rfm_pdd day 3

© Okey Ugweje, PhD

RF/Microwave Systems: Planning, Design &

Deployment

Day 3

Antennas & Transmission LinesAntennas & Transmission Lines

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Antennas Antenna Basics Radiation Pattern Antenna types, composition and operational

principles Antenna gains, patterns, and selection principles Types of Antennas Line-of-Sight Microwave

Antennas Antenna Basics Radiation Pattern Antenna types, composition and operational

principles Antenna gains, patterns, and selection principles Types of Antennas Line-of-Sight Microwave

Day 3

RF/Microwave Systems : PDDProgram Schedule

RF/Microwave Systems : PDDProgram Schedule

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RF/Microwave SystemsRF/Microwave Systems

AntennasAntennas

© Okey Ugweje, PhD


Antenna BasicsAntenna Basics

Antenna Concepts and DefinitionsElectromagnetic Fields and CharacterizationRadiation PatternGain Antenna types, composition and

operational principlesAntenna gains, patterns, and selection

principlesAntenna system testing

Antenna Concepts and DefinitionsElectromagnetic Fields and CharacterizationRadiation PatternGain Antenna types, composition and

operational principlesAntenna gains, patterns, and selection

principlesAntenna system testing

© Okey Ugweje, PhD


Antenna Concepts and Definitions

Antenna Concepts and Definitions

© Okey Ugweje, PhD

Concepts and DefinitionsConcepts and DefinitionsWhat is an antenna? Antenna is a passive device that transmit & receive EM wave Antennas do not require external power to operate

What is an antenna? Antenna is a passive device that transmit & receive EM wave Antennas do not require external power to operate

© Okey Ugweje, PhD

Concepts and DefinitionsConcepts and Definitions The purpose of any antenna is to: Provide a transition between a transmission line and a

free-space radiation To do this, an antenna should

1. have good impedance match (low reflection coefficient) with the transmission line

2. have low ohmic losses (high transmission coefficient)3. direct energy with desired antenna gain in the desired

angular sectors Provide angular selectivity (directivity) for

transmission or reception of plane waves4. minimize energy radiated into undesired sectors

The purpose of any antenna is to: Provide a transition between a transmission line and a

free-space radiation To do this, an antenna should

1. have good impedance match (low reflection coefficient) with the transmission line

2. have low ohmic losses (high transmission coefficient)3. direct energy with desired antenna gain in the desired

angular sectors Provide angular selectivity (directivity) for

transmission or reception of plane waves4. minimize energy radiated into undesired sectors

© Okey Ugweje, PhD

Antennas do not amplify RF energy It can only radiate (at max) what is put into it

If I00% efficient, an antenna will not radiate, more, total power than is delivered to it

Antennas function as directional amplifiers over some specified frequency bandwidth

Antennas do not amplify RF energy It can only radiate (at max) what is put into it

If I00% efficient, an antenna will not radiate, more, total power than is delivered to it

Antennas function as directional amplifiers over some specified frequency bandwidth

© Okey Ugweje, PhD

EM Fields and CharacterizationEM Fields and CharacterizationWhat is an Electric Field?An electric field applies a force on a charge at a distance

where q is the charge in Amps, or coulombs, CThe charge on one electron is 1.6x10-19 C and is the

electric field strength in Volts/m

When a charge, q, is placed in an electric field, a force F will be exerted on it

What is a Magnetic Field?A magnetic field applies a force on a moving charge

What is an Electric Field?An electric field applies a force on a charge at a distance

where q is the charge in Amps, or coulombs, CThe charge on one electron is 1.6x10-19 C and is the

electric field strength in Volts/m

When a charge, q, is placed in an electric field, a force F will be exerted on it

What is a Magnetic Field?A magnetic field applies a force on a moving charge

F qE

E

/E F q

F qv B ��

© Okey Ugweje, PhD

where is the velocity of q in meters/s, and is the magnetic

flux density in weber/meter2 (N/Cs/meters)

Therefore, the total force on a moving charge is

Properties of EM waves in Free SpaceElectric field and magnetic fields are orthogonalThe direction of propagation of the EM wave is orthogonal

to both the electric and magnetic fields

where is the velocity of q in meters/s, and is the magnetic flux density in weber/meter2 (N/Cs/meters)

Therefore, the total force on a moving charge is

Properties of EM waves in Free SpaceElectric field and magnetic fields are orthogonalThe direction of propagation of the EM wave is orthogonal

to both the electric and magnetic fields

F qv B ��

v

B��

F q E v B ��

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Plane Wave Propagation E field in orientated along the x axisB field in orientated along the y axisE & B are orthogonal to each otherBoth E & B oscillate at the same

frequency as they propagateEM wave is propagating in the z directionK, the direction of propagation is

orthogonal to both E and BThe EM wave is horizontal (y) polarized

K is the direction of propagationThe polarization of the EM wave is defined by the orientation of

the electric field

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Frequency, Time and Space

Frequency (f), that an EM wave oscillates

is expressed in Hertz (cycles/sec).

Period (T)time it takes to compete one

cycle of oscillation, T = 1/f sec.

EM waves propagate in free space at the speed of light, c = 3 x 108 m/s

Wavelength () the distance the field travels

during one cycle

Distance c

f

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Phase Phase expresses the directional relationship between two or

more time or spatially varying vectorsmeasure of the relative position in time within a single period

of the signalSpectrumrange of frequencies that a signal contains

Absolute bandwidthwidth of the spectrum of a signal

Effective bandwidth (or just bandwidth)narrow band of frequencies that most of the signal’s energy

is contained in

© Okey Ugweje, PhD

Planewave PropagationPlanewave PropagationThe time variation of an electric

field operating at frequency, f can be expressed as Re{ej2ft}, which means that it oscillates (i.e., rotate in phase by 2) every 1/f seconds

c = λ f, therefore the time to travel a distance λ, is t = λ /c or 1/f

Therefore, the electric field changes phase by 2 for each wavelength of propagation

The time variation of an electric field operating at frequency, f can be expressed as Re{ej2ft}, which means that it oscillates (i.e., rotate in phase by 2) every 1/f seconds

c = λ f, therefore the time to travel a distance λ, is t = λ /c or 1/f

Therefore, the electric field changes phase by 2 for each wavelength of propagation

All the energy in a planewaveis in phase on the plane perpendicular to the direction of propagation

© Okey Ugweje, PhD

Physical laws governing electric and magnetic fieldsFaraday’s Law (1830s)“Time varying magnetic fields produce electric

fields”

