HF Ionospheric Radio Signal Propagation

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means by which signals at VHF and above are heard over extended distances. Read more about

Tropospheric propagation

In addition to these categories, many short range radio communications or wireless systems have

radio propagation scenarios that do not fit neatly into these categories. Many mobile

communications systems along with wi-fi and cellular systems for example need to have theirradio propagation models generated for office, or urban situations. Under these circumstances the

"free space" propagation is modified by multiple reflections, refractions and diffractions. Despite

these complications it is still possible to generate rough guidelines and models for these radiopropagation scenarios.

There are also a number of other, more specialised forms of radio propagation that are used in a

number of instances:

Meteor scatter / Meteor Burst: This form of radio propagation is often used for links of up to

1500 km or more where real time communications are not needed. It is often used for relaying

data from remote sites to a base station. Read more aboutMeteor burst communications

NVIS: This is actually a form of ionospheric propagation. Signals are transmitted with a very

high angle of radiation, and returned to earth over a limited area. It is particularly useful in hilly

or forested regions where normal ground wave propagation may not be able to access all areas

needed. Read more aboutNVIS - near vertical incidence skywave

Areas that affect radio propagation

It is also necessary to understand the differnet areas of the atmosphere, or other areas that affect

radio propagation and radio communications signals. Read more aboutAreas of the atmospherethat affect radio propagation

There are many radio propagation, or radiowave propagation scenarios in real life. Often radio

signals may travel by several means, signals travelling using one type of propagation interacting

with another. However to build up an understanding of how a signal reaches a receiver, it isnecessary to have a good understanding of all the possible methods. By understanding these, the

interactions can be better understood and it is then possible to understand some of the reasons

why mobile radio communications systems, or two way radio communications systems work inthe way they do..

Ground Wave Propagation Tutorial

- ground wave propagation is a form of signal propagation where the signal travels over the

surface of the ground, and as a result it is used to provide regional coverage onth e long and

medium wave bands.

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Ground wave propagation is particularly important on the LF and MF portion of the radiospectrum. Ground wave radio propagation is used to provide relatively local radio

communications coverage, especially by radio broadcast stations that require to cover aparticular locality.

Ground wave radio signal propagation is ideal for relatively short distance propagation on thesefrequencies during the daytime. Sky-wave ionospheric propagation is not possible during the day

because of the attenuation of the signals on these frequencies caused by the D region in the

ionosphere. In view of this, radio communications stations need to rely on the ground-wavepropagation to achieve their coverage.

A ground wave radio signal is made up from a number of constituents. If the antennas are in theline of sight then there will be a direct wave as well as a reflected signal. As the names suggest

the direct signal is one that travels directly between the two antenna and is not affected by the

locality. There will also be a reflected signal as the transmission will be reflected by a number of

objects including the earth's surface and any hills, or large buildings. That may be present.

In addition to this there is surface wave. This tends to follow the curvature of the Earth and

enables coverage to be achieved beyond the horizon. It is the sum of all these components that isknown as the ground wave.

Beyond the horizon the direct and reflected waves are blocked by the curvature of the Earth, andthe signal is purely made up from the diffracted surface wave. It is for this reason that surface

wave is commonly called ground wave propagation.

Surface wave

The radio signal spreads out from the transmitter along the surface of the Earth. Instead of just

travelling in a straight line the radio signals tend to follow the curvature of the Earth. This is

because currents are induced in the surface of the earth and this action slows down the wave-front in this region, causing the wave-front of the radio communications signal to tilt downwards

towards the Earth. With the wave-front tilted in this direction it is able to curve around the Earth

and be received well beyond the horizon.

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Ground wave radio propagation

Effect of frequency on ground wave propagation

As the wavefront of the ground wave travels along the Earth's surface it is attenuated. The degree

of attenuation is dependent upon a variety of factors. Frequency of the radio signal is one of themajor determining factor as losses rise with increasing frequency. As a result it makes this form

of propagation impracticable above the bottom end of the HF portion of the spectrum (3 MHz).

Typically a signal at 3.0 MHz will suffer an attenuation that may be in the region of 20 to 60 dB

more than one at 0.5 MHz dependent upon a variety of factors in the signal path including thedistance. In view of this it can be seen why even high power HF radio broadcast stations may

only be audible for a few miles from the transmitting site via the ground wave.

