Comments on “Near-zone gain of open-ended rectangularwaveguides” [and reply]

The author comments that formulating the problem of radiation from open-ended rectangular waveguides (OEG) using an electric field integral equation (EFIE), Kawalko and Kanda (see ibid., vol.39, p.408-13, 1997) present results for the near-zone gains as a function of both the frequency and distance from the OEG aperture. These values can be considered to be exact. On the alternative methods, this paper observes that the approximate formulas need the measured values of the aperture reflection coefficient and the total radiated power. Kawalko and Kanda reply that the formula for the on-axis gain presented by Selvan (see Inst. Electron. Telecommun. Eng. J. Res., vol.43, p.61-4, 1997) certainly has an advantage over Yaghjian's formula (1984) in that it does not require knowledge of the total radiated power or the reflection coefficient at the aperture. However, this formula still does not account for all of the diffraction effects that occur at the aperture of the OEG     

Near-zone gain of 500 MHz to 2.6 GHz rectangular standard pyramidalhorns

Full-wave solutions to the problem of radiation by rectangular standard pyramidal horn antennas are presented. The radiation problem is formulated in terms of an electric field integral equation (EFIE), which is solved using the method of moments (MoM) for four rectangular standard pyramidal horns covering the frequency range from 500 MHz to 2.6 GHz. Results for the near-zone gains as a function distance from the aperture of the horn antenna are presented. A comparison is made with the analytical formula for the fields and near-zone gains     

基于时域混合场积分方程求解目标瞬态散射特性

当入射平面波的频谱包含目标的谐振频点时,时域电场积分方程和时域磁场积分方程求解的表面电流不稳定,会出现后期震荡现象。通过线性组合时域电场积分方程和时域磁场积分方程,可以获得一种混合场积分方程。数值结果显示,这种混合场积分方程消除了因内部谐振引起的后期震荡,得到了稳定的表面电流分布和远区散射场。     

An iterative current-based hybrid method for complex structures

This paper presents a general unified hybrid method for radiation and scattering problems such as antennas mounted on a large platform. The method uses a coupled electric-field integral equation (EFIE) and magnetic-field integral equation (MFIE) formulation, referred to as the hybrid EFIE-MFIE (HEM), in which the EFIE and MFIE are applied to geometrically distinct regions of an object. The HEM is capable of modeling arbitrary three-dimensional (3-D) metallic structures, including wires and both open and closed surfaces. We show that current-based hybrid techniques that utilize physical optics (PO) are an approximation of the HEM formulation. A numerical solution procedure is given that combines the moment method (EFIE) with an iterative Neumann series technique (MFIE). This permits one to effectively utilize the PO approximation when appropriate, and provides a general and systematic mechanism to correct the errors introduced by PO. Consequently, the HEM overcomes the inherent limitations of hybrid techniques which rely upon ansatz-based improvements of PO. The method is applied to the problem of radiation from objects that can be modeled using wires and metallic surfaces as fundamental elements. A representative example is given to demonstrate that the method can handle the difficult problem of a parasitic monopole located in the deep shadow region     

A novel technique for analysis of electromagnetic scattering frommicrostrip antennas of arbitrary shape

A new numerical procedure is developed for the solution of the electric field integral equation (EFIE) for arbitrary-shaped microstrip structures. This approach is superior over conventional EFIE techniques particularly in the low-frequency region or where the structure to be analyzed is electrically small. A pair of new basis functions is presented which are essential to the solution in the entire frequency range of interest. The new basis functions decompose the surface current density into divergenceless and curl-free parts which essentially get decoupled at the very low end of the frequency spectrum. Typical numerical results are presented for certain examples to illustrate the difference in the results between the two methods     

On the determination of resonant modes of dielectric objects using surface Integral equations

Although surface integral equations have been extensively used for solving the scattering problem of arbitrarily shaped dielectric objects, when applied to the resonance problem, there are still some issues not fully addressed by the literature. In this paper, the method of moments with Rao-Wilton-Glisson basis functions is applied to the electric field integral equation (EFIE) for solving the resonance problem of dielectric objects. The resonant frequency is obtained by searching for the minimum of the reciprocal of the condition number of the impedance matrix in the complex frequency plane, and the modal field distribution is obtained through singular value decomposition (SVD). The determinant of the impedance matrix is not used since it is difficult to find its roots. For the exterior EFIE, the original basis functions are used as testing functions; for the interior EFIE, the basis functions rotated by 90/spl deg/ are used as testing functions. To obtain an accurate modal field solution, the impedance matrix needs to be reduced by half before SVD is applied to it. Numerical results are given and compared with those obtained by using the volume integral equation.     