Physical laws governing electric and magnetic fieldsFaraday’s Law (1830s)“Time varying magnetic fields produce electric

fields”

Ampere-Maxwell Law (1870s)“Moving charge (current) and

time varying electric fields produce magnetic fields”

Ampere-Maxwell Law (1870s)“Moving charge (current) and

time varying electric fields produce magnetic fields”

Gauss’s Law (1840s)“Electric charge produces electric fields”“There is no magnetic charge”

Gauss’s Law (1840s)“Electric charge produces electric fields”“There is no magnetic charge”

© Okey Ugweje, PhD

Accelerating ChargeAccelerating ChargeAn accelerating charge produces time varying electric and

magnetic fieldsA time-varying electric field produces a time varying magnetic

fieldAnd, a time varying magnetic field produces a time-varying

electric fieldThus, propagating electromagnetic waves are producedNon-Accelerating ChargeA stationary charge produces only an electric fieldA charge moving with a constant velocity (DC current)

produces static electric and magnetic fields

An accelerating charge produces time varying electric and magnetic fields

A time-varying electric field produces a time varying magnetic field

And, a time varying magnetic field produces a time-varying electric field

Thus, propagating electromagnetic waves are producedNon-Accelerating ChargeA stationary charge produces only an electric fieldA charge moving with a constant velocity (DC current)

produces static electric and magnetic fields

© Okey Ugweje, PhD

PowerPower

where 0 is the intrinsic impedance of free spacewhere 0 is the intrinsic impedance of free space

2

( )V

P V I v a or wattsR

2 2

0

1E ( / ), , , ,

2aveP watts metersr r

0 377 ( )ohms

© Okey Ugweje, PhD

What’s a decibel (dB)?What’s a decibel (dB)?The dB scale allows us to plot a

function with a wide range of values on a readable scale

It expresses a power ratio

The dB scale allows us to plot a function with a wide range of values on a readable scale

It expresses a power ratio

10log adB

iso

PD

P

© Okey Ugweje, PhD

dB PropertiesdB PropertiesConverting from dB to Linear

Arithmetic operations using dBsMultiplication:

Division:

Raised to a power:

Converting from dB to Linear

Arithmetic operations using dBsMultiplication:

Division:

Raised to a power:

( /10)10 dBxlinearx

(linear) ;

(in dB)

x yz

x y z

(linear)

(in dB)

yx

zx y z

(linear)

(in dB)

ax y

x ay

© Okey Ugweje, PhD

Using dBsUsing dBs If the ratio is unity, you have 0 dBEach time the ratio doubles, add 3 dBEach time the ratio is reduced by 1/2, subtract 3 dBEach time the ratio increases (or decreases) by a power of 10,

add (or subtract) 10 dB

If the ratio is unity, you have 0 dBEach time the ratio doubles, add 3 dBEach time the ratio is reduced by 1/2, subtract 3 dBEach time the ratio increases (or decreases) by a power of 10,

add (or subtract) 10 dB

© Okey Ugweje, PhD

Reference AntennasReference Antennas

Difficult to build or approximate physically, but mathematically simple to describe

A popular reference for 1000 MHz & above PCS, microwave, etc.

Difficult to build or approximate physically, but mathematically simple to describe

A popular reference for 1000 MHz & above PCS, microwave, etc.

Quantity Units

Gain above Isotropic radiator dBi

Gain above Dipole reference dBd

Effective Radiated Power vs. Isotropic (watts or dBm) EIRP

ERP Effective Radiated Power vs. Dipole (watts or dBm) ERP

Isotropic radiator are truly non-directional - in 3 dimensions Isotropic radiator are truly non-directional - in 3 dimensions

Dipole Antenna

Notice that a dipolehas 2.15 dB gaincompared to anisotropic antenna.

Dipole AntennaNon-directional in 2-dimensional plane onlyCan be easily constructed, physically practicalA popular reference: below 1000 MHz

800 MHz cellular, land mobile, TV & FM

Dipole AntennaNon-directional in 2-dimensional plane onlyCan be easily constructed, physically practicalA popular reference: below 1000 MHz

800 MHz cellular, land mobile, TV & FM

© Okey Ugweje, PhD

Antenna Gain And ERP ExamplesAntenna Gain And ERP ExamplesMany wireless systems at 1900 & 800

MHz use omni antennasPatterns are usually drawn in the E-field

radiation units, based on equal power to each antenna

Typical wireless omni antenna concentrates most of its radiation toward the horizon, where users are, at the expense of sending less radiation sharply upward or downward

Wireless antenna’s maximum radiation is 12.1 dB stronger than the isotropic (thus 12.1 dBi gain), and 10 dB stronger than the dipole (so 10 dBd gain).

Many wireless systems at 1900 & 800 MHz use omni antennas

Patterns are usually drawn in the E-field radiation units, based on equal power to each antenna

Typical wireless omni antenna concentrates most of its radiation toward the horizon, where users are, at the expense of sending less radiation sharply upward or downward

Wireless antenna’s maximum radiation is 12.1 dB stronger than the isotropic (thus 12.1 dBi gain), and 10 dB stronger than the dipole (so 10 dBd gain).

© Okey Ugweje, PhD


Antenna ParametersAntenna Parameters

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Directivity, Gain, & Beamwidth(How are they Related?)

Directivity, Gain, & Beamwidth(How are they Related?)

DirectivityDirectivity, D(θ,φ), describes the angular variation in an

antenna’s ability to efficiently transmit or receive plane waves

DirectivityDirectivity, D(θ,φ), describes the angular variation in an

antenna’s ability to efficiently transmit or receive plane waves

Therefore, Dmax is the ratio of the max power intensity radiated by directive antennas to that radiated by isotropic antennas radiating the same total power.

Therefore, Dmax is the ratio of the max power intensity radiated by directive antennas to that radiated by isotropic antennas radiating the same total power.

