双层频率选择表面电磁特性数值模拟研究

给出了一种分析有介质加载的不同栅格外形双层频率选择表面电磁特性的数值模拟方法.介质分离区内前向波和反向波分别关于相应的频率选择表面是周期的,确定了矢量传输及衰减模的表述形式.应用电磁场边界条件获得不同Floquet模系数的矩阵表达式,推导出一组耦合的积分方程,利用矩量法求解得到结构的电磁散射特性.模拟结果表明,由于层间介质内电磁场衰减模的耦合,双层FSS结构的电磁传输特性较单层有很大的改善.     

Hybrid FEM/Floquet Modes/PO Technique for Multi-Incidence RCS Prediction of Array Antennas

An original method is proposed which associates rigorous 3D finite element methods (FEM) with Floquet modes through FACTOPO multidomain formalism for computing the radar cross section (RCS) of large array antennas. The most original aspect of the method is the fact that the source unit cell is characterized by a generalized scattering matrix (GSM) which does not depend on the plane wave incidence impinging the structure. Consequently, the factorization step of the FEM matrix, which is the main computational effort, is performed only once. The assembling procedure consists then in expressing the FEM GSM matrix in the Floquet mode basis for each incidence and to solve a linear system giving the complex amplitude of the Floquet modes on the array/cell interface. Associated with this formalism, lateral and back structure effects can be treated using physical optics (PO) combined with the equivalent current method (ECM) to improve the accuracy for far broadside incidence.     

Element dependency in dielectric tuning of frequency selective surfaces

The dependence on substrate thickness of the resonance frequencies of dipole, square loop and circular patch FSSs is examined. Circular patches contain less fine scale structure, requiring fewer high order Floquet field modes. The evanescent fields are less tightly bound and the air/dielectric boundary is significant at greater substrate thicknesses.<>     

A mode-matching approach to determine the shielding properties of a doubly periodic array of rectangular apertures in a thick conducting screen

The application of the mode-matching technique to determine the shielding properties of a thick doubly periodic conducting screen of rectangular apertures is presented. Floquet waves are used to represent the reflected and transmitted fields, while waveguide modes are used to determine the fields within the screen. Expressions for all fields are formed using Hertzian potentials. After enforcing boundary conditions and forming a system of linear equations, the mode coefficients are determined using standard techniques. Numerical results show the effect of increasing thickness and incidence angle variation on transmitted power. It is shown that by selectively choosing the number of waveguide modes, meaningful results for transmission can be obtained for screens whose thickness is several times the size of the apertures. The results also demonstrate the relationship between this approach and application of the waveguide below cutoff principle. It is also noted that at higher frequencies, higher order Floquet modes will propagate and contribute to the transmitted power.     

Phased array antenna analysis with the hybrid finite element method

A new analysis technique for infinite phased array antennas was developed and demonstrated. It consists of the finite element method (FEM) in combination with integral equation radiation conditions and a novel periodic boundary condition for 3-D FEM grids. Accurate modeling of rectangular, circular and circular-coaxial feeds is accomplished by enforcing continuity between the FEM solution and several waveguide modes across an aperture in the array's ground plane. The radiation condition above the array is enforced by a periodic integral equation in the form of a Floquet mode summation, thus reducing the solution to that of a single array unit cell. The periodic boundary condition at unit cell side walls is enforced through a matrix transformation. That mathematically “folds” opposing side walls onto each other with a phase shift appropriate to the array lattice and scan angle. The unit cell electric field is expanded in vector finite elements. Galerkin's method is used to cast the problem as a matrix equation, which is solved by the conjugate gradient method. A general-purpose computer code was developed and validated for cases of open-ended waveguides, microstrip patches, clad monopoles and printed flared notches, showing that the analysis method is accurate and versatile     

A two-dimensional time-domain finite element formulation for periodic structures

A formulation is presented for a two-dimensional time-domain finite-element method (FEM-TD) that incorporates periodic boundaries. The specifics of the method are shown for scattering problems, but it should be straightforward to extend it to radiation problems. The method solves for a transformed field variable (instead of solving directly for the electric field) in order to easily enable periodic boundary conditions in the time domain. The accuracy and stability of the method is demonstrated by a series of examples where the new formulation is compared with reference solutions. Very accurate results are obtained when the excitation (frequency range) and the geometry are such that no higher order Floquet modes are present. The accuracy is degraded in the presence of higher order modes due to the rather simple absorbing boundary condition that is used with the present formulation. The method is found to be stable even for angles of incidence close to grazing.     

