Rapid Modeling of Thin Wire Antennas With Arbitrary Distributed Impedance Loading Using the

Method of Moments

POCKLINGTON’S INTEGRAL EQUATION

THE UNIVERSITY OF TEXAS AT EL PASO

Pioneering 21st Century Electromagnetics and Photonics

Assumptions 1. Antenna is embedded in an infinite, linear,

homogeneous, isotropic medium. 2. Antenna is perfectly straight. 3. Wire is very thin relative to its length.

The method of moments (MoM) is a variational technique that provides very efficient analysis of metallic structures. In this work, Pocklington’s integral equation is modified to incorporate arbitrary impedance loading.

2

22inc 2

2 4L

jkrL

z z

j eE I z k dz

z r

SOLUTION USING GALERKIN METHOD

Step 1: We write Pocklington’s integral equation in the following form.

2

222 inc

2 4L

jkrL

z z

eI z k dz j E z

z r

Step 2: We expand the current function into a set of basis functions vn(z) with weights an.

z n nn

I z a v z

Step 3: We calculate inner product of both sides of the integral equation against the same basis functions.

2

2 inc

2, ,

4n

jkr

n m n m z

n v

ea v z v z k dz j v z E z

z r

Step 4: We construct a matrix equation. 2

2 inc

2

4m n m

jkr

mn m n m m z

v v v

ez v z v z k dz dz g j v z E z dz

z r

mn n mz a g

PULSE FUNCTIONS

th

th

0 off segment

1 on segmentm

mv z

m

Basis Function Matrix Elements

2 2

2

3

22

1

4

nn

nn

z zz z zjkrjkr

mn mz

z z zz

e jkrz k dz z z e

r r

2 2

mr z z a

incm z mg j E z

Impedance Matrix

mnj z

zk

Z n mi vZ

IMPLEMENTATION

222

22

2

1 2 11 1For , ln

4 4 4 41 2 1

m

m

zz

zjkr

z zz

a ze jkr jk zm n dz dz

r r a z

THIN WIRE EXCITATION

Delta-Gap Source Magnetic Frill Source

INCORPORATING ARBITRARY DISTRIBUTED IMPEDANCE LOADING

diag LZ Z i v