$ ANENNA PROJECT .doc

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learly then, we cannot realise an isotropic radiator in practice since there will be places

on the unit sphere where we cannot specify a uniue "polarisation direction" for the

direction of the electric field. (or e/ample, the lines of longitude on a sphere all meet atthe poles, and the directions 0 and $ are not defined at the poles).

This is sometimes called the "hairy ball" problem. an you comb a hairy ball so that there

is no parting or point of baldness anywhere on the ball1 0o# there must be a discontinuity

in hair direction somewhere.

or this reason, it is impossible to construct, or even envisage, a perfect isotropic radiator.

%t is however possible to have uniform radiation in all a2imuth (see below) directions, or

in all elevation directions at a particular a2imuth plane.

$uch an antenna, having uniform radiation a2imuthally, is called "omnidirectional". This

term is a misnomer, as the antenna is not isotropic and the radiation strength will decrease

if we increase the si2e of the elevation angle. Thus an "omni" antenna does not radiate

eually in all directions.

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1. Radiation direction

%magine you are standing upright on the ground. %f you look straight ahead you are

looking "along boresight". The boresight direction of an antenna is usually taken to be the

direction along which the radiation is most highly concentrated. There can be, therefore,

more than one boresight direction (eg, a vertically orientated half-wave dipole has

uniform radiation in the a2imuth plane, and any direction in this a2imuth plane may be

defined as boresight.)

%f you look around you hori2ontally, you are looking in various "a2imuth" directions. The

a2imuth angle varies from 3 to 453 degrees, allowing you to look in every hori2ontal

direction.

%f you look up or down with respect to your local hori2on, the angle of view up or down

is termed the "elevation". The elevation angle varies from -63 degrees (straight down) to

763 degrees (overhead).

8e shall call the elevation angle "theta" and the a2imuth angle "phi". The distance from

the antenna is the radius "'". These are commonly termed "spherical polar co-ordinates".

The set of angles phi(3 to 453 degrees) and theta(-63 to 63 degrees) allows us to specify

any radiation direction uniuely. %n the far field region (see below), the electric and

magnetic fields fall off proportional to distance '# that is, they go as '. The power

therefore falls off as (')*+ and the total radiated power over the entire spheresurrounding the antenna is independent of distance '.

1.! Directi"it#

9iven a set of spherical polar co-ordinates (', theta, phi) we can determine the power

density in watts(suare metre) for both the antenna being investigated, and the isotropic

reference antenna which is radiating the same total power. The ratio of these powerdensities gives us the "directivity" of the unknown antenna in the

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direction (theta, phi) at a distance ' from the antenna. %f the direction (theta, phi) is not

specified, the "directivity" is taken to be the ma/imum directivity of any of the directions

of radiation. The uoted definition is

"The directivity of an antenna is defined as the ratio of the radiation intensity in a given

direction from the antenna, to the radiation intensity averaged over all directions. This

average radiation intensity is eual to the total power of the antenna divided by ( pi). %f

the direction is not specified, the directivity refers to the direction of ma/imum radiation

intensity". 8e should caveat that this definition is for power radiated in the !' %:;ects which may lie inside the "near field" region of the antenna. (see

below.)

The %::: standards specifically e/clude reductions in total transmitted signal arising

from impedance mismatch (reflection loss) or polarisation mismatch. These reduce the

transmitted signal in any particular application by further amounts, and have to be

considered in any link budget calculation.

!s an e/ample of loss produced by ob>ects close to the antenna radiating structure, there

is a very substantial reduction in gain of the 3 element ?agi array antennas on the roof

of @@ building at about pm in the afternoon, when all the birds come and roost on the

antennas. @irds have a high dielectric loss tangent.

@oth


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These figures are good to a percent, which is adeuate for practical antenna design and

measurement purposes.

1.& Polarisation

The propagating wave has a transverse direction for the electric field called the

"polarisation direction". This normally lies along the direction of electric field in the

waveguide feed, or along the conducting driven rod element in a linear antenna.

%t is of course possible to radiate from a conductor which is not constructed in a straight

line. =owever, there will still be a preferred polarisation direction.

The polarisation direction is necessarily at right angles to the line of sight >oining the

observer to the transmitting antenna. %t is also at right angles to the magnetic field

direction, which is also "transverse".

%t is possible for the plane of polarisation, or the polarisation direction, to change with

time, and to change with distance away from the source antenna. This is called "rotation

of the plane of polarisation".

%f the antenna consists of a heli/, or a crossed array of dipoles fed in uadrature, then the

plane of polarisation can rotate one complete cycle every wavelength. The wave is then

said to be "circularly polarised". %t is possible to have right hand and left hand circularpolarisation.

learly we can rotate the plane of polarisation in time and distance by spinning the

antenna physically about an a/is lying along the boresight direction.

1.' Polar radiation patterns

The general dependence of directivity and gain on the angles (theta, phi) is called the

"radiation pattern".

%n the case of a linear polarised antenna having fi/ed direction of polarisation, one can

draw polar sectional plots in the ":-plane" and in the "=-plane". The :-plane contains the

direction of propagation and the electric field vector. The =-plane contains the direction

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of propagation and the magnetic field vector. The :-plane is at right angles to the =-

plane.

:-plane and =-plane plots are normally regarded as sufficient to characterise an antenna.