Finite-element method coupled with method of lines for the analysis of planar or quasi-planar transmission lines

A full-wave analysis incorporating the finite-element method (FEM) and the method of lines (MoL) is presented in this paper to investigate a planar or quasi-planar transmission-line structure containing complex geometric/material features. For a transmission-line structure being considered, the regions containing complex media are modeled by the FEM while those consisting of simple media with simple geometry are analyzed using the MoL. From the field solutions calculated by MoL, the boundary conditions are constructed. The boundary integrals involved in finite-element analysis are then carried out using these boundary conditions. Since the finite-element analysis is employed only in the complex parts of the structures, while other parts are handled by the MoL, this approach not only retains the major advantage of the FEM in simulating complex structures but also becomes more efficient than the conventional finite-element analysis. Good agreement between the calculated results and those reported in the available literature is obtained and thus validates the present approach. Furthermore, proficient computational efficiency of this method is demonstrated by examining its convergence property. Finally, a number of relevant transmission-line structures are analyzed to illustrate the applications of this approach.     

Frequency-dependent analysis of a shielded microstrip stepdiscontinuity using an efficient mode-matching technique

The basic concepts of the mode-matching technique are used to formulate the boundary condition problem associated with the microstrip step discontinuity problem. The fields on both sides of a discontinuity are expanded in terms of the normal hybrid modes of the shielded microstrip line. The properties of these hybrid modes are determined by applying a previously developed analytical approach due to R. Mittra and T. Itoh (1971) using singular-integral-equation techniques. In addition to propagating modes, higher-order modes are also taken into account. The higher-order modes are evanescent-type waves. The propagation constants of the evanescent waves in general are found to be complex numbers. A mode-matching procedure is developed to determine the reflection and transmission coefficients of the discontinuity. The use of two types of products to treat the boundary conditions for the continuity of the tangential electric and magnetic fields results in a highly efficient and numerically stable solution. Numerical results are computed for several step discontinuities and the results are compared with previously published data     

Impedance boundary conditions for finite planar and curved frequency selective surfaces

We consider the time-harmonic electromagnetic scattering problem from a finite planar or curved, infinitesimally thin, frequency selective surface (FSS), the periodic unit cells of which are constituted, exclusively, by electric conductors and free-space. In order to avoid the meshing of these cells, the problem is solved by employing an integral equation formulation in conjunction with approximate impedance boundary conditions (IBC) prescribed on the sheet that models the FSS. The impedance in the IBC is derived from the exact reflection coefficient calculated, for the fundamental Floquet mode, on the infinite planar FSS illuminated by a plane-wave at a given incidence. When the FSS is curved, and/or the direction of the incident wave is unknown, higher order IBCs are proposed that are valid in a large angular range and can be implemented in a standard method of moments formulation. Also, a simple technique is presented that allows to reproduce the radiating Floquet modes in the scattered field even though those are not accounted for in these IBCs. Their numerical efficiencies are evaluated for a curved strip grating translationally invariant along one direction. Finally, we present an alternative approach where the impedance is approximated by its truncated Fourier series, that considerably enhances the accuracy of the results at the cost, however, of a denser mesh of the sheet.     

High-frequency analysis of an array of line sources on a truncatedground plane

A uniform high-frequency solution is presented for the field radiated at finite distance by a semi-infinite beam-scanning array of magnetic line sources located on a perfectly conducting half-plane. The field is represented in terms of Floquet waves plus their relevant singly and doubly diffracted rays, which arise from both the end of the array and the edge of the half-plane. This representation is uniformly valid also when transition conditions from propagating to evanescent Floquet waves occur. Furthermore, it provides a simple and attractive physical interpretation and is found numerically very effective, due to the fast convergence of the Floquet wave expansion for the field     

A three-dimensional time-domain finite-element formulation for periodic structures

A formulation is presented for a three-dimensional time-domain finite-element method that can be used to analyze the scattering of a plane wave obliquely incident on a (doubly) infinite periodic structure using one unit cell. A broadband frequency response can be obtained in a single execution. The specifics of the method are shown for scattering problems, but it should be straightforward to extend it to radiation problems. The method solves for a transformed field variable (instead of solving directly for the electric field) in order to easily enable periodic boundary conditions in the time domain. The accuracy and stability of the method is demonstrated by a series of examples where the new formulation is compared with reference solutions. Accurate results are obtained when the excitation (frequency range) and the geometry are such that no higher order propagating Floquet modes are present. The accuracy is degraded in the presence of higher order propagating modes due to the rather simple absorbing boundary condition that is used with the present formulation. The method is found to be stable even for angles of incidence close to grazing.     

