Coupled mode analysis of forward and backward coupling in multiconductor transmission lines

The nonorthogonal coupled mode theory is extended to the analysis of multiconductor transmission lines by including backward coupling. Coupling coefficients are expressed as overlap integrals of the eigenfields and currents belonging to individual lines. These eigenmode solutions are calculated using the finite-difference time-domain method, which can provide a broadband solution through a single simulation. General termination conditions are given, and scattering parameters of a multiconductor transmission line can be obtained directly by solving the coupled mode equations subject to these termination conditions. As illustrative examples, several configurations of coupled microstrip lines are analyzed, and numerical results are presented. It is observed that both the forward and backward coupling results agree fairly well with results from Advanced Design System Momentum software.     

基于同心圆光栅和契形光栅的摄像机自标定方法

提出一种利用同心圆光栅和契形光栅作为标定模板,基于正交方向消失点摄像机自标定的新方法。新方法利用相移条纹相位提取精度高的特性来求零相位特征点,避免了传统标记点提取误差给标定结果带来的影响。要求摄像机至少从6个方位拍摄标靶,采用四步相移得到光栅的截断相位并求解零相位交点,计算消失点从而解算出摄像机的内参数。根据模拟实验得到影响消失点标定精度因素的分析结果,制作了含有7个周期的同心圆光栅和4个周期的契形光栅。实际测量实验中分别用光栅靶标和灰度同心圆靶标进行相机标定,对比重投影误差,结果证明新方法提高了基于消失点标定算法的精度和稳健性。     

An efficient algorithm for sensitivity analysis of nonuniform transmission lines

This paper presents a new algorithm that addresses an important issue arising in computation of sensitivity for nonuniform transmission lines using the idea of model reduction through integrated congruence transform. This issue is related extending the concept of implicit basis construction, which was introduced earlier to simulate nonuniform transmission lines, to the task of sensitivity analysis. A new algorithm is presented to compute the orthogonal basis needed to obtain the reduced system used in sensitivity analysis. The proposed algorithm incorporates a new orthogonalization procedure which can be used to find an orthogonal basis for a set of moments derived from inhomogeneous differential equations, but without having to compute those moments explicitly. Numerical results demonstrate that reduced-order systems constructed by the proposed algorithm have improved numerical accuracy in sensitivity computation.     

基于精细积分法的耦合传输线瞬态分析

在耦合传输线的瞬态分析中提出了一种基于精细积分法的龙格-库塔迭代法。这是一种时域内的数值解法，该方法在对电报方程进行空间离散而获得对时间的一阶微分方程之后，没有采用精细计算法，而是采用了龙格-库塔迭代法。避免了大量的矩阵运算，提高了传输线瞬态响应分析的效率。     

Sampling on concentric circles [MRI image reconstructionapplication]

Two forms of a sampling theorem for concentric circles are established for a bandlimited two-dimensional (2-D) function. The location of the samples is prescribed either on equidistant circles or on the roots of the Bessel function J₀(). Both methods give comparable results, however, the number of samples required for their numerical evaluation is significantly less for the root-sampling formulation     

A fast time-domain finite element-boundary integral method forelectromagnetic analysis

A time-domain, finite element-boundary integral (FE-BI) method is presented for analyzing electromagnetic (EM) scattering from two-dimensional (2-D) inhomogeneous objects. The scheme's finite-element component expands transverse fields in terms of a pair of orthogonal vector basis functions and is coupled to its boundary integral component in such a way that the resultant finite element mass matrix is diagonal, and more importantly, the method delivers solutions that are free of spurious modes. The boundary integrals are computed using the multilevel plane-wave time-domain algorithm to enable the simulation of large-scale scattering phenomena. Numerical results demonstrate the capabilities and accuracy of the proposed hybrid scheme     

Analysis of dielectric loaded hybrid mode coaxial horns

This article presents a numerical solution for radiation from a novel coaxial horn with a partial dielectric loading. The horn is represented as a set of three-layer dielectric loaded coaxial waveguide sections. Characteristic equation has been obtained to calculate phase coefficients for hybrid modes in each section. Applying mode matching technique generalised scattering matrices for each junction between the sections have been obtained, besides that power coupling integrals for each of three different type of junctions have been found in closed-form solutions. Cascading these scattering matrices with transmission matrices of each section yields a generalised scattering matrix of the horn. For the given excitation at the throat of the horn, amplitude and phase of eigenmodes at the aperture of the horn have been determined. Finally, Fourier transform integral of the aperture electric field has been applied to solve radiation problem of the horn. Numerical results on propagation and radiation characteristics of the first four hybrid modes of the horn are presented and it is validated that this solution can be successfully used for full-wave electromagnetic analysis and optimisation of multiband dielectric loaded coaxial feeds.     

