Review of hybrid methods on antenna theory

Hybrid methods are robust analysis tools for a large class of complex scattering and radiation problems not amenable to traditional classical methods. In the hybrid technique, a complex radiator is decomposed into parts solved by a combination of numerical and asymptotic methods. Three methods are reviewed here: the hybrid MM/Green’s function method; the field-based hybrid method which combines the method of moments (MM) and the geometrical theory of diffraction (GTD); and the current-based hybrid method which incorporates MM, physical theory of diffraction (PTD), and the Fock theory. The domain of applicability of each method is illustrated with examples.     

Improved PO-MM hybrid formulation for scattering fromthree-dimensional perfectly conducting bodies of arbitrary shape

The method of moments (MM) represents a suitable procedure for dealing with electromagnetic scattering problems of arbitrary geometrical shape in the lower frequency range. However, with increasing frequency both computation time and memory requirement often exceed available computer capacities. Therefore a current based hybrid method combining the MM with the physical optics (PO) approximation suitable for three-dimensional perfectly conducting bodies is proposed in this paper. The hybrid formulation allows a substantial reduction of computation time and memory requirement, while the results are in reasonable agreement with those based on an application of the MM alone. Further improvement can be achieved for flat polygonal parts of the scattering body by a heuristic modification of the PO current density taking into account the effects of edges. As opposed to the physical theory of diffraction (PTD), no additional electric and magnetic line currents along the edges are necessary     

A study of a monopole arbitrarily located on a disk using hybrid MM/GTD techniques

The input impedance of a monopole located off-axis on a disk and oriented in an arbitrary direction is investigated using hybrid method of moments/geometrical theory of diffraction (MM/GTD) techniques. The equivalent currents method (ECM) and the uniform geometrical theory of diffraction (UTD) are used to ensure a proper treatment of each situation. A criterion for switching from UTD to ECM in the vicinity of the axial caustic is discussed. Measurements of impedance have been made in order to check the numerical results and are presented here, showing good agreement with theory.     

理想导体半圆柱TE波散射的混合法解

本文应用混合技术分析了在TE平面波激励下,理想导体半圆柱的双站散射。该混合技术是把半圆柱劈附近的电流表示为未知数,圆柱曲面上的一阶电流应用Fock理论求解,高阶绕射电流表示为含有未知系数的Fock型函数。圆柱平面上的一阶电流用物理光学近似和曲劈的一致性几何绕射理论得到。劈的二阶绕射电流表示为含有未知系数的GTD形式。然后通过磁场积分方程,运用简单矩量法求得劈附近的电流和未知的绕射系数。最后计算了理想导体半圆柱的双站散射截面,结果与矩量法的结果吻合得相当好。     

Improvement of the PO-MoM hybrid method by accounting for effectsof perfectly conducting wedges

A correction of the conventional physical optics (PO) current close-to-perfectly conducting wedges based on an application of the uniform geometrical theory of diffraction (UTD) is presented. This improved PO current is used in a hybrid formulation in combination with the method of moments (MoM) to deal with three-dimensional scattering bodies of arbitrary shape. The accuracy of this hybrid method is demonstrated by some examples. As opposed to an application of the physical theory of diffraction (PTD), only surface current densities and no fictitious electric and magnetic line currents along the edges are involved which allows a uniform treatment of the MoM and the PO region by expressing the surface current density as a superposition of basis functions defined over triangular patches     

Hybrid solutions for large-impedance coated bodies of revolution

Electromagnetic scattering solutions are developed for coated perfectly conducting bodies of revolution (BOR) that satisfy the impedance boundary condition. The integral equation arising from the impedance (Leontovich) boundary condition is solved by use of the method of moments (MM) technique along with an Ansatz for the surface currents that is derived from physical optics (PO) and the Fock theory that is modified for imperfectly conducting surfaces. The MM solution is expressed in terms of two integral (Galerkin) operators. The form of the Galerkin expansion used results in a symmetric MM system matrix. The hybrid solution is specialized for BOR's although the approach is applicable to a broader class of scatterers as well. The results are compared with the Mie solution for penetrable spherical scatterers, which satisfy the impedance boundary condition, and with recently published MM solutions for nonspherical scatterers.     

Hybrid UTD-MM analysis of the scattering by a perfectly conducting semicircular cylinder

A hybrid UTD-MM technique which combines the uniform geometrical theory of diffraction (UTD) and the method of moments (MM) is employed to analyze efficiently the problem of electromagnetic diffraction of transverse electric (TE) and transverse magnetic (TM) waves by a perfectly conducting semicircular cylinder. An analysis of this problem is useful for understanding the coupling between the mechanisms of edge and convex surface diffraction. The accuracy of the numerical results for the far-zone fields based on this solution is established by comparison with an independent formally exact MM solution.     

