Flexibility in the choice of Green's function for the boundaryelement method

Several useful Green's functions are derived for the quasi-static analysis of shielded planar transmission lines by the boundary element method. These newly employed Green's functions satisfy forced boundary conditions in a rectangular region. The integral equation does not have a singular point and the integrand contains only the normal derivative of the electric potential. The present method is proposed to characterize multilayered and multi-conductor structures. Numerical results are presented for a microstrip, a suspended line, and a coplanar waveguide. For the coplanar waveguide, a combined Green's function is also studied. This combined Green's function further reduces the memory size in computation. All of these Green's functions are represented in infinite series. The resulting matrix equation has slowly convergent matrix elements. To reduce the computation time of matrix elements, we split the original series in two parts. The geometric series method is employed to convert one part into a fast convergent form (4 terms). For the other part, only a few terms (less than 20) require computation     

Analysis of a shielded microstrip line with finite metallizationthickness by the boundary element method

A boundary element method is presented for the quasi-static analysis of a shielded microstrip line with finite metallization thickness. The analysis is based on the solution of a system of boundary integral equations which are derived from Green's second identity. Numerical results for the charge distribution along the strip and the effects of metallization thickness on line characteristics are presented. The results show good agreement with data available in the literature     

A spectral Integral method (SIM) for layered media

A spectral integral method is presented for electromagnetic scattering from dielectric and perfectly electric conducting (PEC) objects with a closed boundary embedded in a layered medium. Two-dimensional layered medium Green's functions are computed adaptively by using Gaussian quadratures. The singular terms in the Green's functions and the non-smooth terms in their derivatives are handled appropriately to achieve exponential convergence. Numerical results, compared with the ones obtained by using other methods, demonstrate the spectral accuracy and high efficiency of the proposed method. They also confirm that the spectral integral method (SIM) is applicable to concave objects.     

An integral equation method for the evaluation of conductor anddielectric losses in high-frequency interconnects

An integral equation method is developed to solve for the complex propagation constant in multilayer planar structures with an arbitrary number of strip conductors on different levels. Both dielectric losses in the substrate layers and conductor losses in the strips and ground plane are considered. The Green's function included in the integral equation is derived by using a generalized impedance boundary formulation. The microstrip ohmic losses are evaluated by using an equivalent frequency-dependent impedance surface which is derived by solving for the fields inside the conductors. This impedance surface replaces the conducting strips and takes into account the thickness and skin effect of the strips at high frequencies. The effects of various parameters such as frequency, thickness of the lines, and substrate surface roughness on the complex propagation constant are investigated. Results are presented for single strips, coupled lines, and two-level interconnects. Good agreement with data available in the literature is shown     

Quasi-static analysis of shielded planar transmission lines withfinite metallization thickness by a mixed spectral-space domain method

A new method to analyze shielded planar transmission lines with finite metallization thickness is described. It is based on a mixed spectral-space domain representation of the Green's function. The method allows the accurate determination of the static parameters of the transmission line with great efficiency as compared to methods available in the literature. Several numerical examples are shown on single and coupled planar transmission lines     

A numerical formulation of dyadic Green's functions for planarbianisotropic media with application to printed transmission lines

An integral equation (IE) method with numerical solution is presented to determine the complete Green's dyadic for planar bianisotropic media. This method follows directly from the linearity of Maxwell's equations upon applying the volume equivalence principle for general linear media. The Green's function components are determined by the solution of two coupled one-dimensional IE's, with the regular part determined numerically and the depolarizing dyad contribution determined analytically. This method is appropriate for generating Green's functions for the computation of guided-wave propagation characteristics of conducting transmission lines and dielectric waveguides. The formulation is relatively simple, with the kernels of the IE's to be solved involving only linear combinations of Green's functions for an isotropic half-space. This method is verified by examining various results for microstrip transmission lines with electrically and magnetically anisotropic substrates, nonreciprocal ferrite superstrates, and chiral substrates. New results are presented for microstrip embedded in chiroferrite media     

Analysis of transmission lines of finite thickness above aperiodically perforated ground plane at oblique orientations

