UNIVERSITY OF NAMIBIA

DEPARTMENT

OF

ELECTRONICS AND COMPUTER ENGINEERING

Radio-Wave Propagation and Antennae

TTCR3791

2012

Propagation: How radio waves travel from point A to point B; and the events occurring

in the transmission path that affect the communications between the points, stations, or

operators.

When the electrons in a conductor, (antenna wire) are made to oscillate back and forth,

Electromagnetic Waves (EM waves) are produced.

These waves radiate outwards from the source at the speed of light, 300 million meters

per second.

PROPAGATION

The relationship between electric and magnetic field intensities is analogous to the

relation between voltage and current in circuits

An electromagnetic wave propagating through space consists of electric and magnetic

fields, perpendicular both to each other and to the direction of travel of the wave

This relationship is expressed by: H

EZ

Electric Field, E

Magnetic Field, H

Direction of

Propagation

Two types of waves: Transverse and Longitudinal

Transverse waves: vibration is from side to side; that is, at right angles to the

direction in which they travel

A guitar string vibrates with transverse motion. EM waves are always

transverse.

• Electromagnetic transmissions move in space as Transverse waves

• Waves are characterized by frequency and wavelength:

v f

Longitudinal waves: Vibration is parallel to the direction of propagation. Sound

and pressure waves are longitudinal and oscillate back and forth as vibrations

are along or parallel to their direction of travel

Electromagnetic radiation has a dual nature:

In some cases, it behaves as waves

In other cases, it behaves as particles (photons)

For radio frequencies the wave model is generally more appropriate

EM waves travel in straight lines, unless acted upon by some outside force. They travel

faster through a vacuum than through any other medium.

As EM waves spread out from the point of origin, they decrease in strength in what is

described as an "inverse square relationship".

For example: a signal 2 km from its starting point will be only 1/4 as strong as that 1

km from the source. A signal 3 km from the source will be only 1/9 that at the 1 km

point.

• Power density in space is the amount of power that flows through each square

meter of a surface perpendicular to the direction of travel

Z

EPD

2

Power Density

Radio waves are one form of electromagnetic radiation

Light waves (waves we see)

and

radio waves (waves we hear)

are both EM waves, differing only in

frequency and wavelength.

Electromagnetic Spectrum

Electromagnetic waves can be generated by many means, but all of them involve the

movement of electrical charges

Plane and Spherical Waves

• The simplest source of electromagnetic waves would be a point in space, with

waves radiating equally in all directions. This is called an isotropic radiator

• A wavefront that has a surface on which all the waves are the same phase would be

a sphere

• The polarization of an antenna is the orientation of the electric field with respect to

the Earth's surface and is determined by the physical structure of the antenna and by

its orientation

• Radio waves from a vertical antenna will usually be vertically polarized.

• Radio waves from a horizontal antenna are usually horizontally polarized.

Polarization

Circular Polarization

• The polarization of a plane wave is simply the direction of its electric field vector

• The wave can rotate in either direction - it is called right-handed if it rotates

clockwise

Free-Space Propagation

• Radio waves propagate through free space in a straight line with a velocity of the

speed of light (300,000,000 m/s)

• There is no loss of energy in free space, but there is attenuation due to the spreading

of the waves

Attenuation of Free Space

• An isotropic radiator would produce spherical waves

• The power density of an isotropic radiator is simply be the total power divided by

the surface area of the sphere, according to the square-law:

PD Pt

4r2

Transmitting Antenna Gain

• In practical communication systems, it is important to know the signal strength at

the receiver input

• It depends on the transmitter power and the distance from the transmitter to the

receiver, but also upon the transmitting and receiving antennas

• Two important antenna characteristics are:

– Gain for the transmitting antenna

– Effective area for the receiving antenna

• Antennas are said to have gain in those directions in which the most power is

radiated

Receiving Antenna Gain

• A receiving antenna absorbs some of the energy from radio waves that pass it

• A larger antenna receives more power than a smaller antenna (in relation to

surface area)

• Receiving antennas are considered to have gain just as transmitting antennas do

• The power extracted from a receiving antenna is a function of its physical size

and its gain

Path Loss

• Free-space attenuation is the ratio of received power to transmitted power

• The decibel gain between transmitter and receiver is negative (loss) and the loss

found this way is called free-space loss or path loss

Reflection, Refraction, and Diffraction

• These three properties are shared by light and radio waves

• For both reflection and refraction, it is assumed that the surfaces involved are much

larger than the wavelength; if not, diffraction will occur

Reflection

• Reflection of waves from a smooth surface (specular reflection) results in the angle

of reflection being equal to the angle of incidence

the abrupt change in direction of a wave front at an interface between two dissimilar

media so that the wave front returns into the medium from which it originated.

