Mod3-WirelessSystemsEngineering

8/7/2019 Mod3-WirelessSystemsEngineering

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EECE 483 - Antennas and Propagation

Module 3

Wireless Systems Engineering

Basic antenna concepts; antennas for low, medium and high frequencies; terrestrial and satellite propagation links;

environmental effects on electromagnetic radiation. [3-0-0]

EECE 483 - Antennas and Propagation (Spring 2011) Prof. David G. Michelson

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During these lectures, the instructor will bring up many points and detailsnot given on these slides. Accordingly, it is expected that the studentwill annotate these notes during the lecture.

The lecture only introduces the subject matter. Students must complete

the reading assignments and problems if they are to master the material.



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Introduction

There are considerable differences in the physical realization of antennasfor different purposes and frequencies.

Those involved in the manufacture and deployment of antennas areobviously very interested in the physical details.

Those involved in systems design can take a more abstract view anddescribe antennas in terms of system-level parameters.

Such system-level parameters must be carefully designed to form aminimal yet self-complete set that lends itself to both numericalcalculation and experimental measurement.


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Objectives

Upon completion of this module, EECE 483 students will be able to:

Explain the advantages of employing a systems approach to wirelesssystems design.

Describe the key features of the isotropic radiator concept.

Define the common system-level properties of antennas.

Given the radiation pattern of an antenna, estimate the relevant antennaparameters.

Use the reciprocity theorem and the concept of effective area to solveproblems involving receiving antennas.

Given a description of a transmission or radar system, estimate the signaland noise power at the receiver.



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Outline

1. The Systems Approach

2. The Isotropic Radiator

3. The Fundamental Properties of Antennas

Radiation Pattern Gain Input Impedance Bandwidth Polarization

4. The Reciprocity Theorem and Effective Area

5. Wireless Transmission Systems

6. Radar Systems

7. Noise in Wireless Systems


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1. The Systems Approach

It is useful to separate the functional properties of an antenna from theimplementation details.

By focusing on functional requirements, we are less likely to force thedesigner to take a predetermined (and possibly suboptimal) path.

This separation also allows a small group of systems engineers toeffectively coordinate the efforts of many teams of implementers,

including antenna engineers, RF designers, software developers, etc. Because contractual obligations are often negotiated based upon system

level descriptions, it is necessary to carefully define a consistent set ofparameters that can be used to describe the performance of an antenna.

Many of these parameters are defined in IEEE Standard Definitions ofTerms for Antennas, IEEE Std 145-1983.



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2. Isotropic Radiator

An isotropic radiator radiates uniform spherical waves into space, i.e.,it has a uniform radiation pattern.

If the transmitted power is Pt (W), we can show that the power density

S (W/m2) at a distance r is

S =Pt

4r2.

Because electromagnetic fields are vector fields, it is not possible torealize an isotropic radiator. (How can one prove this?)

Although an isotropic radiator cannot be realized in practice, it is aconvenient (albeit hypothetical) reference against which to compare the

performance of antennas with more complicated radiation patterns.


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Hairy Ball Theorem

The hairy ball theorem of algebraic topology states that, in laymansterms, one cannot comb the hair on a ball smooth.

This fact is immediately convincing to most people, even though theymight not recognize the more formal statement of the theorem,

There is no nonvanishing continuous tangent vector field on thesphere.

Less briefly, if f is a continuous function that assigns a vector in R3 toevery point p on a sphere, and for all p the vector f(p) is a tangentdirection to the sphere at p, then there is at least one p such thatf(p) = 0.

This implies that a device that radiates vector waves, i.e., waves withtransverse components, cannot radiate isotropically.



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Plane and Solid Angles

The measure of a plane angle, , is the radian.

One radian (rad) is defined as the circular arc with length equal to its

radius.

Because the circumference of a circle is 2r, there are 2 rad in a circle.

The measure of a solid angle, , is the steradian.

One steradian (sr) is defined as solid angle that subtends the sphericalcap with area equal to the square of its radius.

Because the area of a sphere is 4r2

, there are 4 sr in a sphere.


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The Steradian

The solid angle may be thought of as the area of the spherical cap Anormalized with respect to the square of its radius r, i.e., = A/r2 .



