Propagation characteristics of a circular waveguide coated inside with a metamaterial

The problem of guided wave propagation of a circular waveguide that is coated on the inside with a metamaterial coating is studied by a boundary value approach and the propagation features cylindrical waveguide are studied by solving the resultant characteristic equation numerically. The results are compared to those with an inside dielectric coating. The variation of the normalized phase constant is studied as a function of the parameters of the coating including the permittivity and permeability, the coating thickness expressed as a ratio of b/a, and frequency. The behavior of the cylindrical waveguide is shown to be significantly different from that with a dielectric coating.     

A new edge element analysis of dispersive waveguiding structures

A new functional is rigorously selected for the edge element method to solve the 2-D¹/₂ guided wave problems. The variational formulation is derived from the vector wave equation without any assumption or simplifications, and therefore the formulation is the full-wave analysis. Moderate to heavy ohmic loss and dielectric loss are taken into account in a natural and consistent manner. As a result, finite cross-section of arbitrary shape and finite conductivity can be handled without imposing the impedance boundary condition (IBC). The DEC may no longer be held for high-speed microelectronics applications, where the cross-section dimension may have been in the same order of the skin depths of some frequency components. The propagation modes are obtained by solving the large scale generalized eigenvalue and eigenvector equations employing the subspace iteration method. The spurious modes are totally suppressed in the whole frequency range of interest. Numerical examples of dielectric waveguides and microstrip transmission lines with finite conductivity are conducted     

Analysis of a microstrip dipole antenna

Assuming a quasi-TEM mode of wave propagation and using a conformal transformation technique, accurate and simple analytic expressions for the characteristic wave resistance and the effective dielectric constant of the microstrip dipole antenna in the mixed dielectric medium have been derived. The theoretical values are in close agreement with the experimental results.     

An integral equation method for the evaluation of conductor anddielectric losses in high-frequency interconnects

An integral equation method is developed to solve for the complex propagation constant in multilayer planar structures with an arbitrary number of strip conductors on different levels. Both dielectric losses in the substrate layers and conductor losses in the strips and ground plane are considered. The Green's function included in the integral equation is derived by using a generalized impedance boundary formulation. The microstrip ohmic losses are evaluated by using an equivalent frequency-dependent impedance surface which is derived by solving for the fields inside the conductors. This impedance surface replaces the conducting strips and takes into account the thickness and skin effect of the strips at high frequencies. The effects of various parameters such as frequency, thickness of the lines, and substrate surface roughness on the complex propagation constant are investigated. Results are presented for single strips, coupled lines, and two-level interconnects. Good agreement with data available in the literature is shown     

Numerical diffraction coefficients for surface waves

The numerical uniform theory of diffraction (UTD) is extended to include surface waves. A method for extracting surface wave diffraction coefficients from moment method data is given and Prony's method is applied to the problem of determining surface wave propagation constants. The method is validated through comparison with the exact solution of the problem of surface wave diffraction by a truncated dielectric slab recessed in a conducting surface. Examples are given for scattering from dielectric slabs and frequency-selective surfaces and for radiation from a conformal microstrip antenna with a truncated substrate. The accuracy obtained is demonstrated by comparison with moment method calculations     

A Perturbation Method for the Analysis of Wave Propagation in Inhomogeneous Dielectric Waveguides with Perturbed Media

This paper presents a perturbation method for determining the modes and the propagation constants of TE and TM waves in inhomogeneous dielectric waveguides whose index distributions depart from well-known profiles; e.g., a parabolic profile for which exact solutions can be obtained. Applying the variable-transformation technique to the wave equations, the wave-equation problem is transformed into the related-equation problem. The approximate solutions of the wave equations are obtained solving the related equation. The method is applied to the analysis of lower order mode propagation in a near-parabolic-index medium. The first-order field functions and the second-order propagation constants are given.     

