N Isotropic Point Sources of Equal Amplitude and Spacing where As - - PowerPoint PPT Presentation

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n isotropic point sources of equal amplitude and spacing
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N Isotropic Point Sources of Equal Amplitude and Spacing where As - - PowerPoint PPT Presentation

Dec 11, 2023 308 likes •539 views

N Isotropic Point Sources of Equal Amplitude and Spacing where As 0, E max = n, E norm 1 Radiation Pattern of N Isotropic Elements Array Array Factor First SLL = 20log0.22 = -13.15dB Radiation Pattern for array of n isotropic radiators of

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SLIDE 1

N Isotropic Point Sources of Equal Amplitude and Spacing

where

As Ψ 0, Emax = n, Enorm

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SLIDE 2

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

Array Factor

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SLIDE 3

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

  • f 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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SLIDE 7

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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SLIDE 9

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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SLIDE 21

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

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