Microwave Antennas and Propagation

8/12/2019 Microwave Antennas and Propagation

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Note: The source of the technical material in this volume is the Professional

Engineering Development Program (PEDP) of Engineering Services.

Warning: The material contained in this document was developed for Saudi

Aramco and is intended for the exclusive use of Saudi Aramcos

employees. Any material contained in this document which is notalready in the public domain may not be copied, reproduced, sold, given,

or disclosed to third parties, or otherwise used in whole, or in part,

without the written permission of the Vice President, Engineering

Services, Saudi Aramco.

Chapter : Communications For additional information on this subject, contact

File Reference: CTR20204 J.S. Phillips on 873-0228

Engineering EncyclopediaSaudi Aramco DeskTop Standards

Microwave Antennas And Propagation


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Engineering Encyclopedia Communications

Microwaave Antennas and Propagation

Saudi Aramco DeskTop Standards

CONTENTS PAGES

DETERMINING CHARACTERISTICS OF MICROWAVE

ANTENNAS ........................................................................................................... 1

Derivation of Antennas from a Transmission Line......................................1

Basic Mechanics of Antenna Radiation.......................................................2

Microwave Feed Horn.................................................................................8

Parabolic Reflector ...................................................................................... 9

Horn Reflector Antenna ............................................................................ 11

Advantages and Disadvantages......................................................13

MICROWAVE TRANSMISSION PATH CHARACTERISTICS .......................14

LOS Propagation ....................................................................................... 14

Free Space Path Loss.................................................................................17

Other Propagation Losses.......................................................................... 18

Atmospheric Absorption................................................................18

Rain Attenuation ............................................................................ 19

Terrain and Obstruction Losses ..................................................... 20

Reflection .................................................................................................. 21

Delay Distortion............................................................................. 24

Multipath Propagation ................................................................... 24

Fresnel Zone Radii ......................................................................... 25

Fade Margin .............................................................................................. 30

Reliability Objectives ................................................................................ 31

Probability of Outages ................................................................... 32

Diversity.........................................................................................36


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Saudi Aramco DeskTop Standards

CALCULATING SYSTEM GAIN....................................................................... 40

Sample Gain Calculation ........................................................................... 43

WORK AID 1: FORMULAS AND REFERENCES FORDETERMINING MICROWAVE ANTENNA

CHARACTERISTICS ................................................................ 47

Determining Microwave Antenna Gain.....................................................47

Determining the Diameter of the Parabolic Reflector ............................... 48

WORK AID 2: PROCEDURE TO CALCULATE SYSTEM GAIN...................50

GLOSSARY ......................................................................................................... 52


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Saudi Aramco DeskTop Standards 1

DETERMINING CHARACTERISTICS OF MICROWAVE ANTENNAS

An antenna is the device that provides a transition of electromagnetic energy from the

transmission line to the free space and vice versa. An antenna is a reciprocal device, which

means that the characteristics that affect a transmitting antenna will have an identical effect ona receiving antenna. This section provides information on the following topics that are

pertinent in the determination of the characteristics of microwave antennas:

Derivation of Antennas from a Transmission Line

Basic Mechanics of Antenna Radiation

Microwave Feed Horn

Parabolic Reflector

Horn Reflector Antenna

Advantages and Disadvantages

Derivation of Antennas from a Transmission Line

The basic operation of an antenna can be understood through use of transmission line theory.

Figure 1 shows how a half-wave dipole can be developed from a quarterwave section of

transmission line. The open-ended section of transmission line develops standing waves of

voltage and current. When the conductors are parallel with each other, the fields that are

generated by the voltage and current are in opposite directions, and these fields will cancel;

therefore, the transmission line will not radiate a signal. If the conductors are spread apart,the fields that are generated will be in the same direction and the antenna will radiate waves

(energy) into free space. If the conductors are spread to a distance that is equal to one-half of

a wavelength of the signal on the transmission line, the antenna will radiate waves that are

one-half of a wavelength (l/2).


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Development of an Antenna from a Section of Transmission Line

Figure 1


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Basic Mechanics of Antenna Radiation

The radiation that is emitted by the antenna is in the form of transverse electromagnetic

(TEM) waves. The TEM wave consists of two components: the electric field (E-field) and

the magnetic field (H-field). Figure 2 shows a representation of the E- and H-fields. The E-field is represented by E-lines that are developed along the length of the antenna. The H-field

is represented by H-lines that are developed circumferentially around the antenna. The H-

field lines are perpendicular to the E-field lines.

The E and H-fields are developed from the standing waves of voltage and current that are 90 o

out-of-phase with each other. The H-field is at minimum intensity when the E-field is at

maximum intensity. The H-field will be at maximum intensity when the E-field is at

minimum intensity.

TEM Wave Radiation from an Antenna

Figure 2


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The following terms are used to describe the characteristics of antennas:

Polarization

Radiation Efficiency

Radiation Pattern

Directivity

Beamwidth

Gain

Capture Area

Bandwidth

Polarization is a term that is used to define the direction of the E-field lines in relation to the

surface of the earth. Because the E-field lines are developed along the length of the antenna,

the polarization of the transmitted wave is achieved through use of the position (horizontal or

vertical) of the transmitting antenna. If the transmitting antenna is vertical, the E-field lines

will be vertical to the surface of the earth, and the emitted wave is said to be vertically

polarized. Likewise, a horizontal antenna will emit a wave with horizontal polarization.

The receiving antenna must be in the same plane of polarization (vertical or horizontal) as the

transmitting antenna for the best reception. For example, a vertical antenna is normally used

to receive vertically polarized waves. A slight amount of twisting of the polarization occursas the TEM wave travels through free space. This twisting is called the faraday effect, and it

is normally not significant except in satellite communications.

The radiation efficiency of an antenna describes the ratio of the radiated power of an antenna

to the applied power of an antenna. Practical antennas will not be 100% efficient because

some of the applied power is lost. The radiation efficiency of an antenna is a function of the

resistance of the antenna. The actual radiation efficiency of an antenna depends on the design

of the antenna.

The term radiation pattern refers to the directional characteristics of an antenna. Nearly all

practical antennas tend to concentrate energy in specific directions rather than emit radiationthat is equal in all directions. A diagram typically is used to show the radiation pattern for an

antenna. Figure 3 shows the radiation patterns from an isotropic radiator and from a

directional antenna. The isotropic radiator equally emits radiation in all directions. The

radiation pattern of the directional antenna is stronger in one direction. The area of most

intense radiation is called the main lobe or major lobe. Other smaller lobes exist, and these

lobes are called minor lobes.


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Radiation Patterns

Figure 3

Directivity describes the ability of an antenna to radiate energy in one direction. In reference

to Figure 3, directivity is the comparison of the amount of energy that is radiated in the main

lobe to the energy that is radiated in the main lobe plus the energy that is radiated in all three

minor lobes. Directivity is defined as the ratio of the maximum power density that is radiated

by an antenna to the average power that is radiated by the same antenna.

