EE4101

Antenna Arrays

1 Introduction Antenna arrays are becoming increasingly important in wireless communications. Advantages of using antenna arrays: 1. They can provide the capability of a steerable beam (radiation direction change) as in smart antennas. 2. They can provide a high gain (array gain) by using simple antenna elements. 3. They provide a diversity gain in multipath signal reception. 4. They enable array signal processing. Hon Tat Hui

1

Antenna Arrays

NUS/ECE

EE4101

An important characteristic of an array is the change of its radiation pattern in response to different excitations of its antenna elements. Unlike a single antenna whose radiation pattern is fixed, an antenna array’s radiation pattern, called the array pattern, can be changed upon exciting its elements with different currents (both current magnitudes and current phases). This gives us a freedom to choose (or design) a certain desired array pattern from an array, without changing its physical dimensions. Furthermore, by manipulating the received signals from the individual antenna elements in different ways, we can achieve many signal processing functions such as spatial filtering, interference suppression, gain enhancement, target tracking, etc. Hon Tat Hui

2

Antenna Arrays

NUS/ECE

EE4101

2 Two Element Arrays

z

Far field observation point

θ

Dipole 2

r1

I 2 = Ie jβ

d

θ

I1 = I

r

r1 = r − d cos θ , 0 ≤ θ ≤ π

Dipole 1

x

Two Hertzian dipoles of length dℓ separated by a distance d and excited by currents with an equal amplitude I but a phase difference β [0 ~ 2π). Hon Tat Hui

3

Antenna Arrays

NUS/ECE

EE4101

E1 = far-zone electric field produced by antenna 1 = E2 = far-zone electric field produced by antenna 2 =

ˆ aθ E1 ˆ aθ E2

η kI1d ⎛ e− jkr ⎞ ⎛ π ⎞ η kd ⎛ e − jkr ⎞ E1 = j ⎜ r ⎟ sin ⎜ θ + 2 ⎟ = j 4π ⎜ r ⎟ cos θ I1 4π ⎝ ⎠ ⎠ ⎝ ⎝ ⎠ η kI 2 d ⎛ e − jkr ⎞ ⎛ π ⎞ η kd ⎛ e− jkr ⎞ E2 = j ⎜ r ⎟ sin ⎜ θ + 2 ⎟ = j 4π ⎜ r ⎟ cos θ I 2 4π ⎝ 1 ⎠ ⎝ ⎠ ⎝ 1 ⎠ 1 1

Use the following far-field approximations:

0≤θ≤π

1 1 ≈ r1 r e − jkr1 = e − jk ( r −d cosθ )

Hon Tat Hui

4

Antenna Arrays

NUS/ECE

EE4101

The total E field is:

E = ( E1 + E2 ) aθ ˆ

η kd ⎛ e− jkr ⎞ ⎡ ⎤ = aθ j cos θ ⎣ I1 + I 2e jkd cosθ ⎦ ˆ ⎜ r ⎟ 4π ⎝ ⎠ η kI1d ⎛ e− jkr ⎞ ⎡1 + e jβ e jkd cosθ ⎤ = aθ j ˆ ⎜ r ⎟ cos θ ⎣ ⎦ 4π ⎝ ⎠ η kId ⎛ e− jkr ⎞ = aθ j ˆ ⎜ r ⎟ cos θ AF 4π ⎝ ⎠ where

Hon Tat Hui

5

Antenna Arrays

NUS/ECE

EE4101

AF = Array Factor = ⎡1 + e jβ e jkd cosθ ⎤ ⎣ ⎦

⎡1 + e e ⎣

jβ

jkd cos θ

⎤ = 2e ⎦

j

1 ( β + kd cos θ ) 2

⎡ 1 β + kd cosθ ⎤ cos ⎢ ( )⎥ ⎣2 ⎦

1 = I1 + I 2e jkd cosθ I1

The magnitude of the total E field is:

[

]

⎛ e − jkr ⎞ η kId E = aθ j ˆ ⎜ r ⎟ cos θ AF 4π ⎝ ⎠ = radiation pattern of a single Hertzian dipole × AF 6

Hon Tat Hui

Antenna Arrays

NUS/ECE

EE4101

Hence we see the total far-field radiation pattern |E| of the array (array pattern) consists of the original radiation pattern of a single Hertzian dipole multiplying with the magnitude of the array factor |AF|. This is a general property of antenna arrays and is called the principle of pattern multiplication. When we plot the array pattern, we usually use the normalized array factor which is: 1 1 ⎡ 1 β + kd cosθ ⎤ AFn = AF = 2cos ⎢ ( )⎥ Γ Γ ⎣2 ⎦ 7

where Γ is a constant to make the maximum value of |AFn| equal to one. Antenna Arrays

Hon Tat Hui

NUS/ECE

EE4101

Examples of array patterns using pattern multiplication:

Array pattern of a two-element array of Hertzian dipoles (β = 0°, and d = λ/4)

1 ⎡ 1 β + kd cosθ ⎤ = 1 2cos ⎡ 1 ⎛ π cosθ ⎞ ⎤ AFn = 2cos ⎢ ( )⎥ ⎜ ⎟⎥ ⎢2⎝ 2 Γ ⎣2 ⎦ Γ ⎠⎦ ⎣ Hon Tat Hui

8

Antenna Arrays

NUS/ECE

EE4101

Array pattern of a two-element array of Hertzian dipoles (β = -90°, and d = λ/4)

1 ⎡ 1 β + kd cosθ ⎤ = 1 2cos ⎡ 1 ⎛ − π + π cosθ ⎞ ⎤ AFn = 2cos ⎢ ( )⎥ ⎜ ⎟⎥ ⎢2⎝ 2 2 Γ ⎣2 ⎦ Γ ⎠⎦ ⎣ Hon Tat Hui

9...