Characteristics of Coupled Microstrip Transmission Lines-I: Coupled-Mode Formulation of Inhomogeneous Lines

This paper consists of two parts. In Part I, coupled-mode theory is employed to determine the effects of reflection at the various ports and unequal inductive and capacitive coupling coefficients on the coupling and directivity of two coupled lines. Since couplers utilizing microstrip lines generally have unequal inductive and capacitive coupling coefficients, the results presented here should be useful in explaining the behavior of microstrip coupled lines. It is shown how the difference in the coupling coefficients leads to finite directivity and, under certain conditions, to "codirectional" instead of "contradirectional coupling." In Part II, the coupling coefficients and other parameters of various microstrip-line geometries are presented. Using these parameters in the results obtained here leads to an improved understanding of and design criteria for coupled microstrip lines.     

Accurate quasi-TEM spectral domain analysis of single and multiplecoupled microstrip lines of arbitrary metallization thickness

The quasi-TEM spectral domain approach (SDA) is extended to rigorously and efficiently analyze single and multiple coupled microstrip lines of arbitrary metallization thickness. The charge distributions on both the horizontal and vertical conductor surfaces are modeled by global basis functions. This results in a relatively small matrix for accurate determination of the line parameters of coupled thick microstrips. A convergence study is performed for the results of a pair of coupled lines with crucial structural parameters to explore the conditions for obtaining reliable solutions using the technique. Results for thick microstrips are validated through comparison with those from available measurements and another theoretical technique. The soundness of the technique is further demonstrated by looking into the trend of the results obtained by a simplified model in which the structural parameters are pushed, step by step, to the numerical extremities. Variations of circuit parameters of a four-line coupled microstrip structure due to the change of finite metallization thickness are presented and discussed     

Scattering Matrix Description of Microwave Resonators

In this paper an analysis of the scattering matrix coefficients (reflectance and transmittances) of the microwave resonators is presented. Two general cases of resonator couplings are considered. One of them is a multiport with one port terminated by the resonator, the other is a resonator coupled, in various ways, to a number of transmission lines. The effect of external circuits on the Q and resonant frequency of the resonator has also been examined. Fundamental parameters for the commonly used microwave resonator couplings are shown in Table L     

Modelling line-of-sight coupled MIMO systems with generalised scattering matrices and spherical wave translations

A model to rigorously characterise line-of-sight MIMO systems is introduced. It is based on the generalised scattering matrix of each antenna, considered as isolated, and the rotation and translation coefficients of spherical modes. The resulting channel matrix rigorously includes the exact spherical vector nature of electromagnetic propagation (which may exert a significant influence over short-range links), mutual coupling effects and real antenna reflection, transmission, reception and scattering features. Numerical results are presented for MIMO systems made up of ideal dipoles.     

The Propagation Characteristics of Signal Lines in a Mesh-Plane Environment

This paper investigates the propagation characteristics of signal lines situated between a pair of mesh reference planes in a homogeneous dielectric. These mesh reference planes, which form the heart of high-performance multichip modules, provide a transmission-line environment for the signals carried between integrated circuit chips. A numerical solution that employs a set of rooftop functions to represent the current density is developed and used to find the propagation velocity and characteristic impedance in mesh plane structures where the conductors have zero thickness and finite sheet resistance. The telegraphist's equations are shown to apply, and are used to find the capacitance and inductance matrices in coupled fine configurations. The near- and far-end crosstalk are calculated when the coupled lines are on the same, and on opposite, sides of a mesh plane. The presence of conductors which run in a direction orthogonal to the signal lines, whether as an array of crossing signal lines or as part of the mesh planes, is shown to significantly affect only the capacitive parameters. The influence of such orthogonal lines on the propagation velocity, characteristic impedance, and crosstalk are given, and a detailed plot clearly indicates the circulating current flow in these lines.     

Exact calculations of scattering parameters of a step slot width discontinuity in a unilateral fin-line

The dominant and the first four higher-order modes in a unilateral fin-line are accurately described from a thorough spectral-domain approach. Then, coupling coefficients between eigenmodes at a step slot width discontinuity to be used in the generalised scattering matrix formulation are directly computed in the spectral domain. Scattering parameters of the dominant mode in the Ka band are presented.     