Reflecting object is large compared to wavelength.

Other Types of Reflection

Corner reflector Parabolic reflector Diffuse Reflection

Refraction

• A transition from one medium to another results in the bending of radio waves, just

as it does with light

• Snell’s Law governs the behavior of electromagnetic waves being refracted:

2211sinsin nn

redirection of a wavefront passing through a medium having a refractive

index that is a continuous function of position (e.g., a graded-index

optical fibre or earth atmosphere) or through a

boundary between two dissimilar media

– For two media of different refractive indices, the angle of refraction is

approximated by Snell's Law known from optics

Diffraction

• As a result of diffraction, electromagnetic waves can appear to “go around

corners”

• Diffraction is more apparent when the object has sharp edges, that is when the

dimensions are small in comparison to the wavelength

the mechanism the waves spread as they pass barriers in obstructed radio

path (through openings or around barriers)

• Diffraction - important when evaluating potential interference between

terrestrial/stations sharing the same frequency.

Scattering

a phenomenon in which the direction (or polarization) of the wave is

changed when the wave encounters propagation medium

discontinuities smaller than the wavelength (e.g. foliage, …)

• Results in a disordered or random change in the energy distribution

Absorption

the conversion of the transmitted EM energy into another form, usually

thermal.

– The conversion takes place as a result of interaction between the

incident energy and the material medium, at the molecular or

atomic level.

– One cause of signal attenuation due to walls, precipitations (rain, snow,

sand) and atmospheric gases

• Signals in the VHF and higher range are not usually returned to earth by the

ionosphere

• Most terrestrial communication at these frequencies uses direct radiation from the

transmitter to the receiver

• This type of propagation is referred to as space-wave, line-of-sight, or tropospheric

propagation

Line-of-Sight Propagation

rt hhd 1717minheightsantennaRxandTxthearehandh

kminRxandTxbetweencedisisd

rt

tan

• Most of the time, radio waves are not quite in free space

• Terrestrial propagation modes include:

– Line-of-sight propagation

– Space-wave propagation

– Ground waves

– Sky waves

RADIO WAVES

SPACE GROUND

SKY REFLECTED DIRECT SURFACE

• Ground Wave is a Surface Wave that propagates or travels close to the surface of the Earth.

• Line of Sight (Ground Wave or Direct Wave) is propagation of waves travelling in a straight line. These waves are deviated (reflected) by obstructions and cannot travel over the horizon or behind obstacles. Most common direct wave occurs with VHF modes and higher frequencies. At higher frequencies and in lower levels of the atmosphere, any obstruction between the transmitting antenna and the receiving antenna will block the signal, just like the light that the eye senses.

• Space Waves: travel directly from an antenna to another without reflection on the ground. Occurs when both antennas are within line of sight of each another, distance is longer that line of sight because most space waves bend near the ground and follow practically a curved path. Antennas must display a very low angle of emission in order that all the power is radiated in direction of the horizon instead of escaping in the sky. A high gain and horizontally polarized antenna is thus highly recommended.

• Sky Wave (Skip/ Hop/ Ionospheric Wave) is the propagation of radio waves bent (refracted) back to the Earth's surface by the ionosphere. HF radio communication (3 and 30 MHz) is a result of sky wave propagation.

