093589 - 00B - Antenna Parameters

8/19/2019 093589 - 00B - Antenna Parameters

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POLIMI, AY 2014-15

Prof. Sergio A. Pignari

POLITECNICO DI MILANO

Dept. of Electronics Information and Bioengineering

Electrical Engineering Section

Milan Italy

Email: [email protected]

Website: http://www.deib.polimi.it/

EMC Group @ POLIMI

Electromagnetic Compatibility B MSc in Electrical Engineering

Radiation Pattern and Antenna Parameters

EMC Group @ POLIMI

Antenna Pattern

The antenna pattern:

• describes the far-field directional properties of anantenna when measured at a fixed distance fromthe antenna

• is a three-dimensional plot that displays thestrength of the power density as a function of thedirection

The direction being specified by the:

• zenith angle

• azimuth angle

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The directional pattern of any antenna is describedin terms of the normalized radiation intensity F (, ),defined as the ratio of the power density S(R, , ) to

Smax , the maximum value of S at a specified range R:

max

( , , )( , ) (dimensionless)

S RF

S

For the Hertzian dipole,

2 2max( , ) sin ( , ) ( ) sinS R S F F

Antenna Pattern cont’d

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For a Hertzian dipole, F is doughnut-shaped withF max = 1 in the broadside direction ( = 90°)


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Example of a three-dimensional pattern of a narrow-beam antenna


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Often it is of interest to characterize the variation ofF (, ) in the form of two-dimensional plots in specificplanes in the pherical coordinate system

The two plane most commonly specificed are:

1. The elevation plane (also called the plane),corresponding to a constant value of

2. The azimuth plane (also calle the plane),specified by = 90°, and corresponding to x–y

plane


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EMC Group @ POLIMI

Some antennas show highly directive patterns withnarrow beams.

In these cases, it is convenient to plot the antennapattern on a dB scale, i.e.,

dB 1010log ( , )F F

This graphical representation allows a convenientinterpretation of the directional distribution andamplitude of the radiation lobes


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Main lobe

An antenna is said to be fairly directive when most ofthe energy is radiated through a narrow angularrange called the main lobe

Side lobes and back lobes

The antenna pattern, in addition to the main lobe,usually exhibits side lobes and back lobes

For most applications, these extra lobes areconsidered undesirable because they represent

wasted energy for transmitting antennas andpotential interference for receiving antennas


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Examples of normalized radiation patterns

Polar form Rectangular form

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Beam Dimensions

Pattern solid angle

For an antenna with a single main lobe, the pattern solid angle Ωp describes the equivalent width of themain lobe of the antenna pattern

It is defined as

4( , ) (sr) p F d

An isotropic antenna is antenna with F(, ) = 1 in alldirection.

For an isotropic antenna Ωp = 4π (sr)

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Beam Dimensions cont’d

The pattern solid angle defines an equivalent coneover which all the radiation of the actual antenna isconcentrated wih equal intensity , equal to themaximum of the actual pattern

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Beam Dimensions cont’d

3-dB Beamwidth

The half-power beamwidth is used to characterizethe width of the main lobe in a given plane.

It is defined as the angular width of the main lobe

between the angles (

1,

2) at which the magnitude ofF(, ) is equal to half of its peak value (−3dB on adecibel scale), i.e.,

For the Hertzian dipole, F() is maximum at = 90°,and

135 45 90

2 1

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Antenna Directivity

The directivity D of an antenna is defined as the ratioof its maximum normalized radiation intensity, F max (which by definition is equal to 1) to the average

value of F (, ) over the solid angle 4π , i.e.,

max

av

4

1

1( , )

4

4(dimensionless)

p

F D

F F d

where Ωp is the pattern solid angle

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Antenna Directivity cont’d

Note that:

1. The narrower Ωp the greater is the antennadirectivity

2. For an isotropic antenna Ωp = 4π , hence itsdirectivity is

isotropic 1 D

3. By recalling that F = S / Smax ,

2rad rad

4 4

2 2max max

4

( , , )

( , ) (W) p

P dP R S R d

R S F d R S

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D can be expressed as

2max

rad

max

av

4 R S

S

S D

P

whererad

av isotropic 24

PS S

R

therefore, D represents the ratio of the maximumpower density radiated by the antenna underconsideration to the power density radiated byan isotropic antenna

4. Usually, D is expressed in decibels, i.e.,

dB 1010log D D 15 of 19

EMC Group @ POLIMI


Hertzian dipole

For the Hertzian dipole,

4

23

0 0

4 4

( , )

4 4 3

4 1.22sin

3

5

p

DF d

d d

or, in decibels,

dB 1010log 1.5 1.76 dB D 16 of 19


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Radiation Efficiency and Gain

Of the total power Pt supplied to the antenna, a part,Prad, is radiated into space, and the remainder, Ploss,is dissipated as heat loss in the antenna structure.

The radiation efficiency is defined as

rad

t

P

P

The antenna gain is defined as

2max

t

4 R S G

P

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By comparing the antenna gain with its directivity

2 2max max

t rad

4 4,

R S R S G D

P P

It is straigthforward to note that

2 2max max rad

rad t tt

rad

4 4

(dimensionless)

R S R S PG D

PP PP

P

D

The gain accounts for ohmic losses in the antennamaterial, whereas the directivity does not


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Since

2 2rad 0 rad loss 0 loss

1 1| | , | |

2 2P I R P I R

where |I0| is the magnitude of the sinusoidal currentexciting the antenna, the antenna efficiency takesthe form

rad rad

t rad loss

rad

rad loss

P P

P P P

R

R R


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093589 - 00B - Antenna Parameters