Antenna & Wave Propagation 3th year Dr. Abdlkhadhum A.

Hasan

Electrical Engineering Department

Chapter Three: Antenna Fundamentals

2.1 Introduction
An antenna is usually metallic device (as a rod or wire) for radiating or receiving radio waves
In other words the antenna is the transitional structure between free-space and a guiding
device. The guiding device or transmission line may take the form of
1- A coaxial line or
2- a waveguide
It is used to transport electromagnetic energy from the transmitting source to the antenna or from
the antenna to the receiver. In the former case, we have a transmitting antenna and in the latter a
receiving antenna as shown in the figure below:

- An antennat converts radio frequency (RF) signal into an electromagnetic (EM) wave of the
same frequency.
- It forms a part of transmitter as well as the receiver circuits.
- Its equivalent circuit is characterized by the presence of resistance (R), inductance (L) and
capacitance (C).
- The current produces a magnetic field and a charge produces an electrostatic
field. These two in turn create an induction field

2.2 Radiation Mechanism

The radiation from the antenna takes place when the electromagnetic field generated by the
source is transmitted to the antenna system through the transmission line and separated from the
antenna into free space

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Antenna & Wave Propagation 3th year Dr. Abdlkhadhum A. Hasan

Electrical Engineering Department

(A) Radiation from a Single Wire

Conducting wires are characterized by the motion of electric charges,which creates of current
flow. Assume that an electric volume charge density, q v (coulombs/m3), is distributed uniformly
in a circular wire of cross-sectional area A and volume V

Current density in a volume with volume charge density q v (C/m3)

At high frequencies, surface current density (Js ) in a section with a surface charge
density qs (C/m2)

Current in a thin wire with a linear charge density ql (C/m)

-To accelerate/decelerate charges, one needs sources of electromotive force and/or

discontinuities of the medium in which the charges move.
- Such discontinuities can be bends or open ends of wires, change in the electrical
properties of the region, etc as shown in the figure.

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Antenna & Wave Propagation 3th year Dr. Abdlkhadhum A. Hasan

Electrical Engineering Department

In summary, for a single wire antenna, it is a fundamental from the principle of radiation
there must be some time varying current with the following.

1.If a charge is not moving, current is not created and there is no radiation
2. If charge is moving with a uniform velocity.
a. There is no radiation if the wire is straight, and infinite in extent
b. There is radiation if the wire is curved, bent, discontinuous, terminated, or
truncated, as shown in Figure
3..If charge is oscillating in a time-motion, it radiates even if the wire is straight

(B) Radiation from a Two Wire

Let us consider a voltage source connected to a two-conductor transmission line which is
connected to an antenna. This is shown in Figure (a). Applying a voltage across the two
conductor transmission line creates an electric field between the conductors.

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Antenna & Wave Propagation 3th year Dr. Abdlkhadhum A. Hasan

Electrical Engineering Department

- The electric lines of force have a tendency to act on the free electrons (easily detachable
from the atoms) associated with each conductor and force them to be displaced.
- The movement of the charges creates a current that in turn creates magnetic field
intensity.
We have accepted that:,
- electric field lines start on positive charges and end on negative charges.
- They also can start on a positive charge and end at infinity, or
- start at infinity and end on a negative charge.
The electric field lines drawn between the two conductors help to exhibit the Distribution
of charge. If we assume that the voltage source is sinusoidal, we expect the electric field
between the conductors to also be sinusoidal with a period equal to that of the applied
source. The creation of time varying electric and magnetic fields between the conductors
forms electromagnetic waves which travel along the transmission line.
The electromagnetic waves enter the antenna and have associated with them electric
charges and corresponding currents. free-space waves can be formed by ―connecting
the open ends of the electric lines (shown dashed). The free-space waves are also periodic
but a constant phase point P0 moves outwardly with the speed of light (c) and travels a
distance of λ/2 (to P1) in the time of one-half of a period.

2.3 Current distribution on a thin wire antenna

Let us consider a lossless two wire transmission line in which the movement of charges
creates a current having value I with each wire. This current at the end of the
transmission line is reflected back, when the transmission line has parallel end points
resulting in formation of standing waves in combination with incident wave. When the
transmission line is flared out at 900 forming geometry of dipole antenna (linear wire
antenna) as shown in the figure below:

Fig. Current distribution on a lossless two-

wire transmission line, flared transmission
.line and linear dipole

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Antenna & Wave Propagation 3th year Dr. Abdlkhadhum A. Hasan

Electrical Engineering Department

the current distribution remains unaltered and the radiated fields not getting cancelled
resulting in net radiation from the dipole with the following cases:

1. If the length of the dipole l< λ/2, the phase of current of the standing wave in each
transmission line remains same.
2. If diameter of each line is small d<< λ/2, the current distribution along the lines will be
sinusoidal with null at end but overall distribution depends on the length of the dipole
(flared out portion of the transmission line)
3- The current distribution for dipole of different length

The current distributions we have seen represent the maximum current excitation for any time.
Also, the current varies as a function of time as well as hown in the figure below:

The dipole arrangement shown in the figure is a very common form of antenna particularly if its
length from tip to tip is equivalent to a half wavelength (l=λ/2) of the signal being radiated.