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3. The Fundamental Properties of Antennas

Practical antennas radiate more intensely in some directions than others.That is, they are directional.

If the antenna is 100% efficient, integrating the power density observedat a given distance over the entire sphere will yield the total radiatedpower. That is,

Prad =

20

0

S(, ) r2 sin d d .

This implies that directional antennas simply focus power in somedirections at the expense of other directions.

As we shall see, almost all system-level antenna properties of interest are

consequences of the inverse square law and conservation of power.


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Fundamental Performance Parameters

From a systems perspective, five performance parameters arefundamental:

radiation pattern

gain

input impedance

bandwidth

polarization

For a linear and passive antenna, all of these antenna properties areidentical for both transmission and reception (by virtue of the reciprocitytheorem).



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Secondary Performance Parameters

Other performance parameters may be derived from the above and areconsidered to be secondary, e.g.,

directivity

efficiency

beamwidth

beam efficiency

sidelobe level

As we shall later see, these functional properties (taken together with ourunderstanding of how antennas function) form the basis for distinguishingantennas which: (1) electrically small, (2) resonant, (3) broadband, or

(4) based upon a radiating aperture.


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Other Systems-Level Performance Parameters

Certain mechanical properties may also be considered to be systems-levelparameters, e.g.,

weight

size

sail area (or wind area)

power handling capabilities

environmental limitations (temperature, vibration, weather)

When designing an antenna, it is often difficult to enhance oneperformance parameter without sacrificing another. Managing suchtrade-offs lies at the heart of the antenna design problem.



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3.1 Antenna Radiation Pattern

The antenna pattern or radiation pattern describes the manner in whichthe power density of the radiated field at a given distance varies with

elevation and azimuth angle. It can be expressed in the form of a three-dimensional surface in either

spherical or rectangular coordinates.

It is more typically expressed in the form of two-dimensional cuts throughthe principal planes (x-y, x-z, y-z).

In the case of both directional antennas and omnidirectional antennas,it is usually sufficient to specify the vertical and horizontal planes alone.(Why?)


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Plotting Radiation Patterns

The antenna radiation patternis typically plotted in dBrelative to the maximumobserved value.

A lobe is the portion of a radiation pattern that is

bounded by nulls in thepattern.

The main lobe is the lobe withthe strongest peak.

All other lobes are referred toas minor lobes or sidelobes.



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Derived Parameters

The half-power beamwidth in a particular plane is defined as the angularextent over which the pattern is within 3 dB of its maximum value.

The beamwidth between (specified) nulls is defined as the angular extent

between nulls in the antenna pattern.

The sidelobe level is expressed in decibels with respect to the maximumof the main beam.

Beam efficiency is defined as the fraction of the total radiated (orreceived) power that is transmitted (or received) within a specified solidangle, e.g., the solid angle that is subtended by the main lobe.

Beam solid angle A is the solid angle through which all the powerwould be radiated if the radiation intensity equalled the maximum value

over the beam area.


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Alternative Conventions for Plotting Radiation Patterns

If the entire pattern (or pattern cut) is of interest, the radiation patternis usually plotted in spherical (or polar) coordinates, e.g.,

if the antenna has a broad beamwidth.

if the utility of the antenna in rejecting interference is of interest.

If only a portion of the pattern is of interest, the radiation pattern isusually plotted in rectangular coordinates, e.g.,

if the antenna is highly directional.

if one wishes to compare sidelobe levels.



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Four Antenna Pattern Plot Types


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NSMA Standard Format for the Electronic Transfer of

Antenna Patterns

Most antenna vendors can supply their products antenna patterns inelectronic, albeit, proprietary formats.

Study Group 16 - Antenna Patterns of The National SpectrumManagers Association (NSMA) has sought to establish a standardformat for the electronic transfer of antenna pattern data between

manufacturers, consultants, coordinators and users.

The intent of the standard is to increase the accuracy and facilitate thetransfer of antenna pattern data.

For details, see http://www.fcc.gov/oet/info/software/nsma/.

Would an XML-based format make more sense? Why or why not?



