On the modeling of a gapped power-bus structure using a hybrid FEM/MoM approach

A hybrid finite-element-method/method-of-moments (FEM/MoM) approach is applied to the analysis of a gapped power-bus structure on a printed circuit board. FEM is used to model the details of the structure. MoM is used to provide a radiation boundary condition to terminate the FEM mesh. Numerical results exhibit significant errors when the FEM/MoM boundary is chosen to coincide with the physical boundary of the board. These errors are due to the inability of hybrid elements on the boundary to enforce the correct boundary condition at a gap edge in a strong sense. A much better alternative is to extend the MoM boundary above the surface of the board.     

Human exposure assessment in the near field of GSM base-station antennas using a hybrid finite element/method of moments technique

A hybrid finite-element method (FEM)/method of moments (MoM) technique is employed for specific absorption rate (SAR) calculations in a human phantom in the near field of a typical group special mobile (GSM) base-station antenna. The MoM is used to model the metallic surfaces and wires of the base-station antenna, and the FEM is used to model the heterogeneous human phantom. The advantages of each of these frequency domain techniques are, thus, exploited, leading to a highly efficient and robust numerical method for addressing this type of bioelectromagnetic problem. The basic mathematical formulation of the hybrid technique is presented. This is followed by a discussion of important implementation details-in particular, the linear algebra routines for sparse, complex FEM matrices combined with dense MoM matrices. The implementation is validated by comparing results to MoM (surface equivalence principle implementation) and finite-difference time-domain (FDTD) solutions of human exposure problems. A comparison of the computational efficiency of the different techniques is presented. The FEM/MoM implementation is then used for whole-body and critical-organ SAR calculations in a phantom at different positions in the near field of a base-station antenna. This problem cannot, in general, be solved using the MoM or FDTD due to computational limitations. This paper shows that the specific hybrid FEM/MoM implementation is an efficient numerical tool for accurate assessment of human exposure in the near field of base-station antennas.     

Theoretical modeling of cavity-backed patch antennas using a hybridtechnique

A hybrid technique that combines the method of moments (MoM) and the finite element method (FEM) to analyze cavity-backed patch antennas is presented. This technique features the use of FEM in solving the electromagnetic field distribution in the cavity and the use of MoM in solving integral equations outside the cavity. The results of MoM and FEM are combined through the continuity conditions on the boundary of the cavity. Due to the flexibility of FEM, complex cavities filled with inhomogeneous media can be analyzed by this technique. The results obtained by this hybrid technique are compared to the finite difference time domain (FDTD) results and good agreement is found     

Emission and Susceptibility Modeling of Finite-Size Power-Ground Planes Using a Hybrid Integral Equation Method

A novel method based on hybrid integral equation for electromagnetic emission and susceptibility modeling of power-ground planes with a finite size is proposed in this paper. First, the entire computational domain is divided into the internal subdomain including the substrate sandwiched between the power and ground planes and the external subdomain surrounding the power-ground planes. The internal subdomain is modeled by using the integral equation with dyadic Green's functions of the rectangular cavity, while the free-space Green's function is used to model the outside subdomain. These two kinds of integral equations are coupled through the equivalent electric and magnetic currents that are placed on the interfaces. The key advantage of this proposed method is its ability to model both emission and susceptibility problems. This method can accurately simulate the impedance of the power-ground planes and the radiated field. In particular, it is able to predict the induced electric currents inside the power-ground planes that result from external interference sources. Therefore, this technique is able to provide a complete solution for the electromagnetic compatibility analysis of the system-level package.      

Higher Order Hybrid FEM-MoM Technique for Analysis of Antennas and Scatterers

A novel higher order large-domain hybrid computational electromagnetic technique based on the finite element method (FEM) and method of moments (MoM) is proposed for three-dimensional analysis of antennas and scatterers in the frequency domain. The geometry of the structure is modeled using generalized curved parametric hexahedral and quadrilateral elements of arbitrary geometrical orders. The fields and currents on elements are modeled using curl- and divergence-conforming hierarchical polynomial vector basis functions of arbitrary approximation orders, and the Galerkin method is used for testing. The elements can be as large as about two wavelengths in each dimension. As multiple MoM objects are possible in a global exterior region, the MoM part provides much greater modeling versatility and potential for applications, especially in antenna problems, than just as a boundary-integral closure to the FEM part. The examples demonstrate excellent accuracy, convergence, efficiency, and versatility of the new FEM-MoM technique, and very effective large-domain meshes that consist of a very small number of large flat and curved FEM and MoM elements, with $p$-refined field and current distributions of high approximation orders. The reduction in the number of unknowns is by two orders of magnitude when compared to available data for low-order FEM-MoM modeling.      

