UNIVERSITY OF CALIFORNIA
Santa Barbara
Department of Electrical and Computer Engineering
Problem Set No. 4
Issued:
October 31, 2007
Fall 2007
Due:
November 9, 2007 5 PM
ECE 201A
1.
If the linear antenna shown in the Figure is an integral number of half wavelengths long, the
current will assume the form
()
s
i
n(
)
2
m
L
Iz
I
kz
=+
regardless of the position of the feed as long as it is not near a current null.
Such an antenna is
said to be of resonant length. Find an expression for the magnetic vector potential for this
antenna.
X
Z
Y
L/ 2
L/2
I(z)
r
θ
2.
The figure below shows a square loop whose sides are electric dipoles each of length 2
l
and
current
I.
II
I
I
2
l
2
l
x
y
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Find the radiation field of the square loop on the
z
axis, which is perpendicular to the
paper.
(b)
Find the radiation field of the square loop on the
x
axis.
3.
Show that the one dimensional Green's function in free space is given by
exp(
' )
(, '
)
2
jkx x
Gxx
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 Cartesian Coordinate System, Electric charge, Fundamental physics concepts

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