use of the Ge and Esselle (G–E) closed‐form Green's functions for layered substrates. The key advantage of this new approach is that all the MoM matrix elements are evaluated using closed‐form expressions, without any numerical integration, and with minimal approximations. Hence a significant increase in computational efficiency has been achieved while maintaining the high precision of the full‐wave MoM. The numerical results obtained from the new method are compared with measured results, and good agreements are observed. © 2003 Wiley Periodicals, Inc. Int J RF and Microwave CAE 13, 389–397, 2003.     

直拉硅单晶非均匀相变温度场最优控制

针对直拉硅单晶固液界面相变温度场的非均匀性导致晶体直径不均匀问题,提出一种基于偏微分方程(PDE)模型的温度场最优控制策略.考虑生长速率波动的影响,建立了一种改进的提拉动力学模型,确定了域边界演化动力学关系.研究基于抛物型PDE的时变空间域对流扩散过程的温度模型,描述了域运动在对流扩散系统上的单向耦合.针对无限维分布参数系统建模控制难问题,采用谱方法进行系统近似,选取整个空间域的全局和正交的空间基函数,通过Galerkin方法对无限维系统进行降维,获得了该系统的近似模型.采用线性二次型方法控制晶体生长温度,通过仿真实验对相变温度场模型进行验证.结果表明,优化后的模型能够获得较为平稳的晶体生长速率,减小了生长直径的波动,使得固液界面径向温度分布更加均匀,验证了该方法的有效性.     

A novel approach for electromagnetic inverse scattering of a two‐dimensional perfect electric conductor object

A two‐dimensional shape determination technique for a perfect electric conductor target using electromagnetic inverse scattering is presented. The proposed algorithm uses the scattered field pattern and an inverse scattering technique derived from Green's function to retrieve the geometry of an unknown target. This method uses the scattering field data over a band of observation points, which is synthesized using frequency domain “method of moment” computational technique. We have verified this algorithm with four different types of numerical examples.     

On integral formulas of the (unit) sphere and their application to numerical computation of integrals

The aim of this paper is the study of integral formulas and methods for optimal numerical approximation of integrals over the (unit) sphere and coefficients being required in connection with series expansions into spherical harmonics. An explicit estimate of the (absolute) error of exact and approximating integral value is given by use of the theory of Green's (surface) functions on the sphere.     

Improved approach to analysis of substrate coupling based on multilayered Green's function

This article presents an improvement on the evaluation of a Green's function method proposed by Niknejad 7 for modeling and analysis of substrate coupling in integrated circuits. By careful combination, the 64‐term summation can be approximated by a four‐term one. Therefore, the computational cost can be reduced. The approximation is effective for contact pairs small compared to their separations. This article also studies quantitatively how small the contact should be in order for approximation to be applicable. Numerical results show that a speed‐up of over 6× could be achieved by adopting the new approach. © 2006 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2006.     

TaBE: Decoupling spatial and spectral processing with Taylor’s unfolding method in the beamspace domain for multi-channel speech enhancement

In recent years, significant advancements have been made in neural beamforming, leveraging spectral and spatial cues to enhance their performance in multi-channel speech enhancement. When the frame-wise processing mechanism is required, there exists a trade-off between performance and algorithmic delay for existing all-neural beamformers. However, from the perspective of multi-source information fusion, the network is often encapsulated into a black box to entangle and fuse the spatial and spectral features into a non-linear feature space, which hinders our understanding of how they work collaboratively for target speech extraction. In this regard, this paper proposes to decouple the spatial and spectral domain processing inspired by Taylor’s approximation theory. Specifically, we reformulate the time-variant beamforming defined in the spatial domain into the adaptive weighting and mixing of different beam components in the beamspace domain. This reformulation enables us to model the recovery of target speech as a weighted sum operation in the beamspace domain, where each beam component is associated with an introduced unknown term for residual interference cancellation. By virtue of Taylor’s series expansion, the recovery process can be decomposed into the superimposition of the 0th-order non-derivative and high-order derivative terms, where the former acts as spatial filtering in the spatial domain, and the latter serves as a residual interference canceller in the spectral domain. We conduct extensive experiments on the spatialized LibriSpeech and L3DAS Challenge datasets. Experimental results show that, compared with existing advanced approaches, the proposed method not only achieves competitive performance in terms of multiple objective metrics but also provides feasible guidance in multi-channel speech enhancement pipeline design.     