A numerical investigation of interior resonances in the hybrid FEM/MoM method

The interior resonance problem that can occur when using a hybrid finite-element method/method of moments (FEM/MoM) method to model electromagnetic scattering problems is investigated. Calculations of the bistatic radar cross section of a coated dielectric sphere are presented using different formulations, solution approaches, and solvers. The solutions using the electric-field integral equation have significant errors near an interior resonance frequency. When the combined-field integral equation is employed, satisfactory solutions can be obtained that do not depend on the particular solution approach or solver.     

Edge-based FEM solution of scattering from inhomogeneous andanisotropic objects

This paper presents an application of the edge-based vector finite element method to scattering problems of anisotropic and inhomogeneous objects. Based on conventional FEM functional, a hybrid finite element-surface integral formulation is established by introducing permittivity and permeability tensors. The space domain is divided into interior and exterior regions by an imaginary surface conformal to the scatterer. Edge vector finite elements are used to model the anisotropic and inhomogeneous interior, and a surface integral equation is used to model the unbounded exterior. Compared to other hybrid techniques, the approach here retains the symmetry and sparsity of the FEM matrix and introduces only one type of unknown equivalent current in the moment matrix equation. To validate the theory, typical 2-D numerical results are first presented, which show excellent agreement with exact eigenmode expansion solutions or accurate MoM data     

Hybrid analytical modeling method for split power bus in multilayered package

As multiple chips are being integrated into a single package with increased operating frequency, switching noise coupling on power buses has become an important design issue. To reduce the noise coupling, a split power bus structure has been generally used in package substrates having multilayered power and ground planes. Consequently, there is an increasing need for an efficient method to analyze a split power bus in a multilayered package. This paper introduces a hybrid analytical modeling method for characterizing a split power bus in a multilayered package. The proposed method uses a resonant cavity model combined with a segmentation method. Furthermore, a port assignment technique and an associated calculation method for the equivalent circuit model parameter of the split gap are proposed. The proposed port assignment technique and the analytical equation make it possible to analyze a split power bus, especially in a multilayered package. To verify the proposed method, multilayered test packages are fabricated and tested by means of frequency-domain measurements. In addition, an optimal power bus design method was successfully demonstrated for suppressing noise coupling between chips on a single package. Finally, the proposed method and optimal power bus design method was verified using a series of frequency-domain and time-domain measurements.     

An efficient multiregion model for electromagnetic scattering and radiation by PEC targets

An efficient multiregion model has been proposed for the fast implementation of the electromagnetic scattering by perfectly electrical conducting (PEC) targets and the radiation of point sources or wire antennas near PEC targets. In the multiregion model, the PEC target under consideration is divided by multiple regions depending on the position of point source/antenna or the incident direction of plane waves. Then the method of moments (MoM) is used on the first region, which is close to the source or is the illuminated region, to obtain the accurate electric current. The mutual coupling between different regions are considered approximately based on the magnetic-field integral equation, from which closed-form approximations for electric currents on other regions are derived. Because MoM is only performed on the first region, the number of unknowns in the new model is much fewer than that in the full MoM analysis, making the new model much more efficient. Compared with the published hybrid methods, the multiregion model gives a more reasonable physical explanation, and provides a better accuracy in both currents and scattered fields. Numerical simulations for two-dimensional (2-D) problems (transverse-magnetic/transverse-electric) and 3-D problems are given to test the validity and efficiency of the proposed modeling.     