Effect of the ground

The surface wave is also very dependent upon the nature of the ground over which the signal

travels. Ground conductivity, terrain roughness and the dielectric constant all affect the signal

attenuation. In addition to this the ground penetration varies, becoming greater at lower

frequencies, and this means that it is not just the surface conductivity that is of interest. At thehigher frequencies this is not of great importance, but at lower frequencies penetration means

that ground strata down to 100 metres may have an effect.

Despite all these variables, it is found that terrain with good conductivity gives the best result.

Thus soil type and the moisture content are of importance. Salty sea water is the best, and rich

agricultural, or marshy land is also good. Dry sandy terrain and city centres are by far the worst.This means sea paths are optimum, although even these are subject to variations due to the

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roughness of the sea, resulting on path losses being slightly dependent upon the weather! It

should also be noted that in view of the fact that signal penetration has an effect, the water table

may have an effect dependent upon the frequency in use.

Polarisation & ground wave propagation

The type of antenna and its polarisation has a major effect on ground wave propagation. Vertical

polarisation is subject to considerably less attenuation than horizontally polarised signals. In

some cases the difference can amount to several tens of decibels. It is for this reason that mediumwave broadcast stations use vertical antennas, even if they have to be made physically short by

adding inductive loading. Ships making use of the MF marine bands often use inverted L

antennas as these are able to radiate a significant proportion of the signal that is vertically

polarised.

At distances that are typically towards the edge of the ground wave coverage area, some sky-wave signal may also be present, especially at night when the D layer attenuation is reduced.

This may serve to reinforce or cancel the overall signal resulting in figures that will differ from

those that may be expected.

HF Ionospheric Radio Signal Propagation

The basics of HF ionospheric radio propagation and how the ionosphere enables radio

communications links to be established over large distances around the globe using what

are termed sky waves or skywaves.

As electromagnetic waves, and in this case, radio signals travel, they interact with objects and

the media in which they travel. As they do this the radio signals can be reflected, refracted or

diffracted. These interactions cause the radio signals to change direction, and to reach areas

which would not be possible if the radio signals travelled in a direct line.

Radio communications signals in the medium and short wave bands travel by two basic means.

The first is known as a ground wave (covered on a separate page in this section), and the

second a sky wave using the ionosphere.

Skywaves

When using ionospheric radio propagation, the radio signals leave the Earth's surface and traveltowards the ionosphere where some of these are returned to Earth. These radio signals are termed

sky waves for obvious reason. If they are returned to Earth, then the ionosphere may (very

simply) be viewed as a vast reflecting surface encompassing the Earth that enables signals to

travel over much greater distances than would otherwise be possible. Naturally this is a greatover simplification because the frequency, time of day and many other parameters govern the

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reflection, or more correctly the refraction of signals back to Earth. There are in fact a number of

layers, or more correctly regions within the ionosphere, and these act in different ways as

described below.

Tropospheric propagation

On frequencies above 30 MHz, it is found that the troposphere has an increasing effect on radio

signals and radio communications systems. The radio signals are able to travel over greater

distances than would be suggested by line of sight calculations.

The reason for the increase in distance travelled by the radio signals is that they are refracted

by small changes that exist in the Earth's atmosphere close to the ground. It is found that the

refractive index of the air close to the ground is very slightly higher than that higher up. As a

result the radio signals are bent towards the area of higher refractive index, which is closer to

the ground. It thereby extends the range of the radio signals.

Enhanced conditions

These extended distances result from much greater changes in the values of refractive index over

the signal path. This enables the signal to achieve a greater degree of bending and as a result

follow the curvature of the Earth over greater distances.

Under some circumstances the change in refractive index may be sufficiently high to bend thesignals back to the Earth's surface at which point they are reflected upwards again by the Earth's

surface. In this way the signals may travel around the curvature of the Earth, being reflected by

its surface. This is one form of "tropospheric duct" that can occur.

It is also possible for tropospheric ducts to occur above the Earth's surface. These elevated

tropospheric ducts occur when a mass of air with a high refractive index has a mass of air with a

lower refractive index underneath and above it as a result of the movement of air that can occurunder some conditions. When these conditions occur the signals may be confined within the

elevated area of air with the high refractive index and they cannot escape and return to earth. As

a result they may travel for several hundred miles, and receive comparatively low levels ofattenuation. They may also not audible to stations underneath the duct and in this way create a

skip or dead zone similar to that experienced with HF ionospheric propagation.

The refractive index of the atmosphere varies according to a variety of factors. Temperature,

atmospheric pressureand water vapor pressureall influence the value. Even small changes in

these variables can make a significant difference because radio signals can be refracted over

whole of the signal path and this may extend for many kilometers.

