Unit 5
Wave Propagation
Figure 1. Plane earth reflection
Sample E-field vectors are shown for the parallel and perpendicular polarization cases. There are two paths from the transmitter (TX) to the receiver (RX):
a line-of-sight (LOS) path and a reflected path. The polarizations of the components shown are also consistent with what we have sketched and derived earlier for the case of a TE/TM polarized wave incident upon a media interface.
The polarization of the LOS path, regardless of the TE/TM polarization case, remains constant; however, for the reflected path, the polarization of the reflected components are shown 180 degrees out of phase with the LOS path.
This results when θi → 90◦ (grazing incidence) at an interface with lossy dielectric (not a PEC). The grazing angle assumption is valid since in many cases the antenna heights h1, h2 are very small compared to the TX-RX separation. We also assume that the earth is treated as a flat surface for this development.
Flat surface
The two paths to the receiver in this case consist of the LOS path (of length R = D + a) and the reflected path (of length S = D + b). That is, each path is an additional length a or b longer than the horizontal separation distance D. Analyzing the larger of the two triangles in the diagram
Using the principle of superposition, the eletric field strength at the receiving antenna is proportional to
The term in parentheses is recognized as a correction term for the reflection, a kind of array factor for an antenna and its image, where the image produces a field of opposite sign as the line-of-sight path because of 180◦ phase shift introduced at the reflection interface. The term outside the parentheses is just a standard line-of-sight propagation term that we also see from an antenna.
The electromagnetic waves emitted by transmitter antenna travel directly from the transmitting antenna to the receiving antenna are called space waves and this type of propagation is called space wave propagation. It is used for line-of-sight communication and satellite communication.
5.3.1 Introduction
High frequency electromagnetic waves cannot be transmitted as ground waves due to high energy losses. These waves are absorbed by ionosphere hence they cannot be transmitted through skywave propagation. Hence such high frequency electromagnetic waves are directly transmitted through earth atmosphere using transmitting antenna. As these waves travel in straight line the receiving antenna must be in line-of-sight of the transmitting antenna.
5.3.2 Field strength relation
The electric field strength :
E = 
S. Zo
We get
E = 
. Zo
If our receiver shows the input voltage Ur at an input impedance of Zi then we have to use the following relationship between the input power Pr and input voltage Ur.
Pr = Ur 2 / Zi
Using this we get
E = 
Ur 2 / Zi . 1/Ar . Zo
Or by rearranging formula we get
E = Ur 
1/Ar . Zo/Zi
The square root expression is known as antenna factor Ka.
Ka = 
1/Ar . Zo/Zi = 
4 π/ Gr. λ 2 . Zo/Zi
Gr is the receiver antenna gain over an isotropic antenna, λ is the wavelength of the received signal Zo is the propagation impedance of free space and Zi is the receiver input impedance.
E = Ur. Ka
Sometime Ka is expressed in dB:
Ka/dB = 20 . log 10(Ka)
Electric field strength is measured in V/m or in μV/m.
5.3.3 Effects of imperfect earth
The field at the receiving point due to space is reduced by earth’s imperfection and roughness
Figure 3. Imperfect earth
The received signal is the sum of two components. The line- of -sight distance is that exact distance at which both the sender and receiver antenna are in sight of each other. So, from the above line if we want to increase the transmission distance then this can be done by simply extending the heights of both the sender as well as the receiver antenna. This type of propagation is used basically in radar and television communication.
5.3.4 Effects of curvature of earth
The propagation of space and ground wave are limited by the curvature of earth.
So, for long distance communication of thousands of km or more are performed by sky waves or ionospheric waves.
Example: Armature radio
5.4.1 Introduction
Sky wave propagation is used when the wave has to travel for longer distance. Here the wave is projected onto the sky and reflected back onto the earth.
Figure 4. Sky wave propagation
The sky wave propagation is well depicted in the above picture. Here the waves are shown to be transmitted from one place and received by many receivers. Hence, it is an example of broadcasting.
The waves, which are transmitted from the transmitter antenna, are reflected from the ionosphere. It consists of several layers of charged particles ranging in altitude from 30- 250 miles above the surface of the earth. Such a travel of the wave from transmitter to the ionosphere and from there to the receiver on Earth is known as Sky Wave Propagation. Ionosphere is the ionized layer around the Earth’s atmosphere, which is suitable for sky wave propagation.