Maximum Directivity Maximum Directivity

max

max

Maximum radiation intensity watts/steradian

Average radiation intensity in watts/steradian

I

/ 4t

D

P

© Okey Ugweje, PhD

Expression for Maximum Directivity

where A/2 is the area of the antenna aperture in 2 and is the aperture efficiency factor

If the power is uniformly distributed across the array and there are no amplitude or phase errors, =1, otherwise <1

The effective aperture area Ae = A

This is the equivalent area of a uniformly distributed aperture that has the same directivity and beamwidth

Expression for Maximum Directivity

where A/2 is the area of the antenna aperture in 2 and is the aperture efficiency factor

If the power is uniformly distributed across the array and there are no amplitude or phase errors, =1, otherwise <1

The effective aperture area Ae = A

This is the equivalent area of a uniformly distributed aperture that has the same directivity and beamwidth

© Okey Ugweje, PhD

Antenna GainAntenna Gain Antennas are passive devices: they do not produce

powerCan only receive power in one form and pass it on in

another, minus incidental lossesCannot generate power or “amplify”

However, an antenna can appear to have “gain” compared against another antenna or condition. This gain can be expressed in dB or as a power ratio. It applies both to radiating and receiving

A directional antenna, in its direction of maximum radiation, appears to have “gain” compared against a non-directional antenna

Gain in one direction comes at the expense of less radiation in other directions

Antennas are passive devices: they do not produce powerCan only receive power in one form and pass it on in

another, minus incidental lossesCannot generate power or “amplify”

However, an antenna can appear to have “gain” compared against another antenna or condition. This gain can be expressed in dB or as a power ratio. It applies both to radiating and receiving

A directional antenna, in its direction of maximum radiation, appears to have “gain” compared against a non-directional antenna

Gain in one direction comes at the expense of less radiation in other directions

Omni-directionalAntenna

DirectionalAntenna

Antenna Gain is RELATIVE, not ABSOLUTEWhen describing antenna “gain”, the comparison

condition must be stated or implied

© Okey Ugweje, PhD

By definition, the Gain of an antenna is:

where Pin is the total power into the antenna

Therefore, Gmax is a ratio of the maximum power intensity radiated by directive antenna to that radiated by a lossless isotropic antenna radiating the same input power

The gain of an antenna can be approximated by:

By definition, the Gain of an antenna is:

where Pin is the total power into the antenna

Therefore, Gmax is a ratio of the maximum power intensity radiated by directive antenna to that radiated by a lossless isotropic antenna radiating the same input power

The gain of an antenna can be approximated by:

max

max

Maximum radiation intensity watts/steradian

Radiation intensity of a isotropic with the same input power

I

/ 4in

G

P

© Okey Ugweje, PhD

Determination of GainDetermination of Gain

Apply the same input power to a lossless isotropic antennaMeasure power received from bothThe difference of the measurement is the gain (P2 - P1)

Apply the same input power to a lossless isotropic antennaMeasure power received from bothThe difference of the measurement is the gain (P2 - P1)

© Okey Ugweje, PhD

Low vs. High Gain AntennasLow vs. High Gain AntennasThe Gain of an antenna can be approximated by

Antennas with gain < 20 dBi is said to be a low gain antenna

The Gain of an antenna can be approximated by

Antennas with gain < 20 dBi is said to be a low gain antenna

2

4AreaGain

© Okey Ugweje, PhD

How Antennas Achieve GainHow Antennas Achieve Gain Quasi-Optical Techniques (reflection, focusing)

Reflectors can be used to concentrate radiation technique works best at microwave

frequencies, where reflectors are smallExamples:

corner reflector used at cellular or higher frequencies

parabolic reflector used at microwave frequencies

grid or single pipe reflector for cellular Array techniques (discrete elements)

Power is fed or coupled to multiple antenna elements; each element radiates

Elements’ radiation in phase in some directions In other directions, a phase delay for each

element creates pattern lobes and nulls

Quasi-Optical Techniques (reflection, focusing)Reflectors can be used to concentrate radiation

technique works best at microwave frequencies, where reflectors are small

Examples:corner reflector used at cellular or higher

frequenciesparabolic reflector used at microwave

frequenciesgrid or single pipe reflector for cellular

Array techniques (discrete elements)Power is fed or coupled to multiple antenna

elements; each element radiatesElements’ radiation in phase in some directions In other directions, a phase delay for each

element creates pattern lobes and nulls

© Okey Ugweje, PhD

Directivity vs Gain Directivity vs Gain Directivity is a ratio of the power radiated by the antenna with

respect to an isotropic antenna radiating the same powerGain is a ratio of the power radiated by an antenna with respect

to a lossless isotropic antenna with the same input power

Directivity is a ratio of the power radiated by the antenna with respect to an isotropic antenna radiating the same power

Gain is a ratio of the power radiated by an antenna with respect to a lossless isotropic antenna with the same input power

The gain of an antenna is the directivity minus the losses in the antenna

The gain of an antenna is the directivity minus the losses in the antenna

The gain of an array with distributed sources can be confusing, but directivity is not

The gain of an array with distributed sources can be confusing, but directivity is not

© Okey Ugweje, PhD

Antenna BeamsAntenna Beams

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Beamwidth Beamwidth

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Directivity & BeamwidthDirectivity & BeamwidthSmall antennas can

coherently add contributions over a wide angular range, but since they collect energy over a small area, the maximum directivity is small

Small antennas can coherently add contributions over a wide angular range, but since they collect energy over a small area, the maximum directivity is small

Large antennas have high directivity because they sum the contributions over a large area but they can only do this over a small angular region

Large antennas have high directivity because they sum the contributions over a large area but they can only do this over a small angular region

small large

© Okey Ugweje, PhD

Beamwidth & DirectivityBeamwidth & Directivity

For an isotropic antenna, the area of the beam is 4 steradians and Dmax = 1.0

For an isotropic antenna, the area of the beam is 4 steradians and Dmax = 1.0

For a directive antenna, area of the beam is ΨxΨy and Dmax = 4LxLy /2 or Dmax = 4/ ΨxΨy

For a directive antenna, area of the beam is ΨxΨy and Dmax = 4LxLy /2 or Dmax = 4/ ΨxΨy

Note:The maximum directivity can

be expressed as the ratio of the steradian area of the beam of an isotropic antenna to the area of the main beam of the directive antenna

The directivity of an antenna is inversely related to the area of it’s main beam. Therefore, you can not have a wide beamwidth and high directivity at the same time

Note:The maximum directivity can

be expressed as the ratio of the steradian area of the beam of an isotropic antenna to the area of the main beam of the directive antenna

The directivity of an antenna is inversely related to the area of it’s main beam. Therefore, you can not have a wide beamwidth and high directivity at the same time

Ly

Lx

© Okey Ugweje, PhD

Antenna PolarizationAntenna Polarization The orientation of the electric field

component of the antenna is called its polarization.

RF current in a conductor causes EM fields that seek to induce current flowing in the same direction in other conductors.

Coupling between two antennas is proportional to the cosine of the angle of their relative orientation

The orientation of the electric field component of the antenna is called its polarization.

RF current in a conductor causes EM fields that seek to induce current flowing in the same direction in other conductors.