The radiated power density may fall into well-defined regions called "lobes", separated

by regions of low intensity called "nulls". $trictly speaking the nulls can only be

precisely 2ero intensity for particular directions (points from a continuous set). There is

the "main lobe", which is usually where the wanted power from the antenna is directed,

and "side lobes" where the antenna sends radiated energy which is regarded as "wasted"

or may even interfere with other transmitting systems.

%t is possible for there to be more than one main lobe having a given ma/imum value of

gain. or e/ample, a linear array of dipoles can have main lobes spaced E3 degrees

apart, and both having the same gain.

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CHAPTER T(O

O)NIDIRECTIONA* ANTENNA+

!ny radiating structure which has rotational invariance around a vertical a/is will radiate

eually in all directions in the hori2ontal plane, because there is nothing to define a

preferred direction of (hori2ontal) radiation.

:/amples are a vertical whip antenna, or a vertical dipole, or a monopole over a ground

plane. These antennas radiate with the electric field vertical, and the magnetic field

hori2ontal.

%n the case of a hori2ontal loop or coil, the radiation is also omnidirectional but the

magnetic field is vertical and the electric field is hori2ontal.

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!n alternative method of producing hori2ontally polarised (nearly) omnidirectional

radiation is to use crossed hori2ontal dipoles fed in phase uadrature. $uch an

arrangement is called a turnstile antenna. :ach dipole produces a characteristic figure-of-

eight radiation pattern in the hori2ontal plane# these are superposed in uadrature so the

pattern, looked at from above, rotates about the a/is once a cycle of radiation. Turnstile

antennas also radiate circular polarisation vertically# the radiation may be concentrated in

the hori2ontal plane by stacking turnstile antennas one above the other and feeding them

in phase with each other. Turnstile antennas are commonly used as transmitting antennas

when hori2ontal polarisation is reuired together with omnidirectional radiation.

%n the early days of A band %% broadcasting, transmitters were hori2ontally polarised and

the electric field was in the hori2ontal plane. This made reception on vertical whip

antennas on motor vehicles unsatisfactory, as the polarisations were crossed. !n ideal

receiving antenna for this configuration would have been a hori2ontal loop above the top

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of the vehicle. Occasionally one can see such an arrangement on the streets. =owever,

this has overheads of comple/ity and so the band %% transmitters

nowadays are slant polarised or elliptically polarised, so that there is a vertical component

of electric field.

The hori2ontal polarisation was adopted because it was found that the reception on

antennas spaced around 3 metres from the ground could be maintained over a slightly

greater service area than was the case when using vertical polarisation. !lso it was found

that the interference from unsuppressed car ignition systems was less for the hori2ontally

polarised case, and it was believed that the multi-path reflections from aircraft flying

overhead were less troublesome for this configuration. %f one measures the signal strength

of a band %% transmission somewhere near a ma>or airport, it is constantly fluctuating due

to these multi-path effects from the moving reflecting surfaces of the aircraft.

.1 Po,er densit#- field strent/- and impedance.

The power density in watts per suare metre is numerically eual to the rms : field in the

wave times the rms = field in the wave. 8e remember the rms values are 3.F3F times the

peak values, or srt(+) times the peak values.

8e recall the $% unit of the electric field : is voltsmetre, and the $% unit of the magnetic

field = is ampsmetre. Thus the product is (volts amps)metre*+ or watts per suare

metre, as e/pected.

The characteristic impedance of free space (that is, vacuum or air) is 4FF ohms or +3 pi

ohms. This is the ratio of : field to = field. %t is called Go. Thus the power density in

watts per suare metre is (=*+)HGo or (:*+)Go. The field strengths are therefore

proportional to the suare root of the power density, and they therefore fall off as ', or

linearly with distance.

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The field strengths therefore fall by a factor of + every time the distance from the antenna

is doubled# the radiated power density falls by a factor of (or 5d@) every time the

distance from the antenna is doubled.

:/ercise for the reader. alculate the electric field strength on boresight, 33 kilometres

away from a transmit antenna which has boresight gain +3d@ and

accepted input power 3 kilowatts. ompare the received voltage from a metre length

of wire antenna (assumed short compared to a wavelength) with the thermal noise voltage

produced by a resistance of FD ohms across a bandwidth of 3 k=2 at a temperature of

433I. =int. @olt2mannJs constant k C .4E H 3*(-+4) watts per degree I. :/press the

signal to noise ratio in d@.

The effective isotropic radiated power (e.i.r.p.) of the antenna is the power which

would have to be radiated by an isotropic source to give the same field strength as

the real antenna under consideration, on boresight.

%n this case, +3d@ antenna gain C an increase in power on boresight of a factor of

33. $o the e.i.r.p is 3,333 times 33 watts, or megawatt.

!t ' C 33 km C 3*D metres, the radiated power density is megawatt( pi

'*+) C F.65 microwattssuare metre.

This must eual (:*+)Go with Go +3 pi ohms, from which we deduce the rms

electric field : C D.E millivolts per metre. ! metre length of wire antenna therefore picks up about DD mK of signal. %t

passes this to the receiver input stage which has noise voltage in the FD ohms

input resistance of srt( I T @ FD) where @ is the bandwidth in =2.

