Efficient electromagnetic modeling of three-dimensional multilayer microstrip antennas and circuits

In the use of the time-domain integral equation (TDIE) method for the analysis of layered media, it is important to have the time-domain layered medium Green's function computed for many source-to-field distances /spl rho/ and time instants t. In this paper, a numerical method is used that computes the mixed potential Green's functions G/sub v/(/spl rho/,t) and G/sub A/(/spl rho/,t) for a multilayered medium for many /spl rho/'s and t's simultaneously. The method is applicable to multilayered media and for lossless or lossy dispersive media. Salient features of the method are: 1) the use of complex /spl omega/ so that the surface wave poles are lifted off the real k/sub /spl rho// axis such that pole extractions are not required; 2) the use of half-space extraction so that the integrand for the Sommerfeld integral decays exponentially along the k/sub /spl rho// axis to obtain fast convergence of the integral; and 3) the use of the fast Hankel transform so that the Green's function is calculated for many values of /spl rho/ simultaneously. For a four-layer medium, we illustrate the numerical results by a three-dimensional plot of /spl rho/G/sub v/(/spl rho/,t) versus /spl rho/ and t and demonstrate the space-time evolution of these Green's functions. For a maximum frequency range of 8 GHz, the method requires only a few CPU minutes to compute a table of 100 (points in /spl rho/) /spl times/ 168 (points in t) uniformly spaced values of G/sub v/(/spl rho/,t) on an 867-MHz Pentium PC.

Closed-form Green?s function representations for cylindrically stratified media, which can be used in conjunction with a Method of Moments, are developed. The closed-form expressions are valid for all possible source and field points including the axial line (ρ = ρ' and θ= θ'), which has not been available before. In the course of obtaining these expressions, the spectral domain Green's function components are calculated efficiently and transformed to the spatial domain using the discrete complex image method with the help of the generalized pencil of function method. Numerical results are presented in the form of a mutual coupling between two current modes and the input impedance of various rectangular microstrip antennas on dielectric coated circular cylinders.

One of the singularity cancellation schemes proposed in the literature is applied to calculate singular integrals arising in the method of moments (MoM) analysis of 2-D periodic planar structures in multilayered media. Discrete complex image method is utilized for the accurate approximation of Green's function which also makes possible the application of the Ewald transformation for the efficient computation of the series associated with the periodic structure. This approximation and transformation modifies the kernel of the integral appearing in the computation of the MoM matrix entries. Formulation of the problem for this new kernel is presented together with numerical results demonstrating the achieved accuracy.

In this letter, we adopt a new procedure in the calculation of the layered Green's functions in the rectangular waveguide structure. In this procedure, the surface-wave poles are extracted first, and then the generalized pencil-of-function (GPOF) method is applied to approximate the spectral-domain Green's function along the real axis of the <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$k_{\rho}$</tex> </formula> plane directly. Because no branch point is introduced in this procedure, improvement can be achieved compared to the traditional discrete complex image method (DCIM). In order to make this procedure more accurate and robust in both near- and far-field regions, a specially devised multiple-times GPOF procedure is applied to approximate the spectral-domain Green's function. Numerical results in this letter demonstrate the accuracy of our method.

In this paper, based on the frequency-varied relationship between surface wave poles and leaky wave poles of spectral Green's functions for a layered medium, a new method for fast locating the leaky wave poles at the given operating frequency is established. This method locates the leaky wave poles at the given operating frequency by consecutive frequency perturbations with the surface wave poles at a proper frequency as starting poles. Numerical examples of this method applied in the combination with the discrete complex image method (DCIM) for evaluation of the Green's functions of microstrip and 2-layered medium models demonstrate the efficiency and accuracy of this method.

Forward electromagnetic scattering from buried dielectric objects is computed by the integral equation method in conjunction with efficient algorithm for half-space dyadic Green's functions. Concise representations of dyadic Green's functions are presented to establish the integral equation for buried dielectric objects. Through moving the spatial differential operator to the outside of the integral sign and computing the rest part by the discrete complex image method, closed forms of Green's functions are obtained. The bottleneck during calculating reaction matrix and scattering fields is overcome since it is not necessary to process the numerical evaluation of Sommerfeld integrals. The proposed method enhances the efficiency of the forward calculation of buried dielectric objects and enough accuracy can be guaranteed.

A special sampling path is proposed to improve the accuracy of the discrete complex image method (DCIM) in evaluating the lateral wave. Different from all the previous DCIM implementations, the proposed sampling path goes through the branch point directly, which helps to evaluate its contribution to the lateral wave more accurately. In this communication, different sampling paths of DCIM have been implemented and compared. It is found that in the situations where the lateral wave dominates the far-field region, DCIM with the new path gives more accurate and stable results.