Beamwidth is a measure of the width of the major lobe of a directional antenna, and it is

measured in degrees. The beamwidth provides an indication of how effective a directional

antenna is at aiming the radiated energy in one main direction; for example, an antenna with

a narrow major lobe will be more effective in aiming the radiated energy than will an antenna

with a wide major lobe.


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The gain of an antenna is also related to the directivity of the antenna because antennas are

essentially passive devices that do not add energy to an applied signal. Because antennas are

passive devices, the gain of an antenna is a directive gain that describes the percentage of

the power that is concentrated in the direction of radiation. Although a dipole is sometimes

used as a reference, an isotropic antenna is the reference point that is used to determine thegain of directional antennas. An isotropic antenna is a theoretical antenna that radiates power

equally in all directions. The gain of an antenna is the ratio of the power density in the

direction of radiation of the antenna to the power density of an isotropic radiator. Power

density is a measure of the strength of the electromagnetic field across a given volume. This

relationship can be expressed mathematically in dB as follows:

gain (dB) = 10 log(Pant/Piso)

Pant = Power density at some distance along the direction of radiation fromthe directional antenna.

Piso = Power density at the same distance from an isotropic radiator.

The gain of a given antenna depends on the size, shape, and efficiency of the antenna.

Capture area is the term that is used to describe the effective area from which an antenna can

capture (receive) transmitted signals. The capture area of a receive antenna is similar to the

beamwidth of a transmit antenna. The major lobe of the capture area represents the direction

from which a receive antenna is best able to receive a transmitted signal.

Bandwidth is the term that is used to describe the specific range of frequencies in which a

given antenna is designed to operate. An antenna that is operated at frequencies that are

above or below the specified bandwidth may not provide satisfactory service.


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Microwave Feed Horn

The microwave feed horn that is shown in Figure 4 is the simplest type of microwave

antenna. Most microwave transmission systems use waveguide in place of conventional

transmission line to connect the transmitter/receiver to the antenna. The microwave feed hornantenna consists of a section of connecting waveguide that is tapered (or flared outward) to

form a horn shape that provides a gradual transition from the characteristic impedance of the

waveguide to the impedance of free space. The operation of the microwave feed horn

antenna is similar to the operation of the half-wave dipole antenna that was previously

described. The spread of the conductors that was shown in Figure 1 is duplicated through use

of the horn of the microwave feed horn antenna. The horn allows the E-field lines and H-field

lines to leave the antenna and travel into free space.

Horn Antenna

Figure 4


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The geometry of the horn is such that one or both dimensions of the horn walls are tapered.

The gain of the microwave feed horn antenna depends on the ratio of the opening of the horn

to the square of the transmitted wavelength, and the gain is limited to approximately 20 dB in

practical applications. Because the gain of the horn antenna is not high enough for most

microwave relay applications, microwave feed horn antennas are used most often in lowperformance applications or they are used in conjunction with parabolic reflectors to form

parabolic antennas.

Parabolic Reflector

The most common antenna for use in microwave applications is the parabolic reflector or

parabolic antenna. The parabolic antenna is sometimes called a dish antenna because of its

unique shape. Saudi Aramco exclusively uses parabolic antennas for microwave

communication system antennas.

The parabolic antenna consists of two main components: the source of the energy andthe reflector. The energy source is commonly referred to as the feed, and it can be an antenna

such as a half-wave dipole or, more commonly, a horn antenna. The reflector is constructed

in the shape of a parabola because the geometry of a parabola is such that any ray of radiation

from the energy source that strikes the parabola will be reflected back in the same direction.

In addition, all of the reflected rays will travel an identical path length. Because all of the rays

are reflected in the same direction and are in-phase, the result is a highly concentrated beam

of radiation.

In order to ensure that all of the reflected rays are in-phase, the feed must be located at the

focus of the parabola. Ideally, the feed should act as a point source. Figure 5 shows the

common methods of feeding a parabolic antenna. Both of the antennas that are shown arecenter-fed, which refers to placement of the feed horn in the center of the parabolic reflector.

The front feed design is an economical approach that consists of a waveguide and a horn

antenna that are placed around the front of the parabolic reflector. The waveguide section and

feed horn will somewhat interfere with the radiation pattern that is produced by the antenna

and will limit the gain of the antenna. An alternate method of feeding the parabolic antenna is

the Cassegrain feed. With the Cassegrain feed, the waveguide and the feed horn are placed

behind the primary parabolic reflector, and a second reflector that is called a hyperboloid is

placed out in front of the primary parabolic reflector. The geometry of the hyperboloid causes

the radiation that is emitted from the feed horn back into the parabolic reflector to appear to

emanate from the focus point of the parabola.


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Methods of Feeding Parabolic Antennas

Figure 5

Parabolic antennas are used in microwave applications because of the high gain that can be

achieved with parabolic antennas. The gain of the parabolic antenna is directly proportional

to the ratio of the diameter of the reflector to the wavelength of the transmitted signal;

therefore, as the ratio of antenna diameter to signal wavelength increases, the gain of the

antenna also increases. This ratio shows that larger diameter reflectors produce higher

antenna gains than do small diameter reflectors, and in practical applications, the diameter ofthe reflector must be at least ten wavelengths. The gain of an antenna is also dependant on

the efficiency of the antenna. Parabolic antennas have a standard efficiency of 55%.


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The three factors (diameter of the reflector, wavelength, and efficiency) that affect the gain of

a parabolic antenna are represented in the equation to calculate antenna gain; however,

wavelength is not used directly because frequency is more convenient. Frequency can be

used to determine the gain because frequency is inversely proportional to wavelength. The

gain of a parabolic antenna with an efficiency of 55% can be calculated through use of thefollowing equation:

GdB= 20logFGHz+ 20logB + 17.8

where: GdB = Gain of a parabolic antenna in dB

FGHz = Frequency of the signal in GHz

B = Diameter of the parabola in meters

17.8 = A constant that accounts for the efficiency of the antenna and forunit conversions.

For example, the gain of a two meter parabola that operates at 6.000 GHz can be calculated as

follows:

GdB = 20logFGHz+ 20logB + 17.8

GdB = 20log(6) + 20log(2) + 17.8

GdB = 20(0.778) + 20(0.301) + 17.8

GdB = 15.6 + 6.0 + 17.8

GdB = 39.4 dB

Figure 15, which is located in Work Aid 1, can also be used to determine the gain of a

parabolic antenna through use of a straight edge that connects between the frequency of the

signal and the diameter of the reflector. The gain of the antenna is the point at which the

straight edge crosses the gain scale.


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The horn reflector antenna that is shown in Figure 6 is actually a special type of parabolic

antenna. The antenna consists of a waveguide and a feed horn that are at the bottom of a

portion of a parabolic reflector. Microwave energy from the waveguide is reflected off of theportion of the parabolic reflector to form a parallel beam that is similar to the parabolic

antenna. The geometry of the horn is curved so that the radiation from the feed horn is

reflected in concentrated parallel beams off the portion of the parabolic reflector. The main

difference between the horn reflector antenna and the parabolic antenna is that the feed

mechanism in the horn reflector antenna does not block the radiation from the reflector.


