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ANTENNA AND PROPAGATION

The electrical signal can then be converted in different forms of energy depending on the

intelligence of the message signal. One of the signals is sound which come out through a

speaker.

Other signals will include data (text) and images.

Antenna Parameters

These are properties used to describe antenna operations usually obtained from other parameters

which the antenna deals with like power voltage and impedance.

They include;

Impedance

Impedance matching

Effective area

Half power beamwidth

Bandwidth

Radiation pattern

Aperture

Efficiency

Directivity

Gain

Polarization

1. Impedance(Z)

The opposition of flow of current through the antenna as measures between the terminals. It is

referred to as impedance become the antenna deals with ac.

It depends on several factors which include.

Material type

Length of the antenna


Capacities effect and inductive effects

Capacitive effect is a function of the dielectric properties of the material i.e. permittivity.

Inductive effect is a function of permeability.

It is very important parameter in the design of antenna since it will affect the flow of electrical

signal being transmitted received.

If the impedance is so high it will attenuate the signal highly leading to poor transmission or

reception.

It is also important parameter in the design of antenna since it will affect the flow of electrical

signal being transmitted or received.

If the impedance is so high it will attenuate the signal highly leading to poor transmission or

reception.

It is also important when dealing with impedance matching.

2. Impedance Matching

Is the process of ensuring that the impedance between two devices being connected together

appear to the same. The impedance should be the same at the point of connection.

This is to reduce power losses i.e. ensure maximum power transfer.

For an antenna this is considered as between the transmission line and the antenna terminals.

If the impedance not matched then the signal will be reflected back.

The following explains the matching between the line and the antenna.


Z

load

Z line

Z line

Vo

V2

The other parameters that shows the level of impedance matching are given by, Reflection

coefficient ( ) , voltage standing wave Ratio (VSWR) and return loss (RL).

They depend on the line impedance and load impedance which affect the reflected voltage

signal.

Reflection coefficient

Is the ratio of the reflected voltage signal to the incoming voltage signal

Can also be determined from the impedance i.e. line and load


For an ideal case the reflection coefficient should be given as O indicating that no voltage is

reflected back i.e. all the voltage signal goes through the load.

Another determining condition is that the Z line= Z load

The worst case will be when the reflection coefficient is 1 or -1 obtained by =

or Z line or

Z load is given by 0.

The most appropriate value of is when it is <10% or <0.1.

Voltage standing wave Ratio

This is the ratio of maximum reflected signal to the minimum reflected signal

VSWR=

When the signal is reflected it results to a standing wave due to the interaction of the input

signal.

refector

The interaction can result to the signal adding or cancelling one another depending on whether

they are in or out of phase.

The VSWR can also be given in terms of reflection coefficient. The acceptable value is given as

return loss.


Return Loss

Is also a function of reflection coefficient and it indicates the loss in dB represented as follows.

RL=-20 Log/ /

The acceptable value around >10db

3. Bandwidth

This is the frequency range of operation of an antenna. This determines the ability of an antenna

to select the frequency it will be able to receive.

This is affected by the impedance matching of the antenna system.

If an antenna is able to operate in large frequency range then the receiver(internal circuitry).

The high the frequency range it can operate the better.

4. Bandwidth

This is the frequency range of operation of an antenna. This determines the ability of an antenna

to select the frequency it will be able to receive.

This is affected by the impedance matching of the antenna system.

If an antenna is able to operate in large frequency range then it can receive signals which can be

selected by the receiver (internal circuitry).

The high the frequency range it can operate the better.

5. Effective area aperture

This is the area of the antenna as seen by the signal.

It determines the amount of signal that can be received by an antenna.

It is commonly applied with the receiving antenna.

It depends on the gain of the antenna and the frequency of operation.


It is mathematically represented as

λ=Operation Wavelength

G=Antenna Gain

The high it is the better the antenna since it will enable the antenna to capture more signal.

6. Radiation Pattern

This is a graphical representation showing the distribution of radiation intensity with respect to

a given angle.

