Numerical analysis of surface wave on microstrip antenna with lossysubstrate

The key to analysing a guided surface wave is to solve its eigenvalue equation. When the medium is dissipative, the eigenvalue equation is a complex transcendental equation. The Kuhn algorithm is applied to work out the eigenvalue equation     

螺旋-圆柱波导系统特征值的研究

本文给出了螺旋-圆柱波导系统的特征方程,首次求得了此结构的复根模,推导出了实根模、虚根模和复根模相互之间的分界条件,并给出了一些特征值曲线。最后,利用特征方程近似计算了一个螺旋-圆锥喇叭天线的远场辐射方向图,数值结果与实验进行了很好的比较。     

Ag-coated Long-period Fiber Grating

Based on coupled-mode theory, the eigenvalue equation of five-layered long-period fiber grating （LPFG） sensor with Ag film and gas-sensitive film overlays are firstly studied. The problem of resolving complex eigenvalue equation on five-layered LPFG is analyzed, and the method of resolution is also given. Then the eigenvalue equation of three-layered metal cladding LPFG is analyzed, and the complex transcendental equation is also discussed. The computing result shows that the coupling between the low order EH modes and the core mode is much stronger than that between the low-order HE modes and the core mode.     

A New Technique for the Analysis of the Dispersion Characteristics of Microstrip Lines

Dispersion characteristics of shielded microstrip lines are investigated using a new technique. The method utilizes the well-known singular integral equation approach for deriving an alternate form of eigenvalue equation with superior convergence properties. It is shown that accurate numerical results may be obtained from this eigenvalue equation using only a 2x2 matrix equation. In comparison, the conventional formulation of the problem requires the use of matrices that are much larger in size. Aside from the numerical efficiency, the simplicity of the method makes it possible to conveniently extract higher order modal solutions for the propagation constants that affect the high-frequency application of microstrip lines. Even though the derivation of the determinantal equation requires some intricate mathematical manipulations, the user may bypass these completely and use the final eigenvalue equation which is programmable on the computer.     

Evaluation of loss factor of multilayered inhomogeneous waveguidesfor magnetostatic waves using efficient finite element formalism

An efficient finite-element solution procedure is developed for calculating propagation losses of magnetostatic waves in multilayered inhomogeneous waveguides. The final matrix equation is reduced to a standard complex eigenvalue problem whose eigenvalue corresponds to the complex phase constant itself. Thus, iteration procedures are not necessary and the phase and attenuation constants can be directly obtained by solving a standard eigenvalue equation. The validity of the method is confirmed by calculating propagation losses of magnetostatic surface waves in a single yttrium-iron-garnet (YIG)-film structure. Numerical results for a triple-layered YIG film structure are also presented. It is found that, in the triple-layered structure, propagation losses are highly dependent on the linewidth of the film in which the magnetostatic potential is well confined     

一种求解微波介质谐振器复介电常数的方法

根据微波谐振系统中电场的波动方程,采用复频率和有耗导体的边界条件,导出以被测介质的复介电常数为本征值的微分和变分方程。使用MATLAB软件中的PDE工具箱,只要是能以二维形式作图表现的微波介质谐振器,都可以求解出其复介电常数,且与实验数据及不同方法计算的结果相吻合,该方法适用面广、计算精确、简洁方便。     

金属包层阶跃平板介质波导导模的二级微扰分析

直接求得的复本征值方程的解作为精确解,由微扰理论得到的一级和二级近似结果与之进行了分析比较,结果表明微扰法是相当好的近似方法,它们给出了与精确值符合相当好的数值结果。分析结果还表明微扰法的二级近似结果对一级近似结果的修正很小,一级近似已可以给出足够精确的结果。     

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.     

反比相关双曲余弦平方势与量子阱的空穴能级

鉴于“方形”势阱描述量子阱中的空穴运动行为过于简单、理想,引入了反比相关的双曲余弦平方势,并在量子力学框架内,利用这个相互作用势把空穴的Schrodinger方程化为了超几何方程,用系统参数和超几何函数严格地求解了空穴的本征值和本征函数,并以Ga1-xAlxAs-GaAs-Ga1-xAlxAs量子阱为例,计算了阱内的空穴跃迂。结果表明,空穴在量子阱中的能量是量子化的,而阱内的能级数目与系统参数有关。     

Analysis of optical fibers with graded-index profile by acombination of modified Airy functions and WKB solutions

An almost exact eigenvalue equation for optical fibers with graded-index profile is derived mathematically based on a combination of the modified Airy functions and the Wentzel, Kramers, Brillouin (WKB) trial solution. By applying proper boundary conditions, a phase shift correction term δ is found out which improves the inherent error problems of the conventional WKB method. It is shown through computer simulations that results of the derived eigenvalue equation are in excellent agreement with those of the finite-element method     

Huygens integral for an axially symmetric phase conjugate resonator

We derive both the Huygens roundtrip integral and the eigenvalue equation for an axially symmetric phase conjugate resonator. Important practical conclusions that can be drawn from this eigenvalue equation, including the possibility of correcting arbitrary thin phase perturbations at the conventional mirror, are discussed.     