The rms noise voltage is srt(.+H3*(-)) volts or .H3*(-F) volts and the

signal to noise voltage ratio is .6H3*D or d@, an enormous amount.

%f we put down the transmitter power to watt, and the range up to 3,333 km,

the signal to noise ratio reduces by a factor of srt(3*) times 3*33 C 3*

and we can still communicate comfortably.

onsidering deep space communications, it is possible to communicate with

watt and a +3d@ antenna over a distance of the order of 33 million km, or from

here to the sun.


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These antenna transmission formulae only apply in the far field region, so we need to

know when we are in the far field.

4.+ The near field, the far field, and the 'ayleigh distance

%n the near field region, the polar radiation pattern depends on distance from the antenna

and there is reactive power flow in and out of the region. One can imagine that the

energy, instead of propagating uniformly and steadily away from the antenna, has an

oscillatory longitudinal component. :nergy is transferred to and from the near field

region which represents the reactive part of the antenna driving point impedance. !s one

moves further away, this oscillatory energy flow reduces leaving >ust the regular power

flow in the resistive characteristic impedance (4FF ohms or +3 pi ohms) of free space.

%n the far field the polar radiation pattern is completely independent of distance from the

radiating source.

The transition from near to far field happens at the "'ayleigh distance", sometimes called

the "far field distance". !n estimate for this distance may be made from the formula (+

d*+)(lambda) where d is the ma/imum dimension of the radiating structure. %n the case

of a circular dish this is >ust the diameter# but in the case of a rectangular horn it is the

diagonal distance across the mouth. This is only an estimate, and nothing suddenly

happens at the far field distance thus estimated.

!s an e/ample, for a 39=2 antenna having dish diameter 43 cm, the wavelength is 4 cm

and +d*+lambda C +H43H434 cm or 5 metres. This is a si2eable distance compared to

the dish dimensions.

%f we consider the Tidbinbilla dish at 59=2, shown elsewhere in this collection of notes,

the wavelength is .3D metres and the diameter FD metres so the 'ayleigh distance is

+HFDHFD3.3D C ++D kilometres. Thus when the dish is pointing upwards we need to be

above the atmosphere before we arrive at the far field region.

or this reason, it is impossible to measure the far field radiation pattern of a deep space

antenna on a terrestrial antenna range. One has to resort to complete measurements of the

near field response, and computer calculation to turn them into a far field pattern.

!lternatively one can measure the beamwidth by scanning across a small radio star.

=owever it is often difficult to obtain reliable measurements of the sidelobe responses.


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!.! Radiation resistance and antenna impedance

&art of the function of an antenna is to match the impedance of the feeder, or driving

transmission line, to the impedance of free space.

! half wave dipole presents a resistive impedance of F4 ohms to a transmission line. %t

also has a small inductive reactance, of about ohms. (The si2e of the reactive part

depends on the lengthdiameter ratio of the rods of the antenna). The impedance close to

resonance varies in a similar manner to a series tuned circuit. %f the dipole is shortened

from lambda+ there is an additional series capacitative impedance and if it is cut too long

there is an additional series inductive impedance. Thus to make a dipole which has

entirely resistive impedance it must be cut a few percent shorter than lambda+. The

precise amount of shortening needed depends on the diameter of the rod elements. %n

general, the amounts of reactive impedance depend on the ratio of diameter to length of

the antenna rods. ! good discussion may be found in ' $ :lliott "!ntenna Theory and


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spaced ends of the thick rods. The combination of shunt capacitance with the radiation

resistance in series with the residual inductance provides an impedance transformer, as is

found in ' power amplifiers for e/ample. This transformer steps up the actual radiation

resistance to a higher driving point resistance# at the same time the shunt capacitance

resonates with the residual inductance. There is an argument that the radiation resistance

which "matters" is the driving point resistance# however, we then find that this is

critically dependent on the gap capacitance and varies with the spacing of the rods, and

whether they are made from solid metal or tubes.

Thus we see that these notions about the impedance of a half-wave dipole are only a

guide to what we would measure in a practical installation. %ndeed, a balanced feeder of

characteristic impedance about F3 ohms is impracticable# so we have to incorporate some

kind of balance-unbalance ("balun") transition between feed and antenna. The separation

of the antenna rods also affects the total antenna length and the feed characteristics, and

the physical feed structure and balun affect the near-field distribution of the dipole. %t is

thus possible to prefer cut-and-try methods for matching practical dipole antennas over

the carefully calculated nostrums of antenna theorists.

@y the time the dipole length has reduced to lambda3 the radiation resistance has

decreased to about + ohms and the reactance has increased to between and D kilohms

depending on the diameter of the rods.

!n infinitesimally short dipole is called a "=ert2ian" dipole and is important theoretically

since in practice all its properties may be calculated analytically.

=owever, it is never used in practice because of its vanishingly low radiation resistance.

or many purposes, calculations on a =ert2ian dipole give a useful guide to the behaviour

of longer dipoles.

or practical reasons, particularly in mobile applications, it is necessary to cut dipoles

short or to use monopoles loaded with inductance over a ground plane. The radiation

resistance of a short dipole is given by the formula 'rad C +3H(piH;lambda)*+ and for a

lambdaE dipole is only 4 ohms. The series capacitative impedance for this length antenna

may be as much as 333 ohms# most of the transmission line voltage is lost across this

capacitative reactance unless it is tuned out. One often sees short monopoles with a coil at

the foot, to provide inductive tuning for this capacitative reactance. =owever, this is poor

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policy as it puts up the N factor and reduces the bandwidth of the antenna. The tuning can

be uite critical, especially in the presence of variable near-field obstacles.