It can show whether an antenna is directive or not.

It can be shown in 2D or 3D form.

It can be in terms of electric field or magnetic field.

In 2D it can show the electric field variation or magnetic field variation.

For an isotropic variation it is supposed to be circular.

Z

Electric field

x

Magnetic field


3D Rep

The X, Y and Z are considered

z

y

x

The radiation is in all directions for an isotropic radiation it forms a sphere for a directive

antenna the following is expected.

OR

The 2D equivalent of the above is given as follows where one fakes the cross section of the 3D.


Directive toward the front and back

Lobes

Isotropic radiation pattern.

IRP is only theoretical since it cannot be achieved practically. The closest one can achieve is that

of a dipole antenna which has an equivalent of the following radiation pattern.

For one to obtain the radiation pattern of electrical field then the azimuth angle should be kept

constant and for magnetic field the elevation angle should be kept constant.

Omnidirectional antennas (dipole) are used in applications which require transmission in all

directions.

Examples include radio & TV transmission and mobile rural area transmission.

Directive antennas are applied in areas with huge population density to provide them with the

required capacity e.g. mobile communication will require use of directive antennas serving

sectorized areas i.e. urban areas.


For 3 sectors

antennas

Another application for directive antennas is in satellite communication systems and radar

systems e.g. horn, parabolic antenna.

The radiation is a very important antenna design parameter.t

The design should be such that to reduce sidelobes and increase the mainlobe. This will increase

the antenna efficiency.

7. Antenna efficiency

This is the ability of the antenna to transform all the energy to expected output energy.

This can happen if losses are reduced to minimum.

It’s a function of the input power output power and reflection coefficient.

There are two forms which when combined give total efficiency these are given by reflection

efficiency(er).

| |

-is the reflection coefficient

the higher the reflection coefficient the lower the


the other forms is referred to as radiation efficiency(e radiation)

The higher the radiated power the higher the efficiency.

The total efficiency is given by the product of the two

Can only be 100% for an ideal antenna.

Acceptable values are form 60%-90% most practical antennas will achieve up to 60%.

Factors which affect efficiency

1. Antenna mismatch

Cable antenna

Polarization mismatch

2. Material-affects the resistance

3. Antenna length

4. Weather

5. Temperature

7. Half power beam width(HPBW)

This is the angular distance between the two lines drawn from the centre to 3 dB down of a given

directive radiation pattern.

HPBW


It can be used to determine the coverage of a given antenna.

The higher it is the better the coverage.

It is a function of the antenna type (design) which will affected the power transmitted in a given

direction.

It determines the directivity of the antenna.

Antenna types

There are different types of antennas classified according to

Construction

Operation

Application

Directivity (D)

Considered as the ratio of radiation intensity in a given direction to the radiation intensity

averaged over all directions.

The radiation intensity ( -This is also one of the antenna parameters which indicates the

radiation of power over the solid angle.

where

-radiated Power

Ω-solid angle


the area under consideration

-eleveation angle

Azimuth angle

∫

∫ ∫

Directivity is given by

Average over all directions

In a given direction

(

Graphically the directivity is related to the radiation e.g. a high directivity antenna will have the

following radiation pattern.


Radiation in a given air

An omnidirectional antenna is not directive has the following pattern

A highly directive antenna will radiate more in a specific direction or applied to omni directional

antenna.

Gain of Antenna (G)

This is defined as the ratio of radiation power intensity in a given direction to the radiated power

intensity by as Isotropic source (antenna).

It depends on the radiation efficiency and directivity of a given antenna.

Mathematically represented as

G=

Where

Radiation efficieny

D-directivity

The gain of the antenna will depend on the applications where an antenna can be considered to

have an appropriate gain for a particular application


Gain can be given in dB

G dB=10logG

The higher the radiation efficiency of directivity then the higher the gain for any antenna to be

designed the gain is a very important parameter.

Radiation resistance (Ω)

This is a part of the antenna impedance which is the opposition of flow of current. It is given by

is the radiation Power

I is the current

average done on the power

Polarization

This is the orientation of an electromagnetic wave as it moves from the antenna to far distance.

