矩形波导铁氧体移相器的有限元分析

本文从麦克斯韦方程推出适合于解决导磁率为张量形式的各向异性介质加载波导本征值问题的全电场有限元方程,讨论识别主模的方法和如何把两种不同媒质界面上的边界条件引入有限元方程。通过所建立的有限元方程,分析了双板铁氧体加载矩形波导的传播特性,并同解析解作比较,两者所得结果吻合得很好。     

介质环加载喇叭的理论分析

本文对介质环加载边界条件特征方程进行了求解。导出了介质环加载波导与光壁波导连接处的模转换计算公式。并且根据这些公式计算了文献[1]设计的介质环加载喇叭的辐射特性,计算结果非常接近实测结果。     

Application of a Variation-Iteration Method to Inhomogeneously Loaded Waveguides

An approximate technique for eigenvalue equations, the variation-iteration method, is commonly used in theoretical physics. Through an adequate numerical treatment it reduces to the inverse iteration method. It is shown here that this technique is most promising. Starting from an initial trial function, iterates are calculated, in which the components relative to the unwanted true eigenfunctions are eliminated. Both an upper and a lower bound of the unknown eigenvalues are calculated. This leads to an approbate eigenvalue within a specified accuracy with respect to the exact (unknown) eigenvalue. An extrapolation technique further accelerates the convergence. The computation time is shorter than when using the Rayleigh-Ritz procedure. The method is applied here to the dielectric-slab loaded waveguide, because the exact solution is available to check the validity of the method. The influence of the geometry, the dielectric constant, and the frequency is evaluated.     

The discontinuity problem of a rectangular dielectric post in arectangular waveguide

A simple numerical technique for the solution of the discontinuity problem of a symmetric loaded rectangular dielectric post centered in a rectangular waveguide is presented. The waveguide is divided into three regions where the field is expressed in suitable waveguide modes. By applying the continuity condition at the common surfaces of the regions, a system of linear equations determining the reflection and transmission coefficients is formed. Several examples are compared with experimental results and show the validity of the method     

An Approach to Permittivity Determination at Microwave Frequencies Through the Eigenvalue Problem

A simple method of solving the inverse medium problem in order to determine the complex dielectric constant of a lossy dielectric material at microwave frequencies is presented. The arbitrarily shaped dielectric sample placed in a rectangular waveguide is considered. Electromagnetic fields in the waveguide are expanded in series of harmonic functions. A set of linear equations is obtained using the finite–difference technique. An additional empirical condition, which is related to the measured reflection and/or transmission coefficients and results in an overdetermined system, is added and then the system is defined by the addition of a trivial extra parameter. The sample's dielectric properties are obtained by solving the resulting eigenvalue problem. An algorithm to extract proper results from the set of eigenvalues is defined by considering the properties of numerical solution. The system is tested by using an alternative method.     

Approximation Technique for Dielectric Loaded Waveguides

An algebraic procedure is described which yields approximate values for the cutoff frequencies and propagation constants of dielectric-loaded waveguides. The procedure is demonstrated for a waveguide completely filled with an anisotropic dielectric and for waveguides partially filled with isotropic dielectrics. For the latter case results are tabulated for five types of waveguide loading. The symmetrically loaded waveguide is used to show the accuracy which may be expected. This procedure is shown to be identical with the Rayleigh-Ritz variational method but with the advantage that it provides a systematic approach to improve the accuracy and to handle a multitude of waveguide geometries.     

Equivalent circuit formulation for an array of phased waveguide apertures

An expression for the radiation admittance of an infinite planar array of rectangular waveguide apertures is formulated and a technique for finding the complete equivalent circuit of the waveguide to space junction is given. The formulation includes multiple layers of dielectric above the array ground plane and waveguide elements which are center loaded with dielectric. Experimental verification of the radiation admittance formulation and the equivalent circuit concepts is given.     

A Variational Theory for Wave Propagation in Inhomogeneous Dielectric Slab Loaded Waveguides

A novel numerical technique based on the variational formulation defined only in the slab is developed to study the loaded rectangular waveguide with an inhomogeneous dielectric slab. The variational equation for the boundary value problem is formulated and solved numerically, using the finite element method with piecewise quadratic trial functions. A comparison of this new technique with the conventional variational ones is presented. Various propagation characteristics, such as the phase constant, useful bandwidth, power handling capacity, and attenuation constants due to conductor and dielectric losses, are investigated for the waveguide centrally loaded with a slab of parabolic dielectric profile. The effects of changes in dielectric profiles are discussed by examining the results for the slabs with constant and parabolic profiles.     