Figure 6


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Advantages and Disadvantages

There are definite advantages and disadvantages that are associated with both the parabolic

reflector antenna and the horn reflector antenna. Each advantage and disadvantage is a directresult of the geometry and the operational characteristics of the antennas.

One of the main advantages of the parabolic reflector antenna is the high overall gain. The

parabolic reflector antenna has a higher gain than does the horn reflector antenna, even when

these antennas are of comparable sizes. The higher gain is due to the complete parabolic

geometry of the parabolic reflector antenna. Also, the complete parabolic shape of the

parabolic reflector antenna provides a more focused or pencil-shaped beam than does the

horn reflector antenna. Pencil-shaped beams have less radiation loss from the transmitter to

the receiver.

The advantages of the parabolic reflector antenna also are the disadvantages of the hornreflector antenna. The horn reflector antenna does not produce a crisp pencil-shaped beam,

and its gain is not as high as that of the parabolic reflector antenna. Both of these

disadvantages are the result of the incomplete parabolic shape.

The horn reflector antenna does provide one distinct advantage because of the placement of

the feed apparatus. Recall that the feed apparatus of the parabolic reflector antenna is in the

path of the radiated signals, and the feed apparatus of the horn reflector antenna is out of the

path of the radiated signals; therefore, the feed apparatus of the horn reflector antenna does

not interfere with the antennas radiation pattern. As a direct result of the feed mechanisms

not interfering with the radiation pattern, the horn reflector antenna produces less noise than

does the parabolic reflector antenna. In the parabolic reflector antenna, the radiated signalbounces off the feed apparatus, which results in the production of noise and a low signal-to-

noise ratio. With the horn reflector antenna, the feed apparatus is not in the path of the

radiated signal, and this situation results in less noise production and a high signal-to-noise

ratio.


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MICROWAVE TRANSMISSION PATH CHARACTERISTICS

Microwave transmissions usually involve a series of microwave links that provide point-to-

point communications. The actual path that the microwave signals travel is critical to

effective and reliable communications. This section provides information on the followingtopics that are pertinent to the determination of microwave transmission path characteristics:

LOS Propagation

Free Space Path Loss

Other Propagation Losses

Reflection

Fade Margin

Reliability Objectives

LOS Propagation

LOS propagation refers to the method that microwave signals travel from one point to a

different point, and this propagation is shown in Figure 7. Figure 7 also shows a transmit

antenna that is mounted on a tower and faces a receive antenna that is also mounted on a

tower. The majority of microwave propagation occurs via space waves in a direct line-of-

sight (LOS) path from the transmit antenna to the receive antenna. Line-of-sight transmission

requires that a clear path be provided between the transmitting and the receiving antennas.

Mountains, trees, and the curvature of the earth limit the distance of a single-hop, line-of-sighttransmission.

In actual applications, the line-of-sight signal does not travel a perfectly straight path between

the antennas because the space wave is refracted by the earths troposphere. The amount of

refraction that occurs depends on the tropospheric conditions. Variations in the density of the

atmosphere at various altitudes and weather fronts will affect the refraction of microwave

signals. The effects of weather fronts are very unpredictable and can change rapidly as the

weather front progresses.

The following effects of tropospheric refraction are possible:

The wave is bent towards the earth.

The wave is not bent.

The wave is bent away from the earth.


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If the wave is bent towards the earth, the net effect is to increase the radio horizon beyond the

optical horizon. An increased radio horizon allows LOS propagation to occur over longer

distances. Under normal tropospheric conditions, signals are bent toward the earth.

When the wave is not bent, the radio horizon equals the optical horizon. In this condition, thedistance that a microwave signal can be propagated is limited to the optical horizon.

If the wave is bent away from the earth, the radio horizon is shorter than the optical horizon.

A shortened radio horizon limits the propagation of microwave signals to distances that are

shorter than the distances that would be possible without the refraction.

The effective earth radius (K) is a useful tool in a discussion of the effects of refraction on

propagation. K multiplied by the real earth radius is the radius of an effective earth curve.

This effective earth curve is equivalent to the relative curvature of the microwave signal with

respect to the curvature of the earth; therefore, any change in the bending of the microwave

signal that is caused by tropospheric refraction can be expressed by a change in K.

K is equal to 4/3 under normal atmospheric conditions. When K is equal to 4/3, the effective

radius of the earth is greater than the actual radius of the earth. The term earth flattening

describes conditions when K is greater than one. The earth can be considered flattened

under these conditions because microwave signals can be propagated for longer distances

before the curvature of the earth blocks the signal.

Under extreme tropospheric conditions, K can be infinite. When K is infinite, the curvature

of the microwave signal exactly matches the curvature of the earth. An infinite K represents a

condition in which microwave signals could be propagated for extremely long distances.

Infinite values of K are not desirable because these conditions allow signals from differentmicrowave systems that are separated by great distances to interfere with each other.

K can also be less than one. Values of K that are less than one represent a bulged earth

condition. The earth can be considered to be bulged because microwave signals cannot be

propagated for as great a distance before the curvature of the earth blocks the signal.

In addition to refraction, reflections of the space wave also occur. Just as light is reflected

from a mirror, microwaves can be reflected from any flat surface such as a building, a lake or

even flat ground. Figure 7 shows a ground reflected wave. The reflected waves normally are

not used as an intentional means of propagation. Instead, the reflected wave is usually

unintentional, and it can cause severe propagation problems. The main problem that is causedby the effect of reflected waves is that the reflected component of the transmitted wave is

often out-of-phase with the direct wave component. The phase difference at the receiving

antenna will result in a reduction of the received signal strength.


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Microwave Propagation

Figure 7


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Free Space Path Loss

As microwave signals propagate from point-to-point, the amplitude of the microwave signal is

attenuated by losses. One loss to which microwave signals are subjected is free space path

loss. Free space path loss is the loss that occurs in an electromagnetic wave as theelectromagnetic wave travels from point-to-point. Free space path loss is defined as the loss

that occurs between two isotropic antennas in free space, where there are no ground

influences or obstructions. Free space path loss does not account for absorption or for

reflection of energy from objects. Free space path loss only accounts for the spreading of an

electromagnetic wave as the electromagnetic wave travels through free space. An example of

free space path loss is the spreading of the electromagnetic energy in a microwave signal as

the microwave signal is propagated from the transmit to the receive antenna.

The spreading occurs in accordance with the inverse square law. The inverse square law

describes the spreading of a field so that the strength of the field at any given point is

inversely proportional to the square of the distance between the given point and the point atwhich the field originates. Recall from the discussion of LOS propagation that an

electromagnetic wave is composed of an electric field and a magnetic field. These fields

spread in accordance with the inverse square law. For example, the strength of the signal at

the receive antenna will be reduced by a factor of four if the distance between a transmit and

receive antenna is doubled.

