The document discusses the principles and configurations of linear and planar antenna arrays, including isotropic sources and their radiation patterns. It covers concepts like pattern multiplication, directivity in endfire arrays, and varying amplitudes and phases between sources. Additionally, it outlines the effects of spacing and phase differences on radiation patterns for arrays of isotropic point sources.

1. Antenna Arrays

2. Linear and Planar Arrays
Arrays of Two Isotropic Sources
Principles of Pattern Multiplication
Linear Array of N Elements with UniformAmplitude
 Broadside
 Ordinary Endfire
 Increased Directivity Endfire Array (IDEA)
 ScanningArray
Linear Arrays with Non-UniformAmplitude
PlanarArrays

3. E  E o e  j  r1
 E o e  j  r2

  k 
2
2 2
2
j
o
 
 j  d
c o s 
 j
2
 j  r
 j  d
c o s  
E  E o e  e
 j  r
 e



 E e

 e


e 


E  2 E cos  2 E c o s   d
c o s  
o  2  o   
   


   d c o s  
2 d
c o s 
=  dsin 
2 d
si n 
d / 2
1 2
d
2
d
cos


r
r1
r2
P
Array of Two Isotropic Point Sources
1
2
r
2
d
2
co s 
r  r 
d
c o s  


r  r  

>> d ,  9 0  

4. Two Isotropic Point Sources of Same Amplitude and Phase
HPBWs = 60° in one plane and 360° in another plane
ф 0° 90° 60°
E 0 1

5. ORIGIN ATELEMENT 1

6. Two Isotropic Point Sources of Same Amplitude and Opposite Phase
HPBW = 120°
ф 0° 90° 60°
E 0 1
HPBWs = 120° in both orthogonal planes

7. Two Isotropic Point Sources of Same Amplitude with
900 Phase Difference atλ/2
ф 0° 60° 90° 120° 180°
E 0 1

8. 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 0.924 0.994 1

9. Two Isotropic Point Sources Of Same Amplitude with
Any Phase Difference

10. Dipole AF
Two Same Dipoles and Pattern Multiplication
Dipole Pattern:
Final Pattern
For δ = 0, Array Factor (AF)
will give max. radiation in
Broadside Direction

11. PATTERN MULTIPLICATION
Array of two dipole
antennas
Dipole Pattern AF Product of Patterns
Dipole E-Field for Vertical Orientation:
Combined E-Field

12. N Isotropic Point Sources of Equal Amplitude and Spacing
where
Enorm

13. Radiation Pattern of N Isotropic Elements Array
Radiation Pattern for array of n isotropic radiators ofequal
amplitude and spacing.
First SLL
= 20log0.22
= -13.15dB
Array
Factor

14. Broadside Array (Sources In Phase)
Field pattern of 4 isotropic point sources with the
same amplitude and phase and spacing of /2.
ф Ψ E
0° π 0
90° π/2 0
120° 0 1

15. 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°

16. 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).
Hansen and Woodyard criteria
Parameter Ordinary end
fire array
Endfire array with
increased Directivity
HPBW 69° 38°
FNBW 106° 74°
Directivity 11 19

17. 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°