A general method is formulated for the analysis of signal lines of finite thickness in the presence of a periodically perforated ground plane. Utilizing the dyadic Green's functions, a set of electric and magnetic field integral equations (EFIE, MFIE) is established, which are then transformed into the spectral domain by the Fourier transform. Galerkin's method is used to solve the combined integral equations. The B-spline functions are chosen as basis functions to achieve a higher order of convergence. The dispersive characteristics of the transmission lines are studied and the characteristic impedance of the signal lines are evaluated by both the voltage-current definition and the power-current definition, with good consistency. The effect of signal locations versus apertures in the ground plane is discussed. Finally, measurements are conducted, and the results agreed very well with the theory     

计算多层印刷传输线色散特性的一种简单方法

本文给出计算多层印刷传输线色散特性的一种简单方法，本方法利用ＴＥ波及ＴＭ波的平面结构谱域等效电路，导出二维谱域并矢格林函数，再利用格林函数由积分方程的解给出传输常数，进而求得特性阻抗表示式。用本文方法所得到的数值结果和更复杂的方法所得到的结果非常一致。     

On the scattering of electromagnetic waves by bodies buried in a half-space with locally rough interface

A method for the scattering of electromagnetic waves from cylindrical bodies of arbitrary materials and cross sections buried beneath a rough interface is presented. The problem is first reduced to the solution of a Fredholm integral equation of the second kind through the Green's function of the background medium. The integral equation is treated here by an application of the method of moments (MoM). The Green's function of the two-part space with rough interface is obtained by a novel approach which is based on the assumption that the perturbations of the rough surface from a planar one are objects located at both sides of the planar boundary. Such an approach allows one to formulate the problem as a scattering of cylindrical waves from buried cylindrical bodies which is solved by means of MoM. The method is effective for surfaces having a localized and arbitrary roughness. Numerical simulations are carried out to validate the results and to show the effects of some parameters on the total field. The present formulation permits one to get the near and far field expression of the scattered wave.     

Propagation characteristics of coplanar-type transmission lineswith lossy media

Lossy coplanar-type transmission lines are analyzed based on the hybrid-mode formulation by combining the spectral-domain approach with the perturbation method. Introducing a finite thickness of metallization and choosing the proper basis functions for the thick conductor model prevent the integrals used for calculating the conductor losses from becoming singular when evaluated at the conductor edge. An orthogonality relation is used to reduce the double infinite or semi-infinite integral to a single integral, thus reducing the computation effort drastically. Numerical computations by new basis functions for the thick conductor show convergence rates as fast as those for the zero-thickness cases. Numerical results include the effective dielectric constants, characteristic impedances, and total losses (conductor and dielectric losses) for slot lines and symmetrical and asymmetrical coplanar waveguides     

Variational method for planar transmission lines with anisotropicmagnetic media

Upper and lower bounds on the line inductances are presented for the first time for planar transmission lines with anisotropic magnetic media. Green's functions are derived for the general structure by using recurrent relations. Numerical examples involving striplines and coplanar waveguide are presented, and the calculated values of the quasi-static characteristics of stripline on an anisotropic magnetic substrate with the tensor permeability are in good agreement with measured values     

Equivalent network representation of boundary conditions involving generalized trial quantities

Virtual adjustable sources are introduced in equivalent network representation of boundary conditions. For this purpose, integral equations are to be solved simple application of analog Kirchoff’s and Ohm’s laws. These adjustable sources represent generalized trial quantities. In order to illustrate this proposed approach, equivalent network representation of lossy planar transmission lines with arbitrary metallization thickness is presented.     

Propagation Parameters of Coupled Microstrip-Like Transmission Lines for Millimeter-Wave Applications

A variational expression is derived for the propagation parameters of coupled microstrip-like transmission lines for millimeter-wave applications using the "transverse transmission line" method. Numerical results are presented for the coupled inverted microstrip lines, and for the coupled suspended microstrip lines. The effects of the top and sidewalls and also of the finite thickness of strip conductors on the even- and odd-mode impedances are studied. The use of a dielectric overlay in equalizing the even- and odd-mode phase velocities is investigated.     