LINE OF SIGHT, GROUND WAVE, SKY

WAVE

Ionospheric Propagation

• Long-range communication in the high-frequency band is possible because of

refraction in a region of the upper atmosphere called the ionosphere

• The ionosphere is divided into three regions known as the D, E, and F layers

• Ionization is different at different heights above the earth and is affected by time of

day and solar activity

Propagation in a Mobile/Portable Environment

• Multipath propagation creates interference for communication systems

• Mobile environments are often so cluttered that the square-law attenuation of free

space does not apply (for example, in a city with many buildings)

Repeaters and Cellular Systems

• Because mobile systems have relatively small antenna heights, systems must be in

place to improve signal strength and reception capabilities

• Mobile units make use of repeaters that are full-duplex and use resonant cavities

called a duplexer

• Cellular systems do not use the horizon as the limit of coverage

• Antennas may still be mounted high, but the range is deliberately limited by using

as low a transmitter power as is possible

Control of Fading in Mobile Systems

• Fading is a problem with mobile systems and increasing power and typical

frequency diversity are not workable solutions to this problem

• Spread-spectrum systems can correct fading through alternative frequency diversity

systems such as CDMA

• Using a rake receiver, a CDMA system can receive several data streams at once

Other Propagation Modes

• Tropospheric Scatter - makes use of the scattering of radio waves in the troposphere

to propagate signals in the 250 MHz –5 GHz range

Ducting

• Under certain conditions, especially over water, a superrefractive layer can form in

the troposphere and return signals to earth

• The signals can then propagate over long distances by alternately reflecting from the

earth and refracting from the superrefractive layer

• A related condition involves a thin tropospheric layer with a high refractive index,

so that a duct forms

Examples of Ducting

TRANSMISSION LINE

A transmission Line consists of conductors separated from each other by a

dielectric.

Two main types of line exist:

- the two wire line

- the coaxial line

The conductors forming a pair have both

resistance (R) and inductance (L) uniformly distributed along their length

capacitance (C) and leakance (G) uniformly distributed between them.

These four quantities are known as primary coefficients of a line.

• RESISTANCE: The resistance R of a unit length of line, or loop resistance, is

the sum of the resistances of the two conductors comprising a pair. At zero

frequency the resistance of a line is the dc resistance Rdc given by:

•

• are the resistivities of the two conductors and

• are their cross-sectional areas

• The a c resistance is proportional to the square root of the frequency

metreperohmsaa

Rdc2

2

1

1

2,1

2,1 aa

tconsaiskwherefkRac tan11

• Inductance and Capacitance. The loop inductance L, and the shunt capacitance C,

of the line in henry per metre and farads per metre respectively, are both more or less

constant with change in frequency

• Leakance. The leakance G, of a line in Siemens per metre represents the leakance of

current between the conductors via the dielectric separating them, and is reciprocal of

insulation resistance. Leakance increases with increase in frequency and at the higher

frequencies it is directly proportional to frequency

tconsaiskfkG tan22

SECONDARY COEFFICIENTS OF A LINE

• The secondary coefficients of a transmission line are its

characteristic impedance attenuation coefficient

phase-change coefficient velocity of propagation

Characteristic Impedance. The characteristic impedance, Zo , of a transmission line is

the input impedance of an infinite length of that line.

Consider an infinite length of line below,

xI

xV

sI

sV

0Z

To infinity

Definition of the characteristic impedance of a line

its input impedance is the ratio of the voltage, Vs, impressed across the sending end terminals to

the current, Is flowing into the line i.e.

Similarly, at any point x, along the line, the ratio is always equal to

Suppose the line is now cut a finite distance from its sending end terminals as shown

The remainder of the line is still of infinite length and so the impedance measured at terminals

2-2 is equal to the characteristic impedance. Thus before the line was cut, terminals 1-1 were

effectively terminated in the impedance

The conditions at the input terminals will not be changed if terminals 1-1 are closed in a

physical impedance equal to and this leads to a more practical definition:

sI 1

0ZsV

To infinity

1

2

2

ohmsI

VZ

s

s0

xx IV0Z

0Z

0Z

sI

0ZsV

0Z

• The characteristic impedance of a transmission line is the input

impedance of a line that is itself terminated in the characteristic

impedance.

• A line that is terminated in its characteristic impedance is said to be

correctly terminated.