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Antenna & Wave Propagation 3th year Dr. Abdlkhadhum A. Hasan

Electrical Engineering Department

2.4 Antenna Equivalent Circuit

A sizable proportion of the energy traveling forward along the transmission line from the
transmitter circuit will detach and radiate into free space with equivalent circuit shown in the
figure

Figure The antenna as an interface between a circuit and free space, along with their Thevenin
equivalent circuits; the subscript r on the antenna model stands for “radiation”

2.5 Some Typical Antennas

Antennas are practically classifed either
- According to the operating frequency such as radio frequency antennas or microwave
frequency antennas.
- According to the shape of the antenna such as Wire antenna, Folded antenna, Array antenna,
Horn antenna and Reflector antenna.
- According to the antenna structure such as simple antenna and compound antenna. In general,
they are classified as follows:
1- Simple Antennas: They are called wire antennas. Figure A.8 shows a number of simple
antennas. They are
-Half Wave Dipole and Folded Dipole antennas
- Quarter Wave Monopole and Folded Monopole antennas
Usually used in personal applications, automobiles, buildings, ships, aircrafts and spacecrafts. short
The monopole in Fig. A.8 is commonly used as an AM receiving antenna on motor vehicles…

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Antenna & Wave Propagation 3th year Dr. Abdlkhadhum A. Hasan

Electrical Engineering Department

2- Compound Antennas
compound antennas that are built up from combinations of active antennas, of the types shown in
Fig. A.8, and passive linear elements. Figure A.9 shows two common antennas, they are the
Yagi-Uda array antenna and the log periodic antenna.

Fig. A.9 Some common compound antennas

The log periodic antenna shown in Fig. A.9 is used when operation is necessary over a wide
band of frequencies. Although it is more complex in construction than the Yagi, its wide
operating bandwidth makes it attractive in many applications

3- Aperture Antennas
Figure A.10 shows a number of aperture and slot antennas, such as Horn antenna, Slot antenna
and reflector antenna along with a bi-cone. Aperture reflectors tend to be used when the
wavelength is much smaller than the diameter of the reflector, so they behave somewhat similar
to optical reflectors of the same type.

Fig. A.10 Aperture, slot and bi-conical antennas

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Antenna & Wave Propagation 3th year Dr. Abdlkhadhum A. Hasan

Electrical Engineering Department

They usually used in aircrafts and space crafts, because these antennas can be flush-mounted.
Reflector antennas are with high gain antennas usually used in radio astronomy, microwave
communication and satellite tracking.

4- Microstrip antennas: rectangular, circular etc. shaped metallic patch above a ground plane.
Used in aircraft, spacecraft, satellites, missiles, cars, mobile phones etc. as shown in the figure

The folded antennas shown in Fig. A.8 tend to have slightly broader bandwidths than their
unfolded counterparts and are often used, particularly the dipole, in more complex structures
such as the Yagi-Uda array illustrated in Fig. A.9.

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Antenna & Wave Propagation 3th year Dr. Abdlkhadhum A. Hasan

Electrical Engineering Department

5- Array Antennas
An antenna array (or array antenna) is a set of multiple connected antennas which work
together as a single antenna, to transmit or receive radio waves as shown in the figure below.

The individual antennas (called elements) are usually connected to a

single receiver oror transmitter by feedlines that feed the power to the elements in a
specific phase relationship. The radio waves radiated by each individual antenna combine
and superpose. An antenna array can achieve higher gain and (directivity), that is a narrower
beam of radio waves, than could be achieved by a single element. In general, the larger the
number of individual antenna elements used, the higher the gain and the narrower the beam.

2.6 History of Antennas (Hertzian dipole Antenna)

Hertzian dipole is a simple practical antenna r shown in the figure below. It is very short length of
wire over which the current distribution can be assumed uniform. This type of antenna is called
a Hertzian dipole, after the German physicist Heinrich Hertz. It was done in 1887. Maxwell’s
equations show that such an antenna when energized by a high frequency current is associated with
an induction field which decreases inversely as square of the distance (E α 1/r2 nantenna) and a
radiation field which decreases inversely as distance only(E α 1/r far rom the antenna).