5.4.2 Structural details of the Ionosphere
There is also a C region below the others, but the level of ionisation is so low that it does not have any effect radio signals and radio communications and rarely used.
Figure 5. Ionosphere
When a sky wave leaves the Earth's surface and travels upwards, the first region of interest that it reaches in the ionosphere is called the D layer or D region.
The D layer or D region mainly has the affect of absorbing or attenuating radio communications signals particularly in the LF and MF portions of the radio spectrum, its affect reduces with increasing frequency.
This region attenuates the signals as they pass through. The level of attenuation depends on the frequency. Low frequencies are attenuated more than higher ones. In fact it is found that the attenuation varies as the inverse square of the frequency, i.e. doubling the frequency reduces the level of attenuation by a factor of four. This means that low frequency signals are often prevented from reaching the higher regions, except at night when the region disappears.
Attenuation = k/f2
Where:
k = constant
f = frequency of operation (Hz)
The E region or E layer is above the D region. It exists at altitudes between about 100 and 125 kilometres. Instead of attenuating radio communications signals this layer refracts them, often to a degree where they are returned to earth. As such they appear to have been reflected by this layer. However, this layer still acts as an attenuator to a certain degree.
At the altitude where the E layer or E region exists, the air density is very much less than it is for the D region. This means that when the free electrons are excited by radio signals and vibrate, far fewer collisions occur. As a result, the way in which the E layer or E region acts is somewhat different. The electrons are again set in motion by the radio signal and tend to re-radiate it. As the signal is travelling in an area where the density of electrons is increasing, the further it progresses into the region, the signal is refracted away from the area of higher electron density. In the case of HF signals, this refraction is often sufficient to bend them back to earth. In effect it appears that the region has "reflected" the signal.
The F1 layer is found at around an altitude of 300 kilometres with the F2 layer above it at around 400 kilometres. The combined F layer may then be centred around 250 to 300 kilometres. The altitude of the all the layers in the ionosphere layers varies considerably and the F layer varies the most. Being the highest of the ionospheric regions it is greatly affected by the state of the Sun as well as other factors including the time of day, the year and so forth.
The F layer acts as a "reflector" of signals in the HF portion of the radio spectrum enabling world -wide radio communications to be established. It is the main region associated with HF signal propagation.
5.4.3 Wave propagation mechanism
The mode of propagation of electromagnetic waves in the atmosphere and in free space may be divided into the following three categories:
In ELF (Extremely low frequency) and VLF (Very low frequency) frequency bands, the Earth, and the ionosphere act as a wave-guide for electromagnetic wave propagation. In these frequency ranges, communication signals practically propagate around the world. The channel bandwidths are small. Therefore, the information is transmitted through these channels has slow speed and confined to digital transmission.
The line of Sight (LOS) Propagation
Figure 6. LOS
The line-of-sight propagation will not be smooth if there occurs any obstacle in its transmission path. As the signal can travel only to lesser distances in this mode, this transmission is used for infrared or microwave transmissions.
Ground Wave Propagation
Ground wave propagation of the wave follows the contour of the earth. Such a wave is called a direct wave. The wave sometimes bends due to the Earth’s magnetic field and gets reflected the receiver. Such a wave can be termed as a reflected wave. The following figure depicts ground wave propagation.
Figure 7. Ground Wave
The wave then propagates through the Earth’s atmosphere is known as a ground wave. The direct wave and reflected wave together contribute the signal at the receiver station. When the wave finally reaches the receiver, the lags are cancelled out. In addition, the signal is filtered to avoid distortion and amplified for clear output.
SkyWave Propagation
Skywave propagation is preferred when the wave has to travel a longer distance. Here the wave is projected onto the sky and it is again reflected back to the earth.
Figure 8. Sky wave propagation
The sky wave propagation is well depicted in the above picture. Here the waves are shown to be transmitted from one place and where it is received by many receivers. Hence, it is an example of broadcasting.
The waves, which are transmitted from the transmitter antenna, are reflected from the ionosphere. It consists of several layers of charged particles ranging in altitude from 30-250 miles above the surface of the earth. Such travel of the wave from the transmitter to the ionosphere and from there to the receiver on Earth is known as Sky Wave Propagation. The ionosphere is the ionized layer around the Earth’s atmosphere, which is suitable for skywave propagation.
