An enhanced transmission line model for conductors with arbitrary cross sections

An enhanced transmission line model (ETL) has been recently proposed to describe the propagation along two parallel wires with circular cross sections up to wavelengths comparable to the distance between the wires. In this paper, a general ETL model is proposed to describe the propagation along interconnects consisting of wires with arbitrary cross sections. Since the ETL model has the same simplicity of the standard transmission line model, it allows investigating high-frequency effects, like radiation and dispersion, with a computational cost which is sensibly lower than that required by a full-wave numerical simulation. The ETL model is obtained, with suitable approximations, starting from a full-wave analysis of the propagation problem and using an integral formulation based on the electromagnetic potentials satisfying the Lorentz gauge. Some case studies are carried out and discussed, including a benchmark test with existing literature, performed to check the validity and accuracy of the proposed model.     

On the backscattering from two arbitrarily located identical parallel wires

A study of the backscattering from two identical perfectly conducting, thin wires illuminated by a plane wave at an arbitrary angle of incidence is presented. The theory is based on an integral equation method. By decomposing the induced currents into symmetric and antisymmetric modes, the simultaneous integral equations for the induced currents are converted into independent integral equations similar to the one for a single wire for which the solution has already been carried out. The induced currents on and the backscattering cross sections of the wires are determined. Numerical examples include nonstaggered, staggered, and collinear cases of both half-wave and full-wave wires. Comparisons are made between the calculated and measured values of the echo area. The experimental results are in good agreement with theory.     

Full-wave analysis of complicated transmission-line circuits using wire models

Three existing wire models based on the method of moments are used to analyze a transmission-line circuit. Simulation results show that the wire model where the current is assumed to flow along the axis and the testing is on the whole surface (around 2/spl pi/) has the best performance when two wires are close. However, this model is still inaccurate when two wires are very close, which is the case in computer chip and circuit problems. We then develop a new wire model that is valid for many cases. Using the new wire model, complicated transmission-line circuits can be accurately analyzed and simulated. Many numerical simulations are given to test the validity of the new model.     

On bounding the equivalent radius

The concept of the equivalent radius, first introduced by Hallén, has been useful in the solution of antenna and scattering problems that involve electrically thin wires of arbitrary cross section. Generally, the solution is first calculated for circular wires of an arbitrary radius, and this radius is then replaced by the equivalent radius of the noncircular wire. In this way the original problem is reduced to that of finding the equivalent radius. Here we bound the equivalent radius through the use of certain isoperimetric inequalities so that the bounds are completely described by knowledge of the wire's cross-sectional area and perimeter. For a given cross-sectional area it is shown that the circular wire possesses the smallest equivalent radius. Applications of these results to problems in shielding and scattering are suggested.     

E/H面不连续腔体的雷达散射截面分析

应用散射参数的级联特性分析不规则腔体的雷达散射截面。针对进气道前端的不规则矩形管道结构，采用全波模式法精确分析了E／H面任意不连续矩形腔体散射参数的求取，再根据等效网络的级联特性求得任意组合不规则矩形管道的散射矩阵，在保持计算精度的条件下克服了模式法只能精确计算规则腔体结构的限制。数值结果验证了该方法的正确性。     

Capacitance matrix calculation of a wire conductor line: a new FEMapproach

An original finite-element approach is presented to calculate the capacitance matrix of a uniform multiconductor wire line. The examined two-dimensional (2-D) domain is discretized by nodal-based triangular elements where the Laplace equation is solved. A new procedure is developed to take into account the presence of the wires, which are assumed to be located in the vertex nodes of the FEM mesh. Through the proposed procedure, the physical dimensions of the wire cross sections are considered modifying the terms of the local stiffness matrix in the finite elements surrounding the wires. A further modification of the local FEM matrices allows one to consider the logarithmic variation of the electrical potential around the wires. The procedure is efficient from a numerical point of view since it avoids the fine discretization of the nonconductive region surrounding the wire while achieving a good numerical accuracy. Numerical examples are given and compared with the analytical solutions for canonical configurations, including wires with a dielectric cover     

EM modeling of aircraft at low frequencies

An efficient computational technique for obtaining scattering cross sections of electrically small aircraft is presented. The technique is based on the wire-grid reaction method. The aircraft shape is approximated by a grid of thin wires, leading to a mathematical representation of the aircraft in the form of an impedance matrix. The inverted matrix yields the scattering data. A variety of wire-grid models were tested. The results show that with proper choice of radius of the wire segments, good agreement with experimental data can be obtained for polarizations parallel to the fuselage axis. For polarizations perpendicular to the fuselage axis, only fair agreement was observed. This computational technique is used to simulate realistic scattering data, which serves as input to information processors for target identification.     

