Discrete Complex Image Method Research Articles

An efficient algorithm for analyzing large-scale microstrip structures using adaptive integral method combined with discrete complex-image method

An efficient algorithm combining the adaptive integral method and the discrete complex-image method (DCIM) is presented in this paper for analyzing large-scale microstrip structures. The arbitrarily shaped microstrips are discretized using triangular elements with Rao-Wilton-Glisson basis functions. These basis functions are then projected onto a rectangular grid, which enables the calculation of the resultant matrix-vector product using the fast Fourier transform. The method retains the advantages of the well-known conjugate-gradient fast-Fourier-transform method, as well as the excellent modeling capability offered by triangular elements. The resulting algorithm has the memory requirement proportional to O(N) and the operation count for the matrix-vector multiplication proportional to O(N log N), where N denotes the number of unknowns. The required spatial Green's functions are computed efficiently using the DCIM, which further speeds up the algorithm. Numerical results for some microstrip circuits and a microstrip antenna array are presented to demonstrate the efficiency and accuracy of this method.

Discrete complex image method for Green's functions of general multilayer media

The discrete complex image method is extended to efficiently and accurately evaluate the Green's functions of multilayer media for the method of moments analysis. The difficulty associated with the surface-wave extraction for muitilayer media is solved by evaluating a contour integral recursively in the complex k/sub p/-plane, With this scheme, the discrete complex image method works in both the near- and far-field regions for general multilayer media, whether open or shielded and lossy or lossless.

Resonant Behaviours of Microstrip Antenna in Multilayered Media: an Efficient Full-Wave Analysis - Abstract

This paper presents an efficient analysis of a microstrip antenna in multilayered media using the method of moments (MoM). The general forms of spectral-domain Green's functions for multilayered media are converted into the spatial-domain Green's functions using the discrete complex image method (DCIM). With the spatial-domain Green's functions, the mixed potential integral equation (MPIE) is discretized in spatial domain, and the resultant system of equations is then solved using the biconjugate gradient (BCG) method. As applications, resonant frequencies of microstrip antennas in multilayered media are analysed. The numerical results show that the present method is an efficient and accurate scheme for analysing microstrip antennas in multilayered media.

Fast inhomogeneous plane wave algorithm for electromagnetic solutions in layered medium structures: Two‐dimensional case

An accurate and efficient algorithm is proposed for solving two‐dimensional electromagnetic scattering problems in a layered medium. As a natural extension of the previously developed fast inhomogeneous plane wave algorithm (FIPWA), this approach has several inherent merits, such as being simple, versatile, and error controllable. The basic idea is first to express the spatial Green's function, encountered in layered medium studies, as Sommerfeld‐type integrals. By observing the similarity of these integrals with the integral representation of the free space Green's function, FIPWA can be applied with ease to accelerate the matrix‐vector multiplication. The multilevel scheme has been implemented, and the computational complexity ofO(NlogN) is achieved. It is noted that the proposed approach is more accurate and more efficient than the existing fast multipole method coupled with the discrete complex image method.

An efficient evaluation of the nonsymmetrical components of the Green's function for multilayered media

This paper is concerned with the evaluation of nonsymmetrical components of the Green's function of a Hertzian dipole present in a multilayered medium. The integrand of these components has a slowly varying tail which makes the discrete complex image method inefficient in representing the near field. In this work, the slowly varying tail is represented using real images whose locations are determined a priori. The amplitudes of these images are evaluated using a simple least square algorithm. The near field computed by this method is shown to yield good results for a half space and microstrip structures. © 2001 John Wiley & Sons, Inc. Microwave Opt Technol Lett 28: 199–202 (2001).

Multilevel fast multipole algorithm for analysis of large-scale microstrip structures

An efficient algorithm combining multilevel fast multipole method and the discrete complex image method is presented for analyzing large-scale microstrip structures. The resulting algorithm has the memory requirement and the CPU time per iteration proportional to O(NlogN), where N denotes the number of unknowns. Numerical results for microstrip antennas are presented to demonstrate the efficiency and accuracy of this method.

