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12 Interference, antenna arrays — cont’d.
We continue with our study of interference eFects and antenna arrays.
x
y
z
θ
φ
r
˜
E
=
ˆ
θ
˜
E
θ
˜
E
×
˜
H
*
θ
±
d
r

ˆ
zd
d
cos
θ
2
d
3
d
•
Beam patterns of
N
element antenna arrays examined last lecture were
isotropic in
φ
direction — the main eFect of increasing the array size
Nd
appeared to be
narrowing
the mainlobe of the pattern in
θ
direction.
New vocabulary:
–
Broadside arrays
–
Array axis
–
Broadside direction
•
These socalled
broadside arrays
—mean
ingtha
ttheyma
in
lyra

diate in the “broadside direction” of the “array axis” — are good for
broadcasting purposes
at relatively high frequencies
ω
2
π
in the ±M band
(
∼
100 MHz),
–
where array sizes
Nd
,inexcesso
fmany
λ
’s, become practicable
(as opposed to in AM band where
ω
2
π
∼
1MHzand
λ
∼
300
m).
•
They may also be used as “elements” of arrays built along
x
or
y
axis
directions which we will consider next.
–
In that case it will be possible to produce antenna beam patterns
anisotropic
in the azimuth plane (in
φ
direction).
–
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y
z
θ
φ
r
˜
E
=
ˆ
θ
˜
E
θ
˜
E
×
˜
H
*
d
d
cos
θ
x
2
d
3
d
r

ˆ
xd
θ
x
•
Consider an array of elements polarized in
ˆ
z
direction positioned along
the
x
axis as shown above. Our initial analysis of this array will assume
equal input currents
I
o
for all the elements. Let
˜
E
0
(
r
)
∝
e

jk

r


r

denote the Feld at the observation point
r
due to the element at the origin.
–
Then, using the paraxial approximation, the Feld phasor at a dis
tant observation point due to the next element at
(
d,
0
,
0)
can be
expressed in terms of
˜
E
0
(
r
)
as
˜
E
1
(
r
)
≈
˜
E
0
(
r
)
e
jkd
cos
θ
x
where
θ
x
is the angle between vectors
r
and
ˆ
x
,i
.e
.
,
cos
θ
x
=ˆ
r
·
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This note was uploaded on 09/27/2011 for the course ECE 450 taught by Professor Staff during the Fall '08 term at University of Illinois, Urbana Champaign.
 Fall '08
 Staff
 Electromagnet

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