MATRUSRI ENGINEERING COLLEGE�DEPARTMENT OF ELECTRONICS & COMMUNICATION ENGINEERING

SUBJECT NAME: ANTENNA & WAVE PROPAGATION (PC504EC)

FACULTY NAME: Dr. Pallavi Khare

Antenna Arrays

MATRUSRI

ENGINEERING COLLEGE

Array of point sources, two element array with equal and unequal amplitudes, different phases, linear n- element array with uniform distribution, Broadside and End fire arrays, Principle of Pattern Multiplication, Effect of inter element phase shift on beam scanning, Binomial array.

Antenna Measurements: Introduction, Antenna Test Site and sources of errors, Radiation Hazards, Patterns to be Measured, Radiation, Gain and Impedance Measurement Techniques.

UNIT-4

OBJECTIVE

To introduce need for antenna arrays and the concepts of measurements of antennas.

OUTCOME

Student are able to apply the principles of antennas, to design antenna arrays and measure various parameters of antennas.

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

Array of Two Isotropic Point Sources

_{E = Eoe}− jβ r_{1 + Eoe}− jβ r₂

λ

β = k = ^2π

2

2

2

j

o

ψ

ψ

• jβ ^d cosφ

• j

2

• jβ r

⎡

jβ ^d cosφ ^⎤

E = E_oe

• e

• jβ r _⎢e

⎢_⎣

⎥

⎥_⎦

= E e

⎡

⎢^e

⎢_⎣

⎤

• ^e ⎥

⎥_⎦

E = 2E cos^{⎛ψ ⎞} = 2E cos^{⎛ π d} cosφ ^⎞

o ⎜ ₂ ⎟

o ⎜ _λ

⎟

⎝ ⎠

⎝

⎠

λ

λ

ψ = β d cosφ = ^{2π d} cosφ

=β dsinθ = ^{2π d} sinθ

d / 2

1

2

d

2

^d cosφ

θ

θ

r

r₁

r₂

P

1

2

2

d

2

cosφ

r ≅ r + ^d cosφ ^⎞

⎟

r ≅ r +

⎠

_⎟ r _>> d ,φ = 90 − θ

⎟

Two Isotropic Point Sources of Same Amplitude and Phase

HPBWs = 60° in one plane and 360° in another plane

ORIGIN AT ELEMENT 1

Two Isotropic Point Sources of Same Amplitude and Opposite Phase

HPBW = 120°

HPBWs = 120° in both orthogonal planes

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

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

Two Isotropic Point Sources Of Same Amplitude with Any Phase Difference

Two Same Dipoles and Pattern Multiplication

Dipole

AF

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

Array Factor

Broadside Array (Sources In Phase)

Field pattern of 4 isotropic point sources with the same amplitude and phase and spacing of λ/2.

Ordinary Endfire Array

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

BWFN=120°

Increased Directivity Endfire Array (IDEA)

Field patterns of end-fire arrays of 10 isotropic point

sources of equal amplitude spaced λ/4 apart.

1. Phase for increased directivity (δ = -0.6π),
2. Phase of an ordinary end-fire array (δ = -0.5π).

Hansen and Woodyard criteria

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°

N Isotropic Point Sources of Equal Amplitude and Spacing

where

As Ψ 0, E_max = n, E_norm

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

Null Directions for Arrays of N Isotropic Point Sources

^Enorm

For Finding Direction of Nulls:

​

🡪

For Broadside Array, δ = 0

​

🡪

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

First Null Beamwidth (FNBW)

For long array, (n-1)d is

equal to array length L

= d/λ

Directions of Max SLL for Arrays of N Isotropic Point Sources

Magnitude of SLL:

​

For very large n:

for k =1 (First SLL)

​

SLL in dB = 20Log 0.212 = -13.5dB

Direction of Minor Lobe Maxima

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/L_λ (radian)

HPBW ~ 2 x (90 - ϕ) = 50.8⁰ /L_λ

= 2.783/n

Aperture, Directivity and Beamwidth

Grating Lobes for Arrays of N Isotropic Point Sources

For Broadside Array:

​

​

For Endfire Array:

To Avoid Grating Lobes:

where is direction of max. radiation

​

🡪

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)

Radiation Pattern of Broadside Arrays with Non-Uniform Amplitude (5 elements with spacing = λ/2, Total Length = 2 λ)

SLL < -13 dB No SLL SLL < -20 dB Grating Lobes

All 5 sources are in same phase but relative amplitudes are different

Binomial Amplitude Distribution Arrays

No side lobe level but broad beamwidth

🡪 Gain decreases (practically not used)

Binomial Amplitude Coefficients are defined by

Non-Uniform Amplitude Distribution

Non-Uniform Amplitude Distribution (Contd.)

Current Distribution for Line-Sources and Linear Array

Radiation Characteristics for Line-Sources and Linear Array

Radiation Characteristics for Circular Aperture and Circular Array

Rectangular Planar Array

where,

Rectangular Planar Array

and where k = 2π/λ

​

The principal maximum(m = n = 0) and grating lobes can be located by:

m = 0, 1, 2,….

n = 0, 1, 2,….

Radiation Pattern of 5x5 Planar Array

Directivity of Planar Array

Directivity of Rectangular Array

For Broadside Array:

​

Directivity of Circular Array