Field distribution in a circular waveguide with a corrugateddielectric lining

The problem of wave propagation through a circular cylinder with a periodically interrupted dielectric lining is solved by a boundary value approach by considering the region between the corrugations as a medium with a tensor permittivity. The characteristic equation for the phase constant is derived by matching the field components. Solutions for the phase constant are obtained and the variation of the phase constant with the physical parameters is studied. The variation of the axial and circumferential electric field components in the transverse plane is also studied     

Dispersion of waves guided along a cylindricalsubstrate-superstrate layered medium

The effects of curvature and of the electrical parameters of thin dielectric layers deposited as superstrates on a perfectly conducting circular cylinder on the modal dispersion of waves guided tangentially along the outer (superstrate) layer of a two-layer geometry are examined. To chart the propagation characteristics of the layer-guided modes relevant to the three-dimensional (dipole-excited) Green's function for this geometry, it is necessary to solve the radial eigenvalue problem for the complex azimuthal propagation constants ν _p(β), p 1, 2, . . ., which also identify poles of the ν-dependent spectral integrand of the Green's function. Here, β is the spectral variable along the axial direction, with the Green's function synthesized as a double spectral integral over ν and β. The pole locations are obtained numerically by solving the dispersion equation using Davidenko's method, and are parameterized in terms of layer radius, dielectric constant, and thickness. The dispersion relation, and hence the propagation constants, are shown to reduce correctly to the corresponding results for the planar geometry in the limit where the superstrate outer radius approaches infinity     

Reconstruction of the permittivity profile using a nonlinear guidedwave technique

A new method is developed to reconstruct the permittivity profile of a dielectric slab in a guided wave formulation. The propagation constants of the slab eigenmodes are used as input data for inversion of the boundary-value problem for the nonlinear differential equation representing the condition of existence of the modes. The permittivity profile is expanded into a set of special functions so that the propagation constant of a particular mode depends mainly on only one term of the set. This ensures fast convergence of an iterative procedure to find the coefficients of expansion. The method is shown to be valid for the discontinuous profiles of high contrast as well as for both symmetrical and asymmetrical profiles provided that in the last case additional measurements of the slab placed on a metal plate are performed. Several simulated and experimental examples are presented     

Spectral-domain analysis of shielded microstrip lines on biaxiallyanisotropic substrates

The spectral-domain technique is extended to the study of shielded microstrip lines on biaxial substrates. The analysis simultaneously includes dielectric and magnetic anisotropy effects. A fourth-order formulation leads to the determination of the appropriate Green's function for the structure. The characteristic equation is formed through the application of the Galerkin method to the equations resulting from the boundary conditions on the strip. Numerical results calculated by this method for isotropic as well as dielectrically anisotropic substrates are compared with the existing data, and in both cases a very good agreement is observed. New data on the propagation constant of the shielded microstrip with different substrate permittivities and permeabilities are presented to illustrate the effects of the material parameters on the characteristics of the microstrip line     

Analysis of printed-circuit antennas with chiral substrates withthe method of lines

In this paper, a new method is presented in order to illustrate how the method of lines can be generalized for the analysis of stratified guided wave structures filled with isotropic chiral dielectric substrates. The new proposed method derives the dyadic Green's function for stratified isotropic chiral dielectric layers from the wave equation in the spectral domain. The result leads to a clear equivalent circuit representation of the whole structure, which can be used to readily handle the hyperbolic nature of the Maxwell equations. The application demonstrates the validity of the method to the well-known example of a single microstrip patch antenna on a single grounded isotropic dielectric layer. The technique is subsequently applied to more complicated structures with multiple isotropic chiral layers and electric sources and/or metallizations in arbitrary interfaces     

Simple and efficient finite-element analysis of microwave andoptical waveguides

A simple and efficient finite-element method for the analysis of microwave and optical waveguiding problems is formulated using three components of the electric or magnetic field. In order to eliminate spurious solutions, edge elements are introduced. In the edge element approach the nodal parameters are not limited to the magnetic field as in the conventional three-component formulation for the dielectric waveguiding problem. An eigenvalue equation that involves only the edge variables in the transversal plane and can provide a direct solution for the propagation constant is derived. To show the validity and usefulness of this approach, computed results are illustrated for microstrip transmission lines and dielectric waveguides     

屏蔽微带线特性的谱域导抗法分析

本文用谱域导抗法分析了微带线的特性,研究了屏蔽盒对微带线传播特性和色散特性的影响。谱域导抗概念的引入大大简化谱域方法中冗长的场公式推导过程,其分析结果又能保证相当高的精度。本文的研究结果表明:屏蔽盒的顶盖使微带线等效介电常数变小,对色散特性影响不大;屏蔽盒的侧壁使微带线等效介电常数变大,并减小了微带线的色散。     

Scattering from a microstrip patch

A solution to the problem of plane wave scattering by a rectangular microstrip patch on a grounded dielectric substrate is presented. The model does not include the microstrip feed, and thus does not include the so-called "antenna mode" component of the scattering. The solution begins by formulating an electric field integral equation for the surface current density on the microstrip patch. The integral equation is solved using the method of moments. Computed data for the patch radar cross section (RCS) is found to be in close agreement with measurements over a broad frequency range. The microstrip RCS versus frequency consists of a number of large peaks which are identified as impedance or pattern factor resonance peaks.     