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NSMA File Format Details

[Antenna Manufacturer] + CRLF

[Antenna Model number] + CRLF

[Comment] + CRLF

[FCC ID number] + CRLF

[reverse pattern ID number] + CRLF

[date of data] + CRLF[Manufacturer ID Number (see filenaming convention)] + CRLF

[frequency range] + CRLF

[mid-band gain] + CRLF

[Half-power beam width] + CRLF

[polarization (char 7) + chr\$(32) + datacount (char 7) + chr\$(32) + CRLF]

[angle(1) (char 7) + chr\$(32) + relative gain in dB(char 7) + chr\$(32) + CRLF]

.

.

[angle(datacount) (char 7) + chr\$(32) + relative gain in dB (char 7) + chr\$(32) + CRLF]

.

.

[polarization (char 7) + chr\$(32) + datacount (char 7) + chr\$(32) + CRLF]

[angle(1) (char 7) + chr\$(32) + relative gain in dB(char 7) + chr\$(32) + CRLF]

.

.

[angle(datacount) (char 7) + chr\$(32) + relative gain in dB (char 7) + chr\$(32) + CRLF]


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Software for plotting NSMA antenna patterns is available from FCC.

A UNIX-based version would likely be most welcome!



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3.2 Gain

The directional characteristics of an antenna are frequently expressed interms of a gain function G(, ).

The gain function is the ratio of: (1) the power density observed in a

particular direction at a particular distance to (2) the power density thatwould be produced at the same location by an isotropic radiator drivenby an identical transmitter.

The power density S at a distance r in the direction (, ) is

S = PtG(, )

4r2.

The maximum value of G(, ) is conventionally referred to as G, the

gain of the antenna.


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Absolute and Relative Gain

In all cases, gain is determined under free space conditions, i.e., noreflections or multipath.

Because the gain of an antenna is typically expressed with respectto the power density produced by an isotropic antenna, it has units ofdBi. Because the reference is absolute, this is referred to as absolute gain.

In some cases, the reference antenna is a half-wave dipole. In such cases,gain is expressed in dBd.

It is common to experimentally compare the gain of one antenna toanother, i.e., to determine the relative gain of an antenna.

It is much more difficult to experimentally determine the absolute gainof an antenna. Why?



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Radiation Intensity

Radiation intensity is a distance independent measure of the powerradiated from an antenna.

It is defined as the power radiated in a given direction from an antennaper unit solid angle and has units of Watts/steradian (W/sr).

Radiation intensity is related to the time-averaged Poynting vector S asfollows:

U(, ) =1

2Re(E H) r2 r

= S(, ) r2 .

Radiation intensity can be expressed as

U(, ) = Um |F(, )|2 ,


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where |F(, )|2 is the normalized power pattern, i.e., |F| = 1 in thedirection max, max .

The total power radiated by an antenna is obtained by integrating theradiation intensity over all angles,

Prad =

U(, ) d ,

where d = sin d d .

For a given antenna, the average radiation intensity is given by

Uave =1

4

U(, ) d =

Prad4

.



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Directivity

Directivity, D, is the ratio of the maximum radiation intensity to theaverage radiation intensity (averaged over all solid angles).

In essence, we are comparing the antenna to itself rather than to anotherantenna.

We pay a price, though:

When estimating gain, it is sufficient to characterize radiation intensityin the direction of interest for both the antenna under test and thereference antenna.

When estimating directivity, we must characterize radiation intensity

over all solid angles.


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Directivity, Gain, and Efficiency

For an antenna which has no conductor or dielectric losses (and which is100% efficient), directivity and gain are equal.

Otherwise,G = D

where is the efficiency of the antenna.

Return loss, ||2, is a related concept that refers to the fraction of powerlost due to impedance mismatch at the antenna terminals.

Return loss is not included in the IEEE standard definition of gain becauseit is usually included as a separate line item in the system link budget.



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Calculating Radiated Power

Recall that the power radiated by an antenna is:

P =

S(, ) dS

=1

2Re

(E H) dS

=1

2Re

(EH

EH

) r2 sin dd

where EH

is the vertically polarized component and EH

is thehorizontally polarized component.


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We can simplify this by recalling that

H =E

and H = E

yielding

P =1

2

(|E|

2 + |E|2) r2 d .



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3.3 Input Impedance

The input impedance, Zin, of an antenna is the impedance presented bythe antenna at its terminals:

Zin = Rin + jXin . The input resistance, which accounts for power dissipated by the antenna,

has two components:Rin = Rrad + Rohmic .