• The characteristic impedance of a line depends upon the values of the

primary coefficients of the line, according to the equation

• At higher frequencies where we can write

this always applies to coaxial cable since they

are always operated at frequencies high enough

to make R and G negligible with respect to

ohmsCjG

LjRZ

0

GCandRL

ohmsC

LZ 0

• EXAMPLE

• A generator of e.m.f 1V and internal resistance 79 Ohms is applied to a line having

L=0.5mH/m and C=0.08 microfarads/m. If the approximate expression for characteristic

impedance may be assumed, calculate

• (a) the sending end current

• (b) the sending end voltage.

sI

790Z

sV

V1

79

791008.0

105.06

3

0Z

mAAI s 33.6158

1

7979

1

VIV ss 5.0

158

17979

• The characteristic impedance for some type of coaxial cables:

For an air-spaced coaxial line, where R is the inner radius of the outer

conductor, and r is the radius of the inner conductor

This lies between 30-100 Ohms. Most practical cables have the value of 50 – 75

Ohms

• For an air-spaced two-wire line, where D is the spacing between the centers of

the two conductors and r is the radius of each conductor.

ohmsr

RZ 100 log138

ohmsr

DZ 100 log276

• Attenuation Coefficient. As a current or voltage is propagated along a

line its amplitude is progressively reduced or attenuated because of losses in the

line.

• The are two type of loses:

- conductor loses caused by power dissipation in the series resistance

- dielectric losses

If the current, or voltage at the sending-end terminals of the line is

, then the current, or voltage, at unit distance along the line is

where is the attenuation coefficient. In the next unit distance the attenuation is the same, and

thus the current at the end of this distance is

RI 2

ss VorI ,

eVVoreII ss 11 ,

2I 212

eIeII s

• The general expression for the attenuation coefficient of a line is complex, however

at frequencies were

the expression simplifies to

• The attenuation coefficient varies with frequency in accordance with the frequency

dependencies of R and G i.e.

• Example

A coaxial cable has loss of 3.5 dB/m at 1 MHz. Calculate its loss at 4 MHz if

(a) The dielectric loss is negligible

(b) The dielectric loss is 10% of the total.

dBNp

mneperfcfc

686.81

/21

GCandRL

22

0

0

GZ

Z

R

Solution:

(a) The dielectric loss is negligible means that the leakance is zero and there is no

variation of G with frequency. This implies that the second term in the expression

for attenuation coefficient is absent i.e.

(b) Dielectric loss at 1 MHz = 0.35dB/m

Conductor loss at 1 MHz = 3.5 – 0.35 = 3.15 dB/m

fc1

mdBMHzatlossMHzatLoss /725.3101

10414

6

6

mdBMHzatLoss /7.725.3101

10435.0

101

10415.34

6

6

6

6

• Phase change Coefficient. A current or voltage wave travels along a line with

velocity and so the current or voltage at the end of a unit length lags the current or

voltage entering that length. The phase difference between the line currents or

voltages at two points which are unit distance apart is known as the Phase-change

coefficient of the line and it is measured in radians per unit distance.

• For a line of length unit distances in length the received current will lag the

sending-end current by

Example. A correctly terminated transmission line has and

and is 3m long. A source, of e.m.f. 2V, is applied to the sending-end terminals of

the line. Calculate

(a) The magnitude of the received current

(b) Its phase relative to the sending-end voltage.

l

l

mdBZ /1,5000

m/300 500

• Solution.

Since the line is correctly terminated its input impedance is equal to its characteristic

impedance. Therefore

(a) Line loss = 3 x 1 = 3 dB

The load and input impedances are both 500 ohms and so use may be made of the expression

Thus

(b) The phase shift introduced by the line is

mAI s 2500500

2

ratiocurrentdBinnAttenuatio 10log20

mAII

rr

22

log203 10

00 90303

• Phase Velocity of propagation. The phase velocity, , of a line is the velocity which a

sinusoidal wave travels along that line.

• Any sinusoidal wave travels with a velocity of one wavelength per cycle. There are

cycles per second and so a wave travels with a velocity of metres per second i.e.

In one wavelength a phase change of 2pi radians occurs, and hence the phase change

per metre is

radians, and is also equal to the phase-change coefficient. Thus

and

meters per second.

pv

f

f

ondpermetresfvp sec

2

22 or

fvor p

22

ANTENNAE

• An antenna is defined according to IEEE standard as a means for radiating or receiving radio

waves.

• The antenna is the transitional structure between free-space and the guiding device or

transmission line which may take the form of a coaxial line or a waveguide and it is used to

transport electromagnetic energy from the transmitting source to the antenna (transmitting),

or from the antenna (receiving) to the receiver.

