Electromagnetic Modeling of Metallic Elliptical Plates

Rizwan H. Alad, S. B. Chakrabarty, Karl E. Lonngren

Antenna Systems Area, Space Applications Center, ISRO, Ahmedabad, India.
Department of Electrical and Computer Engineering, University of Iowa, Iowa City, USA..
Department of Electronics and Communication, Dharmsinh Desai University, Nadiad, India.

DOI: 10.4236/jemaa.2012.411065                

Abstract

This paper presents the evaluation of the capacitance of an isolated elliptical plate and two parallel elliptical plates. Integral equations are formed by relating the previously unknown charges on the elliptical plates and the potential on the metallic plates. The integral equations are solved by applying the method of moments based on the pulse function and point matching. The elements of the matrix in the method of moments are found by dividing the structure into triangular subsections. The matrix equation is solved in order to compute the unknown charges on each subsection. Numerical results on the capacitance as a function of the geometrical parameters of the ellipse are presented.

Keywords

Elliptical Metallic Plate; Capacitance; Pulse Function; Point Matching

1. Introduction

The evaluation of the capacitance of various structures having different geometrical shapes is of importance to study the behavior of electrostatic charge build-up on bodies that are isolated in space such as space-craft structures in orbit. The analysis of three-dimensional spherical, paraboloidal and truncated conical surfaces and two-dimensional square, rectangular, circular and annular metallic disks have been examined using the method of moments [1-6]. In these works, the capacitance of the different geometrical structures was obtained by subdividing the structure into uniform rectangular planar subsections and computing the effect of the charge on each subsection on the potential of the others. The use of rectangular subsection in a curved boundary requires a very fine meshing in order to obtain convergence for the data of the capacitance and charge distribution. Meshing with triangular elements on the other hand facilitates the mapping of the geometrical boundaries of arbitrary shape very accurately [7]. The meshing techniques employed in [3] are limited by the large ratio of the area of the biggest elements to smallest elements, which possibly results in an unstable solution.

This paper presents the analysis of a planar elliptical metallic plate isolated in free space as well as two parallel elliptical plates using the method of moments in which triangular sub-areas were used for the solution of integral equations. A closed form expression for the capacitance of a single elliptical conducting plate has been reported by Liang et al. [8]. They did not present any data on the capacitance for the case of two parallel elliptical plates of finite size. Thus it is worthwhile to carry out the analysis of elliptical structures using the method of moments with triangular subsections for the geometry under consideration unlike that reported in [1-6].

In order to apply the method of moments, the elliptical plate is divided into a number of triangular elements. The unknown charge distribution on the surface of the elliptical plates appears in the form of an integral equation relating the potential function and charge distribution. This integral equation is solved using the method of moments formulation based on a pulse function and point matching. The methods of finding the diagonal and the non-diagonal elements of the matrix are presented. The capacitance is calculated as a function of eccentricity of the ellipse for a unit semi major axis. The validity of the analysis is justified by comparing the data on the capacitance using the present method with that of the closed form expression in [8].

2. General Analysis

2.1. Single Elliptical Plate

Figure 1 shows a single elliptical plate with a semi major axis a and semi minor axis b. In order to compute the capacitance of this structure, the plate is subdivided using triangular elements as shown in Figure 2. The unknown surface charge density on the plate at any point is denoted by. It is assumed that the surface charge density is constant over each subsection

Conflicts of Interest

The authors declare no conflicts of interest.

References

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