A new approach to estimate complex permittivity of dielectricmaterials at microwave frequencies using waveguide measurements

In this paper, a simple waveguide measurement technique is presented to determine the complex dielectric constant of a dielectric material. The dielectric sample is loaded in a short-circuited rectangular waveguide. Using a network analyzer, the reflection coefficient of the waveguide is measured. Using the finite-element method (FEM) the exact reflection coefficient of this configuration is determined as a function of the dielectric constant. The measured and calculated values of the reflection coefficient are then matched using the Newton-Raphson method to estimate the dielectric constant of a material. A comparison of estimated values of the dielectric constant obtained from simple waveguide modal theory and the FEM approach is presented. Numerical results for dielectric constants of Teflon and Plexiglas measured at the X- and Ku-bands are presented. Numerical inaccuracies in the estimate of the dielectric constant due to: 1) the presence of airgaps between sample and sample holder waveguide surfaces and 2) inaccuracy in the sample dimensions are also discussed     

A comparison of formulations for the vector finite element analysisof waveguides

The principal formulations that have been proposed for finding the modes of waveguides by the finite element method are reviewed and compared. In each case, it is shown how Maxwell's equations may be reduced to matrix form using the method of weighted residuals. The formulations are compared from several points of view: their ability to handle spurious modes, lossy materials, and reentrant corners; the number of field components; and the properties of the matrices. Three benchmark problems are described and used to compare the formulations: a rectangular waveguide partially loaded with lossless dielectric; an air-filled, double-ridged waveguide; and a shielded image guide with either lossless or lossy dielectric     

Analysis of radiating slots in a rectangular waveguideinhomogeneously loaded with a dielectric slab

Longitudinal and transverse radiating slots in the broad wall of a rectangular waveguide inhomogeneously loaded with a dielectric slab are analyzed. The formulation used involves the moment method solution of a pair of coupled integral equations containing the dyadic Green's function of the inhomogeneously loaded waveguide. Both an edge-condition for the electric field in the slot aperture and the correct form of the ψ=constant waveguide mode are included in the analysis. Computed and measured results are compared to verify the theoretical analysis     

A multipole analysis of a dielectric loaded coaxial rectangularwaveguide

A multipole analysis of a coaxial rectangular waveguide whose inner conductor is circular is made in order to determine the TE and TM modes of the system. The analysis is based on using multipole (dipole, quadrupole etc.) electric and magnetic current sources to generate field solutions in the waveguide. These solutions are used to match the electromagnetic boundary condition in a homogeneous coaxial rectangular waveguide and to determine the TE and TM eigenvalues of the waveguide system. Eigenvalue results are compared with results of the generalized spectral domain method and to eigenvalue results for a ridged waveguide. Propagation in a coaxial rectangular waveguide is also studied when the coaxial rectangular waveguide is loaded with lossy inhomogeneous dielectric material. A variational formula is used to relate the TEM, TE, and TM modes of an empty coaxial rectangular waveguide to the propagation in the loaded inhomogeneous dielectric waveguide     

Computation of TM and TE modes in waveguides based on a surfaceintegral formulation

The surface integral formulation is used for the computation of TM and TE modes propagating in dielectric loaded waveguides. This formulation makes use of the surface equivalence principle whereby the field at any point internal or external to the waveguide can be expressed in terms of equivalent surface currents. This procedure reduces the original problem into a set of integro-differential equations which is then reduced to a matrix equation using the method of moments. The solution of this matrix equation provides the propagation characteristics of the waveguide and the equivalent surface currents existing on the waveguide walls. The equivalent surface currents can be used to compute the fields at all points, both inside and outside the waveguide. The surface integral method has been used to compute the propagation characteristics of waves propagating in dielectric loaded waveguides. The computed results agree very well with analytical and published data. A method that can be used to remove spurious modes is illustrated     

A computation of the reflection and transmission coefficients for dielectric coated waveguides

A previously developed variational technique for finding the approximate solution to the electromagnetic field inside waveguides of varying shapes and containing non-uniform dielectric and magnetic materials is applied to the specific case of an axisymmetric waveguide containing three layers of different dielectric materials. The magnetic permeability is taken equal to unity. The method enables the problem to be reduced to a two point boundary value problem for a pair of second order, linear, ordinary differential equations. The values of the reflection and transmission coefficients obtained by this method are in good agreement with those derived from solving the partial differential equations for the field.     

