prof. girish kumar · 2017-08-04 · null directions and beam width between first nulls for linear...
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![Page 1: Prof. Girish Kumar · 2017-08-04 · Null directions and beam width between first nulls for linear arrays of n isotropic point sources of equal amplitude and spacing Null Direction](https://reader030.vdocuments.net/reader030/viewer/2022033121/5e78150efe0c050eb64443d2/html5/thumbnails/1.jpg)
Prof. Girish KumarElectrical Engineering Department, IIT Bombay
(022) 2576 7436
Antenna Arrays (Contd.)
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N Isotropic Point Sources of Equal Amplitude and Spacing
where
As Ψ 0, Emax = n, Enorm
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Radiation Pattern of N Isotropic Elements Array
Radiation Pattern for array of n isotropic radiators of equal
amplitude and spacing.
First SLL
= 20log0.22
= -13.15dB
Arr
ay F
act
or
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Null Directions for Arrays of N Isotropic Point Sources
For Broadside Array, δ = 0
For Finding Direction of Nulls:
Enorm
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Null directions and beam width between first nulls for linear arrays
of n isotropic point sources of equal amplitude and spacing
Null Direction and First Null Beamwidth
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First Null Beamwidth (FNBW)
For long array, (n-1)d is
equal to array length L
= d/λ
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Directions of Max SLL for Arrays of N Isotropic Point Sources
Magnitude of SLL:
For very large n:
SLL in dB = 20Log 0.212 = -13.5dB
for k =1 (First SLL)
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Direction of Minor Lobe Maxima
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Half-Power Beamwidth (HPBW) of Array
For large n, HPBW is small :
For calculating HPBW, find Ψ, where radiated power
is reduced to half of its maximum value
~Solution:
nΨ/2 = 1.3915
For Broadside:
Cos ϕ = Sin (90 - ϕ) = 1.3915/ (πnd/λ) = 0.443/Lλ (radian)
HPBW ~ 2 x (90 - ϕ) = 50.80 /Lλ
= 2.783/n
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Aperture, Directivity and Beamwidth
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Grating Lobes for Arrays of N Isotropic Point Sources
To Avoid Grating Lobes:
For Broadside Array:
For Endfire Array:
where is direction of
max. radiation
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Arrays with Missing Source
(a)
Radiation Pattern of linear array of 5 isotropic point sources of equal amplitude and λ/2 spacing (a) all 5 sources ON
(b) one source (next to the edge) OFF (c) one source (at the centre) OFF, and (d) one source (at the edge) OFF
(b)
(c)
(d)
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Radiation Pattern of Broadside Arrays with Non-Uniform Amplitude(5 elements with spacing = λ/2, Total Length = 2 λ)
All 5 sources are in same phase but relative amplitudes are different
SLL < -13 dB No SLL SLL < -20 dB Grating Lobes
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Binomial Amplitude Distribution Arrays
No side lobe level but broad beamwidth
Gain decreases (practically not used)
Binomial Amplitude Coefficients are defined by
m = 5 1 4 6 4 1
m = 6 1 5 10 10 5 1
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Non-Uniform Amplitude Distribution
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Non-Uniform Amplitude Distribution (Contd.)
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Current Distribution for Line-Sources and Linear Array
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Radiation Characteristics for Line-Sources and Linear Array
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Radiation Characteristics for Circular Aperture and Circular Array
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Rectangular Planar Array
where,
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Rectangular Planar Array
where k = 2π/λ
The principal maximum(m = n = 0) and grating lobes can be located by:
and
m = 0, 1, 2,….
n = 0, 1, 2,….
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Radiation Pattern of 5x5 Planar Array
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Directivity of Planar Array
Directivity of Rectangular Array
For Broadside Array:
Directivity of Circular Array