MOM.rar_MOM_method of moments_moments

EC340 Lecture Notes

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5. Method of Moments

Contents

5.1 Introduction

Objectives

5.2 Basic concepts of Method of Moments

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5.3.3 3-D scattering from Bodies of Revolutions (BOR)

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5.4 Summary

5.5 Answers to Review Questions

Computer projects

Further readings

5.1 Introduction

solving EM field problems have become very popular. These are many numerical techniques,

which have been developed over the last few decades. In this section we shall briefly discuss one

of the popular methods for solving EM field problems: Method of moments (MoM). The method

owes its name to the process of taking moments by multiplying with appropriate weighting

functions and integrating. The MoM is essentially the method of weighted residuals.

Objectives

After studying this chapter, you should be able to

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The MoM provides a way to solve such integral equations. Instead of discussing the general

procedure for MoM, here we introduce the basic concepts involved in MoM solution through the

introductory examples from electrostatics.

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section. This produces one equation with N unknowns. By selecting N observation points along

the strip (choose these points at the center of each pulse functions), which are all known to be at a

potential of 1V produce N such equations.

5.2.1 Introductory examples from Electrostatics

In electrostatics, the problem of finding the potential due to a given charge distribution is often

considered. In practical scenario, it is very difficult to specify a charge distribution. We usually

connect a conductor to a voltage source and thus specify the voltage on the conductor. We will

consider MoM to solve for the electric charge distribution when an electric potential is specified.

Consider a straight wire of length l and radius a, placed along the y-axis as shown in Fig. 5.1 (a).

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where

that may be solved by conventional matrix techniques. To do this, let us approximate the

coefficients as follows:

ybIy

)()(

λ

=

=

==

l

n

N

n

I

1

1

0

The basis or expansion functions are chosen in such a way that it can accurately model the

unknown quantity. We will choose our basis functions as pulse functions.

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We will discuss the various commonly used basis functions in the next section. Replacing y by a

yyR

yyR

where

each Z

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∫∫











∆







∆

+









∆

++

=

2

2

all

Z

where l

Therefore the unknown [I] matrix could be solved as

dividing the wire into segments, and then sequentially enforcing the integral equation at the

center of each segment to form a set of linear equations.

As a final introductory example of MoM, let us consider the an example of determining the

charge density and capacitance due to an isolated charged conducting plate, 2a meters on a side

and lying on the 0