Coupling between two antennas is proportional to the cosine of the angle of their relative orientation

To intercept significant energy, a receiving antenna must be oriented parallel to the transmitting antennaA receiving antenna oriented at right angles to the transmitting antenna

is “cross-polarized”; will have very little current inducedVertical polarization is the default convention in wireless telephony In the cluttered urban environment, energy becomes scattered and “de-

polarized” during propagation, so polarization is not as criticalHandset users hold the antennas at seemingly random angles…..

To intercept significant energy, a receiving antenna must be oriented parallel to the transmitting antennaA receiving antenna oriented at right angles to the transmitting antenna

is “cross-polarized”; will have very little current inducedVertical polarization is the default convention in wireless telephony In the cluttered urban environment, energy becomes scattered and “de-

polarized” during propagation, so polarization is not as criticalHandset users hold the antennas at seemingly random angles…..

© Okey Ugweje, PhD

Size of an AntennaSize of an AntennaThe size of an antenna depends on the type of antenna! The size of an antenna depends on the type of antenna!

Suppose you needs an antenna with 15 dBi gain?

it would have to have an ideal square aperture of at least:

Suppose you needs an antenna with 15 dBi gain?

it would have to have an ideal square aperture of at least:

At 38 GHz (new LMDS band), the antenna would be ~ 0.5 in2

At 750 kHz (750-AM, radio), the antenna would be at least 24,965 in2 (4/10ths of a mile)

At 38 GHz (new LMDS band), the antenna would be ~ 0.5 in2

At 750 kHz (750-AM, radio), the antenna would be at least 24,965 in2 (4/10ths of a mile)

2

2 2

4

15dBi2.517

4

AreaGain

Area

© Okey Ugweje, PhD

RF/Microwave Systems RF/Microwave Systems

Antenna RadiationAntenna Radiation

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Radiation PatternsRadiation PatternsAntennas are designed to deliberately direct or minimize

radiation in different angular regionsAntennas can be designed to have:Omni-directional radiation patternsSectoral radiation patternsHigh gain patternsSidelobe control and/or beam shaping

Antennas are designed to deliberately direct or minimize radiation in different angular regions

Antennas can be designed to have:Omni-directional radiation patternsSectoral radiation patternsHigh gain patternsSidelobe control and/or beam shaping

Omni-Directional Radiation PatternAn Omni antenna has a constant 0 dBi

pattern in all directionsAn Omni pattern is what would be

generated by an isotropic antenna

Omni-Directional Radiation PatternAn Omni antenna has a constant 0 dBi

pattern in all directionsAn Omni pattern is what would be

generated by an isotropic antenna

In reality there are no isotropic antennas - but there are some designs that come close

In reality there are no isotropic antennas - but there are some designs that come close

© Okey Ugweje, PhD

Sectoral Radiation PatternSectoral Radiation PatternSectoral radiation patterns are designed to provide beam

coverage within certain angular sectors and reject signals from other angular sectorsThese are used for point to region coverageGains are typically in range of 3 dBi to 20 dBi, dependent

upon the size of the sector coverage (beamwidth) desired

Sectoral radiation patterns are designed to provide beam coverage within certain angular sectors and reject signals from other angular sectorsThese are used for point to region coverageGains are typically in range of 3 dBi to 20 dBi, dependent

upon the size of the sector coverage (beamwidth) desired

Cell towers often has 3 faces for mounting three antennas with 120° azimuth beamwidths

© Okey Ugweje, PhD

SidelobesSidelobesSidelobes are very important in Antenna EngineeringSidelobes are very important in Antenna Engineering

© Okey Ugweje, PhD

Referencing Sidelobe LevelsReferencing Sidelobe Levels

1st sidelobe is +17 dB with respect to isotropic

1st sidelobe is +17 dB with respect to isotropic

1st sidelobe is -13 dB with respect to the main beam

1st sidelobe is -13 dB with respect to the main beam

© Okey Ugweje, PhD

Average Sidelobe Levels Average Sidelobe Levels

SLave is the average sidelobe level wrt isotropic

PS is power in sidelobe region Pt is the total power radiated Pmainbeam is power in the main beam s is the steradian area of the

sidelobes mainbeam is the steradian area of the

main beam

SLave is the average sidelobe level wrt isotropic

PS is power in sidelobe region Pt is the total power radiated Pmainbeam is power in the main beam s is the steradian area of the

sidelobes mainbeam is the steradian area of the

main beam

NoteThe average isotropic sidelobe level is just 1 minus the

fractional power in the main beamTherefore, anything you do that takes power from the main

beam, raises the average sidelobe level

NoteThe average isotropic sidelobe level is just 1 minus the

fractional power in the main beamTherefore, anything you do that takes power from the main

beam, raises the average sidelobe level

4save

t

PSL

P

4

4s mainbeam

avemainbeam t

P PSL

P

1 ( / )

1 ( / 4 )mainbeam t

avemainbeam

P PSL

1 mainbeamave

t

PSL

P

© Okey Ugweje, PhD

Basic Antenna Radiation Patterns Parameters


© Okey Ugweje, PhD



Beam PeakRegion of maximum response, usually a measurement of

Gain (dB relative to isotropic radiator)Main LobeThe “business end” of the antenna, angular area of highest

response 1st Side LobeThe sidelobe nearest to the beam peak, a function of

antenna design illumination taper (energy distribution)Null DepthThe pattern phase reverses 180º, usually an indication of

focusVSWR voltage standing wave ratio, commonly measured as return

loss (dB)

Beam PeakRegion of maximum response, usually a measurement of

Gain (dB relative to isotropic radiator)Main LobeThe “business end” of the antenna, angular area of highest

response 1st Side LobeThe sidelobe nearest to the beam peak, a function of

antenna design illumination taper (energy distribution)Null DepthThe pattern phase reverses 180º, usually an indication of

focusVSWR voltage standing wave ratio, commonly measured as return

loss (dB)

© Okey Ugweje, PhD

Effective Radiated PowerEffective Radiated PowerAn antenna radiates all power fed to it

from the transmitter, minus any incidental losses

Every direction gets some amount of power

Effective Radiated Power (ERP) is the apparent power in a particular directionEqual to the actual transmitter power

times antenna gain in that directionEffective Radiated Power is expressed in

comparison to a standard radiatorERP: compared with dipole antennaEIRP: compared with Isotropic

antenna

An antenna radiates all power fed to it from the transmitter, minus any incidental losses

Every direction gets some amount of power

Effective Radiated Power (ERP) is the apparent power in a particular directionEqual to the actual transmitter power

times antenna gain in that directionEffective Radiated Power is expressed in

comparison to a standard radiatorERP: compared with dipole antennaEIRP: compared with Isotropic

antenna

© Okey Ugweje, PhD

Example:

Antennas A and B each radiate 100 watts from their own transmitters

Antenna A is our referenceAntenna B is directional. In its maximum direction, its signal

seems 2.75 stronger than the signal from antenna AAntenna B’s ERP in this case is 275 watts.

