Analytical and Numerical Studies of the Relative Convergence Phenomenon Arising in the Solution of an Integral Equation by the Moment Method

The relative convergence phenomenon that occurs in the numerical solution of the integral equation for the iris discontinuity problem is studied both analytically and numerically. It is shown that the solution for the aperture field can be highly dependent upon the manner in which the kernel and the unknown function are approximated in the process of constructing a matrix equation by the moment method. An analytical explanation is provided for the above phenomenon and the theoretical predictions are verified numerically. Also incIuded is a suggested numerical algorithm for detecting and alleviating the relative convergence behavior for more general problems.     

TE10 mode scattering by a rectangular resistive film ofarbitrary dimensions placed along the rectangular waveguides axis

Transverse electric (TE)₁₀ mode scattering by a resistive film of arbitrary width (d) and length (l) placed in the longitudinal section of a rectangular waveguide parallel to its narrow faces is investigated. The vector integral equation for the discontinuity of the tangential magnetic field on the film is formulated. The equation is solved by the Galerkin method using basis functions, each of them taking into account the discontinuity behavior near the film edge. For a film that is sufficiently short (l≪d), approximate expressions for the scattering matrix elements are obtained. The scattering matrix for a wide range of values of the film width, length, surface impedance, and frequency is calculated     

Characterization of asymmetric coplanar waveguide discontinuities

A general technique to characterize asymmetric coplanar waveguide (CPW) discontinuities with airbridges where both the fundamental coplanar and slotline modes may be excited together is presented. First, the CPW discontinuity without airbridges is analyzed using the space-domain integral equation (SDIE) approach. Second, the parameters (phase, amplitude, and wavelength) of the coplanar and slotline modes are extracted from an amplitude modulated-like standing wave existing in the CPW feeding lines. Then a 2n×2n generalized scattering matrix of the n-port discontinuity without airbridges is derived which includes the occurring mode conversion. Finally, this generalized scattering matrix is reduced to an n×n matrix by enforcing suitable conditions at the ports which correspond to the excited slotline mode. For the purpose of illustration, the method is applied to a shielded asymmetric short-end CPW shunt stub, the scattering parameters of which are compared with those of a symmetric one. Experiments are performed on both discontinuities and the results are in good agreement with theoretical data. The advantages of using airbridges in CPW circuits as opposed to bond wires are also discussed     

Novel finite element analysis of optical waveguide discontinuity problems

In this paper, a novel finite-element method (FEM) to rigorously and efficiently solve the optical waveguide discontinuity problems is presented. Instead of performing the time-consuming modal solutions on both discontinuity sides, the square root of the characteristic matrix is efficiently approximated using Taylor's series expansion, and then the interface boundary conditions are enforced at the discontinuity plane to solve for the reflected and transmitted fields. The high numerical precision and effectiveness of the proposed method is demonstrated through the analysis of various discontinuity problems, and the excellent agreement of the results obtained using the present finite element method and those obtained using other rigorous approaches in the literature.     

Solving microstrip discontinuities by the measured equation ofinvariance

The measured equation of invariance (MEI) is a newly developed computational method which allows finite-difference (FD) or finite-element (FE) mesh to be terminated very closely to objects of interest. In this paper, the authors show how the MEI method may be applied to microstrip antennas and discontinuity problems. The authors demonstrate its use in general full-wave three-dimensional (3-D) microstrip problems, and give results for open-ended microstrip lines and microstrip bends     

Convergence of Numerical Solutions of Iris-Type Discontinuity Problems

The convergence of numerical solutions of several iris-type discontinuity problems in waveguides and periodic structures is investigated. It is demonstrated that the numerical solution of a set of equations obtained from a mode-matching procedure (which corresponds to an integral equation formulation of the problem generally known as the moment method) may converge to an incorrect value if an improper ratio is chosen between the number of modal terms in the aperture and the number of terms retained in the kernel of the integral equation. Guidelines for efficient numerical computations are indicated.     

测度不变方程法及其应用

本文研究ＭＥＩ法的基本原理，给出ＭＥＩ法的变分解释。文中讨论ＭＥＩ法的各种用途，着重介绍ＭＥＩ法在波导不连续性问题中的应用。     

Analysis of optical waveguide discontinuities

A novel approach for analyzing discontinuity problems in optical waveguides is presented. The method is a combination of the vector-finite-element method and the least-squares boundary residual method. The vector-H-field-finite-element method is capable of providing accurate eigenvalues and eigenvectors for a wide range of optical waveguide problems, including arbitrary shape, arbitrary index distribution, and anisotropic materials. The least-squares boundary residual method matches the continuity of tangential fields in the least-squares sense, taking into account many modes at the discontinuity plane, to give the general scattering matrix. A few results are presented to show the usefulness of the approach     

Full-wave characterization of the mode conversion in a coplanarwaveguide right-angled bend