!.$ Reciprocit#

!;; the above properties of an antenna are identical whether it is used in transmit or

receive mode. There is only one e/ception to this rule called "reciprocity", and that is

when the antenna contains magnetically biased magnetic materials such as ferrites with

resonantly rotating electron spin systems.

The physical reason for reciprocity is that the only difference between outgoing and

incoming waves lies in the arrow of time. $ince the electromagnetic euations are

invariant e/cept for the signs of magnetic fields and currents, under time reversal, there

can be no difference between transmit and receive mode in the physical current and field

distributions. =owever, if we have a magnet providing a steady bias field, under time

reversed conditions we would have to reverse the direction of this bias field. @ut for

incoming and outgoing waves, the bias field direction remains the same. Thus it is

possible for the system to be non-reciprocal.

CHAPTER FOUR

0AND(IDTH AND 0ROAD0ANDIN%

%f we recall the definition of the Nuality factor or N factor as being the ratio of the stored

energy to the energy dissipated per radian of oscillation, it is clear that in an antenna the

part of dissipation is taken chiefly by the radiated energy. The stored energy is held in the

near field region of the antenna structure. $ince the fractional bandwidth (delta f)f is >ust

the reciprocal of the N factor, for a given radiated energy the N will be smaller and the

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bandwidth larger if we minimise the amount of energy stored in the near field region of

the antenna structure.

One way of doing this is to make the antenna elements fatter in relation to their length.

or a very fine wire antenna, the magnetic field for a given current rises as we approach

the a/is of the conductor, as r, where r is the radial distance out from the conductor.

Thus making dipole antennas out of thick rods rather than thin wires is a good method of

broad-banding, up to a point.

The biconical antenna, and its derivatives, the broad-banded ?agi, the bow-tie antenna

and the phantom conical antenna (which doesnJt have a complete conical surface, but >ust

conically disposed rod elements), is a good method of broad-banding a dipole type of

antenna. There is a degenerate form of biconical antenna where the rods are arranged as

an with the upper v and lower * fed as opposing arms of the dipole. This was very

common in the early days of TK broadcasting, and was also relatively broadband

compared to a simple dipole. ! variant of this kind of antenna had the upper and lower

arms of the P as a dipole, and the Q as a reflector. The radiation pattern had a ma/imum

in the direction away from the reflector, but again the antenna structure was more

broadband than a simple = antenna. %t was also easier to construct.

! rule of thumb is that a typical half wave dipole with sensible diameter rods has a

fractional bandwidth of about DB.

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CHAPTER FI2E

THE T3PE+ OF ANTENNA

=ere we list some of the common types of antenna. !part from e/otic applications, such

as the banana tree, most antennas consist of a >u/taposition of conductor and insulator,

which may be dielectric or it may be air or free space. This is not necessary# any structure

which will support a current on its surface, or guide or modify the direction of

propagation of an electromagnetic wave, may be pressed into service as a kind of

antenna.

8ire antennas. The wire need not be straight.;oop antennas. The loop need not be circular. There can be more than one turn.

'od antennas. The diameter of the rod is significant. These antennas include whip

antennas and dipoles of all descriptions.

!perture antennas. :/amples are waveguide horns.

$lot antennas. These are holes in waveguide or cavities.

'eflector antennas. These are used in combination with a "feed" formed from one of the

other types.

=eli/ antennas. sed to generate circular polarisation.


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e/citation can be by means of microstrip transmission line, from either the front, or from

the back through an aperture in the backplane. %t can also be by means of front

illumination from a horn feed# the patches are of different si2es and can mimic the phase

profile of a parabolic reflector dish even though they are deposited on a flat plane surface.

Aicrostrip antennas have substrate dielectric constant in the range 4 upwards. That means

that there is more energy stored in the reactive near field region, so the antennas are

narrow band high N devices compared to other types of antenna. This is not so much of a

problem at the higher microwave freuencies, where narrow fractional bandwidth still

gives useful signal handling capacity.

!rray antennas. These are formed from multiples of the other kinds of antennas. !ctive

arrays have each element individually driven by its own feed, whereas passive arrays

have a primary radiator passing near-field energy to parasitic elements.

?agi-da antennas. ("?agis"). These are passive arrays, with a single driven element,

and the other elements driven parasitically. The elements are strung out along the

direction of propagation. The phase of the currents in each passive element is such that

when the phase delay is added for the wave to get from one element to the ne/t, the

individual element currents all add contributions to the radiated field which are in phase

with each other at the front of the antenna. ! rule of thumb for ?agis is that the boresight

gain (as a field strength factor, not in deci@els) is eual to the number of elements

(including the driven dipole and any reflector) minus 3.D. or e/ample, a three element

?agi has gain about +.D# a si/ element ?agi has gain about D.D, and a ten element ?agi

has gain about 6.D. =ere, we assume the design is near-optimum. This gives us a half-

power-beamwidth for a 3 element ?agi of roughly 43 degrees. To steer a 3 element

?agi off its target, we would have to swing it through about about D degrees. Thus even

uite large ?agis are not as directional as one might think. The 3 element ?agi has

effective area (by the formula above) 3.F5 lambda*+ so it intercepts radiation over an

area euivalent to a disk of radius about 3.D lambda, which is about twice the physical

transverse e/tent of its elements.