© Okey Ugweje, PhD

Radiation PatternsKey Features And Terminology

Radiation PatternsKey Features And Terminology

An antenna’s directivity is expressed as a series of patterns

Horizontal Plane Pattern graphs the radiation as a function of azimuth (i.e., direction N-E-S-W)

Vertical Plane Pattern graphs the radiation as a function of elevation (i.e., up, down, horizontal)

An antenna’s directivity is expressed as a series of patterns

Horizontal Plane Pattern graphs the radiation as a function of azimuth (i.e., direction N-E-S-W)

Vertical Plane Pattern graphs the radiation as a function of elevation (i.e., up, down, horizontal)

Typical ExampleHorizontal Plane Pattern

Antennas are often compared by noting specific landmark points on their patterns: -3 dB (“HPBW”), -6 dB, -10 dB pointsFront-to-back ratioAngles of nulls, minor lobes, etc.

Antennas are often compared by noting specific landmark points on their patterns: -3 dB (“HPBW”), -6 dB, -10 dB pointsFront-to-back ratioAngles of nulls, minor lobes, etc.

© Okey Ugweje, PhD

Other Possible LossesOther Possible LossesPolarization mismatchAntenna angular alignmentRain or other atmospheric effectsTransmission line lossesRefractionAtmospheric losses are larger for low elevation angles

Polarization mismatchAntenna angular alignmentRain or other atmospheric effectsTransmission line lossesRefractionAtmospheric losses are larger for low elevation angles

© Okey Ugweje, PhD

What is Bandwidth? What is Bandwidth? In communication systems it sets the data transmission rate

and in radar the bandwidth determines the range resolution In communication systems it sets the data transmission rate

and in radar the bandwidth determines the range resolution

Antenna carrier frequency is f0, but if data is transmitted or received, the antenna will have to support a signal bandwidth of f0 ± ∆f/2.

Antenna may also have to support a tunable bandwidth where the f0 is tuned or changed

Antenna is required to transmit and receive EM energy over the signal bandwidth without any adjustments. However, it is possible make adjustments when the tunable bandwidth is changed

Antenna carrier frequency is f0, but if data is transmitted or received, the antenna will have to support a signal bandwidth of f0 ± ∆f/2.

Antenna may also have to support a tunable bandwidth where the f0 is tuned or changed

Antenna is required to transmit and receive EM energy over the signal bandwidth without any adjustments. However, it is possible make adjustments when the tunable bandwidth is changed

1Hz

22 m

1Bit Rate = Hertz

f

cr c

f

f

© Okey Ugweje, PhD

Antenna ImpedanceAntenna Impedance

Everything has an impedance, Z: Everything has an impedance, Z:

Where the real component, R, is the radiation resistance and the imaginary component, X, is the reactance

Where the real component, R, is the radiation resistance and the imaginary component, X, is the reactance

Reactance can be either:inductive (like an inductor) or capacitive (like a capacitor)

Reactance can be either:inductive (like an inductor) or capacitive (like a capacitor)

Even air or a vacuum has an impedance – the characteristic impedance of free space:

Even air or a vacuum has an impedance – the characteristic impedance of free space:

© Okey Ugweje, PhD

Power Transfer & Antenna ResonancePower Transfer & Antenna Resonance

For maximum power transfer,

Rantenna = System Z0

jX = 0.0

For maximum power transfer,

Rantenna = System Z0

jX = 0.0

In addition to the standing wave phenomenon, Resonance also describes the impedance response of a structure where:

the reactance goes to zero at a particular frequency

In addition to the standing wave phenomenon, Resonance also describes the impedance response of a structure where:

the reactance goes to zero at a particular frequency

Generally, the most striking resonances occur when an antenna is electrically small - in the neighborhood of a wavelength in size (fundamental and lower order harmonics)

Generally, the most striking resonances occur when an antenna is electrically small - in the neighborhood of a wavelength in size (fundamental and lower order harmonics)

Some antennas have resonances at 0.25λ, 0.50λ, 0.75λ, λ, etc.

and some have resonances at 0.50λ, 1λ, 1.5λ, 2λ, etc.

© Okey Ugweje, PhD


Types of AntennasTypes of Antennas

© Okey Ugweje, PhD

Low Gain Antennas/ApplicationsLow Gain Antennas/Applications

Electrically Small Wire Antennas - Sub-resonant LoopsOften referred to as “Magnetic

Antennas” conceptualize as coupling to the magnetic B-field

VLF, UHFSub-resonant Wire Antennas E.g., Small Coils, Ferrite Loaded

Coils, Resonant Loop AntennasMicrostrip Antennas

Electrically Small Wire Antennas - Sub-resonant LoopsOften referred to as “Magnetic

Antennas” conceptualize as coupling to the magnetic B-field

VLF, UHFSub-resonant Wire Antennas E.g., Small Coils, Ferrite Loaded

Coils, Resonant Loop AntennasMicrostrip Antennas

Low Gain Antennas are OMNI - to - MODERATELY DIRECTIONAL ANTENNA PATTERNS

© Okey Ugweje, PhD

Resonant Wire Antennas - MonopoleCellular, PCS, FM car radio, wireless

handsets, etc

Resonant Wire Antennas - MonopoleCellular, PCS, FM car radio, wireless

handsets, etc

Resonant Wire Antennas - DipoleCellular, PCS, FM receiver, etc

Resonant Wire Antennas - DipoleCellular, PCS, FM receiver, etc

Horn AntennasHorn Antennas

Single Column ArraySingle Column Array

© Okey Ugweje, PhD

Collinear vertical arraysEssentially omni-directional in

horizontal planePower gain approximately equal to

the number of elementsNulls exist in vertical pattern, unless

deliberately filled Arrays in horizontal planeDirectional in horizontal plane:

useful for sectorizationYagi-Uda Arraysone driven element, parasitic

coupling to othersLog-periodicall elements driven/wide bandwidt

Collinear vertical arraysEssentially omni-directional in

horizontal planePower gain approximately equal to

the number of elementsNulls exist in vertical pattern, unless

deliberately filled Arrays in horizontal planeDirectional in horizontal plane:

useful for sectorizationYagi-Uda Arraysone driven element, parasitic

coupling to othersLog-periodicall elements driven/wide bandwidt

© Okey Ugweje, PhD

Collinear Vertical ArraysCollinear Vertical ArraysFor the family of omni-

directional wireless antennas:No. of elements determinesPhysical size & GainBeamwidth, first null angle