High-Field Magnetic Resonance Imaging With Reduced Field/Tissue RF Artefacts—A Modeling Study Using Hybrid MoM/FEM and FDTD Technique

Due to complex field/tissue interactions, high-field magnetic resonance (MR) images suffer significant image distortions that result in compromised diagnostic quality. A new method that attempts to remove these distortions is proposed in this paper and is based on the use of transceiver-phased arrays. The proposed system uses, in the examples presented herein, a shielded four-element transceive-phased array head coil and involves performing two separate scans of the same slice with each scan using different excitations during transmission. By optimizing the amplitudes and phases for each scan, antipodal signal profiles can be obtained, and by combining both the images together, the image distortion can be reduced several fold. A combined hybrid method of moments (MoM)/finite element method (FEM) and finite-difference time-domain (FDTD) technique is proposed and used to elucidate the concept of the new method and to accurately evaluate the electromagnetic field (EMF) in a human head model. In addition, the proposed method is used in conjunction with the generalized auto-calibrating partially parallel acquisitions (GRAPPA) reconstruction technique to enable rapid imaging of the two scans. Simulation results reported herein for 11-T (470-MHz) brain imaging applications show that the new method with GRAPPA reconstruction theoretically results in improved image quality and that the proposed combined hybrid MoM/FEM and FDTD technique is suitable for high-field magnetic resonance imaging (MRI) numerical analysis     

Radiation and scattering from infinite periodic printed antennaswith inhomogeneous media

The hybrid method of moments (MoM)/Green's function method technique is applied to infinite periodic printed antenna arrays containing dielectric inhomogeneities. The solution uses an integral equation for an infinite periodic printed array on or over a homogeneous dielectric substrate, coupled with equivalent volume polarization currents for dielectric inhomogeneities on top of the homogeneous substrate. Volume pulse-basis functions were used to expand the volume polarization currents. A hybrid MoM/Green's function method solution was then obtained through the matrix form of the problem. The two-dimensional (2-D) solution of plane wave scattering from a grounded dielectric slab was used to validate the reaction impedance of the dielectric inhomogeneity. Several infinite periodic printed dipole arrays with dielectric supports and overlays were studied with this solution and good agreement was observed between the hybrid MoM/Green's function method and waveguide simulator experiments     

过孔转换信号完整性分析的区域分解有限元法

提出了一种基于区域分解的二维有限元法分析多层印制电路板电源/地平面中过孔转换结构的信号完整性.过孔电流产生的电磁场呈三维结构,其中,一部分电磁波沿过孔轴向传输,另一部分电磁波在电源/地平面间沿径向传播.采用一虚拟柱面将求解区域分割为过孔区和电源/地平面区.将过孔区建模为以周向磁场为主分量的二维轴对称问题,而将电源/地平面区建为以垂直电场为主分量的二维模型.首先求解电源/地平面区的二维边值问题获得分割边界上节点的波阻抗,然后将该波阻抗代入过孔区模型中分割边界节点的边界条件,从而计算出过孔信号传输的S参数.所提方法通过模型缩减可实现对微细过孔结构信号完整性的精确快速计算,且采用全波电磁场分析软件对算法的有效性和准确性进行了验证.     

高速电路电源/地层间阻抗参数计算与分析

为了快速准确地计算高速电路地层与电源层之间的阻抗参数,基于边界积分方程提出了有效的计算方法.该方法充分利用了实际电源层/地层的结构特征,将三维电磁场问题转化为二维问题,减少了计算时间.由于在计算中不需要考虑整个 电源层/地层结构的格林函数,故该方法可以用于任意边界形状的电路板.基于提出的积分方程法,分析了介质相对电介质...     

Analysis of Antenna Around NURBS Surface With Hybrid MoM-PO Technique

The hybrid method of moments and physical-optics (MoM-PO) approach is used to calculate the radiation pattern of antenna around arbitrarily shaped structure. The structure is modeled with Non-uniform rational B-spline (NURBS) surfaces. The hybrid MoM-PO approach is implemented by modifying the impedance matrix of the MoM region with PO. Formula for the scattered PO field is deduced for cases of antenna located around NURBS surface. The stationary phase method (SPM) is applied for the integral of the induced current in the PO region. Results obtained from this method and from MoM-PO approach based on triangle facet model agree well while the former is more efficient in execution time     

Mixed potential integral equation technique for hybridmicrostrip-slotline multilayered circuits using a mixedrectangular-triangular mesh

