基于矩量法的手机天线辐射的研究

基于矩量法,分析了三维各向同性介质的散射问题。并以此为基础,研究了反映各向同性介质在电磁场下热效应的参数-比吸收率（SAR）。针对实际手机使用中的辐射问题,给出了一个简单模型下的SAR数值仿真结果,并与IEEE标准作了比较,提出了具体的安全距离建议。最后,比较了矩量法,时域有限差分法,有限元法在手机天线辐射研究中的优缺点。     

SAR reduction for handset with two-element phased array antennacomputed using hybrid MoM/FDTD technique

An investigation into a two-element phased antenna array mobile handset using the MoM/FDTD hybrid method is presented. The array is designed to provide a spatial null in the near field zone in the direction of the human head. Compared with an omnidirectional antenna, the overall efficiency and azimuth coverage are improved and the peak specific absorption rate in the head can be reduced by at least 10 dB     

Computation of specific absorption rate in the human body due to base-station antennas using a hybrid formulation

A procedure for computational dosimetry to verify safety standards compliance of mobile communications base stations is presented. Compared with the traditional power density method, a procedure based on more rigorous physics was devised, requiring computation or measurement of the specific absorption rate (SAR) within the biological tissue of a person at an arbitrary distance. This uses a hybrid method of moments/finite difference time domain (MoM/FDTD) numerical method in order to determine the field or SAR distribution in complex penetrable media, without the computational penalties that would result from a wholly FDTD simulation. It is shown that the transmitted power allowed by the more precise SAR method is, in many cases, between two and five times greater than that allowed by standards implementing the power flux density method.     

An FDTD/MoM hybrid technique for modeling complex antennas in thepresence of heterogeneous grounds

Calculating the current distribution and radiation patterns for ground-penetrating radar antennas is a challenging problem because of the complex interaction between the antenna, the ground, and any buried scatterer. Typically, numerical techniques that are well suited for modeling the antennas themselves are not well suited for modeling the heterogeneous grounds, and visa versa. For example the finite-difference time-domain (FDTD) technique is well suited for modeling fields in heterogeneous media, whereas the method of moments (MoM) is well suited for modeling complex antennas in free space. This paper describes a hybrid technique, based upon the equivalence principle, for calculating an antenna's current distribution radiation pattern when the antenna is located near an air-ground interface. The original problem is decomposed into two coupled equivalent problems: one for the antenna geometry and the other for the ground geometry, with field information passing between them via a rapidly converging iterative procedure. The fields in each region may be modeled using numerical techniques best suited to them. Results for several test cases are presented, using FDTD to model the ground problem and MoM for the antenna problem, that demonstrate the accuracy of this hybrid technique     

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     

复杂环境中短波天线的MoM/FDTD混合法分析

利用电磁场数值计算方法中的矩量法/时域有限差分（MoM/FDTD）混合方法,分析了复杂环境中短波天线的电磁辐射性能,建立了短波双极天线的自由空间模型。采用矩量法和时域有限差分法相结合,对其模型进行仿真计算,并将计算结果和已有的文献进行比较,验证了混合方法计算结果的可行性、准确性。总结了该模型对短波天线远区场影响的有益经验,为改善短波天线性能提供了设计参考。     

Use of redundant testing functions in moment-method solutions forblock models

An overconstrained version of the method of moments (MoM) for SAR (specific absorption rate) evaluation in biological bodies is presented. A number of testing functions larger than the number of basis functions is used in order to better constrain the solution near corners and edges. A rectangular system is obtained and solved by means of a pseudoinversion algorithm. Comparisons with results reported in the literature show an enhancement of MoM capabilities in SAR calculations, without a consistent increase in computational requirements     

Numerical computation of fat layer effects on microwave near-fieldradiation to the abdomen of a full-scale human body model