Models with many elements have very narrow beamwidthsRequire stable mounting

and careful alignmentWatch out: be sure nulls do

not fall in important coverage areas

Rod and grid reflectors are sometimes added for mild directivity

For the family of omni-directional wireless antennas:

No. of elements determinesPhysical size & GainBeamwidth, first null angle

Models with many elements have very narrow beamwidthsRequire stable mounting

and careful alignmentWatch out: be sure nulls do

not fall in important coverage areas

Rod and grid reflectors are sometimes added for mild directivity

Vertical Plane Pattern

© Okey Ugweje, PhD

High Gain or Aperture AntennasHigh Gain or Aperture Antennas

High Gain Antennas are characterized by:Narrow BeamNarrow spatial filter or “radio wave telescope”Tracking targetsPoint-to-point communication

Power ConcentrationDetection of weak signalsTransmission/reception over long distances

Used to provide small “pencil beams” to concentrate the antenna field of view to a small angular region

High Gain Antennas are characterized by:Narrow BeamNarrow spatial filter or “radio wave telescope”Tracking targetsPoint-to-point communication

Power ConcentrationDetection of weak signalsTransmission/reception over long distances

Used to provide small “pencil beams” to concentrate the antenna field of view to a small angular region

High Gain Antennas areDIRECTIVE - to - HIGHLY DIRECTIVE ANTENNA PATTERNS

© Okey Ugweje, PhD

High Gain Antenna TypesReflectors - Microwave/Satellite linksLenses - Luneberg, Rotman, Fresnel, DielectricArrays - Fixed beam, scanning beam

High Gain Antenna TypesReflectors - Microwave/Satellite linksLenses - Luneberg, Rotman, Fresnel, DielectricArrays - Fixed beam, scanning beam

Gains are typically in the range of > 30 dBi, with beamwidths on the order of a few degrees or smaller

Antenna design is meanly of the Prime Focus Reflector typeArray Antennas can also be used to obtain high gain

Gains are typically in the range of > 30 dBi, with beamwidths on the order of a few degrees or smaller

Antenna design is meanly of the Prime Focus Reflector typeArray Antennas can also be used to obtain high gain

These are used for fixed point to point communications, object sensing and tracking

These are used for fixed point to point communications, object sensing and tracking

© Okey Ugweje, PhD

Near-Field vs. Far-FieldNear-Field vs. Far-Field Antenna behavior is very different close-in and far

out Near-field region:

The area within about 10 times the spacing between antenna’s internal elements Inside this region, the signal behaves as

independent fields from each element of the antenna, with their individual directivity

Far-field region: The area beyond roughly 10 times the spacing

between the antenna’s internal elementsIn this region, the antenna seems to be a point-

source and the contributions of the individual elements are indistinguishable

The pattern is the composite of the array

Antenna behavior is very different close-in and far out

Near-field region: The area within about 10 times the spacing

between antenna’s internal elements Inside this region, the signal behaves as

independent fields from each element of the antenna, with their individual directivity

Far-field region: The area beyond roughly 10 times the spacing

between the antenna’s internal elementsIn this region, the antenna seems to be a point-

source and the contributions of the individual elements are indistinguishable

The pattern is the composite of the array

Obstructions in the near-field can dramatically alter the antenna performance

© Okey Ugweje, PhD

Local Obstruction at a SiteLocal Obstruction at a SiteObstructions near the site are sometimes unavoidable Near-field obstructions can seriously alter pattern shapeMore distant local obstructions can cause severe blockage, as

for example roof edge in the figure at rightKnife-edge diffraction analysis can help estimate

diffraction loss in these situationsExplore other antenna mounting positions

Obstructions near the site are sometimes unavoidable Near-field obstructions can seriously alter pattern shapeMore distant local obstructions can cause severe blockage, as

for example roof edge in the figure at rightKnife-edge diffraction analysis can help estimate

diffraction loss in these situationsExplore other antenna mounting positions

Local obstruction example

© Okey Ugweje, PhD

Isolation Between AntennasIsolation Between AntennasOften multiple antennas are needed at a site and

interaction is troublesomeElectrical isolation between antennas

Coupling loss between isotropic antennas one wavelength apart is 22 dB

6 dB additional coupling loss with each doubling of separation

Add gain or loss referenced from horizontal plane patterns

Measure vertical separation between centers of the antennasvertical separation usually is very effective

One antenna should not be mounted in main lobe and near-field of anotherTypically within 10 feet @ 800 MHzTypically 5-10 feet @ 1900 MHz

Often multiple antennas are needed at a site and interaction is troublesome

Electrical isolation between antennasCoupling loss between isotropic antennas one

wavelength apart is 22 dB6 dB additional coupling loss with each doubling of

separationAdd gain or loss referenced from horizontal plane

patternsMeasure vertical separation between centers of the

antennasvertical separation usually is very effective

One antenna should not be mounted in main lobe and near-field of anotherTypically within 10 feet @ 800 MHzTypically 5-10 feet @ 1900 MHz

© Okey Ugweje, PhD

Arrays often used in Cellular and Sectoring

Arrays often used in Cellular and Sectoring

Macrocellular range of several km

Microcellular range of several km

Common implementation uses 3 sectors as “cells”

These low gain antennas usually have ±60°azimuth

In-building

Picocell Microcell Macrocell Magacell

Urban

Suburban

Global

© Okey Ugweje, PhD

The Goal of Antenna DowntiltThe Goal of Antenna Downtilt

Downtilt is commonly used for two reasons

1. Reduce InterferenceReduce radiation toward a distant

co-channel cellConcentrate radiation within the

serving cell

Downtilt is commonly used for two reasons

1. Reduce InterferenceReduce radiation toward a distant

co-channel cellConcentrate radiation within the

serving cell

2. Prevent “overshoot”Improve coverage of nearby

targets far below the antenna–otherwise within “null” of antenna pattern

2. Prevent “overshoot”Improve coverage of nearby

targets far below the antenna–otherwise within “null” of antenna pattern

Depression or downtilt of an antenna is the process of redirecting the antenna beam downwards

Depression or downtilt of an antenna is the process of redirecting the antenna beam downwards

© Okey Ugweje, PhD

Vertical Depression AnglesVertical Depression Angles Basic principle:

Important to match vertical pattern against intended coverage targetsCompare the angles toward

objects against the antenna vertical pattern

what’s radiating toward the target?