This paper states that Fitting Green's function Fast Fourier Transformation (FG-FFT) algorithm applies to accelerating matrix vector product of higher order Method of Moments (MoM). For different patch, the local expansion box is employed with the same expansion order of every Gaussian point. Combined the high accuracy of the FG-FFT with this scheme, it makes the FG-FFT very suitable for high order basis function. Therefore, comparing other the FFT-based methods, higher order FG-FFT algorithm is more effective. The numerical examples presented in this paper show that the high order FG-FFT is more accuracy and efficiency for electrically large object.

In this paper, a novel realization of the Integral Equation in combination with the fast Fourier transform for the CFIE is established by Fitting both the Green's function and its Gradient onto the nodes of a uniform Cartesian grid. The new method has been compared with several existing popular FFT-based methods, including the AIM, the IE-FFT, and the p-FFT. The accuracy of the proposed method is significantly higher than other FFT-based methods, and the method is not sensitive to both the grid spacing and the expansion order. The outstanding merit of the proposed method is that the fitting procedure is independent of the basis functions. Therefore, when the higher order basis functions would be adopted in the method of moments, only one fitting procedure for the Green's function and its gradient on a basis function support is needed to meet all of basis functions defined on this support. Some numerical examples are provided in this paper to demonstrate the accuracy and efficiency of the proposed method.

Boundary element methods (BEM) have been successfully applied towards solving a broad array of complicated electromagnetic problems. Most BEM approaches rely on flat triangular discretizations and discretization via the Method of Moments (MoM) and low-order basis functions. Although more complicated from an implementation standpoint, it has been shown that high-order methods based on curvilinear patch mesh discretizations can significantly outperform low-order MoM in both accuracy and computational efficiency. In this work, we review a new high-order Nystrom method based on using Chebyshev basis functions with curvilinear elements that we have recently developed, present a few scattering examples, and discuss related on-going and future work.

Analysis of arbitrarily shaped three-dimensional (3D) objects in a multilayered medium using the method of moments (MoM) requires the computation of the Green's functions. When MoM is applied in the spatial domain, a 3D integral (one for the Sommerfeld integral, the other two for the integral over the source triangle) should be evaluated. The evaluation of the Sommerfeld integrals is a time-consuming process. A commonly encountered solution for this problem is to perform interpolations using preestablished look-up tables. Here, a general 3D interpolation model has been developed. The interpolation scheme is to select M vertical planes (perpendicular to the interfaces of the multilayered medium) to be tabulated in an overlapping manner to interpolate between them. In this scheme, all the grid values on the same vertical plane are tabulated and a single subroutine call is required to evaluate the Green's function. The interpolation model has been employed to calculate the current distributions on a TE 01delta-mode dielectric resonator excited with a microstrip line.

In this paper, an efficient higher order hybrid method of moments (MoM)-physical optics (PO) modeling technique is developed for the analysis of electromagnetic scattering from electrically large conductor objects. This technique utilizes curved triangular patches for geometric modeling, and higher order (HO) basis functions for current modeling, i.e., higher order hierarchical vector (HOHV) basis functions for MoM region and phase-extracted (PE) basis function for PO region. Benefitting from the &#x201C;double&#x201D; higher order discretization in both MoM and PO regions, the number of unknowns can be reduced remarkably, and the accuracy and efficiency increase, in comparison to the conventional low order MoM-PO solution. A numerical example is given to demonstrate the validity and efficiency of this HO-MoM-PO.

We present compact and efficient closed form expressions for the mixed potential Green's functions in multilayered media with general electric and magnetic sources. By generalizing the Sommerfeld identity we can express also the first and second order Sommerfeld integrals in closed form and the spatial domain Green's functions can be obtained in closed form without numerical differentiation. The presented formulation leads to a very efficient method since in each layer the GPOF approximations are needed only for three (source layer) or four (other layers) spectral domain Green's functions. The applied mixed potential integral equations, identical with the Michalski-Zheng (1990) C-formulation (MZC), are solved by the method of moments (Galerkin's method) with the Rao-Wilton-Glisson (RWG) basis functions. The developed method has been applied for the analysis of complicated 3D microstrip structures and scattering by various 3D objects.

Forecasting cyanobacterium Anabaena spp. in the River Murray, South Australia, using B-spline neurofuzzy models

Modeling technique for electromagnetic fields excited by antennas is an important topic in computational electromagnetics, which is concerned with the numerical solution of Maxwell's equations. In this paper, a novel hybrid technique that combines method of moments (MoM) with finite-difference time-domain (FDTD) method is presented to handle the problem. This approach employed Huygen's principle to realize the hybridization of the two classical numerical algorithms. For wideband electromagnetic data, the interpolation scheme is used in the MoM based on the dyadic Green's function. On the other hand, with the help of equivalence principle, the scattered electric and magnetic fields on the Huygen's surface calculated by MoM are taken as the sources for FDTD. Therefore, the electromagnetic fields in the environment can be obtained by employing finite-difference time-domain method. Finally, numerical results show the validity of the proposed technique by analyzing two canonical samples.