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Antenna & Wave Propagation 3th year Dr. Abdlkhadhum A. Hasan

Electrical Engineering Department

Hertz Diople Antenna is an infinitesimal element excited with an alternating. In practice a linear
antenna can be approximated by a Hertz dipole if the linear antenna is of size much smaller the
wavelength.

2.7 Analysis of Hertzian Dipole Antenna

The analysis of Hertz dipole is important to understand the analysis of any complicated radiating
structure, which can be decomposed into Hertz dipoles.
The Hertzian or short dipole antenna is the simplest of all antennas. It is simply an open-
circuited wire, fed at its center as shown in Figure 1.

Figure 1. Short dipole antenna of length L.

The words "short" or "small" in antenna engineering always imply "relative to a wavelength". So
the absolute size of the above dipole antenna does not matter, only the size of the wire relative to
the wavelength of the frequency of operation. Typically, a dipole is short if its length is less than
a tenth of a wavelength:

1. Radiated Fields
If the Hertzian (short dipole) antenna is oriented along the z-axis with the center of the dipole at
z=0, then the current distribution on a thin, short dipole is given by:

The current distribution is plotted in Figure 2. Note that this is the amplitude of the current
distribution; it is oscillating in time sinusoidally at frequency f.

Figure 2. Current distribution along a short dipole antenna.

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Antenna & Wave Propagation 3th year Dr. Abdlkhadhum A. Hasan

Electrical Engineering Department

A treatment of the fields radiated by an antenna requires a field theory treatment and is beyond
this coverage. It is, however, useful to examine well-known expressions for the fields produced
by a so-called short dipole because the fields generated by other antennas can be derived from
the short dipole results; it also allows us to understand the concept of near and far fields. Figure
A.7 shows the geometry of a short dipole in which distance and direction out from the antenna is
described by the radial coordinate r

If the short dipole is carrying a sinusoidal current Ioejωt as shown in the figure, the steps
in finding the radiated fields (both electric field and magnetic field) can be re-
summarized as:
1. Determine A from Js (surface current density).
2. Find H from A using
H= 1/µ( ∇× A).
3. Find E from H using
E = 1/jωε (∇× H)
we should find the vectors potential (Ar, AӨ,AФ) respectively as described in chapter 2.
Then by using Maxwell's equation, the disginated fields component are obtained as
described in the following:

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Antenna & Wave Propagation 3th year Dr. Abdlkhadhum A. Hasan

Electrical Engineering Department

Vector potential due to the Hertz dipole

As shown in the figure
- The Hertz dipole is oriented along the z-axis, has length L=dl and current Ioejωt

- The vector potential due to the Hertz dipole is therefore given as

- Note that the magnetic vector potential is in the z-direction and it has same direction
every where in the space.
-Since the coordinate system used for the antenna analysis is spherical, the components
of the magnetic vector potential in spherical coordinates are

Fields due to the Hertz Dipole

1- The vector magnetic field is obtained from vector potential using

- The magnetic field components can be obtained as

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Antenna & Wave Propagation 3th year Dr. Abdlkhadhum A. Hasan

Electrical Engineering Department

- The Hertz component has only ф-component. That is, the magnetic field loops around
the z-axis.
2- The electric field can be obtained by substituting for H in the source-free Maxwell's
curl equation the electric field can be obtained as

- The Ф-component of the electric field is zero.

Types of Fields

- For the Hertz dipole, the magnetic field has only Ф-component and the electric field
does not have the ф-component. The electric field lies in the (r,Ө) plane.
- The fields can be divided into three categories depending upon their variation as a
function of distance as follows:
1- The field which varies as (1/r3), is called the electrostatic field. This field is dominant
in the close vicinity of the dipole since its amplitude decreases rapidly as function of
distance.
2- The field which varies as(1/r2), , is called the induction field . This field extends little
further than the electrostatic field but still decays rapidly as a function of distance.
3- The field which varies a(1/r), is called the radiation field . This is the field which
extends over farthest distance from the antenna and is responsible for the radiation of
power from the antenna.