The input reactance Xin represents energy stored in the near field of theantenna.

In most cases, Rohmic


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For the special case of a cylindrical wire, the ohmic resistance, R,can be estimated by: (1) determining the skin depth in terms of the RFfrequency and material properties of the metal, (2) using this informationto determine the effective cross-sectional area A of the wire (in squaremetres), then (3) applying the formula

R = L

A

where is the resistivity of the material in ohm-metres and L is thelength of the wire in metres.


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Antenna Efficiency

Antenna efficiency is the ratio of the power actually radiated by theantenna to the power applied to the input terminals

= Prad/Pin

We define Prad, P, and Pin as follows:

Prad = 12

I2 Rrad

P =1

2I2 R

Pin = Prad + P .



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Therefore, we can also show that if

=PradPin

then

=RradRin

=Rrad

Rrad + R.


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3.4 Bandwidth

The bandwidth of an antenna is defined as the range of frequencieswithin which the performance of the antenna, with respect to somecharacteristic, conforms to a specified standard.

For narrowband antennas (e.g., dipoles), bandwidth is normally expressedas a fractional bandwidth in percent, i.e.,

F BW = 100f

f0% .

For broadband antennas (e.g., horn antennas), bandwidth is normallyexpressed as the ratio of the upper to lower frequency, i.e.,

n : 1 =fuf

.



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Antennas that have multiple resonances and are usable in differentfrequency bands are referred to, naturally, as multi-band antennas.

Such antennas are in great demand as different services (cellular and

PCS, or ISM 2450 and U-NII band devices) are integrated into a singledevice.

Antennas with extremely large bandwidths are referred to as frequency-independent antennas. Examples include log-periodic dipole antennasand spiral antennas.

Such antennas were originally developed for use in Electronic Warfareand other applications that require frequency agility over a wide range.

They are once again in demand as interest in UWB technology grows.


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3.5 Polarization

In general, an arbitrarily polarized wave can be decomposed intocomponents with electric field vectors that point in the vertical andhorizontal directions.



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Depending upon the relative amplitude and phase of the two components,the amplitude and orientation of the electric vector will change over time.


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Definition of Polarization

The polarization of an electromagnetic wave refers to the behaviour ofthe electric field over time as observed at a fixed point in space.

In general, the electric field vector will trace an elliptical locus. Specialcases include linear and circular. The shape of the locus, and thedirection in which E is rotating, specify the polarization state of thewave.



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Why is Polarization Important?

Antennas are designed to radiate or receive waves with a particularpolarization state in the direction of maximum radiation intensity.

If the polarization state of the incident wave and the antenna are different,

a mismatch will occur that we must account for.

Apart from physically rotating the antenna, reflection (and transmission)of a wave from (or through) a boundary or complex scatterer can alterthe polarization state of the wave.

For example, we know that reflection and transmission of electromagneticwaves from the boundaries between dielectric media is dependent uponthe orientation of the electric field vector.

The polarization states of the incident, reflected, and transmitted waves

are rarely the same. We need to characterize them in a systematic way.


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Characterizing the Polarization State of a Wave

Because the locus traced by the electric field vector is always an ellipseof some shape and orientation, characterizing the polarization state of awave is not difficult.

An ellipse can always be characterized by a pair of parameters, e.g., its major axis a and minor axis b

its axial ratio AR and tilt angle

its ellipticity angle and tilt angle its polarization ratio E1/E2 and phase angle

its polarization angle and phase angle

We also need to account for the direction of rotation of the locus, eitherright hand (clockwise when the wave is receding from the observer) or lefthand (counterclockwise when the wave is receding from the observer).



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The Geometry of a Polarization Ellipse


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The Ellipticity and Tilt Angles

Visualizing the manner in which polarization state depends upon theellipticity and tilt angles is particularly straightforward. Here, the waveis approaching the observer.



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Definitions of , , , and

The axial ratio AR is given by the ratio of the major and minor axes ora/b where 1 |AR| . It is positive for left-hand polarization andnegative for right-hand polarization.

The ellipticity angle is given by cot1 AR where 45 +45.