5.4.4. Reflection and refraction of sky waves by ionosphere
When a radio wave is transmitted into an ionized layer, refraction, or bending of the wave, occurs.
Refraction is caused by an abrupt change in the velocity of the upper part of a radio wave as it strikes or enters a new medium.
The amount of refraction that occurs depends on three main factors:
Reflection:
When high-frequency signals enter the ionosphere at a low angle they are bent back towards the earth by the ionized layer.
• When operating at frequencies just below the MUF, losses can be quite small, so the radio signal may effectively "bounce" or "skip" between the earth and ionosphere two or more times.
• If the ionization is not great enough, the wave only curves slightly downwards, and subsequently upwards as the ionization peak is passed so that it exits the top of the layer only slightly displaced. The wave then is lost in space.
• To prevent this a lower frequency must be chosen.
Figure 9. Reflection
Figure 10 . Ray path
The various angles at which RF waves strikes the layer are represented by dark lines and designated as rays 1 through 6.
Ray 1 -- the propagation path is long.
Ray 2 and Ray 3-- the rays penetrate deeper into the layer but the range of these rays decreases.
When a certain angle is reached (Ray 3), the refraction of the ray is first returned to Earth , its second refraction from the ionospheric layer.
Ray 4 and Ray 5--the RF energy penetrates the central area of maximum ionization of the layer. These rays are refracted rather slowly and are eventually returned to Earth at great distances.
Ray 6-- the ray is not returned at all, but passes on through the layer.
5.5.1 Critical frequency
The critical frequency is an important figure that gives an indication of the state of the ionosphere and the resulting HF propagation.
It is obtained by sending a signal pulse directly upwards.
Critical frequency is defined as the maximum frequency at which the total internal reflection(TIR) takes place from the ionosphere.
The mathematical representation is given as:
Fc = 9 
Nmax
Where, f c is the critical frequency in Hz
Nmax is the maximum electron density /ionization density (electrons per cubic meter)
Critical frequency varies depending upon atmospheric conditions, time of the day and the angle of incidence of the radio waves by the antenna.
5.5.2 MUF
• When a signal is transmitted using HF propagation, over a given path there is a maximum frequency that can be used.
• A maximum frequency that can be used for communications between two given locations. This frequency is known as the MUF.
• Waves at frequencies above the MUF are normally refracted so slowly that they return to Earth beyond the desired location or pass on through the ionosphere and are lost.
• However, that use of an established MUF certainly does not guarantee successful communications between a transmitting site and a receiving site. Variations in the ionosphere may occur at any time and consequently raise or lower the predetermined MUF.
The mathematical representation of critical frequency as a function of MUF is:
Fc = fMUF / sec 
fMUF = fc/cos 
Where, f c is the critical frequency in Hz
fMUF is the maximum usable frequency (3 to 4 times of f c )
θ is the angle of incidence The factor sec θ is called the MUF factor and it is a function of the path length if the height layer is known.
5.5.3 LUF
Lowest usable frequency
As there is a maximum operating frequency that can be used for communications between two points, there is also a minimum operating frequency. This is known as the LUF.
As the frequency of a radio wave is lowered, the rate of refraction increases. So the wave whose frequency is below the established LUF is refracted back to Earth at a shorter distance than desired, as shown in Figure.
The LUF is defined as the frequency at below which the signal falls below the minimum strength required for satisfactory reception.
The LUF is the practical limit below which communication cannot be maintained between two particular radio communications stations.
Figure 13. Refraction of frequency below LUF.
5.5.4 OF
Neither the MUF nor the LUF is a practical operating frequency.
When the radio waves at the LUF can be refracted back to Earth at the desired location, the signal-to-noise ratio is still much lower than at the higher frequencies, and the probability of multipath propagation is much greater.
Operating at or near the MUF can result in frequent signal fading and dropouts when ionospheric variations alter the length of the transmission path.
The most practical operating frequency is one that you can rely on with the least amount of problems. It should be high enough to avoid the problems of multipath, absorption, and noise encountered at the lower frequencies; but not so high as to result in the adverse effects of rapid changes in the ionosphere.
A frequency that meets the above criteria has been established and is known as the OWF
The frequency, which is being used mostly for a particular transmission and which has been predicted to be used over a particular period of time, over a path, is termed as OWF.