•

RL is used to represent the conduction and dielectric losses associated with the antenna while Rr, referred to as the

radiation resistance , is used to represent radiation by the antenna

Matching

The losses due to the line, antenna, and the standing waves are undesirable.

The losses due to the line can be minimized by selecting low-loss lines while those of

the antenna can be decreased by reducing the loss resistance represented by RL.

The standing waves can be reduced, and the energy storage of the line minimized, by

matching the impedance of the antenna (load) to the characteristic impedance of the

line.

Current and Voltage Distribution in Resonant Antennae

• A resonant antenna is one which is an integral number of wavelengths in length, for example

the half-wavelength dipole shown

• To determine the current and voltage distributions in a resonant antenna consider a

transmission line that is one wavelength long with an open circuit output

The open circuit transmission line

Incident and reflected currents at a

quarter wave length intervals along a

loss-free open-circuit line

The r.m.s. value of the total current at

each point

• The standing wave obtained above is also obtained if the line is open out through 90 degree to form

a dipole antenna and the r.m.s. current and voltage distributions on a half-wave dipole are shown

Current and voltage distribution on a half wave dipole showing a) r.m.s. values b) peak values

Current distribution on Linear dipole

TYPES OF ANTENNAE

Wire antennae: There are various shapes of wired antenna such as straight wire (dipole), loop,

helix which are shown below

TYPES OF ANTENNAE

Aperture antennae: Some forms of aperture antenna are shown below. Antennae of this type

are very useful for aircraft and spacecraft application because they can be very conveniently

flush-mounted on the skin of the aircraft or spacecraft.

TYPES OF ANTENNAE

Microstrip antennae: They are very popular for spaceborn, government and commercial

applications. They consist of a metallic patch on a grounded substrate. The metallic patch can

take many different configuration but rectangular and circular patches shown below are more

popular because of ease of analysis and fabrication.

TYPES OF ANTENNAE

Array antennae: There are many applications that requires radiation characteristics that may

not be achievable by a single element. In this case it is possible that an aggregate of radiating

elements in an electrical and geometrical arrangement (an array) will result in the desired

radiation characteristics Typical examples of arrays are shown below.

TYPES OF ANTENNAE

Reflector antennae: There Because of the need to communicate over great distances,

sophisticated forms of antennae. A very common antenna form for such an application is a

parabolic reflector shown below

FUNDAMENTAL PARAMETERS OF ANTENNAE

To describe the performance of an antenna, definitions of various parameters are necessary. Some

of the parameters are interrelated and not all of them need be specified for complete description

of the antenna performance.

Some of the parameters are:

Radiation pattern

Radiation power density

Radiation Intensity

Beamwidth

Directivity

Antenna Efficiency

Gain

Beam Efficiency

Bandwidth

Polarization

Input Impedance

An antenna radiation pattern or simply antenna pattern is defined as a mathematical function or graphical

representation of the radiation properties of an antenna as a function of space coordinates. It is the angular distribution of

the radiated fields. The radiation pattern is determined in the far field.

Radiation properties includes: Power Flux Density, radiation intensity, field strength, directivity, phase or polarization.

Radiation property of most concern is the 2 or 3 dimensional spatial distribution of radiated energy as a function of the

observer’s position along a path or surface of constant radius

A trace of the received electric or magnetic field at a constant radius is called the amplitude field pattern.

Often the field and power patterns are normalized with respect to their maximum value, yielding normalized field and

power patterns.

Power patterns is usually plotted on a logarithmic scale in dB (desirable because it can accentuate in more details those parts of the

pattern that have very low values(minor lobes) )

Field pattern (in linear scale) typically represents a plot of the magnitude of the electric or magnetic field as a function of

angular space

Power pattern (in linear scale) typically represents a plot of the square of the magnitude of the electric or magnetic field as

a function of angular space

Power pattern (in dB ) represents the magnitude of the electric or magnetic field in dB as a function of angular space.

Radiation Pattern.

Radiation Pattern lobes Various parts of a radiation pattern are referred to as lobes which may be sub-classified into Major or

Minor, side or back lobes. A radiation lobe is a portion of the radiation pattern bounded by regions of

relatively weak radiation intensity.