The tilt angle is the angle between the horizontal and the major axisa where 0 180.

The polarization ratio is the ratio of the vertical and horizontally polarizedcomponents, E2 and E1, where 0 E2/E1 .

The polarization angle is given by tan1 E2/E1 where 0 90.

The phase angle is the phase difference between E2 and E1 where

180 +180.


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The Poincare Sphere

Both (, ) and (, ) are ordered pairs of angles and can be mappedonto the surface of a Poincare sphere where 2 = the latitude, 2 =the longitude.



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The Relationship Between , , , and

We can use spherical trigonometry, including the law of cosines, to deducethe precise relationship between , , , and :

cos2 = cos 2 cos2

tan =tan2

sin2

tan2 = tan 2 cos

sin2 = sin 2 sin

cos a = cos b cos c + sin b sin c cos A


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Polarization Mismatch

In free space, an antenna which presents a particular polarization willreceive nothing if the transmitting antenna (and, as a consequence, theincident wave) is orthogonally polarized.

Vertical and horizontal, and left and right circular are special cases oforthogonal polarizations.

In the general case, any pair of polarization states which are 180 aparton the Poincare sphere will be orthogonal.



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If we know the polarization vector Ei that describes the relationshipbetween E2 and E1 for the incident wave and the corresponding vectorEa for the antenna, the reduction in received power compared to whenthe polarization states are identical is given by

= Ei Ea|Ei| |Ea|.

Alternatively, if the great circle angle between the polarization states is, the polarization mismatch factor is given by

= cos2(/2) .

The polarization mismatch factor can be included as a line item in the

system link budget.


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4. The Reciprocity Theorem and Effective Area

So far, we have assumed in our analyses that that the antenna isradiating. However, the performance of an antenna when it is used toreceive signals is equally important.



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The reciprocity theorem and the concept of effective area are the keys tounderstanding the receiving properties of antennas.

Lets start by considering the reciprocity theorem for linear, passive,bilateral two-port networks.

The transfer impedance V /I will not change when the positions of thegenerator and ammeter are interchanged.

Proof: We generally assume that the generator and ammeter have zeroimpedance, but the result also holds if the generator and ammeter haveequal impedances.

If we make the impedances very large (Z ), what form do thegenerator and ammeter take?

Here, we drive the antenna with a current I, but we measure a voltageV across the terminals of the receiving antenna.


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From the above, if the transmitting and receiving antennas are passive,and the intervening propagation medium is linear, passive, and isotropic,the received signal strength is unchanged when the transmitter andreceiver are exchanged

Thus, we conclude that the transmitting and receiving patterns of anantenna are identical.



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Effective Area

It can be shown that the gain of a radiating aperture containing a uniformelectric field over an area A is

Ga =4A

2.

We can use the result to define the effective area Ae of any antenna as

Ae =2

4 G .

What is the significance of Ae?


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If a plane electromagnetic wave with power density S (W/m2) is incidentupon a uniform aperture antenna with matching polarization and physicalarea A, the power that it receives is

Pr = S A .

If we invoke the reciprocity theorem, we can show that an antenna with

gain G will receive G/Ga as much power.

Thus,Pr = S Ae .

We can interpret Ae as the effective collecting area of the antenna duringreception.



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Interesting Implications

If the area of the antenna is constant (as in the case of a horn antennaor reflector antenna) then the gain of the antenna, then the gain of theantenna will increase with frequency

G =4A

2=

4Af2

c2.

That is, the radiation pattern of an aperture antenna will becomenarrower with increasing frequency.

If the radiation pattern is fixed (as in the case of a wire antenna), thenthe Ae of the antenna will decrease with frequency.

Ae =2G

4 =c2G

4f2 .


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That is, a wire antenna of given size/length (in wavelengths) will becomeless sensitive with increasing frequency.



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5. Wireless Transmission Systems

In wireless transmission systems, a transmitting antenna launches apropagating wave which is intercepted by a receiving antenna somedistance away.

As engineers, we are quite interested in predicting how much power willappear at the output port of the receiving antenna relative to the amountof power applied to the transmitting antenna.

For the free space or line-of-sight (LOS) cases with no reflections, thecalculation is very straightforward.