A hybrid moment method solution for TEz scattering fromlarge planar slot arrays

This paper develops a hybrid moment method (MM) based numerical model for electromagnetic scattering from large finite-by-infinite planar slot arrays. The model incorporates the novel concept of a physical basis function (PBF) to reduce dramatically the number of required unknowns. The model can represent a finite number of slot columns with slots oriented along the infinite axis, surrounded by an arbitrary number of coplanar dielectric slabs. Each slot column can be loaded with a complex impedance to tailor the array's edge currents. An individual slot column is represented by equivalent magnetic scattering currents on an unbroken perfectly conducting plane. Floquet theory reduces the currents to a single reference element. In the array's central portion, where the edge perturbations are negligible, the slot column reference elements are combined into a single basis function. Thus, one PBF can represent an arbitrarily large number of slot columns. A newly developed one-sided Poisson sum formula is used to calculate the mutual coupling between the PBF and the slot columns in the presence of a stratified dielectric media. The array scanning method (ASM) gives the mutual coupling between the individual slot columns. The hybrid method is validated using both numerical and experimental reference data. The results demonstrate the method's accuracy as well as its ability to handle array problems too large for traditional MM solutions     

机载天线辐射方向图的MM—UTD混合法分析

采用矩量法（MM）结合二致性几何绕射理论（UTD）的混合方法计算了机载单极天线的辐射方向图。该混合方法建立的机载天线辐射模型更符合实际，并且它同时具有MM的精确性和UTD的高效率，克服了单一方法的不足。计算结果对于预测天线间的电磁兼容性和优化天线布局具有一定的指导意义。     

Hybrid analysis of reflector antennas including higher order interactions and blockage effects

The analysis of a reflector antenna system consisting of a feeder, a sub-reflector, and a main-reflector in microwave frequency bands, where the electrical dimensions of the antenna become prohibitively large for the use of a rigorous numerical method, has been performed by high-frequency asymptotic techniques (HFATs). As a result, the radiation patterns and input impedances of the antenna system were calculated based on an approximation: the radiation characteristics of the feed, sub-reflector and main-reflector are independent from each other. In this study, as an effort to alleviate the inaccuracy due to the exclusion of higher order mutual interactions existing among those subsystems, three different hybrid methods [finite-element method/method of moment (FEM/MOM) + physical optics (PO), FEM/MOM + geometrical theory of diffraction (GTD), and FEM/MOM + PO + physical theory of diffraction (PTD)] are introduced in the context of an iterative algorithm. The interactions between the feed and sub-reflector are accounted by a hybrid method which combines the FEM with the MOM; FEM/MOM. Whereas, the interactions between the objects in the FEM/MOM domain and the main-reflector are taken into account through the iteration: the fields and currents in the FEM/MOM domain are updated using the fields and currents obtained from the HFAT domain and vise-versa. These three methods are applied to two-dimensional reflector configurations, and corresponding results are compared in terms of accuracy and efficiency. The accuracy of the hybrid methods, especially those of FEM/MOM + GTD and FEM/MOM + PO + PTD, is found to be comparable to that of a rigorous numerical method. Furthermore, their computational costs are almost independent to the size of the main-reflector and to the distance from the feed point to the main-reflector.     

Hybrid methods for analysis of complex scatterers

Depending on the angle of illumination, electrically large scatterers can support a variety of electromagnetic (EM) phenomena, such as traveling waves, creeping waves, and edge/surface diffraction effects. The electrical size of a body limits the tractability of numerical methods such as the method of moments (MM), and the geometric complexity of an object circumscribes the applicability of optics-derived methods. Hybrid methods incorporating both numerical and high-frequency asymptotic techniques have the potential to substantially enlarge the class of EM scattering problems that can be treated. In this discussion, the current-based hybrid formulation is summarized for classes of two- and three-dimensional scatterers. The use of Ansatz solutions derived from physical optics, the physical theory of diffraction, and the Fock theory is illustrated for perfectly conducting, partially penetrable, and totally coated bodies. For the latter, a generalization rooted in the impedance boundary (Leontovich) condition is used. Complementing these Ansatz solutions, the Galerkin representation is used for regions where the foregoing are computationally or physically intractable. The above cases are illustrated by representative solutions explicating the approach     

用UTD-MOM混合法有效分析大型平面阵列天线的辐射特性

采用矩量法(MOM)结合一致性几何绕射理论(UTD)来分析和计算大型平面阵列天线的辐射特性。大型天线阵列含有很多的辐射单元,单独应用矩量法求解时,未知数太多,计算速度慢。而应用MOM-UTD混合方法,未知数的数量大大少于单独用矩量法时的未知数的数量。本文以振子组成的平面阵列为例,说明该方法如何应用。最后给出了数值解的结果,并与单独用矩量法得到的结果进行了比较。比较表明,该方法是有效的、准确的。     

Radiation from wire antennas attached to bodies of revolution: The junction problem

A method of moments (MM) formulation for multiple wires attached to biodes of revolution (BOR) is presented. This formulation builds on previous MM analyses for BOR's and wires. A special junction basis function is introduced to represent the physical currents in the BOR-wire attachment (junction) region. In the formulation, currents are represented by 1) mode-dependent and piecewise-continuous expansion functions on the BOR, 2) piecewise-continuous functions on the wires, and 3) a continuity-preserving basis function for the junction region. The block diagonal character of the MM/BOR matrix formulation and the computational economy of the MM analysis for wires are retained. The analysis is demonstrated for surface-attached radiators such as monopoles and loops as well as surface-attached passive elements.     