Radiation lobes and beam width of an antenna Linear plot of power pattern and its associated beamwidth

A major lobe ( also called main beam) is the radiation lobe containing the direction of maximum radiation. It is

pointing in the direction of teta = 0

A Minor lobe is any lobe except a major lobe. Usually represent radiation in undesired directions and should be

minimized.

A side lobe is a radiation lobe in any direction other than the intended lobe.

A back lobe is a radiation whose axis makes an angle of approximately 180 degrees with respect to the beam of

an antenna

• The level of minor lobes is usually expressed as a ratio of power density in the lobe in question to that of

the major lobe. This ratio is often termed the side lobe ratio or side lobe level. Side lobe levels of -20 dB

or smaller are usually not desirable in most application.

• Attainment of a side lobe level smaller than -30 dB usually requires very careful design and

construction. In most radar systems, low side lobe ratios are very important to minimize false target

indications through the side lobe.

Lobe’s level

Calculating the Half power (-3 dB) relative to the maximum value of the

pattern

You set the value of the

• Field Pattern at 0.707 value of its maximum.

• Power pattern (in a linear scale) at its 0.5 value of its maximum

• Power pattern ( in dB) at -3 dB value of its maximum

Two-dimensional normalized patterns of a 10 element linear

All three patterns yields the same angular separation between the two half-power points, 38,64 degrees.

This is refereed to as HPBW as shown in the figures above.

All three The plus (+) and minus (-) signs in the lobes indicate the relative polarization of the amplitude

between the various lobes which changes alternately as the nulls are crossed

Three and two dimensional power pattern

Types of Pattern

Isotropic radiator: is defined as a hypothetical lossless antenna having equal Radiation in all direction

although it is only an idea and not physically realizable. Often taken as a reference for expressing the

directive properties of actual antennae.

A directional antenna: is one having the property of radiating or receiving electromagnetic wave more

effectively in some direction than others

Omnidirectional pattern is one having essentially nondirectional pattern in a given plane. It is a special

type of a directional pattern

Radiation Power Intensity

HEW

W 2mW

mV

mA

E

H

Electromagnetic waves are used to transport information through a wireless medium or a guiding

structure, from one point to the other. The quantity used to describe the power associated with an

electromagnetic wave is the instantaneous Poynthing vector defined as

Where

instantaneous Poynthing vector

instantaneous electric field intensity

instantaneous magnetic field intensity

Radiation Intensity (power pattern) in a given direction is defined as the power radiated from

an antenna per unit solid angle.

radiation intensity

radiation density

radWrI 2

I

radW2mW

anglesolidunitW

Total power radiated by an antenna is given by

integrating the radiation intensity U over the entire

solid angle of 4 pi

For an isotropic antenna, radiation intensity will be

independent of teta and phi

04 IPrad

ddIradP sin

2

0 0

Beamwidth

Associated with the pattern of an antenna is a parameter designated as beamwidth. The beamwidth of a

pattern is defined as the angular separation between two identical points on opposite side of the pattern

maximum.

In an antenna pattern, there are a number of beamwidths. One of the most widely used beamwidths is the

Half-Power Beamwidth (HPBW) which is defined as: In a plane containing the direction of the

maximum of a beam, the angle between the two directions in which the radiation intensity is one-half

value of the beam

Another important beamwidth is the angular separation between the first nulls of the pattern, and it is

referred to as the First-Null Beamwidth (FNBW).

Both HPBW and FNBW are demonstrated

Example

The normalized radiation intensity of an antenna is represented by

The two dimensional plot of this plotted in a linear scale, is given below. Find

a. Half-Power Beamwidth HPBW (in radians and degrees)

b First-Null Beamwidth FNBW (in radians and degrees)

Solution

a Since radiation intensity represents the power pattern, to find the half power beamwidth you

set the function equal to half of its maximum, or

036000,09000,32

cos2

cos I

hh

hh

I

hh

3cos

707.01cos

707.03coscos

5.032cos2cos This is a transcendental function, it can be solve

iteratively and this gives: 03725.14251.0 radians

h

Since the function for power pattern is symmetrical

about the maximum at teta = 0, then the HPBW is

0745.28502.02 radianshHPBW

Solution

b To find first null beamwidth (FNBW), you set the power pattern equal to zero, or

This leads to two solutions for teta

032cos2cos

nn

I

The one with the smallest value leads to the FNBW.