SOLUTION OF ARBITRARY CROSS-SECTION WAVEGUIDE USING METHOD OF EIGEN WEIGHTED BOUNDARY INTEGRAL EQUATION

Based on the second kind of Green's identity,a boundary integral equation forarbitrary cross-section waveguide is transformed to a system of linear homogeneous algebraicequations by means of expansion of boundary bases and by using the eigenfunctions of a fictitiousregular boundary as weighting functions,which corresponds to less algebraic equations than BEMand simpler coefficients than the modified BEM.The numerical results for some typical metallicwaveguides are given by using the method of eigen-weighted boundary integral equation,and theyare accurate enough with fast convergence.     

谱域直线法及其在三维电磁场边值问题中的应用

本文将直线法和谱城法结合在一起而提出一种分析集成波导三维问题的混合方法——谱域直线法。这种方法吸取了谱域法存储空间小和直线法无相对收敛性的优点,因而是一种计算量小、收敛快和数值稳定的分析方法。对微带和悬置微带谐振器的分析结果与有关文献的数据一致,从而验证了方法的正确性和有效性。     

本征权边界积分法解任意截面波导传输问题

本文选取本征函数作为权函数,由格林第二恒等式建立边界积分方程,并采用边界基形式得到线性齐次方程组。这种方法不仅降低了系数矩阵的维数,而且使其各项仍保持为简单一项,减少了计算量.本文提供了几种常见金属波导的例子,计算结果既收敛快、又足够准确。     

A finite difference approach that employs an asymptotic boundarycondition on a rectangular outer boundary for modeling two-dimensionaltransmission line structures

The derivation of three asymptotic boundary conditions is presented. Techniques for implementing each of these on finite difference meshes with rectangular outer boundaries are discussed. Numerical results obtained using these boundary conditions in the finite difference analysis of both shielded and unshielded transmission lines are shown. The authors present detailed convergence studies on the use of each of these boundary conditions and discuss the memory requirements of each     

Complex modes in shielded suspended coupled microstrip lines

The existence of complex modes in electrically shielded suspended coupled microstrip lines has been studied extensively, and the results are presented. A rigorous full-wave spectral-domain approach (SDA) with a newly proposed and tested set of basis functions can efficiently and accurately determine the propagation characteristics of the dominant, higher-order, and complex modes for planar or quasi-planar transmission lines. These basis functions are validated by comparing the convergence study of field solutions with those obtained by various sets of preconditioned bases and by the unconditioned subdomain ones. Excellent agreement is obtained for the propagation constants and the normalized complex longitudinal and transverse current distributions on conducting strips for the strongly coupled microstrip lines. For all the particular case studies discussed, it is shown that the complex modes may exist in all the shielded suspended coupled microstrip lines, even when the substrate dielectric constant is low. Theoretical results for the fundamental, higher-order, evanescent, and complex modes are presented for suspended coupled microstrip lines     

Exact singular integral equation approach for planar transmission lines

The analysis of planar transmission lines has been completed using a new exact singular integral equation (SIE) technique. Numerical results show that it is an efficient and accurate method.<>     

An Improved Weak-Form BCGS-FFT Combined With DCIM for Analyzing Electromagnetic Scattering by 3-D Objects in Planarly Layered Media

Fast algorithms for electrically large objects buried in layered media are mainly hindered by two time-consuming processes. One is the table filling of Green's function, and the other is the solving of the impedance matrix equation. For the first, to accelerate the evaluation of the time-consuming Sommerfeld integral in the dyadic Green's function (DGF), the discrete complex image method (DCIM) is introduced to get a closed-form DGF. To further accelerate the calculation of DGF for the volume electric field integral equation (EFIE), DGF is split before applying DCIM. For the second, the iterative solver stabilized biconjugate gradient fast Fourier transform (BCGS-FFT) is combined with DCIM for solving the matrix equations. Meanwhile, the closed-form DGF enables the "spherical-mean" Green's function, which eliminates the singularity of Green's function. Numerical results show that the weaker singularity results in a faster and steadier convergence rate for iterative solvers