Digital Signal Processing Reference
In-Depth Information
l
A
tile
=
lw
A
base
E
I
H
q
m
w
E
I
H
Figure 5-17
Simplified hemispherical shape approximating a single surface protrusion:
top and side views; current direction and applied TEM field orientations shown.
structure is a hemisphere, and then the power loss of the flat plane surrounding
the hemisphere is calculated. The total power dissipated is then calculated simply
by adding the results.
For a good conducting protrusion (as opposed to a perfect electrical conductor
protrusion) a plane electromagnetic wave incident on a conducting sphere will
be partly scattered and partly absorbed. The total power scattered and absorbed
from a sphere divided by the incident flux is known as the
total cross section
and is calculated by Jackson [1999] (with units of square meters) as
k
2
m
π
σ
tot
=−
(
2
m
+
1
)
Re[
α(m)
+
β(m)
]
(5-50)
2
π/λ, λ
=
c/f
√
ε
,c
is the speed of light, and the scattering coeffi-
cients are approximated assuming that
kr
where
k
=
1, where
r
is the sphere radius, and
are given by [Jackson, 1999]
2
j
3
(kr)
3
1
−
(δ/r)(
1
+
j)
α(
1
)
=−
(5-51a)
1
+
(δ/
2
r)(
1
+
j)
−
(
4
j/k
2
rδ)
[1
/(
1
2
j
3
(kr)
3
1
−
j)
]
β(
1
)
=−
(5-51b)
1
+
(
2
j/k
2
rδ)
[1
/(
1
−
j)
]
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