A Hybrid Electromagnetic-Circuit Method for Electromagnetic Interference Onto Mass Wires

A current decomposition method is proposed for the analysis of field coupling to mass wires near complex structures. The foremost attribute of the method is the decomposition of the current on each wire into push-pull and push-push mode currents. The former refers to the perturbation current accounting for the interactions among the wires within the bundle, whereas the latter represents the interactions between the mass wire bundle and the surrounding structure. Multiconductor transmission line theory is employed to compute the push-pull mode current by using one of the wires in the bundle as the return/reference conductor. Current induced on a test wire located along the reference line is used to compute the push-push mode. For this analysis, we employed the method of moments for the electromagnetic analysis of surrounding structure and simulation program with integrated circuit emphasis (SPICE)-like simulators for the analysis of a circuit model of the transmission lines extracted via the partial element equivalent circuit method. Several validation examples (including transmission lines inside an automobile) are presented. It is also shown that the traditional transmission line theory based on quasi-static analysis fails with increasing complexity of the surrounding structure.     

A hybrid method for combining quasi-static and full-wave techniquesfor electromagnetic scattering problems

Electromagnetic scattering problems containing subregions which are electrically small but geometrically complex are examined. By utilizing quasi-static methods for the small regions, full-wave methods in the remaining region, and determining necessary coupling relations between the small regions and the overall geometry, a considerable improvement in numerical efficiency is realized. The particular method developed here is valid for quasi-static regions in which magnetic induction can be ignored. Results using the proposed method have been obtained for a pair of closely spaced collinear wires. A comparison of these results with the wire antenna code, MININEC, showed excellent agreement     

Analysis of an untilted wire-excited slot in the narrow wall of arectangular waveguide by including the actual external structure

The admittance of an untilted slot in the narrow wall of a rectangular waveguide is calculated by including the actual external structure. The slot is excited by two tilted thin wires inside the waveguide. The slot is also allowed to extend into the two broad walls of the waveguide to make it sufficiently long for resonance to occur. The external slot admittance is evaluated by using a spectrum of two-dimensional solutions, a method which can handle the arbitrary cross section of the external structure, The analysis predicts that if both the slot and the wires are tuned to resonance, the transmission coefficient gets constant phase over a wide-frequency band. The results also show that resonance can be obtained for any slot length by adjusting the wire length, and this relation between the lengths is presented. The distance between the slot and the wires needed to maximize the radiated power is also shown; some results are confirmed by measurements     

Matrix methods for field problems

A unified treatment of matrix methods useful for field problems is given. The basic mathematical concept is the method of moments, by which the functional equations of field theory are reduced to matrix equations. Several examples of engineering interest are included to illustrate the procedure. The problem of radiation and scattering by wire objects of arbitrary shape is treated in detail, and illustrative computations are given for linear wires. The wire object is represented by an admittance matrix, and excitation of the object by a voltage matrix. The current on the wire object is given by the product of the admittance matrix with the voltage matrix. Computation of a field quantity corresponds to multiplication of the current matrix by a measurement matrix. These concepts can be generalized to apply to objects of arbitrary geometry and arbitrary material.     

Heat Loss of Circular Electric Waves in Helix Waveguides

This paper presents a theoretical calculation of the eddy current losses of circular electric waves in a closely-wound helix waveguide. The wire diameter is assumed large compared to the skin depth, but small compared to the guide diameter and the operating wavelength, so that the fields near the wire are quasistatic and may be determined by conformal mapping. When the wires are in contact, the waveguide wall is effectively a metal surface with grooves of semicircular cross section, the current flow being parallel to the direction of the grooves. The power loss for this case is computed to be about 8.5 per cent higher than in a waveguide with smooth metal walls. When the wires are not in contact, the wall is treated as a grating of parallel, round wires. The increase in power loss over a smooth surface is approximately 22.5 per cent when the wires are separated by a distance equal to their diameter.     

