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ANTENNA THEORY AND DESIGN

FALL 2013

Instructor: Veysel Demir

Antenna Fundamentals and

Definitions



9/13/2013 Prepared by Dr. Veysel Demir, EE, NIU 2

Electromagnetic Waves

Electromagnetic waves in space are the basis of radio

transmission over great distances without direct wire connection

between the transmitting and receiving points.

At the transmitting and receiving stations, radio signals exist in

the form of high-frequency alternating currents in conductors

and in electronic amplifying devices.

Between the transmitter and receiver they exist as

electromagnetic waves in space.

Antennas are the devices that act as go-betweens.




Transmitter and Receiver

Transmitter :

The antenna converts the energy of the electrical currentsinto the form of an electromagnetic field.

It ―launches‖ the waves into space.

Receiver :

The antenna captures energy from the arriving field, and it

converts the field variations into current and voltage replicasof those at the transmitter

The voltages and currents are much smaller in amplitude -

need to use amplifiers.




Characteristics of Electromagnetic Waves

A wave is an oscillatory motion of any kind.

Electromagnetic waves are electric and magnetic field variations

All waves are characterized by the property called propagation.

Waves travel at characteristic speeds

depending on the type of wave and the nature of the propagation

medium

In free space electromagnetic waves travel

In other propagation media their speed is less:

8

3 10 /c m s

r r

cv




Characteristics of Electromagnetic Waves

Electromagnetic waves may not travel through somemedium. At very low radio frequencies radio waves cannot penetrate

the ionosphere; they are reflected from it.

At very high frequencies waves pass through the ionosphereunimpeded.

The atmospheric layer bounded by the ionosphere at the topand Earth’s surface at the bottom forms a guiding structurefor the propagation of radio waves in the HF band.

Atmosphere as guiding structure for radio waves.




Frequency and Wavelength

The oscillations of waves are periodic

They are characterized by a frequency The frequency is expressed in Hertz (Hz)

Complex waves may contain more than one frequency.

A single-frequency wave motion has the form of a sinusoid.

0

2 2( , ) cos

t x y x t A

T

magnitude time period spatial wavelength reference phase

v

f


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Sinusoidal Wave in Lossless Medium

0

2 20 ( , ) cos

t x y x t A

T



Frequency Spectrum



Frequency Spectrum

The electromagnetic spectrum covers an enormous range of

frequencies including cosmic-ray radiation with frequencies in excess of 1020 Hz.

The International Telecommunications Union (ITU), an

organization of the United Nations, makes the general guidelines

for the assignment and use of frequencies.

For the United States,

federal governmental usages coordinated by the National

Telecommunications and Information Agency (NTIA)

nonfederal governmental frequency usages coordinated by Federal

Communications Commission (FCC)



The Radio Frequency Spectrum



Standard Radar Band Designations



Frequency Allocations

Some of the better-known frequency allocations within the United States include:

AM (amplitude modulation) broadcast: 535 –1705 kHz

FM (frequency modulation) broadcast: 88 –108 MHz

Television in 6 MHz bandwidth numbered channels: 2 –6, 54 –60 MHz, . . . , 82 –88 MHz

7 –13, 174 –180 MHz, . . . , 210 –216 MHz 14 –36, 470 –476 MHz, . . . , 600 –608 MHz

Note: 614 –698 MHz (without channel numbers) is allocated to TV. The frequencies608 –806 MHz were previously allocated for TV channels 37 –69.

GPS (global positioning satellite): 1227.6 MHz (military); 1575.42 MHz and1227.6 (civilian);Telemetry on 2227.5 MHz

GSM-850: uplink 824 –849 MHz, downlink 869 –894 MHz

GSM-1900: uplink 1850 –1910 MHz, downlink 1930 –1990 MHz

ISM (industrial, scientific and medical) 902 –928 MHz, 2.4 –2.5 GHz, 5.725 –5.875GHz



Plane Waves

Waves radiated by an EM source, such as an antenna,

have spherical wavefronts as in (a); to a distant observer, however, the wavefront across the observer’s

aperture appears approximately planar as in (b).



Uniform Plane Waves

The electric and magnetic fields are perpendicular to each other

and both are perpendicular to direction of propagation.

These directional properties characterize a transverse

electromagnetic wave.

