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ECE 450
Homework 5
Due: Tue, Feb 22, 2011, 5 PM
1. Three identical
ˆ
z
directed short dipoles are located at
(
x, y, z
)=(

d,
0
,
0)
,
(0
,
0
,
0)
,and(
d,
0
,
0)
and
have input current phasors of
1
∠
0
◦
A,
2
∠
0
◦
A, and
1
∠
0
◦
A, respectively.
a) Show that the radiation Feld of the array of dipoles at an arbitrary location on
xy
plane (i.e.,
θ
=90
◦
plane) su±ciently far away from the origin (so that paraxial approximation can be used)
is proportional to
(
e
j
1
2
kd
cos
φ
+
e

j
1
2
kd
cos
φ
)
2
∝
cos
2
(
1
2
kd
cos
φ
)
.
b) Calculate the distance
d
in wavelengths that will result in a null in the radiation Feld of the
array on the
xy
plane along
±
x
.
2. ²or the same antenna array , assume, next, that the input current phasors for the dipoles at
(

d,
0
,
0)
and
(
d,
0
,
0)
are, respectively,
1
∠
ψ
Aand
1
∠

ψ
A, while the input current phasor for the dipole at
the origin remains unchanged.
a) How is the answer to part (a) of Problem 1 modiFed after introducing the input current phase
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This note was uploaded on 08/25/2011 for the course ECE 350 taught by Professor Kudeki during the Spring '11 term at University of Illinois at Urbana–Champaign.
 Spring '11
 KUDEKI

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