This is also the wave will look like in space as it travels from the source antenna.

There are three main types

Linear

Circular

Elliptical


Linear

It’s an orientation that follows a straight line. It is either the horizontal or vertical.

horizontal

vertical

This is with respect to the earth surface.

Sometimes the interfaces can cause or change of this orientation vertical to the horizontal and

vice versa.

Circular

This is where the signal (waves) follows a circular pattern as it moves in space.


Elliptical

This is a pattern which forms an ellipse. This is the most commonly used form of orientation

Minor axix

Major axis

For an elliptical one can obtain the axial ratio

Antenna types

There are different types of antennas classified according to

Construction

Operation

Application

But most commonly they are classified according to their construction. There are several

categories under which we have several types. These categories include

Wire antennas

Travelling wave antennas

Reflector

Aperture antennas


Log periodic antennas

Other classes-NFC, Fractal

1. Wire antennas

These are constructed using wires (conductive)

These are considered to be the simplest in terms of construction and operation

Rays can be straight, coiled or folded they include

Small dipole antenna

General dipole antenna

Half wave antenna

Broadband antenna

Folded

Monopole antenna

Loop antenna


These wire antennas are modeled using the horizontal dipole antenna as represented in diagram

below.

Ø

Φ

Z

y

x

They are modeled based on the wavelength at which they are operating. This operation will

incorporate the electric and magnetic at a distance r from its location.

As the distance (r) increases the above quantities reduce and hence power at that distance.

(

The power reduces with the inverse of the distance squared. All the other parameters are

obtained from the amount of electric and magnetic field at a distance r.

For the above antenna the electric field E and magnetic field are given as below

∫


Characteristic impedance

wave length

The peak supplied current

length of the antenna

For the above mentioned parameters there is a direct relation with the amount of electric field at

a given distance. The more there are the more the electric field.

This is the distance from the antenna where the electric field is measured is inversely

proportional to the electric field measured

-is the sine of the angle it has a directed relationship with the electric field.

Indicates the oscillation of the electric field which decreases or increase exponentially.

The electric field is basically in the direction where

is spherical coordinates

The magnetic field will be given by

The average power at a given point is determined by the following


Power radiated is given by

( )

This is obtained by integrating the average power as follows

∫ ∫

Antenna parameters

Impedance of this antenna is given by

Where

Resistive component

reactance

The R is usually a function of radiation resistance.

X is the reaction which depends on the length of the antenna and the frequency of the operation.

In which case at resonance the impedance reduces to resistance all resonance

At resonance

The radiation resistance is given by


from

(

)

(

)

The radiation resistance is part of the total resistance.

The other kind of resistance is the ohmic resistance

The resistance should be in such a way that it will be easier for one to achieve impedance

matching.

This value should be close to prevent reflection losses

The dipole the resistivity part is usually 73Ω

Pattern FuntionF(

For this antenna the pattern function is a function of specifically is given by

(

This gives the radiation pattern of an antenna mostly in ideal cases

Φ


Radiation Intensity

This is the amount of radiation in a given direction for this antenna

(

(

)

( | |

This is given by the following pattern

45

45

Because of the the pattern is not a pure sinusoid

HALF POWER BEAM WIDTH(HPBW)

This is determined using the radiation intensity pattern.

From the figure above the resulting HPBW is =450+45

0=90

0

This is not highly directive.

The parameters is considered at 3db down from both sides

Directivity D(

For the antennas directivity is given by

( (


(

)

(

)

(

is when sin=

Gain

(

Efficiency

( | |


Short dipole antenna

It has an open in both sides

antenna

source

It is constructed by taking the two wires and feeding them as shown above. It is equivalent to the

wire which is open at the middle where the following is done. It is referred to as short since its

length is usually considered to be less than the tenth of the wavelength at which it operates.

Where

L-length

Λ-Wavelength

The current distribution for this kind of antenna is given by

( ( | |

)

Where

is the peak current


length

distance

I(Z)

-LL

Most parameters of these antennas are actually similar to once mentioned or discussed for the

Hertzian dipole antenna.

