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Compiled by OMAE OTERI ©2013 1
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
Compiled by OMAE OTERI ©2013 2
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.
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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
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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.
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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.
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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
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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.
Compiled by OMAE OTERI ©2013 8
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.
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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
Compiled by OMAE OTERI ©2013 10
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
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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
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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.
Compiled by OMAE OTERI ©2013 13
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
Compiled by OMAE OTERI ©2013 14
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
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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.
Compiled by OMAE OTERI ©2013 16
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
Compiled by OMAE OTERI ©2013 17
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
Compiled by OMAE OTERI ©2013 18
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
∫
Compiled by OMAE OTERI ©2013 19
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
Compiled by OMAE OTERI ©2013 20
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
Compiled by OMAE OTERI ©2013 21
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
Compiled by OMAE OTERI ©2013 22
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
( (
Compiled by OMAE OTERI ©2013 24
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
Compiled by OMAE OTERI ©2013 25
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
( ∑ (
)
( )
Compiled by OMAE OTERI ©2013 26
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.
Compiled by OMAE OTERI ©2013 27
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
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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.
Compiled by OMAE OTERI ©2013 29
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
Compiled by OMAE OTERI ©2013 30
(
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.
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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
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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
Compiled by OMAE OTERI ©2013 33
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.
Compiled by OMAE OTERI ©2013 34
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
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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
Compiled by OMAE OTERI ©2013 36
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
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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
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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
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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
Compiled by OMAE OTERI ©2013 40
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.
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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
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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.
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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
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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
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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.