A transverse electromagnetic (TEM) wave

0 2 2( , ) cos x t z E z t E T

0

2 2( , ) cos y

t z H z t H

T

0 0 0 E H H

0

377 In free space:



Uniform Plane Waves

Spatial variations of E and H.



Wave Polarization

The polarization of a uniform plane wave describes the shape and locus of the tip of the E vector at a given point in space as a

function of time.

In the most general case, the wave is elliptically polarized

In certain conditions, the ellipse may turn to a circle or a straight

line Circular polarization

Linear polarization

A wave with x- and y- components

ˆ ˆ( ) ( ) ( ) x y E z xE z yE z (46)

0 0( ) , ( ) jkz jkz

x x y y E z E e E z E e (47)



Linear Polarization

Linearly polarized wave traveling in the +z -direction.



Right-Hand Circular (RHC) Polarization

Right-hand circularly polarized wave radiated by a helical antenna.



Circular Polarization

Polarization handedness is defined in terms of rotation of

E

as afunction of time in a fixed plane orthogonal to the direction of

propagation

Circularly polarized plane waves propagating in the +z -direction



Polarization

The polarization is random when there is no fixed polarization or pattern of polarization variation an effect present in light waves emitted from an incandescent source (e.g.,

the sun or an electric light bulb).

It is seldom observed in man made radio emissions.

Such would result if two independently random sources of radio noise

are connected to right-angle-polarized elements of a single antenna. E.g. used in radio and radar military countermeasures, or ―jamming‖

Linear polarization is the most commonly employed by far.

One application for circular polarization is in communications betweenearth and space, to mitigate the effects of polarization rotation causedby the ionosphere



Spherical Waves and the Inverse-Square Law

An electromagnetic wave represents a flow of energy in the direction of

propagation.

The power density of the wave:

The rate at which energy flows through a unit area of surface in space

Energy per unit time per unit of area: watts per square meter.

The average power density of the wave is the time average value of S

2( / ) ( )the poynting veS E H m r W cto

* 21Re ( / )

2

avS E H W m

, : instantaneousfields

, : phasor fields

E H

E H



Spherical Waves and the Inverse-Square Law

Isotropic radiator:

The source radiates power at a constant rate uniformly in alldirections,

The total power flowing through any spherical surface centered at the

source will be uniformly distributed over the surface and must equal the

total power radiated.

24

t R

P S

R P t = total power

S R = power density at a distance R

R

RS



The Inverse-Square Law

A R

B R

2 2,

4 4 A B

t t R R

A B

P P S S

R R

2

A

B

R B

R A

S R

S R

The power density is inversely proportional to the square

of the distance from the source.

However, this is true only within the far field of an antenna,

because an antenna is of finite size andtherefore it is not located solely at apoint.

The far field exists beyond a minimumseparation distance of an antenna, whichdepends on antenna dimensions andwavelength.

A RS

B RS



Decibel (Logarithmic) Expression of Attenuation

Wave attenuation is expressed also in terms of the logarithms of

the power-density or electric-intensity ratios, an alternative method widely used in describing signal amplificationor attenuation in telephone and radio systems.

11 1

2 2 2

10log 10log 20log ( ) E P P

G G dB G dB

P P E

Attenuation due to the spherical spreading

of the wave—that is, as expressed by theinverse-square law—is sometimes calledthe space attenuation of the wave.




Absorption

There may sometimes be attenuation due to absorption of power by the

propagation medium.

This does not occur in a vacuum, but it will occur in a medium thatcontains material particles that interact with the waves.

At some frequencies, for example, certain gases of the earth’s

atmosphere (oxygen and water vapor) cause absorption. This occursslightly in the VHF region and becomes significant over longtransmission paths in the UHF region and above.

Unlike space attenuation, attenuation due to absorption does notdepend on the distance from the source but only on the total distance

traveled by the wave.




Absorption

Certain materials are capable of absorbing radio waves verystrongly.

Waves traveling in these materials will be attenuated greatly withina short distance, of the order of centimeters or meters.

Sometimes such materials are used in antenna design tosuppress radiation in undesired directions, or to prevent―leakage‖ of waves from one part of an antenna to another

where they would have an undesirable effect.