Because the microwave signal spreads in accordance with the inverse square law, only a

portion of a transmitted signal is received by the receive antenna. The portion of the

transmitted signal that is not received is a loss. The portion of the radiated energy that is lost

due to free space path loss can be calculated through use of the following formula:

Lp= 92.4 + 20 log F(GHz) + 20 log D(km)

where: Lp = Free space path loss in db

F(GHz) = Transmission frequency in GHz

D(km) = Distance between transmitting and receiving antennas

in km

For example, the free space path loss of a microwave system that transmits at 6.0 GHz to a

receiving antenna that is 50 km away can be calculated as follows:

Lp = 92.4 + 20 log F(GHz) + 20 log D(km)

Lp = 92.4 + 20 log (6 GHz) + 20 log (50 km)

Lp = 92.4 + 15.6 + 34

Lp = 142 db


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The formula shows that free space path loss is a function of both the distance between

antennas and the frequency of the transmitted signal. Free space path loss will increase with

either an increase in the frequency of the transmitted signal or an increase in the distance

between the antennas.

Other Propagation Losses

Other propagation losses occur to microwave signals because of absorption or blockage of the

microwave signals by items in the propagation path. These other losses can occur in space or

along the ground. Losses in space are due to atmospheric absorption and rain attenuation of

the microwave signal. Losses along the ground are due to terrain and obstruction losses.

Atmospheric Absorption

Oxygen and water vapor in the atmosphere will absorb energy from microwave signals. This

absorption of energy is represented as a loss to the microwave signal. Absorption losses tomicrowave signals are analogous to I2R losses in metallic conductors; the energy that is

absorbed by oxygen and water vapor in the atmosphere is converted to heat, and the result of

the energy absorption is a reduction in the power of the microwave signal.

Oxygen and water vapor absorption is a very minor concern in microwave systems that

operate below 14 GHz. From 2 GHz to 14 GHz, oxygen absorption is only about 0.01 dB to

0.02 dB per kilometer, and the absorption from water vapor is even less. At 2 GHz, water

vapor absorption attenuation is only approximately 0.0003 dB/km. The attenuation that

results from water vapor absorption increases with frequency, and it is approximately equal to

the attenuation that results from oxygen absorption at 14 GHz. Figure 8 is a graph of the

attenuation of microwave signals that results from oxygen and water vapor absorption versusfrequency of the microwave signal. Figure 8 is used to determine the microwave signal losses

that result from oxygen and water vapor absorption.


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Atmospheric Absorption of Electromagnetic Waves

Figure 8

Rain Attenuation

The attenuation of microwave signals that results from rain attenuation is also of very little

concern in microwave systems that operate at 8 GHz or lower; however, at the highermicrowave frequencies, the losses that result from rain attenuation are significant. Rain

attenuation losses are the result of energy absorption by water droplets. The energy that is

absorbed by the water droplets is converted to heat.

The degree of attenuation that results from rainfall is a complex function of many variables.

The three most important variables are the frequency of the microwave signal, the area that is

covered by the rainfall, and the intensity of the rainfall. The total amount of rainfall along the

transmission path over a period of time is not significant. The intensity of the rainfall and the

area that is covered by the rainfall along the transmission path at any given instant are the

significant parameters.

The mechanism of the microwave signal attenuation that results from fog or clouds is

identical to that of rainfall; however, fog or cloud attenuation of microwave signals is much

less significant than rain attenuation. Figure 9 is a graph of attenuation that results from rain,

fog, or clouds at various rainfall rates. Figure 9 is used to determine the microwave signal

losses that result from rainfall, fog, or clouds.


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Attenuation Due to Precipitation

Figure 9


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Terrain and Obstruction Losses

Features of the terrain or man-made obstructions can directly cause losses to a microwave

signal. Such losses are caused by a blockage of the signal or a diffraction of the signal.

Obstructions (natural and man-made) that exist along the transmission path can physically

block the microwave signal. The severity of the signal blockage (complete or partial) that

occurs will depend on the size, shape, and nature of the obstruction. A complete blockage of

the signal results in a total loss of the received signal, and a partial blockage of the signal

results in an additional propagation loss to the signal. Because all signal blockages result in a

loss to the microwave signal, microwave transmission paths should avoid obstructions.

Diffraction occurs when the microwave signal grazes an obstruction, which results in a

scattering of the microwave signal. This signal scattering results in a loss to the microwave

signal, and these losses can reach 6 dB.

Reflection

Electromagnetic waves are subject to electromagnetic reflection during propagation.

Electromagnetic reflection occurs when an incident wave strikes the boundary of two media,

and some or all of the incident waves power does not enter the second medium. The

boundary can exist on the ground or in space. A body of water or a building can be a

reflective surface on the ground, and the boundary between a mass of cool air and a mass of

warm air can act as a reflective surface in space.

There are three types of electromagnetic reflection:

Specular reflection

Diffuse reflection

A combination of specular and diffuse reflection

Electromagnetic reflection is specular when the reflection occurs at a smooth boundary.

Specular electromagnetic reflection results in a reflected wavefront that maintains the shape of

the incident wavefront. Specular electromagnetic reflection of microwave signals is

analogous to the reflection of a flashlight beam in a mirror. Dry lake beds, salt flats, and

atmospheric boundaries present a mirror-like surface that can result in specular reflection of

microwave signals.


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Electromagnetic Reflection

Figure 10


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Delay Distortion

Delay distortion is a problem with microwave systems that is caused by electromagnetic

reflections of microwave signals along the transmission path or within waveguide runs.

Delay distortion occurs when a portion of the microwave signal undergoes reflections so thatthe reflected portion of the signal arrives at the receive antenna at least several wavelengths

behind the unreflected signal. The delayed portion of the signal interferes with the direct

signal, and the end result of the interference that is associated with delay distortion is noise.

Noise is defined as any unwanted component of the received signal that lowers the

performance of a system.

The transmission paths that are most likely to experience delay distortion are paths that

consist of low, flat, intermediate terrain that is between high, elevated antennas. For example,

this type of path can occur when the transmit and receive antennas are located on building

tops and the transmission path is aligned with streets. A path from mountain top to mountain

top with low flat terrain in between could also cause delay distortion.

Reflections within waveguides that occur because of impedance mismatches and irregularities

also cause delay distortion. Delay distortion that is caused by reflections that are within

waveguides can be avoided through minimization of the length of waveguide runs.

Multipath Propagation

Multipath propagation also results from electromagnetic reflection. Multipath propagation

occurs when reflected waves that are out-of-phase with the direct wave arrive at the receive

antenna. Under these conditions, the received signal is the vector sum of all of the various

component waves that vary in phase and amplitude, and there will be short intervals in whichthe various vectors will cancel each other to produce a null. This null production causes most

of the very deep fading that is experienced on many microwave links. Fading is the term that

describes the reduction in the strength of a received signal.