For cases where the path is obstructed (non-line-of-sight or NLOS), thereare multiple propagation paths, or time-varying factors such as weatheror moving objects (people, vehicles) affect transmission along the path,

the calculation is much more involved. (More on this in Module 9 -Radiowave Propagation!)


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Path Loss and the Friis Transmission Formula

The results derived in the previous section allow us to derive an expressionfor the power received by a receiving antenna from a transmitting antennawith both oriented for maximum power transfer and in free space (noobstructions or reflections).

The power received over a wireless link under free space conditions isgiven by

Pr = PtGt 1

4r2 Ae

= Pt Gt Gr

4r

2.

If either antenna is not aligned for maximum power transfer, Gt or Grcan be replaced by the gain function G(, ) for the appropriate direction.



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We can account for polarization mismatch by resolving the fields intoco-polarized and cross-polarized components.

The free space path gain is given by

Gp =

4r2

.

The free space path loss is given by

Lp =

4r

2.

A complete description also accounts for polarization mismatch andimpedance mismatch 1 ||2.


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Link Budget

It is useful to summarize the factors that reduce the power applied atthe transmitter to the power levels observed at the receiver in the formof a spreadsheet.

This allows us to assess the effect of trading off different designparameters on system performance.compare the received power Pr tothe receiver sensitivity Psens.

Simple link budgets compare the received power Pr to the receiversensitivity Psens.

More complicated link budgets will compare the received power Pr tothe noise power at the receiver input in order to estimate the inputsignal-to-noise ratio.



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A Simple Link Budget for a Wireless LAN

Pt - transmitted power 20 dBm

Lt - cable loss (-)3 dBGt - transmit antenna gain 5 dBi

Lp - path loss (-)95 dB

Gr - receive antenna gain 0 dBi

Lr - cable loss (-)3 dB

Pr - received power -76 dBm

Psens - receiver sensitivity -85 dBm

System Margin 9 dB


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Notes on A Simple Link Budget

Cable losses are typically between 1 and 10 dB.

Typical antenna gains include:

0 dBi normal mode helix2.2 dBi half-wave dipole

15 dBi directional antenna

24 dBi parabolic reflector

Receiver sensitivity may range from -70 to -120 dBm.

A reliable link generally requires a margin of at least 10 dB.

EIRP = Effective Isotropic Radiated Power = Pt Gt.



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Rayleigh or Far-Field Criterion

The Friis transmission formula is based upon the assumption that thewave incident upon the receiving antenna is a plane wave.

In practice, the waves radiated by antennas are spherical.

If r (both the separation between the antennas and the radius ofcurvature of the spherical wavefront) is sufficiently large, the wave willbe effectively plane.

How large is sufficient? It depends upon:

The size of the receiving antenna. The variation in phase across the antenna aperture that we can

tolerate.


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Assuming that the angle is small

d

2rand r

d

2 .

Thus, the additional phase shift encountered at the edge of theaperture is

r2

=

d

d

2r.



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The Rayleigh criterion for the transition to an effectively plane waveallows a phase variation across the aperture of the receiving antenna of45 or 22.5.

This occurs whenr = 2d2/.

In the worst case, if both antennas are of significant extent withmaximum aperture dimensions d1 and d2, respectively, the far-fieldcriterion becomes

r = 2(d21 + d22)/.

Exercise: Prove this.


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6. Radar Systems

The possibility of detecting objects at a distance by measuring radiowaves reflected from them was appreciated soon after Hertzs pioneeringexperiments in the late 1880s.

By 1904, Christian Hulsmeyer, a German inventor, had used radio wavesin a (relatively) short-range collision avoidance device for ships.

By the 1930s, researchers at the US Naval Research Lab haddemonstrated detection of aircraft using radio waves.

In 1940, the Chain Home radar system played a decisive role in helpingthe British win the Battle of Britain.

From 1940-1945, the Radiation Lab at MIT was the focus of Anglo-American efforts to develop microwave radar technology in support ofthe war effort.



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Together with the cryptology and cryptographic efforts centered atBletchley Park and Arlington Hall and development of nuclear weaponsby the Manhattan Project, the development of microwave radar at theRadiation Lab represents one of the most significant, massive, secret, andoutstandingly successful technological efforts undertaken by the Anglo-

American alliance during the Second World War. The development of radar technology created the impetus for developing a

host of technologies, including microwave electronics, spectrum analyzers,digital signal processing, and minicomputers.