Mechanism behind tropospheric propagation

Tropospheric propagation effects occur comparatively close to the surface of the Earth. The radio

signals are affected by the region that is below an altitude of about 2 kilometres. As these regions

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sum of all the signals appearing at the antenna. Sometimes these will be in phase with the main

signal and will add to it, increasing its strength. At other times they will interfere with each other.

This will result in the overall signal strength being reduced.

At times there will be changes in the relative path lengths. This could result from either the

transmitter or receiver moving, or any of the objects that provides a reflective surface moving.This will result in the phases of the signals arriving at the receiver changing, and in turn this will

result in the signal strength varying. It is this that causes the fading that is present on many

signals.

It can also be found that the interference may be flat, i.e. applied to all frequencies equally across

a given channel, or it may be selective, i.e. applying to more to some frequencies across achannel than others.A more in depth description of multipath fading is given in a page referenced

in the "Related Articles" section on the left hand side of this page below the main menu.

Interference caused by multipath propagation

Multipath propagation can give rise to interference that can reduce the signal to noise ratio and

reduce bit error rates for digital signals. One cause of a degradation of the signal quality is the

multipath fading already described. However there are other ways in which multipath

propagation can degrade the signal and affect its integrity.

One of the ways which is particularly obvious when driving in a car and listening to an FMradio. At certain points the signal will become distorted and appear to break up. This arises from

the fact that the signal is frequency modulated and at any given time, the frequency of the

received signal provides the instantaneous voltage for the audio output. If multipath propagation

occurs, then two or more signals will appear at the receiver. One is the direct or line of sight

signal, and another is a reflected signal. As these will arrive at different times because of thedifferent path lengths, they will have different frequencies, caused by the fact that the two signals

have been transmitted by the transmitter at slightly different times. Accordingly when the two

signals are received together, distortion can arise if they have similar signal strength levels.

Another form of multipath propagation interference that arises when digital transmissions areused is known as Inter Symbol Interference, ISI. This arises when the delay caused by the

extended path length of the reflected signal. If the delay is significant proportion of a symbol,

then the receiver may receive the direct signal which indicates one part of the symbol or onestate, and another signal which is indicating another logical state. If this occurs, then the data can

be corrupted.

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How intersymbol interference can be avoided

One way of overcoming this is to transmit the data at a rate the signal is sampled, only when allthe reflections have arrived and the data is stable. This naturally limits the rate at which data canbe transmitted, but ensures that data is not corrupted and the bit error rate is minimised. To

calculate this the delay time needs to be calculated using estimates of the maximum delays that

are likely to be encountered from reflections.

Using the latest signal processing techniques, a variety of methods can be used to overcome the

problems with multipath propagation and the possibilities of interference.

OFDM and multipath propagation

In order to meet the requirements to transmit large amounts of data over a radio channel, it isnecessary to choose the most appropriate form of signal bearer format. One form of signal lends

itself to radio data transmissions in an environment where reflections may be present isOrthogonal Frequency Division Multiplex, OFDM. An OFDM signal comprises a large number

of carriers, each of which are modulated with a low bit rate data stream. In this way the two

contracting requirements for high data rate transmission, to meet the capacity requirements, andlow bit rate to meet the intersymbol interference requirements can be met.

Note on OFDM:

Orthogonal Frequency Division Multiplex (OFDM) is a form of transmission that uses a largenumber of close spaced carriers that are modulated with low rate data. Normally these signals

would be expected to interfere with each other, but by making the signals orthogonal to each

other there is no mutual interference. The data to be transmitted is split across all the carriers togive resilience against selective fading from multi-path effects..

Click on the link for anOFDM tutorial

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OFDM is the modulation format that is used for many of today's data transmission formats. Theapplications include 802.11n Wi-Fi, LTE (Long Term Evolution for 3G cellulartelecommunications), LTE Advanced (4G), WiMAX and many more. The fact that OFDM is

being widely used demonstrates that it is an ideal format to overcome multipath propagationproblems.

MIMO

While multipath propagation creates interference for many radio communications systems, it can

also be used to advantage to provide additional capacity on a given channel. Using a scheme

known as MIMO, multiple input multiple output, it is possible to multiple the data capacity of a

given channel several times by using the multipath propagation that exists.