Again because of the symmetry of the pattern

030

6 radiansn

060

32 radiansnFNBW

01

01

306

0cos3

103cos

902

0cos0cos

radians

radians

nn

nn

Directivity

• The directivity of an antenna is defined as the ratio of the radiation intensity in a given

direction from the antenna to the radiation intensity averaged over all direction

• The average radiation intensity is equal to the total power radiated by the antenna divided

by 4 pi.

• If the direction is not specified, the direction of maximum radiation is implied

radrad P

I

P

I

I

ID

4

40 radrad P

I

P

I

I

ID maxmax

0

maxmax

4

4

)(

)(int

)(intmax

)(int

)(dimmax

)(dim

0

max

max

WpowerradiatedtotalP

anglesolidunitWsourceisotropicofensityradiationI

anglesolidunitWensityradiationI

anglesolidunitWensityradiationI

ensionlessydirectivitimumD

ensionlessydirectivitD

rad

Directivity

• Example:

• Find the maximum directivity of an antenna whose radiation intensity is described as

• Solution

• The radiation intensity is given by

• The maximum radiation intensity occurs in the direction along

2

0 sin

r

AWrad

sin0

2 AWrI rad

0max AI

2

radP

ID max

max

4

2

0 0

2

0 00

22

0 sinsin AddAddIPrad

27.144

0

2

0max

A

AD

Antenna Efficiency

RI 2

Antenna efficiency takes into account the looses at the input terminals and within the structure of the

antenna. Such losses may be due to

Reflections because of mismatch between the transmission line and the antenna

The losses

In general the overall efficiency e can be written as

Radiation efficiency

Reflection efficiency

cde

re 2

Γ1r

e

cde

re

de

ce

re e

Antenna Gain

• Is the ratio of the intensity , in a given direction, to the radiation intensity that would be

obtained if the power accepted by the antenna were radiated isotropically

• The total radiated power is related to the input power through the radiation efficiency

according to the equation

• If an antenna is lossless then the radiation efficiency is equal to 1, and the Gain is the same

as the directivity.

• A loss which is not taken into account in the gain is that due to mismatch or reflection

between antenna and transmission line which when taken into account we introduce

absolute Gain

inP

I

poweracceptedinputtotal

ensityradiationGain

,4

)(

int4

incdradPeP

,,,

4, DeGP

IeG

cd

rad

cd

,,,, GeGeeGeGcdrrabs

Example

• A lossless resonant half-wavelength dipole antenna, with input impedance of 73 Ohms, is

connected to a transmission line whose characteristic impedance is 50 Ohms. Assuming that

the pattern of the antenna is given approximately by

Find the maximum absolute gain of this antenna.

• Solution:

3

0sinBI

radP

ID max

max4

4

3sin2sin,

2

00

4

0

2

0 00max

BBddIPBIrad

697.13

164 max

max

radP

ID

297.2697.1log10

697.11

10max

maxmax

dBG

DeGcd

maxmaxmaxGeeGeG

cdroobs

cdcdro

eeee 2

1

965.015073

50731

12

2

cdo

ee

6376.1697.1965.0maxmax

GeGoobs

142.26376.1log1010max

dBGobs

• BANDWIDTH: The bandwidth of an antenna is defined as “the range of frequencies within

which the performance of the antenna, with respect to some characteristic, conforms to a

specified standard.

INPUT IMPEDANCE: The input impedance is defined as “the impedance presented by an

antenna at its terminals. This is made off the resistive part and the reactive part.

• The resistive part also made of

• The radiation resistance is the property of the antenna which characterizes the conversion of

electrical energy into radio wave instead of heat.

• The loss resistance of the antenna is the property of the antenna which characterizes the

conversion of electrical energy into heat.

• For maximum power transfer to the antenna of input impedance and a

transmission line with impedance

AAAjXRZ

LrARRR

AAAjXRZ

LLLjXRZ

LA

gLr

XX

RRR

• The Friis Transmission Equation relates the power received to the power transmitted

between two antenna separated by a distance

• Where D is the largest dimension of either antenna.