An efficient perfectly matched layer based multilevel fast multipole algorithm for large planar microwave structures

An efficient multilevel fast multipole algorithm (MLFMA) formalism to model radiation and scattering by/from large planar microwave structures is presented. The technique relies on an electric field integral equation (EFIE) formulation and a series expansion for the Green dyadic, based on the use of perfectly matched layers (PML). In this way, a new PML-MLFMA is developed to efficiently evaluate matrix-vector multiplications arising in the iterative solution of the scattering problem. The computational complexity of the new algorithm scales down to O(N) for electrically large structures. The theory is validated by means of several illustrative, numerical examples.     

Electro-optic near-field mapping of planar resonators

A comprehensive experimental and theoretical study for the determination of the electric near-field above planar resonators is presented. The transverse component of the electric field is mapped by external electro-optic (EO) sampling technique with high spatial and temporal resolution. The evolution of the near-field radiation pattern of the investigated 7-GHz planar resonator to the onset of the far-field pattern is traced by measurements at various heights above the sample. Frequency-dependent measurements allow to characterize the field pattern changes when the frequency is swept through the main resonance. Additional undesired resonances are identified by the detected mode pattern. The experimental data are reproduced by simulations based upon an electric field integral equation (EFIE) method     

Scattering from structured slabs having two-dimensional periodicity

The problem of a plane wave incident on a structured slab is examined. To analyze the problem, an electric field integral equation (EFIE) is derived that has as its unknown the equivalent surface currents on the plates in the unit cell. The integral equation is discretized and solved approximately using the method of moments with subdomain basis and testing functions. The periodic Green's function is efficiently calculated using the Poisson summation formula. The interaction of the structure with the surrounding environment is described in terms of a generalized scattering matrix. Results are presented showing the reflection coefficient as a function of frequency for arrays of zigzagging strips and honeycomb slabs     

Time-domain electromagnetic computations using a modified EFIE kernel and field-source equilibrium relations

A form for the electric-field dyadic Green's function for free space is derived that allows explicit time evolution of the modified electric-field integral equation (EFIE) applied to surface scattering. The modified EFIE kernel, here called a "source function," has an integrable singularity in the source region, and is shown to be equivalent, in the frequency domain, to the standard dyadic Green's function. With definitions of "local" and "non-local" fields at a conductor surface, both electric and magnetic versions of the relations between non-local fields and equilibrium surface sources (currents and charges) are derived. These field-source equilibrium (FSE) relations are exact if all the non-local fields are included: the interaction fields, as well as the usual incident fields from distant sources. When the interaction fields are neglected, the magnetic-field version of the FSE relations becomes the usual physical optics approximation. Source functions and the FSE relations were used in two three-dimensional, time-domain numerical simulations to compute radiation patterns from a conical helical antenna driven at a fixed frequency, and scattering of a CW plane wave by a perfectly conducting sphere. This surface-scattering simulation was explicit but remained stable. Excellent agreement between the computed and known results validated the approach.     

An advanced numerical model in solving thin-wire integral equations by using semi-orthogonal compactly supported spline wavelets

In this paper, the semi-orthogonal compactly supported spline wavelets are used as basis functions for the efficient solution of the thin-wire electric field integral equation (EFIE) in frequency domain. The method of moments (MoM) is used via the Galerkin procedure. Conventional MoM directly applied to the EFIE, leads to dense matrix which often becomes computationally intractable when large-scale problems are approached. To overcome these difficulties, wavelets can be used as a basis set so obtaining the generation of a sparse matrix; this is due to the local supports and the vanishing moments properties of the wavelets. In the paper, this technique is applied to analyze electromagnetic transients in a lightning protection systems schematized as a thin-wire structure. The study is carried out in frequency domain; a discrete fast Fourier transform algorithm can be used to compute time profiles of the electromagnetic interesting quantities. The unknown longitudinal currents are expressed by using multiscale wavelet expansions. Thus, the thin-wire EFIE is converted into a matrix equation by the Galerkin method. Results for linear spline wavelets along with their comparison with conventional MoM that uses triangular basis functions and the point matching procedure are presented, for two case studies. Good agreement has been reached with a strong reduction of the computational complexity.     