- The electrostatic field is inversely proportional to the frequency. As the frequency of the
current approaches zero, this field diverges to infinity. This field is essentially due to
the accumulation of charges on the tip of the antenna. When the current flows in the
dipole, the opposite charges get accumulated on the tips of the antenna giving a dipole.
With the reversal of the current (every half cycle) dipole reverses its polarity giving an
oscillating dipole. The electrostatic field is due to this oscillating dipole. As the
frequency decreases, the accumulated charge for a given current increases and therefore
the electrostatic field increases.
- The Induction field is independent of frequency.
- The radiation field is proportional to the frequency. This field is therefore practically
absent at low frequencies. This field is essentially a high frequency phenomenon.
The field for any antenna is divided into two types of field as shown in the figure

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Antenna & Wave Propagation 3th year Dr. Abdlkhadhum A. Hasan

Electrical Engineering Department

- The electrostatic and the induction fields together are called the Near Fields, and the
radiation fields are called the Far Fields as shown in the figures below

1- Near field components of antenna

In this type the field components are induction field components since they are induced
with the antenna itself (They are not radiated waves). The electric field for the dipole is
given as (only1/r3 terms)

The total near field is given as

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Antenna & Wave Propagation 3th year Dr. Abdlkhadhum A. Hasan

Electrical Engineering Department

The Near field is minimum in the direction Ө=π/2 and maximum in the directions Ө=0 and Ө=π.
However, along no direction the near field is zero. The near field essentially stores the
electromagnetic energy around the dipole but does not contribute to the power flow from the
antenna.

2- Far field radiation of antenna

In this type the radiated field components are with uniform plane waves.

- In close proximity to a radiating source, the wave is spherical in shape, but at a far distance, it
becomes approximately a plane wave as seen by a receiving antenna.
- The far-field approximation simplifies the math. 3. The distance beyond which the far-field
approximation is valid is called the far-field range (will be defined later)

- The fields radiated from the short dipole antenna in the far field are given by:
If
t
the short dipole is carrying a sinusoidal current

- Important things to note about the far field (radiation field ) are-
< The electric and magnetic fields are in time phase and they are in phase quadrature with the
current. That is, these fields are proportional to the rate of change of current or acceleration of
.charges
< The ratio of the electric and magnetic field at every point in space is equal to the intrinsic
.impedance of the medium

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Antenna & Wave Propagation 3th year Dr. Abdlkhadhum A. Hasan

Electrical Engineering Department

< The wave travels in the r-direction, the electric field is in the Ө -direction and the magnetic
,field is the Ф -direction. That is
they are perpendicular to each other. These fields therefore represent transverse electromagnetic
wave albeit spherical in nature as shown in the figure

< The fields are not uniform in all directions. The field strength is maximum along Ө=π/2
and zero along Ө=0 and Ө=π
< The Hertz dipole hence does not have any radiation along its axis
< The fields die off as 1/r, which indicates the power falls of as

< The fields are proportional to L, indicated a longer dipole will radiate more power. This is true
as long as increasing the length does not cause the short dipole assumption to become invalid.
Also, the fields are proportional to the current amplitude , which should make sense (more
current, more power).

4- The exponential term:

describes the phase-variation of the wave versus distance. The parameter k is known as the
wavenumber. Note also that the fields are oscillating in time at a frequency f in addition to the
above spatial variation.

5- Finally, the spatial variation of the fields as a function of direction from the antenna are given
by

For a vertical antenna oriented along the z-axis, the radiation will be maximum in the x-y plane.
Theoretically, there is no radiation along the z-axis far from the antenna. The details of antennas
characteristics will be explained in the next chapter.

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Antenna & Wave Propagation 3th year Dr. Abdlkhadhum A. Hasan

Electrical Engineering Department

Example 1
The electric field of an electromagnetic wave propagating in a homogeneous
medium is given by

Calculate the frequency, propagation constant, velocity, and the magnetic

field intensity of the wave if the relative permeability of the medium is equal
to unity.

Solution As shown, the given equation of electric field is given in spherical coordinate
system, therefore the given time harmonic electric field must be
converted from cartesian coordinate system to spherical coordinate system (r,Ө, Ф)
.such that:

It is more convient to convert time harmonic field to phasor form. The θ-

component of the electric field can be expressed as:

It clear that the given EM wave propagates in r direction. Comparing the above
equation with the following equation (phasor form of the wave equation)

Hence

And the frequency of the wave is

And the propagation constant (phase constant ) is

The velocity of the wave in the medium is given by

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Antenna & Wave Propagation 3th year Dr. Abdlkhadhum A. Hasan

Electrical Engineering Department

Now, to to find the magnetic field component, express the electric field as a phasor

Substituting this in Maxwell’s equation,

and expressing the curl in spherical coordinates

Expanding the determinant

Since r and Eθ are not functions of φ

Therefore, the magnetic field is given by

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