On the Resonant Frequency of a Reentrant Cylindrical Cavity

A new efficient method determining the resonant frequency of a reentrant cylindrical cavity is suggested. The method is based on solving the Helmholtz equation within two cavity regions and matching the solutions across the boundary surface. Contrary to similar formulations published previously, the continuity conditions on the boundary are imposed in a rigorous way. As a result the solution is obtained in a form of succesive approximations converging to the exact resonant frequency when a number of iterations tend toward infinity. Numerical examples are given for a few reentrant cavities of typical dimensions. Comparison is also made with experimental data as well as other theoretical results.     

基于不同边界条件的SIW谐振腔导模场分析及应用

总结了完备的六种不同边界条件的基片集成波导(SIW)谐振腔结构体系.基于镜像原理和亥姆霍兹方程,给出而不同边界条件下SIW谐振腔的导模场的闭式解.分析了所有边界条件下的谐振腔的场分布,与全波仿真分析、传输线模型法和空腔模型理论给出的结果一致.给出了各种边界条件下SIW谐振腔的谐振频率计算公式.基于提出的传输线附加额外的两个边界条件与谐振腔等效的原理,分析了在SIW谐振腔内,TE模、TM模与TEM模的共存机理.阐述了不同边界条件下的SIW谐振腔的演变关系.最后设计了基于不同边界条件的SIW谐振腔结构的双模带通滤波器和均衡器,该滤波器的两个模式,TE100(TEM模式)和TE102独立可调.器件的实测结果与仿真结果一致,验证了理论分析的正确性,为微波器件的小型化设计提供了思路.     

On the Applicability of the Surface Impedance Integral Equation for Optical and Near Infrared Copper Dipole Antennas

The applicability of the surface impedance integral equation (SI-IE) method for the analysis of optical and near-infrared copper dipole antennas is assessed, and some issues relative to resonant half-wavelength optical dipoles are highlighted. Since at these frequencies the conductivity of copper (and of all metals) is relatively small, the appropriateness of using the standard integral equation method for imperfectly conducting wires, based on a surface impedance boundary condition, needs to be examined. Here it is found that the SI-IE method yields accurate results in the near-infrared regime, and for suitably small wire radius values at low optical frequencies. For the middle and upper optical frequencies the approximate SI-IE is not generally valid. Some results are presented for a half-wave dipole resonant in the upper near-infrared/low optical range, and a discussion of the trade-off between maintaining good polarization selectivity and radiation efficiency is provided     

Exact surface impedance/admittance boundary conditions for complexgeometries: theory and applications

A methodology useful to derive exact and higher order surface impedance/admittance boundary conditions (HOI/ABC's) for complex geometries is presented. It is shown that exact surface boundary conditions are always expressed through dyadic integral operators involving the tangential magnetic and electric fields all over the surface of the body. Quasi-local surface boundary conditions that include curvature effects are shown to be computable through an asymptotic approximation of the integral operators. Finally, an example of a surface admittance boundary condition useful to analyze a structure exhibiting discontinuities along its surface boundary is presented. Practical examples to demonstrate the feasibility of the proposed methodology, as well as the accuracy of the resulting surface boundary conditions are also presented     

Spectral Domain Analysis of Coaxial Cavities

Coaxial cavities are used in high power gyrotrons as the beam-wave interaction structure. Much research has been devoted to their mode selective properties. A coaxial cavity lacks a sharp boundary at its open end, so it has some physical features that can only be observed using a spectral model, such as frequency-dependent field profiles and mode overlapping effects. These properties are important since cold tests are usually conducted in the frequency domain. This study applies the incident/reflected wave boundary condition to the wave equation of a weakly irregular coaxial waveguide. The resistivity of the wall is considered in the analysis. Calculations reveal that the fixed-position spectrum yields an uncertain resonant frequency and quality factor. Although the maximum-field spectrum can uniquely determine the properties of the coaxial cavity, the resonant frequency obtained using the maximum-field spectral model is inconsistent with that obtained using the temporal model. The field-energy spectrum explains the low Q nature of the coaxial cavity. Moreover, resonant frequencies evaluated using the field-energy spectrum agree precisely with those evaluated using the temporal model.     