基于近区后向散射场幅度的二维导体目标的逆散射

本文给出了一种改进的基于多方向多入射频率的平均波照射下的近区散射场度测量值反演导体目标轮廓的逆散射场的幅度值反演导体目标轮廓的逆散射方法。     

Analytical and numerical solution to the two-potentialZakharov-Shabat inverse scattering problem

An analytical and a numerical method are presented in order to solve the inverse scattering problem associated with the two-potential Zakharov-Shabat coupled mode equations. The numerical solution, which uses leapfrogging in space and time, represents a direct numerical solution to the coupled Gel'fand-Levitan-Marchenko (GLM) integral equations as an extension of the authors' previous work on GLM equations of simpler form. The analytical method, which is applied for one-pole reflection coefficients, consists in constructing appropriate differential operators which transform the coupled GLM equations to ordinary linear differential equations. An application of these methods for nonuniform transmission line synthesis is presented     

Edge And Line Detection in Multidimensional Noisy Imagery Data

Detection of edges and lines in multidimensional data is an important operation in a number of image processing applications. The multidimensional picture function is a sampling of the underlying reflectance function of the objects in the scene with the noise added to the true function values. Edges and lines refer to places in the image where there are jumps in the values of the function or its derivatives. The multidimensional greytone surface is expanded as a weighted sum of basis functions. Using multidimensional orthogonal polynomial basis functions, expressions are developed for the coefficients of the fitted quadrautic and cubic surfaces. The parameters of the fitted surfaces are obtained when there is a rotation in the coordinate system. Assuming the noise is Gaussian, statistical tests are devised for the detection of significant edges and lines. Direction isotropic properties of the fitted surfaces are described. For computational efficiency, recursive relations are obtained between the parameters of the fitted surfaces of successive neighborhoods. Furthermore, experimental results are presented by applying the developed theory to multiband Landsat-Imagery Data.     

Efficient simulation of nonuniform transmission lines using integrated congruence transform

This paper presents a new algorithm based on integrated congruence transform for efficient simulation of nonuniform transmission lines. The proposed algorithm introduces the concept of model-order reduction (MOR) via implicit usage of the Hilbert-space moments in distributed networks. The key idea in the proposed algorithm is the development of an orthogonalization procedure that does not require the explicit computation of the Hilbert-space moments in order to find their spanning orthogonal basis. The proposed orthogonalization procedure can thus be used to compute an orthogonal basis for any set of elements that are related through a differential operator in a generalized Hilbert space, without the need to have these elements in an explicit form. The proposed algorithm also addresses the problem of MOR of nonuniform transmission lines, through defining a weighted inner product and norm mappings over the Hilbert space of the moments. Numerical examples demonstrate more accurate numerical approximation capabilities over using the moments explicitly.     

Resonant modes of a concentric spherical cavity with conicallystratified medium

An analysis on electromagnetic fields of a cavity formed by two concentric conducting spheres with a conically stratified medium is presented in this paper. Angular transmission formulation and the radial eigenfunction expansion are used to formulate the field components. Boundary matching methods are applied to obtain the characteristic equations containing various infinite series of spherical Hankel functions and Legendre functions of complex order for resonant frequencies. The first two resonant frequencies and field expansion coefficients are determined numerically. The distribution pattern of angular field components and the forms of typical electric field lines and magnetic field lines for the first resonant fields are also indicated     

Coupled-Mode Analysis of Nonuniform Coupled Transmission Lines

The transmission-line equations describing propagation along coupled transmission lines are cast in coupled-mode form so that the roles of the different coupling coefficients and the impedance variation are more directly observable. Restrictions on the various parameters for obtaining directional coupling with nonuniform lines are then discussed and exact solutions for the coupling response of two nonuniform coupled lines with particular variations of the coupling coefficients are presented. The results obtained from the exact closed-form solutions should aid in the design of tapered couplers.     

Unified approach for constructing multiwavelets with approximation order using refinable super-functions

A unified approach for constructing a large class of multiwavelets is presented. This class includes Geronimo-Hardin-Massopust (1994), Alpert (1993), finite element and Daubechies-like multiwavelets. The approach is based on the characterisation of approximation order of r multiscaling functions using a known compactly supported refinable super-function. The characterisation is formulated as a generalised eigenvalue equation. The generalised left eigenvectors of the finite down-sampled convolution matrix L/sub f/ give the coefficients in the finite linear combination of multiscaling functions that produce the desired super-function. The unified approach based on the super-function theory can be used to construct new multiwavelets with short support, high approximation order and symmetry.