Waveguide Modes Via an Integral Equation Leading to a Linear Matrix Eigenvalue Problem (Correction)

After having examined the above paper, we noticed that the symbol of principal value in integral is inappropriate. In fact, integral can represent the field on sigma only in the limit as the observation point approaches sigma. This oversight, however, does not affect the theory at all.     

波导本征值问题的多极理论分析

本文利用多极理论分析波导本征值问题.给出用多极理论分析波导本征值问题的使用规则和实施方法.实例计算结果表明,用多极理论分析波导本征值问题,不仅具有较高的计算精度,而且可以很方便地应用于波导工程问题的设计与计算,多极理论是一种有效的波导本征值分析方法.     

Waveguides of Arbitrary Cross Section by Solution of a Nonlinear Integral Eigenvalue Equation

The problem of electromagnetic wave propagation in hollow conducting waveguides of arbitrary cross section is formulated as an integro-differential equation in terms of fields at the waveguide boundary. Cutoff wave numbers and wall currents appear as eigenvalues and eigenfunctions of a nonlinear eigenvalue problem involving an integro-differential operator. A variational solution is effected by reducing the problem to matrix form using the method of moments. A specific solution of the problem is developed using triangle expansion functions in the method of moments. The solution is simplified by symmetry considerations and is implemented by two digital computer programs. Listings and full documentation of these programs are available. This solution yields accurate determinations of cutoff wave numbers, wall currents, and distributions of both longitudinal and transverse modal field components for the first several modes. Illustrative computations are presented for the single-ridge waveguide, which has a complicated boundary shape that does not lend itself to exact solution.     

非对称单脊波导的积分方程法分析

基于积分方程法的分析途径，本文提出计算任意截面柱形金属波导中主模和高次模的特征值和特征向量的数值方法。本文运用此方法对非对称单脊波导进行了深入的理论和实验研究，给出了该种波导的本征值、电中心线偏移量、壁电流分布、带宽特性、损耗和功率容量等的理论计算结果，这些结果对非对称单脊彼导共线裂缝阵天线单元设计有较高的实用价值。     

Evaluation of Modes in Dielectric Resonators Using a Surface Integral Equation Formulation

A moment method solution procedure for rotationally symmetric dielectric bodies has been applied to isolated cylindrical dielectric resonators, and the frequencies, as well as Q factors due to radiation, have been determined for several of the lowest modes, including those of hybrid type.     

Matrix Description of Waveguide Discontinuities in the Presence of Evanescent Modes

The properties of the impedance and scattering matrix describing waveguide discontinuities are examined; both propagating and evanescent modes are considered. It is shown how different normalization conditions for the normal mode solutions in the guide affect the impedance matrix. A suitable choice of normalization always leads to a symmetric imaginary impedance matrix for a lossless structure. The scattering matrix is no longer symmetric or unitary.The simple relationship S=(Z- U)(Z+U)/sup -1/ is shown to hold only under special normalization conditions. Next the matrices describing a plane of lossless obstacles arranged in a periodic array are examined. A different type of normalization condition must be used here, since the normal modes are orthogonal in the conjugate sense (biorthogonal). Although the structure is reciprocal, none of the matrices is symmetric. A suitable normalization leads to a skew-hermitian impedance matrix and to a unitary submatrix of the scattering matrix corresponding to propagating modes.     

Numerical Solutions of the Integral Equation for Excitation-Transmission-Radiation of the Beam Waveguide

The numerical method of the Integral Equation has been used to model the electromagnetic excitation, transmission, and radiation problems of the beam waveguide. The Mode Matching Method has been used to describe the impedance matching situation at the exciting aperture of the waveguide. The excitation conditions were established based on the expansion of the waveguide modes and the continuity of the tangential components of the fields. The volume-surface integral equations combined with the equavalence principle have been used to model the wave transmission in the beam waveguide. The numerical solutions of the electromagnetic transmission and aperture radiation of the waveguide have been given by using the Multilevel Fast Multipole Algorithm (MLFMA). It has been demonstrated that the method proposed by this paper is able to provide the efficient and accurate numerical solution for the excitation, propagation and radiation problems of the beam waveguide with arbitrary shape and electrically large size.     

Eigenvalue Distributions of Sums and Products of Large Random Matrices Via Incremental Matrix Expansions

This paper uses an incremental matrix expansion approach to derive asymptotic eigenvalue distributions (a.e.d.s) of sums and products of large random matrices. We show that the result can be derived directly as a consequence of two common assumptions, and matches the results obtained from using - and -transforms in free probability theory. We also give a direct derivation of the a.e.d. of the sum of certain random matrices which are not free. This is used to determine the asymptotic signal-to-interference-ratio of a multiuser code-division multiple-access (CDMA) system with a minimum mean-square error linear receiver.     

求解波导问题FEM线性系统的RIC预条件算法

提出了一种新型RIC预条件COCG迭代技术,用于改善有限元法仿真分析光电工程问题所产生的高度非正定的线性系统的迭代求解.提出的RIC预条件子是针对基本IC算法可能出现的分解崩溃问题,通过对主元进行加强来获得稳定的分解过程,进而产生高效的预条件子.数值试验表明,提出的RIC预条件子不仅能有效避免COCG迭代等方性崩溃,而且比常用的预条件子更高效;此外,RIC对其他若干Krylov子空间迭代法求解性能的改善作用也相当明显.     