金属包层非均匀平板介质波导传输特性分析

用微扰理论和多层分割法求得到金属包层非均匀介质波导导模的传播常数的一级和二级近似解,与用复本征方程求得的精确解进行比较,给出了与精确值符合相当好的数值结果,结果表明微扰法是相当好的近似方法,二级近似结果对一级近似结果的修正很小,一级近似已可以给出足够精确的结果。     

计算表面波特征方程的一种新的数值方法

推导了同轴线馈电的微带天线表面波电磁场表达式及其特征方程.结合遗传算法与参数跟踪策略形成一种新的算法,并基于该算法对表面波特征方程进行了精确数值求解,求解结果与本问题的已有结论吻合的很好.该方法具有简单、通用、求解精度高等优点.     

On the Complete Eigenvalue Solution of Ridged Waveguide

The complete solution of the ridged waveguide eigen-value problem is presented. The solution is obtained by the formulation of an integral eigenvalue equation which is subsequently solved numerically by application of the Ritz-Galerkin method. The significance of the eigenvalue spectrum is discussed and the modes are classified as either hybrid or trough modes. Equations are given for the electric and magnetic fields and a brief discussion of the edge singularity is presented. The theory is illustrated by computing the dominant eigenvalues and characteristic impedances of various unsymmetrical ridged waveguides.     

任意截面波导特性的非正交频域有限差分研究

本文提出了一种求解波导本征问题的非正交频域有限差分(FD-FD)算法。该算法中的数值离散网格可与任意复杂边界形状吻合一致。文中通过所建立的本征方程对波导中各模式的截止频率进行了求解,数值结果与已有结果符合良好。     

Influence of eccentricity on the frequency limitations of circular-pad via-holes

We study the influence of the technologically caused eccentricity of a circular-pad via-hole. We derive an eigenvalue equation using a rigorous method based on a linear transformation of the via-hole polar coordinates. The eigenvalue equation is used to compute the modal resonant frequencies and the modal fields of the eccentric via. It is shown that the via-hole misalignment shifts the modal frequencies and influences its frequency band. The proposed model is verified with published experimental data, and is also compared with results generated with the full-wave simulator Agilent Momentum-2002.     

Eigenvalue equations and numerical analysis of a coaxial cavitywith misaligned inner rod

Based on the Helmholtz equation, the superposition of cylindrical wave functions, and coordinates transformation, the eigenvalue equation is derived rigorously for a coaxial gyrotron cavity with a misaligned inner rod. It is shown that, due to the existence of the structural misalignment, any single normal mode of a perfect coaxial structure (i.e., without misalignment) no longer simultaneously satisfies both the outer and inner boundary conditions; consequently, the superposition of cylindrical wave functions must be taken into account. A numerical approach of solving the eigenvalue equation is proposed in this paper. As a practical application, analysis is given to the higher mode coaxial cavity employed in a 140-GHz/1.5-MW gyrotron device at the Forschungszentrum Karlsruhe, Karlsruhe, Germany. Result shows that the eigenvalue of the operating mode in a misaligned coaxial cavity is affected noticeably by the structural misalignment     

Surface integral formulation for calculating conductor anddielectric losses of various transmission structures

The power-loss method, along with a surface integral formulation, has been used to compute the attenuation constant in microstrip and coplanar structures. This method can be used for the analysis of both open and closed structures. Using the surface equivalence principle, the waveguide walls are replaced by equivalent electric surface currents and dielectric surfaces are replaced by equivalent electric and magnetic surface currents. Enforcing the appropriate boundary condition, and E-field integral equation (EFIE) is developed for these currents. Method of moments with pulse expansion and point matching testing procedure is used to transform the integral equation into a matrix one. The relationship between the propagation constant and frequency is found from the minimum eigenvalue of the moment matrix. The eigenvector pertaining to the minimum eigenvalue gives the unknown electric and magnetic surface currents     

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

A numerical method for determining the modes of a rectanguIar or a circular waveguide strongly perturbed by axial cylindrical conducting objects is presented. The method is based upon an integral equation which leads to a matrix eigenvalue problem by using the Galerkin procedure. Cutoff wavenumbers are simultaneously calculated with very good precision for a number of modes near to the order of the matrix eigenvalue problem. Excellent results are obtained also when the perturbed waveguide section exhibits reentrant parts or edges. Computing time is short and storage requirements are moderate. The method is also applicable for waveguides of arbitrary cross section.     

Correction to the analysis of dielectric guides by transversemagnetic field finite element penalty function method with extensions

Recently a method to obtain the propagation constants of lossless dielectric waveguides using the Helmholtz equation with the finite element method and penalty function method was presented. The advantage of using this approach is that only one final eigenvalue matrix needs to be solved for only two components of the H-fields. We have determine that the results were obtained using an eigenvalue solver that did not account for the asymmetry in the final eigenvalue matrix. In this paper, we present the results of the same cases simulated using the correct eigenvalue solver, and the results obtained are in good agreement with previously published ones. We also show by simulation of appropriate cases, a high penalty factor is correlated to highly coupled modes, while weakly coupled modes may be correlated to small penalty factors. Finally, we have extended the penalty function method to include the complex case without the use of the perturbation method. The gain results obtained for a channel waveguide are in good agreement with previously published ones