From the outset, both the military and civilian sectors made great use ofradar in both aeronautical and maritime applications.

During the last twenty-five years, radar remote sensing (especiallysynthetic aperture radar) has emerged as an important method for

mapping the earths surface (land, water, and ice), tracking changes insurface features, and classifying terrain and ground cover.


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Function and Operation of Radar

Microwave radars function by:

emitting a train of modulated pulses with a given pulse duration , pulserepetition time T, peak power P, and carrier frequency f0

detecting the strength of the signal returned by the target and measuringthe time interval between transmission and reception.



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A Typical Radar


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Radar Equation

If the transmitting and receiving antennas are co-located (or one and thesame), the radar is said to be monostatic.

For a monostatic radar, the time interval t between transmission andreception of the radar pulse is the round-trip travel time.

Accordingly, distance to the target d is given by

d = c t2

where c = 3 108 m/s.

Exercise: How does the choice of and T affect the minimum detectionrange and maximum unambiguous range?



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Radar Range Equation

The maximum range of a radar is determined the strength of the radarreturn compared to the noise floor. Determining the strength of the

radar return is a two-step process. The power density Si of the incident wave at the target is given by

Si =Pt Gt4r2

.

Let the effective area or radar cross section of the target be given by .The power incident upon the target Pi is given by

Pi = Pt Gt 4r2

.


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If we assume that the signal reflected by the target is radiatedisotropically, the power received by the radar is

Pr =Pi Aeff4r2

.

Given that

Aeff =2

4Gr

and combining the previous expressions yields

Pr = Pt2 Gt Gr

(4)3r4.



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Radar Cross Section

The scattering cross section of a target is formally defined as the areaintercepting that amount of power which, when scattered isotropically,would produce an echo equal to that actually returned by the target.

Thus,

= limr

4r2|Es|2

|Ei|2

where Ei is the incident electric field, Es is the scattered electric field,and r is the range at which the scattered field is measured.

Exercise: Show that this definition is consistent with the derivation onthe previous slides.

Radar cross section or RCS refers to the portion of the scattering cross

section that is associated with given transmit and receive polarizations.


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Radar Detection

The chief problem of radar is to detect targets of interest and estimatetheir position and physical characteristics in the presence of interferencefrom clutter returns and noise.

For a point target in space, e.g., an aircraft or spacecraft, the maximumdetection range is generally set by the minimum detectable signal-to-noise ration and can be determined using the radar range equation and

knowledge of the noise characteristics of the radar receiver (see 4.7.)

For a point target in ground clutter, e.g., a man-made object on theearths surface, the maximum detection range is limited by the target-to-clutterratio that is determined by: (1) the RCS of the target and (2) theradar reflectivity of the terrain and the extent of the terrain illuminatedby the radar beam, i.e., the radar resolution cell.



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Detection of a Point Target in Clutter

The area of the radar resolution cell may be determined by either: (1) the beamwidth of

the antenna, yielding the elliptical region above, or, if it is sufficiently short, the length ofthe radar pulse, yielding the shaded portion of the ellipse.


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Probabilities of Detection and False Alarm

The strength of the returns from clutters and targets are statistical in nature and are

best described by probability distributions. Once a decision threshold is set, there is a

finite probability that we will detect something that isnt there (false alarm) or not detect

something that is.



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Radar Cross Section Enhancement

It is often necessary to enhance the radar cross section of a cooperativetarget, either:

to increase the maximum range at which the target can be reliablydetected, or,

to provide a target with a known response which may be used to assistin radar calibration and performance verification.

A flat plate with area A has a large RCS

flat plate = 4A2

2

at a wavelength but acts as a retroreflector only when the angle ofincidence is normal to the plane.


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If two flat plates are placed orthogonal to each other, the resultingdihedral corner reflector will act as a retroreflector for any ray thatstrikes the interior and whose angle of incidence falls in the plane that isnormal to both plates.

If a third flat plate is placed orthogonal to the first two, the resultingtrihedral corner reflector will act as a retroreflector for any ray thatstrikes the interior.

In both cases, the RCS of the corner reflector will have a maximum for

only one angle of incidence.

