24
3 Radar Targets and Its Reflecting Properties
By highlighting near point B, an elementary dipole of dl length and db width,
in which a current dl = ldb flows and using the known from electrodynamics and
antenna system courses the formulas for magnetic vector in far zone, we will obtain
the following expression for this vector near the receiving antenna:
dH sct = j
H 0inc
λR
exp(− jk D 0 )exp(−2 jkD) cos αd S.
(3.5)
The sense of α angle is clear from Fig. 1.8, from where we can see that the product
cos αd S is a projection of lightened area to the plane perpendicular to propagation
direction of incident wave.
Let us introduce a designation: cos αd S = d S
and integrate a Eq. (3.5) in
lightened area: H sct = j
H 0inc
λ 2 R 2
S lgh
e
− jkD cos αd S
.
As in flat wave, the electric and magnetic vectors are proportional, and then, we
obtain the following expression for RCS of flat and convex bodies, the sizes of which
are considerably more than λ:
A =
4π
λ 2
∫
S lgh
exp(− jkD) cos αd S
2
.
(3.6)
Under interval index, there is a fast oscillating function, and hence, at small change
of incident angle α, the RCS will experience the more oscillations the more will be
relation of body linear sizes to wavelength.
Formula (3.6), despite on external simplicity, turns to be in some cases inconvenient as it leads to calculation necessity of complex integral equations. However, with
used assumption that body sizes and its curve radii are much more than wavelength,
we can obtain a more compact and convenient relation.
Let us introduce two typical (characteristic) body dimensions ρ 1 and ρ 2 (this
could be curve radii of surface) and imagine exponent index as follows:
2kD(x, y) = 2k
√
ρ 1 ρ 2
D(x, y)
√
ρ 1 ρ 2
= ρϕ(x, y),
(3.7)
where:
ρ = 2k
√
ρ 1 ρ 2 =
4π
λ
√
ρ 1 ρ 2 1; ϕ(x, y) =
D(x, y)
√
ρ 1 ρ 2
With this in view, write down an integral including to (3.6) formula:
J =
¨
S lgh
exp(− jρϕ(x, y))dxdy.
(3.8)
3 Radar Targets and Its Reflecting Properties
By highlighting near point B, an elementary dipole of dl length and db width,
in which a current dl = ldb flows and using the known from electrodynamics and
antenna system courses the formulas for magnetic vector in far zone, we will obtain
the following expression for this vector near the receiving antenna:
dH sct = j
H 0inc
λR
exp(− jk D 0 )exp(−2 jkD) cos αd S.
(3.5)
The sense of α angle is clear from Fig. 1.8, from where we can see that the product
cos αd S is a projection of lightened area to the plane perpendicular to propagation
direction of incident wave.
Let us introduce a designation: cos αd S = d S
and integrate a Eq. (3.5) in
lightened area: H sct = j
H 0inc
λ 2 R 2
S lgh
e
− jkD cos αd S
.
As in flat wave, the electric and magnetic vectors are proportional, and then, we
obtain the following expression for RCS of flat and convex bodies, the sizes of which
are considerably more than λ:
A =
4π
λ 2
∫
S lgh
exp(− jkD) cos αd S
2
.
(3.6)
Under interval index, there is a fast oscillating function, and hence, at small change
of incident angle α, the RCS will experience the more oscillations the more will be
relation of body linear sizes to wavelength.
Formula (3.6), despite on external simplicity, turns to be in some cases inconvenient as it leads to calculation necessity of complex integral equations. However, with
used assumption that body sizes and its curve radii are much more than wavelength,
we can obtain a more compact and convenient relation.
Let us introduce two typical (characteristic) body dimensions ρ 1 and ρ 2 (this
could be curve radii of surface) and imagine exponent index as follows:
2kD(x, y) = 2k
√
ρ 1 ρ 2
D(x, y)
√
ρ 1 ρ 2
= ρϕ(x, y),
(3.7)
where:
ρ = 2k
√
ρ 1 ρ 2 =
4π
λ
√
ρ 1 ρ 2 1; ϕ(x, y) =
D(x, y)
√
ρ 1 ρ 2
With this in view, write down an integral including to (3.6) formula:
J =
¨
S lgh
exp(− jρϕ(x, y))dxdy.
(3.8)