Note on MIMO:

Two major limitations in communications channels can be multipath interference, and the datathroughput limitations as a result of Shannon's Law. MIMO provides a way of utilising the

multiple signal paths that exist between a transmitter and receiver to significantly improve the

data throughput available on a given channel with its defined bandwidth. By using multipleantennas at the transmitter and receiver along with some complex digital signal processing,

MIMO technology enables the system to set up multiple data streams on the same channel,

thereby increasing the data capacity of a channel.

Click on the link for aMIMO tutorial

In view of the advantages that MIMO offers, many current wireless and radio communications

schemes are using it to make far more efficient use of the available spectrum. The disadvantageto MIMO is that it requires the use of multiple antennas, and with modern portable equipment

such as cell phones being increasingly small, it can be difficult to place tow sufficiently spaced

antennas onto them.

Multipath propagation is an issue for any radio communications system. Ranging from the short

range wireless communications such as Wi-Fi though the cellular and longer range data schemessuch as WiMAX though to VHF links where troposheric propagation may affect the signal path,through to HF systems using the ionosphere for reflections. In all of these systems, the effects of

multipath propagation can be seen and experienced. Any form of communications, therefore has

to be able to accommodate the effects of the multipath propagation in one way or another.

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Free Space Path Loss: Details, Formula, Calculator

- summary, tutorial or overview about the free space path loss, FSPL, and how to calculate

the loss using the RF path loss formula or equation with free space path loss calculator.

The free space path loss, FSPL, is used in many areas for predicting radio signal strengths thatmay be expected in a radio system.

Although the free space path loss does not hold for most terrestrial situations because of other

effects from the ground, objects in the path and the like, there are still very many situations in

which it can be used. It is also useful as the basis for understanding many real life radiopropagation situations.

Accordingly, the free space path loss, FSPL, is an essential basic parameter for many RF

calculations. It can often be used as a first approximation for many short range calculations.Alternatively it can be used as a first approximation for a number of areas where there are few

obstructions. As such it is a valuable tool for many people dealing with radio communicationssystems.

Free space path loss

In addition to this, these free space path loss, FSPL, calculations can be used in wireless survey

tools where the free space loss is calculated and other scenarios added to provide an overall viewof the signal strength at a given point. With the growing requirements to be able to analyse

wireless or radio coverage, wireless survey tools are being used increasingly to enable coverage

to be predicted at the early stages of design. Accordingly these wireless survey tools are beingused increasingly in the development and installation of radio and wireless systems.

Free space path loss basics

The free space path loss, also known as FSPL is the loss in signal strength that occurs when anelectromagnetic wave travels over a line of sight path in free space. In these circumstances thereare no obstacles that might cause the signal to be reflected refracted, or that might cause

additional attenuation.

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The free space path loss calculations only look at the loss of the path itself and do not contain

any factors relating to the transmitter power, antenna gains or the receiver sensitivity levels.

These factors are normally address when calculating a link budget and these will also be usedwithin radio and wireless survey tools and software.

To understand the reasons for the free space path loss, it is possible to imagine a signal spreadingout from a transmitter. It will move away from the source spreading out in the form of a sphere.

As it does so, the surface area of the sphere increases. As this will follow the law of the

conservation of energy, as the surface area of the sphere increases, so the intensity of the signalmust decrease.

As a result of this it is found that the signal decreases in a way that is inversely proportional tothe square of the distance from the source of the radio signal in free space.

Whilst the free space path loss is taken to be inversely proportional to the square of the distance,in most terrestrial (non-free space) cases this basic formula has to be altered because of the

effects of the earth and obstacles including trees, hills, buildings, etc.. In these cases the exponentvalue is typically in the range of 2 to 4. In some environments, such as buildings, stadiums and

other indoor environments, the path loss exponent can reach values in the range of 4 to 6. In

other words for the very worst case scenarios the signal may fall as the distance to the power six.

Tunnels which can act as a form of waveguide can result in a path loss exponent values of less

than 2.

As an example many cellular operators base their calculations for terrestrial signal reduction

around the inverse of the distance to the power 4.

Free space path loss formula

The free space path loss formula or free space path loss equation is quite simple to use. Not onlyis the path loss proportional to the square of the distance between the transmitter and receiver,

but the signal level is also proportional to the square of the frequency in use for other reasons

explained in a section below.

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Where:

FSPLis the Free space path loss

dis the distance of the receiver from the transmitter (metres)is the signal wavelength (metres)

fis the signal frequency (Hertz)

cis the speed of light in a vacuum (metres per second)

The speed of light is 2.99792458 x 10^8 metres per second, although for most practical purposes,

this is taken to be 3 x 10^8 metres per second.