An anechoic chamber

b




Absorption

If a wave propagates in a homogeneous absorbing medium (i.e. x-direction),

its amplitude will decrease as , where e = 2.71828

Thus, if a wave of amplitude E 1 travels a distance x of 1m and is 1Np/m, its new amplitude E 2 is E 1e

−1.

Then, the attenuation in decibels is 20 log (E 1/E 2) = 8.686, and thus anattenuation of 1 Np/m equals 8.868 dB/m.

x

e

: attenuationfactor xe

: attenuationconstant (Np/m)

=8.686dB Np A A

H di



9/13/2013 Prepared by Dr. Veysel Demir, EE, NIU 28Prepared by Dr. Veysel Demir, EE, NIU

How antennas radiate

Electromagnetic ―news‖ propagate with speed of light

An isolated charge induces an electric field at every point

in space.

This field is called the ―Coulombian‖ field

: permittivity of

the medium

: radiusof circle, :speedof light, : timer c t

r ct

R di ti f h




Radiation from a charge

If the charge is moving with a constant speed, the fields move

together with the charge

If the charge is accelerated, then the charge produces a

―disturbance‖ of the fields.

This ―disturbance‖ propagates and this propagation is called

radiation.

Direction of movement

Charge moves with constant velocity

until reaching A

Charge is accelerated between A

and B for seconds

Field lines after t seconds shall be

continuous

t

Field lines generated by the

charge when it was at A, andobserved after t seconds

Field lines generated by the

charge when it was at B, and

observed after secondst t

A B

R di ti f h




Radiation from a charge

A charge moving with constant speed creates a disturbance of

fields in space

But this disturbance is not radiation

It does not emit power

An accelerated charge will create a disturbance

This disturbance carries power radiated from the charge Acceleration of charge is the source of radiation

Radiation is maximum in the direction perpendicular to the

direction of movement

v

R di ti




Radiation

An accelerated charge will create radiation

Time-varying current will create radiation

Why don’t we observe radiation from an AC circuit?

dQ t

I t dt

I t

E t

E t

R di ti f t i i li




Radiation from a transmission line

I

I

R di ti




Radiation

E t

If the distance between the wires is small (compared with thewavelength) the radiated fields from the wires will cancel each other.

Consequently, radiation is negligible, and is neglected in low-frequencya-c circuit theory.

At high frequencies, wavelength is shorter

If the wavelength is comparable with the distance, then there will be

radiation.

R di ti




Radiation

For radiation to occur, the conductor carrying the

current must be reasonably ―in the clear,‖ that is, not enclosed by obstacles that are impenetrable to

electromagnetic waves.

Radiation may be prevented, when desired, byplacing circuits inside closed metallic enclosures; this

is the principle of shielding .

Radiation f om a t ansmission line




Radiation from a transmission line

An open ended transmission line:

Since the end is open, we will observe

standing waves of voltage and currenton the transmission line

magnitude of current (standing

wave pattern)

current

charges

E fields from

top wire

E fields from

bottom wire

H fields from

top wire

H fields from

bottom wire

Although the charges are oscillating(accelerating) sinusoidally, this

structure does not radiate

The radiation from the two wires

cancel each other

What happens if we bend the ends




What happens if we bend the ends

Direction of maximum radiation

The fields generated by the arms

add up and radiate

Antenna Parameters



9/13/2013 Prepared by Dr. Veysel Demir, EE, NIU 379/13/2013

Antenna Parameters

The ideal antenna is one that will

radiate all the power delivered to it by a transmissionline

in the desired direction or directions

and with the desired polarization.

Practical antennas can never fully achieve thisideal performance

Their merit is conveniently described in terms of the degree to which they do so.

Antenna Parameters




Antenna Parameters

The principal parameters of antennas are radiation pattern

radiation efficiency input impedance

bandwidth

Other parameters defined under each of these categories gain

beamwidth beam polarization

minor lobe level,

radiation efficiency,

aperture efficiency,

effective area,

radiation resistance, various ―bandwidths,‖

Some of these parameters are interrelated or correlated.

Antenna structures Size




Antenna structures - Size

There is a general proportionality between

antenna size and the wavelength at the frequency of operation,

but this relationship is not hard and fast.

Large antennas are sometimes used at short wavelengths (high

frequencies) to obtain a highly directional radiation pattern(beam) and high gain in a preferred direction.