If the transmitted power is ,

Then the isotropic power density at a distance from the antenna is

For a non-isotropic transmission antenna power density in the direction we

can write

Since the effective area of the receiving antenna is related to its efficiency and the

directivity by

The power collected by the receiver

22DR

0W

tP

Friis Transmission Equation

R

204 R

PeW t

rad

tt ,

22 4

,

4

,

R

DPe

R

GPW trtt

radtrtt

t

rece

rD

4,

2

rrrrecr DeA

22

222

.,,4

114

, rtrrrtttttcdrcdttrrrecr DDR

eeWDeP

The above formula takes into account the conduction-dielectric losses(radiation efficiency) of the transmitting and receiving

antennae, reflection losses (reflection efficiency) and polarization losses (polarization loss factor or polarization efficiency).

• The radar cross section (RCS) or echo area of a target (scattering object) is define as the

ratio of power density of the signal scattered in the direction of the receiver to the power

density of the radio wave incident upon the scattereing object and has units of square

meters.

The radar range equation relates the power delivered to the receiver load to the input power

transmitted by an antenna, after it has been scattered by a target with a radar cross section

The above formula takes into account the conduction-dielectric losses(radiation efficiency)

of the transmitting and receiving antennae, reflection losses (reflection efficiency) and

polarization losses (polarization loss factor or polarization efficiency).

Radar Range Equation

22

21

22.

44

,,11 rs

rrrttttttcdrcdtr

RR

DDPeeP

• Example:

• Two lossless antennae in the band (8.2 – 12.4 GHz) are separated by a distance of 100

lamda. The reflection coefficients at the terminals of the transmitting and receiving antennae

are 0.1 and 0.2 respectively. The maximum directivities of the transmitting and receiving

antennae are 16 dBi and 20 dBi respectively. Assuming that the input power in the lossless

transmission line connected to the transmitting antenna is 2W, and the antennae are aligned

for maximum radiation between them and polarization-matched, find the power delivered to

the receiver.

We assume the excitation as a time-harmonic signal

at the frequency , which results in a time-

harmonic radiation.

The length of the antenna L is assumed to be much

less than the wavelength:

L << . Typically: L < /50.

The antenna is also assumed as very thin:

ra << .

The current along the antenna is assumed as

uniform:

Electric dipole antenna

A reasonable approximation for the current distribution is

( ) sin 2mI z I k L z

1 2

cos cos cos2 2

cos cos cos2 2

sin

sinsin

a

kL kL

F F

L k

F

k L

Where F() is the radiation pattern:

k is the wave number.

1 2

cos cos cos2 2

cos cos cos2 2

sin

sinsin

a

kL kL

F F

L k

F

k L

The radiation patter F() is :

k is the wave number.

The first term, F1() is the radiation characteristics of one of the elements used to make up the complete

antenna – the element factor. The second term, Fa() is the array (or space) factor – the result of adding all

the radiation contributions of the various elements that form the antenna array as well as their interactions.

L = /2 L = L = 3/2 L = 2

The E-plane radiation patterns for dipoles of different lengths.

If the dipole length exceeds wavelength, the location of the maximum shifts.

Loop antenna

A loop antenna consists of a small

conductive loop with a current

circulating through it.

We have previously discussed that a

loop carrying a current can generate

a magnetic dipole moment. Thus, we

may consider this antenna as

equivalent to a magnetic dipole

antenna.

If the loops circumference C < /10

The antenna is called electrically small. If C is in order of or larger, the antenna

is electrically large. Commonly, these antennas are used in a frequency band from

about 3 MHz to about 3 GHz. Another application of loop antennas is in magnetic

field probes.

Antenna parameters

In addition to the radiation pattern, other parameters can be used to characterize

antennas. Antenna connected to a transmission line can be considered as its load,

leading to:

1. Radiation resistance.

We consider the antenna to be a load impedance ZL of a

transmission line of length L with the characteristic

impedance Zc. To compute the load impedance, we use

the Poynting vector…

If we construct a large imaginary sphere of radius r

(corresponding to the far region) surrounding the

radiating antenna, the power that radiates from the

antenna will pass trough the sphere. The sphere’s radius

can be approximated as r L2/2.

Small values of radiation resistance suggest that this antenna is

not very efficient.