A full-wave algorithm is proposed to analyze thoroughly a 90° bend of coplanar waveguide (CPW). Based on the mixed potential integral equation (MPIE) formulation, the equivalent magnetic current distribution on the apertures is solved by the moment method using overlapping rooftop basis functions and the Galerkln weighting procedure. The matrix pencil approach is then utilized to do the de-embedding procedure and extract both the coplanar and slotline modes scattering off the asymmetric discontinuity. Experiments are performed to measure the scattering parameters and the results verify the accuracy of the present algorithm. The full 4×4 scattering matrix between these two modes is presented from which the occurrence of the mode conversion is investigated. The mode conversion is noticed to become almost complete at certain frequencies, which may be useful in the design of CPW to coupled slotline transition     

IMPROVED GENERALIZED ADMITTANCE MATRIX TECHNIQUE AND ITS APPLICATIONS TO RIGOROUS ANALYSIS OF MILLIMETER-WAVE DEVICES IN RECTANGULAR WAVEGUIDE

An improved generalized admittance (GAM) matrix technique is presented in this paper. Matrix transformation eliminates the singularity factor of GAM, denominator (1+Γ), because of new presentations of GAM. The relationship equations between II-port current and I-port incidence wave is computed by mode matching method. The generalized scattering matrix (GSM) of waveguide structure and its discontinuity problems is obtained with relationship equations and reflection coefficients. The GSM’s of millimeter-wave multistepped bend and T-junction in rectangular waveguide are computed by the improved GAM technique. The results comparisons between the proposed method and commercial software HFSS10.0 show the validity of the proposed method, which improves the validity of the GAM technique and reduces mathematical efforts. It is general, very efficient and can be used to solve other complicated and multiport network problems.     

Étude de transformateurs plan-E dans un système de coordonnées non orthogonales

A taper is a microwave component that ensures the continuity between two waveguides with different sizes. In this paper, we take an interest in perfectly conducting E-plane taper. An E-plane discontinuity excited by the fundamental eigenmode TEOI generates the LSEnl modes in input/output rectangular waveguides. The main purpose is to define the generalized scattering matrix that relates output LSE modes to input LSE modes. For that, Maxwell’s equations are used in covariant form written in a nonorthogonal coordinate system fitted to the taper geometry. Covariant components of fields inside the taper fulfil a differential equation system with nonconstant coefficients. This initial conditions problem requires the definition of independent input vectors. These vectors include the amplitudes of LSE modes generated by the discontinuity. The determination of output LSE modes relies upon the boundary conditions, the continuity equations of fields in waveguide-taper junctions and many numerical integrations with a fourth order Runge Kutta algorithm. Numerical stability is studied.     

Rank Reduction of Ill-Conditioned Matrices in Waveguide Junction Problems

A new low-rank spectral expansion technique for solving the ordinarily intractable matrix equations obtained from waveguide field equivalence theorem decompositions is described. The method facilitates the analysis of waveguide discontinuity problems that resist ordinary methods of solution. The technique is illustrated for the problem of scattering at a slant interface in a rectangular waveguide.     

H-polarization diffraction by a thick metal-dielectricjoin

An analysis is presented of the H-polarization diffraction due to a material discontinuity formed by the junction of a thick dielectric half-plane with a metallic half-plane having the same thickness. This is accomplished by first considering the solution of several subproblems. These include the direct diffraction and coupling due to a plane wave incident on a loaded open-ended parallel plate waveguide and radiation and reflection by a waveguide mode. The final solution for diffraction by the metal-dielectric join is obtained by introducing a perfectly conducting stub within the loaded guide and subsequently using the generalized scattering matrix formulation with the stub brought to the waveguide opening. All the analysis relating to the subproblems is done by the dual integral equation approach. As expected, the final expressions involve several Wiener-Hopf split functions which are evaluated numerically or analytically     

Computations for radiation and surface-wave losses in coplanarwaveguide bandpass filters

A new approach is developed to simulate both radiation and surface-wave losses in general coplanar waveguide (CPW) discontinuity structures. The newly derived formulas are concise, simple, and efficient for computation. Full-wave characterization of CPW filter structures are first accomplished by the mixed-potential integral equation and the method of moments. Given equivalent magnetic-current distributions on the apertures of a CPW, the matrix pencil approach is applied to extract the scattering parameters and the new formulas are employed to obtain the losses and far-field patterns of the space-wave radiation and surface wave. Simulation of the calculated radiation and surface-wave losses by field theory is found to be consistent to the total power loss determined from the scattering parameters by circuit theory, which verifies the correctness of our new expressions     

Wiener-Hopf analysis of the EM diffraction by an impedancediscontinuity in a planar surface and by an impedance half-plane