The free space path loss formula is applicable to situations where only the electromagnetic wave

is present, i.e. for far field situations. It does not hold true for near field situations.

Free space loss formula frequency dependency

Although the free space loss equation given above seems to indicate that the loss is frequencydependent. The attenuation provided by the distance travelled in space is not dependent upon the

frequency. This is constant.

The reason for the frequency dependence is that the equation contains two effects:

1.

The first results from the spreading out of the energy as the sphere over which the energy is

spread increases in area. This is described by the inverse square law.

2.

The second effect results from the antenna aperture change. This affects the way in which any

antenna can pick up signals and this term is frequency dependent.

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Where:

Gtxis the gain of the transmitter antenna relative to an isotropic source (dBi)

Grxis the gain of the receiver antenna relative to an isotropic source (dBi)

Normally the transmitter and receiver gain levels will incorporate any feeder losses which are

subtracted from the antenna gain. In this way performance between the transmitter and receiverinterfaces are provided.

The free space path loss equation or formula given above, is an essential tool that is requiredwhen making calculations for radio and wireless systems either manually or within applications

such as wireless survey tools, etc. By using the free space path loss equation, it is possible to

determine the signal strengths that may be expected in many scenarios. While the free space pathloss formula is not fully applicable where there are other interactions, e.g. reflection, refraction,

etc as are present in most real life applications, the equation can nevertheless be used to give an

indication of what may be expected. It is obviously fully applicable to satellite systems where the

paths conform closely to the totally free space scenarios. .......

Fading

When signals are propagated over extended distances as a result of enhanced tropospheric

propagation conditions, the signals are normally subject to slow deep fading. This is caused bythe fact that the signals are received via a number of different paths. As the winds in the

atmosphere move the air around it means that the different paths will change over a period of

time. Accordingly the signals appearing at the receiver will fall in and out of phase with eachother as a result of the different and changing path lengths, and as a result the strength of the

overall received signal will change.

Any terrestrial signals received at VHF and above will be subject to the prevailing propagationconditions caused by the troposphere. Under normal conditions it should be expected that signals

will be able to be received beyond the normal line of sight distance. However under some

circumstances these distances will be considerably increased and significant levels ofinterference may be experienced.

Radio Signal Path Loss

Radio signal path loss is a particularly important element in the design of any radio communications

system or wireless system. The radio signal path loss will determine many elements of the radio

communications system in particular the transmitter power, and the antennas, especially their gain,height and general location. The radio path loss will also affect other elements such as the required

receiver sensitivity, the form of transmission used and several other factors.

Accordingly, path loss calculations are used in many radio and wireless survey tools for determining

signal strength at various locations. These wireless survey tools are being increasingly used to help

determine what radio signal strengths will be, before installing the equipment. For cellular operators

radio coverage surveys are important because the investment in a macrocell base station is high. Also,

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wireless survey tools provide a very valuable service for applications such as installing wireless LAN

systems in large offices and other centres because they enable problems to be solved before

installation, enabling costs to be considerably reduced. Accordingly there is an increasing importance

being placed onto wireless survey tools and software.

Signal path loss basics

The signal path loss is essentially the reduction in power density of an electromagnetic wave or

signal as it propagates through the environment in which it is travelling.

There are many reasons for the radio path loss that may occur:

Free space loss: The free space loss occurs as the signal travels through space without

any other effects attenuating the signal it will still diminish as it spreads out. This can be

thought of as the radio communications signal spreading out as an ever increasing sphere.

As the signal has to cover a wider area, conservation of energy tells us that the energy in

any given area will reduce as the area covered becomes larger. Absorption losses: Absorption losses occur if the radio signal passes into a medium

which is not totally transparent to radio signals. This can be likened to a light signalpassing through transparent glass.

Diffraction: Diffraction losses occur when an object appears in the path. The signal can

diffract around the object, but losses occur. The loss is higher the more rounded theobject. Radio signals tend to diffract better around sharp edges.

Multipath: In a real terrestrial environment, signals will be reflected and they will reach

the receiver via a number of different paths. These signals may add or subtract from each

other depending upon the relative phases of the signals. If the receiver is moved thescenario will change and the overall received signal will be found vary with position.

Mobile receivers (e.g. cellular telecommunications phones) will be subject to this effectwhich is known as Rayleigh fading.