GIBC formulation for the resonant frequencies and fielddistribution of a substrate-mounted dielectric resonator

Dielectric resonators (DR's) are widely used in telecommunication systems. A method is proposed here to find the resonant frequency and field distribution in a substrate-mounted DR structure. The field of a dielectric rod has been decomposed into a combination of guided modes with unknown coefficients and an unknown continuous spectrum of radiation field. The unknowns are then obtained by applying two generalized impedance boundary conditions (GIBC's) representing the substrate and air layers at the top and bottom of the DR. This leads to the calculation of the total (guided+radiation) field as well as the resonant frequency of the structure     

可调频压电俘能结构研究

提出一种由悬臂梁和分布式压电片构成的可调频压电俘能结构,改变压电片的电场边界条件可改变俘能结构的共振频率,对该结构下的两种不同的压电片结合形式进行了ANSYS仿真验证与比较。结果表明,使用嵌入式结合形式比使用表面粘贴式结合形式可得到更高的频率变化率,频率相对变化率可达3.17%。     

网络分解直线法结合周期边界条件分析开域微带结构

本文用网络分解直线法结合周期边界条件,以平面波激励,通过贴片电流提取相关参数的方法,分析开域微带结构。阻抗元素计算和减缩方程求解,分别使用快速傅里叶变换和网络分解技术,从而大大提高了计算效率。周期边界模拟开域的收敛性研究和计算时间的比较表明了该方法的有效性。最后计算了矩形贴片平面谐振器的谐振频率,其结果与已发表的值吻合很好。     

ANALYSIS OF OPEN MICROSTRIP STRUCTURES BY USING DIAKOPTIC METHOD OF LINES COMBINED WITH PERIODIC BOUNDARY CONDITIONS

This paper presents the analysis of open microstrip structures by using diakoptic method of lines (ML) combined with periodic boundary conditions (PBC). The parameters of microstrip patch are obtained from patch current excited by plane wave. Impedance matrix elements are computed by using fast Fourier transform(FFT), and reduced equation is solved by using diakoptic technique. Consequently, the computing time is reduced significantly. The convergence property of simulating open structure by using PBC and the comparison of the computer time between using PBC and usual absorbing boundary condition (ABC) show the validity of the method proposed in this paper. Finally, the resonant frequency of a microstrip patch is computed. The numerical results obtained are in good agreement with those published.     

Analysis of dielectric resonator cavities using the finiteintegration technique

Resonant modes in shielded dielectric resonators are studied by a numerical technique which yields the resonant frequencies, modal field distribution, and Q-factors of various resonant modes, including the hybrid modes. The technique uses field discretization by virtue of dual electric and magnetic grids and allows for a direct numerical solution of the integral form of Maxwell's equation for specified boundary conditions. The details of the matrix formulation are explained on an example of the cavity subdivided into a grid consisting of 3×3 electric cells. A modal field plot exhibiting a spiraling behavior has been observed     

On the Complex Resonant Frequency of Open Dielectric Resonators

An analytical method is presented for calculating accurately the complex resonant frequency of dielectric pillbox resonators. In this method, an approximated field of the resonator is expanded into a truncated series of solutions of the Hehnholtz equation in the spherical coordinates, and the boundary condtion on the resonator surface is treated in the least-squares sense. The resonant frequency and the intrinsic Q value due to radiation loss are obtained in the form of approximation converging to the exact values. Numericaf results are compared with previously published calculations, which show that the present method is a relatively simple and effective one.     

Analysis of stacked microstrip patches with a mixed potentialintegral equation

A method based on the mixed potential integral equation for the analysis of flat microstrip antennas in a double-layer substrate is presented. The method is used to compute the input impedance of a stacked patch configuration. This structure permits a larger bandwidth and may also provide dual-frequency operation. The Green's functions are discussed in detail, and numerical results are obtained for the propagation constant of the dominant surface wave. Theoretical and experimental results are compared for a dual-frequency and a broadband stacked patch antenna. Theoretical results for the input impedance are in good agreement with measurements. The difference between theoretical and experimental results for the resonant frequency is less than 4.5% in all cases     

Standing spin waves in ferromagnetic thin films

A theory of spin wave resonance in ferromagnetic thin films is discussed in a manner that permits a computation of the real and imaginary parts of the circularly polarized RF fields as well as the power absorption spectrum. The case of the dc field intensity applied normal to the surface of the film is considered, and the saturation magnetization is taken as constant throughout the body of the film. Variations in dc fields near the surfaces are treated in the boundary conditions for the RF magnetization by considering the unsymmetrical nature of the exchange interaction at the surfaces. The boundary conditions are characterized by a constant for each surface that controls the degree of surface pinning in the RF magnetization. Damping is included in the formulation by means of a phenomenological constant in the spin wave equation and by simulaneous solution of this equation with Maxwell's equations for a conductor. The results of a computer program are presented showing the roles of the various parameters in determining the power absorption spectrum and RF fields. A comparison with experimental spectra is made, and an anomalous resonance at field intensities higher than that for the principal resonance is predicted.     