一致性绕射理论的等效边缘电磁流在多边形板双站散射中的应用

介绍一致性绕射理论等效边缘电磁流（ＵＴＤＥＥＣ）的公式。该公式是基于Ｍｉｃｈａｅｌｉ的半平面等效边缘电磁流（ＥＥＣ）表达式，用平截的劈增量条计算等效边缘电磁流。这样可以消除以往计算中的虚假奇异点，对任意入射和观察方向均有良好的性态。本文用此方法计算了方板和梯形板的双站散射，并与高阶等效边缘电磁流的结果比较，具有良好的精度。     

A hybrid MM-GTD technique for the optimization of the power gain of arrays of wire antennas near an elliptic cylinder

The power gain of arrays of wire antennas near an elliptic cylinder is maximized. The hybrid MM-GTD technique is used where the method of moments (MM) and the geometrical theory of diffraction (GTD) are formally combined. Results are presented for some special cases.     

Study of different realizations and calculation models for softsurfaces by using a vertical monopole on a soft disk as a test bed

We study a vertical monopole on a circular metallic disk which is loaded in different ways to provide a soft boundary condition, e.g., by transverse corrugations or by dielectric or lossy material coatings. The different realizations are calculated by the uniform geometrical theory of diffraction (UTD), the incremental theory of diffraction, the moment method (MM) with an impedance boundary model, and MM using equivalent currents on all material interfaces. The calculated results are compared with measured results for specific geometries. Some general characteristics of the different realizations of the soft surfaces are extracted from the results. It is verified that the artificially soft boundary condition can be realized by different surface loadings. In particular, a nearly soft boundary condition can be realized over a large bandwidth by coating a conductor with a thin layer of lossy magnetic material. It is found that the surface impedance model works very well for modeling corrugations. It may also work for material coated surfaces provided the surface wave is prohibited from radiating. The bandwidth of the different soft surfaces are given, including corrugations with different cross-sectional shapes     

A hybrid-iterative method for scattering problems

A new technique, named a hybrid-iterative method (HIM), is presented to solve the magnetic field integral equation (MFIE) for the induced currents on an arbitrary, perfectly conducting scatter. The technique is an evolution from two previous techniques developed earlier. The first of the previous techniques used the moment method (MM) to compute correction currents to an optics-type current. The second of the previous techniques effected a significant improvement by eliminating the use of the moment method to obtain the correction currents, using iteration to obtain them. The technique described here incorporates the edge diffraction theory and the Fock theory into the Ansatz of the iterative scheme. This procedure speeds up the algorithm as well as extending the range of problems that can be solved by the iterative scheme. Furthermore, the present technique incorporates the correction currents into the total currents thereby simplifying the iterative scheme. For intermediate size and larger bodies, the central processing unit (CPU) time is significantly less than that of the moment method. Results are presented for a variety of curved and edged two-dimensional cylinders illuminated by a transverse electric plane wave.     

阻抗劈散射的MM-PO混合算法研究

本文系统地研究了各向异性阻抗劈绕射的矩量法-物理光学(MM-PO)混合算法.首先研究了任意各向异性阻抗面的物理光学模型,推导出表面物理光学等效电磁流计算式.其次,提出了一种有效的含Hankel函数的弱振荡被积函数无穷积分处理方法.最后,将作者已公开发表的修正绕射电流基函数用于各向异性阻抗劈散射场研究,数值结果和已知的一致性绕射理论结果高度吻合.     

PTD analysis of impedance structures

Based on an approximate dyadic diffraction coefficient, equivalent currents (ECs) are derived for computing the scattering by a finite-length impedance wedge of arbitrary angle. The derived equivalent currents are implemented in a standard general purpose physical theory of diffraction (PTD) code and results are presented demonstrating the accuracy of the formulation for a number of impedance and (dielectrically) coated structures. These include typical shapes such as plates, finite-length cones, and cylinders which have been partially or fully coated. The PTD implementation requires a dyadic physical optics diffraction coefficient which is presented in the appendix     

A diffraction coefficient for a cylindrically truncated planar surface

A numerically derived solution of the diffraction coefficient for a source mounted on a perfectly conducting planar surface which is smoothly terminated by a circular cylinder is obtained using the hybrid approach which combines the moment method (MM) with the geometrical theory of diffraction (GTD). This solution is valid not only in the region away from, but also in the region near, the shadow boundary. The accuracy and usefulness of this solution is demonstrated as various structures are treated using it.