Terrain: The terrain over which signals travel will have a significant effect on the

signal. Obviously hills which obstruct the path will considerably attenuate the signal,

often making reception impossible. Additionally at low frequencies the composition of

the earth will have a marked effect. For example on the Long Wave band, it is found thatsignals travel best over more conductive terrain, e.g. sea paths or over areas that are

marshy or damp. Dry sandy terrain gives higher levels of attenuation.

Buil dings and vegetation: For mobile applications, buildings and other obstructionsincluding vegetation have a marked effect. Not only will buildings reflect radio signals,

they will also absorb them. Cellular communications are often significantly impaired

within buildings. Trees and foliage can attenuate radio signals, particularly when wet. Atmosphere: The atmosphere can affect radio signal paths. At lower frequencies,

especially below 30 - 50MHz, the ionosphere has a significant effect, reflecting (or more

correctly refracting) them back to Earth. At frequencies above 50 MHz and more the

troposphere has a major effect, refracting the signals back to earth as a result of changingrefractive index. For UHF broadcast this can extend coverage to approximately a third

beyond the horizon.

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These reasons represent some of the major elements causing signal path loss for any radio

system.

The Fundementals

IntroductionMaxwell's equationsPlane wavesFree space lossGas LossRefractionDiffraction

ReflectionsTroposcatterRain effectsVegetationStatisticsLink budgetsNoiseMultipathMeasurementsModels

Beyond the Horizon

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You might imagine waves travel along straight lines for ever, or until they hit something. For a

transmitter on the ground, any power radiated above the horizon will go into space. Horizontally

beamed signals will travel to the horizon and then be absorbed, signals below horizontal will be

absorbed or scatter into space.

Rule of thumbdistance to radio horizon (km) versus transmitter height (m) d = 4.12h

We know signals do propagate beyond the horizon and the major mechanisms are:

Refraction - bending of signals towards ground

Scattering - from eddies in the air, from rain , from reflecting surfaces and objects

Diffraction - from terrain, buildings and vegetation

Atmospheric Refraction

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To understand refraction, which is the atmospheric bending of the radio path away from a

straight line, we need to remember Snell's law:

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Willebrord Snel van Royen (15801626) was a Dutch astronomer and mathematician and is most

famous for his law of refraction, which is now known as "Snell's law". In 1617 he reported on an

experiment to measure the distance between Alkmaar and Bergen op Zoom which are separated

geographically by one degree with the aim of determining the radius of the Earth. He measured

one degree to be equal to 107.4 km, which was only 3km out. He also developed new method for

calculating . He discovered his law of refraction in 1621.

Refractive index vs Height

As we move to higher altitudes we have lower pressures and lower temperatures. As a result the

refractive index of the atmosphere usually falls with height.

Radio waves get bent downwards and are able to propagate beyond the geometric horizon,

which extends range.

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To find out how much, we need to know how the refractive index of air varies with height. This

requires the introduction of a new "N" unit.

N - Units

The refractive index of air is very close to 1. Typically the refractive index n = 1.0003 at sea

level and this is most tedious - there are lots of decimals that must be used because the fine detail

is important, so we define a new unit, the "N" unit where:

N = (n - 1) x 1 000 000

N is typically 310 at sea level in the UK. The value of N can be calculated from this formula:

Where:

P = dry pressure, ~1000mb

T = temperature, ~300k

e = water vapour partial pressure ~40mb

The dry term depends only on pressure and temperature, the wet term also depends on the watervapour concentration. The temperature, pressure and water vapour pressure vary with time and

space.

Pressure falls exponentially with height, the scale height, where it drops to 1/e of the sea level

value is around 8km. (This value of e is not the water vapour pressure, it is the constant e from

natural logs and has the value 2.718). Scale heights are used frequently in describing functions

that decrease exponentially.

Temperature usually falls by 1oC/100m in the first few km above sea level.

Water partial pressure is much more complex, it is strongly governed by the weather and is

limited to the saturated vapour pressure - the amount of moisture the air can hold. Once thetemperature drops below 0C the excess water vapour condenses out as clouds. The saturated

water vapour pressure is around 40 mbar at 300K (a warm day) and 6mbar at 273K (freezing).

The height above the ground where the air temperature decreases to zero C is called the zero

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degree isotherm. It is typically at a few km in altitude, near the cloud base. Practically, in the UK

climate, the amount of water vapour above 2-3km is negligible.

The result of al this is that the refractive index normally falls exponentially with height in a

standard atmosphere. The scale height of the exponential is ~7.4km and as is shown below, in

the first 1000m we can approximate this pretty well with a straight line with a slope ~ -40 N/km.