The Wiener-Hopf technique is used to solve two canonical problems. The first problem considered is the electromagnetic (EM) diffraction, by a planar surface with an impedance discontinuity (two-part surface), of an arbitrarily polarized plane wave obliquely incident to the axis of the two-dimensional objects. The second problem considers the EM diffraction by a half-plane with equal impedances on both sides. The solutions obtained are cast in a matrix notation which is useful for diffraction problems. The exact formal solutions are expressed in terms of integrals which can be asymptotically evaluated. Uniform asymptotic expressions are obtained where the presence of the geometrical optics (GO) poles as well as the surface-wave poles near the saddle point are fully taken into account. Several numerical examples are presented and it is shown that the solutions are continuous across the shadow boundaries of the GO and surface-wave fields     

Analysis of a Longitudinal Gyroelectric Discontinuity Inside a Fiber Waveguide

The scattering of guided electromagnetic waves from a finite-length longitudinal gyroelectic discontinuity inside a fiber waveguide is treated analytically. An integral equation approach is employed to formulate the corresponding boundary-value problem. The induced field inside the gyroelectic discontinuity region is expanded into a Fourier-type series in terms of the well-known cylindrical waves M and N plus a purely longitudinal wave Q. Then the method of moments is applied to decouple the basic integral equation. The resulting infinite coupled system of equations is truncated and solved numerically. After determining the field inside the discontinuity, the scattered far field inside the dielectric-rod waveguide is computed by employing a steepest descent integration technique. Numerical results for the scattering coefficients of an incident HE/sub 11/ dominant mode are obtained. Finally, design principles are discussed for practical components based on the treated longitudinal gyroelectric discontinuity.     

A Modified Residue-Calculus Technique for Solving a Class of Boundary Value Problems-Part II: Waveguide Phased Arrays, Modulated Surfaces, and Diffraction Gratings

The modified residue-calculus technique (MRCT) described in a companion paper may be combined with scattering matrix, multiple-reflection techniques to provide solutions in scattering matrix form to thick-wall waveguide phased array, modulated surface, and strip grating geometries. Each of these geometries may be regarded as a periodic array of thin plates modified by dielectric fillings, waveguide steps, and terminations. Solutions to the modified geometries are found by combining the exact solution to the thin-wall array problem with approximate solutions to certain waveguide discontinuity problems found by the MRCT. In particular, a value of the dominant mode reflection coefficient versus scan angle for the thick-wall array may be found accurate to two or three significant figures without need for matrix inversion. In general, reduction of matrix size by a factor of 5 or more over conventional methods with equivalent accuracy may be realized.     

Diffraction by Thick Conducting Haft-Plane and a Dielectric-Loaded Waveguide

This paper investigates the problem of diffraction of an incident plane wave by a half-plane with a finite thickness. The generalized scattering matrix procedure, which has been found useful for attacking waveguide discontinuity problems, is shown to apply to open region problems as well. Based on this procedure, a highly convergent Neumann Series solution is derived, and numerical calculations are presented for a wide range of parameters. The method of solution is not restricted to sufficiently thin half-planes only, as is the one discussed by Jones, although the labor in numerical calculation increases with increasing thickness. Comparisons with Jones' results show good agreement in the range where his results are valid. New results are presented for the extended range of thickness of the half-plane. Two other related problems, viz., those of radiation from a waveguide loaded with a dielectric or plasma medium, and diffraction by an inhomogeneously loaded waveguide, are also investigated in this paper.     

一种双站纯方位快速渐进无偏定位算法研究

针对多站无源定位中扩展卡尔曼滤波算法等递推类算法受初始状态影响大,滤波不稳定及将非线性观测方程转化为伪线性方程会产生有偏估计的缺点,提出了一种新的双站纯方位快速渐进无偏定位算法。该算法将扩维伪测量方程的系数误差协方差矩阵引入约束条件,通过对未知状态变量含二次约束的伪线性方程进行约束最小二乘(CLS)极小化处理,最终只需要对一对矩阵束进行广义特征分解,即可获得目标状态估计值。仿真结果表明,该算法与EKF算法及最小二乘算法相比,定位性能更稳定,精度更高,在测量误差较大或者2个观测站测量误差不一致时优势更明显。     

正则化预条件方法在矩量法中的应用

计算电磁学中矩量法产生的系统矩阵是病态矩阵,使用迭代方法求解时很难收敛,即使采用现有的预条件技术也经常不收敛.本文借用不适定问题求解中的正则化方法的概念,提出采用正则化矩阵作为矩量法中矩阵方程的一个预条件矩阵.这种预条件方法可以直接改善原矩阵的特征值分布,而且不需要额外的空间来存储预条件矩阵.此外,本文提出通过正则化矩阵方程的L曲线的二阶导数的最大值点来确定正则化参数,使得预条件矩阵方程求解的效率最高.数值实验表明,对于高阶矩量法求解电场积分方程或者磁场积分方程时分别产生的矩阵方程,采用常见的预条件迭代方法求解时收敛很慢,但是采用本文的预条件迭代方法却可以较快地收敛.