Don’t position a null of the antenna toward an important coverage target!

Sketch and formulateNotice the height and horizontal

distance must be expressed in the same units before dividing (both in feet, both in miles, etc.)

Basic principle: Important to match vertical pattern

against intended coverage targetsCompare the angles toward

objects against the antenna vertical pattern

what’s radiating toward the target?

Don’t position a null of the antenna toward an important coverage target!

Sketch and formulateNotice the height and horizontal

distance must be expressed in the same units before dividing (both in feet, both in miles, etc.)

-1 vertical distance= tan

horizontal distance

© Okey Ugweje, PhD

Types Of DowntiltTypes Of Downtilt

Mechanical downtiltPhysically tilt the antennaThe pattern in front goes down,

and behind goes upPopular for sectorization and

special omni applicationsElectrical downtiltIncremental phase shift is applied

in the feed networkThe pattern “droops” all around,

like an inverted saucerCommon technique when

downtilting omni cells

Mechanical downtiltPhysically tilt the antennaThe pattern in front goes down,

and behind goes upPopular for sectorization and

special omni applicationsElectrical downtiltIncremental phase shift is applied

in the feed networkThe pattern “droops” all around,

like an inverted saucerCommon technique when

downtilting omni cells

© Okey Ugweje, PhD

Reduce Interference - Scenario 1Reduce Interference - Scenario 1The Concept:Radiate a strong signal toward

everything within the serving cell, but significantly reduce radiation toward the area of Cell B

The Concept:Radiate a strong signal toward

everything within the serving cell, but significantly reduce radiation toward the area of Cell B

The Reality:When actually calculated, it’s

surprising how small the difference in angle is between the far edge of cell A and the near edge of Cell BDelta in the example is only 0.3o!!Let’s look at antenna pattern

The Reality:When actually calculated, it’s

surprising how small the difference in angle is between the far edge of cell A and the near edge of Cell BDelta in the example is only 0.3o!!Let’s look at antenna pattern

© Okey Ugweje, PhD

It’s an attractive idea, but usually the

angle between edge of serving cell and nearest edge of distant cell is just too small to exploitDowntilt or not, can’t get much

difference in antenna radiation between θ1 and θ2

Even if the pattern were sharp enough, alignment accuracy and wind-flexing would be problemsθ in this example is < 1o!

Also, if downtilting -- watch out for excessive RSSI and IM involving mobiles near cell!

Soft handoff and good CDMA power control is more important

It’s an attractive idea, but usually the angle between edge of serving cell and nearest edge of distant cell is just too small to exploitDowntilt or not, can’t get much

difference in antenna radiation between θ1 and θ2

Even if the pattern were sharp enough, alignment accuracy and wind-flexing would be problemsθ in this example is < 1o!

Also, if downtilting -- watch out for excessive RSSI and IM involving mobiles near cell!

Soft handoff and good CDMA power control is more important

© Okey Ugweje, PhD

Avoid Overshoot - Scenario 2Avoid Overshoot - Scenario 2Application concern: too little radiation

toward low, close-in coverage targetsThe solution is common-sense matching

of the antenna vertical pattern to the angles where radiation is neededCalculate vertical angles to targets!!Watch the pattern nulls--where do

they fall on the ground?Choose a low-gain antenna with a fat

vertical pattern if you have a wide range of vertical angles to “hit”

Downtilt if appropriateIf needed, investigate special “null-

filled” antennas with smooth patterns

Application concern: too little radiation toward low, close-in coverage targets

The solution is common-sense matching of the antenna vertical pattern to the angles where radiation is neededCalculate vertical angles to targets!!Watch the pattern nulls--where do

they fall on the ground?Choose a low-gain antenna with a fat

vertical pattern if you have a wide range of vertical angles to “hit”

Downtilt if appropriateIf needed, investigate special “null-

filled” antennas with smooth patterns

© Okey Ugweje, PhD

Other Antenna Selection Considerations

Other Antenna Selection Considerations

Before choosing an antenna for widespread deployment, investigate the following:

Manufacturer’s measured patternsObserve pattern at low end of band, mid-band, and high end

of bandAny troublesome back lobes or minor lobes in H or V

patterns?Watch out for nulls which would fall toward populated areasBe suspicious of extremely symmetrical, “clean” measured

patternsObtain Intermodulation Specifications and test results (-130

or better)

Before choosing an antenna for widespread deployment, investigate the following:

Manufacturer’s measured patternsObserve pattern at low end of band, mid-band, and high end

of bandAny troublesome back lobes or minor lobes in H or V

patterns?Watch out for nulls which would fall toward populated areasBe suspicious of extremely symmetrical, “clean” measured

patternsObtain Intermodulation Specifications and test results (-130

or better)

© Okey Ugweje, PhD

Inspect return loss measurements across the band

Inspect a sample unitPhysical integrity? weatherproof?Dissimilar metals in contact anywhere?Collinear vertical antennas: feed method? End (compromise) or center-fed (best)?Complete your own return loss measurements, if possibleIdeally, do your own limited pattern verification

Check with other users for their experiences

Inspect return loss measurements across the band Inspect a sample unitPhysical integrity? weatherproof?Dissimilar metals in contact anywhere?Collinear vertical antennas: feed method? End (compromise) or center-fed (best)?Complete your own return loss measurements, if possibleIdeally, do your own limited pattern verification

Check with other users for their experiences

© Okey Ugweje, PhD

Antenna ApplicationsAntenna ApplicationsTransmission lines, Antennas and Scatterers, provide an EM or

RF link where information/intelligence is exchanged or detected An antenna can be the first or last element of a system

implementation Antennas serve as the interface to a free space interconnected

environment in which the tethers can be removed allowing mobility and remote placement or detection of objects within a three dimensional environment

An antenna alone can serve no purpose, but must be an integral part of a system design to accomplish a specific purpose

These purposes can include but are not limited to:Communication Systems

as in free space propagation links (data, command, control, broadcast, voice, etc.)

Transmission lines, Antennas and Scatterers, provide an EM or RF link where information/intelligence is exchanged or detected

An antenna can be the first or last element of a system implementation

Antennas serve as the interface to a free space interconnected environment in which the tethers can be removed allowing mobility and remote placement or detection of objects within a three dimensional environment

An antenna alone can serve no purpose, but must be an integral part of a system design to accomplish a specific purpose

These purposes can include but are not limited to:Communication Systems

as in free space propagation links (data, command, control, broadcast, voice, etc.)