基于面片拼接的等几何分析方法求解波导本征值问题

基于NURBS的等几何分析方法集成了计算机辅助设计(CAD)和有限元方法的优点,CAD模型、网格划分和数值仿真均采用同样的几何描述.然而,由于单个NURBS曲面片拓扑的局限性,单片等几何分析方法难以处理介质分布不均匀以及截面形式复杂的多连通区域问题.本文基于面片拼接,将等几何分析方法用来求解此类问题的波导本征值.细分前后,NURBS曲面片拼接处的控制点和网格必须匹配.通过Galerkin法来离散波导本征值问题的Helmholtz控制方程,计算结果表明该方法具有自由度消耗小、精度高、收敛速度快等优点.     

Hybrid Modes in a Square Corrugated Waveguide

By using two scalar eigenfunctions, electric and magnetic fields in the rectangular (or square) corrugated waveguide are analyzed. In a rectangular corrugated waveguide, the boundary conditions on two corrugated and two smooth walls can be satisfied to excite the hybrid mode. In a highly oversized waveguide where the wavelength of dominant mode is close to that in vacuum, two smooth walls can be exchanged with the corrugated walls because the boundary condition at those walls is satisfied approximately. The replacement is possible due to almost no penetration of the electromagnetic fields into the gap of the replaced walls when the direction of main electric field is parallel to the gap of replaced walls. This characteristic enables us to rotate the polarization of the hybrid mode in the oversized square waveguide with all four corrugated walls and is applicable to the remote steering antenna for electron cyclotron heating in the ITER.     

Computation of Approximate Polynomial Solutions to TE Modes in an Arbitrarily Shaped Waveguide

Computer programs have been developed to investigate the construction of polynomial approximations to H-modes in empty guide of arbitrary shape. Mathematically this corresponds to the approximate solution of the Helmholtz equation with homogeneous Neumann boundary conditions. The method used is the well-known Rayleigh-Ritz. Both polynomial and piecewise polynomial function spaces have been investigated for several types of waveguide cross section. Particularly good results have been obtained for convexguides.A comprehensive set of H-mode contour plots are presented for four well-known guide sections.     

Extraction of Via-Plate Capacitance of an Eccentric Via by an Integral Approximation Method

An integral approximation method is proposed to extract the via-plate capacitance of an eccentric via in the via hole (anti-pad). An analytical formula is derived for the coaxial capacitance part, which is used as a benchmark to validate the integral approximation method. Furthermore, numerical simulations are also used to validate the method. It is shown that small eccentricity results in only a few percentage increase of the via-plate capacitance, which is helpful in specifying the manufacturing tolerance of via designs.      

An Approximate Wave Equation for an Axially Symmetric Periodic Waveguide

The field problem of wave propagation in a waveguide of periodically varying section is investigated. An orthogonal curvi-linear coordinate system is developed leading to a separable wave equation. As a result, the problem is reduced to solving Hills Equation. The discussion is limited to the case of a waveguide with slowly varying radius but there is some expectation that useful results would be obtained, particularly for axial fields, without this restriction.     

Normal Modes in an Overmoded Circular Waveguide Coated with Lossy Material

The normal modes in an overmoded waveguide coated with a Iossy material are analyzed, particularly for their attenuation properties as a function of coating material, layer thickness, and frequency, When the coating material is not too Iossy, the low-order modes are highly attenuated even with a thin layer of coating. This coated guide serves as a mode suppressor of the low-order modes, which can be particularly useful for reducing the radar cross section (RCS) of a cavity structure such as a jet engine inlet. When the coating material is very Iossy, low-order modes fall into two distinct groups highly and lowly attenuated modes. However, as a/lambda (a = radius of the cylinder; lambda = the free-space wavelength) increases, the separation between these two groups becomes less distinctive. The attenuation constants of most of the low-order modes become small and decrease as a function of lambda/sup 2//a/sup 3/.     

利用矩阵法分析一维非均匀矩形波导的LSE模特性

我们利用矩阵方法建立了一维非均匀填充矩形波导的传播特性方程。在均匀情况下,本方法推出的结果与精确分析解完全一致,并对一些非均匀结构进行了数值计算,给出了一些曲线。     

A Ferrite Boundary-Value Problem in a Rectangular Waveguide

A solution is obtained for the electric field at the air-ferrite interface (z=0) in a rectangular waveguide filled with ferrite in the semi-infinite half (z>0) and magnetized in the direction of the electric field. The field is expressed in terms of a Neumann series obtained by iteration of a singular integral equation which satisfies the boundary conditions at the interface. The equivalent circuit for the junction is also presented.     

Scattering of Guided Modes Caused by an Arbitrarily Shaped Broken End in a Dielectric Slab Waveguide

Electromagnetic scattering of guided modes in a dielectric slab waveguide caused by an arbitrarily shaped broken end is analyzed theoretically by using the integral equation method. By solving the integral equations iteratively, the tangential components of the electric and magnetic fields on the broken end surface are determined, from which the reflected mode power, the radiation wave power and field patterns, and the total scattered power are obtained. Numerical results are presented for the plane-perpendicular, plane-tilted, and arc-shaped end surfaces. Both TE and TM modes are assumed as an incident wave.     

Operation Modes of a Waveguide Y Circulator (Short Papers)

Operation modes of a waveguide Y circulator with a circular and a triangular ferrite post are investigated both theoretically and experimentally. Field analysis is carried out taking into consideration the field variation along the ferrite axis. Frequencies are calculated by assuming TM modes nearly agree with measured frequencies. It is shown that the circulator action occurs at frequencies where two HE modes interfere with each other, besides occurring at HE mode resonance frequencies. Effects of Teflon spacers on circulator performances are investigated in detail.