;og-periodic antennas. These are wideband antennas consisting of dipoles of

successively diminishing length connected in parallel across the feed. Only that dipole

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which is close to a half wavelength long loads the feed# the dipoles behind and in front

act as reflector and director to give the array a little gain.

Transmission line antennas. These are leaky transmission lines whose wave velocity is

close to that of waves in free space. The resulting "phase matching" condition allows

resonant transfer from the transmission line to the free space wave. They can also be used

in wideband applications if the transmission line is reasonably non-dispersive.

!ctive antennas. The individual transmitter modules form part of the radiating structure.

This method is proposed for arrays.

&hased array antennas. @y altering the phase shift between successive elements in an

array antenna, the boresight direction may be steered electronically without physically

moving the antenna structure.

'.1 Aperture antennas

This class of antenna contains important technology for satcoms applications.

The simplest kind of aperture antenna consists of a tapered waveguide transition in the

form of a "pyramidal horn". The T:3 mode in a rectangular waveguide has longitudinal

components of magnetic field. !s the waveguide is flared to form the horn pyramid, the

longitudinal magnetic field components become less and, as the notes on waveguides

e/plain the characteristic impedance of the T: mode approaches that of free space, 4FFohms.

This kind of pyramidal horn aperture antenna is very important in the laboratory, as it is

one of the few types of antenna whose boresight gain may be very accurately calculated

(to within 3. d@). onseuently, it is used for producing reference field strengths and for

calibrating the gains of other antennas.

! variant on the rectangular pyramidal horn is the circular horn feed. $uch an aperture

antenna is commonly used with a circularly symmetric waveguide mode (not the lowest

mode in circular guide, 0@) to produce uniform illumination of a assegrain antenna,

which has a circular reflector dish of much larger diameter than the feed. The large

+
http://www.ee.surrey.ac.uk/Personal/D.Jefferies/aperture.htmlhttp://www.ee.surrey.ac.uk/Personal/D.Jefferies/aperture.html


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reflector dish produces higher gain. The circular waveguide feed can also be used to

produce circular polarisation.

Aost ground based small broadcast satellite receiver dishes have a small horn feed of low

gain placed at the focus of a dish between 3.D and metre diameter. Often the feed is

offset from the boresight direction of the reflector dish# this "offset feed" arrangement

directs the main beam away from the feed, and this results in less blockage and improved

sidelobe performance.

%f the main beam in a assegrain antenna hits the feed, or the sub-reflector, it will be

diffracted around the obstacles and radiation will be scattered or diffracted into the

sidelobe directions. The effective area of the dish is reduced, and the interference with

other satellite systems from the sidelobes will be increased. This is not so important in

deep space antennas. %f we look at the Tidbinbilla deep space tracking antenna, we see

there are two reflectors between the main feeds and the main beam. The sub-reflector at

the focus of the large FD metre dish is conve/. The feeds are pointing along boresight,

and are arranged to have a bean divergence angle which is >ust sufficient completely to

illuminate the sub-reflector. The sub-reflector returns the energy to the main reflector,

and again the reflections are arranged so that there is minimal spillover at the edges of the

dish, although maintaining uniform illumination as far as is possible.

The feeds are also conveniently located at the centre of the main dish, which moves little

as the dish is steered. This has mechanical advantages, and makes the final =&! and

;0! electronics more accessible for servicing.

!perture antennas such as this are used in "very long baseline interferometry" methods.

=ere, two or more high gain large antennas, having large collecting areas, are separated

by many hundreds of kilometres, and used to synthesise an aperture array having the

diameter of the baseline separation of the dishes. 'adio

astronomers use these systems to pinpoint the location of radio sources to great accuracy

in elevation and a2imuth.

'. Arra#s of antenna elements

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%f we want to increase the gain of a dipole antenna we can add another dipole antenna

alongside it. This is the simplest form of array antenna.

8hy is the gain increased, and what is the boresight gain of this "two element array"1

irst, we assume the antennas are fed in phase with each other and spaced lambda+

apart. onsidering the radiation in a direction which is normal to the plane containing the

dipoles, the contribution from each element arrives in phase with the other. The field

strength in this direction is double that for one element, so the radiated power density,

which is the suare of the field strength, is four times that for one element. =owever, the

two elements together are fed with twice the power of a single element. The increase in

gain is therefore a factor + C +.

This calculation scales with the number of elements. %f we use a 3 by 3 array, the

boresight power gain is increased by a factor of 33, which is the number of elements.

The field strength is 33 times more along boresight than for a single element, so the

power density is 3,333 times greater. @ut 33 times the power is being fed to the array

compared with a single element, so the gain increase is a factor of 33 as stated.

This gain increase is over and above any boresight gain of the individual elements. %f we

start off with an array of 33 horn feeds at 39=2, of si2e cm by cm each, their

intrinsic gain is about +3d@ and the array factor gives an additional power gain of 33

which is +3d@ so the combined structure has a boresight gain of 3d@ or so.