Numerical computation results of fat layer effects on the microwave near field radiation to the abdomen of a three-dimensional (3-D) full-scale human body model are presented. The human body is modeled as a 3-D homogeneous muscle phantom with a fat layer covering the abdomen part. The dipole wire-antenna located proximate to the abdomen is used as the microwave radiation source at 915 MHz. This is to study the effects on hyperthermia heating by using the microwave applicator (at 915 MHz) or the near-field exposure from the proximate handset antenna to the human body at ISM band wireless communication band (902-928 MHz). Coupled integral equations (CIE) and the method of moments (MoM) are employed to numerically compute electromagnetic (EM) energy deposition specific absorption rate (SAR) from the radio frequency (RF) antenna applicator into the proximate fat layer covered abdomen. The antenna input impedance (proximate to the body), return loss (RL), and the resonant antenna length (proximate to the body) will also be numerically determined to increase the microwave power delivered into the body. The study of fat layer effects is important for microwave hyperthermia applications. It is also important for the investigation of the potential health hazard from the near-field radiation of a wireless communication antenna     

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     

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.      

Study of the coupling between human head and cellular phone helical antennas

The interaction between normal-mode helical antennas and human head models is analyzed, using both a novel accurate semi-analytical method and finite-difference time-domain (FDTD) simulations. The semi-analytical method is based on the combination of Green's functions theory with the method of moments (Green/MoM) and is able to model arbitrarily shaped wire antennas radiating in the close proximity of layered lossy dielectric spheres representing simplified models of the human head. The purpose of the development of the Green/MoM technique is to provide a reliable tool for preliminary (worst case) estimation of human head exposure to the field generated by different antenna configurations with emphasis on the helical antenna, representing the most diffused antenna type used in modern cellular handsets. Furthermore, the accurate semi-analytical character of the Green/MoM technique permits the accuracy assessment of purely numerical techniques, such as the FDTD, which is currently the most widely used computational method in mobile communication dosimetric problems, since it allows modeling of anatomically based head models. After appropriate benchmarking, FDTD simulations are used to study the interaction between a heterogeneous anatomically correct model of the human head exposed to a normal-mode helix monopole operating at 1710 MHz mounted on the top of a metal box representing a realistic mobile communication terminal. The study of both canonical and realistic exposure problems includes computations of specific absorption rates (SARs) inside the human head, total power absorbed by the head and assessment of antenna performance. Emphasis is placed on the comparative dosimetric assessment between adults and children head models.     

On the interior resonance problem when applying a hybrid FEM/MoMapproach to model printed circuit boards

A hybrid finite element method/method of moments (FEM/MoM) technique is used to analyze a printed circuit board power bus structure where the source and observation points are in the near field. The FEM is used to model the lossy region between the planes of the board including the source. The MoM is used to model the region outside the planes and provide a radiation boundary condition to terminate the FEM mesh. Numerical results for a bridged power bus structure are compared with measurements. A nonphysical interior resonance of the electric field integral equation is observed. The problem can be avoided by using a hybrid technique based on a combined field integral equation     

Efficient evaluation of spatial-domain MoM matrix entries in theanalysis of planar stratified geometries

An efficient hybrid method for evaluation of spatial-domain method-of-moments (MoM) matrix entries is presented in this paper. It has already been demonstrated that the introduction of the closed-form Green's functions into the MoM formulation results in a significant computational improvement in filling up MoM matrices and, consequently, in the analysis of planar geometries. To achieve further improvement in the computational efficiency of the MoM matrix entries, a hybrid method is proposed in this paper and, through some examples, it is demonstrated that it provides significant acceleration in filling up MoM matrices while preserving the accuracy of the results     

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.     

Threshold Power of Canonical Antennas for Inducing SAR at Compliance Limits in the 300–3000 MHz Frequency Range

A study of the specific absorption rate (SAR) in an exposed body induced by canonical antennas is presented, with the aim of determining an upper bound for the antenna transmit power that demonstrates that a product is inherently compliant with internationally accepted radio frequency (RF) exposure limits. Starting from the fundamental limits in antenna quality factor (Q) and the corresponding bandwidth, several antenna sizes are selected, and their SAR distributions are computed using the method of moments (MoM) and finite-difference time domain (FDTD) method in the frequency range 300-3000 MHz. The threshold powers are then determined, below which the peak 1-g and 10-g averaged SAR would not exceed the limits specified in international exposure standards. From the data, simple expressions are derived to estimate the threshold power over a wide range of antenna sizes, frequencies, and distances from the body. It is demonstrated that the results presented in this paper are conservative in comparison with the measured SAR data of real products as well as other published data     