Estimates the maximum frequency that must be used for a given critical frequency and incident angle. It is the frequency chosen to avoid the irregularities of the atmosphere.
OWF = 0.85 MUF = 0.85 fc/ cos 
5.5.5 Virtual height and skip distance
Figure 14. Curve path
As shown in Figure, the curve path reaches an altitude of h1 before being returned to the Earth.
If the incident and returned rays are extrapolated to a vertex, they meet at a height h’, which is called the virtual reflection height of the ionospheric layer.
Figure 15. Curved path of refracted ray associated with frequency fob.
Skip distance sky zone
The skip distance is the distance over the Earth's surface between the point where a radio signal is transmitted, and the point where it is received having travelled to the ionosphere, and been refracted back by the ionosphere.
D skip = 2h 
(fMUF/fc) 2 - 1
Where, Dskip: skip distance
h: height at which reflection happens
fMUF: maximum usable frequency
f c : critical frequency
Figure 16. Sky zone
The size of the skip distance depends on
The SKIP ZONE is a zone of silence between the point where the ground wave becomes too weak for reception and the point where the sky wave is first returned to Earth.
The size of the skip zone depends on the extent of the ground wave coverage and the skip distance.
When the ground wave coverage is great enough or the skip distance is short enough that no zone of silence occurs, there is no skip zone.
Figure 17. Relation between skip zone , skip distance and ground coverage.
5.5.6 Relation between MUF and skip distance
The ionosphere has many tiny layers , for atmospheric refraction
Figure 18. Ionosphere
no sin 
= n1 sin 
= n2 sin 
--------------------- nk sin 
k -----------------------2)
The condition for the wave to return to earth is to have total internal reflection(TIR), which begins when the refracted angle ,θr is 900 . • If this happens at the k th layer,
no sin 
= nk sin 90 = nk
since no=1
sin 
= nk sin 2 
= nk 2 = 
nk= √
Figure 19. Reflection
h= height of the layer
d=skip distance of the flat surface.
cos 
= h/√(h2 + d2/4)
cos 
=2 h/√(4h2 + d2/4)
f2 MUF = fc2 / cos 2 
f2 MUF / f2 c = 1/ cos 2 
= ( √ d2 + 4 h2 / 2h ) 2 = d2 + 4h2 / 4h2
f2 MUF / fc2 = fc √ d2/4h2 +1
tan 
c = h/d/2
h=d/2 tan 
d = 2h/tan 
dskip = 2h [ ( f muf/fc) 2 – 1] ½
5.5.7 Multi hop propagation
Multiple reflections from the ionosphere and returned to the earth like Multi-Hops
• Ionosphere- Reflector
• Earth- Reflector
Figure20. Multi hop propagation
Need of Multi-hop Propagation
5.5.8 Wave characteristics
Radio wave frequencies range from Extremely Low Frequencies (ELF) 3 kilohertz (kHz) to Extremely High Frequencies (EHF) 300 gigahertz (GHz).
• EHF are often called the millimeter band because its wavelengths range from 1 to 10 mm. • Wavelengths in and around this band are called millimeter waves (mmW).
• Worldwide, 5G will use spectrum in the existing 4G LTE frequency range 600 MHz to 3 GHz (Ultra High Frequency, UHF) and even up to 6 GHz, as well as millimeter wave bands 24 to 86 GHz (Super High Frequency to Extremely High Frequency).
• Ultra High Frequency (UHF) spectrum is also being used by some Carriers for 5G.
• UHF band has a frequency range of 300 MHz to 3 GHz. It is already being used since years in many other applications such as TV broadcasting, cordless phones, Wi-Fi, GPS, and Bluetooth.
A radio frequency band is a small contiguous section of the radio spectrum frequencies, in which channels are usually used or set aside for use.
• For example, broadcasting, mobile radio, or navigation devices, will be allocated in nonoverlapping ranges of frequencies. For each of these bands the ITU has a band plan which dictates how it is to be used and shared, to avoid interference and to set protocol for the compatibility of transmitters and receivers.
References:
Antenna Theory: Analysis and Design Book by Constantine A. Balanis
Antenna and Wave Propagation Book by Deepak Handa and K. D. Prasad
Antenna and Wave Propagation Book by Ranjana Trivedi
ANTENNAS AND WAVE PROPAGATION Book by SACHIN D. DR RUIKAR