0ow consider, are we "getting something for nothing" or does this increased gain along

the boresight come at the e/pense of gain elsewhere in the radiation pattern1 The answer

is clearly that the array concentrates the total radiated power along certain directions at

the e/pense of others.

%f we go back to our + element dipole array, spaced lambda+, there can be no radiation

along a line >oining the centres of the two dipoles as their contributions are in anti-phase

in this direction, there being a lambda+ path difference to get from one to the other.

%n general then, the element pattern times the array pattern euals the total radiation

pattern of the arrangement. 8hat is the array pattern1 %t is the pattern you would observe

for a set of isotropic radiators spaced as the array elements are actually spaced, and fed

with the same amplitudes and phases of signals that the actual array elements receive.

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%f you want to read more about the fascinating sub>ect of array antenna design, consult '

$ :lliott Lop citM.

'.! 2er# *on 0aseline Interferometr# 42*0I5

%f we use two aperture antennas, spaced by a great many wavelengths, as an

interferometer, the fringe spacing will be of the order of the angle subtended by an ob>ect

of diameter one wavelength at a distance eual to the separation of the aperture antennas.

or e/ample, at 39=2 the free space wavelength is 4cm or 3.34m, so if we separate the

antennas by 4333km or :E wavelengths, we can resolve radio sources about :-E

radians across, or about + milliseconds of arc. @y comparison, the beam width of one of

the aperture antennas will be of the order of the angle subtended by a wavelength of

radiation at a distance eual to the diameter of the reflector. Thus, if we considered a

system where there were two 43 metre diameter antennas separated by 4333km, there

would be (4:5)43 C 33,333 interference fringes within the main beam of one of the

apertures. Of course, the sensitivity of the interferometer is still governed by the total

capture area of the two dishes# but the resolution is now comparable with that of a dish of

diameter 4333km.

The interference fringes from these two circular dishes will form parallel straight linesacross the circular beam, as can be seen in the pictures belowR-

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Two circular apertures spaced a distance apart

The interference bands from the apertures above

%n order to get resolution at right angles to these bands it is necessary to add a third

aperture at the verte/ of a triangle, whose base is delimited by the first two apertures.

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'.$ Reflector Antenna

The main focus of this pro>ect is the parabolic reflector antenna. %t begins with a history

of how reflectors were first used by %saac 0ewton and continues until parabolic reflectors

were launched into outer space for broadcasting television signals. Then methods of

modifying parabolic reflectors are discussed such as changing the impedance

characteristics or by simply altering the shape of the parabolic reflector. !fter a basic

introduction to parabolic reflectors the report then goes into further detail on the

mathematics behind parabolic reflectors. $everal euations are e/pressed and discussed,

which are commonly used when working on reflector surface designs.


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9ala/y. Aany large radio telescopes were built in the 6D3Ss including a +D3-foot

telescope at odrell @ank in :ngland, which received signals from the 'ussian satellite

$putnik. %n 65+ the first telecommunications satellite was launched into space.

&arabolic reflectors were used to receive live trans-!tlantic television signals. Aany

similar satellites have been launched since that time

'.$.Performance

8hen constructing a reflector antenna there are three characteristics to consider that will

affect the performance of the antenna. The first are spatial characteristics. There are

many ways to refer to the spatial characteristics of a reflector antenna. One way is

through its radiation patterns. The radiation patterns of a reflector antenna are a

representation of the relative power in the different directions it travels. !nother way is

through polari2ation. &olari2ation is the shape and orientation of the locus of the

e/tremities of the field as a function of time. The ability of a feed to concentrate power

into a narrow region of space, referred to as the gain, of a reflector antenna is another

way one can describe the spatial characteristics. ?et another is through the efficiency of

the reflector antenna. The efficiency is the ratio of the effective radiating area of an

antenna to the physical radiating area. ;astly is the phase center. The phase center is a

theoretical point along the a/is of the antenna, which corresponds to the center of the

phase fronts of the spherical waves.

The second characteristic of a reflector antenna is the impedance characteristic. 8hen

looking at the antenna from behind, it can be represented as a load impedance that

depends on the radiation patterns of the antenna, which therefore depends on the design

of the antenna. %n a well-designed antenna the load impedance will match that of the

transmission line that is connecting the antenna to the transmitter or receiver. %mpedancemismatching will result in signal reflection back through the transmission line.

The final characteristic of a reflector antenna is the freuency characteristic.The

performance of a reflector antenna changes with the operational freuency, therefore,

reflector antennas are built to work at a single freuency. !ntennas are normally

represented by their spatial or impedance characteristics, but they are sometimes

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specified as narrowband or wideband. These terms are not normally used, as there is no

precise definition for a narrowband or wideband reflector antenna.

'.$.!+/apes

The most effective way to ad>ust the way waves radiate outward from a parabolic

reflector is by changing the shape of the reflecting surface. %n this section, five separate

parabolic reflecting surface shapes are discussed. The first version of the parabolic

reflector is one without any modifications to the reflector. The reflector to the right is an

e/ample of a parabolic reflector. %t can be seen that all of the waves are traveling

outward from the focal point and are reflected at an angle such that all of the waves are

radiated in a parallel manner.