A hybrid symmetric FEM/MOM formulation applied to scattering byinhomogeneous bodies of revolution

A new symmetric formulation of the hybrid finite element method (HFEM) is described which combines elements of the electric field integral equation (EFIE) and the magnetic field integral equation (MFIE) for the exterior region along with the finite element solution for the interior region. The formulation is applied to scattering by inhomogeneous bodies of revolution. To avoid spurious modes in the interior region a combination of vector and nodal based finite elements are used. Integral equations in the exterior region are used to enforce the Sommerfeld radiation condition by matching both the tangential electric and magnetic fields between interior and exterior regions. Results from this symmetric formulation as well as formulations based solely on the EFIE or MFIE are compared to exact series solutions and integral equation solutions for a number of examples. The behaviors of the symmetric, EFIE, and MFIE solutions are examined at potential resonant frequencies of the interior and exterior regions, demonstrating the advantage of this symmetric formulation     

同心导体圆盘-圆环结构散射场的一种分析方法

本文从电场积分方程出发,经傅氏变换,并分离出电荷对散射场的贡献,导出了平面波投射于同心圆盘-圆环结构时,分析散射场的一个形式简单且便于求解的积分方程。当平面波正投射时解法尤为简单。据此求解圆盘和/或圆环结构上感应电流分布和相应的散射场。为验证本方法的准确性,对圆盘雷达散射截面(RCS)的计算结果与精确解进行了比较,结果吻合很好。文中还给出了当平面波正投射时,同心圆盘-圆环结构上感应电流各分量的幅度分布和散射场分布。     

一种改进的电场积分方程对天线辐射特性的研究

采用矩量法求解闭合结构的天线问题时可以使用混合场积分方程.然而实际运用中的一些天线常常是一部分结构属于开放结构,一部分结构属于闭合结构.对于这类问题,混合场积分方程并不能保证场解的唯一性,若使用电场积分方程来求解,则产生的阻抗矩阵性态差.因此,对于这类问题我们使用了一种改进的电场积分方程来求解,并用此种方法求解了天线的辐射方向图.文章中给出了算例,结果表明该方法是有效的.     

Comparison of theoretical and experimental data for the near fieldof an open-ended rectangular waveguide

A comparison of theoretical and experimental data on the radiating near field of an open-ended waveguide (OEG) is presented. Two theoretical methods are examined. The first is an approximation based on simple plane-wave equations with the electric field expressed in terms of the gain of the OEG. The gain equation is an empirical equation obtained from scaled measured data. The second approach is based on far-field-to-near-field transformations. Its purpose is to provide an alternate method for computing the fields as well as a means of assessing the accuracy of the first approach. Theoretical data computed using both methods are presented along with measured data obtained in the anechoic chamber. The discrepancy between the two theoretical approaches is typically less than 0.5 dB and increases with the distance between the OEG and the field point. For the measured data, ripples attributed to internal reflections in the chamber are observed. Also observed was a trend whereby the measured data fell consistently below the expected value for r⩾3λ. Although the cause of this trend is difficult to isolate without additional experimental work, it is believed to be due to the measurement setup and not by the near-field effect of the OEG     

Rigorous combined mode-matching integral equation analysis of hornantennas with arbitrary cross section