A method of reducing the effects of anode aperture in high-perveance convergent electron guns

A new theoretical method of designing convergent electron guns of high perveance for use in microwave tubes is presented here. A differential equation which represents electron trajectories in a convergent electron stream has been deduced under certain approximations. Electron trajectories in an electron stream and boundary values along its boundary were numerically calculated by solving the differential equation by means of an electronic computer. Boundary values on the virtual anode surface under space-charge-limited conditions were used as the initial values for the calculations. Focusing electrodes were determined to satisfy the boundary conditions on the stream boundary. The design procedure is also shown. The electron guns designed by this method are somewhat different in structure from the conventional ones which are usually designed experimentally rather than theoretically. In these new electron guns, nearly uniform current densities will be obtained over the whole cathode area, while in conventional convergent guns of high perveance, electron emission density near the center of the cathodes is usually reduced due to the influence of the anode aperture. Laminar flow will be obtained at points near the minimum stream diameter also in guns designed by this method. Digital computer experiments were performed and the results proved this hypothesis to be reasonable. An electron gun of 1.72 × 10^-6perveance and area convergence ratio of 70:1 is shown as an example.     

On combined source solutions for bodies with impedance boundary conditions

Numerical solutions to the impedance boundary condition (IBC) combined source integral equation (CSIE) for scattering from impedance spheres are presented. The CSIE formulation is a well-posed alternative to the IBC electric and magnetic field integral equations which can be contaminated by spurious resonant modes. Compared with the IBC combined field integral equation (CFIE), CSIE solutions have the same accuracy when the combined source coupling admittance is chosen to be the same value as the combined field coupling admittance. However, the CSIE formulation is better suited than the CFIE for creating a general purpose computer code capable of handling aperture radiation problems and/or a scatterer which has a spatially varying surface impedance.     

Computer designs for beam pentodes

A computer program for the solution of Poisson's equation in two dimensions with mixed boundary conditions has been used to solve for electron trajectories in beam pentodes with circularly cylindrical cathode contours and round wire grids in the general configuration of many Pierce guns in parallel. Such designs can have nearly uniform cathode current density over the entire cathode surface and zero grid interception under all conditions of interest, including positive grid conditions. Operation with the plate voltage as low as 5 per cent of the screen grid voltage provides satisfactory secondary electron retention in a typical design for which complete transfer characteristics are computed.     

Variational Solution of Integral Equations

A variational solution of the Fredholm integral equation of the first kind resulting from Laplace's equation with Dirichlet boundary conditions is discussed. Positive-definiteness of the integral operator is used to guarantee convergence. The square parallel plate capacitor is given as an example with several different types of trial functions. Special singular functions to handle known field behavior are shown to result in improved accuracy with reduced computing cost. The air-dielectric interface condition is related to a general Neumann-mixed boundary condition for which a variational method with a positive-definite integral operator is presented. Multiple boundary conditions are handled by mutually constraining separate variational expressions for each boundary condition. A T-shaped conductor on a dielectric slab, representative of quasi-static solutions of microstrip discontinuities, is presented as a three-dimensional example with multiple boundary conditions. Generally, it is shown how the finite-element method for the solution of partial differential equations may be extended to handle integral equation formulations.     

Nonparabolicity effects and the spin-split electron dwell time in symmetric III-V double-barrier structures

We start from the fourth-order nonparabolic and anisotropic conduction band bulk dispersion relation to obtain a one-band effective Hamiltonian, which we apply to an AlGaSb symmetric double-barrier structure with resonant energies significantly (more than 200 meV) above the well bottom. The spin-splitting is described by the k³ Dresselhaus spin-orbit coupling term modifying only the effective mass of the spin eigenstates in the investigated structure. Apart from the bulk-like resonant energy shift due to the band nonparabolicity, we obtain a substantial shift depending on the choice of boundary conditions for the envelope functions at interfaces between different materials. The shift of resonant energy levels leads to the change of spin-splitting and the magnitude of the dwell times. We attempt to explain the influence of both the nonparabolicity and boundary conditions choice by introducing various effective masses.     

Propagation characteristics of dielectric-rod-loaded waveguides

A general technique for calculating the propagation characteristics of a waveguide with arbitrary cross-sectional shape loaded with a circular dielectric rod is presented. The waveguide fields, which are represented as a sum of functions satisfying the homogeneous Helmholtz equation and the boundary conditions at the rod surface, are point-matched at the surface of the waveguide. Numerical examples of a rod centered in a square guide and off center in a circular guide are given, and results for a rod centered in a rectangular cavity are compared with measured data     

Coupling finite element and integral equation solutions usingdecoupled boundary meshes [electromagnetic scattering]

A method is outlined for calculating scattered fields from inhomogeneous penetrable objects using a coupled finite element-integral equation solution. The finite element equation can efficiently model fields in penetrable and inhomogeneous regions, while the integral equation exactly models fields on the finite element mesh boundary and in the exterior region. By decoupling the interior finite element and exterior integral equation meshes, considerable flexibility is found in both the number of field expansion points as well as their density. Only the nonmetal portions of the object need be modeled using a finite element expansion; exterior perfect conducting surfaces are modeled using an integral equation with a single unknown field since E _tan is identically zero on these surfaces. Numerical convergence, accuracy, and stability at interior resonant frequencies are studied in detail