Graphics Programs Reference
In-Depth Information
)
π
Nkd
sin
2
ψ
---
----------------------
=
±
(
2
l
+
1
;
l
=
12…
,,
(8.40)
Solving for
ψ
yields
------
2
l
λ
2
d
+
N
1
ψ
l
=
asin
±
--------------
;
l
=
12…
,,
(8.41)
where the subscript is used as an indication of sidelobe maxima. The nulls of
the radiation pattern occur when only the numerator of Eq. (8.36) is zero. More
precisely,
l
=
nN
2
N
…
n
12…
,,
N
----
kd
sin
ψ
=
±
n
π
;
(8.42)
≠
,
,
Again solving for
ψ
yields
=
nN
2
N
…
n
12…
,,
λ
---
n
----
ψ
n
=
asin
±
;
(8.43)
≠
,
,
where the subscript is used as a null indicator. Define the angle which corre-
sponds to the half power point as
n
ψ
h
. It follows that the half power (3 dB)
beamwidth is
2 ψ
m
ψ
h
. This occurs when
N
----
kd
λ
2π
d
----------
2.782
N
-------------
sin
ψ
h
=
1.391
radians
⇒
ψ
h
=
asin
(8.44)
8.4.1. Array Tapering
Fig. 8.6a
shows a normalized two-way radiation pattern of a uniformly
excited linear array of size , element spacing . The first side-
lobe is about below the main lobe, and for most radar applications
this may not be sufficient.
Fig. 8.6b
shows the 3-D plot for the radiation pattern
shown in Fig. 8.6.a.
N
=
8
d
=
λ 2
⁄
13.46
dB
In order to reduce the sidelobe levels, the array must be designed to radiate
more power towards the center, and much less at the edges. This can be
achieved through tapering (windowing) the current distribution over the face
of the array. There are many possible tapering sequences that can be used for
this purpose. However, as known from spectral analysis, windowing reduces
sidelobe levels at the expense of widening the main beam. Thus, for a given
radar application, the choice of the tapering sequence must be based on the
trade-off between sidelobe reduction and main beam widening. The MATLAB
signal processing toolbox provides users with a wide variety of built-in win-
dows. This list includes:
ÐBartlett, Barthannwin, Blackmanharris, Bohman-
win, Chebwin, Gausswin, Hamming, Hann, Kaiser, Nuttallwin, Rectwin,
Triang, and Tukeywin.Ñ
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