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ωµ
0
I
e
2
j
π
k
ρ
E
s
jk
ρ
-----------------
=
---------
e
(11.97)
4
∞
∑
e
jk
ρ
0
cos
(
ϕϕ
0
)
d
n
j
ν
sin
νϕ α
(
)
sin
νϕ
0
(
α
)
n
=
0
11.6.2. Plane Wave Excitation
For plane wave excitation (
ρ
0
→
∞
), the expression in Eqs. (11.87) and
(11.88) reduce to
πωȺI
2
j
ν
−
jkρ
b
=−
−−
0
e
j
e
0
n
2
παβ πkρ
0
(11.98)
()() ()()
()
()()
()
()()
kJ
′
ka J
k a
−
k J
ka J
′
k a
πωȺI
2
j
ν
−
jkρ
v
v
1
1
v
v
1
c
=
0
e
j
e
0
n
2
παβ πkρ
−−
′
2
2
′
kH
ka J
k a
−
k H
ka J
k a
0
ν
v
1
1
ν
v
1
where the complex amplitude of the incident plane wave,
E
0
, can be given by
ωµ
2
j
−
jk
ρ
EI
=−
0
e
(11.99)
0
0
e
4
πρ
k
0
In this case, the field components can be evaluated in regions I and II only.
11.6.3. Special Cases
Case I:
αβ
=
(reference at bisector); The definition of
ν
reduces to
nπ
ν
=
(11.100)
(
)
2
πβ
−
and the same expression will hold for the coefficients (with
αβ
=
).
Case II:
α
=
0
(reference at face); the definition of
ν
takes on the form
nπ
(11.101)
ν
=
2
πβ
−
and the same expression will hold for the coefficients (with
α
=
0
).
Case III:
(PEC cap); Fields at region I will vanish, and the coeffi-
cients will be given by
k
1
→
∞
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