On the effect of ground‐plane thickness on an aperture‐coupled dielectric resonator antenna

A hemispherical dielectric resonator antenna excited by a microstrip feedline through a narrow slot in a thick ground plane is studied theoretically and experimentally. A numerical method based on a combination of the spectral Green's function, modal Green's function, and the method of moment is used to investigate the input characteristics of the dielectric resonator antenna system. The effects of ground‐plane thickness on input resistance, resonant frequency, and impedance bandwidth of the dielectric resonator antenna are discussed. © 2000 John Wiley & Sons, Inc. Int J RF and Microwave CAE 10: 271–277, 2000.     

Adaptive output feedback tracking control of stochastic nonlinear systems with dynamic uncertainties

In this paper, adaptive output feedback tracking control is developed for a class of stochastic nonlinear systems with dynamic uncertainties and unmeasured states. Neural networks are used to approximate the unknown nonlinear functions. K‐filters are designed to estimate the unmeasured states. An available dynamic signal is introduced to dominate the unmodeled dynamics. By combining dynamic surface control technique with backstepping, the condition in which the approximation error is assumed to be bounded is avoided. Using It ô formula and Chebyshev's inequality, it is shown that all signals in the closed‐loop system are bounded in probability, and the error signals are semi‐globally uniformly ultimately bounded in mean square or the sense of four‐moment. Simulation results are provided to illustrate the effectiveness of the proposed approach. Copyright © 2014 John Wiley & Sons, Ltd.     

Full-wave spectral-domain analysis for open microstrip discontinuities of arbitrary shape including radiation and surface-wave losses (invited paper)

This article is a survey of the theoretical background for full-wave spectral-domain analysis of open microstrip discontinuities of arbitrary shape. The spectral-domain dyadic Green's function, which takes into account all the physical effects, such as radiation and surface waves, is used to formulate an electric field integral equation. The method of moments is then employed to find the current distribution on the microstrips, and subsequently, the scattering parameters of the junctions. Since all field components can be expressed in terms of the dyadic Green's function and the current distribution, the losses due to both radiation and surface waves are further determined through a rigorous Poynting vector analysis. To model the discontinuities of arbitrary shape, both rectangular and triangular subdomain functions are used as the current expansion functions in the moment method procedure. In addition, the semi-infinite traveling wave functions are applied to simulate the feeding structure and isolate individual junction effects. Several examples are demonstrated to illustrate the utility of different techniques in this analysis. Comparison of some numerical results with available experimental data shows excellent agreement. Finally, this approach is most natural for the characterization of 3-D integrated circuits and the design of printed antennas including excitation circuit effects. © 1992 John Wiley & Sons, Inc.     

Fusion of multispectral and panchromatic satellite sensor imagery based on tailored filtering in the Fourier domain

A new methodology for fusing satellite sensor imagery, based on tailored filtering in the Fourier domain is proposed. Finite‐duration Impulse Response (FIR) filters have been designed through an objective criterion, which depends on source image characteristics only. The designed filters allow a weighted fusion of the information contained in a fine spatial resolution image (PAN) and in a multispectral image (MULTI), respectively, establishing a trade‐off between spatial and spectral quality of the resulting fused image. This new technique has been tested with Landsat Enhanced Thematic Mapper Plus (ETM+) imagery. Spatial and spectral quality of the fused images was compared with the results provided by Mallat's Wavelet algorithm. The images fused by the proposed method were characterized by a spatial resolution very close to the PAN image, and by the spectral resolution of the MULTI image.     

Family of quadratic spline difference schemes for a convection–diffusion problem

We consider the finite difference approximation of a singularly perturbed one-dimensional convection–diffusion two-point boundary value problem. It is discretized using quadratic splines as approximation functions, equations with various piecewise constant coefficients as collocation equations and a piecewise uniform mesh of Shishkin type. The family of schemes is derived using the collocation method. The numerical methods developed here are non-monotone and therefore apart from the consistency error we use Green's grid function analysis to prove uniform convergence. We prove the almost first order of convergence and furthermore show that some of the schemes have almost second-order convergence. Numerical experiments presented in the paper confirm our theoretical results.     