An integral transform technique for analysis of planar dielectricstructures

This paper presents a novel efficient technique for the study of planar dielectric waveguides for submillimeter-wave and optical applications. In an appropriate integral transform domain, which is determined by the Green's function of the substrate structure, higher-order boundary conditions are enforced in conjunction with Taylor expansions of the fields to derive an equivalent one-dimensional integral equation for the corresponding two-dimensional waveguide geometry. This reduction in the dimensionality of the boundary-value problem can easily be extended to three-dimensional planar structures, with equivalent two-dimensional integral equations being formulated. The reduced integral equations are solved numerically by invoking the method of moments, in which the transform-domain unknowns are expanded in a smooth localized entire-domain basis. It is demonstrated that using orthogonal Hermite-Gauss functions as an expansion basis provides very satisfactory results with only a few expansion terms. For the validation of the technique, single and coupled dielectric slab waveguides are treated     

Slotted Line Measurements for Propagation Constant in Lossy Waveguide (Short Papers)

The propagation coefficient in a slotted waveguide partially loaded with a lossy dielectric can be determined accurately, in terms of the measured standing-wave pattern, by means of a computer program solving a set of transcendental equations. This determination is a necessary step in a permittivity measurement technique which was recently proposed by several authors.     

Propagation Along Transversely Inhomogeneous Coaxial Transmission Lines (Short papers)

Numerical "shooting" methods are employed in obtaining the dispersion curves of a coaxial waveguide loaded with a radially inhomogeneous dielectric. The utility of this technique is tested by comparing results with known analytical solutions. The method is also used to find the dispersion curves of a coaxial waveguide loaded with a radially Gaussian-distributed plasma.     

Stepped Transformers for Partially-Filled Transmission Lines (Comments)

The use of a lumped equivalent circuit for the transverse section of a waveguide has been used to determine the cutoff frequency of ridged guide. In essence, the transverse section of the guide is equated to an LC tank and the resonant frequency of the tank is determined by the usual formula. Sullivan and Parkes have extended this method to the analysis of a ridged guide partially loaded with dielectric. They account for the additional capacitance introduced by the dielectric and include this capacitance as part of the LC tank to be analyzed for the resonant frequency. While the simplified lumped-network equivalents are always desirable in analyzing microwave networks, we should be wary of overgeneralizing them. In the case of dielectric slab loading in a waveguide, the location of the added capacitance as well as its maguitude has an effect in determining the cutoff frequency. (This can also be said of the discontinuity capacitance at the edge of a ridge.) Note how a dielectric slab when centered in a rectangular waveguide will lower the cutoff frequency far more than when flush with the sidewall. This is not accounted for in the LC tank equivalent. The effect of each increment of capacitance due to each lamina of dielectric will be largely determined by the distance from the lamina to the short-circuit walls. Therefore, the author believes that the case of a partially dielectric-loaded guide can only be genuinely analyzed by the transverse resonance method or by some other method which accounts for the distributed parameters involved.     

Characteristics of coupling between parallel-plate waveguides with and without dielectric plugs

An analysis is presented of the coupling between parallel-plate waveguides excited in TE modes. Integro-differential equations are formulated for finite arrays of such waveguides with arbitrary widths and spacings. The waveguides, moreover, may be loaded with dielectric plugs having different dielectric constants and thicknesses. Solutions to these equations are effected by the method of moments. Extensive numerical data are obtained for the coupling between two waveguides, and their characteristics are examined in detail. The results show that in unloaded situations the coupling diminishes monotonically with increasings/lambda, wheresis the separation between the waveguides andlambdais the wavelength. At a given frequency, moreover, the coupling for largesdecreases asymptotically ass^{-3/2}. By contrast, an asymptotic dependence ofs^{-3/2}was uncovered earlier for TM-mode coupling. It is found that substantially different coupling behavior may result when the waveguides are loaded by dielectric plugs because of the excitation by the aperture discontinuity of higher order modes, which propagate inside the dielectric but are attenuated in the unloaded waveguide region. Of particular interest is the observation, under suitable conditions, of resonance characteristics in the coupling as functions of both the frequency and the thickness of the dielectric plug. These resonances are found to occur when the impedances of a certain higher order mode satisfy the transverse resonance condition, and thus are the manifestation of the resonances of such modes inside the cavity formed by the dielectric plug.     

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.