In this paper, a mixed potential integral equation (MPIE) formulation for hybrid microstrip-slotline multilayered circuits is presented. This integral equation is solved with the method of moments (MoM) in combination with Galerkin's method. The vector-valued rooftop functions defined over a mixed rectangular-triangular mesh are used to model the electric and magnetic currents on the microstrip and slotline structures. An efficient calculation technique for the quadruple interaction integrals between two cells in the system matrix equation is presented. Two examples of hybrid microstrip-slotline circuits are discussed. The first example compares the simulation results for a microstrip-slotline transition with measured data. The second example illustrates the use of the simulation technique in the design process of a broadband slot-coupled microstrip line transition     

利用近场Gordon积分近似的矩量法-物理光学混合方法

针对电大金属目标的电磁计算, 提出了一种新的矩量法-物理光学(Method of Moment-Physical Optics, MoM-PO)混合方法, 以解决传统的MoM-PO混合法中PO区域和MoM区域耦合项的计算时间过长问题.用Gordon积分计算目标的PO区域对MoM区域的作用, 并加入近场近似处理.该方法避免了传统的MoM-PO混合法中耦合项积分方程的计算, 加大PO区域的剖分面元的大小, 能够有效地降低矩阵规模和未知数个数, 因而降低了内存, 减少了计算时间.数值算例结果表明, 近场Gordon积分近似的MoM-PO混合方法能够有效地减少耦合项的计算时间, 并能达到理想的精度.     

Circuit models for power bus structures on printed circuit boards using a hybrid FEM-SPICE method

Power bus structures consisting of two parallel conducting planes are widely used on high-speed printed circuit boards. In this paper, a full-wave finite-element method (FEM) method is used to analyze power bus structures, and the resulting matrix equations are converted to equivalent circuits that can be analyzed using SPICE programs. Using this method of combining FEM and SPICE, power bus structures of arbitrary shape can be modeled efficiently both in the time-domain and frequency-domain, along with the circuit components connected to the bus. Dielectric loss and losses due to the finite resistance of the power planes can also be modeled. Practical examples are presented to validate this method.     

Impedance boundary conditions in a hybrid FEM/MOM formulation

When numerically modeling structures with imperfect conductors or conductors coated with a dielectric material, impedance boundary conditions (IBCs) can substantially reduce the amount of computation required. This paper incorporates the IBC in the finite-element method (FEM) part of a FEM/method of moments (FEM/MoM) modeling code. Properties of the new formulation are investigated and the formulation is used to model three practical electromagnetic problems. Results are compared to either measured data or other numerical results. The effect of the IBC on the condition number of hybrid FEM/MoM matrices is also discussed.     

Ferrite-loaded cavity-backed antennas including nonuniform and nonlinear magnetization effects

A method of analyzing both the electromagnetic and the magnetostatic phenomena involved in ferrite-loaded cavity-backed antennas is presented. The high-frequency modeling of the antenna is based on a hybrid of the finite element method (FEM) with the method of moments (MoM). The (magnetostatic) demagnetizing process of the finite ferrite loadings is modeled with the use of a nonlinear static FEM. The results of the magnetostatic analysis are used to compute the internal field of the ferrite samples. Through the use of an appropriate ferrite permeability tensor, the nonuniform internal bias field is incorporated into the high-frequency FEM/MoM analysis. The input impedance characteristics of two different ultrahigh-frequency (UHF) antennas are presented using different ferrite models. Results for the tuning range and sensitivity are presented for different bias directions. The numerical results are also compared with experimental data.     

Parameters Extraction of Millimeter Wave Circuits by Hybrid Vector Finite Element and Moment Method Combined with SOC Technique

This paper presents a hybrid method, which couples the vector finite element method (FEM) and method of moment (MOM) for analyzing the field and current distribution of the millimeter wave circuits. The FEM is applied to handle the interior region of dielectric bodies and MOM is used to solve surface integral equations. Then, These integral expressions are coupled into the FEM equations through the continuity of the tangential fields across the connection boundaries. Simultaneously, the short-open calibration (SOC) technique is used for predicting accurately the scattering parameters of the circuits. Numerical results are well compared with those published in the previous literatures.