Multipath propagation can result from electromagnetic reflections that occur in the

atmosphere or on the ground. Electromagnetic reflection in the atmosphere occurs when a

microwave signal strikes the boundary between two layers in the atmosphere. Layers in the

atmosphere are produced from temperature inversions and weather fronts.

Temperature inversions produce layers in the atmosphere when the air that is just above the

ground cools more rapidly than do higher portions of the atmosphere. When a temperatureinversion occurs, the cool air is trapped beneath warmer air and a reflective boundary is

formed at the interface. Temperature inversions normally occur at night because of the

radiative cooling of the ground. Temperature inversions also can occur during the day;

however, these temperature inversions infrequently occur.


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Temperature inversions are very common along Saudi Aramco microwave transmission

paths. Unfortunately, there is nothing that can be done to overcome the effects of temperature

inversions that are in progress. If a temperature inversion is in progress, layers exist in the

atmosphere; therefore, multipath propagation will occur.

Weather fronts can also produce layers in the atmosphere. When a weather front moves into

an area, the weather front is often accompanied by a sudden decrease in temperature at lower

elevations in the atmosphere. This phenomenon creates boundaries between the layers in the

atmosphere at which electromagnetic reflection can occur. The layers that are produced by

weather fronts are not nearly as stable as those layers that are produced by temperature

inversions; therefore, multipath fades that are produced by weather fronts generally do not last

as long as the fades that are produced by temperature inversions.

Ground reflections occur when the transmission path travels over a smooth or semi-rough

surface. Examples of smooth surfaces that can cause multipath propagation are dry lake beds

and salt flats. Sand dunes and road beds are examples of semi-rough surfaces that canproduce multipath propagation. Recall from the discussion of reflection that the reflections

from smooth surfaces are stronger than reflections from semi-rough surfaces; therefore, the

fades that are produced from smooth surfaces are deeper than the fades that are produced

from semi-rough surfaces.

The transmission path has a bearing on the susceptibility of the system to multipath

propagation. Long paths tend to produce more multipath propagation than do short paths.

Multipath propagation also is somewhat greater at higher frequencies. The incidence of

multipath fading varies not only as a function of path length and frequency, but also as a

function of climate. In the most favorable areas such as paths in dry, windy areas, multipath

fading may be non-existent. Hot, humid areas typically have a high incidence of multipathfading.

Fresnel Zone Radii

If transmit and receive antennas were located in empty space, reflected signals would not

exist, and free space path loss would be the only loss. The strength of the resultant signal at

the receive antenna would be equal to the transmitted power minus the free space path loss.

Because the transmit and receive antennas are located on earth, the signal strength at the

receive antenna now is also dependent on the nature of the reflected signals that are present at

the receive antenna. The presence of in-phase reflected waves results in a greater signal

strength than would occur with no reflected waves being present; therefore, in-phasereflected waves result in signal addition (gain). For similar reasons, out-of-phase reflected

waves result in signal attenuation (loss).


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Fresnel Zones are used to determine the effects that reflected waves have on reception.

Because reflected waves travel a greater distance than do primary waves, the reflected and

primary waves will not always arrive at the receive antenna in-phase. Fresnel zones define

the boundaries at which reflections can occur such that the reflected and primary waves arrive

in-phase or out-of-phase.

As previously discussed, the electromagnetic reflection must occur at a narrow angle of

incidence in order for the reflected wavefront to reach the receive antenna. A consequence of

reflection at a narrow angle of incidence is that a 180o phase shift of the reflected wave is

produced at the point of reflection.

If the reflected path length is one half wavelength longer than the primary path length, the

reflected waves will arrive at the receive antenna one-half wavelength behind the primary

waves. One half wavelength is equal to 180o; therefore, a one half wavelength longer

reflected path produces a 180o phase shift between the reflected waves and the primary

waves. Likewise, a reflected path length that is one wavelength longer than the primarypathlength produces a net zero phase shift between the reflected waves and the primary

waves.

In-phase reflection occurs when the reflective path is one half wavelength longer than the

primary path. The 180o phase shift that results from reflection combines with the 180o phase

shift that results from the one half wavelength longer pathlength to produce a net zero phase

difference between the primary and reflected waves. Out-of-phase reflection occurs when the

reflected path length is one wavelength longer than the primary path because the net phase

shift is 180o.

The first Fresnel Zone consists of all those points at which reflections can occur so that thepath length of a reflected wave is exactly one half wavelength longer than the path length of a

primary wave. If all the points that constitute the first Fresnel zone were plotted between a

transmitting antenna and a receiving antenna, a long, narrow ellipsoid would be produced.

The radius of the first Fresnel zone ellipsoid can be calculated for any point along the

transmission path through use of the following equation:


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where: F1 = First fresnel zone radius in m

d1 = Distance from one end of the transmission path to thereflection point in km

D = Total transmission path length in km

d2 = D - d1

f = Frequency in GHz


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The second Fresnel Zone consists of all those points at which reflections can occur so that the

path length of the reflected waves is exactly one wavelength longer than the path length of

primary wave. Each successive Fresnel Zone continues the pattern through description of a

reflected wave pathlength that is one half wavelength longer than the reflected wave

pathlength of the previous Fresnel Zone. If reflection occurs at the ellipsoid that is defined byan odd numbered Fresnel zone, the reflected signal will arrive at the receive antenna in-phase

with the direct signal; therefore, odd numbered Fresnel zones produce additive reflections.

Likewise, all even numbered Fresnel zones produce subtractive reflections.

The radius for any fresnel zone, n, at a given point along a path can be calculated through use

of the following equation:

where: Fn = Fresnel zone radius in m

F1 = First Fresnel zone radius at that point of the path in m

n = Number of fresnel zone

Figure 11 illustrates the ellipsoids that make up the first three Fresnel Zones. The ellipsoid

that constitutes the second Fresnel Zone is somewhat larger than the ellipsoid that constitutes

the first Fresnel Zone. The difference in the radius between Fresnel Zones decreases as the

number of the Fresnel Zones increase. Restated, the difference in the size of the first and

second Fresnel Zone is greater than the difference in the size of the second and third Fresnel

Zones.

The radius of the first Fresnel Zone at point A of Figure 11 can be calculated through use of

the following formula and the data that are given in Figure 11:

F1A = 17.3 (10)(10)/(2.000)(20)

F1A = 17.3 2.5

F1A = (17.3)(1.58)

F1A = 27.3 meters


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The radius of the second and third Fresnel Zones can be calculated now that the radius of the

first Fresnel Zone is known. The radius at point A of the second Fresnel Zone is calculated as

follows:

F2A = F1An

F2A = (27.3) (2)

F2A = (27.3)(1.41)

F2A = 38.5 meters

The radius at point A of the third Fresnel Zone is calculated as follows:

F3A = F1An

F3A = 27.3 3

F3A = (27.3)(1.73)

F3A = 47.2 meters


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Fresnel Zones

Figure 11

Fade Margin

Fade margin is a factor that is considered during a system design and that accounts for the

effects of fading. Essentially, fade margin represents the amount of fading loss that the

system can overcome and still meet the desired quality objectives of the system. The fademargin of a system determines the extent to which a system is over-engineered. Restated, the

fade margin results in an unfaded signal strength that is stronger than the signal needs to be.

