18. Synthesis Problems
Given affordable SLL, No. of elements,
how to synthesize?
Ideal case: narrow beam, constant side-lobe envelope
Approaches: Dolph-Chebyshev, Taylor Line Source….
Secret behind: to synthesize a polynomial like pattern….
24. Synthesis Standards
SLL=-20log R (dB)
so ]cosh)1cosh[()( 0
1
01 xPxTR P
−
− −==
]cosh
1
1
cosh( 1
0 R
P
x −
−
=
−=
−
π
γ
λ
1
cos
1
1
optd
−=
−
π
γλ
1
cos
1
2
1
optd
Optimum spacing,
Broadside: Endfire:
)]1ln(
1
1
cosh[ 2
−+
−
= RR
P
γ, where
25. Beamwidth and Directivity
In general, d
HP h
β
ψ
π 1
cos2 −
−= (broadside)
)1(cos 1
d
HP h
β
ψ
−= − (endfire)
, where
−
−
=
−
−
−
]cosh
1
1
cosh[
]
2
cosh
1
1
cosh[
cos2
1
1
1
R
P
R
P
nψ
An approximation for the broadside:
L
RHP
λ
π
)2ln(
1
=
Beambroadening factor: )2ln(637.0
866.0
)2ln(
1
R
R
bHP == π
HPR
R
D 2
2
1
2
+
=Directivity:
33. Tapering may not reduce sidelobes.
• The dish antenna theory: Tapering of the current distribution at the apperture
leads to the side lobes decrease.
• This statement may not be true at the case of the arrays. Tapering is
multiplication of the UV coverage with the tapering function. So at the
image plane, it leads to the convolution of the untapered beam pattern with
the Fourier transform of the tapering function. The convolution leads to the
broadening of the main beam as well of the sidelobes. But the level of
sidelobes may not be reduced, if the distance between the sidelobes is bigger
than the width of the Fourier transform of the tapering function
38. Conventional Antennas & Arrays
Antenna
Top View
Antenna
Array
Top View
Omnidirectional Sectorized
39. WHY SMART ANTENNA ARRAYS ARE
SUPERIOR TO CONVENTIONAL ANTENNAS
Switched Beam System Adaptive Array
Antenna
Array
Desired
User
Interfering
User
Antenna
Array
Active
Beam