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The ne/t type of parabolic reflector is the truncated reflector. ! picture of a truncated

reflector is shown to the right in picture !. %t shows how the reflector is cut so that only

the darkened areas of the reflector remain. $ince the reflector is still hori2ontally

parabolic it still reflects all of the waves that are traveling towards it in that area. The

8aves that would have normally been reflected by the missing portions are now allowed

to spread out. This creates a vertically fan shaped beam. Truncated reflectors of this

type are used for detecting aircrafts at different altitudes.

!nother form of a truncated reflector is shown to the right in picture @. %t acts the same

as the hori2ontally truncated reflector, e/cept it is vertically oriented. To be e/pected,

this causes the beam from the reflector to spread out hori2ontally while being reflected

vertically. This creates a hori2ontal fan rather than a vertical pattern as seen in the

previous reflector. Truncated reflectors of this type are often used to determine elevation.

The fourth form of parabolic reflector is the orange-peel reflector, correctly named due to

its shape similar to an orange peel. ! picture of the orange- peel reflector is shown to the

right. The orange-peel reflector in the figure will have a beam with a wide hori2ontal

plane and a narrow vertical plane. This is due to the large curvature in the vertical

direction of parabolic reflection and the reduction in the curvature in the hori2ontal

direction of the reflector. The shape of a beam coming out of an orange-peel reflector

can be compared to a beaver tail. Orange-peel reflectors are often used in height finding

euipment.

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The final type of parabolic reflector that will be discussed is the cylindrical reflector,

which is shown to the right. ! cylindrical reflector is used when a wave is reuired to

be significantly longer in one direction than in another. ! beam that is sent out from a

cylindrical reflector is rectangular in shape. %n the case of the reflector pictured, the

beam would be noticeably wider than it would be tall. ! cylindrical reflector, unlike a

parabolic reflector, has a series of focal points rather than one point. ylindrical

reflectors are commonly used for search radar systems and ground control approach

radars.

'.$.$Antenna C/aracteristics and Desin T/eor#

'eflector antennas generally improve upon all of the basic characteristics of dipole

antennas. %n order to study the changes caused by adding a reflector to an antenna

system, the basic antenna characteristics will be introduced followed by a discussion of

how the use of reflectors improve each factor.

Radiation PatternsR

The radiation pattern of an antenna is a three-dimensional plot of its electromagnetic

wave radiation shape as it emerges from an antenna. The pattern function is the portion

of the : or = field far-2one euation that shows the variation in magnitude with direction.

The voltage or field pattern is a plot of the : field. ! plot of the suare of the magnitude

of the : field is called the power pattern. The pattern function for a =ert2ian dipole

(U) C sin U, and the power pattern function is V(U) C sin V(U). igure shows the plot

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of the power pattern for a dipole. @y e/amining the radiation pattern, the spatial

distribution of :A power can be analy2ed. The half power beam width (=&@8) is the

angle between the half power points. The smaller the =&@8, the more directive the

antenna. or a dipole, the =&@8 is 63W, while for a reflector antenna the =&@8 is less

than 63W.

Fiure 1.


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The power pattern function is taken from the new far-field euation and plotted to show

the new radiation pattern. The new pattern or resultant pattern is the unit pattern

multiplied by the group pattern. The unit pattern is from the original driven element and

the group pattern is from the image array. Fiure $shows how two typical patterns are

combined to create a resultant pattern.

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Fiure $also shows how the total power distribution is improved in one direction and the

HP0( is reduced to give good directivity. The side lobes here are small but still

important because if too many side lobes are formed the overall power efficiency in the

direction of desired propagation will be reduced. Aore of the total power will be

contained in the side lobes combined than the lobe in the desired direction. &arabolic

reflector antennas commonly called dish antennas are the best shape for improving on the

basic antenna characteristics. &arabolic reflectors are used mostly for high freuency

applications due to the smaller si2e of dish reuired. The power gain and radiation

patterns of dish antennas create a very directive design and thus the most useful of all the

reflector antennas. The factors of dish antennas that affect directivity include the

aperture radius to freuency ratio and the aperture efficiency. The formula for directivity

is

8here : is the aperture

efficiency with a value between 3 and . igure Dshows a parabolic reflector with the

aperture radius and feed at focus.

Fiure &. &arabolic reflector

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The simplest reflector antenna has two components# a reflecting surface and a feed

antenna, which is located at the reflectorSs focal point. %n the previous sections, many

types of implemented reflectors were discussed. The most popular reflector used today is

the parabolic reflector. This type of reflector can provide high gain and good efficiency in

the = and Aicrowave freuency spectrums. &arabolic dish antennas are an e/cellent

reflector but can sometimes be large, e/pensive, and not easily mounted so they can be

rotated. &arabolic antennas are a good design, which achieve a high gain, minimal side

lobe radiation patterns, polari2ation isolation, and bandwidth specifications of the

smallest aperture si2e allowing for weight reduction and ease of manufacture. $hort

electromagnetic waves used for TK and radiobroadcast communications can be transmitted

and received with small, easily built reflector antennas. They are easy to set up and simple to

build using hand tools and commonly available materials. The parabolic antenna will provide

noticeable improvements in gain and directivity over a dipole above a ground plane. @y

impedance matching through a low loss transmission feed, this system will result in uality

transmission and reception. !n antenna dish, however, is not a perfect solution. $urface

irregularities on the reflector cause signal reflection errors. nwanted signals may also enter the

feed unit. Other waves will be diffracted and scattered at the rim of the reflector dish.

ltimately, it is possible that some noise waves or even the desired signal may be

absorbed rather than reflected by the antenna dish.