At long wavelengths (low frequencies) very small antennas maybe used for reception when efficiency is not important.

An antenna appreciably less than a half wavelength is termed―electrically small.‖

Even a physically large antenna may be electrically small at verylow frequencies.

Antenna structures Feed Lines




Antenna structures - Feed Lines

Part of antenna design:

The design of a feed line (transmission line) any necessary impedance-matching devices

power-dividing devices

Transmission lines:

Wavegides Coaxial cables

Two-wire lines

Microstrip lines

Stripline lines

Coplanar waveguides

The line connects to the antenna at its input terminalsor input port.

Antenna structures Conductors and isolators




Antenna structures – Conductors and isolators

Metals of high conductivity, such as copper and

aluminum (and its alloys), are naturally preferred.

The conducting portions of an antenna not only carry

rf currents but also have rf voltages between their

different parts and between the conductors andground.

To avoid ―short circuiting‖ these voltage, insulators

must sometimes be used between the antenna andits supports, or between different parts of the

antenna.

Antenna structures Weather protection




Antenna structures – Weather protection

Since antennas are ordinarily ―outdoors,‖ they mustwithstand wind, rain, ice and snow, lightning, andsometimes corrosive gases or salt-laden air.

Sometimes an antenna (such as a rotatingparaboloidal reflector or lens) is totally enclosed in a

protective housing of low-loss insulating material thatis practically transparent to the electromagneticradiation.

Such a housing is called a radome.

Radiation Pattern




Radiation Pattern

If an antenna is imagined to be located at the center of

a spherical coordinate system, its radiation pattern is determined by measuring the electric field

intensity over the surface of a sphere at some fixed distance, r .

A pattern that represents field strength as a function of

angular direction at a fixed distance from the antenna is

identical to a plot of distance for a constant field

strength.

Since the field E is then a function of the two variable

and , it is written E ( , ) in functional notation.

ˆ, sin4

j R I z e E j

R

Example

Radiation Pattern




Radiation Pattern

The power density of the field, p ( , ), can also be computedwhen E ( , ) is known

A plot in terms of p( , ) conveys the same information as a plotof the magnitude of E ( , ).

The phase pattern In some circumstances, the phase of the field is of interest, and a

plot may be made of the phase angle of E ( , ) as well as itsmagnitude;

Ordinarily antenna pattern implies only the magnitude of E or p.

The polarization pattern

Sometimes the polarization properties of E may also be plotted.

2 377 p E

Patterns in a plane




Patterns in a plane

Principal planes of the coordinate system

xy-plane: = 90o,

=0 o

-360 o

xz-plane: = 0o-180o, =0 o

yz-plane: = 0o-180o, =90 o

Patterns in a plane




Patterns in a plane

xy-plane

xz-plane

yz-plane

Polar plot vs rectangular coordinate plot




Polar plot vs rectangular coordinate plot

Rectangular coordinate plot

distorts the appearance of the pattern geometrically

but preserves the

interpretability of an angle

representation and makesthe plotting and reading of

the low-amplitude portions

of the pattern easier.

E-plane and H-plane




E plane and H plane

When the radiation of an antenna is polarized so that the E -vector lies in a plane (usually one of the principal planes), thepattern in this plane is sometimes referred to as the E -plane

pattern;

and the pattern in the plane perpendicular to it, in which the H -vector lies, is called the H -plane pattern.

ˆsin4

j R I z e H j

R

ˆsin4

j R I z e

E j R

Example

E-plane H-plane

3D view

Absolute and relative patterns




Absolute and relative patterns

Absolute pattern: if radiation pattern is plotted in

terms of the electric field strength in volts per meter

or the power density in watts per square meter.

Relative pattern: Often, the pattern is plotted inrelative terms, that is, the field strength or power density is represented in terms of its ratio to somereference value.

The reference usually chosen is the field level in the

maximum-field-strength direction.