微电子器件封装铜线键合可行性分析

虽然在集成电路封装工艺中金导线键合是主流制程,但是目前采用铜导线替代金导线键合已经在半导体封装领域形成重要研究趋势。文章对微电子封装中铜导线键合可行性进行了分析,主要包括铜导线与金导线的性能比较(包括电学性能、物理参数、机械参数等),铜导线制备和微组织结构分析,铜导线焊合中的工艺研发及铜导线焊合可靠性分析等。当今半导体生产商关注铜导线不仅是因为其价格成本优势,更由于铜导线具有良好的电学和机械特性,同时文中也介绍了铜导线键合工艺存在的诸多问题和挑战,对将来铜导线在集成电路封装中的大规模应用和发展具有一定的参考意义。     

Plane wave reflection from a rectangular-mesh ground screen

The theory of scattering of electromagnetic plane waves of arbitrary incidence and polarization from an infinite rectangular-mesh ground screen is treated. The screen is composed of thin wires of circular cross section, and is parallel to the interface between two homogeneous media. The theoretical results for parallel-wire screens are obtained in the limit of large wire spacing for one dimension of the mesh screen. Results presented for incident parallel polarized plane waves indicate that both the parallel-wire and mesh screens may exhibit a change in reflecting properties as the plane of incidence is varied from the wire axis direction. In addition, it is shown that the parallel-wire screen can produce appreciably higher cross-polarized fields than a square-mesh screen of the same wire spacing.     

Transient field produced by a traveling-wave wire antenna

The electromagnetic fields of a transient traveling wave current on a straight wire segment are calculated directly in the time domain. Retarded potential theory is used to establish an impulse response valid in both far and near zones. A closed-form expression for the field due to a rectangular current pulse is obtained, and corresponding plots are given. Numerical results from this permit the investigation of the differences between near versus far zones and coated versus uncoated wires. Experimental findings for both coated and uncoated wires show good agreement with theory. A formula for far-zone radiation from an arbitrarily shaped wire is developed; results for a proposed directive antenna geometry are presented     

A new hybrid mode-matching/numerical method for the analysis ofarbitrarily shaped inductive obstacles and discontinuities inrectangular waveguides

A new and efficient hybrid mode-matching method is presented for the analysis of arbitrarily shaped inductive obstacles and/or discontinuities in a rectangular waveguide. The irregular region with obstacles and/or discontinuities is characterized using a full-wave hybrid spectral/numerical open-space technique expanding the fields in cylindrical wave functions. Next, a full-wave mode-matching procedure is used to match the cylindrical wave functions to guided modes in all ports and a generalized scattering matrix for the structure is finally obtained. The obstacles can be metallic or dielectric with complex permittivities and arbitrary geometries. The structure presents an arbitrary number of ports, each one with different orientation and dimensions. The accuracy of the method is validated comparing with results for several complex problems found in the literature. CPU times are also included to show the efficiency of the new method     

Scattering from cylinders with arbitrary surface impedance

This paper presents an integral equation method for the solution of the field scattered by a set of cylinders with arbitrary cross-sectional shape, and arbitrarily varying anisotropic surface impedance. The integral equations are given for an arbitrary source with arbitrary harmonic variation along the cylinder axis. The scattering problem can be solved for arbitrary three-dimensional sources by expansion of the source in a Fourier integral over the axial propagation constant. The integral equations have been programmed for a CDC 1604A computer. The program developed has been used to solve a great variety of scattering, antenna, and propagation problems, and, depending upon accuracy desired, will handle cylinders up to about 150-wavelengths total perimeter. Numerical results on scattering from cylinders with specific cross sections are presented to illustrate the utility of the program developed.     

Two-dimensional microwave imaging by a numerical inverse scatteringsolution

A numerical approach that aims to detect, by means of interrogating microwaves, the locations and the dielectric permittivities of unknown inhomogeneous dielectric cylindrical objects of arbitrary cross sections that might be present inside a fixed area of interest is proposed. An illumination is assumed with the electric field vector polarized along the cylindrical axis. The two-dimensional Lippman-Schwinger integral equation of electromagnetic scattering is transformed into matrix form by the moment method. The system obtained is solved by using a pseudoinversion algorithm to overcome ill-conditioning problems. The first-order Born approximation is also applied when the dielectric inhomogeneities are weakly scattering. Computer simulations have been performed by means of a numerical program. Results show the capabilities and limitations of the proposed approach     

Scattering from irregular-edged planar and curved surfaces

An electric field integral equation (EFIE) formulation is used to describe the electromagnetic scattering from finite planar and curved perfect electrical conducting surfaces truncated by an irregular edge. The edge can have an arbitrary form if it satisfies certain differentiability requirements. Similarly, the generating curve describing the surface can be convex, concave, or a combination of both. An edge-dependent entire domain Galerkin expansion is used for the current variation along the surface in the direction of translation. A subdomain expansion is used along the orthogonal direction. The backscatter cross sections obtained from the method of moments are compared with experimental data