! focal point well outside the aperture plane increases the chance of receiving unwanted

signals and noise. $ignals from the feed horn may miss the edge of dish. This effect is

known as over-illumination. The ratio of focal distance to the dish diameter is f


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offset reflector virtually eliminates the coupling between the transmitting and receiving

ports via reflection from the reflector surface into the feed.

'.$.9Dual Reflector Antennas

This design allows transmission lines that are shorter and easier to construct. The dual

reflector antenna consists of two reflectors and a feed, which is conveniently located at

the ape/ of the main reflector. Fiure 9shows a typical dual reflector design. The

virtual focal point is the point from which transmitted rays appear to radiate with a

spherical wave front after a reflection off of the sub reflector.

Fiure 9.


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'.$.:)ulti Element 3aiUda Arra# Antenna

:stablished from the previous discussions of isotropic dipole antennas and parabolic dish

antennas, the primary aspects of reflector antennas are directivity, radiation patterns, andpower gain. hoosing the proper antenna for any given scenario is as important a factor

as any. The two key factors to consider when choosing an appropriate antenna are the

structural design reuirements and operational freuency. ective of this array is to generate a

traveling plane wave with very high directivity and gain. There is a compromise between

directionality and gain, however, very similar to the parabolic dish antenna. 8hile a

simple isotropic dipole

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Fiure :. $even :lement ?agi-da !ntennas

!ntenna radiates power in a spherically outward pattern centered around the antenna, the?agi focuses radiates power mainly in a forward direction similar to the parabolic

reflector. ! radiation pattern of a pair of isotropic dipoles can be seen in igure 6-and a

typical radiation pattern of a ?agi antenna can be seen in igure 3.

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when the (overall) dipole length is an integer multiple of a half-wavelength (termed a

resonant dipole). !t this length, a complete half-wave sinusoidal standing current wave

is induced by an electric field along with its respective voltage wave. !t this half-

wavelength dipole length, the respective comple/ impedance of the element is completely

real therefore yielding only resistive power losses from the element. The ability to

change the length of these elements and alter the comple/ impedance of an element is

what gives the ?agi its directivity and gain. Aodifying its length and respective position

to another element can alter the impedance and power loss of an element. @y shortening

or lengthening an element slightly with respect to its resonant length, the relative phase

between the induced current and voltage waves alter the comple/ impedance to include

either a capacitive or inductive reactance element. This comple/ impedance results in

both resistive power losses and reactive energy power losses. The reactive power stored

determines whether each individual element will constructively or destructively add to

the radiation pattern. The reflector element is made slightly longer than the resonant

active element, which results in an inductive reactance. This inductive reactance

generates an inverse plane wave in the reverse direction, which cancels out any active

element generated wave activity. The director elements are made slightly shorter than the

resonant active element, which results in a capacitive reactance. This capacitive

reactance generates an identical wave in the forward direction which constructively adds

to the overall desired wave activity and gain. The spacing between the elements is an

important design characteristic as well. The spacing is set so that the constructive and

destructive generated waveforms are all in phase with one another. %n order to obtain the

ma/imum forward gain with the largest front-to-back gain ratio, the spacing must be set

so as not to lose any power due to phase mismatch.

!s mentioned earlier, the limitations of the ?agi antenna depend only upon si2e and cost.

%t is uite obvious that a larger wavelength reuires a larger element length. There comes

a point when the element length is too long to build a feasible si2ed antenna and the

elementSs weight cannot be supported. There also comes a point when an additional

reflector or director element no longer makes a significant contribution to the forward

gain for the additional reuired cost. This makes sense, as the forward signal gain from

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the ?agi antenna is simply the superposition of the induced current-generated waves from

each element. The farther away from the active element you move, the electric fields will

:ventually reduce in magnitude e/ponentially. The typical amount of reflectors needed

is one or two. The limit on director elements is typically around fifteen.

The type of antenna chosen for a particular application depends heavily upon cost, si2e,

and operational freuency. ?agi antennas are a convenient choice for certain situations

due to their high directivity, high power gain, and si2e. These properties make ?agi

antennas a good candidate for applications such as amateur radio, TK broadcast, A

broadcast and air traffic control.

Conclusion

&arabolic reflector antennas and ?agi-da antennas have uickly found ways into our

every day lives. They are used e/tensively by broadcasting companies for both radio and

television. They are also used by our military, for tracking the altitudes of airplanes and

search radar. The mathematics and design of reflector antennas can be intimidating at

first, but the concepts behind them are fairly straightforward. $ome of these concepts

were shown visually in the report, like the effects of reflector shape, instead of working

through all of the reuired euations that were involved. %n conclusion, whether a

parabolic, cylindrical, corner, or ?agi antenna is utili2ed, the same purpose holds true for

each. They all complete the same ob>ective in their own specific way, which is to direct

:A waves in a specific direction and that is the backbone for all reflector antennas.

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Documents

$ ANENNA PROJECT .doc