Microstrip lines on substrates with segmented or continuouspermittivity profiles

The propagation properties of microstrip lines on a substrate with inhomogeneous permittivity and conductivity profiles are analyzed. The eigenmodes in each inhomogeneous layer are obtained by solving an eigen equation. These eigenmodes are then used to formulate the Green's function of the stratified medium. An integral equation is next derived in terms of the surface current on the strip. Galerkin's method is then applied to obtain a determinantal equation to be solved for the propagation constant. The effect of several permittivity and conductivity profiles are analyzed     

Simple nonparaxial beam-propagation method for integrated optics

A simple beam-propagation method for solving the scalar TE nonparaxial or Helmoltz equation is presented. This versatile algorithm, based on a two-step finite-difference scheme for solving the propagation coordinate, is amenable to be easily extended to solve vector wave equations, which could take into account nonlinear effects. In addition, a general procedure to check its stability is given in detail. The applicability of the present method and its distinction from paraxial or Fresnel solutions are demonstrated through several examples, including very strongly guided structures of variable transverse section     

The radiation resistance of a microstrip element

The radiation resistance of a rectangular microstrip element printed on a grounded dielectric is evaluated through the use of a bidimensional Fourier transform. The antenna is assumed to be half a guided wavelength long and to have a given width. The Q-factor of the antenna is assumed to be high so that the current in the feed at resonance is negligible. The longitudinal current distribution along the patch is assumed to resemble that of a resonant end-fed half-wavelength segment of a microstrip transmission line. The transversal current is taken to be constant. The resulting integrals are estimated in an asymptotic form using finite series and product expansions. An empirical formula replaces the former one for higher values of dielectric constants. The simple expressions thus derived lend insight into the nature of dependence of the radiation resistance on the various parameters such as width, thickness, and relative dielectric constant. In spite of their simplicity, the formulas provide quite accurate results     

Full-wave characterization of high-Tcsuperconducting transmission lines

A full-wave numerical analysis is applied to accurately characterize superconducting transmission lines embedded in a layered dielectric medium. A volume integral equation formulation is developed by using a spectral domain dyadic Green's function for stratified media. Galerkin's method with rooftop basis functions for the electric field distribution inside the superconductor is then employed to solve the complex propagation constant. The thickness of the superconducting film is arbitrary in this analysis, and the formulation rigorously accounts for the anisotropy of the superconducting film. The propagation characteristics of a superconducting microstrip transmission line with a thin dielectric buffer layer are investigated. A superconducting stripline configuration with an air gap is also studied     

Radiation from cylindrical leaky waves

Formulas are derived for the far-infrared radiation pattern of cylindrical leaky waves propagating on a planar surface. The formulas can be used to predict the radiation pattern of a general class of leaky-wave antennas, consisting of a finite-size source which excites a radially propagating leaky wave on some planar surface. Leaky-wave antennas consisting of antenna elements embedded in dielectric layers (microstrip elements) fall into this category. Using the equivalence principle, formulas are derived for both transverse electric (TE) and transverse magnetic (TM) leaky waves with arbitrary propagation constants. The formulas allow for radiation from cylindrical apertures of arbitrary size, so that the effect of truncating the supporting planar surface with an absorbing material can be determined. Particular attention is devoted to the case of a leaky wave for which the real and imaginary parts of the complex propagation constant are equal, since this type of wave has been shown to be responsible for broadside radiation in certain leaky-wave antennas comprised of dielectric layers     

基于双向抛物线方程电波传播分析的矩量法验证研究

求解复杂环境下的电波传播问题,双向抛物线方程(2W-PE)是一种常用、准确、高效的方法,但其计算精度的验证一直是一个难题。为了在介质地面和障碍物条件下验证双向抛物线方程的计算精度,提出一种利用矩量法(MoM)验证双向抛物线方程的计算方法。该方法首先引入抛物线方程和矩量法统一的波源设置,然后推导了场型格林函数和PMCHW方程,构造了矩阵方程,利用增强离散复镜像方法(E-DCIM)对存在介质地面的格林函数进行有效处理,并给出和数值积分法的对比结果,从而得出了矩量法计算空间电波传播场值的近距离计算方法。数值示例显示,矩量法的解析计算结果足以有效验证双向抛物线方程的计算精度。