Finite-difference time-domain calculations of absorbed power in theankle for 10-100 MHz plane wave exposure

This paper presents finite-difference time-domain (FDTD) calculations of the short-circuit current and the specific energy absorption rate (SAR) in the ankle. Plane wave exposures from 10 to 100 MHz for an adult, a 10-year old and 5-year old are considered. The calculations are performed in two parts. Firstly, the coupling between a homogeneous whole body phantom and the applied field is calculated. The region around a lower leg is then expanded, the leg being described by a realistic fine-scale, heterogeneous model. Tangential electric field components from the first part are used as boundary conditions on the reduced domain of the second part. Electric field values based on a maximum SAR of 20 W . kg-1 are presented.     

Efficient wide-band evaluation of mobile communications antennasusing [Z] or [Y] matrix interpolation with the method of moments

The development of novel antennas for mobile communications often relies on performance simulations. The evaluation of the antenna surface currents for many frequencies using the method of moments (MoM) can take a long time since the impedance matrix must be computed for each new frequency. This paper investigates and compares two efficient methods for the computation of the broad-band performance of mobile communications antennas using frequency interpolation of either the MoM impedance matrix [Z] or admittance matrix [Y]. In either method, the elements of only a few matrices at relatively large frequency intervals are directly computed. These matrices are then used to interpolate the elements of the respective [Z] or [Y] matrices at the intermediate frequencies. Both methods reduce the time it takes to compute the antenna performance over a wide frequency band. The implementation of each method to evaluate the performance of several different antennas used for mobile communications is discussed. Examples with both frequency-domain and time-domain results are presented and both near-field and far-field quantities are considered. The accuracy, the simulation run times, and the computational requirements of direct MoM, [Z] matrix interpolation, and [Y] matrix interpolation are compared     

Numerical simulation of SAR and B1-field inhomogeneityof shielded RF coils loaded with the human head

The finite-difference time-domain (FDTD) method is combined with the method of moments (MoM) to compute the electromagnetic fields of shielded radio-frequency (RF) coils loaded with an anatomically accurate model of a human head for high-frequency magnetic resonance imaging (MRI) applications. The combined method can predict both the specific energy absorption rate (SAR) and the magnetic field (known as the B₁ field) excited by any RF coils. Results for SAR and B₁ field distribution, excited by shielded and end-capped birdcage coils, are calculated at 64, 128, 171, and 256 MHz. The results show that the value of SAR increases when the frequency of the B₁ field increases and the B₁ field exhibits a strong inhomogeneity at high frequencies     

Use of the Finite-Difference Time-Domain Method in Calculating EM Absorption in Human Tissues

Although there are acceptable methods for calculating whole body electromagnetic absorption, no completely acceptable method for calculating the local specific absorption rate (SAR) at points within the body has been developed. Frequency domain methods, such as the method of moments (MoM) have achieved some success; however, MoM requires computer storage on the order of (3N) 2 and computation time on the order of (3N) 3 where N is the number of cells. The finite-difference time-domain (FDTD) method has been employed extensively in calculating the scattering of metallic objects, and recently is seeing some use in calculating the interaction of EM fields with complex, lossy dielectric bodies. Since the FDTD method has storage and time requirements proportional to N, it presents an attractive alternative to calculating SAR distribution in large bodies. This paper describes the FDTD method and evaluates it by comparing its results to analytic solutions in two and three dimensions. The utility of the FDTD method is demonstrated by a 3D scan of the human torso. The results obtained demonstrate that the FDTD method is capable of calculating internal SAR distribution with acceptable accuracy. With the availability of supercomputers, such as the CRAY II, the calculation of SAR distribution in a man model of 50 000 cells (1.27 cm per cell) appears to be feasible.     

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.