Application is in the TV for indoor where the signal levels is excellent

General dipole antenna

This is the antenna includes the analysis of all antennas and their general properties.

The current distribution is given by

( ∑ (

)

( )


The plots of the distributions of

and λ are given above.

The electric field of this antenna is given by

∫

∫

(

Where the function

(

L=length of the antenna

The ( is the radiation pattern function which varies with change in the length.


The radiation pattern for

,λ and 1.5λ are given as follows

1.5 λ Is the most directional directive when compared with the other two in 3D the patterns

will be as follows

1.5λ


The impedance of this antenna is given by the usually impedance as follows

For different lengths one can be able to plot the impedance as follows

+ve 1000

-100 Ve

00.5 2 1.5 2 length

-x

For the lower values i.e. less than the impedance is capacitive while at the higher values is

inductive

At slightly less than

precisely around 0.48λ the impedance is pure resistive.

At this point the antenna resonates in which case the capacitive reactance is same as inductive

reactance.

The directivity of this antenna also varies with the change in the length.


A plot of the same is given below

directivity

5

4

3

2

1

0.5 1 1.5 2 2.5 3

They resonate at odd multiples of

i.e. 0.5,1.5,2.5……………

Half wave dipole antenna

This is a special kind of dipole antenna.

It has the following kinds of parameter characteristics

Its length is half of the wavelength of the frequency used in communication.

For instance if the frequency is 300 MHz then the length will be given as


(

and are the same

The radiation pattern is given as follows

The HPBW is given by

Its impedance is given as

It is noted that this antenna is inductive since the x value is positive

If the length is reduced slightly to around then the antenna will be pure resistive.

This practice is applicable for easier impedance matching.

The directivity of this antenna is given by

D=1.64 and dB

Broadband dipole antenna

It is basically a dipole antenna with larger radius when the radius of this antenna is increased its

bandwidth will also increase.


It also has one effect on the length which reduces in size

0.05

0.015

0.01m

Su

length

From the plot above antenna with a larger radius compared with wavelength it will have a large

bandwidth but shorter length.

These antennas are preferred in high BW applications


Monopole antenna

The monopole has half the length of dipole antenna

L

Infinite conductivity ground

plane

L

L

dipole

Most of its characteristics will be half of the dipole antenna.

Taking a half wave dipole the monopole will have a length of


It also omnidirectional just like the dipole antenna

Its impedance is also given as

It is also inductive since X value is positive.

The directivity of the antenna is given by

Folded dipole antenna

feed

length

d

It is constructed by the two end of the dipole antenna.

When the ends are stretched to a width of a while. The length is given by L

It is analyzed using the concept of transmission lines.


It is assumed to two parallel lines.

The impedance is approximated as

Where

Transmission line impedance

dipole antenna impedance

Where

is the initial impedance

wave number

length of line

Loop antenna

Z

X

Y


It is actually circular in nature and can be taken to be i.e on the X-Y plane.

It has a radius of which is usually considered to be less than the wavelength.

Also called the magnetic antenna since it is mostly inductive.

A small current passing through the loop will actually result to magnetic field.

As opposed to small dipole antenna which actually result to capacitive reactance the loop

antenna results to inductive reactance.

The electric field is the azimuth as opposed to for dipole antenna which is in elevation.

The E field is given by

The magnetic field is actually negative and given by

Where

Ω-Is the intrinsic impedance

-Is the wavelength number

-Is the radius of the loop

-Is the radius of the current

-Is the distance of measurement

-Is the elevation angle

-Azimuth angle


The pattern function given by a function of

(

The radiation resistance is given by

(

Which can be computed as

(

)

Where

N=Number of turns

S=Loop surface area

Λ=Wavelength

These antennas have a high bandwidth but very high input impedance that makes them difficult

to match therefore are basically preferred for reception.

