15 dB
62
62
22
10
5
ε = 10.5
10.4 found at JPG. The solid curve is the beam pattern within the plane of the transect
and is perpendicular to the direction of antenna polarization. The dotted curve is the
beam pattern in the plane of the antenna polarization, which is perpendicular to the
transect direction. Individual pattern 3-dB beamwidths are indicated at the point of
the arrows. A typical form of the radiated wavelet is also shown. The curves assume
that the transmitter and receiver antennas are coincident. They are actually spaced
about 15 cm apart in the 300-MHz unit and slightly less in the 600-MHz unit.
cal factor equal to the solid angle subtended by the sur-
face of a perfect electric conductor (PEC), where the
face required to exclude the singularity when r equals
r′, divided by 4π. Thus at a point on a smooth, i.e.,
tangential electric field E is negligible. In terms of
locally flat surface, α is one-half. The surface currents
integrals over the metal surface S,
J are equal to n H, where the unit normal vector n
^
^
α(r)E(r) = ∫∫ dS ′ iω g(r, r ′)J(r ′) +
points outward from the surface, while the tangential
electric field, proportional to n E, has been consid-
S
^
ered negligible (perfect conductor). The scalar Green
iω
( ) ()
()
inc
+
∇∇g r, r ′ ⋅ J r ′ E r
(7)
function g is
k2
eikR
g=
R ≡ r r′ .
() ()
( ) ( ) ()
,
(8)
c
inc
α r H r = ∫∫ dS ′ ∇g r, r ′ J r ′ H r
4πR
S
^
Taking the vector cross product of n with equation
where r and r′ are observation and integration field
(7) for H leads to
points, respectively; is the magnetic permeability of
{
α (r) J (r) ∫∫ dS′ (n (r) ⋅ J(r′))∇g(r, r′)
the soil, taken here to be that of free space (4π 107
^
H/m); k is the electromagnetic wavenumber (m1); and
S
E (V/m) and H (A/m) are the radiated electric and mag-
}
J(r ′)(n(r) ⋅ ∇g(r, r ′)) = n(r) H(r)inc . (9)
netic fields, respectively. The quantity α is a geometri-
^
^
21
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