Civil Engineering Reference
In-Depth Information
Assuming
|
v
|
constant over the surface, its radiated power is given by
2
Re
jρ
0
ω
v
(M
0
)G(M,M
0
)
v
∗
(M)
d
S(M
0
)
d
S(M)
1
rad
=
S
S
Re
jρ
0
ω
2
=
|
υ
|
sin
φy
0
)
]
G(M,M
0
)
exp [
jk
0
sin
θ(
cos
φx
+
sin
φy)
]d
x
d
y
d
x
0
d
y
0
exp[
−
jk
sin
θ(
cos
φx
0
+
2
S
S
(12.9)
and thus its radiation efficiency is
rad
ρ
0
cS
Re
(Z
R
)
ρ
0
c
σ
R
=
=
(12.10)
V
2
with
jρ
0
ω
S
p
i
(M
0
)G(M,M
0
) p
i
(M)
d
S(M
0
)
d
S(M)
Z
R
=
S
S
jρ
0
ω
S
(12.11)
=
exp[
−
jk
t
(
cos
φx
0
+
sin
φy
0
)
]
G(M,M
0
)
S
S
×
exp[
jk
t
(
cos
φx
+
sin
φy)
]d
x
d
y
d
x
0
d
y
0
where
k
t
k
0
sin
θ
. Note that radiation impedance
Z
R
only depends on the geometry of
the panel and the angles of incidence
θ
and
φ
.
Using this correction, the transmitted power becomes
=
S
cos
θτ
∞
ρ
0
c
1
2
t
=
σ
R
(k
t
,ϕ)
cos
θ
(12.12)
Since the transmitted power for the infinite size panel is given by
1
2
S
cos
θ
ρ
0
c
0
τ
∞
t,
∞
=
(12.13)
one obtains
t
=
t,
∞
σ
R
(k
t
,ϕ)
cos
θ
(12.14)
Figure 12.1 plots the expression of the heading averaged geometrical radiation efficiency
2
π
2
π
1
2
π
1
2
π
Re
(Z
R
)
ρ
0
c
0
S
d
ϕ
σ
R
(θ)
=
σ
R
(k
t
(θ),ϕ)
d
ϕ
=
(12.15)
0
0
as a function of incidence angle
θ
for different frequencies. The corresponding radiation
efficiency for an infinite panel is also represented. It is clearly seen that the correction
is primarily important for low frequencies and near grazing angles. In consequence the
computation algorithm can be modified to apply this correction selectively. Appendix
12.A presents a numerical algorithm to estimate
Z
R
.