( , )( , ) ( , )

(max)rel

E F E

E

( , )( , ) ( , )

(max)rel

S P S

S

normalized field patternpower pattern

Example




Example

For an element of current (ideal dipole):

sin4

j R I z e E j

R

2(max) 4

j R I z e

E j R

( , ) ( , ) sinrel F E

Decibel scale




Decibel scale

It is fairly common to express the relative field

strength F or power density P in decibels.The value at the maximum of the pattern is

therefore zero decibels,

and at other angles the decibel values are

negative (since the logarithm of a fractionalnumber is negative

10 1010log ( , ) 20log ( , ) P F

2( , ) ( , ) P F

Power pattern



9/13/2013 Prepared by Dr. Veysel Demir, EE, NIU 529/13/2013 Prepared by Dr. Veysel Demir, EE, NIU 52

Power patternA normalized power pattern for a uniform line source

polar – linear scale polar – dB scale

rectangular – dB scalerectangular – linear scale

Near-field and far-field




Near field and far field

Antenna radiation patterns are graphical

representations of the radiation in the far-field of theantenna.

The far-field region is where the angular fielddistribution is essentially independent of the distancefrom the antenna.

The minimum permissible distance, for a far-fieldmeasurement, depends on the dimensions of theantenna in relation to the wavelength.

The distance from the antenna where the far-field begins:

22 ff

Dr

D: maximum dimension of antenna

Farfield conditions




Farfield conditions

22 Dr

r Dr

Farfield conditions

3

23

2

0 0.62

20.62

2

D

D D

D

r: Distance from antenna

Reactive near field

Radiating near field

Far field

The near-field region is further subdivided between

the reactive near-field and radiating near-field

regions.

However, the total field present is actually the vector

sum of the reactive and radiating fields..

The Ideal Dipole – Near and farfields




The Ideal Dipole Near and farfields

Hertzian electric dipole, infinitesimal dipole, elemental dipole

x

y

z

I

Assumptions:

The line is electrically very short

The current I is uniform on the line

0 sin 2 I t I ft

See Section 2.3 in the text book

Magnetic field:1

ˆ1 sin4

j r I z e H j

j r r

Example: The Ideal (elemental or Hertzian) Dipole




p ( ) p

Electric field: 1

E H j

Farfield term Near-field terms

2 2 3 2 2ˆ ˆsin cos

4 2

j r j r j r j r j r

I z e e e I z e e E j j r r j r r r r

Farfields




Farfields

If ˆsin

4

j r I z e H j

r

ˆsin4

j r

I z e E jr

1r

Farfield terms

sin4

sin4

j r

j r

I z e j

E r

I z e H jr

Intrinsic

impedance

Farfield Power Density




a e d o e e s ty

2

1ˆ ˆ

sin sin2 4 4

sinˆ

2 4

j r j r I z e I z e

S E H j jr r

I z r

r

2

sinˆ

2 4

I z real S real r

R

Real power density propagating:

Farfield Power Density




y

Total power flowing out through a sphere with radius R

22

2

0 0

2

sinˆ ˆ sin

2 4

12

r

I z P S ds r rr d d

r

I z

Radiated power

The Nearfields of Ideal Dipole




p

Magnetic field:2

ˆsin4

j r nf I ze H

r

Electric field:3 3

ˆˆsin cos

4 2

j r j r nf I z e I z e

E j j r

r r

If 1 R

2

2

5

1 1ˆ

ˆ

2 2

1ˆ

ˆsin sin2 4

nf nf nf nf nf nf nf

RS E H E H r E H

j I z r

r

Poynting vector:

Imaginary: so this is not real power

Example




p

Radiation Pattern of a Uniform Line Source




For a uniform line source:

0sin cos / 2

sin4 cos / 2

j R L j I Le E

R L

0

2

(max)4

j R j I Le E

R

sin cos / 2( , ) sin

cos / 2

L F

L


( , ) sin F

Element factor – pattern factor




p

( , ) ( , ) ( , ) F g f

A normalized field pattern can be written as product of

element factor and pattern factor

element

factor

pattern

factor

For a uniform line source:

sin / 2 cos

( , ) sin /2 cos

L

F L

element

factor pattern

factor

Ideal

dipole

A line source can be

considered as a combination

of Ideal dipoles

Line

source

Radiation pattern parameters




p p

Major lobe, main lobe, main beam: The radiation lobe

containing the direction of maximum radiation.

Minor lobe: any lobe other than the main lobe.Side lobes

Back lobes: directly opposite to the main lobe

Beamwidth




When the radiated power of an antenna is

concentrated into a single major ―lobe,‖ the angular width of this lobe is the beamwidth.

