antenna introduction
Sep 28, 2015
how antenna radiates
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EE642A: Antenna Analysis and Synthesis
Frequencies of Interest
Phasors
Radiation
Accelerating Charge
Field of a charge
The charge accelerates for a short duration
After some time
Observer here does not know about the event
Transmission Line
A pair of conductors, open circuited at one end
Is there any current on the conductor?
Transmission Line - Fields
Electric Field
Magnetic Field
Boundary conditions on the surface of a PEC?
Does it radiate?
Surface Current
We can make it radiate!
How to compute the fields? (Analysis)
Assume: Current distribution
Vector Potential Approach
Vector Wave Equation
Solution of the Wave Equation
Solution of
Consider
x
y
z
P(x,y,z)
r
In spherical coordinate system:
At points away from source, and in the limit the source is point,
Solution:
Some Heuristics
Static situation, w = 0 k = 0
is a solution of
Consider Poissons equation:
whose solution is:
Therefore, the solution of
will be of the form:
More rigorous solution
x
y
z
P(x,y,z)
G(R) has spherical symmetry.
Delta Function
Limit of a sequence of functions
The area under the curve of Un(x-x) is unity for all n.
J
A
k
A
m
-
=
+
2
2
z
z
z
J
A
k
A
m
-
=
+
2
2
z
z
J
a
J
=
2
2
2
2
2
2
2
sin
1
sin
sin
1
1
f
y
q
q
y
q
q
q
y
y
+
+
=
r
r
r
r
r
r
0
1
2
2
2
2
2
=
+
=
+
z
z
z
z
A
k
r
A
r
r
r
A
k
A
r
e
C
A
jkr
z
=
r
C
A
z
=
0
2
=
z
A
e
r
f
-
=
2
=
V
v
d
r
r
pe
f
4
1
=
-
V
jkr
z
z
v
d
r
e
z
y
x
J
A
)
,
,
(
4
p
m
)
(
)
,
(
)
,
(
2
2
r
r
r
r
G
k
r
r
G
-
-
=
+
d
r
r
)
,
,
(
z
y
x
R
V
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