The system changes that can result from an excess margin to fading include stronger

transmitters, more sensitive receivers, or shorter pathlengths. Because over-engineering is

expensive, fade margin is limited to the amount that is necessary to meet the reliability

objectives of the system.


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Fades are caused by both terrain and atmospheric effects; therefore, the following equation

can be used in calculations of fade margin that include factors to account for both effects:

FM = 30 logD + 10 log(6ABF) - 10 log(1-R) - 70

where: FM = Fade margin in dB

D = Path length in km

A = Roughness factor

- 4 over water or smooth terrain

- 1 over average terrain

- 0.25 over rough mountainous terrain

B = Factor to convert the worst month probability to an

annual probability

- 0.5 for hot, humid areas

- 0.25 for average inland areas

- 0.125 for very dry or mountainous areas

F = Frequency in GHz

R = Reliability

The term 30 logD accounts for atmospheric effects because a longer path is more likely to

experience fading. The term 10 log(6ABF) accounts for terrain effects because the nature of

the terrain affects the probability that fades will occur. The reliability term is included

because a system that requires higher reliability will require a higher fade margin.


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Reliability Objectives

A reliability objective is an objective that describes the acceptable outage time for a system.

This reliability objective is expressed as a reliability percentage. An outage time is a time

when the received signal level is below the level that is acceptable. The minimum acceptablesignal level is that signal level that allows the system to meet the performance objectives of

the system. If the signal level falls below the minimum acceptable level, the receiver may

still produce an output; however, this output will not meet the performance objectives of the

system. The term outage is not meant to imply that the received signal is totally lost. The

term outage only means that the received signal is not acceptable.

This section provides information on the following topics that are pertinent to reliability

objectives:

Probability of Outages

Diversity

Probability of Outages

The reliability percentage is related to the acceptable outage time through use of the following

expression:

Acceptable outage time = 1 - reliability percentage

For example, if the reliability objective is a reliability percentage of 99.99%, the acceptable

outage time would be .01% of the time or about 53 minutes a year. Restated, the received

signal level may fade below the level that is acceptable for about 53 minutes a year. Because

a reliability objective implies an allowable outage time, the probability of an outage can be

used to determine if the reliability objective will be met. For example, an outage probability

of 0.0001% implies an outage time of 31.5 seconds a year. As long as the allowable outage

time is less than 31.5 seconds a year, the reliability objectives will be met.


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The following equations can be used to calculate rm and ryr, which are both indications of

fade probability:

rm(worst month) = a x 10-5x (f4)1.5x (D/1.61)3

where: a = Roughness factor



ryr(over a year) = b x r m

where: b = Factor to convert the worst month probability to an

annual probability

rm = Fade probability on the worst month

The equation for Undp can be simplified through use of the equations for rm and ryr to yield

the following new equations for Undp:

Undp = ryrx 10F/19

where: Undp = Non-diversity annual outage probability

ryr = Fade probability over a year

F = Fade margin in dB


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Undp = b x r mx 10F/19

where: Undp = Non-diversity annual outage probability

b = Factor to convert the worst month probability to anannual probability

rm = Fade probability on the worst month

F = Fade margin in dB

The reliability objectives of a system influence the selection of the transmission path. The

probability of an outage for a system is influenced by the terrain and climate along the

transmission path. A path that has a higher probability of an outage will cause the system to

be less able to meet the reliability objectives of the system. The effect of the reliability

objectives on the selection of the transmission path can be illustrated through an examinationof an example microwave system.

The example microwave system has a reliability objective of 99.999%. This reliability

objective can be converted to the following acceptable outage time:

Acceptable outage time = 1 - reliability percentage

Acceptable outage time = 1 - 99.999%

Acceptable outage time = 0.001%

Because the acceptable outage time is 0.001%, the nondiversity outage probability cannot begreater than 0.001% (0.00001).

The example system operates at 2.120 GHz, and the path length is 45 km. If the path is over

very dry terrain of average roughness, the fade margin that is required to produce a

nondiversity outage probability of 0.00001 can be determined as follows:

Undp = a x b x (3.0 x 10-7) x f1.5x D3x 10-F/10

10-F/10= Undp/(a x b x (3.0 x 10 -7) f1.5x D3)

10-F/10

= 0.00001/(1 x 1/8 x (3.0 x 10-7

) x (2.120)1.5

x (45)3

)

10-F/10 = 9.48 x 10-4

F = -(10)(log(9.48 x 10-4))

F = 30.2 dB


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If the example system had a transmission path over smooth terrain in a hot, moist area, the

fade margin that is required would be much higher. The fade margin that is required for these

conditions can be calculated as follows:

Undp = a x b x (3.0 x 10-7) x f1.5x D3x 10-F/10

10-F/10 = Undp/(a x b x (3.0 x 10 -7) x f1.5x D3)

10-F/10 = 0.00001/(4 x 1/2 x (3.0 x 10-7) x (2.120)1.5x 453)

10-F/10 = 5.93 x 10-5

F = -(10)(log(5.93 x 10-5)

F = 42.3 dB

The fade margin that is required of the system with the transmission path over the smooth

terrain in a hot, moist area is 12.1 dB greater than the fade margin that is required of the

system with rolling terrain in a dry area. The greater fade margin that is required of the

second system could result in shorter path lengths, more powerful transmitters, more sensitive

receivers, or even a less reliable system. As stated in the discussion of fade margin, added

fade margin is expensive; therefore, the selection of the transmission path not only affects the

reliability of the system. It also affects the costs of the system.

Diversity

The purpose of diversity systems is to increase system reliability. System reliability is

increased through use of diversity systems because they reduce the effect that disruptiveatmospheric conditions have on the microwave system. The following are the three types of

diversity systems:

Space diversity

Frequency diversity

Quad diversity

Space diversity systems use a single transmitter to transmit to two physically separated

receiving antennas. Space diversity systems reduce atmospheric effects because it is unlikelythat the effects are the same along both transmission paths at the same points in time.


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Frequency diversity systems use two sets of transmitters and receivers that are usually

connected to a single antenna and that operate at different frequencies. Frequency diversity

systems take advantage of the fact that many atmospheric effects are frequency dependent and

therefore will not affect both channels simultaneously.

Quad diversity systems are a combination of the two previous diversity systems. Using two

transmitters and four receivers, quad diversity systems have the benefits of both space and

frequency diversity.

The measure of the benefit of diversity systems to system reliability is dependent upon the

correlation of fading between the separate paths. Each individual diversity configuration has

a correlation coefficient that describes the amount of correlation between the paths. The

coefficient ranges between 0 and 1. At 0, there would be completely independent fading

between the paths, and at 1, the separate paths would fade identically. Completely

independent fading is the ideal objective of all diversity systems. Completely independent

fading implies that the atmospheric conditions that affect one path will not affect the otherpath; therefore, the likelihood of both paths fading simultaneously is greatly reduced. The

typical correlation coefficients that result from frequency diversity systems are somewhat

higher than 0.8. The typical correlation coefficients that result from space diversity systems

range from 0.6 to 0.7.