Some antennas have a pattern consisting of many

lobes.

Generally a narrower beam implies a greater gain. Beam may have different widths in different planes

through the beam axis

Therefore it is customary to give the widths of the beam in

two planes at right angles, usually the principal planes of thecoordinate system.





Half power beam width (HP) : Angular separation of the

points where the main beam of the power pattern equals

one-half the maximum value., , HP left HP right HP

For an element of current (ideal dipole): ( , ) sinrel E

1sin 45 , 135 135 45 902

o o o o o HP

2 1 HP





Side lobe level (SLL) : A measure how well the power is

concentrated into the main beam.

( ) pattern valueof sidelobepeak

pattern valueof themain lobe (max)

E SLLSLL

E

10

0.39

20log ( ) 8.2dB

SLL

SLL SLL dB





Broadside: The main beam is in a direction normal to the

plane containing the antenna

Endfire: Main beam is in the plane containing the antenna

Fan beam

Pencil beam

Radiation Resistance and Efficiency




In a large class of antennas the radiation is associated with a flow of RF current in a conductor or conductors.

Thus, when a current I flows in a resistance R , an amount of power P = RI 2 will be dissipated and converted into heat.

In general, the input impedance of an antenna is complex.

Resistive part is the sum of radiation resistance and loss

in

Z

( )in radiation loss ohmic Z R R jX

Antenna Impedance




For most antennas

Ohmic loss is significant for electrically small antennas

ohmic radiation R R

The input impedance of an antenna at its terminals:

The power that leaves the antenna and never returns (radiation)

Ohmic losses associated with heating

A A A Z R jX

in radiation ohmic R R R

radiation R

ohmic R

A X : power stored in the near field

The input impedance of antenna is the same when receiving and

transmitting (reciprocity)

Input impedance is affected by the other antennas around

Antenna Impedance




Average power dissipated in the antenna 21

2in A A P R I

A I : current at the antenna terminal

2 21 1

2 2in ohmic rad A ohmic A P P P R I R I 2

2 rad rad

A

P R

I

2

12rad P I z


2

2

2 2 212

2

2

2 2

2 22

6 6

2 1 2 22 26 6 3

I z rad

rad I

A

p

P R z f z

I

u z z z

2

280 ( )rad

z R

For an ideal dipole the radiation

resistance is very small

Antenna Impedance




Radiation efficiencyrad rad rad rad

r

in ohmic rad rad ohmic in

P P R Rk

P P P R R R

Ohmic resistance of wire antenna

At high frequencies the skin depth is : 2

Surface resistance :2

s R

Ohmic resistance of wire antenna with uniform current:

, : wire radius, : length2

ohmic s L R R a L

a

Bandwidth




All antennas are limited in the range of frequency over whichthey will operate satisfactorily.

This frequency range, whatever it may be, is called thebandwidth of the antenna.

Some antennas are required to operate only at a fixedfrequency with a signal that is narrow in its bandwidth;

consequently there is no bandwidth problem in designing such anantenna.

But in other applications much greater bandwidths may be

required; in such cases special techniques are needed.

Bandwidth




Bandwidth as a percent of the center frequency

Bandwidth as a ratio

Antenna pattern: pattern bandwidth The beamwidth, gain, sidelobe level, beam direction, and

polarization are parameters associated with the pattern

bandwidth

Input impedance: impedance bandwidth

input impedance, radiation resistance, and efficiency are

associated with the impedance bandwidth.

100%U L

P C

f f B

f

U r

L

f B

f

Bandwidth




Return loss of an antenna

6.98 5.7100% %20

6.34 P B

6.981.225

5.7r B

Directivity and Gain




Isotropic radiator:

The source radiates power at a constant rate uniformly in all

directions,

The total power flowing through any spherical surface centered at the

source will be uniformly distributed over the surface and must equal the

total power radiated.

24

t R

P S R

P t = total power S R = power density at a distance R

R

R p Actually an isotropic radiator is not physically realizable;

All actual antennas have some degree of nonuniformity

in their radiation patterns.

A nonisotropic antenna will radiate more power in some

directions than in others and therefore has a directional

pattern.