双层FSS结构电性能研究

提出了一种研究不同栅格及单元外形并有介质加载的双层频率选择表面(FSS)电性能的理论分析方法.通过确定双层FSS之间介质内传输波和反射波分别对相应的FSS具有周期性而得到矢量Floquet传输模和衰减模表达形式,应用切向电磁场边界条件推导出一组耦合积分方程,利用矩量法求解得到结构的电磁特性.以Y形缝隙作为FSS谐振单元,计算结果表明,双层FSS结构通过层间电磁场衰减模的耦合能够修正频率响应曲线,电性能较单层有很大的改善.     

阶梯波导的传输矩阵研究

用模式匹配方法分析H面阶梯波导的TE模式,首先将各区域的场写为x函数矩阵与z函数矩阵以及本区域的场系数向量相乘的形式,然后对相邻区域的x函数矩阵进行加权积分得到矩阵形式的匹配方程组。不仅在表达形式上简洁紧凑,而且能够方便的推导出考虑高次凋落模的传输矩阵。通过传输矩阵求解场,未知数个数成倍减小,运算量显著降低。数值例子验证了方法的正确性。     

3D target recognition based on projective invariant relationships

In this paper, we propose a new 3D target recognition algorithm using a single image. Our approach is based on geometrically invariant relationships. By employing a practical CCD camera model for projective image formation, and analyzing the constraints on the projection parameters, we derive two invariant relationships using six pairs of 3D space features and corresponding image features, such as points and lines. Compared to the conventional approach in which only a single invariant relationship is derived from six point pairs based on the general finite projective camera model, the two relationships obtained from the practical camera model can increase the effectiveness of matching. Based on the derived invariant relationships, a new view-invariant object recognition algorithm using a single image is proposed. The performance of the proposed recognition algorithm is demonstrated by various computer simulations on synthetic and real images of objects. The experimental results show that 3D objects in the image can be robustly recognized, using the linear features, by the proposed algorithm.     

Discretized Boundary Equation Method for Two-Dimensional Scattering Problems

A unified approach, named discretized boundary equation (DBE) method, is introduced for two-dimensional (2-D) scattering problems. It is based on the discretization of field expressions for one or two components of the scattered field. The DBEs can be used either on the object surface to obtain the solution directly or on the truncation boundary of a finite difference (FD) or finite element (FE) mesh as termination conditions. This paper describes the general theory of the DBE method and key points or limitations for its implementation. A new on-surface formulation for the solution of scattering by perfectly conducting cylinders is presented as an application of the two-component version of the DBE method and validated through numerical examples. Mesh termination conditions for the FD or FE method are derived based on the one-component formulation of the DBE method and their equivalence and difference to the measured equation of invariance are discussed. In particular, the DBE obtained with the minimum norm least squares solution is investigated thoroughly and its validity and features are demonstrated through numerical results, generated together with the FD method, for scattering by cylinders with various material properties.     

Frequency- and time-domain Green's functions for a phasedsemi-infinite periodic line array of dipoles

We extend a previous prototype study of Felsen and Capolino (see ibid. vol.48, p.921-931, June 2000) of frequency-domain (FD) and time-domain (TD) Green's functions for an infinite periodic phased line array of dipoles to account for the effects of truncation, as modeled by a semi-infinite array. These canonical problems are to be used eventually for the systematic analysis and synthesis of actual rectangular TD plane phased arrays. In the presentation, we rely on the analytic results and phenomenologies pertaining to the infinite array, which are reviewed. Major emphasis is then placed on the modifications introduced by the truncation. Finite Poisson summation is used to convert the individual dipole radiations into collective truncated wavefields, the FD and TD Floquet waves (FW). In the TD, exact closed-form solutions are obtained, and are examined asymptotically to extract FD and TD periodicity-matched conical truncated FW fields (both propagating and nonpropagating), corresponding tip-diffracted periodicity-matched spherical waves, and uniform transition functions connecting both across the FD and TD-FW truncation boundaries. These new effects can again be incorporated in a FW-modulated geometrical theory of diffraction. A numerical example of radiation from a finite phased TD dipole array with band-limited excitation demonstrates the accuracy and efficiency of the FW-(diffracted field) asymptotic algorithm when compared with an element-by-element summation reference solution     

