A POSSIBLE REMEDY FOR THE OSCILLATIONS OCCURRING IN THIN-WIRE MoM ANALYSIS OF CYLINDRICAL ANTENNAS

Abstract

Abstract-Approximate, non-singular kernels are often used in moment-method formulations coping with thin-wire structures. Their use has important consequences, one of which is the appearance of oscillations in the computed currents when the number of sub-domain basis functions is sufficiently large. These oscillations are not due to round-off errors. In this paper, a smoothing procedure is used in conjunction with Galerkin's formulation with piecewise sinusoidal functions, which yields non-oscillating current distributions. Special attention is paid to the solutions over a wide range of discretization levels (number of basis/testing functions), in order to examine and illustrate the similarities and differences between results obtained with and without the proposed remedy. Finally, a comparison with results derived with the exact kernel is provided.

An Efficient Analysis of Vertical Dipole Antennas Above a Lossy Half-Space

“…To eliminate one of the double integrals for an efficient numerical solution of the integral equation, the reduced kernel approximation [5,17] for thin wires [18][19][20] under the conditions that a λ and a l is employed. Realizing that for both the source point and field point on the antenna surface, the radial distance d = (x − x ) 2 +(y − y ) 2 = 4a 2 sin 2 (φ/2) can be approximated by its median value d = a for a thin wire.…”

On the Extended Thin-Wire Kernel

“…These oscillations have been associated with the nonsolvability 2 of the underlying integral equations and occur when the number of basis functions becomes sufficiently larger than the length-to-diameter ratio of the wire antenna (the usual criterion of number of basis functions or points per wavelength is not relevant here). It is stressed that the said oscillations should not be blamed on finite computer wordlength or matrix ill-conditioning effects, which are also important but separate [1][2][3][4][5][6][7][8][9]. Matrix ill-conditioning effects occur when small perturbations (due to roundoff, errors in numerical integrations etc.)…”

“…The primary purpose of the present paper is to extend the investigations of [1][2][3][4][5][6][7][8][9] to the so-called "extended" thin-wire kernel, which was proposed by Poggio and Adams in the 1970s with the aim of improving the well-known Numerical Electromagnetics Code (NEC) [11]. The extended kernel is obtained from a certain series representation of the well-known exact kernel for thin wires by retaining its zero-order and first-order terms.…”

“…Recent studies have revealed that numerical methods applied to Hallén's and Pocklington's equations 1 with the approximate kernel yield current distributions corrupted by unphysical oscillations near the ends of the antenna and possibly near the driving point, depending on the type of the driving source [1][2][3][4][5][6][7][8][9]. These oscillations have been associated with the nonsolvability 2 of the underlying integral equations and occur when the number of basis functions becomes sufficiently larger than the length-to-diameter ratio of the wire antenna (the usual criterion of number of basis functions or points per wavelength is not relevant here).…”

Practicability Analysis and Application of PBG Structures on Cylindrical Conformal Microstrip Antenna and Array

“…Full-wave analysis method can accurately simulate the performance of antennas, typically, such as using method of moments (MoM) to analyze radiation and scattering characteristics of array antenna accurately [6][7][8][9], finite difference time domain (FDTD) method to dual-frequency microstrip patch antenna [10], and finite element method (FEM) to radiation characteristics of cylindrical conformal antenna [11,12]. All these researches above are doing these based on traditional conformal antennas, no respect from media substrate is concerned to improve the inherent disadvantage such as low efficiency and dielectric loss due to the surface wave losses.…”