Magnetic Field Integral Equation for Electromagnetic Scattering By Conducting Bodies of Revolution in Layered Media - Abstract

This work presents a new formulation for conducting bodies of revolution (BOR) in layered media. It is derived using magnetic field integral equation (MFIE). The discrete complex image method is used to transform the Sommerfeld integrals into closed form solutions. For large closed objects, the use of the magnetic field formulation is shown to be more advantageous than the electric field integral equation (EFIE) concerning the convergence of the solution. The obtained formulation is applied to the contiguous half-spaces case. Results of both the magnetic and electric field integral equation formulations are presented.

Efficient electromagnetic modeling of microstrip structures in multilayer media

This paper presents an efficient method-of-moments solution of the mixed-potential integral equation for a general microstrip structure in multilayer media. In this method, the general forms of the spectral-domain Green's functions for multilayer media are derived first. The spatial-domain Green's functions are then obtained by the discrete complex-image method, which obviates the time-consuming numerical evaluation of the Sommerfeld integral. The Rao-Wilton-Glisson basis functions are employed to provide necessary flexibility to model arbitrary shapes. To expedite the computation of frequency response over a broad band, a reduced-order model is presented using asymptotic waveform evaluation. Numerical results of multilayer circuits and antennas are presented to show the efficiency and accuracy of this method.

A fast full-wave analysis of scattering and radiation from large finite arrays of microstrip antennas

A fast full-wave analysis technique that can be used to analyze the scattering and radiation from large finite arrays of microstrip antennas is presented. The technique discretizes the mixed potential integral equation (MPIE) in the spatial domain by means of a full-wave discrete complex image method. The del operators on the Green's functions are transferred from the singular kernel to the expansion and testing functions. The resultant system of equations is solved using the biconjugate gradient (BCG) method in which the matrix-vector product is evaluated efficiently using the fast Fourier transform (FFT). This results in an efficient and accurate computation of the scattering and radiation from finite arrays of microstrip antennas. Several numerical results are presented, demonstrating the accuracy, efficiency, and capability of this technique.

Scattering and radiation analysis of microstrip antennas using discrete complex image method and reciprocity theorem

A simple and efficient method is presented to characterize the scattering and radiation properties of arbitrarily shaped microstrip patch antennas. The method employs the discrete complex image technique to circumvent the time-consuming evaluation of the doubly infinite integrals in the spectral domain method of moments. Furthermore, the method calculates the scattered/radiated fields using the reciprocity theorem, which is found to be more straightforward than the commonly used stationary phase method. Numerical results are presented for arbitrarily shaped microstrip antennas and arrays to demonstrate the accuracy and efficiency of the method. © 1997 John Wiley & Sons, Inc. Microwave Opt Technol Lett 16: 212–216, 1997

Discrete Complex Image Mixed-Potential Integral Equation Analysis of Microstrip Patch Antennas with Vertical Probe Feeds

ABSTRACT The discrete complex image method (DCIM) is combined with a hybrid mixed-potential integral equation (MPIE) formulation for microstrip patch antennas with vertical probe feeds. The properties and performance of the DCIM are investigated. To assess the accuracy and efficiency of the DCIM-MPIE approach, it is applied to a finite array of vertical probe fed microstrip patch antennas. The same structure is also analyzed by a well-established approach based on a rigorous numerical treatment of the Sommerfeld integrals and the results of the two methods are compared.

Discrete complex image MPIE analysis of coax-fed coupled vertical monopoles in grounded dielectric substrate: two formulations

Two distinct mixed-potential integral equation (MPIE) formulations are combined with the discrete complex image method (DCIM) and applied to analyse isolated and coupled coax-fed vertical monopoles embedded in a grounded substrate. Both DCIM-MPIE approaches are shown to be accurate, efficient, and well suited for the modelling of vertical probe feeds, shorting posts and plates, and vias in microstrip structures. One of the two formulations uses the scalar potential associated with a horizontal Hertzian dipole, and thus may easily be integrated with existing MPIE-based algorithms for strictly planar microstrip geometries to extend them to also accommodate vertical elements.