Representing an exponential function as a straight line is cheating, but it is a good enough

approximation up to 1-2km or so. Beware of this cheat when planning systems on top ofmountains.

Super-refraction

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If dN/dh exceeds -157 N units, signals will be refracted by more than the curvature of the Earth

and be trapped. We call this super-refraction.

Why the -157 figure? To explain, recall that N typically falls by 40 units per km of height. We

call this the lapse rate of N.

The rate of change of angle of the ray d/dh ~ dn/dh ~ dN/dh x106 which we find from Snellslaw and through applying the small angle approximation sin()~tan()~() and

The radius of the Earth is ~ 6371 km. To just follow Earth curvature, d/dh needs to equal thecurvature of the earth, which is found to be -1.57x10-4 radians/km if you do the maths.

Remember N units are a million x ( refractive index - 1). So that is why dN/dh = -157 N units/kmis the figure required for a radio wave to just follow Earth.

The equivalent Earth radius

Many models are simpler if we can treat radio waves as if they were traveling along straight linesin a standard atmosphere (dN/dh = -40)We can achieve this by pretending the Earth has a larger radius which we call the equivalent

Earth radius Re.

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We define the k factor k such that Re= k R. Typically Re= 4/3 R in the UK, i.e. the k factor is4/3.

Having done this we can then study paths for clearance by drawing straight lines rather than

curves across a terrain profile. The ability to draw straight lines is practically, very important. It

also simplifies propagation prediction software used in link planning. Nobody does it by hand

any more. The image shows a path profile where line of sight is blocked. The red ovals show theFresnel ellipsoids, in this case the first. These will be covered when we come on to study

diffraction, but for a link to be line of sight, no-terrain should enter into this Fresnel ellipsoid.

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Duct depth and Roughness are also important. If the duct depth is small compared to thewavelength, energy will not be trapped. If the roughness is large compared to the wavelength,energy will be scattered out of the duct. Surface ducts have the ground as the lower boundary and

energy will be lost to the terrain, vegetation etc.

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Elevated ducts can allow signals to propagate for very long distances beyond the geometric

horizon. It is possible for intermediate terminals to be below the elevated duct and not able to

couple into itresulting in non-monotonic path loss with range, rather similar to the skip zone atHF. A good example of the temperature inversion occurred on 7th November 2006. Strong

inversions like this are unusual in the UK.

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The refractivity profiles (http://weather.uwyo.edu/upperair/sounding.html)show a widespread

sharp decrease in N with height. This gave rise to strong super-refraction and caused someinteresting anomalous propagation effects with long range interference to services.

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What causes conditions like this?

Causes of Ducting

Briefly the weather alters the temperature, pressure and humidity of regions of air as they are

moved about, mixed up, elevated and depressed by cyclones and anti-cyclones, and are heated bythe sun and cool down through radiation at night. There are several major ducting mechanisms:

Evaporation Ducts

There is usually a region extending for a few metres above the surface of the sea where the watervapour pressure is high due to evaporation. This also occurs over large bodies of inland water,

for example the great lakes. The thickness of this evaporation duct varies with temperature,

typically it extends to 5m above the surface in the North sea, 10-15m in the Mediterranean and

often much more over warm seas as in the Caribbean and Gulf. These ducts have a significanteffect on Shipping and have been extensively researched. It is the reason that VHF/UHF

propagation over sea can extend to great distances causing all sorts of international frequency co-ordination problems. It is also why you might want to get your warships anti-aircraft radarantenna nice and high.

Temperature Inversions

Usually, temperature falls with height by about 1 degree centigrade per 100m. On clear nightsthe ground cools quickly by radiation and this can result in a temperature inversion, where the air

temperature rises with height. This happens when solar radiation during the day heats up the

ground and the warm ground raises the temperature of the air near to it. This warm air rises as

thermals. On clear nights the ground can cool very quickly, also cooling the air close to it. This

results in the situation just after sunset where there is cool air close to the ground with warm airabove it. This is a temperature inversion.

If the air is dry, the temperature term in the equation of N above becomes dominant and super

refraction and ducting can occur. This is effect particularly common in desert regions.

If there is significant water vapour the relative humidity can quickly rise to 100% and excess

vapour condenses out as fog. This condensation reduces the water vapour density near the

ground. There is then cold dry air near the ground, with warmer moister air above. This results insub-refraction which can lead to multipath on otherwise apparently perfectly good line of sight

links.

