Antenna Arrays Prof. Girish Kumar Electrical Engineering - - PowerPoint PPT Presentation

• Prof. Girish Kumar

Electrical Engineering Department, IIT Bombay

gkumar@ee.iitb.ac.in (022) 2576 7436

Antenna Arrays

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Linear and Planar Arrays

• Arrays of Two Isotropic Sources
• Principles of Pattern Multiplication
• Linear Array of N Elements with Uniform Amplitude
• Broadside
• Ordinary Endfire
• Increased Directivity Endfire Array (IDEA)
• Scanning Array
• Linear Arrays with Non-Uniform Amplitude
• Planar Arrays

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1 2

j r j r

• E

E e E e

   

 

2 k     

cos cos 2 2 2 2 d d j j j r

• j

j j r

• E

E e e e E e e e

           

                   

2 cos 2 cos cos 2

• d

E E E                   2 cos cos 2 = dsin sin d d d              

/ 2 d

1 2 d

cos 2 d 





r

1

r

2

r P

Array of Two Isotropic Point Sources

1 2

cos 2 , 90 cos 2 d r r r d d r r                

>>

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Two Isotropic Point Sources of Same Amplitude and Phase

HPBWs = 60° in one plane and 360° in another plane ф 0° 90° 60° E 1

Normalized E:

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ORIGIN AT ELEMENT 1

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Two Isotropic Point Sources of Same Amplitude and Opposite Phase

HPBW = 120° ф 0° 90° 60° E 1 HPBWs = 120° in both orthogonal planes

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Two Isotropic Point Sources of Same Amplitude with 900 Phase Difference at λ/2

ф 0° 60° 90° 120° 180° E 1

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Two Isotropic Point Sources of Same Amplitude with 900 Phase Difference at λ/4

HPBW = 180° Spacing between the sources is reduced to λ/4 ф 0° 90° 120° 150° 180° E 0.924 0.994 1

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Two Isotropic Point Sources Of Same Amplitude with Any Phase Difference

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Dipole

AF

Two Same Dipoles and Pattern Multiplication

Horizontal Dipole:

Final Pattern

For δ = 0, Array Factor (AF) will give max. radiation in Broadside Direction

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PATTERN MULTIPLICATION

Array of two vertical dipole antennas Dipole Pattern AF Product of Patterns Dipole E-Field for Vertical Orientation: Combined E-Field

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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

Array Factor

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Broadside Array (Sources In Phase)

Field pattern of 4 isotropic point sources with the same amplitude and phase. Spacing = /2. ф Ψ E 0° π 60° π/2 90° 1

and n = 4

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Ordinary Endfire Array

Field pattern of ordinary end-fire array of 4 isotropic point sources of same amplitude. Spacing is /2 and the phase angle  = -.

BWFN=120° For d = /2, ϕ = 00 and Ψ = 0

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Increased Directivity Endfire Array (IDEA)

Field patterns of end-fire arrays of 10 isotropic point sources of equal amplitude spaced /4 apart. (a) Phase for increased directivity ( = - 0.6), (b) Phase of an ordinary end-fire array ( = - 0.5).

For endfire array

Parameter Ordinary end fire array Increased Directivity endfire array HPBW 69° 38° FNBW 106° 74° Directivity 11 19

For increased directivity endfire array

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Array with Maximum Field in any Arbitrary Direction

Field pattern of array of 4 isotropic point sources of equal amplitude with phase adjusted to give the maximum at ф = 60° for spacing d = λ/2 For Beam Maxima at ϕ = 60°

For d = λ / 2, dr = π

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