A BMI approach for ℋ︁∞ gain scheduling of discrete time‐varying systems

The problem of gain‐scheduled state feedback control for discrete‐time linear systems with time‐varying parameters is considered in this paper. The time‐varying parameters are assumed to belong to the unit simplex and to have bounded rates of variation, which depend on the values of the parameters and can vary from slow to arbitrarily fast. An augmented state vector is defined to take into account possible time‐delayed inputs, allowing a simplified closed‐loop analysis by means of parameter‐dependent Lyapunov functions. A gain‐scheduled state feedback controller that minimizes an upper bound to the ??_∞ performance of the closed‐loop system is proposed. No grids in the parametric space are used. The design conditions are expressed in terms of bilinear matrix inequalities (BMIs) due to the use of extra variables introduced by the Finsler's lemma. By fixing some of the extra variables, the BMIs reduce to a convex optimization problem, providing an alternate semi‐definite programming algorithm to solve the problem. Robust controllers for time‐invariant uncertain parameters, as well as gain‐scheduled controllers for arbitrarily time‐varying parameters, can be obtained as particular cases of the proposed conditions. As illustrated by numerical examples, the extra variables in the BMIs can provide better results in terms of the closed‐loop ??_∞ performance. Copyright © 2009 John Wiley & Sons, Ltd.     

一种分数阶微积分算子的有理函数逼近方法

基于有理函数逼近理论, 提出了一种分数阶微积分算子s域最佳有理逼近函数的构造方法. 详细讨论了构造最佳有理逼近函数的思路、方法及具体算法. 运用最佳有理逼近定义及特征定理, 对所构造的分数阶积分算子最佳有理逼近函数进行了验证. 其结果表明:该分数阶微积分算子最佳有理逼近函数构造方法是有效的, 且对确定的逼近误差及逼近频带, 所构造的最佳有理逼近函数能够以最低阶次取得最佳逼近特性.     

Multipole-accelerated capacitance computation for 3-D structures in a stratified dielectric medium using a closed-form Green's function

In this article, the capacitance matrices of three-dimensional conducting structures embedded in a stratified dielectric medium are computed by using the fast muitipole method in conjunction with a closed-form approximation of the appropriate Green's function. Image charges that result from the employment of this Green's function are incorporated into the fast multipole method. This technique is used to accelerate the iterative generalized minimal residual-based solution of the system of equations generated by the method of moments. This yields the charge distributions on the conductors and thereby the required capacitance matrix. It is shown that the use of this technique typically results in a speedup of more than an order of magnitude over iterative and direct methods without a compromise of the numerical accuracy.     

Generalized Jacobi Rational Spectral Method and Its Applications

We introduce an orthogonal system on the whole line, induced by the generalized Jacobi functions. Some results on the generalized Jacobi rational approximation are established, which play important roles in the related spectral methods. As examples of applications, the rational spectral schemes are proposed for sine-Gordon, Klein-Gordon and Fisher equations, with the convergence analysis. Numerical results demonstrate their efficiency.     

Observer‐based decentralized adaptive control for large‐scale pure‐feedback systems with unknown time‐delayed nonlinear interactions

This paper presents an approximation design for a decentralized adaptive output‐feedback control of large‐scale pure‐feedback nonlinear systems with unknown time‐varying delayed interconnections. The interaction terms are bounded by unknown nonlinear bounding functions including unmeasurable state variables of subsystems. These bounding functions together with the algebraic loop problem of virtual and actual control inputs in the pure‐feedback form make the output‐feedback controller design difficult and challenging. To overcome the design difficulties, the observer‐based dynamic surface memoryless local controller for each subsystem is designed using appropriate Lyapunov‐Krasovskii functionals, the function approximation technique based on neural networks, and the additional first‐order low‐pass filter for the actual control input. It is shown that all signals in the total controlled closed‐loop system are semiglobally uniformly bounded and control errors converge to an adjustable neighborhood of the origin. Finally, simulation examples are provided to illustrate the effectiveness of the proposed decentralized control scheme. Copyright © 2013 John Wiley & Sons, Ltd.     

Efficient and Accurate Computation of Electric Field Dyadic Green’s Function in Layered Media

Concise and explicit formulas for dyadic Green’s functions, representing the electric and magnetic fields due to a dipole source placed in layered media, are derived in this paper. First, the electric and magnetic fields in the spectral domain for the half space are expressed using Fresnel reflection and transmission coefficients. Each component of electric field in the spectral domain constitutes the spectral Green’s function in layered media. The Green’s function in the spatial domain is then recovered involving Sommerfeld integrals for each component in the spectral domain. By using Bessel identities, the number of Sommerfeld integrals are reduced, resulting in much simpler and more efficient formulas for numerical implementation compared with previous results. This approach is extended to the three-layer Green’s function. In addition, the singular part of the Green’s function is naturally separated out so that integral equation methods developed for free space Green’s functions can be used with minimal modification. Numerical results are included to show efficiency and accuracy of the derived formulas.