© Okey Ugweje, PhD

Some Basic Antenna ApplicationsSome Basic Antenna Applications Fixed Services

Point to Point, Point to Multipoint, backhaul Mobile Services

Paging, Cellular, Trunked Radio, Maritime Mobile

Fixed ServicesPoint to Point, Point to Multipoint, backhaul

Mobile ServicesPaging, Cellular, Trunked Radio, Maritime Mobile

RadiodeterminationGPS, Radar, ILS, LORAN-C

BroadcastingRadio, TV, Direct-Broadcast Sat. (DBS), TVRO (Receive Only)

Safety (emergency and distress) ServicesPolice, Fire, National Weather Service (NWS)

Vehicular, Land, Sea, Air and SpaceCommunications, Navigation, Collision Avoidance, Imaging

Building MountedCellular, WLAN, Bluetooth, Wi Fi (IEEE 802.11)

CommercialRF tagging, Automatic toll, Process monitoring, Remote control

RadiodeterminationGPS, Radar, ILS, LORAN-C

BroadcastingRadio, TV, Direct-Broadcast Sat. (DBS), TVRO (Receive Only)

Safety (emergency and distress) ServicesPolice, Fire, National Weather Service (NWS)

Vehicular, Land, Sea, Air and SpaceCommunications, Navigation, Collision Avoidance, Imaging

Building MountedCellular, WLAN, Bluetooth, Wi Fi (IEEE 802.11)

CommercialRF tagging, Automatic toll, Process monitoring, Remote control

© Okey Ugweje, PhD

sensors as in direction finding, field measurements, radar,

weather/meteorology and environmental detectionPublic SafetyWeather alertEmergency servicesLocal Law Enforcement

Transportation (Aviation)Air Traffic ControlNavigationEmergency Locator Transmitter

Military/DefenseMany applications here

sensors as in direction finding, field measurements, radar,

weather/meteorology and environmental detectionPublic SafetyWeather alertEmergency servicesLocal Law Enforcement

Transportation (Aviation)Air Traffic ControlNavigationEmergency Locator Transmitter

Military/DefenseMany applications here

© Okey Ugweje, PhD

Antenna Performance IssuesAntenna Performance Issues

Electrical ParametersFrequency

Bandwidth Fixed/TunableGain/Directivity

Omni-directionalSectoralSidelobe SpecificationsFront-Back Ratio

Power HandlingAveragePeak

Electrical ParametersFrequency

Bandwidth Fixed/TunableGain/Directivity

Omni-directionalSectoralSidelobe SpecificationsFront-Back Ratio

Power HandlingAveragePeak

Mechanical ParametersConstructionSizeWeightEnvironmentHeating/Cooling

Mechanical ParametersConstructionSizeWeightEnvironmentHeating/Cooling

Antenna performance is limited by the physical/mechanical design and operational frequency

Likewise, antenna performance is strongly coupled to the environment in which it must operate

Antenna performance is limited by the physical/mechanical design and operational frequency

Likewise, antenna performance is strongly coupled to the environment in which it must operate

© Okey Ugweje, PhD

Basic Antenna PerformanceBasic Antenna PerformanceAntennas are typically designed to provide point to point links,

or area coverageThe frequency of operation impacts performance of these

systems. At lower frequencies such as HF, radio waves propagate through the ionosphere and well beyond the horizon of the earth

As the frequency is increased, (VHF, UHF and Microwave), the waves tend to propagate primarily in a line of site (LOS) mode

Also, the shorter the wavelength or the higher the frequency, there is increased space loss of the transmitted wave. These features can and tend to severely impact antenna placement.

Antennas are typically designed to provide point to point links, or area coverage

The frequency of operation impacts performance of these systems. At lower frequencies such as HF, radio waves propagate through the ionosphere and well beyond the horizon of the earth

As the frequency is increased, (VHF, UHF and Microwave), the waves tend to propagate primarily in a line of site (LOS) mode

Also, the shorter the wavelength or the higher the frequency, there is increased space loss of the transmitted wave. These features can and tend to severely impact antenna placement.

© Okey Ugweje, PhD

Blockage ErrorBlockage ErrorDefinition: An obstruction which blocks part of the antenna aperture

Definition: An obstruction which blocks part of the antenna aperture

Effects of BlockageReduces directivityLoss in directivity ≈ (Blockage area)/(Antenna area)

Perturbs SidelobesResulting sidelobes are generally higherA specific sidelobe may go up or down

Beamwidth generally reducedImpacts monopulse performance

Effects of BlockageReduces directivityLoss in directivity ≈ (Blockage area)/(Antenna area)

Perturbs SidelobesResulting sidelobes are generally higherA specific sidelobe may go up or down

Beamwidth generally reducedImpacts monopulse performance

© Okey Ugweje, PhD

Optimum LocationOptimum LocationFinding the best location for an antenna requires trial and error.We don’t have software to tell us the best antenna location.Current software barely computes performance for a given

locationThat’s because environments are so complex.

Finding the best location for an antenna requires trial and error.We don’t have software to tell us the best antenna location.Current software barely computes performance for a given

locationThat’s because environments are so complex.

For siting on terrain, one would like to model the precise contours of the terrain and a map of the constitutive parameters.

Usually this information is not available, and the terrain can be described only in statistical terms.Often there is digital terrain elevation data (DTED), but

only statistics or estimates of other parameters

For siting on terrain, one would like to model the precise contours of the terrain and a map of the constitutive parameters.

Usually this information is not available, and the terrain can be described only in statistical terms.Often there is digital terrain elevation data (DTED), but

only statistics or estimates of other parameters

© Okey Ugweje, PhD

Best approach to antenna-on-vehicle problem is model the

whole vehicleThis is not practical for vehicles more than 10 or 15

wavelengths longThus, asymptotic methods (high-frequency

approximations) are needed for most antenna siting problems on vehicles

Best approach to antenna-on-vehicle problem is model the whole vehicle

This is not practical for vehicles more than 10 or 15 wavelengths longThus, asymptotic methods (high-frequency

approximations) are needed for most antenna siting problems on vehicles

For siting within buildings or among buildings, approaches are similar to the terrain case, but sometimes full-wave solutions are possible

For siting within buildings or among buildings, approaches are similar to the terrain case, but sometimes full-wave solutions are possible

© Okey Ugweje, PhD

Passive RepeaterPassive Repeater

Passive reflectors or repeaters are used to redirect line of sight (LOS) propagation paths between fixed assets.

Passive reflectors or repeaters are used to redirect line of sight (LOS) propagation paths between fixed assets.

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