Subsidence

This is a mechanism that can lead to elevated ducts and is associated with high pressure weathersystems - anticyclones. Descending air that has been forced downwards by the anticyclone heats

up as it is compressed. Remember, air pressure always falls with height so air that is descending

must be compressed and compressing air causes it to heat up. This descending air may becomewarmer than the air below it, leading to an elevated temperature inversion. This all happens at

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around 1-2km above the ground, which is too high to affect anyone except highly elevated

stations, as the angle will be too large for a ground based station to couple into the duct. As the

anticyclone evolves the air around the edges subsides and this brings the inversion layer closer tothe ground. A similar descending effect can happen at night. In general, the inversion layer is at

its lowest close to the edge of the anticyclone and at its highest highest in the middle.

Anticyclones and consequently temperature inversions, often exist over large continents for longperiods.

Advection

This is the movement of air masses, typically occurring in early evening in the summer when air

from a warm land surface advects over the cooler sea. This warm air mixes with the cooler airwhich will be relatively moist as it is close to the surface of the sea. This then extends the height

of the evaporation duct and can cause high humidity gradients together with temperature

inversion that forms a surface duct within the first few 100m above the sea. These ducts do not

persist over land and are a coastal effect. Typically in the UK they are associated with warm

anticyclonic weather over the continent of Europe and advection out over the north sea. Theytend to be weaker than subsidence ducts but they do occur relatively often over the North Sea

and can persist for many days. For example, it is relatively common for UHF signals topropagate well beyond line of sight from the East coast of England across the North Sea into the

low countries.

The picture below shows what the ITU-R consider to be the global incidence of ducting. It

replaces an earlier model that only used Latitude.This really does still need to be tested some

more as it may be more of a reflection of Matlab plotting routines for sparse data than actual

reality. Use with care.

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The original model was very crude:

Frequency of occurrence

Evaporation ducts - happen all the time around the UK and a widespread duct frequently forms

over the sea. Surface ducts occur for around 6% of time, they tend to be up to 300m in height andcover ~100km. This is a fairly low incidence compared to other regions. Surface ducts occur foraround 50% of the time in the Gulf, so they are not considered as anomalous in that region.

Elevated ducts exist for around 7% of time, they occur up to 3km in altitude, and cover ~100km.

Again this is low incidence compared to other regions Elevated ducts happen for 40% of the time

in Gulf.

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Next

Mike Willis May 5th, 2007

Tropospheric ducting occurs when a radio signal is reflected off of thetroposphereand continues

on a path that allows the signal to travel much farther than it normally would. This occurs whenthe temperature in the atmosphere experiences a shift called an inversion. When a temperature

inversion occurs,radio wavesthat would normally continue into space beyond the Earthsatmosphere are instead reflected and continue to follow the curvature of the planet. Radio waves

have been able to travel in excess of 1,000 miles (about 1,600 km) because of troposphericducting.

The Earths troposphere is the lowest layer of the atmosphere. It extends from 4 to 40 miles(about 6 to 60 km) above the surface. During normal conditions, this layer allows radio waves to

pass through into theupper atmosphere.Other layers, such as theionosphere,prevent waves

from being reflected higher up and returning to the ground.

During times of meteorological instability, the properties of the troposphere can change. When

cold air that is low to the ground has a warmer air mass pass over top of it, it causes a conditioncalled a temperature inversion. The cool air near the ground is moving slower than the warm air.

This means radio waves that encounter a temperature inversion will be carried faster over the

cold mass, bending the path of the wave downward and allowing it to curve with the surface.

Periods of relatively calm weather with clear skies are when tropospheric ducting is most oftenexperienced, which is indicative of the high pressure fronts that can cause temperatureinversions. The air masses have a high refractive index at this time, causing the radio waves to

move more slowly and aiding in the bending of their trajectory. The actual landscape between

the source of the signal and the horizon also can affect the distance it can travel, with flat landand water being the most effective.

There are other natural occurrences that can cause tropospheric ducting. Cool water coming offof a body of water under sun-warmed upper air masses can be a cause. In some areas of the

Mediterranean, the effect can last for months at a time.

An entire branch of enthusiasts has developed around tropospheric ducting and, more broadly,tropospheric propagation. People who attempt to receive signals from long distances via

tropospheric ducting are called DXers. The term comes from the radio code DX, which stands

for distance. DXers are classified by groups depending on the type of signal they are attemptingto detect. These signals can be radio, ultra-high frequency (UHF)or very-high frequency (VHF).