ECE 3030: Electromagnetic Fields and Waves
Fall 2009
DEMO 12 INSTRUCTOR NOTES: Reflectors and 2 and 3Dimensional Arrays
Reminder: Prelim 3 on Thursday night.
Date: Tuesday 11/17
1.
Prelim 3 Thursday night, November 19...no Workshop 12.
2.
Problem 17.8
A short dipole of physical length
d
,
pointing in the
z
direction, and carrying a current pha
sor
I
, is located at (
h, h,
0) in the (
x, y, z
) coordinate
system, as shown in the figure to the right. The space
for which
x <
0 or
y <
0 is filled with a perfect con
ductor.
a.
Find the expression for the farfield electric field
vector of the radiation and explain your result.
b.
Find an exact expression for the gain
G
(
θ, φ
) of the
antenna. What value of
h
(in terms of the wavelength
λ
) will give the maximum value for the gain and in
which directions (
θ, φ
) does this maximum value of
Gain occur?
c.
Sketch the radiation pattern
p
(
θ, φ
) in the
x

y
plane
assuming that the distance
h
equals
λ
.
y
x
h
•
h
∞
=
σ
Figure 1: A short dipole with a
corner reflector.
Solution:
Pattern from a corner reflector.
a.
Note that there are three image dipoles in this problem. (Draw the
figure.) The far field only exits for
x >
0 and
y >
0 with
~
E
ff
(
~
r ) =
{
Element Factor
} × {
Array Factor
}
The two factors are
{
Element Factor
}
=
j
kId
eff
4
πr
e

jkr
sin
θ
{
Array Factor
}
= e
jk
ˆ
r
·
~
h
1

e
jk
ˆ
r
·
~
h
2
+ e
jk
ˆ
r
·
~
h
3

e
jk
ˆ
r
·
~
h
4
where the effective length of the dipole and its images is
d
eff
=
d
2
, and
the signs account for the current reversals of the images. We need the
dot products, but first make sure the class understands the pieces. The
unit vector ˆ
r =
~
r
/r
is
ˆ
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 '06
 RANA
 Electromagnet, Sin, Cos, Cornell University, WES SWARTZ

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