Solid angle




Solid angle is the angle that, seen from the center of a sphere,includes a given area on the surface of the sphere.

The value of the solid angle is numerically equal to the size of that area divided by the square the radius of the sphere.

Mathematically the solid angle is unitless, but for practicalreasons the steradian (s.r.) is assigned so that 1 steradian = 1 radian2.

22

0 0

22 2

0 0

sin

4

sphere Area dA r d d

r d r

2 2

sin

4

4

d d d

r d r

d Element of solid angle

Radiation intensity




Total power radiated by an antenna can be

calculated as

Radiation intensity is a range-independent quantity

Total radiated power equals the sum of all radiation

intensity that encloses the antenna.

2 2

2 2 2

0 0 0 0, , sin , ,t P r dA S r r d d S r r d

2, , ,U S r r

2 2

0 0 0 0, sin ,

t P U d d U d

Directivity




(Maximum) Directivity D is a quantitative measure of an

antenna’s ability to concentrate energy in a certain direction.

Specifically, D is the ratio of the maximum radiation intensityU max to the average radiation intensity U av .

Directivity: (directive gain) the ratio of the radiation intensity in a

certain direction to the average radiation intensity

max

ave

U D

U

( , )

( , ) ave

U

D U

Directivity as a function of direction( , ) D

Maximum directivity D

Directivity




If the radiation is isotropic, the radiation intensity in every

direction is U av .

Directivity:

Directivity is calculated by integrating relative values of an

antenna’s radiation pattern,

and this does not require knowledge of an absolute value

24t

isotropic P S R

2

24

t ave

P U r r

4t ave

P U

max max max

2

20 0

0 0max

4 4 4

,, sinave t

U U U D

U P U U d d d U

2

2

max max max

, , , , ,,

, , , ,

U S r E r F

U S r E r

Directivity




Beam solid angle: is the solid angle through which all the

power would be radiated if the radiation intensity equaled the

maximum over the beam area.

2

0 0 max

4 4

,sin

A

DU

d d U

maxt A P U

A

2

0 0max

,sin A

U d d

U

A

Gain




Gain: (power gain)

The directivity is based on the radiated power , P r .

The gain is based on the input power to the antenna, P i . The gain therefore accounts for the efficiency of the antenna as

well

max max max4

/ 4ave r r

U U U D

U P P

max4

in

U G

P

Radiation efficiencyr

in

P k

P

G kD

, ,G kD

Gain as a function of direction( , )G

Maximum gainG

Directivity and Gain in Decibels




Directivity

Gain

Relative Gain: Frequently gain is used to describe the

performance of an antenna relative to some standard

reference antenna

1010logdB D D

1010logdBG G

max

max,ref

U G

U

Gain relative to a half-wave dipole: dBd

Gain relative to an isotropic antenna: dBi

Gain of half-wave dipole is given as 2.15 dBi

Gain of an X antenna is given as 6.1 dBi

The gain of the X antenna relative to half-

wave dipole:Gd=6.1-2.15 = 3.95 dBd

Example




The pattern expression for an omni-directional antenna is given as:

1 21,( , ) 3 3

0,rel

E

otherwise

Find the beam solid angle and maximum directivity D. A

222 23

03

2

3

3

( , ) 1 sin

2 cos 2

A rel E d d d

4 42

2 A

D

( , )rel E

maxt A P U

max4

r

U D

P

Example




Determine the electric field intensity at a distance of 10 km from an antenna (in the

direction of maximum radiation) having maximum directivity 5 dB and radiating a

total power 20 KW.

0.5

105 10log ( ) 10 3.162 D D

max max max4

/ 4ave

U U U D

U P P

max

4

DP U

2

max maxU S r

max24

DP S

r

-5

max2

3.162 200005.032479 10

4 10000S

2

max max max

10.1948 /

2S E E V m

Example



The radiation intensity of an antenna is given as

32sin sin , 0 ,0 ,

( , ) 0,U otherwise

Find the directivity D.

max

ave

U DU

max 2U 1 ( , )

4aveU U d

3

0 0

2 3 3 2

0 0 0 0

1( , ) 2 sin sin sin

4

1 1sin sin sin sin

2 2

1

aveU U d d d

d d d d

2U

( , ) E

antenna theory and design slides 1

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