A combined rigorous method is presented for the analysis of horn antennas with arbitrary cross section and general outer surface. The horn taper is described by the mode-matching (MM) method where the cross-section eigenvalue problem is solved by a two-dimensional (2-D) finite element (FE) technique. For the exterior horn surface including the radiating aperture, the application of the Kirchhoff-Huygens principle yields two expressions for the admittance matrix which are based on the electric (EFIE) and the magnetic (MFIE) field integral equation, respectively. The equations are solved numerically by the method of moments (MoM). For the preferred EFIE formulation, the eigenvectors of the last waveguide taper section and RWG functions for triangular patches are utilized as basis-functions for the magnetic or electric surface current densities, respectively. The presented method is verified by available reference values or measurements for a waveguide radiator with a peripheral choke, a conical and a rectangular horn. Its flexibility is demonstrated at the example of a conical ridged waveguide horn     

Contamination of the Accuracy of the Combined-Field Integral Equation With the Discretization Error of the Magnetic-Field Integral Equation

We investigate the accuracy of the combined-field integral equation (CFIE) discretized with the Rao-Wilton-Glisson (RWG) basis functions for the solution of scattering and radiation problems involving three-dimensional conducting objects. Such a low-order discretization with the RWG functions renders the two components of CFIE, i.e., the electric-field integral equation (EFIE) and the magnetic-field integral equation (MFIE), incompatible, mainly because of the excessive discretization error of MFIE. Solutions obtained with CFIE are contaminated with the MFIE inaccuracy, and CFIE is also incompatible with EFIE and MFIE. We show that, in an iterative solution, the minimization of the residual error for CFIE involves a breakpoint, where a further reduction of the residual error does not improve the solution in terms of compatibility with EFIE, which provides a more accurate reference solution. This breakpoint corresponds to the last useful iteration, where the accuracy of CFIE is saturated and a further reduction of the residual error is practically unnecessary.     

粗糙面下方金属目标复合电磁散射的快速算法

为快速有效计算粗糙面下金属目标的复合电磁散射,提出了一种基于前后向迭代算法(FBM)和共轭梯度(CG)法的快速互耦迭代算(CCIA).首先建立目标与粗糙面的耦合积分方程组,并采用矩量法将其离散为矩阵方程.其次针对得到的耦合积分方程,用FBM求解粗糙面表面电流分布,用CG法求解目标表面电流分布,目标和粗糙面的相互作用通过更新两方程的激励项完成.最后,计算了高斯粗糙面下方无限长金属圆柱目标的复合电磁散射系数,当目标尺寸趋于零或目标深度趋于无穷时的结果与单独介质粗糙面相一致,验证了该数值方法的正确性;同时,讨论了不同粗糙面情况下该方法的收敛性,并分析了不同粗糙面媒质、目标尺寸和目标位置对双站散射系数的影响.     

Diagonal preconditioners for the EFIE using a wavelet basis

The electric field integral equation (EFIE) has found widespread use and in practice has been accepted as a stable method. However, mathematically, the solution of the EFIE is an “ill-posed” problem. In practical terms, as one uses more and more expansion and testing functions per wavelength, the condition number of the resulting moment-method matrix increases (without bound). This means that for high-sampling densities, iterative methods such as conjugate gradients converge more slowly. However, there is a way to change all this. The EFIE is considered using a wavelet basis for expansion and for testing functions. Then, the resulting matrix is multiplied on both sides by a diagonal matrix. This results in a well-conditioned matrix which behaves much like the matrix for the magnetic field integral equation (MFIE). Consequences for the stability and convergence rate of iterative methods are described     

Synthetic-Functions Analysis of Large Aperture-Coupled Antennas

The application is described the synthetic function expansion (SFX) approach to large arrays of aperture-coupled antennas. The problem is formulated in terms of coupled magnetic-field continuity integral equations (MFCIE) and electric field integral equations (EFIE), and discretized via the method of moments (MoM). The SFX is a domain-decomposition technique; on each block of the broken-down structure, functions are generated with domain over the entire block. These “synthetic functions” (SF) are obtained from the solution of the electromagnetic problem for the isolated block upon specification of appropriate sources on the block bounding box, and from a further singular value decomposition (SVD)-based procedure to select the relevant terms. The complete problem is solved using the SFs as basis functions for the MoM. This results in a strong reduction of the MoM matrix size. Applications are presented to configurations of open and cavity-backed radiators.