Antennas

• Radiated Power

• Radiation Pattern– Beamwidth– Pattern Solid Angle– Directivity– Efficiency– Gain

Antennas

Wires passing an alternating current emit, or radiate, electromagnetic energy. The shape and size of the current carrying structure determines how much energy is radiated as well as the direction of radiation.

Transmitting Antenna: Any structure designed to efficiently radiate electromagnetic radiation in a preferred direction is called a transmitting antenna.

We also know that an electromagnetic field will induce current in a wire. The shape and size of the structure determines how efficiently the field is converted into current, or put another way, determines how well the radiation is captured. The shape and size also determines from which direction the radiation is preferentially captured.

Receiving Antenna: Any structure designed to efficiently receive electromagnetic radiation is called a transmitting antenna

Antennas – Radiation PowerLet us consider a transmitting antenna (transmitter) is located at the origin of a spherical coordinate system. In the far-field, the radiated waves resemble plane waves propagating in the radiation direction and time-harmonic fields can be related by the chapter 5 equations.

r

r

1

s o s

s s

o

and

E a H

H a E

*1, , Re

2s sr P E H

The time-averaged power density vector of the wave is found by the Poynting Theorem

, , , ,r P r rP a

2, , , , sin radP r d P r r d d P S

The total power radiated by the antenna is found by integrating over a closed spherical surface,

Electric and Magnetic Fields:

Power Density:

Radiated Power:

Antennas – Radiation PatternsRadiation patterns usually indicate either electric field intensity or power intensity. Magnetic field intensity has the same radiation pattern as the electric field intensity, related by o

max

, ,,n

P rP

P

It is customary to divide the field or power component by its maximum value and to plot a normalized function

Normalized radiation intensity:

Isotropic antenna: The antenna radiates electromagnetic waves equally in all directions.

, 1n isoP

Antennas – Radiation Patterns

A directional antenna radiates and receives preferentially in some direction.

A polar plot

A rectangular plot

It is customary, then, to take slices of the pattern and generate two-dimensional plots.

The polar plot can also be in terms of decibels.

max

, ,,n

E rE

E

, 20 log ,n nE dB E

, 10 log ,n nP dB P

It is interesting to note that a normalized electric field pattern in dB will be identical to the power pattern in dB.

Radiation Pattern:

Antennas – Radiation Patterns A polar plot

A rectangular plot

It is clear in Figure that in some very specific directions there are zeros, or nulls, in the pattern indicating no radiation.

The protuberances between the nulls are referred to as lobes, and the main, or major, lobe is in the direction of maximum radiation.

There are also side lobes and back lobes. These other lobes divert power away from the main beam and are desired as small as possible.

One measure of a beam’s directional nature is the beamwidth, also called the half-power beamwidth or 3-dB beamwidth.

Radiation Pattern:

Beam Width:

Antennas – S

A radian is defined with the aid of Figure a). It is the angle subtended by an arc along the perimeter of the circle with length equal to the radius. A steradian may be defined using Figure (b). Here, one steradian (sr) is subtended by an area r2 at the surface of a sphere of radius r.

sin .d d d

A differential solid angle, d, in sr, is defined as

2

0 0

sin 4 ( ).d d sr

For a sphere, the solid angle is found by integrating

An antenna’s pattern solid angle,

,p nP d

Antenna Pattern Solid Angle:

All of the radiation emitted by the antenna is concentrated in a cone of solid angle p over which the radiation is constant and equal to the antenna’s maximum radiation value.