At 10 GHz, all of the corner reflectors on the following slide present thesame maximum radar cross section, = 4500 m2.

Those that are physically small have a much smaller RCS beamwidth. Asphere with the same RCS will have a diameter of over 75 metres.



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Relative Size of Corner Reflectors with Identical


80

7. Noise in Wireless Systems

Receiving systems must contend with both internally generated noiseand noise that the receiving antenna collects from the surroundingenvironment.

We need to predict the noise developed at the antenna output for tworeasons.

First, in most communications and radar systems, we must take steps toensure that the desired signal is sufficiently above the noise floor.

Second, in passive remote sensing systems (radiometers), the noise poweris the signal of interest.

It is convenient to express the noise power at the output of the antennain terms of a fictitious antenna temperature.



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Antenna Temperature


82

Antenna Temperature - 2

If a resistor has a physical temperature T (K), the noise power developedat the output over a bandwidth B (Hz) is

PN = k T B

where k = Boltzmanns constant = 1.38 1023 J/K.

In the same manner, the antenna temperature TA is a fictitious quantitythat relates the radiation resistance of the antenna to the noise powerdeveloped at the antenna output, i.e.,

PNA = k TA B



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The brightness temperature of an object or scene is given by

TB(, ) = (, )Tphysical

where is the emissivity of the object.

Neither the brightness temperature of the scene TB(, ) nor the radiationpattern of the antenna G(, ) are uniform with direction.

In particular, TB(, ) has two main components: sky noise (TB = 5K toward the zenith, 100-150 K toward the horizon) and ground noise(TB 300 K).

Accordingly,

TA = 1A

0

20

TB(, ) G(, ) d


84

where

A =1

Gmax

G(, ) d =

|F((, )|2 d

is the beam solid angle.

If the temperature of the scene is uniform,

TA =T0A

0

20

G(, ) d =T0A

A = T0 .

For a small discrete source with angular extent s and temperature Ts,G(, ) 1 over the source, so

TA =sA

Ts .



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System Noise Temperature

For the purposes of determining the signal-to-noise ratio at thedemodulator or detector, the system noise Psys can be expressed as

Psys = k(Tr + TA)B = k(Tsys)B

where the system noise temperature Tsys is given Tr + TA and thereceiver noise temperature is Tr.


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The receiver temperature Tr is related to the noise factorof the receiver,

F =SNRiSNRo

by the relationTr = 290(F 1) .

The noise figure of the receiver is related to the noise factor by 10log F

(dB).



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The Figure of Merit G/Tsys

Consider an antenna used with a satellite earth station.

If the antenna has high sidelobes in the direction of the earth (e.g.,

due to spillover from the primary feed), then it will pick up substantialground noise and have a relatively high TA.

Conversely, if the antenna has low sidelobes in the direction of the earth,then it will have a much lower TA.

A figure of merit often used with satellite earth terminals is G/Tsys,which is the antenna gain divided by the system noise temperature. It isusually expressed in dB/K.

High values of G/Tsys, indicating high antenna gain and low system

noise temperature, are desirable.


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Summary

We have introduced (or, in some cases, reviewed):

The advantages of the systems approach to design.

The nature of isotropic radiators.

The system-level properties of antennas, including fundamental properties

such as the radiation pattern, gain, input impedance, bandwidth, andpolarization; secondary properties such as directivity, and mechanicalproperties.

Use of the reciprocity theorem and the concept of effective area to revealthe properties of receiving antennas.

Use of the Friis transmission equation and link budgets to predict theperformance of wireless transmission systems.



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Use of the radar and radar range equations to predict the performanceof radar systems.

Use of antenna and system noise temperature to characterize noise inwireless systems


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References

[1] F. Gross, Smart Antennas for Wireless Communications withMATLAB. McGraw-Hill, 2005, chap. 2.

[2] C.A. Balanis, Antenna Theory - Analysis and Design, 3rd ed. Wiley,2005, chap. 2.

[3] W.L. Stutzman and G.A. Thiele, Antenna Theory and Design, 2nd ed.New York, Wiley, 1998, chaps. 1, 2, 9.

[4] IEEE Standard Definitions of Terms for Antennas, IEEE Std 145-1983.

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