A more convenient term to describe the benefits of diversity systems is diversity improvement

factor. The diversity improvement factor (I) is used with Undp to calculate the diversity

outage probability (Udiv). The diversity outage probability is the probability that outages will

occur in a system that employs a diversity system. Undp and Udiv are related by the

following equation:

Udiv= Undp/I

where: Udiv = Diversity outage probability

Undp = Non diversity outage probability

I = Diversity improvement factor

The diversity improvement factor can be used for either space diversity or frequency

diversity. The space diversity improvement factor depends on the spacing between the

receive antennas, the path length, the transmitted frequency, and the fade margin. The spacediversity improvement factor is calculated with the following equation:


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where: Isd = Improvement diversity factor


s = Vertical spacing between receive antennas in meters

F = Fade Margin in dB

D = Path length

For example, if a 2.12 GHz system has a non-diversity outage probability of 1.1 x 10-5 and

the vertical spacing between the antennas is 12 meters, the diversity outage probability can be

calculated if the diversity improvement factor is known. The diversity improvement factor

can be calculated as follows:

After the diversity improvement factor is calculated, the diversity outage probability can becalculated as follows:

Udiv = Undp/I

Udiv = 1.1 x 10-5/8.14

Udiv = 1.4 x 10-6

The non-diversity outage probability for this example was given as 1.1 x 10-5, and the

diversity outage probability is 1.4 x 10-6; therefore, this space diversity system increased the

reliability of the system by approximately a factor of 10. A greater vertical separation

between antennas or a higher fade margin would result in an even greater improvement.

The frequency diversity improvement factor is not easily determined. All of the data that

relates to frequency diversity improvements is experimentally derived and is based on only

the 4 GHz and 6 GHz bands. Also, all of the data that are obtained from the experiments only

relate to average length paths (40 - 50 km).

The following general relationships tend to exist in frequency diversity systems:


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The frequency diversity improvement factor decreases when the frequency

of the two transmitters increases for a given difference in transmitter

frequencies. For example, a 200 MHz difference in the 4 GHz band

provides twice the improvement as a 200 MHz difference in the 6 GHz

band would provide.

The frequency diversity improvement factor increases when the difference

in frequency between the two transmitters increases.

The frequency diversity improvement factor also increases as the fade

margin increases.

System reliability improvement from quad diversity systems is almost exclusively the result

of the space diversity component of the system; therefore, the quad diversity improvement

factor equals the space diversity factor. The quad diversity improvement factor is calculated

as if a straight space diversity system was used.


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CALCULATING SYSTEM GAIN

System gain is the difference between the transmitter output power and the minimum receiver

input power. If the system is to operate correctly, system gain must be greater than or equal

to the sum of all the gains and losses that are incurred by a signal between the transmitter andreceiver. If system gain is less than the sum of these gains and losses, the received signal

level will be less than the receiver sensitivity (threshold), and the system performance will be

degraded.

Figure 12 illustrates a typical microwave system link, and it includes the locations where

gains and losses occur in the system. The microwave power amp (Pt) is the transmitter for the

system. The signal from the microwave power amp goes to the channel combining network

(Lb) where losses may occur. From the channel combining network, the signal is fed via

some transmission medium (either coaxial cable or elliptical waveguide) to the antenna feed.

There are losses (Lf) that are associated with the transmission medium. The signal is

transmitted from the antenna that provides a gain (At). As the signal is propagated, variouslosses (Lp) occur. The microwave signal is captured by the receive antenna that also provides

a gain (Ar). From the receive antenna, the signal is again fed through a transmission medium

that also results in a loss (Lf). Finally, the signal is fed through a channel separation network

that results in an additional loss (Lb). If the system has been designed properly, the resultant

signal that arrives at the receiver input is greater than the microwave threshold (Cmin).


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System Gains and Losses

Figure 12

Mathematically, system gain can be expressed with the following formula:

Gs= P t- Cmin

where: Gs = System gain (dB)

Pt = Transmitter output power (dBm)

Cmin = Receiver threshold (dBm)


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For a properly designed system, the difference between the transmitter output power (dBm)

and the receiver threshold (dBm) must be greater than or equal to the losses plus the gains as

previously stated. The following is a mathematical expression of this relationship:

Pt- Cmin> losses + gains

where: Pt = Transmitter output power (dBm)


The following are the individual gains that must be considered in a calculation of system gain:

At = Transmit antenna gain (dB) relative to an isotropic radiator.

Ar = Receive antenna gain (dB) relative to an isotropic radiator.

The following are the individual losses that must be considered in a calculation of system

gain:

Lp = Free-space path loss between antennas (dB).

Lf = Waveguide or coaxial cable feeder loss (dB) between the

distribution network (channel combining network or channel

separation network) and its respective antenna.

Lb = Total coupling or branching loss (dB) in the circulators, filters,

and distribution network between the output of a transmitter or

the input to a receiver and its respective waveguide feed orcoaxial connector.

FM = Fade margin for a given reliability objective.

The previously stated equations can be combined to yield the following system gain equation:

Gs= P t- Cmin> FM +Lp+ L f+ Lb- At- Ar

where: Gs = System gain (dB)

Pt = Transmitter output power (dBm)


FM = Fade margin


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Lp = Free space path loss (dB)

Lf = Waveguide or coaxial cable feeder loss (dB)

Lb = Total coupling or branching loss (dB)

At = Transmit antenna gain (dB)

Ar = Receive antenna gain (dB)

Because system gain is indicative of a net loss, the losses are represented with positive dB

values, and the gains are represented with negative dB values.

Sample Gain Calculation

Figure 13 illustrates a simple microwave link. The output power of the transmitter is 37 dBm

and the transmit frequency is 2.100 GHz. Both the transmit antenna and the receive antenna

have a gain of 33.2 dB. There is 50 km of dry mountainous terrain that separates the

transmitter and receiver. The transmitter and receiver both have 30 meters of coaxial cable

that connect them to their respective antennas. The coaxial cable that is used has a

characteristic loss of 4.0 dB/100 meters. A reliability of 99.999% is desired of the system.

The total coupling loss is 3 dB. This given information can be used to calculate the gain of

the simple microwave link that is shown in Figure 13.

Typical 2 GHz Microwave System Link

Figure 13


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The following system gain equation can be used to calculate the maximum receiver threshold

that is required:

Gs= P t- Ccim

The system gain equation can be rearranged to solve for the maximum receiver threshold as

follows:

Ccim= P t- Gs

Recall that the system gain must be greater than or equal to the sum of the gains and losses of

the system. If the gains and losses are inserted into the above equation, the following

expression results:

Cmin Pt- (FM + Lp+ Lf+ Lb- At- Ar)

The previous equation showed that to determine the maximum receiver threshold, the

transmitter power, gains, and losses of the system must be determined.