Antennas – Directivity

,,

,n

n avg

P

PD

The directive gain,, of an antenna is the ratio of the normalized power in a particular direction to the average normalized power, or

maxmax max

,

,, n

n avg

PD D

P

The directivity, Dmax, is the maximum directive gain,

max

4

p

D

Directivity:

,

,4

n p

n avg

P dP

d

Where the normalized power’s average value taken over the entire spherical solid angle is

max

1,nP Using

*

22

2

*

*

1 1, , Re Re

2 2

1 1Re Re

2 2

1Re sin

2

sin sin

sin sin sin sin

s s

oo

o s s

j j j jo o o o o o

r

I

r

I I

r r

I e I e I e I e

r r r r

P E H a a

a a a a

a a 2

2r2

1sin

2o

o

I

r

a

8.1: In free space, suppose a wave propagating radially away from an antenna at the origin has

Example

sin s

s

I

rH a

where the driving current phasor js oI I e

Find (1) Es

r r rsin sin sin s s o s

s o s o o

I I I

r r r

a a aE a H a a

Find (2) P(r,,)

2

22

, ,1

sin2

oorI

Pr

Magnitude:

2

22

22

223

20 0

223

20 0

2

2

, , , , sin

sin

1sin

2

1 sin

2

1 sin

2

1 4 2

2 3rad

rad

rad

rad

rad

oo

oo

oo

ooP

P r d P r r d d

P r d d

P d d

P d

I

r

I

r

Id

r

I

r

P S

24

3o oI

Find (3) Prad

Find (4) Pn(r,,) Normalized Power Pattern

max

, ,,n

P rP

P

2

22

, ,1

sin2

oorI

Pr

2

max 2

1

2o

o

IP

r

2, sinnP

We make use of the formula3

3 cos

sin cos3

d

33

0 0

3 3

cos

sin cos3

cos cos 0cos cos 0

3 3

1 1 2 41 1 2

3 3 3 3

d

Find (5) Beam Width

2, sinnP 21sin

2 HP1

sin2

HP

1sin

2HP

,1 45HP ,2 135HP and

135 45 90Beamwidth BW

,1 45HP

,2 135HP

90BW

0.5nP

0.5nP

z

(6) Pattern Solid Angle Ωp (Integrate over the entire sphere!)

2 2

2 3 3

0 0 0 0

4 8

sin sin sin sin 23 3P d d dd d d

,p nP d

(7) directivity Dmax

max

4 4 21.5

8 33

P

D

(8) Half-power Pattern Solid Angle Ωp,HP (Integrate over the beamwidth!)

2 135 135 2

2 3 3,

0 045 45

5 5 2

sin sin sin sin 233 2

P HP d d dd d d

, ,p HP nP d

135 3 3135 33

45 45

cos 135 cos 45cos

sin cos cos 135 cos 453 3 3

1 1 1 1 2 2 10 5

2 6 2 2 6 2 2 6 2 6 2 3 2

d

Power radiated through the beam width

,

5 25 23 0.88 (or) 88%

8 83

P HPBW

P

P

BW

z

= 88%BWP

Antennas – Efficiency

Power is fed to an antenna through a T-Line and the antenna appears as a complex impedance

Efficiency

.ant ant antZ R jX

ant rad disR R R

where the antenna resistance consists of radiation resistance and and a dissipative resistance.

21

2rad o radP I R 21

2diss o dissP I R

The power dissipated by ohmic losses isThe power radiated by the antenna is

An antenna efficiency e can be defined as the ratio of the radiated power to the total power fed to the antenna.

rad rad

rad diss rad diss

P Re

P P R R

For the antenna is driven by phasor current jo sI I e

Antennas – GainGain

, ,G eD

The power gain, G, of an antenna is very much like its directive gain, but also takes into account efficiency

The maximum power gain

max maxG eD

The maximum power gain is often expressed in dB.

max max1010 logG GdB

Example

D8.3: Suppose an antenna has D = 4, Rrad = 40 and Rdiss = 10 . Find antenna efficiency and maximum power gain. (Ans: e = 0.80, Gmax = 3.2).

40

10 400.8 (or) 80%rad

rad diss

Re

R R

Antenna efficiency

Maximum power gain

max max 4 0.8 3.2G eD

max max10 1010 log 10 log 3.2 5.05G GdB

Maximum power gain in dB