Prof. Girish Kumar Electrical Engineering Department, IIT Bombay [email protected] (022) 2576 7436 Antenna Arrays
Mar 27, 2021
Prof. Girish KumarElectrical Engineering Department, IIT Bombay
(022) 2576 7436
Antenna Arrays
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
1 2j r j ro oE E e E e
2k
cos cos2 2
2 2
d dj j
j ro
j jj r
o
E E e e e
E e e e
2 cos 2 cos cos2
o o
dE E E
2cos cos
2 = dsin sin
dd
d
/ 2d1 2
d
cos2
d
r
1r
2r
P
Array of Two Isotropic Point Sources
1
2
cos2
, 90
cos2
dr r
r dd
r r
>>
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
ORIGIN AT ELEMENT 1
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
Two Isotropic Point Sources of Same Amplitude with 900 Phase Difference at λ/2
ф 0° 60° 90° 120° 180°
E 0 1
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
Two Isotropic Point Sources Of Same Amplitude withAny Phase Difference
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
PATTERN MULTIPLICATION
Array of two dipole
antennas
Dipole Pattern AF Product of Patterns
Dipole E-Field for Vertical Orientation:
Combined E-Field
N Isotropic Point Sources of Equal Amplitude and Spacing
where
Enorm
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
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
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°
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
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°