Time-domain Green's function for an infinite sequentially excitedperiodic line array of dipoles

Green's functions based on truncated periodicity play an important role in the efficient analysis of radiation from, or scattering by, phased-array antennas, frequency selective surfaces and related applications. Such Green's functions exploit the equivalence between summation over the contributions from individual elements in an array and their collective treatment via Poisson summation in terms of an infinite series of Floquet waves (FW). While numerous explorations have been carried out in the frequency domain (FD), much less has been done for transient excitation. In order to gain understanding of the FW critical parameters and phenomenologies governing time-domain (TD) periodicity, we consider the simple canonical problem of radiation from an infinite periodic line array of sequentially pulsed axial dipoles. This problem can be solved in closed form and also by a variety of alternative representations, which include inversion from the FD, spectral decomposition into TD plane waves, the complex space-time analytic signal formulation, and the Cagniard-de Hoop method. These alternatives, some of which apply traditionally only for nondispersive TD events, are shown to still work here because of the special character of the FW dispersion. Particular attention is given to evanescent TB-FWs and their transition through cutoff. Asymptotic techniques grant insight into the TD-FW behavior by identifying their instantaneous frequencies, wavenumbers, and other physics-based parameterizations. A basic question concerns the definition of what constitutes a physically “observable” (causal, etc.) TD-FW. The proposed answer is based on consistency among models arrived at by alternative routes     

A matrix method for studying TM modes of optical planar waveguideswith arbitrary index profiles

Application of a previously proposed matrix method (which can only be used for TE mode solutions) to studying the wave characteristics of TM modes is described. To derive the matrix equation for TM-mode solutions of slab waveguides, the gradient of a continuous field is defined as the sum of a continuous function and a stepwise function so that boundary conditions are satisfied. By expanding both the index profile and mode field distribution into a truncated Fourier series, a particular matrix equation for determining mode indices and mode field distributions is obtained. Such a matrix equation can be generalized as BX = β²X, where B is a constant matrix, ß is the propagation constant, and the vector X accounts for the mode field distribution. Wave characteristics of TM modes of slab waveguides with arbitrary index profiles can thus be obtained following the solution of a linear algebra problem in a way similar to that for studying TE modes. The matrix B here, however, as indicated by this work, is different from that for TE mode solutions. Also, it is pointed out in this paper that the matrix B for TM-mode solutions has a different form as a different kind of waveguide is considered. Numerical results presented herein show that a sufficiently high accuracy can be obtained by using the proposed method     

双压电复合薄圆板驱动器的理论分析

双压电膜是由压电材料层、环氧树脂层、金属层组成的复合薄圆板。将多层双压电膜组合在一起构成管内移动微小机器人的驱动器。文章基于压电和金属材料的弹性薄板理论，应用瑞利-李兹近似求解法，推导了在固支与简支两种边界条件下，双压电膜的弯曲振动的固有频率与相对庆的振型的计算表达式。将理论计算与有限元分析的结果进行对比分析，结果表明，两者的计算结果吻合好，验证理论分析的正确性。分析与讨论了压电层与金属层的厚度对固有频率的影响。此研究为微小型机器人驱动器的优化设计提供理论依据。     

Microwave Biomedical Data Inversion Using the Finite-Difference Contrast Source Inversion Method

We present a contrast source inversion (CSI) technique which is based on a finite-difference (FD) solver for use in microwave biomedical imaging. The algorithm is capable of inverting complex-permittivity biomedical data sets without the explicit use of a forward solver at each iteration. The FD solver is based in the frequency domain, utilizes perfectly matched layer (PML) boundary conditions, and the stiffness matrix is solved via an LU decomposition and Gaussian elimination. An important feature of the FD-CSI algorithm is that the stiffness matrix associated with the FD solver depends only upon the background medium and frequency, and thus the LU decomposition is only performed once, before the iterative inversion process. Unlike the usual Integral Equation (IE) based inversion techniques, the FD-CSI algorithm is readily capable of utilizing an arbitrary background medium for the inversion process.