Transmitter power is given by the manufacturer. In the example system, transmitter power is

37 dBm.

As discussed previously, fade margin is dependent on the reliability objectives of the system

and the nature of the terrain that is between the transmitter and the receiver. The following

equation is used to calculate FM:

FM = 30 logD + 10 log(6ABF) - 10 log(1 - R) - 70




- 4 over water or smooth terrain

- 1 over average terrain

- 0.25 over a very rough, mountainous terrain

B = The factor to convert a worst-month probability to an

annual probability

- 0.5 for hot humid areas


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- 0.25 for average inland areas

- 0.125 for very dry or mountainous areas


R = Desired system reliability

The following variables should be inserted into the FM equation for the example system:

D = 50 km

A = 0.25

B = 0.125

F = 2.100 GHz

R = .99999

The fade margin for the example system now can be calculated as follows:


FM = 30 log(50) + 10 log(6 x 0.25 x 0.125 x 2.1) - 10

log(1-.99999) - 70

FM = 30(1.6990) + 10(-0.4048) - 10(-5) - 70

FM = 50.97 + (-4.048) - (-50) - 70

FM = 26.9 dB

The following equation is used to calculate free space path loss:

Lp = 92.4 + 20 logF(GHz) + 20 logD(km)


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The free space path loss for the example system can now be calculated as follows:

Lp = 92.4 + 20 logF(GHz) + 20 logD(km)

= 92.4 + 20 log(2.1) + 20 log(50)

= 92.4 + 20(0.3222) + 20(1.6990)

= 92.4 + 6.4 + 34.0

= 132.8 dB

If the system operated at a higher frequency, losses that result from atmospheric and rain

absorption would be added to the free space path loss.

The feeder loss of the system equals the characteristic loss of the waveguide or coaxial cable

multiplied by the length of the run, and this loss can be mathematically stated with the

following equation:

Lf = (length of run)(characteristic loss)

The feeder loss of the example system now can be calculated as follows:

Lf = (length of run(characteristic loss)

= (60 meters)(4 dB/100 meters)

= 2.4 dB

The total branching loss of the system was given as 3 dB, and the gain of both the transmitter

and receiver antennas was given as 33.2 dB.

With the transmitter power, the gains, and the losses of the system having been determined,

the maximum receiver threshold can be calculated as follows:

Cmin Pt- (FM + Lp+ Lf+ Lb- At- Ar)

Cmin 37 dBm - (26.9 dB + 132.8 dB + 2.4 dB + 3 dB - 33.2 dB - 332

dB)

Cmin 37 dBm - (98.7 dB)

Cmin - 61.7 dBm

For the example system, the receiver threshold must be less than or equal to 61.7 dBm if the

system is to operate properly.


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WORK AID 1: FORMULAS AND REFERENCES FOR DETERMINING

MICROWAVE ANTENNA CHARACTERISTICS

Determining Microwave Antenna Gain

The gain that is provided by a standard parabolic antenna with 55% efficiency and a given

diameter can be determined through use of the following equation:

GdB= 20 logFGHz+ 20 logB + 17.8




The gain of a parabolic antenna also can be determined through use of Figure 14. To

determine the gain of a parabolic antenna with Figure 14, use a straight edge to connect

between the frequency of the signal and the diameter of the reflector. The gain of the antenna

is read at the point at which the straight edge crosses the gain scale.


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Parabolic Antenna Gain

Figure 14

Determining the Diameter of the Parabolic Reflector

The required diameter for a parabolic antenna to produce a given gain can be determined

through use of the following equation:

where: B = Antenna diameter in meters

Gdb = Antenna Gain in dB


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FGHz = Frequency in GHz

The required parabolic antenna diameter also can be determined through use of Figure 14.

Use a straight edge to connect between the frequency of the signal and the gain of the

antenna. The diameter of the antenna is read at the point at which the straight edge crossesthe diameter scale.


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WORK AID 2: PROCEDURE TO CALCULATE SYSTEM GAIN

1. Evaluate the given information to determine the equation that is needed to calculate

system gain.

2. If the transmitter power and receiver sensitivity are given, solve the following

equation:

Gs= P t- Cmin

where: Gs = System gain

Pt = Transmitter power

Cmin = Receiver threshold

3. To determine if the gain of a system is sufficient for the gains and losses of the system,

the following relationship must be true:

Gs FM + Lp + Lf + Lb - At - Ar

To determine the sum of the gains and losses, the magnitude of each individual gain or loss

must first be determined.

3a. To calculate fade margin, solve the following equation:





= 4 over water or smooth terrain

= 1 over average terrain

= 0.25 over rough mountainous terrain

B = Factor to convert the worst month

probability to an annual probability

= 0.5 for hot, humid areas

= 0.25 for average inland areas

= 0.125 for very dry or mountainous areas


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R = Reliability

3b. To calculate the free space path loss, solve the following equation:

Lp= 92.4 + 20 logFGHz+ 20 logDkm

where: FGHz = Frequency in GHz


3c. To calculate feeder losses, multiply the characteristic loss of the waveguide

or coaxial cable by the length of the waveguide or coax run.

3d. Coupling losses are provided by the manufacturer.

3e. To calculate antenna gain, solve the following equation:

GdB= 20 logFGHz+ 20 logB + 17.8





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GLOSSARY

antenna The ratio of the power that is radiated by an antenna to the sum

of the power that is radiated from an antenna and the power that

is dissipated from an antenna as losses.

correlation coefficient The relationship of fading components in two separate diversity

paths.

E-field Electric field.

EIRP Effective Isotropic Radiated Power.

E-lines Electrostatic lines of forces that make up the E-field.

fading Any loss in signal strength at the receiving antenna.

fade margin An uncertainty factor in the system gain equation that accounts

for multipath propagation, terrain sensitivity, and reliability

objectives.

fresnel zones Areas of reflection that surround a transmission path that

alternately provide aiding and canceling effects.

H-field Magnetic field.

H-lines Magnetic lines of force that make up the H-field.

homogeneous medium A medium with uniform properties throughout.

isotropic radiator A theoretical antenna that emits radiation equally in all

directions.

k Equivalent earth radius.

multipath propagation The effect of radiowaves that travel by more than one path.

noise figure The signal-to-noise ratio of an ideal noiseless device divided by

the signal-to-noise ratio at the output of an amplifier or areceiver.

polarization The angular alignment of the radiated E-lines with respect to the

surface of the earth.

radiation The equivalent resistance that would dissipate the same amount

of power that is radiated by an antenna.


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reciprocity The property of mutual exchange in two directions.

specular reflection A reflection from a relatively smooth surface.

system gain The difference between the nominal output power of atransmitter and the minimum input power to a receiver.

terrain sensitivity The effect that various terrains have on a transmitted radio wave.

Microwave Antennas and Propagation

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