For very small loop antennas the reactive component is usually given by

(

)

Where

frequency

permeability

radius

radius in consideration


This antenna is usually preferred for the use with systems that are used close to the body.

This is because our bodies are largely capacitive compared will affect the electric field a

lot(conductive electric field) as opposed to magnetic field.

For instance mobile phones and wireless body networks, Bluetooth phones as the radius of the

loop antenna increases its impedances tends more pure resistance.

Travelling wave antenna

These are antennas that have moving current along their operating axis.

They incude

Helical

Yogi uda antenna

Spiral antenna

Helical antenna

It is antenna which is constructed by taking a wire and coiling it in space.

These will make a pattern equivalent to a cock screw.

Some of the most important parameter include

Diameter of the coil D

Height of the antenna H

Separation between two connective coils

The angle that will determine the separation

The ground plane.

The number of turns N

Diameter gives the circumference C which lies between the following

for better operation


The angle

α

L

S

The impedance of the antenna is pure resistive and is given by

The radiation pattern is a function of where it sketched as below

E-Plane


H-Plane

The half power beam width is also given as

√

Where N is the number of turn

S is the separation

λ is the wavelength

The gain of this antenna is around 8.3 as an approximation but can be given by the following

formula.

The axial ratio depends on the number of turns and is given by


It’s circularly polarized which can either be to the left or to the right. For instance the above has

eight polarizations because of the way it’s constructed.

It has several advantages which include

High bandwidth

Easy to construct

Has pure resistance

Yogi uda antenna

Is one of the most commonly used antennas in TV reception and considered as the most brilliant

invention in terms of antennas.

It was invented by uda and Yogi did analysis in English from Japanese in 1929.

One of the most important parameter that made it to be famous is the easy of design and

construction and the high gain of up to around 19 distances 10dB

Construction

Support

Director

Reflector

Feeder

The reflector is the longest of all the elements.

This because of the two reasons.

Increase the surface area which leads to a higher reflection.


When longer than the feeder then it is inductive and therefore the current lags the voltage

Feeder has a wavelength close for the resonance and is approximately

Can be a dipole or a folded dipole.

This is when the terminals are connected.

The director elements are after the feed and are shorter in length.

This makes them capacitive enabling different phases which will result to travelling have in a

given direction.

This is supported by the reflector.

They form an array. It is an array antenna

End five array types antenna

Factors which affect the gain of this antenna

The reflector

Number of reflector even though to a small extent

Distance between the director elements

Surface area of the element.

The size of the element support


The radiation pattern is given as

E-Plane

H-Plane

Commonly used in reception of the range in frequency HF to UHF

It can be designed and implemented using experimental data provided where change of different

parameters has been done to obtain optimal parameters.

For instance the distance between the elements is 0.2m for optimal performance.

Most data for its design is provided in several papers and books

Spiral antennas

This is considered as frequency independent antenna

It can give good performance for a very large range of frequency for instance from around 3Ghz-

300Ghz.


Structural consideration

Spiral length-The large is it is the better the performance

Surface area the larger it is the better the performance

Flare distance rate of growth is determined by the wider the better

Radius

Field structure

Number of turns

Around 1.5 will give the best performance

Radius

It is very small then it becomes capacitive it needs to be larger.

It finds applications in wideband.

It has a circular polarization which can either be right or left.

Reflector antennas

Operates on principal of reflection like the parabolic dish antenna which are commonly used in

satellite and radar systems communications one of the most important parameters is the aperture

area which will affect the gain of the antenna to a great extent.

They are directive and can transmit long distances


dish

feed

They have a large directive gain.

Their impedance will highly depend on the material and their feed design.

Aperture antennas

One of the antennas under this is the horn antenna

There operation and construction is similar to those of a parabolic dish antennas.

Commonly used in waveguides


Micro strip antennas

One of the most commonly used is the patch antenna

substrate

Antenna(Metallic)

Transmission

lines

It has a metallic printed section on a substrate feed from transmission line.

Commonly used in small devices and more so integrated devices where the antenna is printed.

Affected by the size but design can allow the reduction of size with increase performance.

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